Finite Group Databasebeta

← #32170254

Subgroups — #32170254

Order 18176.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596668C211yesmaximal, characteristic, complemented
2#22596661C211yesmaximal, characteristic, complemented
3#22596653C211yesmaximal, characteristic, complemented
4#22596637C211yesmaximal, characteristic, complemented
5#22594405C211yesmaximal, characteristic, complemented
6#22594343C211yesmaximal, characteristic, complemented
7#22594330C211yesmaximal, characteristic, complemented
8#22594328C211yesmaximal, characteristic, complemented
9#22593000C211yesmaximal, characteristic, complemented
10#22593000C211yesmaximal, characteristic, complemented
11#22592902C211yesmaximal, characteristic, complemented
12#22592900C211yesmaximal, characteristic, complemented
13#22592841C211yesmaximal, characteristic, complemented
14#22592668C211yesmaximal, characteristic, complemented
15#22592580C211yesmaximal, characteristic, complemented
16#22592460C211yesmaximal, characteristic, complemented
17#22592393C211yesmaximal, characteristic, complemented
18#22592279C211yesmaximal, characteristic, complemented
19#22592092C211yesmaximal, characteristic, complemented
20#22592001C211yesmaximal, characteristic, complemented
21#22591893C211yesmaximal, characteristic, complemented
22#22591730C211yesmaximal, characteristic, complemented
23#22591714C211yesmaximal, characteristic
24#22591663C211yesmaximal, characteristic, complemented
25#22591073C211yesmaximal, characteristic, complemented
26#22590998C211yesmaximal, characteristic, complemented
27#22590974C211yesmaximal, characteristic, complemented
28#22590938C211yesmaximal, characteristic, complemented
29C4×#14556097C211yesmaximal, characteristic, complemented
30C2×C4×C22⋊Dic71C211yesmaximal, characteristic, complemented
31C2×#386×C71C211yesmaximal, characteristic, complemented
32C2×#14556121C2211yescharacteristic, complemented
33C2×#14556114C2211yescharacteristic, complemented
34C2×#14556112C2211yescharacteristic, complemented
35C2×#14556109C2211yescharacteristic
36C2×#14556109C2211yescharacteristic
37C2×#14556107C2211yescharacteristic
38C2×#14556105C2211yescharacteristic, complemented
39C2×#14556100C2211yescharacteristic
40C2×#14556100C2211yescharacteristic
41C2×#14556097C2211yescharacteristic
42C2×#14556097C2211yescharacteristic
43C2×C4×C22⋊D71C2211yescharacteristic
44C2×C4×C22⋊D71C2211yescharacteristic, complemented
45C2×C4×C22⋊D71C2211yescharacteristic, complemented
46C22×C22⋊Dic71C2211yescharacteristic
47C22×C22⋊Dic71C2211yescharacteristic
48C22×C4×Dic71C2211yescharacteristic, complemented
49C22×C4×Dic71C2211yescharacteristic, complemented
50C71⋊#401C2211yescharacteristic, complemented
51#17985941C2211yescharacteristic, complemented
52#17985940C2211yescharacteristic, complemented
53#17985940C2211yescharacteristic, complemented
54#17985939C2211yescharacteristic, complemented
55#17985935C2211yescharacteristic, complemented
56#17985933C2211yescharacteristic, complemented
57#17985928C2211yescharacteristic, complemented
58#17985927C2211yescharacteristic, complemented
59#17985927C2211yescharacteristic, complemented
60#17985927C2211yescharacteristic, complemented
61#17985926C2211yescharacteristic, complemented
62#17985924C2211yescharacteristic, complemented
63#17985924C2211yescharacteristic, complemented
64#17985924C2211yescharacteristic, complemented
65#17985922C2211yescharacteristic, complemented
66#17985922C2211yescharacteristic, complemented
67#17985922C2211yescharacteristic, complemented
68#17985915C2211yescharacteristic, complemented
69#17985915C2211yescharacteristic, complemented
70#17985915C2211yescharacteristic, complemented
71#17985914C2211yescharacteristic, complemented
72#17985913C2211yescharacteristic
73#17985913C2211yescharacteristic
74#17985913C2211yescharacteristic
75#17985913C2211yescharacteristic
76#17985913C2211yescharacteristic
77#17985913C2211yescharacteristic
78#17985911C2211yescharacteristic, complemented
79#17985911C2211yescharacteristic, complemented
80#17985907C2211yescharacteristic
81#17985907C2211yescharacteristic
82#17985903C2211yescharacteristic, complemented
83#17985903C2211yescharacteristic, complemented
84#17985899C2211yescharacteristic, complemented
85#17985899C2211yescharacteristic, complemented
86#17985899C2211yescharacteristic, complemented
87#17985896C2211yescharacteristic, complemented
88#17985896C2211yescharacteristic, complemented
89#17985896C2211yescharacteristic, complemented
90#17985893C2211yescharacteristic, complemented
91#17985893C2211yescharacteristic, complemented
92#17985893C2211yescharacteristic, complemented
93#17985892C2211yescharacteristic, complemented
94#17985892C2211yescharacteristic, complemented
95#17985892C2211yescharacteristic, complemented
96#17985892C2211yescharacteristic, complemented
97#17985892C2211yescharacteristic, complemented
98#17985892C2211yescharacteristic, complemented
99#17985892C2211yescharacteristic, complemented
100#17985892C2211yescharacteristic, complemented
101#17985892C2211yescharacteristic, complemented
102#17985892C2211yescharacteristic, complemented
103#17985891C2211yescharacteristic, complemented
104#17985888C2211yescharacteristic, complemented
105#17985888C2211yescharacteristic, complemented
106#17985888C2211yescharacteristic, complemented
107#17985887C2211yescharacteristic, complemented
108#17985887C2211yescharacteristic, complemented
109#17985887C2211yescharacteristic, complemented
110#17985887C2211yescharacteristic, complemented
111#17985886C2211yescharacteristic, complemented
112#17985886C2211yescharacteristic, complemented
113#17985884C2211yescharacteristic, complemented
114#17985882C2211yescharacteristic, complemented
115#17985882C2211yescharacteristic, complemented
116#17985882C2211yescharacteristic, complemented
117#17985881C2211yescharacteristic, complemented
118#17985881C2211yescharacteristic, complemented
119#17985881C2211yescharacteristic, complemented
120#17985879C2211yescharacteristic
121#17985879C2211yescharacteristic
122#17985879C2211yescharacteristic
123#17985879C2211yescharacteristic
124#17985878C2211yescharacteristic
125#17985878C2211yescharacteristic
126#17985878C2211yescharacteristic
127#17985878C2211yescharacteristic
128#17985878C2211yescharacteristic, complemented
129#17985878C2211yescharacteristic, complemented
130#17985876C2211yescharacteristic, complemented
131#17985875C2211yescharacteristic, complemented
132#17985875C2211yescharacteristic, complemented
133#17985874C2211yescharacteristic, complemented
134#17985874C2211yescharacteristic, complemented
135#17985872C2211yescharacteristic
136#17985872C2211yescharacteristic
137#17985872C2211yescharacteristic
138#17985872C2211yescharacteristic
139#17985872C2211yescharacteristic
140#17985872C2211yescharacteristic
141#17985872C2211yescharacteristic, complemented
142#17985872C2211yescharacteristic, complemented
143#17985871C2211yescharacteristic, complemented
144#17985866C2211yescharacteristic, complemented
145#17985866C2211yescharacteristic, complemented
146#17985863C2211yescharacteristic, complemented
147#17985863C2211yescharacteristic, complemented
148#17985861C2211yescharacteristic, complemented
149#17985860C2211yescharacteristic, complemented
150#17985859C2211yescharacteristic
151#17985859C2211yescharacteristic
152#17985859C2211yescharacteristic
153#17985858C2211yescharacteristic, complemented
154#17985857C2211yescharacteristic, complemented
155#17985855C2211yescharacteristic
156#17985855C2211yescharacteristic
157#17985855C2211yescharacteristic
158#17985855C2211yescharacteristic
159C4×C22⋊Dic71C2211yescharacteristic
160C4×C22⋊Dic71C2211yescharacteristic
161C4×C22⋊Dic71C2211yescharacteristic
162C4×C22⋊Dic71C2211yescharacteristic
163C4×C22⋊Dic71C2211yescharacteristic
164C4×C22⋊Dic71C2211yescharacteristic, complemented
165C4×C22⋊Dic71C2211yescharacteristic, complemented
166C4×C22⋊Dic71C2211yescharacteristic, complemented
167C4×C22⋊Dic71C2211yescharacteristic, complemented
168C4×C22⋊Dic71C2211yescharacteristic, complemented
169C4×C22⋊Dic71C2211yescharacteristic, complemented
170C2×C71⋊#95C2211yescharacteristic, complemented
171C2×C71⋊#95C2211yescharacteristic, complemented
172C23×D4×C71C2211yescharacteristic
173C24×C4×C71C2211yescharacteristic
174C22×C22⋊C4×C71C2211yescharacteristic
175C22×C22⋊C4×C71C2211yescharacteristic
176C22×C22⋊C4×C71C2211yescharacteristic
177#386×C71C2211yescharacteristic
178#386×C71C2211yescharacteristic
179#386×C71C2211yescharacteristic
180#386×C71C2211yescharacteristic
181#386×C71C2211yescharacteristic
182#386×C71C2211yescharacteristic
183#386×C71C2211yescharacteristic
184#386×C71C2211yescharacteristic
185C2×#95×C71C2211yescharacteristic
186C2×#95×C71C2211yescharacteristic
187C22×Dic142C2311yescharacteristic
188C22×C22⋊D71C2311yescharacteristic
189C22×C22⋊D71C2311yescharacteristic
190C22×C22⋊D71C2311yescharacteristic
191C22×C22⋊D71C2311yescharacteristic
192C22×C22⋊D71C2311yescharacteristic
193C23×Dic71C2311yescharacteristic
194C23×Dic71C2311yescharacteristic
195C23×Dic71C2311yescharacteristic
196C23×Dic71C2311yescharacteristic
197C22×C4×D71C2311yescharacteristic
198#14556121—42no—
199#14556114—42no—
200#14556112—42no—
201#14556109—42no—
202#14556109—42no—
203#14556107—24no—
204#14556105—42no—
205#14556100—42no—
206#14556100—42no—
207#14556097—24no—
208#14556097—24no—
209C4×C22⋊D71—24no—
210C4×C22⋊D71—42no—
211C4×C22⋊D71—42no—
212C2×C4⋊Dic71C2311yescharacteristic
213C2×C4⋊Dic71C2311yescharacteristic
214C2×C4⋊Dic71C2311yescharacteristic
215C2×C4⋊Dic71C2311yescharacteristic
216C2×C4⋊Dic71C2311yescharacteristic
217C2×C4⋊Dic71C2311yescharacteristic
218C2×C4⋊Dic71C2311yescharacteristic
219C2×Dic71⋊C4C2311yescharacteristic
220C2×Dic71⋊C4C2311yescharacteristic
221C2×Dic71⋊C4C2311yescharacteristic
222C2×Dic71⋊C4C2311yescharacteristic
223C2×Dic71⋊C4C2311yescharacteristic
224C2×Dic71⋊C4C2311yescharacteristic
225C2×Dic71⋊C4C2311yescharacteristic
226C2×Dic71⋊C4C2311yescharacteristic
227C2×Dic71⋊C4C2311yescharacteristic
228C2×Dic71⋊C4C2311yescharacteristic
229C2×Dic71⋊C4C2311yescharacteristic
230C2×Dic71⋊C4C2311yescharacteristic
231C2×Dic71⋊C4C2311yescharacteristic
232C2×Dic71⋊C4C2311yescharacteristic
233C2×Dic71⋊C4C2311yescharacteristic
234C2×C22⋊Dic71—24no—
235C2×C22⋊Dic71—24no—
236C2×C22⋊Dic71C2311yescharacteristic
237C2×C22⋊Dic71C2311yescharacteristic
238C2×C22⋊Dic71C2311yescharacteristic
239C2×C22⋊Dic71C2311yescharacteristic
240C2×C22⋊Dic71C2311yescharacteristic
241C2×C22⋊Dic71C2311yescharacteristic
242C2×C22⋊Dic71C2311yescharacteristic
243C2×C22⋊Dic71C2311yescharacteristic
244C2×C22⋊Dic71C2311yescharacteristic
245C2×C22⋊Dic71C2311yescharacteristic
246C2×C22⋊Dic71C2311yescharacteristic
247C2×C22⋊Dic71C2311yescharacteristic
248C2×C22⋊Dic71C2311yescharacteristic
249C2×C22⋊Dic71C2311yescharacteristic
250C2×C22⋊Dic71C2311yescharacteristic
251C2×C22⋊Dic71C2311yescharacteristic
252C2×C22⋊Dic71C2311yescharacteristic
253C2×C22⋊Dic71C2311yescharacteristic
254C2×C22⋊Dic71C2311yescharacteristic
255C2×C22⋊Dic71C2311yescharacteristic
256C2×C22⋊Dic71C2311yescharacteristic
257C2×C22⋊Dic71C2311yescharacteristic
258C2×C22⋊Dic71C2311yescharacteristic
259C2×C22⋊Dic71C2311yescharacteristic
260C2×C22⋊Dic71C2311yescharacteristic
261C2×C22⋊Dic71C2311yescharacteristic
262C2×C22⋊Dic71C2311yescharacteristic
263C2×C22⋊Dic71C2311yescharacteristic
264C2×C22⋊Dic71C2311yescharacteristic
265C2×C22⋊Dic71C2311yescharacteristic
266C2×C22⋊Dic71C2311yescharacteristic
267C2×(C2×D71)⋊C4C2311yescharacteristic
268C2×(C2×D71)⋊C4C2311yescharacteristic
269C2×(C2×D71)⋊C4C2311yescharacteristic
270C2×(C2×D71)⋊C4C2311yescharacteristic
271C2×(C2×D71)⋊C4C2311yescharacteristic
272C2×(C2×D71)⋊C4C2311yescharacteristic
273C2×(C2×D71)⋊C4C2311yescharacteristic
274C2×(C2×D71)⋊C4C2311yescharacteristic
275C2×(C2×D71)⋊C4C2311yescharacteristic
276C2×C4×Dic71—42no—
277C2×C4×Dic71—42no—
278C2×C4×Dic71C2311yescharacteristic
279C2×C4×Dic71C2311yescharacteristic
280C2×C4×Dic71C2311yescharacteristic
281C2×C4×Dic71C2311yescharacteristic
282C2×C4×Dic71C2311yescharacteristic
283C2×C4×Dic71C2311yescharacteristic
284C2×C4×Dic71C2311yescharacteristic
285C2×C4×Dic71C2311yescharacteristic
286C2×C4×Dic71C2311yescharacteristic
287C2×C4×Dic71C2311yescharacteristic
288C2×C4×Dic71C2311yescharacteristic
289C71⋊#95C2311yescharacteristic
290C71⋊#95C2311yescharacteristic
291C71⋊#95C2311yescharacteristic
292C71⋊#95C2311yescharacteristic
293C71⋊#95C2311yescharacteristic
294C71⋊#95C2311yescharacteristic
295C71⋊#95C2311yescharacteristic
296C71⋊#95C2311yescharacteristic
297C71⋊#95C2311yescharacteristic
298C71⋊#95C2311yescharacteristic
299C71⋊#95C2311yescharacteristic
300C71⋊#95C2311yescharacteristic
301C71⋊#95C2311yescharacteristic
302C71⋊#95C2311yescharacteristic
303C71⋊#95C2311yescharacteristic
304C71⋊#95C2311yescharacteristic
305C71⋊#95C2311yescharacteristic
306C71⋊#95C2311yescharacteristic
307C71⋊#95C2311yescharacteristic
308C71⋊#95C2311yescharacteristic
309C71⋊#95C2311yescharacteristic
310C71⋊#95C2311yescharacteristic
311C71⋊#95C2311yescharacteristic
312C71⋊#95C2311yescharacteristic
313C71⋊#95C2311yescharacteristic
314C71⋊#95C2311yescharacteristic
315C71⋊#95C2311yescharacteristic
316C71⋊#95C2311yescharacteristic
317C71⋊#95C2311yescharacteristic
318C71⋊#95C2311yescharacteristic
319C71⋊#95C2311yescharacteristic
320C71⋊#95C2311yescharacteristic
321C71⋊#95C2311yescharacteristic
322C71⋊#95C2311yescharacteristic
323C71⋊#95C2311yescharacteristic
324C71⋊#95C2311yescharacteristic
325C25×C71C2311yescharacteristic
326C25×C71C2311yescharacteristic
327C22×D4×C71—24no—
328C22×D4×C71—42no—
329C22×D4×C71—42no—
330C22×D4×C71C2311yescharacteristic
331C22×D4×C71C2311yescharacteristic
332C22×D4×C71C2311yescharacteristic
333C22×D4×C71C2311yescharacteristic
334C23×C4×C71—24no—
335C23×C4×C71—42no—
336C23×C4×C71—42no—
337C23×C4×C71C2311yescharacteristic
338C23×C4×C71C2311yescharacteristic
339C23×C4×C71C2311yescharacteristic
340C23×C4×C71C2311yescharacteristic
341C23×C4×C71C2311yescharacteristic
342C23×C4×C71C2311yescharacteristic
343C23×C4×C71C2311yescharacteristic
344C23×C4×C71C2311yescharacteristic
345C23×C4×C71C2311yescharacteristic
346C2×C22⋊C4×C71—24no—
347C2×C22⋊C4×C71—42no—
348C2×C22⋊C4×C71—42no—
349C2×C22⋊C4×C71C2311yescharacteristic
350C2×C22⋊C4×C71C2311yescharacteristic
351C2×C22⋊C4×C71C2311yescharacteristic
352C2×C22⋊C4×C71C2311yescharacteristic
353C2×C22⋊C4×C71C2311yescharacteristic
354C2×C22⋊C4×C71C2311yescharacteristic
355C2×C22⋊C4×C71C2311yescharacteristic
356C2×C22⋊C4×C71C2311yescharacteristic
357C2×C22⋊C4×C71C2311yescharacteristic
358C2×C22⋊C4×C71C2311yescharacteristic
359C2×C22⋊C4×C71C2311yescharacteristic
360C2×C22⋊C4×C71C2311yescharacteristic
361#95×C71C2311yescharacteristic
362#95×C71C2311yescharacteristic
363#95×C71C2311yescharacteristic
364#95×C71C2311yescharacteristic
365#95×C71C2311yescharacteristic
366#95×C71C2311yescharacteristic
367#95×C71C2311yescharacteristic
368#95×C71C2311yescharacteristic
369C23×D71C2411yescharacteristic
370C2×Dic142—22no—
371C2×Dic142—41no—
372C2×Dic142—41no—
373C2×C22⋊D71—22no—
374C2×C22⋊D71—22no—
375C2×C22⋊D71—22no—
376C2×C22⋊D71—22no—
377C2×C22⋊D71—22no—
378C2×C22⋊D71—22no—
379C2×C22⋊D71—22no—
380C2×C22⋊D71—22no—
381C2×C22⋊D71—22no—
382C2×C22⋊D71—41no—
383C2×C22⋊D71—41no—
384C2×C22⋊D71—41no—
385C2×C22⋊D71—41no—
386C2×C22⋊D71—41no—
387C2×C22⋊D71—41no—
388C22×Dic71—22no—
389C22×Dic71—22no—
390C22×Dic71—22no—
391C22×Dic71—22no—
392C22×Dic71—22no—
393C22×Dic71—22no—
394C22×Dic71—22no—
395C22×Dic71—22no—
396C22×Dic71—41no—
397C22×Dic71—41no—
398C22×Dic71—41no—
399C22×Dic71—41no—
400C22×Dic71C2411yescharacteristic
401C22×Dic71C2411yescharacteristic
402C22×Dic71C2411yescharacteristic
403C22×Dic71C2411yescharacteristic
404C22×Dic71C2411yescharacteristic
405C22×Dic71C2411yescharacteristic
406C22×Dic71C2411yescharacteristic
407C22×Dic71C2411yescharacteristic
408C22×Dic71C2411yescharacteristic
409C22×Dic71C2411yescharacteristic
410C22×Dic71C2411yescharacteristic
411C22×Dic71C2411yescharacteristic
412C22×Dic71C2411yescharacteristic
413C22×Dic71C2411yescharacteristic
414C22×Dic71C2411yescharacteristic
415C2×C4×D71—22no—
416C2×C4×D71—41no—
417C2×C4×D71—41no—
418C4⋊Dic71—22no—
419C4⋊Dic71—41no—
420C4⋊Dic71—41no—
421C4⋊Dic71—41no—
422C4⋊Dic71—41no—
423C4⋊Dic71—41no—
424C4⋊Dic71—41no—
425Dic71⋊C4—22no—
426Dic71⋊C4—22no—
427Dic71⋊C4—22no—
428Dic71⋊C4—22no—
429Dic71⋊C4—41no—
430Dic71⋊C4—41no—
431Dic71⋊C4—41no—
432Dic71⋊C4—41no—
433Dic71⋊C4—41no—
434Dic71⋊C4—41no—
435Dic71⋊C4—41no—
436Dic71⋊C4—41no—
437Dic71⋊C4—41no—
438Dic71⋊C4—41no—
439Dic71⋊C4—41no—
440C22⋊Dic71—22no—
441C22⋊Dic71—22no—
442C22⋊Dic71—22no—
443C22⋊Dic71—22no—
444C22⋊Dic71—22no—
445C22⋊Dic71—22no—
446C22⋊Dic71—22no—
447C22⋊Dic71—22no—
448C22⋊Dic71—22no—
449C22⋊Dic71—22no—
450C22⋊Dic71—22no—
451C22⋊Dic71—22no—
452C22⋊Dic71—22no—
453C22⋊Dic71—22no—
454C22⋊Dic71—22no—
455C22⋊Dic71—22no—
456C22⋊Dic71—41no—
457C22⋊Dic71—41no—
458C22⋊Dic71—41no—
459C22⋊Dic71—41no—
460C22⋊Dic71—41no—
461C22⋊Dic71—41no—
462C22⋊Dic71—41no—
463C22⋊Dic71—41no—
464C22⋊Dic71—41no—
465C22⋊Dic71—41no—
466C22⋊Dic71—41no—
467C22⋊Dic71—41no—
468C22⋊Dic71—41no—
469C22⋊Dic71—41no—
470C22⋊Dic71#4114yes—
471(C2×D71)⋊C4—22no—
472(C2×D71)⋊C4—22no—
473(C2×D71)⋊C4—41no—
474(C2×D71)⋊C4—41no—
475(C2×D71)⋊C4—41no—
476(C2×D71)⋊C4—41no—
477(C2×D71)⋊C4—41no—
478(C2×D71)⋊C4—41no—
479(C2×D71)⋊C4—41no—
480C4×Dic71—22no—
481C4×Dic71—22no—
482C4×Dic71—22no—
483C4×Dic71—41no—
484C4×Dic71—41no—
485C4×Dic71—41no—
486C4×Dic71—41no—
487C4×Dic71—41no—
488C4×Dic71—41no—
489C4×Dic71—41no—
490C4×Dic71—41no—
491C24×C71—22no—
492C24×C71—22no—
493C24×C71—22no—
494C24×C71—22no—
495C24×C71—22no—
496C24×C71—22no—
497C24×C71—22no—
498C24×C71—41no—
499C24×C71—41no—
500C24×C71—41no—
501C24×C71—41no—
502C24×C71—41no—
503C24×C71—41no—
504C24×C71#4114yes—
505C24×C71C2411yescharacteristic
506C24×C71C2411yescharacteristic
507C24×C71C2411yescharacteristic
508C24×C71C2411yescharacteristic
509C24×C71C2411yescharacteristic
510C2×D4×C71—22no—
511C2×D4×C71—22no—
512C2×D4×C71—22no—
513C2×D4×C71—22no—
514C2×D4×C71—22no—
515C2×D4×C71—22no—
516C2×D4×C71—22no—
517C2×D4×C71—22no—
518C2×D4×C71—41no—
519C2×D4×C71—41no—
520C2×D4×C71—41no—
521C2×D4×C71—41no—
522C2×D4×C71—416no—
523C22×C4×C71—22no—
524C22×C4×C71—22no—
525C22×C4×C71—22no—
526C22×C4×C71—22no—
527C22×C4×C71—22no—
528C22×C4×C71—22no—
529C22×C4×C71—22no—
530C22×C4×C71—22no—
531C22×C4×C71—22no—
532C22×C4×C71—22no—
533C22×C4×C71—22no—
534C22×C4×C71—22no—
535C22×C4×C71—22no—
536C22×C4×C71—41no—
537C22×C4×C71—41no—
538C22×C4×C71—41no—
539C22×C4×C71—41no—
540C22×C4×C71—41no—
541C22×C4×C71—41no—
542C22×C4×C71—41no—
543C22×C4×C71—41no—
544C22×C4×C71—41no—
545C22×C4×C71—41no—
546C22×C4×C71—41no—
547C22×C4×C71—41no—
548C22×C4×C71—41no—
549C22×C4×C71—416no—
550C22×C4×C71#4114yes—
551C22×C4×C71C2411yescharacteristic
552C22×C4×C71C2411yescharacteristic
553C22×C4×C71C2411yescharacteristic
554C22×C4×C71C2411yescharacteristic
555C22×C4×C71C2411yescharacteristic
556C22×C4×C71C2411yescharacteristic
557C22×C4×C71C2411yescharacteristic
558C22×C4×C71C2411yescharacteristic
559C22×C4×C71C2411yescharacteristic
560C22×C4×C71C2411yescharacteristic
561C22⋊C4×C71—22no—
562C22⋊C4×C71—22no—
563C22⋊C4×C71—22no—
564C22⋊C4×C71—22no—
565C22⋊C4×C71—22no—
566C22⋊C4×C71—22no—
567C22⋊C4×C71—22no—
568C22⋊C4×C71—22no—
569C22⋊C4×C71—41no—
570C22⋊C4×C71—41no—
571C22⋊C4×C71—41no—
572C22⋊C4×C71—41no—
573C23×C71—21no—
574C23×C71—21no—
575C23×C71—21no—
576C23×C71—21no—
577C23×C71—21no—
578C23×C71—21no—
579C23×C71—21no—
580C23×C71—21no—
581C23×C71—28no—
582C23×C71—28no—
583C23×C71—21no—
584C23×C71—21no—
585C23×C71—21no—
586C23×C71—21no—
587C23×C71—21no—
588C23×C71—21no—
589C23×C71—21no—
590C23×C71—21no—
591C23×C71—21no—
592C23×C71—21no—
593C23×C71—21no—
594C23×C71—21no—
595C23×C71—21no—
596C23×C71—21no—
597C23×C71—21no—
598C23×C71—21no—
599C23×C71—21no—
600C23×C71—21no—
601C23×C71—21no—
602C23×C71—21no—
603C23×C71—44no—
604C23×C71—44no—
605C23×C71—44no—
606C23×C71—44no—
607C23×C71—44no—
608C23×C71—44no—
609C23×C71—44no—
610C23×C71—44no—
611C23×C71—82no—
612C23×C71—82no—
613C23×C71—82no—
614C23×C71—82no—
615C23×C71C2×#4112yes—
616C23×C71C2×#4112yes—
617C23×C71C2×#4112yes—
618C23×C71C2×#4112yes—
619C23×C71C2×#4112yes—
620C23×C71H(5,𝔽2)12yes—
621C23×C71H(5,𝔽2)12yes—
622C23×C71C2511yescharacteristic
623C22×D71—21no—
624C22×D71—21no—
625C22×D71—21no—
626C22×D71—21no—
627C22×D71—21no—
628C22×D71—21no—
629C22×D71—21no—
630D4×C71—44no—
631D4×C71—44no—
632D4×C71—44no—
633D4×C71—44no—
634C2×C4×C71—28no—
635C2×C4×C71—21no—
636C2×C4×C71—21no—
637C2×C4×C71—21no—
638C2×C4×C71—21no—
639C2×C4×C71—21no—
640C2×C4×C71—21no—
641C2×C4×C71—21no—
642C2×C4×C71—21no—
643C2×C4×C71—21no—
644C2×C4×C71—21no—
645C2×C4×C71—21no—
646C2×C4×C71—21no—
647C2×C4×C71—21no—
648C2×C4×C71—21no—
649C2×C4×C71—21no—
650C2×C4×C71—21no—
651C2×C4×C71—21no—
652C2×C4×C71—21no—
653C2×C4×C71—21no—
654C2×C4×C71—21no—
655C2×C4×C71—21no—
656C2×C4×C71—21no—
657C2×C4×C71—21no—
658C2×C4×C71—21no—
659C2×C4×C71—21no—
660C2×C4×C71—21no—
661C2×C4×C71—21no—
662C2×C4×C71—44no—
663C2×C4×C71—44no—
664C2×C4×C71—44no—
665C2×C4×C71—44no—
666C2×C4×C71—44no—
667C2×C4×C71—44no—
668C2×C4×C71—82no—
669C2×C4×C71—82no—
670C2×C4×C71C2×#4112yes—
671C2×C4×C71C2×#4112yes—
672C2×C4×C71H(5,𝔽2)12yes—
673C22⋊D71—44no—
674C22⋊D71—44no—
675C22⋊D71—44no—
676C22⋊D71—82no—
677C22⋊D71—82no—
678C2×Dic71—21no—
679C2×Dic71—21no—
680C2×Dic71—21no—
681C2×Dic71—21no—
682C2×Dic71—21no—
683C2×Dic71—21no—
684C2×Dic71—21no—
685C2×Dic71—21no—
686C2×Dic71—21no—
687C2×Dic71—21no—
688C2×Dic71—21no—
689C2×Dic71—21no—
690C2×Dic71—21no—
691C2×Dic71—21no—
692C2×Dic71—21no—
693C2×Dic71—21no—
694C2×Dic71—21no—
695C2×Dic71—21no—
696C2×Dic71—21no—
697C2×Dic71—21no—
698C2×Dic71—21no—
699C2×Dic71—21no—
700C2×Dic71—21no—
701C2×Dic71—21no—
702C2×Dic71—21no—
703C2×Dic71—21no—
704C2×Dic71—21no—
705C2×Dic71—21no—
706C2×Dic71—21no—
707C2×Dic71—21no—
708C2×Dic71—21no—
709C2×Dic71—21no—
710C2×Dic71—21no—
711C2×Dic71—21no—
712C2×Dic71—21no—
713C2×Dic71—21no—
714C2×Dic71—21no—
715C2×Dic71—21no—
716C2×Dic71—21no—
717C2×Dic71—21no—
718C2×Dic71—21no—
719C2×Dic71—21no—
720C2×Dic71—21no—
721C2×Dic71—44no—
722C2×Dic71—44no—
723C2×Dic71—44no—
724C2×Dic71—44no—
725C2×Dic71C2×#4112yes—
726C2×Dic71C2×#4112yes—
727C4×D71—82no—
728Dic142—82no—
729C22×C71—22no—
730C22×C71—22no—
731C22×C71—22no—
732C22×C71—22no—
733C22×C71—22no—
734C22×C71—22no—
735C22×C71—22no—
736C22×C71—22no—
737C22×C71—22no—
738C22×C71—22no—
739C22×C71—22no—
740C22×C71—22no—
741C22×C71—22no—
742C22×C71—22no—
743C22×C71—22no—
744C22×C71—416no—
745C22×C71—41no—
746C22×C71—41no—
747C22×C71—41no—
748C22×C71—41no—
749C22×C71—41no—
750C22×C71—41no—
751C22×C71—41no—
752C22×C71—41no—
753C22×C71—41no—
754C22×C71—41no—
755C22×C71—41no—
756C22×C71—41no—
757C22×C71—41no—
758C22×C71—41no—
759C22×C71—41no—
760C22×C71—41no—
761C22×C71—41no—
762C22×C71—41no—
763C22×C71—88no—
764C22×C71#52914yes—
765C22×C71#53814yes—
766C22×C71C22×#4111yescharacteristic
767C22×C71C22×#4111yescharacteristic
768C22×C71C22×#4111yescharacteristic
769C22×C71C2×H(5,𝔽2)11yescharacteristic
770C22×C71C2×H(5,𝔽2)11yescharacteristic
771C22×C71C2×H(5,𝔽2)11yescharacteristic
772C22×C71#58511yescharacteristic
773C2×D71—41no—
774C2×D71—41no—
775C2×D71—41no—
776C2×D71—41no—
777C2×D71—41no—
778C2×D71—41no—
779C2×D71—41no—
780C4×C71—22no—
781C4×C71—22no—
782C4×C71—22no—
783C4×C71—41no—
784C4×C71—41no—
785C4×C71—41no—
786C4×C71—41no—
787C4×C71—41no—
788C4×C71—41no—
789C4×C71—41no—
790Dic71—22no—
791Dic71—22no—
792Dic71—41no—
793Dic71—41no—
794Dic71—41no—
795Dic71—41no—
796Dic71—41no—
797Dic71—41no—
798Dic71—41no—
799Dic71—41no—
800Dic71—41no—
801Dic71—41no—
802Dic71—41no—
803Dic71—41no—
804Dic71—41no—
805#34998—711nomaximal, Sylow
806C2×C71—24no—
807C2×C71—24no—
808C2×C71—42no—
809C2×C71—81no—
810C2×C71—81no—
811C2×C71C2×#52911yescharacteristic
812C2×C71C2×#53811yescharacteristic
813C2×C71#345911yescharacteristic
814C2×C71#349011yescharacteristic
815C2×C71#349411yescharacteristic
816C2×C71#351311yescharacteristic
817C2×C71#351911yescharacteristic
818D71—81no—
819#2854—711no—
820#2853—711no—
821#2852—711no—
822#2850—711no—
823#2653—711no—
824#2649—711no—
825#2648—711no—
826#2648—711no—
827#2518—711no—
828#2518—711no—
829#2510—711no—
830#2510—711no—
831#2505—711no—
832#2488—711no—
833#2480—711no—
834#2472—711no—
835#2467—711no—
836#2459—711no—
837#2444—711no—
838#2437—711no—
839#2425—711no—
840#2412—711no—
841#2410—711no—
842#2405—711no—
843#2329—711no—
844#2321—711no—
845#2318—711no—
846#2312—711no—
847C4×#120—711no—
848C2×#386D7111yescharacteristic, complemented
849C2×C4×C22⋊C4—711no—
850C71#3499811yescharacteristic, complemented, Sylow
851C23×D4C2×D7111yescharacteristic
852C24×C4C2×D7111yescharacteristic
853C2×#126—711no—
854C2×#124—711no—
855C2×#123—711no—
856C2×#123—711no—
857C2×#123—711no—
858C2×C22⋊Q8—711no—
859C2×C22⋊Q8—711no—
860C2×#121—711no—
861C2×#121—711no—
862C2×#120—711no—
863C2×#120—711no—
864C2×C4×D4—711no—
865C2×C4×D4—711no—
866C2×C4×D4—711no—
867C22×C22⋊C4—711no—
868C22×C22⋊C4—711no—
869C22×C22⋊C4C2×D7111yescharacteristic
870C22×C22⋊C4C2×D7111yescharacteristic
871C22×C22⋊C4C2×D7111yescharacteristic
872C22×C42—711no—
873C22×C42—711no—
874#401—711no—
875#400—711no—
876#400—711no—
877#400—711no—
878#400—711no—
879#399—711no—
880#398—711no—
881#397—711no—
882#397—711no—
883#397—711no—
884#397—711no—
885#397—711no—
886#397—711no—
887#397—711no—
888#397—711no—
889#396—711no—
890#396—711no—
891#396—711no—
892#394—711no—
893#394—711no—
894#394—711no—
895#394—711no—
896#394—711no—
897#394—711no—
898#394—711no—
899#394—711no—
900#394—711no—
901#394—711no—
902#393—711no—
903#393—711no—
904#392—711no—
905#392—711no—
906#391—711no—
907#391—711no—
908#390—711no—
909#390—711no—
910#390—711no—
911#389—711no—
912#389—711no—
913#389—711no—
914#388—711no—
915#388—711no—
916#388—711no—
917#388—711no—
918#388—711no—
919#388—711no—
920#388—711no—
921#388—711no—
922#388—711no—
923#388—711no—
924#388—711no—
925#388—711no—
926#388—711no—
927#388—711no—
928#388—711no—
929#388—711no—
930#388—711no—
931#388—711no—
932#388—711no—
933#388—711no—
934#388—711no—
935#387—711no—
936#387—711no—
937#387—711no—
938#387—711no—
939#387—711no—
940#387—711no—
941#387—711no—
942#387—711no—
943#387—711no—
944#386—711no—
945#386—711no—
946#386—711no—
947#386—711no—
948#386—711no—
949#386—711no—
950#386—711no—
951#386—711no—
952#386—711no—
953#386—711no—
954#386—711no—
955#386—711no—
956#386—711no—
957#386C2×D7111yescharacteristic
958#386C2×D7111yescharacteristic
959#386C2×D7111yescharacteristic
960#386C2×D7111yescharacteristic
961#386C2×D7111yescharacteristic
962#386C2×D7111yescharacteristic
963#386C2×D7111yescharacteristic
964#386C2×D7111yescharacteristic
965#385—711no—
966#385—711no—
967#385—711no—
968#385—711no—
969#385—711no—
970#385—711no—
971#385—711no—
972#385—711no—
973#385—711no—
974#385—711no—
975#385—711no—
976#383—711no—
977#383—711no—
978#382—711no—
979#382—711no—
980#381—711no—
981#381—711no—
982#380—711no—
983#380—711no—
984#380—711no—
985#380—711no—
986#380—711no—
987#379—711no—
988#379—711no—
989#379—711no—
990#379—711no—
991C4×C22⋊C4—711no—
992C4×C22⋊C4—711no—
993C4×C22⋊C4—711no—
994C4×C22⋊C4—711no—
995C4×C22⋊C4—711no—
996C4×C22⋊C4—711no—
997C4×C22⋊C4—711no—
998C4×C22⋊C4—711no—
999C4×C22⋊C4—711no—
1000C4×C22⋊C4—711no—
1001C4×C22⋊C4—711no—
1002C2×#95—711no—
1003C2×#95—711no—
1004C2×#95C2×D7111yescharacteristic
1005C2×#95C2×D7111yescharacteristic
1006C25C22×D7111yescharacteristic
1007C25C22×D7111yescharacteristic
1008C22×Q8—711no—
1009C22×D4—24no—
1010C22×D4—42no—
1011C22×D4—42no—
1012C22×D4—711no—
1013C22×D4—711no—
1014C22×D4—711no—
1015C22×D4—711no—
1016C22×D4—711no—
1017C22×D4C22×D7111yescharacteristic
1018C22×D4C22×D7111yescharacteristic
1019C22×D4C22×D7111yescharacteristic
1020C22×D4C22×D7111yescharacteristic
1021C23×C4—24no—
1022C23×C4—42no—
1023C23×C4—42no—
1024C23×C4—711no—
1025C23×C4—711no—
1026C23×C4—711no—
1027C23×C4—711no—
1028C23×C4—711no—
1029C23×C4C22×D7111yescharacteristic
1030C23×C4C22×D7111yescharacteristic
1031C23×C4C22×D7111yescharacteristic
1032C23×C4C22×D7111yescharacteristic
1033C23×C4C22×D7111yescharacteristic
1034C23×C4C22×D7111yescharacteristic
1035C23×C4C22×D7111yescharacteristic
1036C23×C4C22×D7111yescharacteristic
1037C23×C4C22×D7111yescharacteristic
1038#126—2842no—
1039#124—2842no—
1040#123—2842no—
1041#123—2842no—
1042#123—2842no—
1043C22⋊Q8—2842no—
1044C22⋊Q8—1424no—
1045#121—2842no—
1046#121—2842no—
1047#120—1424no—
1048#120—1424no—
1049C4×D4—2842no—
1050C4×D4—2842no—
1051C4×D4—1424no—
1052C2×C4⋊C4—711no—
1053C2×C4⋊C4—711no—
1054C2×C4⋊C4—711no—
1055C2×C4⋊C4—711no—
1056C2×C4⋊C4—711no—
1057C2×C4⋊C4—711no—
1058C2×C4⋊C4—711no—
1059C2×C4⋊C4—711no—
1060C2×C4⋊C4—711no—
1061C2×C4⋊C4—711no—
1062C2×C4⋊C4—711no—
1063C2×C4⋊C4—711no—
1064C2×C4⋊C4—711no—
1065C2×C4⋊C4—711no—
1066C2×C4⋊C4—711no—
1067C2×C4⋊C4—711no—
1068C2×C4⋊C4—711no—
1069C2×C4⋊C4—711no—
1070C2×C4⋊C4—711no—
1071C2×C4⋊C4—711no—
1072C2×C4⋊C4—711no—
1073C2×C4⋊C4—711no—
1074C2×C22⋊C4—24no—
1075C2×C22⋊C4—42no—
1076C2×C22⋊C4—42no—
1077C2×C22⋊C4—711no—
1078C2×C22⋊C4—711no—
1079C2×C22⋊C4—711no—
1080C2×C22⋊C4—711no—
1081C2×C22⋊C4—711no—
1082C2×C22⋊C4—711no—
1083C2×C22⋊C4—711no—
1084C2×C22⋊C4—711no—
1085C2×C22⋊C4—711no—
1086C2×C22⋊C4—711no—
1087C2×C22⋊C4—711no—
1088C2×C22⋊C4—711no—
1089C2×C22⋊C4—711no—
1090C2×C22⋊C4—711no—
1091C2×C22⋊C4—711no—
1092C2×C22⋊C4—711no—
1093C2×C22⋊C4—711no—
1094C2×C22⋊C4—711no—
1095C2×C22⋊C4—711no—
1096C2×C22⋊C4—711no—
1097C2×C22⋊C4—711no—
1098C2×C22⋊C4—711no—
1099C2×C22⋊C4—711no—
1100C2×C22⋊C4—711no—
1101C2×C22⋊C4—711no—
1102C2×C22⋊C4—711no—
1103C2×C22⋊C4—711no—
1104C2×C22⋊C4—711no—
1105C2×C22⋊C4—711no—
1106C2×C22⋊C4—711no—
1107C2×C22⋊C4—711no—
1108C2×C22⋊C4—711no—
1109C2×C22⋊C4—711no—
1110C2×C22⋊C4—711no—
1111C2×C22⋊C4—711no—
1112C2×C22⋊C4—711no—
1113C2×C22⋊C4—711no—
1114C2×C22⋊C4—711no—
1115C2×C22⋊C4—711no—
1116C2×C22⋊C4—711no—
1117C2×C22⋊C4—1424no—
1118C2×C22⋊C4—1424no—
1119C2×C22⋊C4C22×D7111yescharacteristic
1120C2×C22⋊C4C22×D7111yescharacteristic
1121C2×C22⋊C4C22×D7111yescharacteristic
1122C2×C22⋊C4C22×D7111yescharacteristic
1123C2×C22⋊C4C22×D7111yescharacteristic
1124C2×C22⋊C4C22×D7111yescharacteristic
1125C2×C22⋊C4C22×D7111yescharacteristic
1126C2×C22⋊C4C22×D7111yescharacteristic
1127C2×C22⋊C4C22×D7111yescharacteristic
1128C2×C22⋊C4C22×D7111yescharacteristic
1129C2×C22⋊C4C22×D7111yescharacteristic
1130C2×C22⋊C4C22×D7111yescharacteristic
1131C2×C42—2842no—
1132C2×C42—2842no—
1133C2×C42—711no—
1134C2×C42—711no—
1135C2×C42—711no—
1136C2×C42—711no—
1137C2×C42—711no—
1138C2×C42—711no—
1139C2×C42—711no—
1140C2×C42—711no—
1141C2×C42—711no—
1142C2×C42—711no—
1143C2×C42—711no—
1144#95—711no—
1145#95—711no—
1146#95—711no—
1147#95—711no—
1148#95—711no—
1149#95—711no—
1150#95—711no—
1151#95—711no—
1152#95—711no—
1153#95—711no—
1154#95—711no—
1155#95—711no—
1156#95—711no—
1157#95—711no—
1158#95—711no—
1159#95—711no—
1160#95—711no—
1161#95—711no—
1162#95—711no—
1163#95—711no—
1164#95—711no—
1165#95—711no—
1166#95—711no—
1167#95—711no—
1168#95—711no—
1169#95—711no—
1170#95—711no—
1171#95—711no—
1172#95—711no—
1173#95—711no—
1174#95—711no—
1175#95—711no—
1176#95—711no—
1177#95—711no—
1178#95—711no—
1179#95—711no—
1180#95C22×D7111yescharacteristic
1181#95C22×D7111yescharacteristic
1182#95C22×D7111yescharacteristic
1183#95C22×D7111yescharacteristic
1184#95C22×D7111yescharacteristic
1185#95C22×D7111yescharacteristic
1186#95C22×D7111yescharacteristic
1187#95C22×D7111yescharacteristic
1188C24—22no—
1189C24—22no—
1190C24—22no—
1191C24—22no—
1192C24—22no—
1193C24—22no—
1194C24—22no—
1195C24—41no—
1196C24—41no—
1197C24—41no—
1198C24—41no—
1199C24—41no—
1200C24—41no—
1201C24—711no—
1202C24#1176586514yes—
1203C24C23×D7111yescharacteristic
1204C24C23×D7111yescharacteristic
1205C24C23×D7111yescharacteristic
1206C24C23×D7111yescharacteristic
1207C24C23×D7111yescharacteristic
1208C2×Q8—2841no—
1209C2×Q8—2841no—
1210C2×Q8—1422no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—22no—
1214C2×D4—22no—
1215C2×D4—22no—
1216C2×D4—22no—
1217C2×D4—22no—
1218C2×D4—22no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—416no—
1224C2×D4—2841no—
1225C2×D4—2841no—
1226C2×D4—2841no—
1227C2×D4—2841no—
1228C2×D4—2841no—
1229C2×D4—2841no—
1230C2×D4—1422no—
1231C2×D4—1422no—
1232C2×D4—1422no—
1233C2×D4—1422no—
1234C2×D4—1422no—
1235C2×D4—1422no—
1236C2×D4—1422no—
1237C2×D4—1422no—
1238C2×D4—1422no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—41no—
1259C22×C4—41no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—416no—
1266C22×C4—2841no—
1267C22×C4—2841no—
1268C22×C4—2841no—
1269C22×C4—2841no—
1270C22×C4—2841no—
1271C22×C4—2841no—
1272C22×C4—711no—
1273C22×C4—711no—
1274C22×C4—711no—
1275C22×C4—711no—
1276C22×C4—711no—
1277C22×C4—711no—
1278C22×C4—711no—
1279C22×C4—711no—
1280C22×C4—711no—
1281C22×C4—711no—
1282C22×C4—711no—
1283C22×C4—711no—
1284C22×C4—711no—
1285C22×C4—711no—
1286C22×C4—711no—
1287C22×C4—1422no—
1288C22×C4—1422no—
1289C22×C4—1422no—
1290C22×C4—1422no—
1291C22×C4—1422no—
1292C22×C4—1422no—
1293C22×C4—1422no—
1294C22×C4—1422no—
1295C22×C4—1422no—
1296C22×C4#1176586414yes—
1297C22×C4C23×D7111yescharacteristic
1298C22×C4C23×D7111yescharacteristic
1299C22×C4C23×D7111yescharacteristic
1300C22×C4C23×D7111yescharacteristic
1301C22×C4C23×D7111yescharacteristic
1302C22×C4C23×D7111yescharacteristic
1303C22×C4C23×D7111yescharacteristic
1304C22×C4C23×D7111yescharacteristic
1305C22×C4C23×D7111yescharacteristic
1306C22×C4C23×D7111yescharacteristic
1307C4⋊C4—2841no—
1308C4⋊C4—2841no—
1309C4⋊C4—2841no—
1310C4⋊C4—2841no—
1311C4⋊C4—2841no—
1312C4⋊C4—2841no—
1313C4⋊C4—2841no—
1314C4⋊C4—2841no—
1315C4⋊C4—2841no—
1316C4⋊C4—2841no—
1317C4⋊C4—2841no—
1318C4⋊C4—2841no—
1319C4⋊C4—2841no—
1320C4⋊C4—2841no—
1321C4⋊C4—2841no—
1322C4⋊C4—2841no—
1323C4⋊C4—2841no—
1324C4⋊C4—1422no—
1325C4⋊C4—1422no—
1326C4⋊C4—1422no—
1327C4⋊C4—1422no—
1328C4⋊C4—1422no—
1329C22⋊C4—22no—
1330C22⋊C4—22no—
1331C22⋊C4—22no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—22no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—2841no—
1342C22⋊C4—2841no—
1343C22⋊C4—2841no—
1344C22⋊C4—2841no—
1345C22⋊C4—2841no—
1346C22⋊C4—2841no—
1347C22⋊C4—2841no—
1348C22⋊C4—2841no—
1349C22⋊C4—2841no—
1350C22⋊C4—2841no—
1351C22⋊C4—2841no—
1352C22⋊C4—2841no—
1353C22⋊C4—2841no—
1354C22⋊C4—2841no—
1355C22⋊C4—2841no—
1356C22⋊C4—2841no—
1357C22⋊C4—2841no—
1358C22⋊C4—2841no—
1359C22⋊C4—2841no—
1360C22⋊C4—2841no—
1361C22⋊C4—2841no—
1362C22⋊C4—714no—
1363C22⋊C4—1422no—
1364C22⋊C4—1422no—
1365C22⋊C4—1422no—
1366C22⋊C4—1422no—
1367C22⋊C4—1422no—
1368C22⋊C4—1422no—
1369C22⋊C4—1422no—
1370C22⋊C4—1422no—
1371C22⋊C4—1422no—
1372C22⋊C4—1422no—
1373C22⋊C4—1422no—
1374C22⋊C4—1422no—
1375C22⋊C4—1422no—
1376C22⋊C4—1422no—
1377C22⋊C4—1422no—
1378C22⋊C4—1422no—
1379C22⋊C4—1422no—
1380C22⋊C4—1422no—
1381C42—2841no—
1382C42—2841no—
1383C42—2841no—
1384C42—2841no—
1385C42—2841no—
1386C42—2841no—
1387C42—2841no—
1388C42—2841no—
1389C42—1422no—
1390C42—1422no—
1391C42—1422no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—28no—
1407C23—28no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—44no—
1423C23—44no—
1424C23—44no—
1425C23—44no—
1426C23—44no—
1427C23—44no—
1428C23—44no—
1429C23—44no—
1430C23—82no—
1431C23—82no—
1432C23—82no—
1433C23—82no—
1434C23—1421no—
1435C23—1421no—
1436C23—1421no—
1437C23—1421no—
1438C23—1421no—
1439C23—1421no—
1440C23—1421no—
1441C23#41×D7112yes—
1442C23C2×#1176586412yes—
1443C23C2×#1176586512yes—
1444C23C2×#1176586512yes—
1445C23C2×#1176586512yes—
1446C23#1455617312yes—
1447C23#1455617312yes—
1448C23C24×D7111yescharacteristic
1449Q8—5682no—
1450D4—44no—
1451D4—44no—
1452D4—44no—
1453D4—44no—
1454D4—2844no—
1455D4—2844no—
1456D4—2844no—
1457D4—5682no—
1458D4—5682no—
1459C2×C4—28no—
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—44no—
1488C2×C4—44no—
1489C2×C4—44no—
1490C2×C4—44no—
1491C2×C4—44no—
1492C2×C4—44no—
1493C2×C4—82no—
1494C2×C4—82no—
1495C2×C4—2844no—
1496C2×C4—2844no—
1497C2×C4—2844no—
1498C2×C4—2844no—
1499C2×C4—5682no—
1500C2×C4—712no—
1501C2×C4—712no—
1502C2×C4—1421no—
1503C2×C4—1421no—
1504C2×C4—1421no—
1505C2×C4—1421no—
1506C2×C4—1421no—
1507C2×C4—1421no—
1508C2×C4—1421no—
1509C2×C4—1421no—
1510C2×C4—1421no—
1511C2×C4—1421no—
1512C2×C4—1421no—
1513C2×C4—1421no—
1514C2×C4—1421no—
1515C2×C4—1421no—
1516C2×C4—1421no—
1517C2×C4—1421no—
1518C2×C4—1421no—
1519C2×C4—1421no—
1520C2×C4—1421no—
1521C2×C4—1421no—
1522C2×C4—1421no—
1523C2×C4—1421no—
1524C2×C4—1421no—
1525C2×C4—1421no—
1526C2×C4—1421no—
1527C2×C4—1421no—
1528C2×C4—1421no—
1529C2×C4—1421no—
1530C2×C4—1421no—
1531C2×C4—1421no—
1532C2×C4—1421no—
1533C2×C4—1421no—
1534C2×C4—1421no—
1535C2×C4—1421no—
1536C2×C4—1421no—
1537C2×C4—1421no—
1538C2×C4—1421no—
1539C2×C4—1421no—
1540C2×C4—1421no—
1541C2×C4—1421no—
1542C2×C4—1421no—
1543C2×C4—1421no—
1544C2×C4—1421no—
1545C2×C4C2×#1176586412yes—
1546C2×C4C2×#1176586412yes—
1547C2×C4#1455617312yes—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—22no—
1552C22—22no—
1553C22—22no—
1554C22—22no—
1555C22—22no—
1556C22—22no—
1557C22—22no—
1558C22—22no—
1559C22—22no—
1560C22—22no—
1561C22—22no—
1562C22—22no—
1563C22—416no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—41no—
1569C22—41no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—41no—
1575C22—41no—
1576C22—41no—
1577C22—41no—
1578C22—41no—
1579C22—41no—
1580C22—41no—
1581C22—41no—
1582C22—88no—
1583C22—2841no—
1584C22—2841no—
1585C22—2841no—
1586C22—2841no—
1587C22—2841no—
1588C22—2841no—
1589C22—2841no—
1590C22#1798652914yes—
1591C22#1798658714yes—
1592C22C2×#41×D7111yescharacteristic
1593C22C22×#1176586411yescharacteristic
1594C22C22×#1176586511yescharacteristic
1595C22C2×#1455617311yescharacteristic
1596C22C2×#1455617311yescharacteristic
1597C22C2×#1455617311yescharacteristic
1598C22#1798683511yescharacteristic
1599C4—22no—
1600C4—22no—
1601C4—22no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—41no—
1609C4—2841no—
1610C4—2841no—
1611C4—2841no—
1612C4—2841no—
1613C4—2841no—
1614C4—2841no—
1615C4—2841no—
1616C4—2841no—
1617C4—2841no—
1618C4—2841no—
1619C4—2841no—
1620C4—2841no—
1621C4—2841no—
1622C4—1422no—
1623C4—1422no—
1624C2—24no—
1625C2—24no—
1626C2—42no—
1627C2—81no—
1628C2—81no—
1629C2—5681no—
1630C2C2×#1798652911yescharacteristic
1631C2C2×#1798658711yescharacteristic
1632C2#2260174911yescharacteristic
1633C2#2260202711yescharacteristic
1634C2#2260206911yescharacteristic
1635C2#2260227211yescharacteristic
1636C2#2260236611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC2×#386×C71C2
prime radical#22591714C2
hypercenterC2×#386D71
hypocenterC71#34998
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. #22596668C2semidirect
2. #22596661C2semidirect
3. #22596653C2semidirect
4. #22596637C2semidirect
5. #22594405C2semidirect
6. #22594343C2semidirect
7. #22594330C2semidirect
8. #22594328C2semidirect
9. #22593000C2semidirect
10. #22593000C2semidirect
11. #22592902C2semidirect
12. #22592900C2semidirect
13. #22592841C2semidirect
14. #22592668C2semidirect
15. #22592580C2semidirect
16. #22592460C2semidirect
17. #22592393C2semidirect
18. #22592279C2semidirect
19. #22592092C2semidirect
20. #22592001C2semidirect
21. #22591893C2semidirect
22. #22591730C2semidirect
24. #22591663C2semidirect
25. #22591073C2semidirect
26. #22590998C2semidirect
27. #22590974C2semidirect
28. #22590938C2semidirect
29. C4×#14556097C2semidirect
30. C2×C4×C22⋊Dic71C2semidirect
31. C2×#386×C71C2semidirect
32. C2×#14556121C22semidirect
33. C2×#14556114C22semidirect
34. C2×#14556112C22semidirect
38. C2×#14556105C22semidirect
44. C2×C4×C22⋊D71C22semidirect
45. C2×C4×C22⋊D71C22semidirect
48. C22×C4×Dic71C22semidirect
49. C22×C4×Dic71C22semidirect
50. C71⋊#401C22semidirect
51. #17985941C22semidirect
52. #17985940C22semidirect
53. #17985940C22semidirect
54. #17985939C22semidirect
55. #17985935C22semidirect
56. #17985933C22semidirect
57. #17985928C22semidirect
58. #17985927C22semidirect
59. #17985927C22semidirect
60. #17985927C22semidirect
61. #17985926C22semidirect
62. #17985924C22semidirect
63. #17985924C22semidirect
64. #17985924C22semidirect
65. #17985922C22semidirect
66. #17985922C22semidirect
67. #17985922C22semidirect
68. #17985915C22semidirect
69. #17985915C22semidirect
70. #17985915C22semidirect
71. #17985914C22semidirect
78. #17985911C22semidirect
79. #17985911C22semidirect
82. #17985903C22semidirect
83. #17985903C22semidirect
84. #17985899C22semidirect
85. #17985899C22semidirect
86. #17985899C22semidirect
87. #17985896C22semidirect
88. #17985896C22semidirect
89. #17985896C22semidirect
90. #17985893C22semidirect
91. #17985893C22semidirect
92. #17985893C22semidirect
93. #17985892C22semidirect
94. #17985892C22semidirect
95. #17985892C22semidirect
96. #17985892C22semidirect
97. #17985892C22semidirect
98. #17985892C22semidirect
99. #17985892C22semidirect
100. #17985892C22semidirect
101. #17985892C22semidirect
102. #17985892C22semidirect
103. #17985891C22semidirect
104. #17985888C22semidirect
105. #17985888C22semidirect
106. #17985888C22semidirect
107. #17985887C22semidirect
108. #17985887C22semidirect
109. #17985887C22semidirect
110. #17985887C22semidirect
111. #17985886C22semidirect
112. #17985886C22semidirect
113. #17985884C22semidirect
114. #17985882C22semidirect
115. #17985882C22semidirect
116. #17985882C22semidirect
117. #17985881C22semidirect
118. #17985881C22semidirect
119. #17985881C22semidirect
128. #17985878C22semidirect
129. #17985878C22semidirect
130. #17985876C22semidirect
131. #17985875C22semidirect
132. #17985875C22semidirect
133. #17985874C22semidirect
134. #17985874C22semidirect
141. #17985872C22semidirect
142. #17985872C22semidirect
143. #17985871C22semidirect
144. #17985866C22semidirect
145. #17985866C22semidirect
146. #17985863C22semidirect
147. #17985863C22semidirect
148. #17985861C22semidirect
149. #17985860C22semidirect
153. #17985858C22semidirect
154. #17985857C22semidirect
164. C4×C22⋊Dic71C22semidirect
165. C4×C22⋊Dic71C22semidirect
166. C4×C22⋊Dic71C22semidirect
167. C4×C22⋊Dic71C22semidirect
168. C4×C22⋊Dic71C22semidirect
169. C4×C22⋊Dic71C22semidirect
170. C2×C71⋊#95C22semidirect
171. C2×C71⋊#95C22semidirect
848. C2×#386D71semidirect
850. C71#34998semidirect

Maximal subgroups

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

subgroupindex
#225966682
#225966612
#225966532
#225966372
#225944052
#225943432
#225943302
#225943282
#225930002
#225929022
#225929002
#225928412
#225926682
#225925802
#225924602
#225923932
#225922792
#225920922
#225920012
#225918932
#225917302
#225917142
#225916632
#225910732
#225909982
#225909742
#225909382
C4×#145560972
C2×C4×C22⋊Dic712
C2×#386×C712
#3499871