Finite Group Databasebeta

← #31064691

Subgroups — #31064691

Order 17152.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22568500C211yesmaximal, characteristic, complemented
2#22568497C211yesmaximal, characteristic, complemented
3#22568044C211yesmaximal, characteristic, complemented
4#22567597C211yesmaximal, characteristic, complemented
5#22567550C211yesmaximal, characteristic, complemented
6#22567455C211yesmaximal, characteristic, complemented
7#22567259C211yesmaximal, characteristic, complemented
8#22567213C211yesmaximal, characteristic, complemented
9#22567126C211yesmaximal, characteristic, complemented
10#22567022C211yesmaximal, characteristic, complemented
11#22566980C211yesmaximal, characteristic, complemented
12#22566944C211yesmaximal, characteristic, complemented
13#22566884C211yesmaximal, characteristic, complemented
14#22566826C211yesmaximal, characteristic, complemented
15#22566806C211yesmaximal, characteristic, complemented
16#22566694C211yesmaximal, characteristic, complemented
17#22566619C211yesmaximal, characteristic, complemented
18#22566463C211yesmaximal, characteristic, complemented
19#22566017C211yesmaximal, characteristic, complemented
20#22565986C211yesmaximal, characteristic, complemented
21#22565220C211yesmaximal, characteristic, complemented
22#22564460C211yesmaximal, characteristic, complemented
23#22564460C211yesmaximal, characteristic, complemented
24#22564340C211yesmaximal, characteristic, complemented
25#22564340C211yesmaximal, characteristic, complemented
26#22563861C211yesmaximal, characteristic, complemented
27#22563565C211yesmaximal, characteristic
28#22562944C211yesmaximal, characteristic, complemented
29#22562842C211yesmaximal, characteristic, complemented
30C2×#16863274C211yesmaximal, characteristic, complemented
31C67×#2564C211yesmaximal, characteristic, complemented
32C23×D268C2211yescharacteristic
33C23×C4×D67C2211yescharacteristic
34C2×#14524038C2211yescharacteristic, complemented
35C2×#14524038C2211yescharacteristic, complemented
36C2×#14524032C2211yescharacteristic
37C2×#14524032C2211yescharacteristic
38C2×#14524029C2211yescharacteristic, complemented
39C2×#14524029C2211yescharacteristic, complemented
40C2×#14524025C2211yescharacteristic, complemented
41C2×#14524025C2211yescharacteristic, complemented
42C2×#14524023C2211yescharacteristic, complemented
43C2×#14524023C2211yescharacteristic, complemented
44C2×#14524022C2211yescharacteristic
45C2×#14524022C2211yescharacteristic
46C2×#14524017C2211yescharacteristic
47C2×#14524017C2211yescharacteristic
48C2×#14524011C2211yescharacteristic
49C2×#14524011C2211yescharacteristic
50C22×(C2×D67)⋊C4C2211yescharacteristic
51C22×(C2×D67)⋊C4C2211yescharacteristic
52C22×(C2×D67)⋊C4C2211yescharacteristic
53#16863333C2211yescharacteristic, complemented
54#16863333C2211yescharacteristic, complemented
55#16863330C2211yescharacteristic, complemented
56#16863330C2211yescharacteristic, complemented
57#16863325C2211yescharacteristic, complemented
58#16863325C2211yescharacteristic, complemented
59#16863325C2211yescharacteristic, complemented
60#16863325C2211yescharacteristic, complemented
61#16863325C2211yescharacteristic, complemented
62#16863325C2211yescharacteristic, complemented
63#16863323C2211yescharacteristic, complemented
64#16863323C2211yescharacteristic, complemented
65#16863323C2211yescharacteristic, complemented
66#16863323C2211yescharacteristic, complemented
67#16863322C2211yescharacteristic, complemented
68#16863322C2211yescharacteristic, complemented
69#16863318C2211yescharacteristic, complemented
70#16863318C2211yescharacteristic, complemented
71#16863318C2211yescharacteristic, complemented
72#16863318C2211yescharacteristic, complemented
73#16863318C2211yescharacteristic, complemented
74#16863318C2211yescharacteristic, complemented
75#16863317C2211yescharacteristic, complemented
76#16863317C2211yescharacteristic, complemented
77#16863313C2211yescharacteristic
78#16863313C2211yescharacteristic
79#16863313C2211yescharacteristic
80#16863313C2211yescharacteristic
81#16863313C2211yescharacteristic
82#16863313C2211yescharacteristic
83#16863312C2211yescharacteristic, complemented
84#16863312C2211yescharacteristic, complemented
85#16863312C2211yescharacteristic, complemented
86#16863312C2211yescharacteristic, complemented
87#16863311C2211yescharacteristic, complemented
88#16863311C2211yescharacteristic, complemented
89#16863311C2211yescharacteristic, complemented
90#16863311C2211yescharacteristic, complemented
91#16863309C2211yescharacteristic, complemented
92#16863309C2211yescharacteristic, complemented
93#16863309C2211yescharacteristic, complemented
94#16863309C2211yescharacteristic, complemented
95#16863305C2211yescharacteristic
96#16863305C2211yescharacteristic
97#16863303C2211yescharacteristic, complemented
98#16863303C2211yescharacteristic, complemented
99#16863300C2211yescharacteristic, complemented
100#16863300C2211yescharacteristic, complemented
101#16863298C2211yescharacteristic
102#16863298C2211yescharacteristic
103#16863297C2211yescharacteristic
104#16863297C2211yescharacteristic
105#16863296C2211yescharacteristic, complemented
106#16863296C2211yescharacteristic, complemented
107#16863295C2211yescharacteristic, complemented
108#16863295C2211yescharacteristic, complemented
109#16863293C2211yescharacteristic, complemented
110#16863293C2211yescharacteristic, complemented
111#16863289C2211yescharacteristic, complemented
112#16863289C2211yescharacteristic, complemented
113#16863288C2211yescharacteristic, complemented
114#16863288C2211yescharacteristic, complemented
115#16863288C2211yescharacteristic, complemented
116#16863288C2211yescharacteristic, complemented
117#16863286C2211yescharacteristic, complemented
118#16863286C2211yescharacteristic, complemented
119#16863285C2211yescharacteristic, complemented
120#16863285C2211yescharacteristic, complemented
121#16863285C2211yescharacteristic, complemented
122#16863285C2211yescharacteristic, complemented
123#16863282C2211yescharacteristic, complemented
124#16863282C2211yescharacteristic, complemented
125#16863282C2211yescharacteristic, complemented
126#16863282C2211yescharacteristic, complemented
127#16863282C2211yescharacteristic, complemented
128#16863282C2211yescharacteristic, complemented
129#16863276C2211yescharacteristic
130#16863276C2211yescharacteristic
131#16863274C2211yescharacteristic
132#16863274C2211yescharacteristic
133#16863274C2211yescharacteristic
134#16863274C2211yescharacteristic
135#16863274C2211yescharacteristic
136#16863274C2211yescharacteristic
137#16863274C2211yescharacteristic
138#16863274C2211yescharacteristic
139#16863272C2211yescharacteristic, complemented
140#16863272C2211yescharacteristic, complemented
141#16863271C2211yescharacteristic
142#16863271C2211yescharacteristic
143#16863271C2211yescharacteristic
144#16863271C2211yescharacteristic
145#16863270C2211yescharacteristic, complemented
146#16863270C2211yescharacteristic, complemented
147#16863270C2211yescharacteristic, complemented
148#16863270C2211yescharacteristic, complemented
149#16863270C2211yescharacteristic, complemented
150#16863270C2211yescharacteristic, complemented
151#16863269C2211yescharacteristic
152#16863269C2211yescharacteristic
153#16863264C2211yescharacteristic, complemented
154#16863262C2211yescharacteristic, complemented
155#16863259C2211yescharacteristic, complemented
156#16863258C2211yescharacteristic, complemented
157#16863258C2211yescharacteristic, complemented
158#16863256C2211yescharacteristic
159#16863256C2211yescharacteristic, complemented
160#16863253C2211yescharacteristic, complemented
161#16863253C2211yescharacteristic, complemented
162#16863251C2211yescharacteristic
163#16863251C2211yescharacteristic
164#16863251C2211yescharacteristic
165#16863251C2211yescharacteristic
166#16863251C2211yescharacteristic
167#16863251C2211yescharacteristic
168C22⋊C4×Dic67C2211yescharacteristic
169C22⋊C4×Dic67C2211yescharacteristic
170C4×C22⋊Dic67C2211yescharacteristic
171C2×C67⋊#95C2211yescharacteristic
172C2×C22⋊Q8×C67C2211yescharacteristic
173C2×C4×D4×C67C2211yescharacteristic
174#400×C67C2211yescharacteristic, complemented
175#399×C67C2211yescharacteristic, complemented
176#395×C67C2211yescharacteristic, complemented
177#393×C67C2211yescharacteristic, complemented
178#387×C67C2211yescharacteristic, complemented
179#387×C67C2211yescharacteristic, complemented
180#386×C67C2211yescharacteristic
181#386×C67C2211yescharacteristic
182#385×C67C2211yescharacteristic, complemented
183#385×C67C2211yescharacteristic, complemented
184#380×C67C2211yescharacteristic
185#380×C67C2211yescharacteristic
186C2×#95×C67C2211yescharacteristic
187C24×D67C2311yescharacteristic
188C24×D67C2311yescharacteristic
189C22×Dic134C2311yescharacteristic
190C22×Dic134C2311yescharacteristic
191C22×D268—24no—
192C22×D268—42no—
193C22×D268—42no—
194C22×D268C2311yescharacteristic
195C22×D268C2311yescharacteristic
196C22×D268C2311yescharacteristic
197C22×D268C2311yescharacteristic
198C22×C22⋊D67C2311yescharacteristic
199C22×C22⋊D67C2311yescharacteristic
200C22×C22⋊D67C2311yescharacteristic
201C22×C22⋊D67C2311yescharacteristic
202C23×Dic67C2311yescharacteristic
203C23×Dic67C2311yescharacteristic
204C22×C4×D67—42no—
205C22×C4×D67—42no—
206C22×C4×D67—42no—
207C22×C4×D67C2311yescharacteristic
208C22×C4×D67C2311yescharacteristic
209C22×C4×D67C2311yescharacteristic
210C22×C4×D67C2311yescharacteristic
211#14524038—42no—
212#14524038—42no—
213#14524032—42no—
214#14524032—42no—
215#14524029—42no—
216#14524029—42no—
217#14524025—42no—
218#14524025—42no—
219#14524023—42no—
220#14524023—42no—
221#14524022—42no—
222#14524022—42no—
223#14524017—42no—
224#14524017—42no—
225#14524011—42no—
226#14524011—42no—
227C2×C4⋊Dic67C2311yescharacteristic
228C2×C4⋊Dic67C2311yescharacteristic
229C2×C4⋊Dic67C2311yescharacteristic
230C2×C4⋊Dic67C2311yescharacteristic
231C2×C4⋊Dic67C2311yescharacteristic
232C2×C4⋊Dic67C2311yescharacteristic
233C2×C4⋊Dic67C2311yescharacteristic
234C2×C4⋊Dic67C2311yescharacteristic
235C2×C4⋊Dic67C2311yescharacteristic
236C2×C4⋊Dic67C2311yescharacteristic
237C2×C4⋊Dic67C2311yescharacteristic
238C2×C4⋊Dic67C2311yescharacteristic
239C2×Dic67⋊C4C2311yescharacteristic
240C2×Dic67⋊C4C2311yescharacteristic
241C2×Dic67⋊C4C2311yescharacteristic
242C2×Dic67⋊C4C2311yescharacteristic
243C2×Dic67⋊C4C2311yescharacteristic
244C2×Dic67⋊C4C2311yescharacteristic
245C2×Dic67⋊C4C2311yescharacteristic
246C2×Dic67⋊C4C2311yescharacteristic
247C2×C22⋊Dic67C2311yescharacteristic
248C2×C22⋊Dic67C2311yescharacteristic
249C2×C22⋊Dic67C2311yescharacteristic
250C2×C22⋊Dic67C2311yescharacteristic
251C2×C22⋊Dic67C2311yescharacteristic
252C2×C22⋊Dic67C2311yescharacteristic
253C2×C22⋊Dic67C2311yescharacteristic
254C2×C22⋊Dic67C2311yescharacteristic
255C2×(C2×D67)⋊C4—42no—
256C2×(C2×D67)⋊C4—42no—
257C2×(C2×D67)⋊C4—42no—
258C2×(C2×D67)⋊C4C2311yescharacteristic
259C2×(C2×D67)⋊C4C2311yescharacteristic
260C2×(C2×D67)⋊C4C2311yescharacteristic
261C2×(C2×D67)⋊C4C2311yescharacteristic
262C2×(C2×D67)⋊C4C2311yescharacteristic
263C2×(C2×D67)⋊C4C2311yescharacteristic
264C2×(C2×D67)⋊C4C2311yescharacteristic
265C2×(C2×D67)⋊C4C2311yescharacteristic
266C2×(C2×D67)⋊C4C2311yescharacteristic
267C2×(C2×D67)⋊C4C2311yescharacteristic
268C2×(C2×D67)⋊C4C2311yescharacteristic
269C2×(C2×D67)⋊C4C2311yescharacteristic
270C2×(C2×D67)⋊C4C2311yescharacteristic
271C2×(C2×D67)⋊C4C2311yescharacteristic
272C2×(C2×D67)⋊C4C2311yescharacteristic
273C2×(C2×D67)⋊C4C2311yescharacteristic
274C2×(C2×D67)⋊C4C2311yescharacteristic
275C2×(C2×D67)⋊C4C2311yescharacteristic
276C2×(C2×D67)⋊C4C2311yescharacteristic
277C2×(C2×D67)⋊C4C2311yescharacteristic
278C2×(C2×D67)⋊C4C2311yescharacteristic
279C2×(C2×D67)⋊C4C2311yescharacteristic
280C2×(C2×D67)⋊C4C2311yescharacteristic
281C2×(C2×D67)⋊C4C2311yescharacteristic
282C2×(C2×D67)⋊C4C2311yescharacteristic
283C2×(C2×D67)⋊C4C2311yescharacteristic
284C2×(C2×D67)⋊C4C2311yescharacteristic
285C2×(C2×D67)⋊C4C2311yescharacteristic
286C2×(C2×D67)⋊C4C2311yescharacteristic
287C2×(C2×D67)⋊C4C2311yescharacteristic
288C2×(C2×D67)⋊C4C2311yescharacteristic
289C2×(C2×D67)⋊C4C2311yescharacteristic
290C2×(C2×D67)⋊C4C2311yescharacteristic
291C2×(C2×D67)⋊C4C2311yescharacteristic
292C2×(C2×D67)⋊C4C2311yescharacteristic
293C2×(C2×D67)⋊C4C2311yescharacteristic
294C2×(C2×D67)⋊C4C2311yescharacteristic
295C2×(C2×D67)⋊C4C2311yescharacteristic
296C2×(C2×D67)⋊C4C2311yescharacteristic
297C2×(C2×D67)⋊C4C2311yescharacteristic
298C2×C4×Dic67C2311yescharacteristic
299C2×C4×Dic67C2311yescharacteristic
300C2×C4×Dic67C2311yescharacteristic
301C2×C4×Dic67C2311yescharacteristic
302C2×C4×Dic67C2311yescharacteristic
303C2×C4×Dic67C2311yescharacteristic
304C67⋊#95C2311yescharacteristic
305C67⋊#95C2311yescharacteristic
306C67⋊#95C2311yescharacteristic
307C67⋊#95C2311yescharacteristic
308C67⋊#95C2311yescharacteristic
309C67⋊#95C2311yescharacteristic
310C67⋊#95C2311yescharacteristic
311C67⋊#95C2311yescharacteristic
312C67⋊#95C2311yescharacteristic
313C67⋊#95C2311yescharacteristic
314C67⋊#95C2311yescharacteristic
315C67⋊#95C2311yescharacteristic
316C67⋊#95C2311yescharacteristic
317C67⋊#95C2311yescharacteristic
318C67⋊#95C2311yescharacteristic
319C67⋊#95C2311yescharacteristic
320C67⋊#95C2311yescharacteristic
321C67⋊#95C2311yescharacteristic
322C67⋊#95C2311yescharacteristic
323C67⋊#95C2311yescharacteristic
324C67⋊#95C2311yescharacteristic
325C67⋊#95C2311yescharacteristic
326C67⋊#95C2311yescharacteristic
327C67⋊#95C2311yescharacteristic
328C67⋊#95C2311yescharacteristic
329C67⋊#95C2311yescharacteristic
330C67⋊#95C2311yescharacteristic
331C67⋊#95C2311yescharacteristic
332C22×Q8×C67C2311yescharacteristic
333C22×D4×C67C2311yescharacteristic
334C23×C4×C67C2311yescharacteristic
335C23×C4×C67C2311yescharacteristic
336C23×C4×C67C2311yescharacteristic
337C23×C4×C67C2311yescharacteristic
338C22⋊Q8×C67—24no—
339C4×D4×C67—24no—
340C2×C4⋊C4×C67C2311yescharacteristic
341C2×C4⋊C4×C67C2311yescharacteristic
342C2×C4⋊C4×C67C2311yescharacteristic
343C2×C4⋊C4×C67C2311yescharacteristic
344C2×C4⋊C4×C67C2311yescharacteristic
345C2×C4⋊C4×C67C2311yescharacteristic
346C2×C4⋊C4×C67C2311yescharacteristic
347C2×C4⋊C4×C67C2311yescharacteristic
348C2×C22⋊C4×C67C2311yescharacteristic
349C2×C22⋊C4×C67C2311yescharacteristic
350C2×C22⋊C4×C67C2311yescharacteristic
351C2×C22⋊C4×C67C2311yescharacteristic
352C2×C22⋊C4×C67C2311yescharacteristic
353C2×C22⋊C4×C67C2311yescharacteristic
354C2×C22⋊C4×C67C2311yescharacteristic
355C2×C22⋊C4×C67C2311yescharacteristic
356C2×C42×C67C2311yescharacteristic
357#95×C67C2311yescharacteristic
358#95×C67C2311yescharacteristic
359#95×C67C2311yescharacteristic
360#95×C67C2311yescharacteristic
361#95×C67C2311yescharacteristic
362#95×C67C2311yescharacteristic
363#95×C67C2311yescharacteristic
364#95×C67C2311yescharacteristic
365#95×C67C2311yescharacteristic
366#95×C67C2311yescharacteristic
367#95×C67C2311yescharacteristic
368#95×C67C2311yescharacteristic
369C23×D67—22no—
370C23×D67—22no—
371C23×D67—22no—
372C23×D67—22no—
373C23×D67—22no—
374C23×D67—22no—
375C23×D67—22no—
376C23×D67—22no—
377C23×D67—41no—
378C23×D67—41no—
379C23×D67—41no—
380C23×D67—41no—
381C23×D67—41no—
382C23×D67—41no—
383C23×D67C2411yescharacteristic
384C23×D67C2411yescharacteristic
385C23×D67C2411yescharacteristic
386C23×D67C2411yescharacteristic
387C2×Dic134—22no—
388C2×Dic134—41no—
389C2×Dic134—41no—
390C2×Dic134—41no—
391C2×Dic134—41no—
392C2×Dic134—41no—
393C2×D268—22no—
394C2×D268—22no—
395C2×D268—22no—
396C2×D268—22no—
397C2×D268—22no—
398C2×D268—22no—
399C2×D268—22no—
400C2×D268—22no—
401C2×D268—41no—
402C2×D268—41no—
403C2×D268—41no—
404C2×D268—41no—
405C2×D268—416no—
406C2×C22⋊D67—22no—
407C2×C22⋊D67—22no—
408C2×C22⋊D67—41no—
409C2×C22⋊D67—41no—
410C2×C22⋊D67—41no—
411C2×C22⋊D67—41no—
412C2×C22⋊D67—41no—
413C2×C22⋊D67—41no—
414C2×C22⋊D67—41no—
415C2×C22⋊D67—41no—
416C2×C22⋊D67—41no—
417C2×C22⋊D67—41no—
418C22×Dic67—22no—
419C22×Dic67—22no—
420C22×Dic67—41no—
421C22×Dic67—41no—
422C22×Dic67—41no—
423C22×Dic67—41no—
424C22×Dic67C2411yescharacteristic
425C22×Dic67C2411yescharacteristic
426C22×Dic67C2411yescharacteristic
427C22×Dic67C2411yescharacteristic
428C22×Dic67C2411yescharacteristic
429C22×Dic67C2411yescharacteristic
430C22×Dic67C2411yescharacteristic
431C22×Dic67C2411yescharacteristic
432C22×Dic67C2411yescharacteristic
433C22×Dic67C2411yescharacteristic
434C22×Dic67C2411yescharacteristic
435C22×Dic67C2411yescharacteristic
436C2×C4×D67—22no—
437C2×C4×D67—22no—
438C2×C4×D67—22no—
439C2×C4×D67—22no—
440C2×C4×D67—41no—
441C2×C4×D67—41no—
442C2×C4×D67—41no—
443C2×C4×D67—41no—
444C2×C4×D67—41no—
445C2×C4×D67—41no—
446C2×C4×D67—41no—
447C2×C4×D67—41no—
448C2×C4×D67—416no—
449C4⋊Dic67—41no—
450C4⋊Dic67—41no—
451C4⋊Dic67—41no—
452C4⋊Dic67—41no—
453C4⋊Dic67—41no—
454C4⋊Dic67—41no—
455C4⋊Dic67—41no—
456C4⋊Dic67—41no—
457C4⋊Dic67—41no—
458C4⋊Dic67—41no—
459C4⋊Dic67—41no—
460C4⋊Dic67—41no—
461Dic67⋊C4—22no—
462Dic67⋊C4—41no—
463Dic67⋊C4—41no—
464Dic67⋊C4—41no—
465Dic67⋊C4—41no—
466Dic67⋊C4—41no—
467Dic67⋊C4—41no—
468Dic67⋊C4—41no—
469C22⋊Dic67—22no—
470C22⋊Dic67—22no—
471C22⋊Dic67—22no—
472C22⋊Dic67—22no—
473C22⋊Dic67—41no—
474C22⋊Dic67—41no—
475C22⋊Dic67—41no—
476C22⋊Dic67—41no—
477(C2×D67)⋊C4—22no—
478(C2×D67)⋊C4—22no—
479(C2×D67)⋊C4—22no—
480(C2×D67)⋊C4—22no—
481(C2×D67)⋊C4—22no—
482(C2×D67)⋊C4—22no—
483(C2×D67)⋊C4—22no—
484(C2×D67)⋊C4—22no—
485(C2×D67)⋊C4—22no—
486(C2×D67)⋊C4—22no—
487(C2×D67)⋊C4—41no—
488(C2×D67)⋊C4—41no—
489(C2×D67)⋊C4—41no—
490(C2×D67)⋊C4—41no—
491(C2×D67)⋊C4—41no—
492(C2×D67)⋊C4—41no—
493(C2×D67)⋊C4—41no—
494(C2×D67)⋊C4—41no—
495(C2×D67)⋊C4—41no—
496(C2×D67)⋊C4—41no—
497(C2×D67)⋊C4—41no—
498(C2×D67)⋊C4—41no—
499(C2×D67)⋊C4—41no—
500(C2×D67)⋊C4—41no—
501(C2×D67)⋊C4—41no—
502(C2×D67)⋊C4—41no—
503(C2×D67)⋊C4—41no—
504(C2×D67)⋊C4—41no—
505(C2×D67)⋊C4—41no—
506(C2×D67)⋊C4—41no—
507(C2×D67)⋊C4—41no—
508(C2×D67)⋊C4—41no—
509(C2×D67)⋊C4—41no—
510(C2×D67)⋊C4—41no—
511(C2×D67)⋊C4—41no—
512(C2×D67)⋊C4—41no—
513(C2×D67)⋊C4—41no—
514(C2×D67)⋊C4—41no—
515(C2×D67)⋊C4—41no—
516(C2×D67)⋊C4—41no—
517C4×Dic67—41no—
518C4×Dic67—41no—
519C4×Dic67—41no—
520C4×Dic67—41no—
521C4×Dic67—41no—
522C4×Dic67—41no—
523C24×C67C2411yescharacteristic
524C24×C67C2411yescharacteristic
525C2×Q8×C67—22no—
526C2×Q8×C67—41no—
527C2×Q8×C67—41no—
528C2×D4×C67—22no—
529C2×D4×C67—22no—
530C2×D4×C67—22no—
531C22×C4×C67—22no—
532C22×C4×C67—22no—
533C22×C4×C67—22no—
534C22×C4×C67—22no—
535C22×C4×C67—41no—
536C22×C4×C67—41no—
537C22×C4×C67—41no—
538C22×C4×C67—41no—
539C22×C4×C67—41no—
540C22×C4×C67—41no—
541C22×C4×C67—41no—
542C22×C4×C67#4114yes—
543C22×C4×C67C2411yescharacteristic
544C22×C4×C67C2411yescharacteristic
545C22×C4×C67C2411yescharacteristic
546C22×C4×C67C2411yescharacteristic
547C22×C4×C67C2411yescharacteristic
548C22×C4×C67C2411yescharacteristic
549C22×C4×C67C2411yescharacteristic
550C22×C4×C67C2411yescharacteristic
551C22×C4×C67C2411yescharacteristic
552C22×C4×C67C2411yescharacteristic
553C22×C4×C67C2411yescharacteristic
554C22×C4×C67C2411yescharacteristic
555C22×C4×C67C2411yescharacteristic
556C4⋊C4×C67—22no—
557C4⋊C4×C67—22no—
558C4⋊C4×C67—22no—
559C4⋊C4×C67—22no—
560C4⋊C4×C67—22no—
561C4⋊C4×C67—41no—
562C4⋊C4×C67—41no—
563C4⋊C4×C67—41no—
564C22⋊C4×C67—22no—
565C22⋊C4×C67—22no—
566C22⋊C4×C67—22no—
567C22⋊C4×C67—22no—
568C22⋊C4×C67—22no—
569C22⋊C4×C67—41no—
570C22⋊C4×C67—41no—
571C22⋊C4×C67—41no—
572C42×C67—22no—
573C23×C67—21no—
574C23×C67—21no—
575C23×C67—21no—
576C23×C67—21no—
577C23×C67—21no—
578C23×C67—21no—
579C23×C67—21no—
580C23×C67—21no—
581C23×C67—21no—
582C23×C67—21no—
583C23×C67—21no—
584C23×C67C2×#4112yes—
585C23×C67H(5,𝔽2)12yes—
586C23×C672−1+412yes—
587C23×C67C2511yescharacteristic
588C22×D67—28no—
589C22×D67—21no—
590C22×D67—21no—
591C22×D67—21no—
592C22×D67—21no—
593C22×D67—21no—
594C22×D67—21no—
595C22×D67—21no—
596C22×D67—21no—
597C22×D67—21no—
598C22×D67—21no—
599C22×D67—21no—
600C22×D67—21no—
601C22×D67—21no—
602C22×D67—21no—
603C22×D67—21no—
604C22×D67—21no—
605C22×D67—21no—
606C22×D67—21no—
607C22×D67—21no—
608C22×D67—21no—
609C22×D67—21no—
610C22×D67—21no—
611C22×D67—21no—
612C22×D67—21no—
613C22×D67—21no—
614C22×D67—21no—
615C22×D67—44no—
616C22×D67—44no—
617C22×D67—44no—
618C22×D67—44no—
619C22×D67—44no—
620C22×D67—44no—
621C22×D67—44no—
622C22×D67—44no—
623C22×D67—44no—
624C22×D67—82no—
625C22×D67—82no—
626C22×D67—82no—
627C22×D67—82no—
628C22×D67H(5,𝔽2)12yes—
629C22×D67H(5,𝔽2)12yes—
630Q8×C67—82no—
631D4×C67—44no—
632C2×C4×C67—21no—
633C2×C4×C67—21no—
634C2×C4×C67—21no—
635C2×C4×C67—21no—
636C2×C4×C67—21no—
637C2×C4×C67—21no—
638C2×C4×C67—21no—
639C2×C4×C67—21no—
640C2×C4×C67—21no—
641C2×C4×C67—21no—
642C2×C4×C67—21no—
643C2×C4×C67—21no—
644C2×C4×C67—21no—
645C2×C4×C67—21no—
646C2×C4×C67—21no—
647C2×C4×C67—21no—
648C2×C4×C67—21no—
649C2×C4×C67—21no—
650C2×C4×C67—21no—
651C2×C4×C67—21no—
652C2×C4×C67—21no—
653C2×C4×C67—21no—
654C2×C4×C67—21no—
655C2×C4×C67—21no—
656C2×C4×C67—21no—
657C2×C4×C67—21no—
658C2×C4×C67—21no—
659C2×C4×C67—21no—
660C2×C4×C67—21no—
661C2×C4×C67—21no—
662C2×C4×C67—21no—
663C2×C4×C67—21no—
664C2×C4×C67—21no—
665C2×C4×C67—21no—
666C2×C4×C67—21no—
667C2×C4×C67—21no—
668C2×C4×C67—44no—
669C2×C4×C67—44no—
670C2×C4×C67—82no—
671C2×C4×C67—82no—
672C2×C4×C67C2×#4112yes—
673C2×C4×C67C2×#4112yes—
674C2×C4×C67H(5,𝔽2)12yes—
675C22⋊D67—82no—
676C22⋊D67—82no—
677C22⋊D67—82no—
678C22⋊D67—82no—
679C2×Dic67—21no—
680C2×Dic67—21no—
681C2×Dic67—21no—
682C2×Dic67—21no—
683C2×Dic67—21no—
684C2×Dic67—21no—
685C2×Dic67—21no—
686C2×Dic67—21no—
687C2×Dic67—21no—
688C2×Dic67—21no—
689C2×Dic67—21no—
690C2×Dic67—21no—
691C2×Dic67—21no—
692C2×Dic67—21no—
693C2×Dic67—21no—
694C2×Dic67—21no—
695C2×Dic67—21no—
696C2×Dic67—21no—
697C2×Dic67—21no—
698C2×Dic67—21no—
699C2×Dic67—21no—
700C2×Dic67—21no—
701C2×Dic67—21no—
702C2×Dic67—21no—
703C2×Dic67—21no—
704C2×Dic67—21no—
705C2×Dic67—21no—
706C2×Dic67—21no—
707C2×Dic67—21no—
708C2×Dic67—21no—
709C2×Dic67—21no—
710C2×Dic67—21no—
711C2×Dic67—21no—
712C2×Dic67—21no—
713C2×Dic67—21no—
714C2×Dic67—21no—
715C2×Dic67—44no—
716C2×Dic67—82no—
717D268—44no—
718D268—44no—
719D268—44no—
720D268—44no—
721C4×D67—44no—
722C4×D67—44no—
723C4×D67—44no—
724C4×D67—44no—
725Dic134—82no—
726Dic134—82no—
727C22×C67—22no—
728C22×C67—22no—
729C22×C67—22no—
730C22×C67—22no—
731C22×C67—22no—
732C22×C67—22no—
733C22×C67—41no—
734C22×C67—41no—
735C22×C67—41no—
736C22×C67—41no—
737C22×C67—41no—
738C22×C67—41no—
739C22×C67—41no—
740C22×C67#54214yes—
741C22×C67C22×#4111yescharacteristic
742C22×C67C2×H(5,𝔽2)11yescharacteristic
743C22×C67C2×H(5,𝔽2)11yescharacteristic
744C22×C67C2×H(5,𝔽2)11yescharacteristic
745C22×C67C2×H(5,𝔽2)11yescharacteristic
746C22×C67C2×2−1+411yescharacteristic
747C22×C67#58511yescharacteristic
748C2×D67—22no—
749C2×D67—22no—
750C2×D67—22no—
751C2×D67—22no—
752C2×D67—22no—
753C2×D67—22no—
754C2×D67—416no—
755C2×D67—41no—
756C2×D67—41no—
757C2×D67—41no—
758C2×D67—41no—
759C2×D67—41no—
760C2×D67—41no—
761C2×D67—41no—
762C2×D67—41no—
763C2×D67—41no—
764C2×D67—41no—
765C2×D67—41no—
766C2×D67—41no—
767C2×D67—41no—
768C2×D67—41no—
769C2×D67—41no—
770C2×D67—41no—
771C2×D67—41no—
772C2×D67—41no—
773C2×D67—41no—
774C2×D67—41no—
775C2×D67—41no—
776C2×D67—41no—
777C2×D67—88no—
778C4×C67—22no—
779C4×C67—22no—
780C4×C67—22no—
781C4×C67—41no—
782C4×C67—41no—
783C4×C67—41no—
784C4×C67—41no—
785C4×C67—41no—
786C4×C67—41no—
787C4×C67—41no—
788C4×C67—41no—
789C4×C67—41no—
790C4×C67—41no—
791Dic67—41no—
792Dic67—41no—
793Dic67—41no—
794Dic67—41no—
795Dic67—41no—
796Dic67—41no—
797Dic67—41no—
798Dic67—41no—
799Dic67—41no—
800Dic67—41no—
801Dic67—41no—
802Dic67—41no—
803#36793—671nomaximal, Sylow
804C2×C67—24no—
805C2×C67—81no—
806C2×C67C2×#54211yescharacteristic
807C2×C67#349011yescharacteristic
808C2×C67#350611yescharacteristic
809C2×C67#353211yescharacteristic
810C2×C67#353411yescharacteristic
811C2×C67#353511yescharacteristic
812C2×C67#353611yescharacteristic
813D67—42no—
814D67—42no—
815D67—81no—
816D67—81no—
817#2849—671no—
818#2848—671no—
819#2796—671no—
820#2761—671no—
821#2757—671no—
822#2751—671no—
823#2737—671no—
824#2730—671no—
825#2723—671no—
826#2715—671no—
827#2712—671no—
828#2710—671no—
829#2705—671no—
830#2701—671no—
831#2700—671no—
832#2691—671no—
833#2686—671no—
834#2672—671no—
835#2626—671no—
836#2622—671no—
837#2564D6711yescharacteristic, complemented
838#2549—671no—
839#2480—671no—
840#2480—671no—
841#2472—671no—
842#2472—671no—
843#2435—671no—
844#2408—671no—
845#2329—671no—
846#2318—671no—
847C2×#386—671no—
848C67#3679311yescharacteristic, complemented, Sylow
849C23×D4—671no—
850C24×C4—671no—
851C2×#126—671no—
852C2×#126—671no—
853C2×#124—671no—
854C2×#124—671no—
855C2×#124—671no—
856C2×#124—671no—
857C2×#123—671no—
858C2×#123—671no—
859C2×C22⋊Q8—671no—
860C2×C22⋊Q8—671no—
861C2×C22⋊Q8—671no—
862C2×C22⋊Q8—671no—
863C2×C22⋊Q8C2×D6711yescharacteristic
864C2×#121—671no—
865C2×#121—671no—
866C2×#120—671no—
867C2×#120—671no—
868C2×C4×D4C2×D6711yescharacteristic
869C22×C22⋊C4—671no—
870C22×C22⋊C4—671no—
871C22×C22⋊C4—671no—
872#400C2×D6711yescharacteristic, complemented
873#399—671no—
874#399—671no—
875#399C2×D6711yescharacteristic, complemented
876#398—671no—
877#398—671no—
878#397—671no—
879#397—671no—
880#397—671no—
881#397—671no—
882#397—671no—
883#397—671no—
884#397—671no—
885#397—671no—
886#397—671no—
887#397—671no—
888#397—671no—
889#397—671no—
890#396—671no—
891#396—671no—
892#396—671no—
893#396—671no—
894#396—671no—
895#396—671no—
896#395—671no—
897#395—671no—
898#395C2×D6711yescharacteristic, complemented
899#394—671no—
900#394—671no—
901#394—671no—
902#394—671no—
903#394—671no—
904#394—671no—
905#394—671no—
906#394—671no—
907#394—671no—
908#394—671no—
909#394—671no—
910#394—671no—
911#394—671no—
912#394—671no—
913#393—671no—
914#393—671no—
915#393—671no—
916#393—671no—
917#393C2×D6711yescharacteristic, complemented
918#392—671no—
919#392—671no—
920#391—671no—
921#391—671no—
922#391—671no—
923#391—671no—
924#390—671no—
925#390—671no—
926#390—671no—
927#390—671no—
928#390—671no—
929#390—671no—
930#389—671no—
931#389—671no—
932#389—671no—
933#389—671no—
934#388—671no—
935#388—671no—
936#388—671no—
937#388—671no—
938#388—671no—
939#388—671no—
940#388—671no—
941#388—671no—
942#388—671no—
943#388—671no—
944#388—671no—
945#388—671no—
946#387—671no—
947#387—671no—
948#387—671no—
949#387—671no—
950#387—671no—
951#387—671no—
952#387C2×D6711yescharacteristic, complemented
953#387C2×D6711yescharacteristic, complemented
954#386—671no—
955#386—671no—
956#386—671no—
957#386—671no—
958#386—671no—
959#386—671no—
960#386—671no—
961#386—671no—
962#386—671no—
963#386—671no—
964#386—671no—
965#386—671no—
966#386C2×D6711yescharacteristic
967#386C2×D6711yescharacteristic
968#385—671no—
969#385—671no—
970#385—671no—
971#385—671no—
972#385—671no—
973#385—671no—
974#385—671no—
975#385—671no—
976#385—671no—
977#385—671no—
978#385—671no—
979#385—671no—
980#385C2×D6711yescharacteristic, complemented
981#385C2×D6711yescharacteristic, complemented
982#383—671no—
983#382—671no—
984#381—671no—
985#381—671no—
986#381—671no—
987#380—671no—
988#380—671no—
989#380—671no—
990#380—671no—
991#380C2×D6711yescharacteristic
992#380C2×D6711yescharacteristic
993#379—671no—
994#379—671no—
995#379—671no—
996#379—671no—
997#379—671no—
998#379—671no—
999C4×C22⋊C4—671no—
1000C4×C22⋊C4—671no—
1001C4×C22⋊C4—671no—
1002C2×#95—671no—
1003C2×#95C2×D6711yescharacteristic
1004C25—671no—
1005C25—671no—
1006C22×Q8—671no—
1007C22×Q8—671no—
1008C22×Q8C22×D6711yescharacteristic
1009C22×D4—2682no—
1010C22×D4—2682no—
1011C22×D4—671no—
1012C22×D4—671no—
1013C22×D4—671no—
1014C22×D4—671no—
1015C22×D4—671no—
1016C22×D4—671no—
1017C22×D4—671no—
1018C22×D4—671no—
1019C22×D4—1344no—
1020C22×D4C22×D6711yescharacteristic
1021C23×C4—2682no—
1022C23×C4—2682no—
1023C23×C4—2682no—
1024C23×C4—671no—
1025C23×C4—671no—
1026C23×C4—671no—
1027C23×C4—671no—
1028C23×C4—671no—
1029C23×C4—671no—
1030C23×C4C22×D6711yescharacteristic
1031C23×C4C22×D6711yescharacteristic
1032C23×C4C22×D6711yescharacteristic
1033C23×C4C22×D6711yescharacteristic
1034#126—2682no—
1035#126—2682no—
1036#124—2682no—
1037#124—2682no—
1038#124—2682no—
1039#124—2682no—
1040#123—2682no—
1041#123—2682no—
1042C22⋊Q8—24no—
1043C22⋊Q8—2682no—
1044C22⋊Q8—2682no—
1045C22⋊Q8—2682no—
1046C22⋊Q8—2682no—
1047#121—2682no—
1048#121—2682no—
1049#120—2682no—
1050#120—2682no—
1051C4×D4—24no—
1052C2×C4⋊C4—671no—
1053C2×C4⋊C4—671no—
1054C2×C4⋊C4—671no—
1055C2×C4⋊C4—671no—
1056C2×C4⋊C4—671no—
1057C2×C4⋊C4—671no—
1058C2×C4⋊C4—671no—
1059C2×C4⋊C4—671no—
1060C2×C4⋊C4—671no—
1061C2×C4⋊C4—671no—
1062C2×C4⋊C4—671no—
1063C2×C4⋊C4—671no—
1064C2×C4⋊C4—671no—
1065C2×C4⋊C4—671no—
1066C2×C4⋊C4—671no—
1067C2×C4⋊C4—671no—
1068C2×C4⋊C4—671no—
1069C2×C4⋊C4—671no—
1070C2×C4⋊C4—671no—
1071C2×C4⋊C4—671no—
1072C2×C4⋊C4C22×D6711yescharacteristic
1073C2×C4⋊C4C22×D6711yescharacteristic
1074C2×C4⋊C4C22×D6711yescharacteristic
1075C2×C4⋊C4C22×D6711yescharacteristic
1076C2×C4⋊C4C22×D6711yescharacteristic
1077C2×C4⋊C4C22×D6711yescharacteristic
1078C2×C4⋊C4C22×D6711yescharacteristic
1079C2×C4⋊C4C22×D6711yescharacteristic
1080C2×C22⋊C4—2682no—
1081C2×C22⋊C4—2682no—
1082C2×C22⋊C4—2682no—
1083C2×C22⋊C4—671no—
1084C2×C22⋊C4—671no—
1085C2×C22⋊C4—671no—
1086C2×C22⋊C4—671no—
1087C2×C22⋊C4—671no—
1088C2×C22⋊C4—671no—
1089C2×C22⋊C4—671no—
1090C2×C22⋊C4—671no—
1091C2×C22⋊C4—671no—
1092C2×C22⋊C4—671no—
1093C2×C22⋊C4—671no—
1094C2×C22⋊C4—671no—
1095C2×C22⋊C4—671no—
1096C2×C22⋊C4—671no—
1097C2×C22⋊C4—671no—
1098C2×C22⋊C4—671no—
1099C2×C22⋊C4—671no—
1100C2×C22⋊C4—671no—
1101C2×C22⋊C4—671no—
1102C2×C22⋊C4—671no—
1103C2×C22⋊C4—671no—
1104C2×C22⋊C4—671no—
1105C2×C22⋊C4—671no—
1106C2×C22⋊C4—671no—
1107C2×C22⋊C4—671no—
1108C2×C22⋊C4—671no—
1109C2×C22⋊C4—671no—
1110C2×C22⋊C4—671no—
1111C2×C22⋊C4—671no—
1112C2×C22⋊C4—671no—
1113C2×C22⋊C4—671no—
1114C2×C22⋊C4—671no—
1115C2×C22⋊C4—671no—
1116C2×C22⋊C4—671no—
1117C2×C22⋊C4—671no—
1118C2×C22⋊C4—671no—
1119C2×C22⋊C4—671no—
1120C2×C22⋊C4—671no—
1121C2×C22⋊C4—671no—
1122C2×C22⋊C4—671no—
1123C2×C22⋊C4—671no—
1124C2×C22⋊C4—671no—
1125C2×C22⋊C4—671no—
1126C2×C22⋊C4—671no—
1127C2×C22⋊C4—671no—
1128C2×C22⋊C4—671no—
1129C2×C22⋊C4—671no—
1130C2×C22⋊C4—671no—
1131C2×C22⋊C4C22×D6711yescharacteristic
1132C2×C22⋊C4C22×D6711yescharacteristic
1133C2×C22⋊C4C22×D6711yescharacteristic
1134C2×C22⋊C4C22×D6711yescharacteristic
1135C2×C22⋊C4C22×D6711yescharacteristic
1136C2×C22⋊C4C22×D6711yescharacteristic
1137C2×C22⋊C4C22×D6711yescharacteristic
1138C2×C22⋊C4C22×D6711yescharacteristic
1139C2×C42—671no—
1140C2×C42—671no—
1141C2×C42—671no—
1142C2×C42—671no—
1143C2×C42—671no—
1144C2×C42—671no—
1145C2×C42C22×D6711yescharacteristic
1146#95—671no—
1147#95—671no—
1148#95—671no—
1149#95—671no—
1150#95—671no—
1151#95—671no—
1152#95—671no—
1153#95—671no—
1154#95—671no—
1155#95—671no—
1156#95—671no—
1157#95—671no—
1158#95—671no—
1159#95—671no—
1160#95—671no—
1161#95—671no—
1162#95—671no—
1163#95—671no—
1164#95—671no—
1165#95—671no—
1166#95—671no—
1167#95—671no—
1168#95—671no—
1169#95—671no—
1170#95—671no—
1171#95—671no—
1172#95—671no—
1173#95—671no—
1174#95C22×D6711yescharacteristic
1175#95C22×D6711yescharacteristic
1176#95C22×D6711yescharacteristic
1177#95C22×D6711yescharacteristic
1178#95C22×D6711yescharacteristic
1179#95C22×D6711yescharacteristic
1180#95C22×D6711yescharacteristic
1181#95C22×D6711yescharacteristic
1182#95C22×D6711yescharacteristic
1183#95C22×D6711yescharacteristic
1184#95C22×D6711yescharacteristic
1185#95C22×D6711yescharacteristic
1186C24—2681no—
1187C24—2681no—
1188C24—2681no—
1189C24—2681no—
1190C24—2681no—
1191C24—2681no—
1192C24—671no—
1193C24—671no—
1194C24—671no—
1195C24—671no—
1196C24—1342no—
1197C24—1342no—
1198C24—1342no—
1199C24—1342no—
1200C24—1342no—
1201C24—1342no—
1202C24—1342no—
1203C24—1342no—
1204C24C23×D6711yescharacteristic
1205C24C23×D6711yescharacteristic
1206C2×Q8—22no—
1207C2×Q8—41no—
1208C2×Q8—41no—
1209C2×Q8—2681no—
1210C2×Q8—2681no—
1211C2×Q8—2681no—
1212C2×Q8—2681no—
1213C2×Q8—2681no—
1214C2×Q8—1342no—
1215C2×D4—22no—
1216C2×D4—22no—
1217C2×D4—22no—
1218C2×D4—2681no—
1219C2×D4—2681no—
1220C2×D4—2681no—
1221C2×D4—2681no—
1222C2×D4—26816no—
1223C2×D4—2681no—
1224C2×D4—2681no—
1225C2×D4—2681no—
1226C2×D4—2681no—
1227C2×D4—2681no—
1228C2×D4—2681no—
1229C2×D4—2681no—
1230C2×D4—2681no—
1231C2×D4—2681no—
1232C2×D4—2681no—
1233C2×D4—1342no—
1234C2×D4—1342no—
1235C2×D4—1342no—
1236C2×D4—1342no—
1237C2×D4—1342no—
1238C2×D4—1342no—
1239C2×D4—1342no—
1240C2×D4—1342no—
1241C2×D4—1342no—
1242C2×D4—1342no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—41no—
1248C22×C4—41no—
1249C22×C4—41no—
1250C22×C4—41no—
1251C22×C4—41no—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—2681no—
1255C22×C4—2681no—
1256C22×C4—2681no—
1257C22×C4—2681no—
1258C22×C4—2681no—
1259C22×C4—2681no—
1260C22×C4—2681no—
1261C22×C4—2681no—
1262C22×C4—26816no—
1263C22×C4—2681no—
1264C22×C4—2681no—
1265C22×C4—2681no—
1266C22×C4—2681no—
1267C22×C4—671no—
1268C22×C4—671no—
1269C22×C4—671no—
1270C22×C4—671no—
1271C22×C4—671no—
1272C22×C4—671no—
1273C22×C4—671no—
1274C22×C4—671no—
1275C22×C4—671no—
1276C22×C4—671no—
1277C22×C4—671no—
1278C22×C4—671no—
1279C22×C4—1342no—
1280C22×C4—1342no—
1281C22×C4—1342no—
1282C22×C4—1342no—
1283C22×C4—1342no—
1284C22×C4—1342no—
1285C22×C4#1176162714yes—
1286C22×C4C23×D6711yescharacteristic
1287C22×C4C23×D6711yescharacteristic
1288C22×C4C23×D6711yescharacteristic
1289C22×C4C23×D6711yescharacteristic
1290C22×C4C23×D6711yescharacteristic
1291C22×C4C23×D6711yescharacteristic
1292C22×C4C23×D6711yescharacteristic
1293C22×C4C23×D6711yescharacteristic
1294C22×C4C23×D6711yescharacteristic
1295C22×C4C23×D6711yescharacteristic
1296C22×C4C23×D6711yescharacteristic
1297C22×C4C23×D6711yescharacteristic
1298C22×C4C23×D6711yescharacteristic
1299C4⋊C4—22no—
1300C4⋊C4—22no—
1301C4⋊C4—22no—
1302C4⋊C4—22no—
1303C4⋊C4—22no—
1304C4⋊C4—41no—
1305C4⋊C4—41no—
1306C4⋊C4—41no—
1307C4⋊C4—2681no—
1308C4⋊C4—2681no—
1309C4⋊C4—2681no—
1310C4⋊C4—2681no—
1311C4⋊C4—2681no—
1312C4⋊C4—2681no—
1313C4⋊C4—2681no—
1314C4⋊C4—2681no—
1315C4⋊C4—2681no—
1316C4⋊C4—2681no—
1317C4⋊C4—2681no—
1318C4⋊C4—2681no—
1319C4⋊C4—2681no—
1320C4⋊C4—2681no—
1321C4⋊C4—2681no—
1322C4⋊C4—2681no—
1323C4⋊C4—2681no—
1324C4⋊C4—2681no—
1325C4⋊C4—2681no—
1326C4⋊C4—1342no—
1327C22⋊C4—22no—
1328C22⋊C4—22no—
1329C22⋊C4—22no—
1330C22⋊C4—22no—
1331C22⋊C4—22no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—41no—
1335C22⋊C4—2681no—
1336C22⋊C4—2681no—
1337C22⋊C4—2681no—
1338C22⋊C4—2681no—
1339C22⋊C4—2681no—
1340C22⋊C4—2681no—
1341C22⋊C4—2681no—
1342C22⋊C4—2681no—
1343C22⋊C4—2681no—
1344C22⋊C4—2681no—
1345C22⋊C4—2681no—
1346C22⋊C4—2681no—
1347C22⋊C4—2681no—
1348C22⋊C4—2681no—
1349C22⋊C4—2681no—
1350C22⋊C4—2681no—
1351C22⋊C4—2681no—
1352C22⋊C4—2681no—
1353C22⋊C4—2681no—
1354C22⋊C4—2681no—
1355C22⋊C4—2681no—
1356C22⋊C4—2681no—
1357C22⋊C4—2681no—
1358C22⋊C4—2681no—
1359C22⋊C4—2681no—
1360C22⋊C4—2681no—
1361C22⋊C4—2681no—
1362C22⋊C4—2681no—
1363C22⋊C4—2681no—
1364C22⋊C4—2681no—
1365C22⋊C4—2681no—
1366C22⋊C4—2681no—
1367C22⋊C4—2681no—
1368C22⋊C4—2681no—
1369C22⋊C4—1342no—
1370C22⋊C4—1342no—
1371C22⋊C4—1342no—
1372C22⋊C4—1342no—
1373C22⋊C4—1342no—
1374C22⋊C4—1342no—
1375C22⋊C4—1342no—
1376C22⋊C4—1342no—
1377C22⋊C4—1342no—
1378C22⋊C4—1342no—
1379C22⋊C4—1342no—
1380C22⋊C4—1342no—
1381C22⋊C4—1342no—
1382C22⋊C4—1342no—
1383C42—22no—
1384C42—2681no—
1385C42—2681no—
1386C42—2681no—
1387C42—2681no—
1388C42—2681no—
1389C42—2681no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—2684no—
1402C23—2684no—
1403C23—2684no—
1404C23—2684no—
1405C23—2684no—
1406C23—2684no—
1407C23—2684no—
1408C23—2684no—
1409C23—2684no—
1410C23—5362no—
1411C23—5362no—
1412C23—5362no—
1413C23—5362no—
1414C23—672no—
1415C23—672no—
1416C23—1348no—
1417C23—1341no—
1418C23—1341no—
1419C23—1341no—
1420C23—1341no—
1421C23—1341no—
1422C23—1341no—
1423C23—1341no—
1424C23—1341no—
1425C23—1341no—
1426C23—1341no—
1427C23—1341no—
1428C23—1341no—
1429C23—1341no—
1430C23—1341no—
1431C23—1341no—
1432C23—1341no—
1433C23—1341no—
1434C23—1341no—
1435C23—1341no—
1436C23—1341no—
1437C23—1341no—
1438C23—1341no—
1439C23—1341no—
1440C23—1341no—
1441C23—1341no—
1442C23—1341no—
1443C23C2×#1176162712yes—
1444C23#1452408912yes—
1445C23#1452409112yes—
1446C23C24×D6711yescharacteristic
1447Q8—82no—
1448Q8—5362no—
1449Q8—5362no—
1450D4—44no—
1451D4—2684no—
1452D4—2684no—
1453D4—2684no—
1454D4—2684no—
1455D4—5362no—
1456D4—5362no—
1457D4—5362no—
1458D4—5362no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—44no—
1496C2×C4—44no—
1497C2×C4—82no—
1498C2×C4—82no—
1499C2×C4—2684no—
1500C2×C4—2684no—
1501C2×C4—2684no—
1502C2×C4—2684no—
1503C2×C4—2684no—
1504C2×C4—5362no—
1505C2×C4—1341no—
1506C2×C4—1341no—
1507C2×C4—1341no—
1508C2×C4—1341no—
1509C2×C4—1341no—
1510C2×C4—1341no—
1511C2×C4—1341no—
1512C2×C4—1341no—
1513C2×C4—1341no—
1514C2×C4—1341no—
1515C2×C4—1341no—
1516C2×C4—1341no—
1517C2×C4—1341no—
1518C2×C4—1341no—
1519C2×C4—1341no—
1520C2×C4—1341no—
1521C2×C4—1341no—
1522C2×C4—1341no—
1523C2×C4—1341no—
1524C2×C4—1341no—
1525C2×C4—1341no—
1526C2×C4—1341no—
1527C2×C4—1341no—
1528C2×C4—1341no—
1529C2×C4—1341no—
1530C2×C4—1341no—
1531C2×C4—1341no—
1532C2×C4—1341no—
1533C2×C4—1341no—
1534C2×C4—1341no—
1535C2×C4—1341no—
1536C2×C4—1341no—
1537C2×C4—1341no—
1538C2×C4—1341no—
1539C2×C4—1341no—
1540C2×C4—1341no—
1541C2×C4C2×#1176162712yes—
1542C2×C4C2×#1176162712yes—
1543C2×C4#1452408912yes—
1544C22—22no—
1545C22—22no—
1546C22—22no—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—26816no—
1558C22—2681no—
1559C22—2681no—
1560C22—2681no—
1561C22—2681no—
1562C22—2681no—
1563C22—2681no—
1564C22—2681no—
1565C22—2681no—
1566C22—2681no—
1567C22—2681no—
1568C22—2681no—
1569C22—2681no—
1570C22—2681no—
1571C22—2681no—
1572C22—2681no—
1573C22—2681no—
1574C22—2681no—
1575C22—2681no—
1576C22—2681no—
1577C22—2681no—
1578C22—2681no—
1579C22—2681no—
1580C22—5368no—
1581C22—1342no—
1582C22—1342no—
1583C22—1342no—
1584C22—1342no—
1585C22—1342no—
1586C22—1342no—
1587C22#1686401914yes—
1588C22C22×#1176162711yescharacteristic
1589C22H(5,𝔽2)×D6711yescharacteristic
1590C22H(5,𝔽2)×D6711yescharacteristic
1591C22C2×#1452408911yescharacteristic
1592C22C2×#1452408911yescharacteristic
1593C22C2×#1452409111yescharacteristic
1594C22#1686423211yescharacteristic
1595C4—22no—
1596C4—22no—
1597C4—22no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—2681no—
1609C4—2681no—
1610C4—2681no—
1611C4—2681no—
1612C4—2681no—
1613C4—2681no—
1614C4—2681no—
1615C4—2681no—
1616C4—2681no—
1617C4—2681no—
1618C4—2681no—
1619C4—2681no—
1620C2—24no—
1621C2—81no—
1622C2—2682no—
1623C2—2682no—
1624C2—5361no—
1625C2—5361no—
1626C2C2×#1686401911yescharacteristic
1627C2#2257389711yescharacteristic
1628C2#2257405811yescharacteristic
1629C2#2257436511yescharacteristic
1630C2#2257440211yescharacteristic
1631C2#2257441311yescharacteristic
1632C2#2257443711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D67
commutator, socle, cosocleC23×C67C25
FittingC67×#2564C2
prime radical#22563565C2
hypercenter#2564D67
hypocenterC67#36793
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C23 ◁ #2564

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22568500C2semidirect
2. #22568497C2semidirect
3. #22568044C2semidirect
4. #22567597C2semidirect
5. #22567550C2semidirect
6. #22567455C2semidirect
7. #22567259C2semidirect
8. #22567213C2semidirect
9. #22567126C2semidirect
10. #22567022C2semidirect
11. #22566980C2semidirect
12. #22566944C2semidirect
13. #22566884C2semidirect
14. #22566826C2semidirect
15. #22566806C2semidirect
16. #22566694C2semidirect
17. #22566619C2semidirect
18. #22566463C2semidirect
19. #22566017C2semidirect
20. #22565986C2semidirect
21. #22565220C2semidirect
22. #22564460C2semidirect
23. #22564460C2semidirect
24. #22564340C2semidirect
25. #22564340C2semidirect
26. #22563861C2semidirect
28. #22562944C2semidirect
29. #22562842C2semidirect
30. C2×#16863274C2semidirect
31. C67×#2564C2semidirect
34. C2×#14524038C22semidirect
35. C2×#14524038C22semidirect
38. C2×#14524029C22semidirect
39. C2×#14524029C22semidirect
40. C2×#14524025C22semidirect
41. C2×#14524025C22semidirect
42. C2×#14524023C22semidirect
43. C2×#14524023C22semidirect
53. #16863333C22semidirect
54. #16863333C22semidirect
55. #16863330C22semidirect
56. #16863330C22semidirect
57. #16863325C22semidirect
58. #16863325C22semidirect
59. #16863325C22semidirect
60. #16863325C22semidirect
61. #16863325C22semidirect
62. #16863325C22semidirect
63. #16863323C22semidirect
64. #16863323C22semidirect
65. #16863323C22semidirect
66. #16863323C22semidirect
67. #16863322C22semidirect
68. #16863322C22semidirect
69. #16863318C22semidirect
70. #16863318C22semidirect
71. #16863318C22semidirect
72. #16863318C22semidirect
73. #16863318C22semidirect
74. #16863318C22semidirect
75. #16863317C22semidirect
76. #16863317C22semidirect
83. #16863312C22semidirect
84. #16863312C22semidirect
85. #16863312C22semidirect
86. #16863312C22semidirect
87. #16863311C22semidirect
88. #16863311C22semidirect
89. #16863311C22semidirect
90. #16863311C22semidirect
91. #16863309C22semidirect
92. #16863309C22semidirect
93. #16863309C22semidirect
94. #16863309C22semidirect
97. #16863303C22semidirect
98. #16863303C22semidirect
99. #16863300C22semidirect
100. #16863300C22semidirect
105. #16863296C22semidirect
106. #16863296C22semidirect
107. #16863295C22semidirect
108. #16863295C22semidirect
109. #16863293C22semidirect
110. #16863293C22semidirect
111. #16863289C22semidirect
112. #16863289C22semidirect
113. #16863288C22semidirect
114. #16863288C22semidirect
115. #16863288C22semidirect
116. #16863288C22semidirect
117. #16863286C22semidirect
118. #16863286C22semidirect
119. #16863285C22semidirect
120. #16863285C22semidirect
121. #16863285C22semidirect
122. #16863285C22semidirect
123. #16863282C22semidirect
124. #16863282C22semidirect
125. #16863282C22semidirect
126. #16863282C22semidirect
127. #16863282C22semidirect
128. #16863282C22semidirect
139. #16863272C22semidirect
140. #16863272C22semidirect
145. #16863270C22semidirect
146. #16863270C22semidirect
147. #16863270C22semidirect
148. #16863270C22semidirect
149. #16863270C22semidirect
150. #16863270C22semidirect
153. #16863264C22semidirect
154. #16863262C22semidirect
155. #16863259C22semidirect
156. #16863258C22semidirect
157. #16863258C22semidirect
159. #16863256C22semidirect
160. #16863253C22semidirect
161. #16863253C22semidirect
174. #400×C67C22semidirect
175. #399×C67C22semidirect
176. #395×C67C22semidirect
177. #393×C67C22semidirect
178. #387×C67C22semidirect
179. #387×C67C22semidirect
182. #385×C67C22semidirect
183. #385×C67C22semidirect
837. #2564D67semidirect
848. C67#36793semidirect
872. #400C2×D67semidirect
875. #399C2×D67semidirect
898. #395C2×D67semidirect
917. #393C2×D67semidirect
952. #387C2×D67semidirect
953. #387C2×D67semidirect
980. #385C2×D67semidirect
981. #385C2×D67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225685002
#225684972
#225680442
#225675972
#225675502
#225674552
#225672592
#225672132
#225671262
#225670222
#225669802
#225669442
#225668842
#225668262
#225668062
#225666942
#225666192
#225664632
#225660172
#225659862
#225652202
#225644602
#225643402
#225638612
#225635652
#225629442
#225628422
C2×#168632742
C67×#25642
#3679367