Finite Group Databasebeta

← #31919086

Subgroups — #31919086

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×#17985889C211yesmaximal, characteristic
2C2×#17985888C211yesmaximal, characteristic
3C2×#17985873C211yesmaximal, characteristic
4#22586578C211yesmaximal, characteristic
5#22586576C211yesmaximal, characteristic
6#22586574C211yesmaximal, characteristic, complemented
7#22586573C211yesmaximal, characteristic, complemented
8#22586571C211yesmaximal, characteristic, complemented
9#22586569C211yesmaximal, characteristic, complemented
10Dic71⋊#95C211yesmaximal, characteristic, complemented
11#22586565C211yesmaximal, characteristic, complemented
12#22586564C211yesmaximal, characteristic, complemented
13(C2×D71)⋊#95C211yesmaximal, characteristic
14(C2×D71)⋊#95C211yesmaximal, characteristic
15C71×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C22×C4⋊Dic71C2211yescharacteristic
18C22×Dic71⋊C4C2211yescharacteristic
19C22×Dic71⋊C4C2211yescharacteristic
20C22×(C2×D71)⋊C4C2211yescharacteristic
21C22×(C2×D71)⋊C4C2211yescharacteristic
22C22×(C2×D71)⋊C4C2211yescharacteristic
23C22×(C2×D71)⋊C4C2211yescharacteristic
24C22×(C2×D71)⋊C4C2211yescharacteristic
25C22×(C2×D71)⋊C4C2211yescharacteristic
26C22×C4×Dic71C2211yescharacteristic
27C22×C4×Dic71C2211yescharacteristic
28C22×C4×Dic71C2211yescharacteristic
29#17985889C418yescomplemented
30#17985888C418yescomplemented
31#17985873C418yescomplemented
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
47C22×C4⋊C4×C71C2211yescharacteristic
48C22×C42×C71C2211yescharacteristic
49C2×#95×C71C2211yescharacteristic
50C2×#95×C71C2211yescharacteristic
51C2×#95×C71C2211yescharacteristic
52C2×#95×C71C2211yescharacteristic
53C2×#95×C71C2211yescharacteristic
54C24×D71C2311yescharacteristic
55C23×Dic71C2311yescharacteristic
56C23×Dic71C2311yescharacteristic
57C23×Dic71C2311yescharacteristic
58C23×Dic71C2311yescharacteristic
59C23×Dic71C2311yescharacteristic
60C23×Dic71C2311yescharacteristic
61C23×Dic71C2311yescharacteristic
62C22×C4×D71—41no—
63C22×C4×D71—41no—
64C22×C4×D71—41no—
65C22×C4×D71—41no—
66C22×C4×D71—41no—
67C22×C4×D71—41no—
68C22×C4×D71C2×C414yes—
69C2×C4⋊Dic71—41no—
70C2×C4⋊Dic71—41no—
71C2×C4⋊Dic71C2×C414yes—
72C2×Dic71⋊C4—41no—
73C2×Dic71⋊C4—41no—
74C2×Dic71⋊C4—41no—
75C2×Dic71⋊C4—41no—
76C2×Dic71⋊C4C2×C414yes—
77C2×Dic71⋊C4C2×C414yescomplemented
78C2×(C2×D71)⋊C4—41no—
79C2×(C2×D71)⋊C4—41no—
80C2×(C2×D71)⋊C4—41no—
81C2×(C2×D71)⋊C4—41no—
82C2×(C2×D71)⋊C4—41no—
83C2×(C2×D71)⋊C4—41no—
84C2×(C2×D71)⋊C4—41no—
85C2×(C2×D71)⋊C4—41no—
86C2×(C2×D71)⋊C4—41no—
87C2×(C2×D71)⋊C4—41no—
88C2×(C2×D71)⋊C4C2×C414yes—
89C2×(C2×D71)⋊C4C2×C414yes—
90C2×(C2×D71)⋊C4C2×C414yes—
91C2×(C2×D71)⋊C4C2×C414yes—
92C2×(C2×D71)⋊C4C2×C414yes—
93C2×(C2×D71)⋊C4C2×C414yes—
94C2×(C2×D71)⋊C4C2×C414yes—
95C2×(C2×D71)⋊C4C2×C414yes—
96C2×C4×Dic71—41no—
97C2×C4×Dic71—41no—
98C2×C4×Dic71—41no—
99C2×C4×Dic71—41no—
100C2×C4×Dic71—41no—
101C2×C4×Dic71—41no—
102C2×C4×Dic71—41no—
103C2×C4×Dic71C2×C414yescomplemented
104C2×C4×Dic71C2×C414yescomplemented
105C71⋊#95—41no—
106C71⋊#95—41no—
107C71⋊#95—41no—
108C71⋊#95—41no—
109C71⋊#95—41no—
110C71⋊#95—41no—
111C71⋊#95—41no—
112C71⋊#95—41no—
113C71⋊#95—41no—
114C71⋊#95—41no—
115C71⋊#95—41no—
116C71⋊#95C2×C414yes—
117C71⋊#95C2×C414yescomplemented
118C71⋊#95C2×C414yescomplemented
119C71⋊#95C2×C414yescomplemented
120C23×C4×C71C2311yescharacteristic
121C23×C4×C71C2311yescharacteristic
122C23×C4×C71C2311yescharacteristic
123C23×C4×C71C2311yescharacteristic
124C23×C4×C71C2311yescharacteristic
125C23×C4×C71C2311yescharacteristic
126C23×C4×C71C2311yescharacteristic
127C2×C4⋊C4×C71—41no—
128C2×C4⋊C4×C71—41no—
129C2×C4⋊C4×C71C2×C414yescomplemented
130C2×C42×C71—41no—
131C2×C42×C71—41no—
132C2×C42×C71—41no—
133#95×C71—41no—
134#95×C71—41no—
135#95×C71—41no—
136#95×C71C2×C414yes—
137#95×C71C2×C414yescomplemented
138C23×D71—21no—
139C23×D71—21no—
140C23×D71—21no—
141C23×D71—21no—
142C23×D71—21no—
143C23×D71—21no—
144C23×D71—21no—
145C23×D71—21no—
146C23×D71—21no—
147C23×D71—21no—
148C23×D71—21no—
149C23×D71—21no—
150C23×D71C22×C412yes—
151C23×D71C22×C412yes—
152C23×D71C22×C412yes—
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×Dic71—21no—
183C22×Dic71—21no—
184C22×Dic71—21no—
185C22×Dic71—21no—
186C22×Dic71—21no—
187C22×Dic71—21no—
188C22×Dic71—21no—
189C22×Dic71—21no—
190C22×Dic71—21no—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71C22×C412yes—
194C22×Dic71C22×C412yes—
195C22×Dic71C22×C412yes—
196C22×Dic71C22×C412yes—
197C22×Dic71C22×C412yes—
198C22×Dic71C22×C412yes—
199C22×Dic71C22×C412yes—
200C22×Dic71C22×C412yes—
201C22×Dic71C22×C412yes—
202C2×C4×D71—44no—
203C2×C4×D71—44no—
204C2×C4×D71—44no—
205C2×C4×D71—44no—
206C2×C4×D71—44no—
207C2×C4×D71—44no—
208C2×C4×D71—44no—
209C4⋊Dic71—44no—
210Dic71⋊C4—44no—
211Dic71⋊C4—44no—
212(C2×D71)⋊C4—44no—
213(C2×D71)⋊C4—44no—
214(C2×D71)⋊C4—44no—
215(C2×D71)⋊C4—44no—
216(C2×D71)⋊C4—44no—
217(C2×D71)⋊C4C42116yescomplemented
218C4×Dic71—44no—
219C4×Dic71—44no—
220C4×Dic71—44no—
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—21no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71C22×C412yes—
263C22×C4×C71C22×C412yes—
264C22×C4×C71C22×C412yes—
265C22×C4×C71C22×C412yes—
266C22×C4×C71C22×C412yes—
267C22×C4×C71C22×C412yes—
268C22×C4×C71C22×C412yes—
269C22×C4×C71C22×C412yes—
270C22×C4×C71C22×C412yes—
271C4⋊C4×C71—44no—
272C42×C71—44no—
273C23×C71C23×C411yescharacteristic
274C23×C71C23×C411yescharacteristic
275C23×C71C23×C411yescharacteristic
276C23×C71H(5,𝔽2)11yescharacteristic
277C23×C71H(5,𝔽2)11yescharacteristic
278C23×C71H(5,𝔽2)11yescharacteristic
279C23×C71H(5,𝔽2)11yescharacteristic
280C23×C71H(5,𝔽2)11yescharacteristic
281C23×C71H(5,𝔽2)11yescharacteristic
282C23×C71H(5,𝔽2)11yescharacteristic
283C23×C71H(5,𝔽2)11yescharacteristic
284C23×C712−1+411yescharacteristic
285C23×C712−1+411yescharacteristic
286C23×C712−1+411yescharacteristic
287C23×C712−1+411yescharacteristic
288C22×D71—22no—
289C22×D71—22no—
290C22×D71—22no—
291C22×D71—22no—
292C22×D71—22no—
293C22×D71—22no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—22no—
297C22×D71—22no—
298C22×D71—22no—
299C22×D71—22no—
300C22×D71—22no—
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—22no—
306C22×D71—41no—
307C22×D71—41no—
308C22×D71—41no—
309C22×D71—41no—
310C22×D71—41no—
311C22×D71—41no—
312C22×D71—41no—
313C22×D71—41no—
314C22×D71—41no—
315C22×D71—41no—
316C22×D71—41no—
317C22×D71—41no—
318C22×D71—41no—
319C22×D71—41no—
320C22×D71—41no—
321C22×D71—41no—
322C22×D71C2×C4214yes—
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—22no—
342C2×C4×C71—22no—
343C2×C4×C71—22no—
344C2×C4×C71—22no—
345C2×C4×C71—22no—
346C2×C4×C71—22no—
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×C4×C71—41no—
367C2×C4×C71—41no—
368C2×C4×C71—41no—
369C2×C4×C71—41no—
370C2×C4×C71—41no—
371C2×C4×C71C2×C4214yes—
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—
421C4×D71—416no—
422C22×C71C22×C4211yescharacteristic
423C22×C71#51811yescharacteristic
424C22×C71#51811yescharacteristic
425C22×C71#51811yescharacteristic
426C22×C71#51811yescharacteristic
427C22×C71#51811yescharacteristic
428C22×C71#51811yescharacteristic
429C22×C71#51811yescharacteristic
430C22×C71#51911yescharacteristic
431C22×C71#52011yescharacteristic
432C22×C71#52011yescharacteristic
433C22×C71#52011yescharacteristic
434C22×C71#52011yescharacteristic
435C22×C71#52011yescharacteristic
436C22×C71#52011yescharacteristic
437C22×C71#52011yescharacteristic
438C22×C71#52011yescharacteristic
439C22×C71#52011yescharacteristic
440C22×C71#52011yescharacteristic
441C22×C71#56011yescharacteristic
442C22×C71#56011yescharacteristic
443C22×C71#56011yescharacteristic
444C22×C71#56011yescharacteristic
445C22×C71H(3,𝔽4)11yescharacteristic
446C22×C71#56211yescharacteristic
447C22×C71#56211yescharacteristic
448C22×C71#56211yescharacteristic
449C22×C71#56211yescharacteristic
450C22×C71#56211yescharacteristic
451C22×C71#56211yescharacteristic
452C22×C71#56311yescharacteristic
453C22×C71#56311yescharacteristic
454C22×C71#56311yescharacteristic
455C22×C71#56311yescharacteristic
456C22×C71#56311yescharacteristic
457C2×D71—24no—
458C2×D71—24no—
459C2×D71—24no—
460C2×D71—42no—
461C2×D71—42no—
462C2×D71—42no—
463C2×D71—42no—
464C2×D71—42no—
465C2×D71—42no—
466C2×D71—42no—
467C2×D71—42no—
468C2×D71—42no—
469C2×D71—42no—
470C2×D71—42no—
471C2×D71—42no—
472C4×C71—24no—
473C4×C71—42no—
474C4×C71—42no—
475C4×C71—42no—
476C4×C71—42no—
477C4×C71—42no—
478C4×C71—42no—
479Dic71—24no—
480Dic71—42no—
481Dic71—42no—
482Dic71—42no—
483Dic71—42no—
484Dic71—42no—
485Dic71—42no—
486#13831—711nomaximal, Sylow
487C2×C71#227411yescharacteristic
488C2×C71#227511yescharacteristic
489C2×C71#227511yescharacteristic
490C2×C71#237511yescharacteristic
491C2×C71#237611yescharacteristic
492C2×C71#237611yescharacteristic
493C2×C71#237611yescharacteristic
494C2×C71#237711yescharacteristic
495C2×C71#237711yescharacteristic
496C2×C71#237811yescharacteristic
497C2×C71#237811yescharacteristic
498C2×C71#237911yescharacteristic
499C2×C71#237911yescharacteristic
500C2×C71#238311yescharacteristic
501C2×C71#238311yescharacteristic
502D71—44no—
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#1436D7111yescharacteristic, complemented
512C4⋊#95—711no—
513C4⋊#95—711no—
514#1434—711no—
515#1434—711no—
516C22⋊#95—711no—
517C22⋊#95—711no—
518C71#1383111yescharacteristic, complemented, Sylow
519C24×C4—711no—
520C22×C4⋊C4—711no—
521C22×C4⋊C4—711no—
522C22×C4⋊C4—711no—
523C22×C4⋊C4C2×D7111yescharacteristic
524C22×C22⋊C4—711no—
525C22×C22⋊C4—711no—
526C22×C22⋊C4—711no—
527C22×C22⋊C4—711no—
528C22×C22⋊C4—711no—
529C22×C22⋊C4—711no—
530C22×C42—711no—
531C22×C42—711no—
532C22×C42—711no—
533C22×C42C2×D7111yescharacteristic
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×#95C2×D7111yescharacteristic
553C2×#95C2×D7111yescharacteristic
554C2×#95C2×D7111yescharacteristic
555C2×#95C2×D7111yescharacteristic
556C2×#95C2×D7111yescharacteristic
557C25—711no—
558C23×C4—2841no—
559C23×C4—2841no—
560C23×C4—2841no—
561C23×C4—2841no—
562C23×C4—2841no—
563C23×C4—2841no—
564C23×C4—714no—
565C23×C4—711no—
566C23×C4—711no—
567C23×C4—711no—
568C23×C4—711no—
569C23×C4—711no—
570C23×C4—711no—
571C23×C4—711no—
572C23×C4C22×D7111yescharacteristic
573C23×C4C22×D7111yescharacteristic
574C23×C4C22×D7111yescharacteristic
575C23×C4C22×D7111yescharacteristic
576C23×C4C22×D7111yescharacteristic
577C23×C4C22×D7111yescharacteristic
578C23×C4C22×D7111yescharacteristic
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
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⋊C4C4×D7114yescomplemented
591C2×C22⋊C4—2841no—
592C2×C22⋊C4—2841no—
593C2×C22⋊C4—2841no—
594C2×C22⋊C4—2841no—
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⋊C4—714no—
608C2×C22⋊C4—714no—
609C2×C42—41no—
610C2×C42—41no—
611C2×C42—41no—
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—2841no—
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#95C4×D7114yes—
640#95C4×D7114yescomplemented
641C24—712no—
642C24—712no—
643C24—712no—
644C24—1421no—
645C24—1421no—
646C24—1421no—
647C24—1421no—
648C24—1421no—
649C24—1421no—
650C24—1421no—
651C24—1421no—
652C24—1421no—
653C24—1421no—
654C24—1421no—
655C24—1421no—
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—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—2844no—
698C22×C4—2844no—
699C22×C4—2844no—
700C22×C4—2844no—
701C22×C4—2844no—
702C22×C4—2844no—
703C22×C4—2844no—
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—712no—
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×C4C2×C4×D7112yes—
754C22×C4C2×C4×D7112yes—
755C22×C4C2×C4×D7112yes—
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—44no—
763C4⋊C4—2844no—
764C4⋊C4—2844no—
765C4⋊C4—2844no—
766C22⋊C4—2844no—
767C22⋊C4—2844no—
768C22⋊C4—2844no—
769C22⋊C4—2844no—
770C22⋊C4—2844no—
771C22⋊C4—7116no—
772C42—44no—
773C42—2844no—
774C42—2844no—
775C42—2844no—
776C23—2841no—
777C23—2841no—
778C23—2841no—
779C23—2841no—
780C23—2841no—
781C23—2841no—
782C23—2841no—
783C23—2841no—
784C23—2841no—
785C23—2841no—
786C23—2841no—
787C23—2841no—
788C23—2841no—
789C23—2841no—
790C23—2841no—
791C23—2841no—
792C23—714no—
793C23—1422no—
794C23—1422no—
795C23—1422no—
796C23—1422no—
797C23—1422no—
798C23—1422no—
799C23—1422no—
800C23—1422no—
801C23—1422no—
802C23—1422no—
803C23—1422no—
804C23—1422no—
805C23—1422no—
806C23—1422no—
807C23—1422no—
808C23—1422no—
809C23—1422no—
810C23—1422no—
811C23C22×C4×D7111yescharacteristic
812C23C22×C4×D7111yescharacteristic
813C23C22×C4×D7111yescharacteristic
814C23#1455617311yescharacteristic
815C23#1455617311yescharacteristic
816C23#1455617311yescharacteristic
817C23#1455617311yescharacteristic
818C23#1455617411yescharacteristic
819C23#1455617411yescharacteristic
820C23#1455617411yescharacteristic
821C23#1455617411yescharacteristic
822C23#1455617511yescharacteristic
823C23#1455617511yescharacteristic
824C23#1455617611yescharacteristic
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—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
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—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—28416no—
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—2841no—
894C2×C4—2841no—
895C2×C4—2841no—
896C2×C4—2841no—
897C2×C4—2841no—
898C2×C4—2841no—
899C2×C4—714no—
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×C4C42×D7114yes—
925C22—2842no—
926C22—2842no—
927C22—2842no—
928C22—2842no—
929C22—2842no—
930C22—2842no—
931C22—2842no—
932C22—2842no—
933C22—2842no—
934C22—2842no—
935C22—2842no—
936C22—2842no—
937C22—1424no—
938C22—1424no—
939C22—1424no—
940C22C2×C42×D7111yescharacteristic
941C22#1798647111yescharacteristic
942C22#1798647111yescharacteristic
943C22#1798647111yescharacteristic
944C22#1798647111yescharacteristic
945C22#1798647111yescharacteristic
946C22#1798647211yescharacteristic
947C22#1798647311yescharacteristic
948C22#1798647511yescharacteristic
949C22#1798647811yescharacteristic
950C22#1798647811yescharacteristic
951C22#1798647811yescharacteristic
952C22#1798647911yescharacteristic
953C22#1798647911yescharacteristic
954C22#1798648011yescharacteristic
955C22#1798648011yescharacteristic
956C22#1798648111yescharacteristic
957C22#1798648111yescharacteristic
958C22#1798648111yescharacteristic
959C22#1798673711yescharacteristic
960C22#1798673811yescharacteristic
961C22#1798673911yescharacteristic
962C22#1798674011yescharacteristic
963C22#1798674111yescharacteristic
964C22#1798674411yescharacteristic
965C22#1798674511yescharacteristic
966C22#1798674511yescharacteristic
967C22#1798674511yescharacteristic
968C22#1798674611yescharacteristic
969C22#1798674611yescharacteristic
970C22#1798674811yescharacteristic
971C22#1798675011yescharacteristic
972C22#1798675111yescharacteristic
973C22#1798675311yescharacteristic
974C22#1798675311yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—2842no—
983C4—2842no—
984C4—2842no—
985C4—2842no—
986C4—2842no—
987C4—2842no—
988C4—1424no—
989C2—2844no—
990C2#2259069411yescharacteristic
991C2#2259069911yescharacteristic
992C2#2259070011yescharacteristic
993C2#2259148011yescharacteristic
994C2#2259148711yescharacteristic
995C2#2259148711yescharacteristic
996C2#2259148911yescharacteristic
997C2#2259149611yescharacteristic
998C2#2259149811yescharacteristic
999C2#2259150211yescharacteristic
1000C2#2259150411yescharacteristic
1001C2#2259150911yescharacteristic
1002C2#2259151211yescharacteristic
1003C2#2259153011yescharacteristic
1004C2#2259153111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC71×#1436C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenter#1436D71
hypocenterC71#13831
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
6. #22586574C2semidirect
7. #22586573C2semidirect
8. #22586571C2semidirect
9. #22586569C2semidirect
10. Dic71⋊#95C2semidirect
11. #22586565C2semidirect
12. #22586564C2semidirect
15. C71×#1436C2semidirect
29. #17985889C4semidirect
30. #17985888C4semidirect
31. #17985873C4semidirect
77. C2×Dic71⋊C4C2×C4semidirect
103. C2×C4×Dic71C2×C4semidirect
104. C2×C4×Dic71C2×C4semidirect
117. C71⋊#95C2×C4semidirect
118. C71⋊#95C2×C4semidirect
119. C71⋊#95C2×C4semidirect
129. C2×C4⋊C4×C71C2×C4semidirect
137. #95×C71C2×C4semidirect
217. (C2×D71)⋊C4C42semidirect
511. #1436D71semidirect
518. C71#13831semidirect
590. C2×C4⋊C4C4×D71semidirect
640. #95C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179858892
C2×#179858882
C2×#179858732
#225865782
#225865762
#225865742
#225865732
#225865712
#225865692
Dic71⋊#952
#225865652
#225865642
(C2×D71)⋊#952
C71×#14362
#1383171