Finite Group Databasebeta

← #31919087

Subgroups — #31919087

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×#17985892C211yesmaximal, characteristic
2C2×#17985874C211yesmaximal, characteristic
3#22586577C211yesmaximal, characteristic
4#22586577C211yesmaximal, characteristic
5#22586574C211yesmaximal, characteristic, complemented
6#22586574C211yesmaximal, characteristic, complemented
7#22586574C211yesmaximal, characteristic, complemented
8#22586572C211yesmaximal, characteristic, complemented
9#22586570C211yesmaximal, characteristic, complemented
10#22586569C211yesmaximal, characteristic, complemented
11#22586567C211yesmaximal, characteristic, complemented
12#22586565C211yesmaximal, characteristic, complemented
13#22586562C211yesmaximal, characteristic
14#22586562C211yesmaximal, characteristic
15C2×#388×C71C211yesmaximal, characteristic
16C24×Dic71C2211yescharacteristic
17C22×C4⋊Dic71C2211yescharacteristic
18C22×C4⋊Dic71C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20C22×C22⋊Dic71C2211yescharacteristic
21C22×C22⋊Dic71C2211yescharacteristic
22C22×C22⋊Dic71C2211yescharacteristic
23C22×C4×Dic71C2211yescharacteristic
24C22×C4×Dic71C2211yescharacteristic
25C22×C4×Dic71C2211yescharacteristic
26#17985892C418yescomplemented
27#17985874C418yescomplemented
28C2×C71⋊#95C2211yescharacteristic
29C2×C71⋊#95C2211yescharacteristic
30C2×C71⋊#95C2211yescharacteristic
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
46C22×C4⋊C4×C71C2211yescharacteristic
47C22×C22⋊C4×C71C2211yescharacteristic
48C22×C22⋊C4×C71C2211yescharacteristic
49C22×C22⋊C4×C71C2211yescharacteristic
50C22×C42×C71C2211yescharacteristic
51#388×C71C418yescomplemented
52C2×#95×C71C2211yescharacteristic
53C2×#95×C71C2211yescharacteristic
54C23×Dic71—41no—
55C23×Dic71—41no—
56C23×Dic71—41no—
57C23×Dic71—41no—
58C23×Dic71—41no—
59C23×Dic71—41no—
60C23×Dic71C2×C414yes—
61C23×Dic71C2311yescharacteristic
62C23×Dic71C2311yescharacteristic
63C23×Dic71C2311yescharacteristic
64C23×Dic71C2311yescharacteristic
65C23×Dic71C2311yescharacteristic
66C23×Dic71C2311yescharacteristic
67C23×Dic71C2311yescharacteristic
68C23×Dic71C2311yescharacteristic
69C2×C4⋊Dic71—41no—
70C2×C4⋊Dic71—41no—
71C2×C4⋊Dic71—41no—
72C2×C4⋊Dic71—41no—
73C2×C4⋊Dic71—41no—
74C2×C4⋊Dic71—41no—
75C2×C4⋊Dic71C2×C414yes—
76C2×C4⋊Dic71C2×C414yes—
77C2×C4⋊Dic71C2×C414yescomplemented
78C2×C22⋊Dic71—41no—
79C2×C22⋊Dic71—41no—
80C2×C22⋊Dic71—41no—
81C2×C22⋊Dic71—41no—
82C2×C22⋊Dic71—41no—
83C2×C22⋊Dic71—41no—
84C2×C22⋊Dic71C2×C414yes—
85C2×C22⋊Dic71C2×C414yes—
86C2×C22⋊Dic71C2×C414yes—
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×Dic71C2×C414yescomplemented
96C71⋊#95—41no—
97C71⋊#95—41no—
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⋊#95—41no—
109C71⋊#95—41no—
110C71⋊#95C2×C414yes—
111C71⋊#95C2×C414yes—
112C71⋊#95C2×C414yescomplemented
113C71⋊#95C2×C414yescomplemented
114C25×C71C2311yescharacteristic
115C23×C4×C71C2311yescharacteristic
116C23×C4×C71C2311yescharacteristic
117C23×C4×C71C2311yescharacteristic
118C23×C4×C71C2311yescharacteristic
119C23×C4×C71C2311yescharacteristic
120C23×C4×C71C2311yescharacteristic
121C2×C4⋊C4×C71—41no—
122C2×C4⋊C4×C71—41no—
123C2×C4⋊C4×C71C2×C414yescomplemented
124C2×C22⋊C4×C71—41no—
125C2×C22⋊C4×C71—41no—
126C2×C22⋊C4×C71—41no—
127C2×C22⋊C4×C71—41no—
128C2×C22⋊C4×C71C2×C414yes—
129C2×C22⋊C4×C71C2×C414yes—
130C2×C22⋊C4×C71C2×C414yes—
131C2×C22⋊C4×C71C2×C414yes—
132C2×C22⋊C4×C71C2×C414yes—
133C2×C42×C71—41no—
134C2×C42×C71—41no—
135C2×C42×C71C2×C414yescomplemented
136#95×C71C2×C414yescomplemented
137#95×C71C2×C414yescomplemented
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×Dic71—21no—
183C22×Dic71—21no—
184C22×Dic71—21no—
185C22×Dic71—21no—
186C22×Dic71—44no—
187C22×Dic71—44no—
188C22×Dic71—44no—
189C22×Dic71—44no—
190C22×Dic71—44no—
191C22×Dic71—44no—
192C22×Dic71—44no—
193C22×Dic71C22×C412yes—
194C22×Dic71C22×C412yes—
195C22×Dic71C22×C412yes—
196C22×Dic71C22×C412yes—
197C22×Dic71C22×C412yes—
198C22×Dic71C22×C412yes—
199C22×Dic71C22×C412yes—
200C22×Dic71C22×C412yes—
201C4⋊Dic71—44no—
202C4⋊Dic71—44no—
203C4⋊Dic71—44no—
204C22⋊Dic71—44no—
205C22⋊Dic71—44no—
206C22⋊Dic71—44no—
207C4×Dic71—44no—
208C4×Dic71—44no—
209C4×Dic71—44no—
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×C71—21no—
219C24×C71—21no—
220C24×C71—21no—
221C24×C71—21no—
222C24×C71C22×C412yes—
223C24×C71C22×C412yes—
224C24×C71C22×C412yes—
225C24×C71C2411yescharacteristic
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×C71C22×C412yes—
259C22×C4×C71C22×C412yes—
260C22×C4×C71C22×C412yes—
261C22×C4×C71C22×C412yes—
262C22×C4×C71C22×C412yes—
263C22×C4×C71C22×C412yes—
264C22×C4×C71C22×C412yes—
265C22×C4×C71C22×C412yes—
266C22×C4×C71C22×C412yes—
267C22×C4×C71C22×C412yes—
268C4⋊C4×C71—44no—
269C22⋊C4×C71—44no—
270C22⋊C4×C71—44no—
271C22⋊C4×C71C42116yescomplemented
272C42×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—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×C71C2×C4214yes—
364C2×C4×C71C2×C4214yes—
365C2×Dic71—22no—
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—416no—
390C2×Dic71—41no—
391C2×Dic71—41no—
392C2×Dic71—41no—
393C2×Dic71—41no—
394C2×Dic71—41no—
395C2×Dic71—41no—
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×Dic71—41no—
421C2×Dic71—41no—
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—24no—
473C4×C71—24no—
474C4×C71—42no—
475C4×C71—42no—
476C4×C71—42no—
477C4×C71—42no—
478Dic71—42no—
479Dic71—42no—
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×#388D7111yescharacteristic
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⋊#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⋊C4C2×D7111yescharacteristic
528C22×C22⋊C4C2×D7111yescharacteristic
529C22×C22⋊C4C2×D7111yescharacteristic
530C22×C42—711no—
531C22×C42—711no—
532C22×C42—711no—
533C22×C42C2×D7111yescharacteristic
534#388—718no—
535#388Dic7118yescomplemented
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×#95—711no—
554C2×#95—711no—
555C2×#95C2×D7111yescharacteristic
556C2×#95C2×D7111yescharacteristic
557C25C22×D7111yescharacteristic
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×C4—711no—
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⋊C4C2×Dic7114yescomplemented
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⋊C4C4×D7114yes—
605C2×C22⋊C4C4×D7114yes—
606C2×C22⋊C4C2×Dic7114yes—
607C2×C22⋊C4C2×Dic7114yes—
608C2×C22⋊C4C2×Dic7114yes—
609C2×C42—41no—
610C2×C42—41no—
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×C42C2×Dic7114yescomplemented
621#95—2841no—
622#95—2841no—
623#95—2841no—
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#95C2×Dic7114yescomplemented
640#95C2×Dic7114yescomplemented
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—
655C24C22×Dic7112yes—
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—2844no—
690C22×C4—2844no—
691C22×C4—2844no—
692C22×C4—2844no—
693C22×C4—2844no—
694C22×C4—2844no—
695C22×C4—2844no—
696C22×C4—712no—
697C22×C4—712no—
698C22×C4—712no—
699C22×C4—712no—
700C22×C4—712no—
701C22×C4—712no—
702C22×C4—712no—
703C22×C4—712no—
704C22×C4—1421no—
705C22×C4—1421no—
706C22×C4—1421no—
707C22×C4—1421no—
708C22×C4—1421no—
709C22×C4—1421no—
710C22×C4—1421no—
711C22×C4—1421no—
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×C4C2×C4×D7112yes—
753C22×C4C2×C4×D7112yes—
754C22×C4C2×C4×D7112yes—
755C22×C4C2×C4×D7112yes—
756C22×C4C22×Dic7112yes—
757C22×C4C22×Dic7112yes—
758C22×C4C22×Dic7112yes—
759C22×C4C22×Dic7112yes—
760C22×C4C22×Dic7112yes—
761C22×C4C22×Dic7112yes—
762C4⋊C4—44no—
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⋊C4C4×Dic71116yescomplemented
772C42—44no—
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—
810C23C2×C4×Dic7114yes—
811C23C22×C4×D7111yescharacteristic
812C23C22×C4×D7111yescharacteristic
813C23C23×Dic7111yescharacteristic
814C23#1455617311yescharacteristic
815C23#1455617311yescharacteristic
816C23#1455617311yescharacteristic
817C23#1455617311yescharacteristic
818C23#1455617411yescharacteristic
819C23#1455617411yescharacteristic
820C23#1455617411yescharacteristic
821C23#1455617411yescharacteristic
822C23#1455617511yescharacteristic
823C23#1455617511yescharacteristic
824C23#1455617511yescharacteristic
825C23#1455617511yescharacteristic
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—28416no—
867C2×C4—2841no—
868C2×C4—2841no—
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—2841no—
894C2×C4—2841no—
895C2×C4—2841no—
896C2×C4—2841no—
897C2×C4—2841no—
898C2×C4—2841no—
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×C4C2×C4×Dic7114yes—
924C2×C4C2×C4×Dic7114yes—
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—
940C22C22×C4×Dic7111yescharacteristic
941C22#1798647111yescharacteristic
942C22#1798647111yescharacteristic
943C22#1798647111yescharacteristic
944C22#1798647111yescharacteristic
945C22#1798647311yescharacteristic
946C22#1798647411yescharacteristic
947C22#1798647411yescharacteristic
948C22#1798647611yescharacteristic
949C22#1798647811yescharacteristic
950C22#1798647811yescharacteristic
951C22#1798647811yescharacteristic
952C22#1798647811yescharacteristic
953C22#1798647911yescharacteristic
954C22#1798647911yescharacteristic
955C22#1798648211yescharacteristic
956C22#1798648211yescharacteristic
957C22#1798648211yescharacteristic
958C22#1798648211yescharacteristic
959C22#1798673711yescharacteristic
960C22#1798673711yescharacteristic
961C22#1798673911yescharacteristic
962C22#1798674011yescharacteristic
963C22#1798674111yescharacteristic
964C22#1798674311yescharacteristic
965C22#1798674311yescharacteristic
966C22#1798674411yescharacteristic
967C22#1798674411yescharacteristic
968C22#1798674611yescharacteristic
969C22#1798674611yescharacteristic
970C22#1798674911yescharacteristic
971C22#1798675111yescharacteristic
972C22#1798675111yescharacteristic
973C22#1798675111yescharacteristic
974C22#1798675211yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—2842no—
982C4—2842no—
983C4—2842no—
984C4—2842no—
985C4—2842no—
986C4—2842no—
987C4—2842no—
988C4—2842no—
989C2—44no—
990C2#2259069611yescharacteristic
991C2#2259070111yescharacteristic
992C2#2259070111yescharacteristic
993C2#2259148011yescharacteristic
994C2#2259148211yescharacteristic
995C2#2259148611yescharacteristic
996C2#2259148811yescharacteristic
997C2#2259149311yescharacteristic
998C2#2259149711yescharacteristic
999C2#2259150011yescharacteristic
1000C2#2259150711yescharacteristic
1001C2#2259150911yescharacteristic
1002C2#2259151411yescharacteristic
1003C2#2259152711yescharacteristic
1004C2#2259153211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC2×#388×C71C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#388D71
hypocenterC71#13831
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
5. #22586574C2semidirect
6. #22586574C2semidirect
7. #22586574C2semidirect
8. #22586572C2semidirect
9. #22586570C2semidirect
10. #22586569C2semidirect
11. #22586567C2semidirect
12. #22586565C2semidirect
26. #17985892C4semidirect
27. #17985874C4semidirect
51. #388×C71C4semidirect
77. C2×C4⋊Dic71C2×C4semidirect
95. C2×C4×Dic71C2×C4semidirect
112. C71⋊#95C2×C4semidirect
113. C71⋊#95C2×C4semidirect
123. C2×C4⋊C4×C71C2×C4semidirect
135. C2×C42×C71C2×C4semidirect
136. #95×C71C2×C4semidirect
137. #95×C71C2×C4semidirect
271. C22⋊C4×C71C42semidirect
518. C71#13831semidirect
535. #388Dic71semidirect
590. C2×C4⋊C4C2×Dic71semidirect
620. C2×C42C2×Dic71semidirect
639. #95C2×Dic71semidirect
640. #95C2×Dic71semidirect
771. C22⋊C4C4×Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179858922
C2×#179858742
#225865772
#225865742
#225865722
#225865702
#225865692
#225865672
#225865652
#225865622
C2×#388×C712
#1383171