Finite Group Databasebeta

← #31919085

Subgroups — #31919085

Order 18176.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985893C211yesmaximal, characteristic
2C2×#17985887C211yesmaximal, characteristic
3C2×#17985872C211yesmaximal, characteristic
4#22586577C211yesmaximal, characteristic
5#22586577C211yesmaximal, characteristic
6#22586575C211yesmaximal, characteristic, complemented
7#22586571C211yesmaximal, characteristic, complemented
8#22586571C211yesmaximal, characteristic, complemented
9#22586571C211yesmaximal, characteristic, complemented
10Dic71⋊#95C211yesmaximal, characteristic, complemented
11Dic71⋊#95C211yesmaximal, characteristic, complemented
12#22586566C211yesmaximal, characteristic, complemented
13#22586564C211yesmaximal, characteristic, complemented
14#22586563C211yesmaximal, characteristic
15C71×C22⋊#95C211yesmaximal, characteristic
16C22×Dic71⋊C4C2211yescharacteristic
17C22×Dic71⋊C4C2211yescharacteristic
18C22×Dic71⋊C4C2211yescharacteristic
19C22×Dic71⋊C4C2211yescharacteristic
20C22×C22⋊Dic71C2211yescharacteristic
21C22×C22⋊Dic71C2211yescharacteristic
22C22×C22⋊Dic71C2211yescharacteristic
23C22×C22⋊Dic71C2211yescharacteristic
24C22×C4×Dic71C2211yescharacteristic
25C22×C4×Dic71C2211yescharacteristic
26C22×C4×Dic71C2211yescharacteristic
27C22×C4×Dic71C2211yescharacteristic
28#17985893C418yescomplemented
29#17985887C418yescomplemented
30#17985872C418yescomplemented
31C2×C71⋊#95C2211yescharacteristic
32C2×C71⋊#95C2211yescharacteristic
33C2×C71⋊#95C2211yescharacteristic
34C2×C71⋊#95C2211yescharacteristic
35C2×C71⋊#95C2211yescharacteristic
36C2×C71⋊#95C2211yescharacteristic
37C2×C71⋊#95C2211yescharacteristic
38C2×C71⋊#95C2211yescharacteristic
39C2×C71⋊#95C2211yescharacteristic
40C2×C71⋊#95C2211yescharacteristic
41C2×C71⋊#95C2211yescharacteristic
42C2×C71⋊#95C2211yescharacteristic
43C2×C71⋊#95C2211yescharacteristic
44C2×C71⋊#95C2211yescharacteristic
45C2×C71⋊#95C2211yescharacteristic
46C2×C71⋊#95C2211yescharacteristic
47C24×C4×C71C2211yescharacteristic
48C22×C22⋊C4×C71C2211yescharacteristic
49C22×C22⋊C4×C71C2211yescharacteristic
50C2×#95×C71C2211yescharacteristic
51C2×#95×C71C2211yescharacteristic
52C2×#95×C71C2211yescharacteristic
53C2×#95×C71C2211yescharacteristic
54C23×Dic71C2311yescharacteristic
55C23×Dic71C2311yescharacteristic
56C23×Dic71C2311yescharacteristic
57C23×Dic71C2311yescharacteristic
58C23×Dic71C2311yescharacteristic
59C23×Dic71C2311yescharacteristic
60C23×Dic71C2311yescharacteristic
61C23×Dic71C2311yescharacteristic
62C2×Dic71⋊C4—41no—
63C2×Dic71⋊C4—41no—
64C2×Dic71⋊C4—41no—
65C2×Dic71⋊C4—41no—
66C2×Dic71⋊C4—41no—
67C2×Dic71⋊C4—41no—
68C2×Dic71⋊C4—41no—
69C2×Dic71⋊C4—41no—
70C2×Dic71⋊C4C2×C414yes—
71C2×Dic71⋊C4C2×C414yes—
72C2×Dic71⋊C4C2×C414yescomplemented
73C2×Dic71⋊C4C2×C414yescomplemented
74C2×C22⋊Dic71—41no—
75C2×C22⋊Dic71—41no—
76C2×C22⋊Dic71—41no—
77C2×C22⋊Dic71—41no—
78C2×C22⋊Dic71—41no—
79C2×C22⋊Dic71—41no—
80C2×C22⋊Dic71C2×C414yes—
81C2×C22⋊Dic71C2×C414yes—
82C2×C22⋊Dic71C2×C414yes—
83C2×C22⋊Dic71C2×C414yes—
84C2×C22⋊Dic71C2×C414yes—
85C2×C22⋊Dic71C2×C414yes—
86C2×C4×Dic71—41no—
87C2×C4×Dic71—41no—
88C2×C4×Dic71—41no—
89C2×C4×Dic71—41no—
90C2×C4×Dic71—41no—
91C2×C4×Dic71—41no—
92C2×C4×Dic71—41no—
93C2×C4×Dic71—41no—
94C2×C4×Dic71—41no—
95C2×C4×Dic71—41no—
96C2×C4×Dic71C2×C414yescomplemented
97C2×C4×Dic71C2×C414yescomplemented
98C71⋊#95—41no—
99C71⋊#95—41no—
100C71⋊#95—41no—
101C71⋊#95—41no—
102C71⋊#95—41no—
103C71⋊#95—41no—
104C71⋊#95—41no—
105C71⋊#95—41no—
106C71⋊#95—41no—
107C71⋊#95—41no—
108C71⋊#95C2×C414yes—
109C71⋊#95C2×C414yes—
110C71⋊#95C2×C414yescomplemented
111C71⋊#95C2×C414yescomplemented
112C71⋊#95C2×C414yescomplemented
113C71⋊#95C2×C414yescomplemented
114C25×C71C2311yescharacteristic
115C23×C4×C71—41no—
116C23×C4×C71—41no—
117C23×C4×C71—41no—
118C23×C4×C71—41no—
119C23×C4×C71—41no—
120C23×C4×C71—41no—
121C23×C4×C71C2×C414yes—
122C23×C4×C71C2311yescharacteristic
123C23×C4×C71C2311yescharacteristic
124C23×C4×C71C2311yescharacteristic
125C23×C4×C71C2311yescharacteristic
126C23×C4×C71C2311yescharacteristic
127C23×C4×C71C2311yescharacteristic
128C2×C22⋊C4×C71—41no—
129C2×C22⋊C4×C71—41no—
130C2×C22⋊C4×C71—41no—
131C2×C22⋊C4×C71—41no—
132C2×C22⋊C4×C71C2×C414yes—
133C2×C22⋊C4×C71C2×C414yes—
134#95×C71—41no—
135#95×C71—41no—
136#95×C71—41no—
137#95×C71—41no—
138C22×Dic71—21no—
139C22×Dic71—21no—
140C22×Dic71—21no—
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145C22×Dic71—21no—
146C22×Dic71—21no—
147C22×Dic71—21no—
148C22×Dic71—21no—
149C22×Dic71—21no—
150C22×Dic71—21no—
151C22×Dic71—21no—
152C22×Dic71—21no—
153C22×Dic71—21no—
154C22×Dic71—21no—
155C22×Dic71—21no—
156C22×Dic71—21no—
157C22×Dic71—21no—
158C22×Dic71—21no—
159C22×Dic71—21no—
160C22×Dic71—21no—
161C22×Dic71—21no—
162C22×Dic71—21no—
163C22×Dic71—21no—
164C22×Dic71—21no—
165C22×Dic71—21no—
166C22×Dic71—21no—
167C22×Dic71—21no—
168C22×Dic71—21no—
169C22×Dic71—21no—
170C22×Dic71—21no—
171C22×Dic71—21no—
172C22×Dic71—21no—
173C22×Dic71—21no—
174C22×Dic71—21no—
175C22×Dic71—21no—
176C22×Dic71—21no—
177C22×Dic71—21no—
178C22×Dic71—21no—
179C22×Dic71—21no—
180C22×Dic71—21no—
181C22×Dic71—21no—
182C22×Dic71C22×C412yes—
183C22×Dic71C22×C412yes—
184C22×Dic71C22×C412yes—
185C22×Dic71C22×C412yes—
186C22×Dic71C22×C412yes—
187C22×Dic71C22×C412yes—
188C22×Dic71C22×C412yes—
189C22×Dic71C22×C412yes—
190C22×Dic71C22×C412yes—
191C22×Dic71C22×C412yes—
192C22×Dic71C22×C412yes—
193C22×Dic71C22×C412yes—
194Dic71⋊C4—44no—
195Dic71⋊C4—44no—
196Dic71⋊C4—44no—
197Dic71⋊C4—44no—
198C22⋊Dic71—44no—
199C22⋊Dic71—44no—
200C22⋊Dic71—44no—
201C22⋊Dic71C42116yescomplemented
202C4×Dic71—44no—
203C4×Dic71—44no—
204C4×Dic71—44no—
205C4×Dic71—44no—
206C24×C71—21no—
207C24×C71—21no—
208C24×C71—21no—
209C24×C71—21no—
210C24×C71—21no—
211C24×C71—21no—
212C24×C71—21no—
213C24×C71—21no—
214C24×C71—21no—
215C24×C71—21no—
216C24×C71—21no—
217C24×C71—21no—
218C24×C71C22×C412yes—
219C24×C71C22×C412yes—
220C24×C71C22×C412yes—
221C24×C71C2411yescharacteristic
222C22×C4×C71—21no—
223C22×C4×C71—21no—
224C22×C4×C71—21no—
225C22×C4×C71—21no—
226C22×C4×C71—21no—
227C22×C4×C71—21no—
228C22×C4×C71—21no—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—44no—
259C22×C4×C71—44no—
260C22×C4×C71—44no—
261C22×C4×C71—44no—
262C22×C4×C71—44no—
263C22×C4×C71—44no—
264C22×C4×C71—44no—
265C22×C4×C71C22×C412yes—
266C22×C4×C71C22×C412yes—
267C22×C4×C71C22×C412yes—
268C22×C4×C71C22×C412yes—
269C22×C4×C71C22×C412yes—
270C22×C4×C71C22×C412yes—
271C22⋊C4×C71—44no—
272C22⋊C4×C71—44no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—22no—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—22no—
287C23×C71—22no—
288C23×C71—22no—
289C23×C71—22no—
290C23×C71—22no—
291C23×C71—41no—
292C23×C71—41no—
293C23×C71—41no—
294C23×C71—41no—
295C23×C71—41no—
296C23×C71—41no—
297C23×C71—41no—
298C23×C71—41no—
299C23×C71—41no—
300C23×C71—41no—
301C23×C71—41no—
302C23×C71—41no—
303C23×C71—41no—
304C23×C71—41no—
305C23×C71—41no—
306C23×C71—41no—
307C23×C71C2×C4214yes—
308C23×C71C23×C411yescharacteristic
309C23×C71C23×C411yescharacteristic
310C23×C71C23×C411yescharacteristic
311C23×C71H(5,𝔽2)11yescharacteristic
312C23×C71H(5,𝔽2)11yescharacteristic
313C23×C71H(5,𝔽2)11yescharacteristic
314C23×C71H(5,𝔽2)11yescharacteristic
315C23×C71H(5,𝔽2)11yescharacteristic
316C23×C71H(5,𝔽2)11yescharacteristic
317C23×C71H(5,𝔽2)11yescharacteristic
318C23×C71H(5,𝔽2)11yescharacteristic
319C23×C712−1+411yescharacteristic
320C23×C712−1+411yescharacteristic
321C23×C712−1+411yescharacteristic
322C23×C712−1+411yescharacteristic
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—22no—
334C2×C4×C71—22no—
335C2×C4×C71—22no—
336C2×C4×C71—22no—
337C2×C4×C71—22no—
338C2×C4×C71—22no—
339C2×C4×C71—22no—
340C2×C4×C71—22no—
341C2×C4×C71—416no—
342C2×C4×C71—41no—
343C2×C4×C71—41no—
344C2×C4×C71—41no—
345C2×C4×C71—41no—
346C2×C4×C71—41no—
347C2×C4×C71—41no—
348C2×C4×C71—41no—
349C2×C4×C71—41no—
350C2×C4×C71—41no—
351C2×C4×C71—41no—
352C2×C4×C71—41no—
353C2×C4×C71—41no—
354C2×C4×C71—41no—
355C2×C4×C71—41no—
356C2×C4×C71—41no—
357C2×C4×C71—41no—
358C2×C4×C71—41no—
359C2×C4×C71—41no—
360C2×C4×C71—41no—
361C2×C4×C71—41no—
362C2×C4×C71—41no—
363C2×C4×C71—41no—
364C2×C4×C71—41no—
365C2×C4×C71—41no—
366C2×Dic71—22no—
367C2×Dic71—22no—
368C2×Dic71—22no—
369C2×Dic71—22no—
370C2×Dic71—22no—
371C2×Dic71—22no—
372C2×Dic71—22no—
373C2×Dic71—22no—
374C2×Dic71—22no—
375C2×Dic71—22no—
376C2×Dic71—22no—
377C2×Dic71—22no—
378C2×Dic71—22no—
379C2×Dic71—22no—
380C2×Dic71—22no—
381C2×Dic71—22no—
382C2×Dic71—22no—
383C2×Dic71—22no—
384C2×Dic71—22no—
385C2×Dic71—22no—
386C2×Dic71—22no—
387C2×Dic71—22no—
388C2×Dic71—22no—
389C2×Dic71—22no—
390C2×Dic71—22no—
391C2×Dic71—22no—
392C2×Dic71—22no—
393C2×Dic71—22no—
394C2×Dic71—22no—
395C2×Dic71—22no—
396C2×Dic71—41no—
397C2×Dic71—41no—
398C2×Dic71—41no—
399C2×Dic71—41no—
400C2×Dic71—41no—
401C2×Dic71—41no—
402C2×Dic71—41no—
403C2×Dic71—41no—
404C2×Dic71—41no—
405C2×Dic71—41no—
406C2×Dic71—41no—
407C2×Dic71—41no—
408C2×Dic71—41no—
409C2×Dic71—41no—
410C2×Dic71—41no—
411C2×Dic71—41no—
412C2×Dic71—41no—
413C2×Dic71—41no—
414C2×Dic71—41no—
415C2×Dic71—41no—
416C2×Dic71—41no—
417C2×Dic71—41no—
418C2×Dic71—41no—
419C2×Dic71—41no—
420C2×Dic71C2×C4214yes—
421C2×Dic71C2×C4214yes—
422C22×C71—24no—
423C22×C71—24no—
424C22×C71—24no—
425C22×C71—42no—
426C22×C71—42no—
427C22×C71—42no—
428C22×C71—42no—
429C22×C71—42no—
430C22×C71—42no—
431C22×C71—42no—
432C22×C71—42no—
433C22×C71—42no—
434C22×C71—42no—
435C22×C71—42no—
436C22×C71—42no—
437C22×C71C22×C4211yescharacteristic
438C22×C71#51811yescharacteristic
439C22×C71#51811yescharacteristic
440C22×C71#51811yescharacteristic
441C22×C71#51811yescharacteristic
442C22×C71#51811yescharacteristic
443C22×C71#51811yescharacteristic
444C22×C71#51811yescharacteristic
445C22×C71#51911yescharacteristic
446C22×C71#52011yescharacteristic
447C22×C71#52011yescharacteristic
448C22×C71#52011yescharacteristic
449C22×C71#52011yescharacteristic
450C22×C71#52011yescharacteristic
451C22×C71#52011yescharacteristic
452C22×C71#52011yescharacteristic
453C22×C71#52011yescharacteristic
454C22×C71#52011yescharacteristic
455C22×C71#52011yescharacteristic
456C22×C71#56011yescharacteristic
457C22×C71#56011yescharacteristic
458C22×C71#56011yescharacteristic
459C22×C71#56011yescharacteristic
460C22×C71H(3,𝔽4)11yescharacteristic
461C22×C71#56211yescharacteristic
462C22×C71#56211yescharacteristic
463C22×C71#56211yescharacteristic
464C22×C71#56211yescharacteristic
465C22×C71#56211yescharacteristic
466C22×C71#56211yescharacteristic
467C22×C71#56311yescharacteristic
468C22×C71#56311yescharacteristic
469C22×C71#56311yescharacteristic
470C22×C71#56311yescharacteristic
471C22×C71#56311yescharacteristic
472C4×C71—42no—
473C4×C71—42no—
474C4×C71—42no—
475C4×C71—42no—
476C4×C71—42no—
477C4×C71—42no—
478Dic71—24no—
479Dic71—24no—
480Dic71—42no—
481Dic71—42no—
482Dic71—42no—
483Dic71—42no—
484Dic71—42no—
485Dic71—42no—
486#13831—711nomaximal, Sylow
487C2×C71—44no—
488C2×C71#227411yescharacteristic
489C2×C71#227511yescharacteristic
490C2×C71#227511yescharacteristic
491C2×C71#237511yescharacteristic
492C2×C71#237611yescharacteristic
493C2×C71#237611yescharacteristic
494C2×C71#237611yescharacteristic
495C2×C71#237711yescharacteristic
496C2×C71#237711yescharacteristic
497C2×C71#237811yescharacteristic
498C2×C71#237811yescharacteristic
499C2×C71#237911yescharacteristic
500C2×C71#237911yescharacteristic
501C2×C71#238311yescharacteristic
502C2×C71#238311yescharacteristic
503C2×#388—711no—
504C2×#388—711no—
505C2×#385—711no—
506#1437—711no—
507#1437—711no—
508#1436—711no—
509#1436—711no—
510#1436—711no—
511#1436—711no—
512C4⋊#95—711no—
513C4⋊#95—711no—
514#1434—711no—
515#1434—711no—
516C22⋊#95—711no—
517C22⋊#95D7111yescharacteristic
518C71#1383111yescharacteristic, complemented, Sylow
519C24×C4C2×D7111yescharacteristic
520C22×C4⋊C4—711no—
521C22×C4⋊C4—711no—
522C22×C4⋊C4—711no—
523C22×C4⋊C4—711no—
524C22×C22⋊C4—711no—
525C22×C22⋊C4—711no—
526C22×C22⋊C4—711no—
527C22×C22⋊C4—711no—
528C22×C22⋊C4C2×D7111yescharacteristic
529C22×C22⋊C4C2×D7111yescharacteristic
530C22×C42—711no—
531C22×C42—711no—
532C22×C42—711no—
533C22×C42—711no—
534#388—718no—
535#388—718no—
536#385—718no—
537C2×#95—711no—
538C2×#95—711no—
539C2×#95—711no—
540C2×#95—711no—
541C2×#95—711no—
542C2×#95—711no—
543C2×#95—711no—
544C2×#95—711no—
545C2×#95—711no—
546C2×#95—711no—
547C2×#95—711no—
548C2×#95—711no—
549C2×#95—711no—
550C2×#95—711no—
551C2×#95—711no—
552C2×#95—711no—
553C2×#95C2×D7111yescharacteristic
554C2×#95C2×D7111yescharacteristic
555C2×#95C2×D7111yescharacteristic
556C2×#95C2×D7111yescharacteristic
557C25C22×D7111yescharacteristic
558C23×C4—41no—
559C23×C4—41no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4—711no—
565C23×C4—711no—
566C23×C4—711no—
567C23×C4—711no—
568C23×C4—711no—
569C23×C4—711no—
570C23×C4—711no—
571C23×C4—711no—
572C23×C4C4×D7114yes—
573C23×C4C22×D7111yescharacteristic
574C23×C4C22×D7111yescharacteristic
575C23×C4C22×D7111yescharacteristic
576C23×C4C22×D7111yescharacteristic
577C23×C4C22×D7111yescharacteristic
578C23×C4C22×D7111yescharacteristic
579C2×C4⋊C4—2841no—
580C2×C4⋊C4—2841no—
581C2×C4⋊C4—2841no—
582C2×C4⋊C4—2841no—
583C2×C4⋊C4—2841no—
584C2×C4⋊C4—2841no—
585C2×C4⋊C4—2841no—
586C2×C4⋊C4—2841no—
587C2×C4⋊C4—714no—
588C2×C4⋊C4—714no—
589C2×C4⋊C4—714no—
590C2×C4⋊C4—714no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—2841no—
596C2×C22⋊C4—2841no—
597C2×C22⋊C4—2841no—
598C2×C22⋊C4—2841no—
599C2×C22⋊C4—2841no—
600C2×C22⋊C4—2841no—
601C2×C22⋊C4—714no—
602C2×C22⋊C4—714no—
603C2×C22⋊C4—714no—
604C2×C22⋊C4—714no—
605C2×C22⋊C4—714no—
606C2×C22⋊C4—714no—
607C2×C22⋊C4C4×D7114yes—
608C2×C22⋊C4C4×D7114yes—
609C2×C42—2841no—
610C2×C42—2841no—
611C2×C42—2841no—
612C2×C42—2841no—
613C2×C42—2841no—
614C2×C42—2841no—
615C2×C42—2841no—
616C2×C42—2841no—
617C2×C42—2841no—
618C2×C42—2841no—
619C2×C42—714no—
620C2×C42—714no—
621#95—41no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95—2841no—
626#95—2841no—
627#95—2841no—
628#95—2841no—
629#95—2841no—
630#95—2841no—
631#95—2841no—
632#95—2841no—
633#95—2841no—
634#95—2841no—
635#95—714no—
636#95—714no—
637#95—714no—
638#95—714no—
639#95—714no—
640#95—714no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D7112yes—
654C24C2×C4×D7112yes—
655C24C2×C4×D7112yes—
656C24C23×D7111yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—712no—
701C22×C4—712no—
702C22×C4—712no—
703C22×C4—712no—
704C22×C4—712no—
705C22×C4—712no—
706C22×C4—712no—
707C22×C4—712no—
708C22×C4—712no—
709C22×C4—712no—
710C22×C4—712no—
711C22×C4—712no—
712C22×C4—1421no—
713C22×C4—1421no—
714C22×C4—1421no—
715C22×C4—1421no—
716C22×C4—1421no—
717C22×C4—1421no—
718C22×C4—1421no—
719C22×C4—1421no—
720C22×C4—1421no—
721C22×C4—1421no—
722C22×C4—1421no—
723C22×C4—1421no—
724C22×C4—1421no—
725C22×C4—1421no—
726C22×C4—1421no—
727C22×C4—1421no—
728C22×C4—1421no—
729C22×C4—1421no—
730C22×C4—1421no—
731C22×C4—1421no—
732C22×C4—1421no—
733C22×C4—1421no—
734C22×C4—1421no—
735C22×C4—1421no—
736C22×C4—1421no—
737C22×C4—1421no—
738C22×C4—1421no—
739C22×C4—1421no—
740C22×C4—1421no—
741C22×C4—1421no—
742C22×C4—1421no—
743C22×C4—1421no—
744C22×C4—1421no—
745C22×C4—1421no—
746C22×C4—1421no—
747C22×C4—1421no—
748C22×C4—1421no—
749C22×C4—1421no—
750C22×C4—1421no—
751C22×C4—1421no—
752C22×C4—1421no—
753C22×C4—1421no—
754C22×C4—1421no—
755C22×C4—1421no—
756C22×C4C2×C4×D7112yes—
757C22×C4C2×C4×D7112yes—
758C22×C4C2×C4×D7112yes—
759C22×C4C2×C4×D7112yes—
760C22×C4C2×C4×D7112yes—
761C22×C4C2×C4×D7112yes—
762C4⋊C4—2844no—
763C4⋊C4—2844no—
764C4⋊C4—2844no—
765C4⋊C4—2844no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—2844no—
769C22⋊C4—2844no—
770C22⋊C4—2844no—
771C22⋊C4—7116no—
772C42—2844no—
773C42—2844no—
774C42—2844no—
775C42—2844no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C42×D7114yes—
811C23C22×C4×D7111yescharacteristic
812C23C22×C4×D7111yescharacteristic
813C23C22×C4×D7111yescharacteristic
814C23#1455617311yescharacteristic
815C23#1455617311yescharacteristic
816C23#1455617311yescharacteristic
817C23#1455617311yescharacteristic
818C23#1455617311yescharacteristic
819C23#1455617311yescharacteristic
820C23#1455617311yescharacteristic
821C23#1455617411yescharacteristic
822C23#1455617511yescharacteristic
823C23#1455617511yescharacteristic
824C23#1455617511yescharacteristic
825C23#1455617611yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—416no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—2841no—
870C2×C4—2841no—
871C2×C4—2841no—
872C2×C4—2841no—
873C2×C4—2841no—
874C2×C4—2841no—
875C2×C4—2841no—
876C2×C4—2841no—
877C2×C4—2841no—
878C2×C4—2841no—
879C2×C4—2841no—
880C2×C4—2841no—
881C2×C4—2841no—
882C2×C4—2841no—
883C2×C4—2841no—
884C2×C4—2841no—
885C2×C4—2841no—
886C2×C4—2841no—
887C2×C4—2841no—
888C2×C4—2841no—
889C2×C4—2841no—
890C2×C4—2841no—
891C2×C4—2841no—
892C2×C4—2841no—
893C2×C4—714no—
894C2×C4—714no—
895C2×C4—1422no—
896C2×C4—1422no—
897C2×C4—1422no—
898C2×C4—1422no—
899C2×C4—1422no—
900C2×C4—1422no—
901C2×C4—1422no—
902C2×C4—1422no—
903C2×C4—1422no—
904C2×C4—1422no—
905C2×C4—1422no—
906C2×C4—1422no—
907C2×C4—1422no—
908C2×C4—1422no—
909C2×C4—1422no—
910C2×C4—1422no—
911C2×C4—1422no—
912C2×C4—1422no—
913C2×C4—1422no—
914C2×C4—1422no—
915C2×C4—1422no—
916C2×C4—1422no—
917C2×C4—1422no—
918C2×C4—1422no—
919C2×C4—1422no—
920C2×C4—1422no—
921C2×C4—1422no—
922C2×C4—1422no—
923C2×C4—1422no—
924C2×C4—1422no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C2×C42×D7111yescharacteristic
941C22#1798647111yescharacteristic
942C22#1798647111yescharacteristic
943C22#1798647211yescharacteristic
944C22#1798647211yescharacteristic
945C22#1798647211yescharacteristic
946C22#1798647211yescharacteristic
947C22#1798647211yescharacteristic
948C22#1798647611yescharacteristic
949C22#1798647811yescharacteristic
950C22#1798647811yescharacteristic
951C22#1798647811yescharacteristic
952C22#1798647811yescharacteristic
953C22#1798647811yescharacteristic
954C22#1798647811yescharacteristic
955C22#1798647911yescharacteristic
956C22#1798648011yescharacteristic
957C22#1798648011yescharacteristic
958C22#1798648011yescharacteristic
959C22#1798673711yescharacteristic
960C22#1798673811yescharacteristic
961C22#1798673811yescharacteristic
962C22#1798673811yescharacteristic
963C22#1798674211yescharacteristic
964C22#1798674411yescharacteristic
965C22#1798674411yescharacteristic
966C22#1798674411yescharacteristic
967C22#1798674511yescharacteristic
968C22#1798674611yescharacteristic
969C22#1798674611yescharacteristic
970C22#1798675011yescharacteristic
971C22#1798675011yescharacteristic
972C22#1798675011yescharacteristic
973C22#1798675211yescharacteristic
974C22#1798675211yescharacteristic
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—2842no—
982C4—2842no—
983C4—2842no—
984C4—2842no—
985C4—2842no—
986C4—2842no—
987C4—1424no—
988C4—1424no—
989C2—44no—
990C2#2259069511yescharacteristic
991C2#2259069811yescharacteristic
992C2#2259069911yescharacteristic
993C2#2259147911yescharacteristic
994C2#2259148311yescharacteristic
995C2#2259148411yescharacteristic
996C2#2259148911yescharacteristic
997C2#2259149211yescharacteristic
998C2#2259149811yescharacteristic
999C2#2259150311yescharacteristic
1000C2#2259150811yescharacteristic
1001C2#2259151011yescharacteristic
1002C2#2259151311yescharacteristic
1003C2#2259152811yescharacteristic
1004C2#2259152811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC71×C22⋊#95C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC22⋊#95D71
hypocenterC71#13831
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
6. #22586575C2semidirect
7. #22586571C2semidirect
8. #22586571C2semidirect
9. #22586571C2semidirect
10. Dic71⋊#95C2semidirect
11. Dic71⋊#95C2semidirect
12. #22586566C2semidirect
13. #22586564C2semidirect
28. #17985893C4semidirect
29. #17985887C4semidirect
30. #17985872C4semidirect
72. C2×Dic71⋊C4C2×C4semidirect
73. C2×Dic71⋊C4C2×C4semidirect
96. C2×C4×Dic71C2×C4semidirect
97. C2×C4×Dic71C2×C4semidirect
110. C71⋊#95C2×C4semidirect
111. C71⋊#95C2×C4semidirect
112. C71⋊#95C2×C4semidirect
113. C71⋊#95C2×C4semidirect
201. C22⋊Dic71C42semidirect
518. C71#13831semidirect

Maximal subgroups

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

subgroupindex
C2×#179858932
C2×#179858872
C2×#179858722
#225865772
#225865752
#225865712
Dic71⋊#952
#225865662
#225865642
#225865632
C71×C22⋊#952
#1383171