Finite Group Databasebeta

← #32007258

Subgroups — #32007258

Order 18176.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22590723C211yesmaximal, characteristic, complemented
2C2×#17985859C211yesmaximal, characteristic, complemented
3#22589326C212yesmaximal, complemented
4#22589177C212yesmaximal, complemented
5#22588794C214yesmaximal, complemented
6#22588328C214yesmaximal, complemented
7C2×#525×C71C211yesmaximal, characteristic
8C2×#14556087—21no—
9C22×C4⋊Dic71—21no—
10C22×C22⋊Dic71C2212yes—
11C2×#14556043C2218yes—
12#17985862—21no—
13#17985859—21no—
14#17985859—21no—
15#17985859—21no—
16#17985859C2212yes—
17#17985859C2212yes—
18#17985859C2212yes—
19#17985855C2212yes—
20C4×C22⋊Dic71—21no—
21C4×C22⋊Dic71C2212yes—
22C2×C71⋊#95—21no—
23#17985766C2218yes—
24C22×#41×C71C411yescharacteristic, complemented
25C24×C4×C71C2211yescharacteristic
26#525×C71—21no—
27#525×C71—21no—
28#525×C71—21no—
29#525×C71—21no—
30#525×C71—21no—
31#525×C71—21no—
32#525×C71—21no—
33#525×C71—21no—
34C2×#123×C71C412yescomplemented
35C2×C22⋊Q8×C71C411yescharacteristic, complemented
36C2×C22⋊Q8×C71C2211yescharacteristic
37C2×#121×C71C411yescharacteristic, complemented
38C2×#121×C71C2211yescharacteristic
39C2×#120×C71C2212yes—
40C2×C4×D4×C71C412yescomplemented
41C2×C4×D4×C71C2212yes—
42C2×#117×C71C411yescharacteristic, complemented
43C23×Dic71—22no—
44#14556087—44no—
45C2×C4⋊Dic71—22no—
46C2×C4⋊Dic71—22no—
47C2×C4⋊Dic71—22no—
48C2×C4⋊Dic71—44no—
49C2×C22⋊Dic71—22no—
50C2×C22⋊Dic71—22no—
51C2×C22⋊Dic71—22no—
52C2×C22⋊Dic71—44no—
53C2×C22⋊Dic71C2314yes—
54C2×C22⋊Dic71C2314yes—
55C2×C4×Dic71—22no—
56#14556043—48no—
57C71⋊#95—22no—
58C71⋊#95—22no—
59C71⋊#95—22no—
60C71⋊#95—22no—
61C25×C71C2311yescharacteristic
62C2×#41×C71—21no—
63C2×#41×C71—21no—
64C2×#41×C71—21no—
65C2×#41×C71—21no—
66C2×#41×C71—44no—
67C22×Q8×C71C2×C411yescharacteristic, complemented
68C22×D4×C71C2×C412yes—
69C22×D4×C71C2×C412yes—
70C22×D4×C71C2×C411yescharacteristic, complemented
71C22×D4×C71C2312yes—
72C23×C4×C71—44no—
73C23×C4×C71C2×C411yescharacteristic
74C23×C4×C71C2×C411yescharacteristic
75C23×C4×C71C2×C411yescharacteristic
76C23×C4×C71C2×C411yescharacteristic
77C23×C4×C71C2×C412yescomplemented
78C23×C4×C71D411yescharacteristic
79C23×C4×C71D411yescharacteristic
80C23×C4×C71D411yescharacteristic
81C23×C4×C71D411yescharacteristic
82C23×C4×C71D411yescharacteristic
83C23×C4×C71D411yescharacteristic
84C23×C4×C71D411yescharacteristic
85C23×C4×C71D411yescharacteristic
86C23×C4×C71C2311yescharacteristic
87C23×C4×C71C2311yescharacteristic
88#123×C71—22no—
89#123×C71—22no—
90#123×C71—22no—
91#123×C71—22no—
92C22⋊Q8×C71—21no—
93C22⋊Q8×C71—21no—
94C22⋊Q8×C71—21no—
95C22⋊Q8×C71—21no—
96C22⋊Q8×C71—21no—
97C22⋊Q8×C71—21no—
98C22⋊Q8×C71—21no—
99C22⋊Q8×C71—21no—
100#121×C71—21no—
101#121×C71—21no—
102#121×C71—21no—
103#121×C71—21no—
104#121×C71—21no—
105#121×C71—21no—
106#121×C71—21no—
107#121×C71—21no—
108#120×C71—22no—
109#120×C71—22no—
110#120×C71—22no—
111#120×C71—22no—
112C4×D4×C71—22no—
113C4×D4×C71—22no—
114C4×D4×C71—22no—
115C4×D4×C71—22no—
116C4×D4×C71—22no—
117C4×D4×C71—22no—
118C4×D4×C71—22no—
119C4×D4×C71—22no—
120#117×C71—21no—
121#117×C71—21no—
122#117×C71—21no—
123#117×C71—21no—
124C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
125C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
126C2×C4⋊C4×C71C2×C412yescomplemented
127C2×C4⋊C4×C71C2×C412yescomplemented
128C2×C22⋊C4×C71C2×C412yes—
129C2×C22⋊C4×C71C2×C412yes—
130C2×C22⋊C4×C71C2×C412yescomplemented
131C2×C22⋊C4×C71C2×C412yescomplemented
132C2×C22⋊C4×C71C2312yes—
133C2×C42×C71C2×C412yescomplemented
134C22×Dic71—24no—
135C22×Dic71—24no—
136C22×Dic71—44no—
137C22×Dic71—44no—
138C22×Dic71—44no—
139C4⋊Dic71—44no—
140C4⋊Dic71—44no—
141C4⋊Dic71—44no—
142C22⋊Dic71—24no—
143C22⋊Dic71—28no—
144C22⋊Dic71—24no—
145C22⋊Dic71—44no—
146C22⋊Dic71—44no—
147C22⋊Dic71—44no—
148C4×Dic71—44no—
149C24×C71—22no—
150C24×C71—22no—
151C24×C71—42no—
152C24×C71—42no—
153C24×C71C22×C411yescharacteristic
154C24×C71C22×C411yescharacteristic
155C24×C71C22×C412yes—
156C24×C71C2×D411yescharacteristic
157C24×C71C2×D411yescharacteristic
158C24×C71C2×D411yescharacteristic
159C24×C71C2×D411yescharacteristic
160C24×C71C2411yescharacteristic
161#41×C71—44no—
162#41×C71—44no—
163#41×C71—44no—
164#41×C71—44no—
165C2×Q8×C71—21no—
166C2×Q8×C71—21no—
167C2×Q8×C71—42no—
168C2×D4×C71—22no—
169C2×D4×C71—22no—
170C2×D4×C71—22no—
171C2×D4×C71—22no—
172C2×D4×C71—22no—
173C2×D4×C71—22no—
174C2×D4×C71—24no—
175C2×D4×C71—24no—
176C2×D4×C71—21no—
177C2×D4×C71—21no—
178C2×D4×C71—42no—
179C2×D4×C71—44no—
180C2×D4×C71—44no—
181C22×C4×C71—24no—
182C22×C4×C71—24no—
183C22×C4×C71—24no—
184C22×C4×C71—22no—
185C22×C4×C71—22no—
186C22×C4×C71—42no—
187C22×C4×C71—42no—
188C22×C4×C71—42no—
189C22×C4×C71—42no—
190C22×C4×C71—42no—
191C22×C4×C71—42no—
192C22×C4×C71—42no—
193C22×C4×C71—42no—
194C22×C4×C71—42no—
195C22×C4×C71—42no—
196C22×C4×C71—42no—
197C22×C4×C71—44no—
198C22×C4×C71C22⋊C411yescharacteristic
199C22×C4×C71C22⋊C411yescharacteristic
200C22×C4×C71C22⋊C411yescharacteristic
201C22×C4×C71C22⋊C411yescharacteristic
202C22×C4×C71C22⋊C411yescharacteristic
203C22×C4×C71C22⋊C411yescharacteristic
204C22×C4×C71C22⋊C411yescharacteristic
205C22×C4×C71C22⋊C411yescharacteristic
206C22×C4×C71C22⋊C411yescharacteristic
207C22×C4×C71C22⋊C411yescharacteristic
208C22×C4×C71C22⋊C411yescharacteristic
209C22×C4×C71C22⋊C411yescharacteristic
210C22×C4×C71C22⋊C411yescharacteristic
211C22×C4×C71C22⋊C411yescharacteristic
212C22×C4×C71C22⋊C411yescharacteristic
213C22×C4×C71C22⋊C411yescharacteristic
214C22×C4×C71C22×C412yes—
215C22×C4×C71C22×C411yescharacteristic
216C22×C4×C71C22×C411yescharacteristic
217C22×C4×C71C22×C412yes—
218C22×C4×C71C22×C412yes—
219C22×C4×C71C22×C411yescharacteristic
220C22×C4×C71C22×C411yescharacteristic
221C22×C4×C71C2×D411yescharacteristic
222C22×C4×C71C2×D411yescharacteristic
223C22×C4×C71C2×D411yescharacteristic
224C22×C4×C71C2×D411yescharacteristic
225C22×C4×C71C2×D411yescharacteristic
226C22×C4×C71C2×D411yescharacteristic
227C22×C4×C71C2×D411yescharacteristic
228C22×C4×C71C2×D411yescharacteristic
229C4⋊C4×C71—21no—
230C4⋊C4×C71—21no—
231C4⋊C4×C71—21no—
232C4⋊C4×C71—21no—
233C4⋊C4×C71—22no—
234C4⋊C4×C71—22no—
235C4⋊C4×C71—22no—
236C4⋊C4×C71—22no—
237C22⋊C4×C71—22no—
238C22⋊C4×C71—22no—
239C22⋊C4×C71—22no—
240C22⋊C4×C71—22no—
241C22⋊C4×C71—22no—
242C22⋊C4×C71—22no—
243C22⋊C4×C71—22no—
244C22⋊C4×C71—22no—
245C22⋊C4×C71—22no—
246C22⋊C4×C71—22no—
247C42×C71—22no—
248C42×C71—22no—
249C23×C71—21no—
250C23×C71—21no—
251C23×C71—22no—
252C23×C71—22no—
253C23×C71—22no—
254C23×C71—22no—
255C23×C71—21no—
256C23×C71—21no—
257C23×C71—22no—
258C23×C71—22no—
259C23×C71—22no—
260C23×C71—22no—
261C23×C71—22no—
262C23×C71—22no—
263C23×C71—22no—
264C23×C71—24no—
265C23×C71—41no—
266C23×C71—41no—
267C23×C71—41no—
268C23×C71—41no—
269C23×C71—41no—
270C23×C71—41no—
271C23×C71—41no—
272C23×C71—41no—
273C23×C71—48no—
274C23×C71—48no—
275C23×C71—42no—
276C23×C71—42no—
277C23×C71C2×C22⋊C411yescharacteristic
278C23×C71C2×C22⋊C411yescharacteristic
279C23×C71C2×C22⋊C411yescharacteristic
280C23×C71C2×C22⋊C411yescharacteristic
281C23×C71C23×C411yescharacteristic
282C23×C71C22×D411yescharacteristic
283C23×C71C22×D411yescharacteristic
284C23×C71H(5,𝔽2)12yes—
285C23×C712−1+412yes—
286Q8×C71—42no—
287Q8×C71—42no—
288D4×C71—42no—
289D4×C71—44no—
290D4×C71—44no—
291D4×C71—42no—
292D4×C71—42no—
293D4×C71—44no—
294D4×C71—44no—
295D4×C71—44no—
296D4×C71—42no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—24no—
316C2×C4×C71—41no—
317C2×C4×C71—41no—
318C2×C4×C71—41no—
319C2×C4×C71—41no—
320C2×C4×C71—41no—
321C2×C4×C71—41no—
322C2×C4×C71—41no—
323C2×C4×C71—41no—
324C2×C4×C71—41no—
325C2×C4×C71—41no—
326C2×C4×C71—41no—
327C2×C4×C71—41no—
328C2×C4×C71—44no—
329C2×C4×C71—44no—
330C2×C4×C71—42no—
331C2×C4×C71—42no—
332C2×C4×C71#9914yescomplemented
333C2×C4×C71C2×C22⋊C411yescharacteristic
334C2×C4×C71C2×C22⋊C411yescharacteristic
335C2×C4×C71C2×C22⋊C411yescharacteristic
336C2×C4×C71C2×C22⋊C411yescharacteristic
337C2×C4×C71C2×C22⋊C411yescharacteristic
338C2×C4×C71C2×C22⋊C411yescharacteristic
339C2×C4×C71C2×C22⋊C411yescharacteristic
340C2×C4×C71C2×C22⋊C411yescharacteristic
341C2×Dic71—44no—
342C2×Dic71—44no—
343C2×Dic71—44no—
344C2×Dic71—44no—
345C2×Dic71—44no—
346C2×Dic71—44no—
347C2×Dic71—88no—
348C22×C71—24no—
349C22×C71—24no—
350C22×C71—21no—
351C22×C71—21no—
352C22×C71—21no—
353C22×C71—21no—
354C22×C71—21no—
355C22×C71—21no—
356C22×C71—21no—
357C22×C71—21no—
358C22×C71—21no—
359C22×C71—21no—
360C22×C71—21no—
361C22×C71—21no—
362C22×C71—21no—
363C22×C71—21no—
364C22×C71—21no—
365C22×C71—21no—
366C22×C71—42no—
367C22×C71—42no—
368C22×C71—44no—
369C22×C71—44no—
370C22×C71—44no—
371C22×C71—44no—
372C22×C71—42no—
373C22×C71—42no—
374C22×C71—42no—
375C22×C71—42no—
376C22×C71—42no—
377C22×C71—84no—
378C22×C71C2×#9912yes—
379C22×C71#41012yes—
380C22×C71C22×C22⋊C411yescharacteristic
381C22×C71#52012yes—
382C22×C71#53511yescharacteristic
383C22×C71#53611yescharacteristic
384C22×C71#53712yes—
385C4×C71—21no—
386C4×C71—21no—
387C4×C71—21no—
388C4×C71—21no—
389C4×C71—21no—
390C4×C71—21no—
391C4×C71—42no—
392C4×C71—42no—
393C4×C71—42no—
394C4×C71C2×#9912yes—
395C4×C71C2×#9912yes—
396Dic71—84no—
397Dic71—84no—
398#21874—711nomaximal, Sylow
399C2×C71—21no—
400C2×C71—22no—
401C2×C71—21no—
402C2×C71—22no—
403C2×C71—22no—
404C2×C71—22no—
405C2×C71—41no—
406C2×C71—41no—
407C2×C71—82no—
408C2×C71#231111yescharacteristic
409C2×C71C22×#9911yescharacteristic
410C2×C71C2×#41011yescharacteristic
411C2×#525D7111yescharacteristic
412#2280—711no—
413C2×#380—711no—
414#1996—712no—
415#1964—712no—
416#1898—714no—
417#1799—714no—
418C71#2187411yescharacteristic, complemented, Sylow
419C22×#41Dic7111yescharacteristic, complemented
420C24×C4C2×D7111yescharacteristic
421#525—21no—
422#525—21no—
423#525—21no—
424#525—21no—
425#525—21no—
426#525—21no—
427#525—21no—
428#525—21no—
429C2×#123Dic7112yescomplemented
430C2×C22⋊Q8Dic7111yescharacteristic, complemented
431C2×C22⋊Q8C2×D7111yescharacteristic
432C2×#121Dic7111yescharacteristic, complemented
433C2×#121C2×D7111yescharacteristic
434C2×#120C2×D7112yes—
435C2×C4×D4Dic7112yescomplemented
436C2×C4×D4C2×D7112yes—
437C2×#117—1421no—
438C2×#117Dic7111yescharacteristic, complemented
439C22×C4⋊C4—1421no—
440C22×C22⋊C4—712no—
441C2×#99—718no—
442#381—1421no—
443#380—712no—
444#380—712no—
445#380—712no—
446#380—1421no—
447#380—1421no—
448#380—1421no—
449#379—712no—
450C4×C22⋊C4—712no—
451C4×C22⋊C4—1421no—
452C2×#95—1421no—
453#342—718no—
454C25C22×D7111yescharacteristic
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—44no—
460C22×Q8C2×Dic7111yescharacteristic, complemented
461C22×D4C2×Dic7112yes—
462C22×D4C2×Dic7112yes—
463C22×D4C2×Dic7111yescharacteristic, complemented
464C22×D4C22×D7112yes—
465C23×C4—44no—
466C23×C4—1422no—
467C23×C4C2×Dic7111yescharacteristic
468C23×C4C2×Dic7111yescharacteristic
469C23×C4C2×Dic7111yescharacteristic
470C23×C4C2×Dic7111yescharacteristic
471C23×C4C2×Dic7112yescomplemented
472C23×C4C22⋊D7111yescharacteristic
473C23×C4C22⋊D7111yescharacteristic
474C23×C4C22⋊D7111yescharacteristic
475C23×C4C22⋊D7111yescharacteristic
476C23×C4C22⋊D7111yescharacteristic
477C23×C4C22⋊D7111yescharacteristic
478C23×C4C22⋊D7111yescharacteristic
479C23×C4C22⋊D7111yescharacteristic
480C23×C4C22×D7111yescharacteristic
481C23×C4C22×D7111yescharacteristic
482#123—22no—
483#123—22no—
484#123—22no—
485#123—22no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#120—22no—
503#120—22no—
504#120—22no—
505#120—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117—2844no—
519C2×C4⋊C4—2844no—
520C2×C4⋊C4—1422no—
521C2×C4⋊C4—1422no—
522C2×C4⋊C4—1422no—
523C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
524C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
525C2×C4⋊C4C2×Dic7112yescomplemented
526C2×C4⋊C4C2×Dic7112yescomplemented
527C2×C22⋊C4—2844no—
528C2×C22⋊C4—714no—
529C2×C22⋊C4—714no—
530C2×C22⋊C4—1422no—
531C2×C22⋊C4—1422no—
532C2×C22⋊C4—1422no—
533C2×C22⋊C4C2×Dic7112yes—
534C2×C22⋊C4C2×Dic7112yes—
535C2×C22⋊C4C2×Dic7112yescomplemented
536C2×C22⋊C4C2×Dic7112yescomplemented
537C2×C22⋊C4C22×D7112yes—
538C2×C42—1422no—
539C2×C42C2×Dic7112yescomplemented
540#99—2848no—
541#95—1422no—
542#95—1422no—
543#95—1422no—
544#95—1422no—
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24C22×Dic7111yescharacteristic
550C24C22×Dic7111yescharacteristic
551C24C22×Dic7112yes—
552C24C2×C22⋊D7111yescharacteristic
553C24C2×C22⋊D7111yescharacteristic
554C24C2×C22⋊D7111yescharacteristic
555C24C2×C22⋊D7111yescharacteristic
556C24C23×D7111yescharacteristic
557#41—44no—
558#41—44no—
559#41—44no—
560#41—44no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—44no—
576C2×D4—44no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—44no—
594C22×C4—2844no—
595C22×C4—2844no—
596C22×C4—2844no—
597C22×C4—1424no—
598C22×C4—1424no—
599C22×C4C22⋊Dic7111yescharacteristic
600C22×C4C22⋊Dic7111yescharacteristic
601C22×C4C22⋊Dic7111yescharacteristic
602C22×C4C22⋊Dic7111yescharacteristic
603C22×C4C22⋊Dic7111yescharacteristic
604C22×C4C22⋊Dic7111yescharacteristic
605C22×C4C22⋊Dic7111yescharacteristic
606C22×C4C22⋊Dic7111yescharacteristic
607C22×C4C22⋊Dic7111yescharacteristic
608C22×C4C22⋊Dic7111yescharacteristic
609C22×C4C22⋊Dic7111yescharacteristic
610C22×C4C22⋊Dic7111yescharacteristic
611C22×C4C22⋊Dic7111yescharacteristic
612C22×C4C22⋊Dic7111yescharacteristic
613C22×C4C22⋊Dic7111yescharacteristic
614C22×C4C22⋊Dic7111yescharacteristic
615C22×C4C22×Dic7112yes—
616C22×C4C22×Dic7111yescharacteristic
617C22×C4C22×Dic7111yescharacteristic
618C22×C4C22×Dic7112yes—
619C22×C4C22×Dic7112yes—
620C22×C4C22×Dic7111yescharacteristic
621C22×C4C22×Dic7111yescharacteristic
622C22×C4C2×C22⋊D7111yescharacteristic
623C22×C4C2×C22⋊D7111yescharacteristic
624C22×C4C2×C22⋊D7111yescharacteristic
625C22×C4C2×C22⋊D7111yescharacteristic
626C22×C4C2×C22⋊D7111yescharacteristic
627C22×C4C2×C22⋊D7111yescharacteristic
628C22×C4C2×C22⋊D7111yescharacteristic
629C22×C4C2×C22⋊D7111yescharacteristic
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—2844no—
639C4⋊C4—2844no—
640C4⋊C4—2844no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—2844no—
652C22⋊C4—2844no—
653C22⋊C4—2844no—
654C22⋊C4—1424no—
655C22⋊C4—1428no—
656C22⋊C4—1424no—
657C42—22no—
658C42—22no—
659C42—2844no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—48no—
685C23—48no—
686C23—42no—
687C23—42no—
688C23C2×C22⋊Dic7111yescharacteristic
689C23C2×C22⋊Dic7111yescharacteristic
690C23C2×C22⋊Dic7111yescharacteristic
691C23C2×C22⋊Dic7111yescharacteristic
692C23C23×Dic7111yescharacteristic
693C23C22×C22⋊D7111yescharacteristic
694C23C22×C22⋊D7111yescharacteristic
695C23#1455617412yes—
696C23#1455617512yes—
697Q8—42no—
698Q8—42no—
699D4—42no—
700D4—44no—
701D4—44no—
702D4—42no—
703D4—42no—
704D4—44no—
705D4—44no—
706D4—44no—
707D4—42no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—2844no—
744C2×C4—2844no—
745C2×C4—2844no—
746C2×C4—2844no—
747C2×C4—2844no—
748C2×C4—2844no—
749C2×C4—5688no—
750C2×C4#1455604314yescomplemented
751C2×C4C2×C22⋊Dic7111yescharacteristic
752C2×C4C2×C22⋊Dic7111yescharacteristic
753C2×C4C2×C22⋊Dic7111yescharacteristic
754C2×C4C2×C22⋊Dic7111yescharacteristic
755C2×C4C2×C22⋊Dic7111yescharacteristic
756C2×C4C2×C22⋊Dic7111yescharacteristic
757C2×C4C2×C22⋊Dic7111yescharacteristic
758C2×C4C2×C22⋊Dic7111yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22C2×#1455604312yes—
790C22#1798597312yes—
791C22C22×C22⋊Dic7111yescharacteristic
792C22#1798648212yes—
793C22#1798656311yescharacteristic
794C22#1798657011yescharacteristic
795C22#1798657712yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—5684no—
806C4—5684no—
807C4C2×#1455604312yes—
808C4C2×#1455604312yes—
809C2—21no—
810C2—22no—
811C2—21no—
812C2—22no—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2#2259093211yescharacteristic
819C2C22×#1455604311yescharacteristic
820C2C2×#1798597311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic71
commutatorC23×C71C23×C4
FrattiniC24C23×D71
Fitting, prime radicalC2×#525×C71C2
socleC22×C71C22×C22⋊C4
cosocleC24×C71C24
hypercenterC2×#525D71
hypocenterC71#21874
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #22590723C2semidirect
2. C2×#17985859C2semidirect
3. #22589326C2semidirect
4. #22589177C2semidirect
5. #22588794C2semidirect
6. #22588328C2semidirect
24. C22×#41×C71C4semidirect
34. C2×#123×C71C4semidirect
35. C2×C22⋊Q8×C71C4semidirect
37. C2×#121×C71C4semidirect
40. C2×C4×D4×C71C4semidirect
42. C2×#117×C71C4semidirect
67. C22×Q8×C71C2×C4semidirect
70. C22×D4×C71C2×C4semidirect
77. C23×C4×C71C2×C4semidirect
124. C2×C4⋊C4×C71C2×C4semidirect
125. C2×C4⋊C4×C71C2×C4semidirect
126. C2×C4⋊C4×C71C2×C4semidirect
127. C2×C4⋊C4×C71C2×C4semidirect
130. C2×C22⋊C4×C71C2×C4semidirect
131. C2×C22⋊C4×C71C2×C4semidirect
133. C2×C42×C71C2×C4semidirect
332. C2×C4×C71#99semidirect
418. C71#21874semidirect
419. C22×#41Dic71semidirect
429. C2×#123Dic71semidirect
430. C2×C22⋊Q8Dic71semidirect
432. C2×#121Dic71semidirect
435. C2×C4×D4Dic71semidirect
438. C2×#117Dic71semidirect
460. C22×Q8C2×Dic71semidirect
463. C22×D4C2×Dic71semidirect
471. C23×C4C2×Dic71semidirect
523. C2×C4⋊C4C2×Dic71semidirect
524. C2×C4⋊C4C2×Dic71semidirect
525. C2×C4⋊C4C2×Dic71semidirect
526. C2×C4⋊C4C2×Dic71semidirect
535. C2×C22⋊C4C2×Dic71semidirect
536. C2×C22⋊C4C2×Dic71semidirect
539. C2×C42C2×Dic71semidirect
750. C2×C4#14556043semidirect

Maximal subgroups

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

subgroupindex
#225907232
C2×#179858592
#225893262
#225891772
#225887942
#225883282
C2×#525×C712
#2187471