Finite Group Databasebeta

← #35566536

Subgroups — #35566536

Order 21248.

2396 conjugacy classes of subgroups.

The subgroup lattice has 1522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128374C211yesmaximal, characteristic
2#24910593C211yesmaximal, characteristic, complemented
3#24910591C211yesmaximal, characteristic, complemented
4#24910586C211yesmaximal, characteristic, complemented
5#24910586C211yesmaximal, characteristic, complemented
6#24910544C211yesmaximal, characteristic, complemented
7#24910537C211yesmaximal, characteristic, complemented
8#24910489C211yesmaximal, characteristic, complemented
9#24910459C211yesmaximal, characteristic, complemented
10#24910443C211yesmaximal, characteristic
11#24910433C211yesmaximal, characteristic, complemented
12#24910401C211yesmaximal, characteristic, complemented
13#24910355C211yesmaximal, characteristic, complemented
14#24910325C211yesmaximal, characteristic, complemented
15#24910310C211yesmaximal, characteristic, complemented
16#24910305C211yesmaximal, characteristic, complemented
17#24910277C211yesmaximal, characteristic, complemented
18#24910248C211yesmaximal, characteristic, complemented
19#24910243C211yesmaximal, characteristic, complemented
20#24910215C211yesmaximal, characteristic, complemented
21#24910117C211yesmaximal, characteristic
22#24910013C211yesmaximal, characteristic, complemented
23C4×#14581769C211yesmaximal, characteristic, complemented
24#24909982C211yesmaximal, characteristic, complemented
25#24909955C211yesmaximal, characteristic, complemented
26#24909899C211yesmaximal, characteristic, complemented
27C2×#19127591C211yesmaximal, characteristic, complemented
28#24909820C211yesmaximal, characteristic, complemented
29#24909815C211yesmaximal, characteristic, complemented
30C4×D4×Dic83C211yesmaximal, characteristic, complemented
31C83×#2322C211yesmaximal, characteristic, complemented
32#19128374C4116yescomplemented
33C2×#14581787C2211yescharacteristic
34C2×#14581787C2211yescharacteristic
35C2×#14581778C2211yescharacteristic
36C2×#14581776C2211yescharacteristic
37C2×#14581774C2211yescharacteristic
38C2×#14581772C2211yescharacteristic
39C2×#14581769C2211yescharacteristic
40C2×#14581760C2211yescharacteristic
41C2×C4×Dic166C2211yescharacteristic, complemented
42C2×D4×Dic83C2211yescharacteristic
43C2×D4×Dic83C2211yescharacteristic
44C2×(C22⋊D83)⋊C4C2211yescharacteristic
45C2×(C22⋊D83)⋊C4C2211yescharacteristic
46C2×#14581751C2211yescharacteristic
47C2×#14581751C2211yescharacteristic
48C2×#14581750C2211yescharacteristic
49C2×#14581750C2211yescharacteristic
50C22×(C2×D83)⋊C4C2211yescharacteristic
51C22×(C2×D83)⋊C4C2211yescharacteristic
52C22×(C2×D83)⋊C4C2211yescharacteristic
53C2×C22⋊C4×D83C2211yescharacteristic
54C2×C22⋊C4×D83C2211yescharacteristic
55C22×C4×Dic83C2211yescharacteristic
56C22×C4×Dic83C2211yescharacteristic, complemented
57#19127606C2211yescharacteristic, complemented
58#19127605C2211yescharacteristic, complemented
59#19127605C2211yescharacteristic, complemented
60#19127601C2211yescharacteristic
61#19127601C2211yescharacteristic
62#19127601C2211yescharacteristic
63#19127600C2211yescharacteristic, complemented
64#19127598C2211yescharacteristic, complemented
65#19127595C2211yescharacteristic, complemented
66#19127594C2211yescharacteristic, complemented
67#19127594C2211yescharacteristic, complemented
68#19127593C2211yescharacteristic
69#19127593C2211yescharacteristic
70#19127593C2211yescharacteristic
71#19127593C2211yescharacteristic
72#19127593C2211yescharacteristic
73#19127592C2211yescharacteristic
74#19127592C2211yescharacteristic
75#19127591C2211yescharacteristic
76#19127591C2211yescharacteristic
77#19127591C2211yescharacteristic
78#19127591C2211yescharacteristic
79#19127591C2211yescharacteristic
80#19127591C2211yescharacteristic
81#19127591C2211yescharacteristic
82#19127591C2211yescharacteristic
83#19127591C2211yescharacteristic
84#19127591C2211yescharacteristic
85#19127591C2211yescharacteristic
86#19127591C2211yescharacteristic
87#19127590C2211yescharacteristic
88#19127590C2211yescharacteristic
89#19127590C2211yescharacteristic
90#19127589C2211yescharacteristic, complemented
91#19127588C2211yescharacteristic, complemented
92#19127587C2211yescharacteristic, complemented
93#19127587C2211yescharacteristic, complemented
94#19127586C2211yescharacteristic, complemented
95#19127586C2211yescharacteristic, complemented
96#19127586C2211yescharacteristic, complemented
97#19127586C2211yescharacteristic, complemented
98#19127584C2211yescharacteristic, complemented
99#19127584C2211yescharacteristic, complemented
100#19127584C2211yescharacteristic, complemented
101#19127584C2211yescharacteristic, complemented
102#19127583C2211yescharacteristic, complemented
103#19127582C2211yescharacteristic, complemented
104#19127582C2211yescharacteristic, complemented
105#19127581C2211yescharacteristic
106#19127580C2211yescharacteristic
107#19127580C2211yescharacteristic
108#19127578C2211yescharacteristic
109#19127577C2211yescharacteristic
110#19127576C2211yescharacteristic
111#19127576C2211yescharacteristic, complemented
112#19127575C2211yescharacteristic
113#19127575C2211yescharacteristic
114#19127575C2211yescharacteristic
115#19127573C2211yescharacteristic
116#19127573C2211yescharacteristic
117#19127568C2211yescharacteristic, complemented
118#19127568C2211yescharacteristic, complemented
119#19127565C2211yescharacteristic, complemented
120#19127563C2211yescharacteristic
121#19127562C2211yescharacteristic, complemented
122#19127559C2211yescharacteristic
123#19127558C2211yescharacteristic
124#19127556C2211yescharacteristic
125C4⋊C4×Dic83C2211yescharacteristic, complemented
126C4⋊C4×Dic83C2211yescharacteristic, complemented
127C4⋊C4×Dic83C2211yescharacteristic, complemented
128C4⋊C4×Dic83C2211yescharacteristic, complemented
129C4⋊C4×Dic83C2211yescharacteristic, complemented
130C4⋊C4×Dic83C2211yescharacteristic, complemented
131C4⋊C4×Dic83C2211yescharacteristic, complemented
132C4⋊C4×Dic83C2211yescharacteristic, complemented
133C4⋊C4×Dic83C2211yescharacteristic, complemented
134C4⋊C4×Dic83C2211yescharacteristic, complemented
135C4⋊C4×Dic83C2211yescharacteristic, complemented
136C4⋊C4×Dic83C2211yescharacteristic, complemented
137C4×Dic83⋊C4C2211yescharacteristic, complemented
138C4×Dic83⋊C4C2211yescharacteristic, complemented
139C4×C4⋊Dic83C2211yescharacteristic, complemented
140C4×C4⋊Dic83C2211yescharacteristic, complemented
141#19127552C2211yescharacteristic, complemented
142#19127552C2211yescharacteristic, complemented
143C22⋊C4×Dic83C2211yescharacteristic
144C22⋊C4×Dic83C2211yescharacteristic
145C22⋊C4×Dic83C2211yescharacteristic
146C22⋊C4×Dic83C2211yescharacteristic
147C22⋊C4×Dic83C2211yescharacteristic, complemented
148C22⋊C4×Dic83C2211yescharacteristic, complemented
149C22⋊C4×Dic83C2211yescharacteristic, complemented
150C22⋊C4×Dic83C2211yescharacteristic, complemented
151C4×(C2×D83)⋊C4C2211yescharacteristic
152C4×(C2×D83)⋊C4C2211yescharacteristic
153C4×(C2×D83)⋊C4C2211yescharacteristic
154C4×(C2×D83)⋊C4C2211yescharacteristic
155C4×C22⋊Dic83C2211yescharacteristic
156C4×C22⋊Dic83C2211yescharacteristic
157C4×C22⋊Dic83C2211yescharacteristic
158C4×C22⋊Dic83C2211yescharacteristic
159C4×C22⋊Dic83C2211yescharacteristic, complemented
160#19127548C2211yescharacteristic
161#19127548C2211yescharacteristic
162#19127548C2211yescharacteristic
163#19127548C2211yescharacteristic
164#19127548C2211yescharacteristic
165#19127548C2211yescharacteristic
166#19127548C2211yescharacteristic
167#19127548C2211yescharacteristic
168#19127546C2211yescharacteristic, complemented
169#19127546C2211yescharacteristic, complemented
170C2×C83⋊#95C2211yescharacteristic
171C2×C83⋊#95C2211yescharacteristic
172C42×Dic83C2211yescharacteristic, complemented
173C2×#123×C83C2211yescharacteristic
174C2×C4×D4×C83C2211yescharacteristic
175C22×C4⋊C4×C83C2211yescharacteristic
176#389×C83C2211yescharacteristic, complemented
177#389×C83C2211yescharacteristic, complemented
178#388×C83C2211yescharacteristic, complemented
179#388×C83C2211yescharacteristic, complemented
180#387×C83C2211yescharacteristic, complemented
181#387×C83C2211yescharacteristic, complemented
182#386×C83C2211yescharacteristic
183#385×C83C2211yescharacteristic
184#385×C83C2211yescharacteristic, complemented
185#385×C83C2211yescharacteristic, complemented
186#381×C83C2211yescharacteristic
187C4×C22⋊C4×C83C2211yescharacteristic
188C24×D83C2311yescharacteristic
189C22×Dic166C2311yescharacteristic
190C22×C22⋊D83C2311yescharacteristic
191C22×C22⋊D83C2311yescharacteristic
192C23×Dic83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C23×Dic83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C23×Dic83C2311yescharacteristic
197C22×C4×D83C2311yescharacteristic
198C22×C4×D83C2311yescharacteristic
199C22×C4×D83C2311yescharacteristic
200C22×C4×D83C2311yescharacteristic
201#14581787C2×C418yescomplemented
202#14581787C2×C418yescomplemented
203#14581778C2×C418yescomplemented
204#14581776C2×C418yescomplemented
205#14581774C2×C418yescomplemented
206#14581772C2×C418yescomplemented
207#14581769C2×C418yescomplemented
208#14581760C2×C418yes—
209C4×Dic166—42no—
210D4×Dic83—24no—
211D4×Dic83C2×C418yescomplemented
212(C22⋊D83)⋊C4—42no—
213(C22⋊D83)⋊C4C2×C418yescomplemented
214#14581751—24no—
215#14581751C2×C418yescomplemented
216#14581750—42no—
217#14581750C2×C418yescomplemented
218C2×C4⋊Dic83C2311yescharacteristic
219C2×C4⋊Dic83C2311yescharacteristic
220C2×C4⋊Dic83C2311yescharacteristic
221C2×C4⋊Dic83C2311yescharacteristic
222C2×C4⋊Dic83C2311yescharacteristic
223C2×C4⋊Dic83C2311yescharacteristic
224C2×C4⋊Dic83C2311yescharacteristic
225C2×C4⋊Dic83C2311yescharacteristic
226C2×C4⋊Dic83C2311yescharacteristic
227C2×Dic83⋊C4C2311yescharacteristic
228C2×Dic83⋊C4C2311yescharacteristic
229C2×Dic83⋊C4C2311yescharacteristic
230C2×Dic83⋊C4C2311yescharacteristic
231C2×Dic83⋊C4C2311yescharacteristic
232C2×Dic83⋊C4C2311yescharacteristic
233C2×Dic83⋊C4C2311yescharacteristic
234C2×Dic83⋊C4C2311yescharacteristic
235C2×C22⋊Dic83C2311yescharacteristic
236C2×C22⋊Dic83C2311yescharacteristic
237C2×C22⋊Dic83C2311yescharacteristic
238C2×C22⋊Dic83C2311yescharacteristic
239C2×C22⋊Dic83C2311yescharacteristic
240C2×C22⋊Dic83C2311yescharacteristic
241C2×C22⋊Dic83C2311yescharacteristic
242C2×C22⋊Dic83C2311yescharacteristic
243C2×(C2×D83)⋊C4—24no—
244C2×(C2×D83)⋊C4—42no—
245C2×(C2×D83)⋊C4C2×C418yescomplemented
246C2×(C2×D83)⋊C4C2311yescharacteristic
247C2×(C2×D83)⋊C4C2311yescharacteristic
248C2×(C2×D83)⋊C4C2311yescharacteristic
249C2×(C2×D83)⋊C4C2311yescharacteristic
250C2×(C2×D83)⋊C4C2311yescharacteristic
251C2×(C2×D83)⋊C4C2311yescharacteristic
252C2×(C2×D83)⋊C4C2311yescharacteristic
253C2×(C2×D83)⋊C4C2311yescharacteristic
254C2×(C2×D83)⋊C4C2311yescharacteristic
255C2×(C2×D83)⋊C4C2311yescharacteristic
256C2×(C2×D83)⋊C4C2311yescharacteristic
257C2×(C2×D83)⋊C4C2311yescharacteristic
258C2×(C2×D83)⋊C4C2311yescharacteristic
259C2×(C2×D83)⋊C4C2311yescharacteristic
260C2×(C2×D83)⋊C4C2311yescharacteristic
261C2×(C2×D83)⋊C4C2311yescharacteristic
262C2×(C2×D83)⋊C4C2311yescharacteristic
263C2×(C2×D83)⋊C4C2311yescharacteristic
264C2×(C2×D83)⋊C4C2311yescharacteristic
265C2×(C2×D83)⋊C4C2311yescharacteristic
266C2×(C2×D83)⋊C4C2311yescharacteristic
267C2×(C2×D83)⋊C4C2311yescharacteristic
268C22⋊C4×D83—24no—
269C22⋊C4×D83C2×C418yescomplemented
270C2×C4×Dic83—42no—
271C2×C4×Dic83—42no—
272C2×C4×Dic83C2311yescharacteristic
273C2×C4×Dic83C2311yescharacteristic
274C2×C4×Dic83C2311yescharacteristic
275C2×C4×Dic83C2311yescharacteristic
276C2×C4×Dic83C2311yescharacteristic
277C2×C4×Dic83C2311yescharacteristic
278C2×C4×Dic83C2311yescharacteristic
279C2×C4×Dic83C2311yescharacteristic
280C2×C4×Dic83C2311yescharacteristic
281C2×C4×Dic83C2311yescharacteristic
282C2×C4×Dic83C2311yescharacteristic
283C2×C4×Dic83C2311yescharacteristic
284C2×C4×Dic83C2311yescharacteristic
285C2×C4×Dic83C2311yescharacteristic
286C2×C4×Dic83C2311yescharacteristic
287C2×C4×Dic83C2311yescharacteristic
288C2×C4×Dic83C2311yescharacteristic
289C2×C4×Dic83C2311yescharacteristic
290C2×C4×Dic83C2311yescharacteristic
291C2×C4×Dic83C2311yescharacteristic
292C2×C4×Dic83C2311yescharacteristic
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
296C2×C4×Dic83C2311yescharacteristic
297C2×C4×Dic83C2311yescharacteristic
298C83⋊#95C2311yescharacteristic
299C83⋊#95C2311yescharacteristic
300C83⋊#95C2311yescharacteristic
301C83⋊#95C2311yescharacteristic
302C83⋊#95C2311yescharacteristic
303C83⋊#95C2311yescharacteristic
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
310C83⋊#95C2311yescharacteristic
311C83⋊#95C2311yescharacteristic
312C83⋊#95C2311yescharacteristic
313C83⋊#95C2311yescharacteristic
314C83⋊#95C2311yescharacteristic
315C83⋊#95C2311yescharacteristic
316C83⋊#95C2311yescharacteristic
317C83⋊#95C2311yescharacteristic
318C83⋊#95C2311yescharacteristic
319C83⋊#95C2311yescharacteristic
320C83⋊#95C2311yescharacteristic
321C83⋊#95C2311yescharacteristic
322C83⋊#95C2311yescharacteristic
323C83⋊#95C2311yescharacteristic
324C83⋊#95C2311yescharacteristic
325C83⋊#95C2311yescharacteristic
326C83⋊#95C2311yescharacteristic
327C83⋊#95C2311yescharacteristic
328C83⋊#95C2311yescharacteristic
329C83⋊#95C2311yescharacteristic
330C83⋊#95C2311yescharacteristic
331C83⋊#95C2311yescharacteristic
332C22×D4×C83C2311yescharacteristic
333C23×C4×C83C2311yescharacteristic
334C23×C4×C83C2311yescharacteristic
335C23×C4×C83C2311yescharacteristic
336C23×C4×C83C2311yescharacteristic
337#123×C83C2×C418yescomplemented
338C4×D4×C83—24no—
339C2×C4⋊C4×C83—24no—
340C2×C4⋊C4×C83C2311yescharacteristic
341C2×C4⋊C4×C83C2311yescharacteristic
342C2×C4⋊C4×C83C2311yescharacteristic
343C2×C4⋊C4×C83C2311yescharacteristic
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C4⋊C4×C83C2311yescharacteristic
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C4⋊C4×C83C2311yescharacteristic
349C2×C22⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83C2311yescharacteristic
355C2×C22⋊C4×C83C2311yescharacteristic
356C2×C22⋊C4×C83C2311yescharacteristic
357C2×C42×C83C2311yescharacteristic
358C2×C42×C83C2311yescharacteristic
359C2×C42×C83C2311yescharacteristic
360#95×C83C2311yescharacteristic
361#95×C83C2311yescharacteristic
362#95×C83C2311yescharacteristic
363#95×C83C2311yescharacteristic
364#95×C83C2311yescharacteristic
365#95×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370C23×D83—22no—
371C23×D83—22no—
372C23×D83—41no—
373C23×D83—41no—
374C23×D83—41no—
375C23×D83—41no—
376C23×D83C22×C414yes—
377C23×D83C2411yescharacteristic
378C23×D83C2411yescharacteristic
379C2×Dic166—41no—
380C2×Dic166—41no—
381C2×Dic166C22×C414yes—
382C2×C22⋊D83—41no—
383C2×C22⋊D83—41no—
384C2×C22⋊D83—41no—
385C2×C22⋊D83—41no—
386C2×C22⋊D83C22×C414yes—
387C2×C22⋊D83C22×C414yes—
388C22×Dic83—22no—
389C22×Dic83—22no—
390C22×Dic83—22no—
391C22×Dic83—22no—
392C22×Dic83—22no—
393C22×Dic83—41no—
394C22×Dic83—41no—
395C22×Dic83—41no—
396C22×Dic83—41no—
397C22×Dic83—41no—
398C22×Dic83—41no—
399C22×Dic83—41no—
400C22×Dic83—41no—
401C22×Dic83C22×C414yes—
402C22×Dic83C22×C414yes—
403C22×Dic83C2411yescharacteristic
404C22×Dic83C2411yescharacteristic
405C22×Dic83C2411yescharacteristic
406C22×Dic83C2411yescharacteristic
407C22×Dic83C2411yescharacteristic
408C22×Dic83C2411yescharacteristic
409C22×Dic83C2411yescharacteristic
410C22×Dic83C2411yescharacteristic
411C22×Dic83C2411yescharacteristic
412C22×Dic83C2411yescharacteristic
413C22×Dic83C2411yescharacteristic
414C22×Dic83C2411yescharacteristic
415C22×Dic83C2411yescharacteristic
416C22×Dic83C2411yescharacteristic
417C2×C4×D83—22no—
418C2×C4×D83—22no—
419C2×C4×D83—41no—
420C2×C4×D83—41no—
421C2×C4×D83—41no—
422C2×C4×D83—41no—
423C2×C4×D83—41no—
424C2×C4×D83—41no—
425C2×C4×D83—41no—
426C2×C4×D83—41no—
427C2×C4×D83C22×C414yes—
428C2×C4×D83C22×C414yes—
429C4⋊Dic83—22no—
430C4⋊Dic83—22no—
431C4⋊Dic83—22no—
432C4⋊Dic83—22no—
433C4⋊Dic83—41no—
434C4⋊Dic83C22×C414yes—
435C4⋊Dic83C22×C414yes—
436C4⋊Dic83C22×C414yes—
437C4⋊Dic83C22×C414yes—
438Dic83⋊C4—22no—
439Dic83⋊C4—41no—
440Dic83⋊C4—41no—
441Dic83⋊C4—41no—
442Dic83⋊C4—41no—
443Dic83⋊C4—41no—
444Dic83⋊C4C22×C414yes—
445Dic83⋊C4C22×C414yes—
446C22⋊Dic83—22no—
447C22⋊Dic83—22no—
448C22⋊Dic83—41no—
449C22⋊Dic83—41no—
450C22⋊Dic83C22×C414yes—
451C22⋊Dic83C22×C414yes—
452C22⋊Dic83C22×C414yes—
453C22⋊Dic83#4114yes—
454(C2×D83)⋊C4—22no—
455(C2×D83)⋊C4—22no—
456(C2×D83)⋊C4—22no—
457(C2×D83)⋊C4—22no—
458(C2×D83)⋊C4—22no—
459(C2×D83)⋊C4—22no—
460(C2×D83)⋊C4—22no—
461(C2×D83)⋊C4—22no—
462(C2×D83)⋊C4—41no—
463(C2×D83)⋊C4—41no—
464(C2×D83)⋊C4—41no—
465(C2×D83)⋊C4—41no—
466(C2×D83)⋊C4—41no—
467(C2×D83)⋊C4—41no—
468(C2×D83)⋊C4C22×C414yes—
469(C2×D83)⋊C4C22×C414yes—
470(C2×D83)⋊C4C22×C414yes—
471(C2×D83)⋊C4C22×C414yes—
472(C2×D83)⋊C4C22×C414yes—
473(C2×D83)⋊C4C22×C414yes—
474(C2×D83)⋊C4C22×C414yes—
475(C2×D83)⋊C4C22×C414yes—
476C4×Dic83—22no—
477C4×Dic83—22no—
478C4×Dic83—22no—
479C4×Dic83—22no—
480C4×Dic83—22no—
481C4×Dic83—22no—
482C4×Dic83—41no—
483C4×Dic83—41no—
484C4×Dic83—41no—
485C4×Dic83—41no—
486C4×Dic83—41no—
487C4×Dic83—41no—
488C4×Dic83—41no—
489C4×Dic83—41no—
490C4×Dic83—41no—
491C4×Dic83—41no—
492C4×Dic83—41no—
493C4×Dic83—41no—
494C4×Dic83—41no—
495C4×Dic83—41no—
496C4×Dic83—41no—
497C4×Dic83—41no—
498C4×Dic83—41no—
499C4×Dic83C22×C414yes—
500C4×Dic83C22×C414yes—
501C4×Dic83C22×C414yes—
502C24×C83C2411yescharacteristic
503C24×C83C2411yescharacteristic
504C2×D4×C83—22no—
505C2×D4×C83—22no—
506C2×D4×C83C22×C414yes—
507C22×C4×C83—22no—
508C22×C4×C83—22no—
509C22×C4×C83—22no—
510C22×C4×C83—22no—
511C22×C4×C83—41no—
512C22×C4×C83—41no—
513C22×C4×C83—41no—
514C22×C4×C83—41no—
515C22×C4×C83—41no—
516C22×C4×C83—41no—
517C22×C4×C83C22×C414yes—
518C22×C4×C83#4114yes—
519C22×C4×C83C2411yescharacteristic
520C22×C4×C83C2411yescharacteristic
521C22×C4×C83C2411yescharacteristic
522C22×C4×C83C2411yescharacteristic
523C22×C4×C83C2411yescharacteristic
524C22×C4×C83C2411yescharacteristic
525C22×C4×C83C2411yescharacteristic
526C22×C4×C83C2411yescharacteristic
527C22×C4×C83C2411yescharacteristic
528C22×C4×C83C2411yescharacteristic
529C22×C4×C83C2411yescharacteristic
530C22×C4×C83C2411yescharacteristic
531C22×C4×C83C2411yescharacteristic
532C4⋊C4×C83—22no—
533C4⋊C4×C83—22no—
534C4⋊C4×C83—22no—
535C4⋊C4×C83—22no—
536C4⋊C4×C83—22no—
537C4⋊C4×C83—41no—
538C4⋊C4×C83—41no—
539C4⋊C4×C83C22×C414yes—
540C4⋊C4×C83C22×C414yes—
541C22⋊C4×C83—22no—
542C22⋊C4×C83—22no—
543C22⋊C4×C83—22no—
544C22⋊C4×C83—41no—
545C22⋊C4×C83—41no—
546C22⋊C4×C83C22×C414yes—
547C22⋊C4×C83C22×C414yes—
548C22⋊C4×C83C22×C414yes—
549C42×C83—22no—
550C42×C83—41no—
551C42×C83—41no—
552C23×C83—21no—
553C23×C83—21no—
554C23×C83—21no—
555C23×C83—21no—
556C23×C83—21no—
557C23×C83—21no—
558C23×C83—21no—
559C23×C83—21no—
560C23×C83—21no—
561C23×C83—21no—
562C23×C83C23×C412yes—
563C23×C83C23×C412yes—
564C23×C83C2×#4112yes—
565C23×C83C2×#4112yes—
566C23×C83C2511yescharacteristic
567C22×D83—21no—
568C22×D83—21no—
569C22×D83—21no—
570C22×D83—21no—
571C22×D83—21no—
572C22×D83—21no—
573C22×D83—21no—
574C22×D83—21no—
575C22×D83—21no—
576C22×D83—21no—
577C22×D83—21no—
578C22×D83—21no—
579C22×D83—28no—
580C22×D83—44no—
581C22×D83—44no—
582C22×D83—82no—
583C22×D83—82no—
584C22×D83—82no—
585C22×D83—82no—
586C22×D83C23×C412yes—
587C22×D83C23×C412yes—
588D4×C83—28no—
589C2×C4×C83—28no—
590C2×C4×C83—21no—
591C2×C4×C83—21no—
592C2×C4×C83—21no—
593C2×C4×C83—21no—
594C2×C4×C83—21no—
595C2×C4×C83—21no—
596C2×C4×C83—21no—
597C2×C4×C83—21no—
598C2×C4×C83—21no—
599C2×C4×C83—21no—
600C2×C4×C83—21no—
601C2×C4×C83—21no—
602C2×C4×C83—21no—
603C2×C4×C83—21no—
604C2×C4×C83—21no—
605C2×C4×C83—21no—
606C2×C4×C83—21no—
607C2×C4×C83—21no—
608C2×C4×C83—21no—
609C2×C4×C83—21no—
610C2×C4×C83—21no—
611C2×C4×C83—21no—
612C2×C4×C83—21no—
613C2×C4×C83—21no—
614C2×C4×C83—21no—
615C2×C4×C83—21no—
616C2×C4×C83—21no—
617C2×C4×C83—21no—
618C2×C4×C83—21no—
619C2×C4×C83—21no—
620C2×C4×C83—21no—
621C2×C4×C83—21no—
622C2×C4×C83—44no—
623C2×C4×C83—44no—
624C2×C4×C83—82no—
625C2×C4×C83C23×C412yes—
626C2×C4×C83C23×C412yes—
627C2×C4×C83C23×C412yes—
628C2×C4×C83C23×C412yes—
629C2×C4×C83C23×C412yes—
630C2×C4×C83C2×#4112yes—
631C2×C4×C83C2×#4112yes—
632C22⋊D83—44no—
633C22⋊D83—44no—
634C2×Dic83—21no—
635C2×Dic83—21no—
636C2×Dic83—21no—
637C2×Dic83—21no—
638C2×Dic83—21no—
639C2×Dic83—21no—
640C2×Dic83—21no—
641C2×Dic83—21no—
642C2×Dic83—21no—
643C2×Dic83—21no—
644C2×Dic83—21no—
645C2×Dic83—21no—
646C2×Dic83—21no—
647C2×Dic83—21no—
648C2×Dic83—21no—
649C2×Dic83—21no—
650C2×Dic83—21no—
651C2×Dic83—21no—
652C2×Dic83—21no—
653C2×Dic83—21no—
654C2×Dic83—21no—
655C2×Dic83—21no—
656C2×Dic83—21no—
657C2×Dic83—21no—
658C2×Dic83—21no—
659C2×Dic83—21no—
660C2×Dic83—21no—
661C2×Dic83—21no—
662C2×Dic83—21no—
663C2×Dic83—21no—
664C2×Dic83—21no—
665C2×Dic83—21no—
666C2×Dic83—21no—
667C2×Dic83—44no—
668C2×Dic83—44no—
669C2×Dic83—44no—
670C2×Dic83—44no—
671C2×Dic83—82no—
672C2×Dic83C23×C412yes—
673C2×Dic83C23×C412yes—
674C2×Dic83C23×C412yes—
675C2×Dic83C23×C412yes—
676C2×Dic83C23×C412yes—
677C2×Dic83C23×C412yes—
678C2×Dic83C2×#4112yes—
679C2×Dic83C2×#4112yes—
680C2×Dic83H(5,𝔽2)12yes—
681C4×D83—44no—
682C4×D83—44no—
683C4×D83—82no—
684C4×D83—82no—
685Dic166—44no—
686C22×C83—22no—
687C22×C83—22no—
688C22×C83—22no—
689C22×C83—22no—
690C22×C83—22no—
691C22×C83—22no—
692C22×C83—22no—
693C22×C83—22no—
694C22×C83—22no—
695C22×C83—41no—
696C22×C83—41no—
697C22×C83—41no—
698C22×C83—41no—
699C22×C83C4×#4114yes—
700C22×C83C24×C411yescharacteristic
701C22×C83C22×#4111yescharacteristic
702C22×C83C22×#4111yescharacteristic
703C22×C83C2×H(5,𝔽2)11yescharacteristic
704C22×C83#58511yescharacteristic
705C22×C83#58511yescharacteristic
706C22×C83#58511yescharacteristic
707C2×D83—22no—
708C2×D83—22no—
709C2×D83—22no—
710C2×D83—22no—
711C2×D83—22no—
712C2×D83—22no—
713C2×D83—41no—
714C2×D83—41no—
715C2×D83—41no—
716C2×D83—41no—
717C2×D83—41no—
718C2×D83—41no—
719C2×D83—41no—
720C2×D83—41no—
721C2×D83—88no—
722C4×C83—22no—
723C4×C83—22no—
724C4×C83—22no—
725C4×C83—22no—
726C4×C83—22no—
727C4×C83—22no—
728C4×C83—22no—
729C4×C83—41no—
730C4×C83—41no—
731C4×C83—41no—
732C4×C83—41no—
733C4×C83—41no—
734C4×C83—41no—
735Dic83—22no—
736Dic83—22no—
737Dic83—22no—
738Dic83—22no—
739Dic83—22no—
740Dic83—22no—
741Dic83—22no—
742Dic83—22no—
743Dic83—22no—
744Dic83—41no—
745Dic83—41no—
746Dic83—41no—
747Dic83—41no—
748Dic83—41no—
749#34315—831nomaximal, Sylow
750C2×C83—24no—
751C2×C83—42no—
752C2×C83C2×C4×#4111yescharacteristic
753C2×C83#342811yescharacteristic
754C2×C83C4×H(5,𝔽2)11yescharacteristic
755C2×C83#350511yescharacteristic
756C2×C83#351011yescharacteristic
757C2×C83#351311yescharacteristic
758C2×C83#352111yescharacteristic
759D83—42no—
760D83—42no—
761C2×#551—831no—
762#2374—831no—
763#2374—831no—
764#2373—831no—
765#2373—831no—
766#2368—831no—
767#2367—831no—
768#2362—831no—
769#2359—831no—
770#2358—831no—
771#2357—831no—
772#2353—831no—
773#2347—831no—
774#2343—831no—
775#2342—831no—
776#2342—831no—
777#2337—831no—
778#2335—831no—
779#2334—831no—
780#2332—831no—
781#2322D8311yescharacteristic, complemented
782#2321—831no—
783C4×#126—831no—
784C4×C22⋊Q8—831no—
785C4×#123—831no—
786#2298—831no—
787#2290—831no—
788C2×#388—831no—
789#2274—831no—
790#2273—831no—
791C42×D4—831no—
792C83#3431511yescharacteristic, complemented, Sylow
793#551—8316no—
794C2×#126—831no—
795C2×#126—831no—
796C2×#124—831no—
797C2×#123—831no—
798C2×#123—831no—
799C2×#123C2×D8311yescharacteristic
800C2×C22⋊Q8—831no—
801C2×C22⋊Q8—831no—
802C2×#120—831no—
803C2×C4×Q8—831no—
804C2×C4×D4—831no—
805C2×C4×D4—831no—
806C2×C4×D4—831no—
807C2×C4×D4—831no—
808C2×C4×D4C2×D8311yescharacteristic
809C2×#117—831no—
810C2×#117—831no—
811C2×#117—831no—
812C2×#117—831no—
813C22×C4⋊C4C2×D8311yescharacteristic
814C22×C22⋊C4—831no—
815C22×C22⋊C4—831no—
816C22×C22⋊C4—831no—
817C22×C22⋊C4—831no—
818C22×C22⋊C4—831no—
819C22×C42—831no—
820C22×C42—831no—
821#391—831no—
822#391—831no—
823#391—831no—
824#390—831no—
825#390—831no—
826#390—831no—
827#389—831no—
828#389—831no—
829#389C2×D8311yescharacteristic, complemented
830#389C2×D8311yescharacteristic, complemented
831#388—831no—
832#388—831no—
833#388—831no—
834#388—831no—
835#388—831no—
836#388—831no—
837#388—831no—
838#388—831no—
839#388—831no—
840#388—831no—
841#388—831no—
842#388—831no—
843#388—831no—
844#388—831no—
845#388—831no—
846#388—831no—
847#388—831no—
848#388—831no—
849#388—831no—
850#388—831no—
851#388—831no—
852#388—831no—
853#388—831no—
854#388—831no—
855#388—831no—
856#388—831no—
857#388C2×D8311yescharacteristic, complemented
858#388C2×D8311yescharacteristic, complemented
859#387—831no—
860#387—831no—
861#387—831no—
862#387—831no—
863#387—831no—
864#387—831no—
865#387—831no—
866#387—831no—
867#387—831no—
868#387—831no—
869#387—831no—
870#387—831no—
871#387—831no—
872#387—831no—
873#387C2×D8311yescharacteristic, complemented
874#387C2×D8311yescharacteristic, complemented
875#386—831no—
876#386—831no—
877#386—831no—
878#386—831no—
879#386—831no—
880#386C2×D8311yescharacteristic
881#385—831no—
882#385—831no—
883#385—831no—
884#385—831no—
885#385—831no—
886#385—831no—
887#385—831no—
888#385C2×D8311yescharacteristic
889#385C2×D8311yescharacteristic, complemented
890#385C2×D8311yescharacteristic, complemented
891#383—831no—
892#383—831no—
893#382—831no—
894#381—831no—
895#381—831no—
896#381C2×D8311yescharacteristic
897#380—831no—
898#380—831no—
899#379—831no—
900C4×C4⋊C4—831no—
901C4×C4⋊C4—831no—
902C4×C4⋊C4—831no—
903C4×C4⋊C4—831no—
904C4×C4⋊C4—831no—
905C4×C4⋊C4—831no—
906C4×C4⋊C4—831no—
907C4×C4⋊C4—831no—
908C4×C4⋊C4—831no—
909C4×C4⋊C4—831no—
910C4×C4⋊C4—831no—
911C4×C4⋊C4—831no—
912C4×C4⋊C4—831no—
913C4×C4⋊C4—831no—
914C4×C4⋊C4—831no—
915C4×C4⋊C4—831no—
916C4×C4⋊C4—831no—
917C4×C4⋊C4—831no—
918C4×C22⋊C4—831no—
919C4×C22⋊C4—831no—
920C4×C22⋊C4—831no—
921C4×C22⋊C4—831no—
922C4×C22⋊C4—831no—
923C4×C22⋊C4—831no—
924C4×C22⋊C4—831no—
925C4×C22⋊C4—831no—
926C4×C22⋊C4—831no—
927C4×C22⋊C4—831no—
928C4×C22⋊C4—831no—
929C4×C22⋊C4—831no—
930C4×C22⋊C4—831no—
931C4×C22⋊C4—831no—
932C4×C22⋊C4—831no—
933C4×C22⋊C4—831no—
934C4×C22⋊C4—831no—
935C4×C22⋊C4—831no—
936C4×C22⋊C4—831no—
937C4×C22⋊C4—831no—
938C4×C22⋊C4—831no—
939C4×C22⋊C4—831no—
940C4×C22⋊C4—831no—
941C4×C22⋊C4—831no—
942C4×C22⋊C4—831no—
943C4×C22⋊C4C2×D8311yescharacteristic
944#376—831no—
945#376—831no—
946C2×#95—831no—
947C2×#95—831no—
948C43—831no—
949C25—831no—
950C22×Q8—831no—
951C22×D4—831no—
952C22×D4—831no—
953C22×D4C22×D8311yescharacteristic
954C23×C4—831no—
955C23×C4—831no—
956C23×C4—831no—
957C23×C4—831no—
958C23×C4—831no—
959C23×C4—831no—
960C23×C4—831no—
961C23×C4—831no—
962C23×C4—831no—
963C23×C4C22×D8311yescharacteristic
964C23×C4C22×D8311yescharacteristic
965C23×C4C22×D8311yescharacteristic
966C23×C4C22×D8311yescharacteristic
967#126—838no—
968#126—838no—
969#124—838no—
970#123—838no—
971#123—838no—
972#123C4×D8318yescomplemented
973C22⋊Q8—838no—
974C22⋊Q8—838no—
975#120—838no—
976C4×Q8—3322no—
977C4×D4—24no—
978C4×D4—3322no—
979C4×D4—838no—
980C4×D4—838no—
981C4×D4—1664no—
982#117—3322no—
983#117—838no—
984#117—838no—
985#117—1664no—
986C2×C4⋊C4—24no—
987C2×C4⋊C4—831no—
988C2×C4⋊C4—831no—
989C2×C4⋊C4—831no—
990C2×C4⋊C4—831no—
991C2×C4⋊C4—831no—
992C2×C4⋊C4—831no—
993C2×C4⋊C4—831no—
994C2×C4⋊C4—831no—
995C2×C4⋊C4—831no—
996C2×C4⋊C4—831no—
997C2×C4⋊C4—831no—
998C2×C4⋊C4—831no—
999C2×C4⋊C4—831no—
1000C2×C4⋊C4—831no—
1001C2×C4⋊C4—831no—
1002C2×C4⋊C4—831no—
1003C2×C4⋊C4—831no—
1004C2×C4⋊C4C22×D8311yescharacteristic
1005C2×C4⋊C4C22×D8311yescharacteristic
1006C2×C4⋊C4C22×D8311yescharacteristic
1007C2×C4⋊C4C22×D8311yescharacteristic
1008C2×C4⋊C4C22×D8311yescharacteristic
1009C2×C4⋊C4C22×D8311yescharacteristic
1010C2×C4⋊C4C22×D8311yescharacteristic
1011C2×C4⋊C4C22×D8311yescharacteristic
1012C2×C4⋊C4C22×D8311yescharacteristic
1013C2×C22⋊C4—3322no—
1014C2×C22⋊C4—831no—
1015C2×C22⋊C4—831no—
1016C2×C22⋊C4—831no—
1017C2×C22⋊C4—831no—
1018C2×C22⋊C4—831no—
1019C2×C22⋊C4—831no—
1020C2×C22⋊C4—831no—
1021C2×C22⋊C4—831no—
1022C2×C22⋊C4—831no—
1023C2×C22⋊C4—831no—
1024C2×C22⋊C4—831no—
1025C2×C22⋊C4—831no—
1026C2×C22⋊C4—838no—
1027C2×C22⋊C4—831no—
1028C2×C22⋊C4—831no—
1029C2×C22⋊C4—831no—
1030C2×C22⋊C4—831no—
1031C2×C22⋊C4—831no—
1032C2×C22⋊C4—831no—
1033C2×C22⋊C4—831no—
1034C2×C22⋊C4—831no—
1035C2×C22⋊C4—838no—
1036C2×C22⋊C4—831no—
1037C2×C22⋊C4—831no—
1038C2×C22⋊C4—831no—
1039C2×C22⋊C4—831no—
1040C2×C22⋊C4—831no—
1041C2×C22⋊C4—831no—
1042C2×C22⋊C4—831no—
1043C2×C22⋊C4—831no—
1044C2×C22⋊C4—831no—
1045C2×C22⋊C4—831no—
1046C2×C22⋊C4—1664no—
1047C2×C22⋊C4—1664no—
1048C2×C22⋊C4C22×D8311yescharacteristic
1049C2×C22⋊C4C22×D8311yescharacteristic
1050C2×C22⋊C4C22×D8311yescharacteristic
1051C2×C22⋊C4C22×D8311yescharacteristic
1052C2×C22⋊C4C22×D8311yescharacteristic
1053C2×C22⋊C4C22×D8311yescharacteristic
1054C2×C22⋊C4C22×D8311yescharacteristic
1055C2×C22⋊C4C22×D8311yescharacteristic
1056C2×C42—3322no—
1057C2×C42—3322no—
1058C2×C42—831no—
1059C2×C42—831no—
1060C2×C42—831no—
1061C2×C42—831no—
1062C2×C42—831no—
1063C2×C42—831no—
1064C2×C42—831no—
1065C2×C42—831no—
1066C2×C42—831no—
1067C2×C42—831no—
1068C2×C42—831no—
1069C2×C42—831no—
1070C2×C42—831no—
1071C2×C42—831no—
1072C2×C42—831no—
1073C2×C42—831no—
1074C2×C42—831no—
1075C2×C42—831no—
1076C2×C42—831no—
1077C2×C42—831no—
1078C2×C42—831no—
1079C2×C42—831no—
1080C2×C42—831no—
1081C2×C42—831no—
1082C2×C42—831no—
1083C2×C42—831no—
1084C2×C42C22×D8311yescharacteristic
1085C2×C42C22×D8311yescharacteristic
1086C2×C42C22×D8311yescharacteristic
1087#95—831no—
1088#95—831no—
1089#95—831no—
1090#95—831no—
1091#95—831no—
1092#95—831no—
1093#95—831no—
1094#95—831no—
1095#95—831no—
1096#95—831no—
1097#95—831no—
1098#95—831no—
1099#95—831no—
1100#95—831no—
1101#95—831no—
1102#95—831no—
1103#95—831no—
1104#95—831no—
1105#95—831no—
1106#95—831no—
1107#95—831no—
1108#95—831no—
1109#95—831no—
1110#95—831no—
1111#95—831no—
1112#95—831no—
1113#95—831no—
1114#95—831no—
1115#95—831no—
1116#95—831no—
1117#95—831no—
1118#95—831no—
1119#95—831no—
1120#95—831no—
1121#95C22×D8311yescharacteristic
1122#95C22×D8311yescharacteristic
1123#95C22×D8311yescharacteristic
1124#95C22×D8311yescharacteristic
1125#95C22×D8311yescharacteristic
1126#95C22×D8311yescharacteristic
1127#95C22×D8311yescharacteristic
1128#95C22×D8311yescharacteristic
1129#95C22×D8311yescharacteristic
1130#95C22×D8311yescharacteristic
1131C24—3321no—
1132C24—3321no—
1133C24—3321no—
1134C24—3321no—
1135C24—834no—
1136C24—831no—
1137C24—831no—
1138C24—1662no—
1139C24—1662no—
1140C24C23×D8311yescharacteristic
1141C24C23×D8311yescharacteristic
1142C2×Q8—3321no—
1143C2×Q8—3321no—
1144C2×Q8—834no—
1145C2×D4—22no—
1146C2×D4—22no—
1147C2×D4—3321no—
1148C2×D4—3321no—
1149C2×D4—3321no—
1150C2×D4—3321no—
1151C2×D4—834no—
1152C2×D4—834no—
1153C2×D4C2×C4×D8314yes—
1154C22×C4—22no—
1155C22×C4—22no—
1156C22×C4—22no—
1157C22×C4—22no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—41no—
1163C22×C4—41no—
1164C22×C4—3321no—
1165C22×C4—3321no—
1166C22×C4—3321no—
1167C22×C4—3321no—
1168C22×C4—3321no—
1169C22×C4—3321no—
1170C22×C4—3321no—
1171C22×C4—3321no—
1172C22×C4—3321no—
1173C22×C4—3321no—
1174C22×C4—3321no—
1175C22×C4—3321no—
1176C22×C4—3321no—
1177C22×C4—3321no—
1178C22×C4—3321no—
1179C22×C4—3321no—
1180C22×C4—834no—
1181C22×C4—834no—
1182C22×C4—834no—
1183C22×C4—834no—
1184C22×C4—831no—
1185C22×C4—831no—
1186C22×C4—831no—
1187C22×C4—831no—
1188C22×C4—831no—
1189C22×C4—831no—
1190C22×C4—831no—
1191C22×C4—831no—
1192C22×C4—831no—
1193C22×C4—831no—
1194C22×C4—831no—
1195C22×C4—831no—
1196C22×C4—831no—
1197C22×C4—831no—
1198C22×C4—1662no—
1199C22×C4—1662no—
1200C22×C4—1662no—
1201C22×C4—1662no—
1202C22×C4—1662no—
1203C22×C4—1662no—
1204C22×C4—1662no—
1205C22×C4C2×C4×D8314yes—
1206C22×C4#1305058914yes—
1207C22×C4C23×D8311yescharacteristic
1208C22×C4C23×D8311yescharacteristic
1209C22×C4C23×D8311yescharacteristic
1210C22×C4C23×D8311yescharacteristic
1211C22×C4C23×D8311yescharacteristic
1212C22×C4C23×D8311yescharacteristic
1213C22×C4C23×D8311yescharacteristic
1214C22×C4C23×D8311yescharacteristic
1215C22×C4C23×D8311yescharacteristic
1216C22×C4C23×D8311yescharacteristic
1217C22×C4C23×D8311yescharacteristic
1218C22×C4C23×D8311yescharacteristic
1219C22×C4C23×D8311yescharacteristic
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—22no—
1223C4⋊C4—22no—
1224C4⋊C4—22no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C4⋊C4—3321no—
1228C4⋊C4—3321no—
1229C4⋊C4—3321no—
1230C4⋊C4—3321no—
1231C4⋊C4—3321no—
1232C4⋊C4—3321no—
1233C4⋊C4—834no—
1234C4⋊C4—834no—
1235C4⋊C4—834no—
1236C4⋊C4—834no—
1237C4⋊C4—834no—
1238C4⋊C4—834no—
1239C4⋊C4—1662no—
1240C4⋊C4—1662no—
1241C4⋊C4—1662no—
1242C4⋊C4—1662no—
1243C4⋊C4—1662no—
1244C4⋊C4C2×C4×D8314yes—
1245C4⋊C4C2×C4×D8314yes—
1246C22⋊C4—22no—
1247C22⋊C4—22no—
1248C22⋊C4—22no—
1249C22⋊C4—41no—
1250C22⋊C4—41no—
1251C22⋊C4—3321no—
1252C22⋊C4—3321no—
1253C22⋊C4—3321no—
1254C22⋊C4—3321no—
1255C22⋊C4—3321no—
1256C22⋊C4—3321no—
1257C22⋊C4—3321no—
1258C22⋊C4—3321no—
1259C22⋊C4—834no—
1260C22⋊C4—834no—
1261C22⋊C4—834no—
1262C22⋊C4—834no—
1263C22⋊C4—834no—
1264C22⋊C4—834no—
1265C22⋊C4—834no—
1266C22⋊C4—834no—
1267C22⋊C4—834no—
1268C22⋊C4—834no—
1269C22⋊C4—834no—
1270C22⋊C4—834no—
1271C22⋊C4—1662no—
1272C22⋊C4—1662no—
1273C22⋊C4—1662no—
1274C22⋊C4—1662no—
1275C22⋊C4—1662no—
1276C22⋊C4—1662no—
1277C22⋊C4—1662no—
1278C22⋊C4—1662no—
1279C22⋊C4—1662no—
1280C22⋊C4—1662no—
1281C22⋊C4C2×C4×D8314yes—
1282C22⋊C4C2×C4×D8314yes—
1283C22⋊C4C2×C4×D8314yes—
1284C42—22no—
1285C42—41no—
1286C42—41no—
1287C42—3321no—
1288C42—3321no—
1289C42—3321no—
1290C42—3321no—
1291C42—3321no—
1292C42—3321no—
1293C42—3321no—
1294C42—3321no—
1295C42—3321no—
1296C42—3321no—
1297C42—3321no—
1298C42—3321no—
1299C42—3321no—
1300C42—3321no—
1301C42—3321no—
1302C42—3321no—
1303C42—3321no—
1304C42—834no—
1305C42—834no—
1306C42—834no—
1307C42—1662no—
1308C42—1662no—
1309C42—1662no—
1310C42—1662no—
1311C42—1662no—
1312C42—1662no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—3324no—
1324C23—3324no—
1325C23—832no—
1326C23—832no—
1327C23—6642no—
1328C23—6642no—
1329C23—6642no—
1330C23—6642no—
1331C23—1661no—
1332C23—1661no—
1333C23—1661no—
1334C23—1661no—
1335C23—1661no—
1336C23—1661no—
1337C23—1661no—
1338C23—1661no—
1339C23—1661no—
1340C23—1661no—
1341C23—1661no—
1342C23—1661no—
1343C23—1668no—
1344C23C22×C4×D8312yes—
1345C23C22×C4×D8312yes—
1346C23#41×D8312yes—
1347C23C2×#1305058912yes—
1348C23C24×D8311yescharacteristic
1349Q8—3324no—
1350D4—28no—
1351D4—3324no—
1352D4—3324no—
1353C2×C4—28no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—44no—
1387C2×C4—44no—
1388C2×C4—82no—
1389C2×C4—3324no—
1390C2×C4—3324no—
1391C2×C4—3324no—
1392C2×C4—3324no—
1393C2×C4—3324no—
1394C2×C4—3324no—
1395C2×C4—832no—
1396C2×C4—832no—
1397C2×C4—832no—
1398C2×C4—832no—
1399C2×C4—832no—
1400C2×C4—832no—
1401C2×C4—832no—
1402C2×C4—832no—
1403C2×C4—832no—
1404C2×C4—6642no—
1405C2×C4—6642no—
1406C2×C4—6642no—
1407C2×C4—1661no—
1408C2×C4—1661no—
1409C2×C4—1661no—
1410C2×C4—1661no—
1411C2×C4—1661no—
1412C2×C4—1661no—
1413C2×C4—1661no—
1414C2×C4—1661no—
1415C2×C4—1661no—
1416C2×C4—1661no—
1417C2×C4—1661no—
1418C2×C4—1661no—
1419C2×C4—1661no—
1420C2×C4—1661no—
1421C2×C4—1661no—
1422C2×C4—1661no—
1423C2×C4—1661no—
1424C2×C4—1661no—
1425C2×C4—1661no—
1426C2×C4—1661no—
1427C2×C4—1661no—
1428C2×C4—1661no—
1429C2×C4—1661no—
1430C2×C4—1661no—
1431C2×C4—1661no—
1432C2×C4—1661no—
1433C2×C4—1661no—
1434C2×C4—1661no—
1435C2×C4—1661no—
1436C2×C4—1661no—
1437C2×C4—1661no—
1438C2×C4—1661no—
1439C2×C4—1661no—
1440C2×C4C22×C4×D8312yes—
1441C2×C4C22×C4×D8312yes—
1442C2×C4C22×C4×D8312yes—
1443C2×C4C22×C4×D8312yes—
1444C2×C4C22×C4×D8312yes—
1445C2×C4C2×#1305058912yes—
1446C2×C4C2×#1305058912yes—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—22no—
1451C22—22no—
1452C22—22no—
1453C22—22no—
1454C22—22no—
1455C22—22no—
1456C22—41no—
1457C22—41no—
1458C22—41no—
1459C22—41no—
1460C22—3321no—
1461C22—3321no—
1462C22—3321no—
1463C22—3321no—
1464C22—3321no—
1465C22—3321no—
1466C22—3321no—
1467C22—3321no—
1468C22—6648no—
1469C22—1662no—
1470C22—1662no—
1471C22—1662no—
1472C22—1662no—
1473C22—1662no—
1474C22—1662no—
1475C22C4×#1305058914yes—
1476C22C23×C4×D8311yescharacteristic
1477C22C2×#41×D8311yescharacteristic
1478C22C22×#1305058911yescharacteristic
1479C22H(5,𝔽2)×D8311yescharacteristic
1480C22#1912853611yescharacteristic
1481C22#1912853811yescharacteristic
1482C22#1912853811yescharacteristic
1483C4—22no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—22no—
1488C4—22no—
1489C4—22no—
1490C4—41no—
1491C4—41no—
1492C4—41no—
1493C4—41no—
1494C4—41no—
1495C4—41no—
1496C4—3321no—
1497C4—3321no—
1498C4—3321no—
1499C4—3321no—
1500C4—3321no—
1501C4—1662no—
1502C4—1662no—
1503C4—1662no—
1504C4—1662no—
1505C4—1662no—
1506C4—1662no—
1507C4—1662no—
1508C4—1662no—
1509C4—1662no—
1510C2—24no—
1511C2—42no—
1512C2—3322no—
1513C2—3322no—
1514C2C2×C4×#1305058911yescharacteristic
1515C2#2492066311yescharacteristic
1516C2#2492066911yescharacteristic
1517C2#2492130011yescharacteristic
1518C2#2492136211yescharacteristic
1519C2#2492139311yescharacteristic
1520C2#2492152111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2322C2
socle, cosocleC23×C83C25
prime radicalC2×#14581760C22
hypercenter#2322D83
hypocenterC83#34315
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2322

Complements

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

NH ≅ G/Ntype
2. #24910593C2semidirect
3. #24910591C2semidirect
4. #24910586C2semidirect
5. #24910586C2semidirect
6. #24910544C2semidirect
7. #24910537C2semidirect
8. #24910489C2semidirect
9. #24910459C2semidirect
11. #24910433C2semidirect
12. #24910401C2semidirect
13. #24910355C2semidirect
14. #24910325C2semidirect
15. #24910310C2semidirect
16. #24910305C2semidirect
17. #24910277C2semidirect
18. #24910248C2semidirect
19. #24910243C2semidirect
20. #24910215C2semidirect
22. #24910013C2semidirect
23. C4×#14581769C2semidirect
24. #24909982C2semidirect
25. #24909955C2semidirect
26. #24909899C2semidirect
27. C2×#19127591C2semidirect
28. #24909820C2semidirect
29. #24909815C2semidirect
30. C4×D4×Dic83C2semidirect
31. C83×#2322C2semidirect
32. #19128374C4semidirect
41. C2×C4×Dic166C22semidirect
56. C22×C4×Dic83C22semidirect
57. #19127606C22semidirect
58. #19127605C22semidirect
59. #19127605C22semidirect
63. #19127600C22semidirect
64. #19127598C22semidirect
65. #19127595C22semidirect
66. #19127594C22semidirect
67. #19127594C22semidirect
90. #19127589C22semidirect
91. #19127588C22semidirect
92. #19127587C22semidirect
93. #19127587C22semidirect
94. #19127586C22semidirect
95. #19127586C22semidirect
96. #19127586C22semidirect
97. #19127586C22semidirect
98. #19127584C22semidirect
99. #19127584C22semidirect
100. #19127584C22semidirect
101. #19127584C22semidirect
102. #19127583C22semidirect
103. #19127582C22semidirect
104. #19127582C22semidirect
111. #19127576C22semidirect
117. #19127568C22semidirect
118. #19127568C22semidirect
119. #19127565C22semidirect
121. #19127562C22semidirect
125. C4⋊C4×Dic83C22semidirect
126. C4⋊C4×Dic83C22semidirect
127. C4⋊C4×Dic83C22semidirect
128. C4⋊C4×Dic83C22semidirect
129. C4⋊C4×Dic83C22semidirect
130. C4⋊C4×Dic83C22semidirect
131. C4⋊C4×Dic83C22semidirect
132. C4⋊C4×Dic83C22semidirect
133. C4⋊C4×Dic83C22semidirect
134. C4⋊C4×Dic83C22semidirect
135. C4⋊C4×Dic83C22semidirect
136. C4⋊C4×Dic83C22semidirect
137. C4×Dic83⋊C4C22semidirect
138. C4×Dic83⋊C4C22semidirect
139. C4×C4⋊Dic83C22semidirect
140. C4×C4⋊Dic83C22semidirect
141. #19127552C22semidirect
142. #19127552C22semidirect
147. C22⋊C4×Dic83C22semidirect
148. C22⋊C4×Dic83C22semidirect
149. C22⋊C4×Dic83C22semidirect
150. C22⋊C4×Dic83C22semidirect
159. C4×C22⋊Dic83C22semidirect
168. #19127546C22semidirect
169. #19127546C22semidirect
172. C42×Dic83C22semidirect
176. #389×C83C22semidirect
177. #389×C83C22semidirect
178. #388×C83C22semidirect
179. #388×C83C22semidirect
180. #387×C83C22semidirect
181. #387×C83C22semidirect
184. #385×C83C22semidirect
185. #385×C83C22semidirect
201. #14581787C2×C4semidirect
202. #14581787C2×C4semidirect
203. #14581778C2×C4semidirect
204. #14581776C2×C4semidirect
205. #14581774C2×C4semidirect
206. #14581772C2×C4semidirect
207. #14581769C2×C4semidirect
211. D4×Dic83C2×C4semidirect
213. (C22⋊D83)⋊C4C2×C4semidirect
215. #14581751C2×C4semidirect
217. #14581750C2×C4semidirect
245. C2×(C2×D83)⋊C4C2×C4semidirect
269. C22⋊C4×D83C2×C4semidirect
337. #123×C83C2×C4semidirect
781. #2322D83semidirect
792. C83#34315semidirect
829. #389C2×D83semidirect
830. #389C2×D83semidirect
857. #388C2×D83semidirect
858. #388C2×D83semidirect
873. #387C2×D83semidirect
874. #387C2×D83semidirect
889. #385C2×D83semidirect
890. #385C2×D83semidirect
972. #123C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283742
#249105932
#249105912
#249105862
#249105442
#249105372
#249104892
#249104592
#249104432
#249104332
#249104012
#249103552
#249103252
#249103102
#249103052
#249102772
#249102482
#249102432
#249102152
#249101172
#249100132
C4×#145817692
#249099822
#249099552
#249098992
C2×#191275912
#249098202
#249098152
C4×D4×Dic832
C83×#23222
#3431583