Finite Group Databasebeta

← #31918794

Subgroups — #31918794

Order 18176.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985892C211yesmaximal, characteristic
2C2×#17985892C211yesmaximal, characteristic
3C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic71C211yesmaximal, characteristic
5#22586577C211yesmaximal, characteristic
6#22586577C211yesmaximal, characteristic
7#22586574C211yesmaximal, characteristic, complemented
8#22586574C211yesmaximal, characteristic, complemented
9#22586572C211yesmaximal, characteristic, complemented
10#22586572C211yesmaximal, characteristic, complemented
11#22586569C211yesmaximal, characteristic, complemented
12#22586565C211yesmaximal, characteristic, complemented
13#22586563C211yesmaximal, characteristic
14#95×Dic71C211yesmaximal, characteristic, complemented
15C2×#385×C71C211yesmaximal, characteristic
16C22×C4⋊Dic71C2211yescharacteristic
17C22×C4⋊Dic71C2211yescharacteristic
18C22×C22⋊Dic71C2211yescharacteristic
19C22×C22⋊Dic71C2211yescharacteristic
20C22×C22⋊Dic71C2211yescharacteristic
21C22×C22⋊Dic71C2211yescharacteristic
22C22×C4×Dic71C2211yescharacteristic
23C22×C4×Dic71C2211yescharacteristic
24C22×C4×Dic71C2211yescharacteristic
25C22×C4×Dic71C2211yescharacteristic
26C22×C4×Dic71C2211yescharacteristic
27C22×C4×Dic71C2211yescharacteristic
28#17985892C418yescomplemented
29#17985892C418yescomplemented
30C4⋊C4×Dic71—24no—
31C4×C22⋊Dic71—24no—
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
47C2×C71⋊#95C2211yescharacteristic
48C24×C4×C71C2211yescharacteristic
49C22×C4⋊C4×C71C2211yescharacteristic
50C22×C4⋊C4×C71C2211yescharacteristic
51C22×C22⋊C4×C71C2211yescharacteristic
52C22×C22⋊C4×C71C2211yescharacteristic
53#385×C71C418yescomplemented
54C2×#95×C71C2211yescharacteristic
55C2×#95×C71C2211yescharacteristic
56C23×Dic71C2311yescharacteristic
57C23×Dic71C2311yescharacteristic
58C23×Dic71C2311yescharacteristic
59C23×Dic71C2311yescharacteristic
60C23×Dic71C2311yescharacteristic
61C23×Dic71C2311yescharacteristic
62C23×Dic71C2311yescharacteristic
63C23×Dic71C2311yescharacteristic
64C2×C4⋊Dic71—22no—
65C2×C4⋊Dic71—22no—
66C2×C4⋊Dic71—41no—
67C2×C4⋊Dic71—41no—
68C2×C4⋊Dic71C2×C414yescomplemented
69C2×C4⋊Dic71C2×C414yescomplemented
70C2×C22⋊Dic71—22no—
71C2×C22⋊Dic71—22no—
72C2×C22⋊Dic71—22no—
73C2×C22⋊Dic71—22no—
74C2×C22⋊Dic71—41no—
75C2×C22⋊Dic71—41no—
76C2×C22⋊Dic71—41no—
77C2×C22⋊Dic71—41no—
78C2×C22⋊Dic71C2×C414yes—
79C2×C22⋊Dic71C2×C414yes—
80C2×C22⋊Dic71C2×C414yes—
81C2×C22⋊Dic71C2×C414yes—
82C2×C4×Dic71—22no—
83C2×C4×Dic71—22no—
84C2×C4×Dic71—22no—
85C2×C4×Dic71—22no—
86C2×C4×Dic71—22no—
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×Dic71—41no—
97C2×C4×Dic71C2×C414yescomplemented
98C2×C4×Dic71C2×C414yescomplemented
99C2×C4×Dic71D414yes—
100C71⋊#95—22no—
101C71⋊#95—22no—
102C71⋊#95—22no—
103C71⋊#95—22no—
104C71⋊#95—22no—
105C71⋊#95—22no—
106C71⋊#95—41no—
107C71⋊#95—41no—
108C71⋊#95—41no—
109C71⋊#95—41no—
110C71⋊#95—41no—
111C71⋊#95—41no—
112C71⋊#95C2×C414yescomplemented
113C71⋊#95C2×C414yescomplemented
114C71⋊#95C2×C414yescomplemented
115C71⋊#95C2×C414yescomplemented
116C25×C71C2311yescharacteristic
117C23×C4×C71—22no—
118C23×C4×C71—22no—
119C23×C4×C71—41no—
120C23×C4×C71—41no—
121C23×C4×C71—41no—
122C23×C4×C71—41no—
123C23×C4×C71C2×C414yes—
124C23×C4×C71C2311yescharacteristic
125C23×C4×C71C2311yescharacteristic
126C23×C4×C71C2311yescharacteristic
127C23×C4×C71C2311yescharacteristic
128C23×C4×C71C2311yescharacteristic
129C23×C4×C71C2311yescharacteristic
130C2×C4⋊C4×C71—22no—
131C2×C4⋊C4×C71—22no—
132C2×C4⋊C4×C71—41no—
133C2×C4⋊C4×C71—41no—
134C2×C4⋊C4×C71C2×C414yes—
135C2×C4⋊C4×C71C2×C414yes—
136C2×C22⋊C4×C71—41no—
137C2×C22⋊C4×C71—41no—
138C2×C22⋊C4×C71C2×C414yes—
139C2×C22⋊C4×C71C2×C414yes—
140C2×C22⋊C4×C71C2×C414yes—
141C2×C22⋊C4×C71C2×C414yes—
142#95×C71C2×C414yes—
143#95×C71C2×C414yes—
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—21no—
187C22×Dic71—21no—
188C22×Dic71C22×C412yes—
189C22×Dic71C22×C412yes—
190C22×Dic71C22×C412yes—
191C22×Dic71C22×C412yes—
192C22×Dic71C22×C412yes—
193C22×Dic71C22×C412yes—
194C22×Dic71C22×C412yes—
195C22×Dic71C22×C412yes—
196C22×Dic71C2×D412yes—
197C22×Dic71C2×D412yes—
198C22×Dic71#4112yes—
199C22×Dic71#4112yes—
200C4⋊Dic71—28no—
201C4⋊Dic71—44no—
202C22⋊Dic71—28no—
203C22⋊Dic71—28no—
204C22⋊Dic71—44no—
205C22⋊Dic71—44no—
206C4×Dic71—28no—
207C4×Dic71—44no—
208C4×Dic71—44no—
209C4×Dic71—44no—
210C4×Dic71—44no—
211C4×Dic71—44no—
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×C71—21no—
223C24×C71—21no—
224C24×C71C22×C412yes—
225C24×C71C22×C412yes—
226C24×C71C22×C412yes—
227C24×C71C2411yescharacteristic
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—28no—
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×C71C22×C412yes—
272C22×C4×C71C22×C412yes—
273C22×C4×C71C22×C412yes—
274C22×C4×C71C22×C412yes—
275C22×C4×C71C2×D412yes—
276C22×C4×C71#4112yes—
277C4⋊C4×C71—28no—
278C4⋊C4×C71—44no—
279C22⋊C4×C71—44no—
280C22⋊C4×C71C42116yescomplemented
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—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
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×C71—41no—
308C23×C71—41no—
309C23×C71—41no—
310C23×C71—41no—
311C23×C71—41no—
312C23×C71—41no—
313C23×C71—41no—
314C23×C71—41no—
315C23×C71C2×C4214yes—
316C23×C71C23×C411yescharacteristic
317C23×C71C23×C411yescharacteristic
318C23×C71C23×C411yescharacteristic
319C23×C71C22×D411yescharacteristic
320C23×C71C2×#4111yescharacteristic
321C23×C71C2×#4111yescharacteristic
322C23×C71C2×#4111yescharacteristic
323C23×C71H(5,𝔽2)11yescharacteristic
324C23×C71H(5,𝔽2)11yescharacteristic
325C23×C71H(5,𝔽2)11yescharacteristic
326C23×C71H(5,𝔽2)11yescharacteristic
327C23×C71H(5,𝔽2)11yescharacteristic
328C23×C712−1+411yescharacteristic
329C23×C712−1+411yescharacteristic
330C23×C712−1+411yescharacteristic
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—22no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
353C2×C4×C71—22no—
354C2×C4×C71—22no—
355C2×C4×C71—22no—
356C2×C4×C71—22no—
357C2×C4×C71—22no—
358C2×C4×C71—416no—
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×C4×C71C2×C4214yes—
373C2×C4×C71C4×D414yes—
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—22no—
397C2×Dic71—22no—
398C2×Dic71—22no—
399C2×Dic71—22no—
400C2×Dic71—22no—
401C2×Dic71—22no—
402C2×Dic71—22no—
403C2×Dic71—22no—
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—
422C2×Dic71—41no—
423C2×Dic71—41no—
424C2×Dic71—41no—
425C2×Dic71—41no—
426C2×Dic71—41no—
427C2×Dic71—41no—
428C2×Dic71C4×D414yes—
429C2×Dic71C4×D414yes—
430C22×C71—24no—
431C22×C71—24no—
432C22×C71—24no—
433C22×C71—42no—
434C22×C71—42no—
435C22×C71—42no—
436C22×C71—42no—
437C22×C71—42no—
438C22×C71—42no—
439C22×C71—42no—
440C22×C71—42no—
441C22×C71—42no—
442C22×C71—42no—
443C22×C71—42no—
444C22×C71—42no—
445C22×C71C22×C4211yescharacteristic
446C22×C71C2×C4×D411yescharacteristic
447C22×C71C2×C4×D411yescharacteristic
448C22×C71C2×C4×D411yescharacteristic
449C22×C71C4×#4111yescharacteristic
450C22×C71C4×#4111yescharacteristic
451C22×C71C4×#4111yescharacteristic
452C22×C71#51811yescharacteristic
453C22×C71#51811yescharacteristic
454C22×C71#51811yescharacteristic
455C22×C71#51811yescharacteristic
456C22×C71#51911yescharacteristic
457C22×C71#52011yescharacteristic
458C22×C71#52011yescharacteristic
459C22×C71#52011yescharacteristic
460C22×C71#52011yescharacteristic
461C22×C71#52011yescharacteristic
462C22×C71#52011yescharacteristic
463C22×C71#52011yescharacteristic
464C22×C71#53411yescharacteristic
465C22×C71#53511yescharacteristic
466C22×C71#53611yescharacteristic
467C22×C71#53711yescharacteristic
468C22×C71#53811yescharacteristic
469C22×C71#53811yescharacteristic
470C22×C71#53811yescharacteristic
471C22×C71#53911yescharacteristic
472C22×C71#53911yescharacteristic
473C22×C71#53911yescharacteristic
474C22×C71#54011yescharacteristic
475C22×C71#54111yescharacteristic
476C22×C71#54211yescharacteristic
477C22×C71#54211yescharacteristic
478C22×C71#54211yescharacteristic
479C22×C71#54211yescharacteristic
480C4×C71—24no—
481C4×C71—24no—
482C4×C71—24no—
483C4×C71—42no—
484C4×C71—42no—
485C4×C71—42no—
486Dic71—24no—
487Dic71—24no—
488Dic71—42no—
489Dic71—42no—
490Dic71—42no—
491Dic71—42no—
492Dic71—42no—
493Dic71—42no—
494#13789—711nomaximal, Sylow
495C2×C71—44no—
496C2×C71C42×D411yescharacteristic
497C2×C71#227411yescharacteristic
498C2×C71#227511yescharacteristic
499C2×C71#232111yescharacteristic
500C2×C71#232211yescharacteristic
501C2×C71#232311yescharacteristic
502C2×C71#232411yescharacteristic
503C2×C71#232511yescharacteristic
504C2×C71#232611yescharacteristic
505C2×C71#233211yescharacteristic
506C2×C71#233411yescharacteristic
507C2×C71#233411yescharacteristic
508C2×C71#233511yescharacteristic
509C2×C71#233511yescharacteristic
510C2×C71#233711yescharacteristic
511C2×#388—711no—
512C2×#388—711no—
513C2×#385D7111yescharacteristic
514C2×C4×C4⋊C4—711no—
515C2×C4×C22⋊C4—711no—
516#1437—711no—
517#1437—711no—
518#1436—711no—
519#1436—711no—
520#1436—711no—
521#1436—711no—
522C4⋊#95—711no—
523#1434—711no—
524C22⋊#95—711no—
525C4×#95—711no—
526C71#1378911yescharacteristic, complemented, Sylow
527C24×C4C2×D7111yescharacteristic
528C22×C4⋊C4—711no—
529C22×C4⋊C4—711no—
530C22×C4⋊C4C2×D7111yescharacteristic
531C22×C4⋊C4C2×D7111yescharacteristic
532C22×C22⋊C4—711no—
533C22×C22⋊C4—711no—
534C22×C22⋊C4—711no—
535C22×C22⋊C4—711no—
536C22×C22⋊C4C2×D7111yescharacteristic
537C22×C22⋊C4C2×D7111yescharacteristic
538C22×C42—711no—
539C22×C42—711no—
540C22×C42—711no—
541C22×C42—711no—
542C22×C42—711no—
543C22×C42—711no—
544#388—718no—
545#388—718no—
546#385Dic7118yescomplemented
547C4×C4⋊C4—1424no—
548C4×C22⋊C4—1424no—
549C2×#95—711no—
550C2×#95—711no—
551C2×#95—711no—
552C2×#95—711no—
553C2×#95—711no—
554C2×#95—711no—
555C2×#95—711no—
556C2×#95—711no—
557C2×#95—711no—
558C2×#95—711no—
559C2×#95—711no—
560C2×#95—711no—
561C2×#95—711no—
562C2×#95—711no—
563C2×#95—711no—
564C2×#95—711no—
565C2×#95C2×D7111yescharacteristic
566C2×#95C2×D7111yescharacteristic
567C25C22×D7111yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—711no—
575C23×C4—711no—
576C23×C4—711no—
577C23×C4—711no—
578C23×C4—711no—
579C23×C4—711no—
580C23×C4—711no—
581C23×C4—711no—
582C23×C4C2×Dic7114yes—
583C23×C4C22×D7111yescharacteristic
584C23×C4C22×D7111yescharacteristic
585C23×C4C22×D7111yescharacteristic
586C23×C4C22×D7111yescharacteristic
587C23×C4C22×D7111yescharacteristic
588C23×C4C22×D7111yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—2841no—
594C2×C4⋊C4—2841no—
595C2×C4⋊C4—714no—
596C2×C4⋊C4—714no—
597C2×C4⋊C4—1422no—
598C2×C4⋊C4—1422no—
599C2×C4⋊C4C2×Dic7114yes—
600C2×C4⋊C4C2×Dic7114yes—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—2841no—
604C2×C22⋊C4—2841no—
605C2×C22⋊C4—2841no—
606C2×C22⋊C4—2841no—
607C2×C22⋊C4—714no—
608C2×C22⋊C4—714no—
609C2×C22⋊C4—714no—
610C2×C22⋊C4—714no—
611C2×C22⋊C4—1422no—
612C2×C22⋊C4—1422no—
613C2×C22⋊C4—1422no—
614C2×C22⋊C4—1422no—
615C2×C22⋊C4C4×D7114yes—
616C2×C22⋊C4C4×D7114yes—
617C2×C22⋊C4C2×Dic7114yes—
618C2×C22⋊C4C2×Dic7114yes—
619C2×C42—2841no—
620C2×C42—2841no—
621C2×C42—2841no—
622C2×C42—2841no—
623C2×C42—2841no—
624C2×C42—2841no—
625C2×C42—2841no—
626C2×C42—2841no—
627C2×C42—2841no—
628C2×C42—2841no—
629C2×C42—714no—
630C2×C42—714no—
631C2×C42—714no—
632C2×C42—1422no—
633C2×C42—1422no—
634C2×C42—1422no—
635C2×C42—1422no—
636C2×C42—1422no—
637#95—2841no—
638#95—2841no—
639#95—2841no—
640#95—2841no—
641#95—2841no—
642#95—2841no—
643#95—714no—
644#95—714no—
645#95—714no—
646#95—714no—
647#95—1422no—
648#95—1422no—
649#95—1422no—
650#95—1422no—
651#95—1422no—
652#95—1422no—
653#95C2×Dic7114yes—
654#95C2×Dic7114yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×C4×D7112yes—
668C24C2×C4×D7112yes—
669C24C22×Dic7112yes—
670C24C23×D7111yescharacteristic
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—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—28no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—712no—
709C22×C4—712no—
710C22×C4—712no—
711C22×C4—712no—
712C22×C4—712no—
713C22×C4—712no—
714C22×C4—712no—
715C22×C4—712no—
716C22×C4—712no—
717C22×C4—712no—
718C22×C4—712no—
719C22×C4—712no—
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×C4—1421no—
757C22×C4—1421no—
758C22×C4—1421no—
759C22×C4—1421no—
760C22×C4—1421no—
761C22×C4—1421no—
762C22×C4—1421no—
763C22×C4—1421no—
764C22×C4C2×C4×D7112yes—
765C22×C4C2×C4×D7112yes—
766C22×C4C2×C4×D7112yes—
767C22×C4C2×C4×D7112yes—
768C22×C4C22×Dic7112yes—
769C22×C4C22×Dic7112yes—
770C22×C4C22×Dic7112yes—
771C22×C4C22×Dic7112yes—
772C22×C4C22×Dic7112yes—
773C22×C4C22×Dic7112yes—
774C22×C4D4×D7112yes—
775C22×C4#1176586412yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—2844no—
779C4⋊C4—1428no—
780C22⋊C4—44no—
781C22⋊C4—2844no—
782C22⋊C4—2844no—
783C22⋊C4—1428no—
784C22⋊C4—1428no—
785C22⋊C4C4×Dic71116yescomplemented
786C42—2844no—
787C42—2844no—
788C42—2844no—
789C42—2844no—
790C42—2844no—
791C42—1428no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4×Dic7114yes—
827C23C22×C4×D7111yescharacteristic
828C23C22×C4×D7111yescharacteristic
829C23C23×Dic7111yescharacteristic
830C23C2×D4×D7111yescharacteristic
831C23#41×D7111yescharacteristic
832C23#41×D7111yescharacteristic
833C23C2×#1176586411yescharacteristic
834C23#1455617311yescharacteristic
835C23#1455617311yescharacteristic
836C23#1455617311yescharacteristic
837C23#1455617311yescharacteristic
838C23#1455617411yescharacteristic
839C23#1455617511yescharacteristic
840C23#1455617611yescharacteristic
841C23#1455617611yescharacteristic
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—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—416no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
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—2841no—
900C2×C4—2841no—
901C2×C4—2841no—
902C2×C4—2841no—
903C2×C4—2841no—
904C2×C4—2841no—
905C2×C4—2841no—
906C2×C4—714no—
907C2×C4—714no—
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—
925C2×C4—1422no—
926C2×C4—1422no—
927C2×C4—1422no—
928C2×C4—1422no—
929C2×C4—1422no—
930C2×C4—1422no—
931C2×C4—1422no—
932C2×C4—1422no—
933C2×C4—1422no—
934C2×C4—1422no—
935C2×C4—1422no—
936C2×C4—1422no—
937C2×C4—1422no—
938C2×C4C2×C4×Dic7114yes—
939C2×C4C2×C4×Dic7114yes—
940C2×C4D4×Dic7114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4×Dic7111yescharacteristic
957C22C4×D4×D7111yescharacteristic
958C22C4×D4×D7111yescharacteristic
959C22C2×D4×Dic7111yescharacteristic
960C22C4×#1176586411yescharacteristic
961C22C4×#1176586411yescharacteristic
962C22#41×Dic7111yescharacteristic
963C22#1798647111yescharacteristic
964C22#1798647111yescharacteristic
965C22#1798647411yescharacteristic
966C22#1798647411yescharacteristic
967C22#1798647711yescharacteristic
968C22#1798647811yescharacteristic
969C22#1798647811yescharacteristic
970C22#1798648011yescharacteristic
971C22#1798648011yescharacteristic
972C22#1798648011yescharacteristic
973C22#1798648011yescharacteristic
974C22#1798648211yescharacteristic
975C22#1798655911yescharacteristic
976C22#1798656411yescharacteristic
977C22#1798657211yescharacteristic
978C22#1798657911yescharacteristic
979C22#1798658411yescharacteristic
980C22#1798658411yescharacteristic
981C22#1798658511yescharacteristic
982C22#1798659211yescharacteristic
983C22#1798659511yescharacteristic
984C22#1798659511yescharacteristic
985C22#1798660111yescharacteristic
986C22#1798660911yescharacteristic
987C22#1798661711yescharacteristic
988C22#1798661911yescharacteristic
989C22#1798661911yescharacteristic
990C22#1798662211yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—2842no—
998C4—2842no—
999C4—2842no—
1000C4—2842no—
1001C4—2842no—
1002C4—2842no—
1003C4—1424no—
1004C4—1424no—
1005C2—44no—
1006C2C4×D4×Dic7111yescharacteristic
1007C2#2259069711yescharacteristic
1008C2#2259070111yescharacteristic
1009C2#2259100111yescharacteristic
1010C2#2259100711yescharacteristic
1011C2#2259102411yescharacteristic
1012C2#2259103211yescharacteristic
1013C2#2259103711yescharacteristic
1014C2#2259104611yescharacteristic
1015C2#2259109811yescharacteristic
1016C2#2259111011yescharacteristic
1017C2#2259111611yescharacteristic
1018C2#2259112511yescharacteristic
1019C2#2259113411yescharacteristic
1020C2#2259115411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC2×#385×C71C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#385D71
hypocenterC71#13789
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic71C2semidirect
7. #22586574C2semidirect
8. #22586574C2semidirect
9. #22586572C2semidirect
10. #22586572C2semidirect
11. #22586569C2semidirect
12. #22586565C2semidirect
14. #95×Dic71C2semidirect
28. #17985892C4semidirect
29. #17985892C4semidirect
53. #385×C71C4semidirect
68. C2×C4⋊Dic71C2×C4semidirect
69. C2×C4⋊Dic71C2×C4semidirect
97. C2×C4×Dic71C2×C4semidirect
98. C2×C4×Dic71C2×C4semidirect
112. C71⋊#95C2×C4semidirect
113. C71⋊#95C2×C4semidirect
114. C71⋊#95C2×C4semidirect
115. C71⋊#95C2×C4semidirect
280. C22⋊C4×C71C42semidirect
526. C71#13789semidirect
546. #385Dic71semidirect
785. 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×C4⋊C4×Dic712
C2×C4×C22⋊Dic712
#225865772
#225865742
#225865722
#225865692
#225865652
#225865632
#95×Dic712
C2×#385×C712
#1378971