Finite Group Databasebeta

← #31964810

Subgroups — #31964810

Order 18176.

1470 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊(C71⋊C8)C211yesmaximal, characteristic, complemented
2#22590723C211yesmaximal, characteristic, complemented
3#22586912C212yesmaximal, complemented
4#22586908C212yesmaximal, complemented
5#22586896C214yesmaximal, complemented
6#22586831C214yesmaximal, complemented
7C2×#525×C71C211yesmaximal, characteristic
8C23×C71⋊C8—21no—
9C2×#14556087—21no—
10C2×C22⋊(C71⋊C8)—21no—
11C2×C22⋊(C71⋊C8)—21no—
12C2×C22⋊(C71⋊C8)—21no—
13C2×C22⋊(C71⋊C8)C2212yes—
14C2×C22⋊(C71⋊C8)C2212yescomplemented
15C2×C22⋊(C71⋊C8)C2212yescomplemented
16#17985862C2212yescomplemented
17#17985859—21no—
18#17985859C2212yes—
19#17985855—21no—
20C4×C22⋊Dic71—21no—
21C4×C22⋊Dic71C2212yescomplemented
22#17985736C2218yescomplemented
23#17985733C2218yescomplemented
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×C71C412yescomplemented
31#525×C71C412yescomplemented
32#525×C71C2212yes—
33#525×C71C2212yes—
34C2×#123×C71—21no—
35C2×C22⋊Q8×C71C411yescharacteristic, complemented
36C2×C22⋊Q8×C71C2211yescharacteristic
37C2×#121×C71C411yescharacteristic, complemented
38C2×#121×C71C2211yescharacteristic
39C2×#120×C71—21no—
40C2×C4×D4×C71—21no—
41C2×C4×D4×C71—21no—
42C2×#117×C71C411yescharacteristic, complemented
43C22×C71⋊C8—22no—
44C22×C71⋊C8—22no—
45C22×C71⋊C8—22no—
46C22×C71⋊C8—44no—
47#14556087—44no—
48C2×C4⋊Dic71—22no—
49C2×C22⋊Dic71—22no—
50C2×C22⋊Dic71—22no—
51C2×C22⋊Dic71—22no—
52C2×C4×Dic71—22no—
53C22⋊(C71⋊C8)—22no—
54C22⋊(C71⋊C8)—22no—
55C22⋊(C71⋊C8)—22no—
56C22⋊(C71⋊C8)C2314yes—
57C71⋊#95—22no—
58C71⋊#95C2314yes—
59C25×C71D411yescharacteristic
60C2×#41×C71—21no—
61C2×#41×C71—21no—
62C2×#41×C71—44no—
63C2×#41×C71C2×C412yes—
64C2×#41×C71C2×C412yes—
65C22×Q8×C71C2×C411yescharacteristic
66C22×D4×C71—21no—
67C22×D4×C71—21no—
68C22×D4×C71—21no—
69C22×D4×C71C2×C411yescharacteristic
70C23×C4×C71—21no—
71C23×C4×C71—44no—
72C23×C4×C71C2×C411yescharacteristic
73C23×C4×C71C2×C411yescharacteristic
74C23×C4×C71C2×C411yescharacteristic
75C23×C4×C71C2×C411yescharacteristic
76C23×C4×C71D411yescharacteristic
77C23×C4×C71D411yescharacteristic
78C23×C4×C71D411yescharacteristic
79C23×C4×C71D411yescharacteristic
80C23×C4×C71D411yescharacteristic
81C23×C4×C71D411yescharacteristic
82C23×C4×C71D411yescharacteristic
83C23×C4×C71C2311yescharacteristic
84C23×C4×C71C2311yescharacteristic
85C23×C4×C71C2311yescharacteristic
86#123×C71—22no—
87#123×C71—22no—
88#123×C71—22no—
89#123×C71—22no—
90C22⋊Q8×C71—21no—
91C22⋊Q8×C71—21no—
92C22⋊Q8×C71—21no—
93C22⋊Q8×C71—21no—
94C22⋊Q8×C71C2×C412yes—
95C22⋊Q8×C71C2×C412yes—
96C22⋊Q8×C71C2×C412yes—
97C22⋊Q8×C71C2312yes—
98#121×C71—21no—
99#121×C71—21no—
100#121×C71—21no—
101#121×C71—21no—
102#121×C71C2×C412yes—
103#121×C71C2×C412yes—
104#121×C71C2×C412yes—
105#121×C71C2312yes—
106#120×C71—22no—
107#120×C71—22no—
108#120×C71—22no—
109#120×C71—22no—
110C4×D4×C71—22no—
111C4×D4×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—
118#117×C71—21no—
119#117×C71—21no—
120#117×C71C2×C412yes—
121#117×C71C2×C412yes—
122C2×C4⋊C4×C71—21no—
123C2×C4⋊C4×C71—21no—
124C2×C4⋊C4×C71C2×C411yescharacteristic
125C2×C4⋊C4×C71C2×C411yescharacteristic
126C2×C22⋊C4×C71—21no—
127C2×C22⋊C4×C71—21no—
128C2×C22⋊C4×C71—21no—
129C2×C22⋊C4×C71—21no—
130C2×C22⋊C4×C71—21no—
131C2×C42×C71—21no—
132C22×Dic71—24no—
133C2×C71⋊C8—24no—
134C2×C71⋊C8—44no—
135C2×C71⋊C8—44no—
136C2×C71⋊C8—44no—
137C4⋊Dic71—44no—
138C22⋊Dic71—44no—
139C22⋊Dic71—44no—
140C22⋊Dic71—44no—
141C4×Dic71—44no—
142C24×C71—24no—
143C24×C71—21no—
144C24×C71—42no—
145C24×C71—42no—
146C24×C71C22⋊C411yescharacteristic
147C24×C71C22⋊C411yescharacteristic
148C24×C71C22⋊C411yescharacteristic
149C24×C71C22⋊C411yescharacteristic
150C24×C71C2×D411yescharacteristic
151C24×C71C2×D411yescharacteristic
152C24×C71C2×D411yescharacteristic
153#41×C71—44no—
154#41×C71—44no—
155#41×C71—44no—
156#41×C71—44no—
157C2×Q8×C71—21no—
158C2×Q8×C71—42no—
159C2×Q8×C71C22×C412yes—
160C2×D4×C71—22no—
161C2×D4×C71—22no—
162C2×D4×C71—22no—
163C2×D4×C71—22no—
164C2×D4×C71—22no—
165C2×D4×C71—22no—
166C2×D4×C71—21no—
167C2×D4×C71—42no—
168C2×D4×C71—44no—
169C2×D4×C71—44no—
170C2×D4×C71—44no—
171C2×D4×C71C22×C412yes—
172C22×C4×C71—24no—
173C22×C4×C71—24no—
174C22×C4×C71—24no—
175C22×C4×C71—21no—
176C22×C4×C71—21no—
177C22×C4×C71—21no—
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71—42no—
181C22×C4×C71—42no—
182C22×C4×C71—42no—
183C22×C4×C71—42no—
184C22×C4×C71—42no—
185C22×C4×C71—42no—
186C22×C4×C71—42no—
187C22×C4×C71—42no—
188C22×C4×C71—42no—
189C22×C4×C71—42no—
190C22×C4×C71—42no—
191C22×C4×C71—44no—
192C22×C4×C71C22⋊C411yescharacteristic
193C22×C4×C71C22⋊C411yescharacteristic
194C22×C4×C71C22⋊C411yescharacteristic
195C22×C4×C71C22⋊C411yescharacteristic
196C22×C4×C71C22⋊C411yescharacteristic
197C22×C4×C71C22⋊C411yescharacteristic
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×C71C2×D411yescharacteristic
211C22×C4×C71C2×D411yescharacteristic
212C22×C4×C71C2×D411yescharacteristic
213C22×C4×C71C2×D411yescharacteristic
214C22×C4×C71C2×D411yescharacteristic
215C22×C4×C71C2×D411yescharacteristic
216C22×C4×C71C2×D411yescharacteristic
217C22×C4×C71C2×D411yescharacteristic
218C22×C4×C71C2×D411yescharacteristic
219C22×C4×C71C2411yescharacteristic
220C4⋊C4×C71—22no—
221C4⋊C4×C71—22no—
222C4⋊C4×C71—22no—
223C4⋊C4×C71—21no—
224C4⋊C4×C71—21no—
225C4⋊C4×C71—22no—
226C4⋊C4×C71C22×C412yes—
227C4⋊C4×C71C22×C412yes—
228C22⋊C4×C71—22no—
229C22⋊C4×C71—22no—
230C22⋊C4×C71—22no—
231C22⋊C4×C71—22no—
232C22⋊C4×C71—22no—
233C22⋊C4×C71—22no—
234C22⋊C4×C71—22no—
235C22⋊C4×C71—22no—
236C22⋊C4×C71—22no—
237C22⋊C4×C71—22no—
238C42×C71—22no—
239C42×C71—22no—
240C23×C71—22no—
241C23×C71—22no—
242C23×C71—22no—
243C23×C71—22no—
244C23×C71—22no—
245C23×C71—22no—
246C23×C71—22no—
247C23×C71—22no—
248C23×C71—22no—
249C23×C71—22no—
250C23×C71—22no—
251C23×C71—22no—
252C23×C71—22no—
253C23×C71—41no—
254C23×C71—41no—
255C23×C71—41no—
256C23×C71—41no—
257C23×C71—41no—
258C23×C71—41no—
259C23×C71—41no—
260C23×C71—41no—
261C23×C71—416no—
262C23×C71—42no—
263C23×C71—42no—
264C23×C71—42no—
265C23×C71C2×C22⋊C411yescharacteristic
266C23×C71C2×C22⋊C411yescharacteristic
267C23×C71C2×C22⋊C411yescharacteristic
268C23×C71C2×C22⋊C411yescharacteristic
269C23×C71C2×C22⋊C411yescharacteristic
270C23×C71C2×C22⋊C411yescharacteristic
271C23×C71#13514yes—
272C23×C71C22×D411yescharacteristic
273Q8×C71—42no—
274Q8×C71—42no—
275D4×C71—42no—
276D4×C71—44no—
277D4×C71—44no—
278D4×C71—44no—
279D4×C71—44no—
280D4×C71—44no—
281D4×C71—44no—
282D4×C71—42no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
303C2×C4×C71—41no—
304C2×C4×C71—41no—
305C2×C4×C71—41no—
306C2×C4×C71—41no—
307C2×C4×C71—41no—
308C2×C4×C71—41no—
309C2×C4×C71—41no—
310C2×C4×C71—41no—
311C2×C4×C71—41no—
312C2×C4×C71—41no—
313C2×C4×C71—44no—
314C2×C4×C71—42no—
315C2×C4×C71—42no—
316C2×C4×C71—42no—
317C2×C4×C71—44no—
318C2×C4×C71#9914yes—
319C2×C4×C71C2×C22⋊C411yescharacteristic
320C2×C4×C71C2×C22⋊C411yescharacteristic
321C2×C4×C71C2×C22⋊C411yescharacteristic
322C2×C4×C71C2×C22⋊C411yescharacteristic
323C2×C4×C71C2×C22⋊C411yescharacteristic
324C2×C4×C71C2×C22⋊C411yescharacteristic
325C2×C4×C71C23×C411yescharacteristic
326C2×C4×C71C22×D411yescharacteristic
327C2×Dic71—44no—
328C2×Dic71—44no—
329C2×Dic71—44no—
330C71⋊C8—44no—
331C22×C71—28no—
332C22×C71—21no—
333C22×C71—21no—
334C22×C71—21no—
335C22×C71—21no—
336C22×C71—21no—
337C22×C71—21no—
338C22×C71—21no—
339C22×C71—21no—
340C22×C71—21no—
341C22×C71—21no—
342C22×C71—21no—
343C22×C71—21no—
344C22×C71—21no—
345C22×C71—21no—
346C22×C71—21no—
347C22×C71—21no—
348C22×C71—44no—
349C22×C71—44no—
350C22×C71—44no—
351C22×C71—44no—
352C22×C71—44no—
353C22×C71—44no—
354C22×C71—42no—
355C22×C71—42no—
356C22×C71—42no—
357C22×C71—84no—
358C22×C71C2×#9912yes—
359C22×C71#41612yes—
360C22×C71#41612yes—
361C22×C71#42112yes—
362C22×C71C22×C22⋊C411yescharacteristic
363C22×C71C2×#13512yes—
364C4×C71—21no—
365C4×C71—21no—
366C4×C71—21no—
367C4×C71—21no—
368C4×C71—21no—
369C4×C71—21no—
370C4×C71—42no—
371C4×C71—42no—
372C4×C71—42no—
373C4×C71C2×#9912yes—
374C4×C71C2×#9912yes—
375Dic71—84no—
376#17572—711nomaximal, Sylow
377C2×C71—22no—
378C2×C71—22no—
379C2×C71—22no—
380C2×C71—22no—
381C2×C71—22no—
382C2×C71—41no—
383C2×C71—41no—
384C2×C71—82no—
385C2×C71C22×#9911yescharacteristic
386C2×C71C2×#41611yescharacteristic
387C2×C71C2×#42111yescharacteristic
388C2×#525D7111yescharacteristic
389C22×C22⋊C8—711no—
390#2280—711no—
391#1520—712no—
392#1519—712no—
393#1516—714no—
394#1501—714no—
395C71#1757211yescharacteristic, complemented, Sylow
396C22×#41Dic7111yescharacteristic, complemented
397C24×C4C2×D7111yescharacteristic
398C23×C8—1421no—
399#525—21no—
400#525—21no—
401#525—21no—
402#525—21no—
403#525Dic7112yescomplemented
404#525Dic7112yescomplemented
405#525C2×D7112yes—
406#525C2×D7112yes—
407C2×#123—21no—
408C2×C22⋊Q8Dic7111yescharacteristic, complemented
409C2×C22⋊Q8C2×D7111yescharacteristic
410C2×#121Dic7111yescharacteristic, complemented
411C2×#121C2×D7111yescharacteristic
412C2×#120—21no—
413C2×C4×D4—21no—
414C2×C4×D4—21no—
415C2×#117—1421no—
416C2×#117Dic7111yescharacteristic, complemented
417C2×C22⋊C8—712no—
418C2×C22⋊C8—712no—
419C2×C22⋊C8—712no—
420C2×C22⋊C8—1421no—
421C2×C22⋊C8—1421no—
422C2×C22⋊C8—1421no—
423#381—712no—
424#380—712no—
425#380—1421no—
426#379—1421no—
427C4×C22⋊C4—712no—
428C4×C22⋊C4—1421no—
429#328—718no—
430#327—718no—
431C25C22⋊D7111yescharacteristic
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—44no—
435C2×#41C2×Dic7112yes—
436C2×#41C2×Dic7112yes—
437C22×Q8C2×Dic7111yescharacteristic
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C2×Dic7111yescharacteristic
442C23×C4—21no—
443C23×C4—44no—
444C23×C4C2×Dic7111yescharacteristic
445C23×C4C2×Dic7111yescharacteristic
446C23×C4C2×Dic7111yescharacteristic
447C23×C4C2×Dic7111yescharacteristic
448C23×C4C22⋊D7111yescharacteristic
449C23×C4C22⋊D7111yescharacteristic
450C23×C4C22⋊D7111yescharacteristic
451C23×C4C22⋊D7111yescharacteristic
452C23×C4C22⋊D7111yescharacteristic
453C23×C4C22⋊D7111yescharacteristic
454C23×C4C22⋊D7111yescharacteristic
455C23×C4C22×D7111yescharacteristic
456C23×C4C22×D7111yescharacteristic
457C23×C4C22×D7111yescharacteristic
458C22×C8—2844no—
459C22×C8—1422no—
460C22×C8—1422no—
461C22×C8—1422no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—22no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8C2×Dic7112yes—
471C22⋊Q8C2×Dic7112yes—
472C22⋊Q8C2×Dic7112yes—
473C22⋊Q8C22×D7112yes—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121C2×Dic7112yes—
479#121C2×Dic7112yes—
480#121C2×Dic7112yes—
481#121C22×D7112yes—
482#120—22no—
483#120—22no—
484#120—22no—
485#120—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494#117—21no—
495#117—21no—
496#117—2844no—
497#117C2×Dic7112yes—
498#117C2×Dic7112yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—1422no—
502C2×C4⋊C4C2×Dic7111yescharacteristic
503C2×C4⋊C4C2×Dic7111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—1422no—
510C2×C22⋊C4—1422no—
511C2×C22⋊C4—1422no—
512C2×C42—21no—
513C2×C42—1422no—
514C22⋊C8—714no—
515C22⋊C8—1422no—
516C22⋊C8—1422no—
517C22⋊C8—1422no—
518#95—714no—
519#95—1422no—
520C24—24no—
521C24—21no—
522C24—42no—
523C24—42no—
524C24C22⋊Dic7111yescharacteristic
525C24C22⋊Dic7111yescharacteristic
526C24C22⋊Dic7111yescharacteristic
527C24C22⋊Dic7111yescharacteristic
528C24C2×C22⋊D7111yescharacteristic
529C24C2×C22⋊D7111yescharacteristic
530C24C2×C22⋊D7111yescharacteristic
531#41—44no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—42no—
537C2×Q8C22×Dic7112yes—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4C22×Dic7112yes—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—44no—
570C22×C4—1424no—
571C22×C4C22⋊Dic7111yescharacteristic
572C22×C4C22⋊Dic7111yescharacteristic
573C22×C4C22⋊Dic7111yescharacteristic
574C22×C4C22⋊Dic7111yescharacteristic
575C22×C4C22⋊Dic7111yescharacteristic
576C22×C4C22⋊Dic7111yescharacteristic
577C22×C4C22⋊Dic7111yescharacteristic
578C22×C4C22⋊Dic7111yescharacteristic
579C22×C4C22⋊Dic7111yescharacteristic
580C22×C4C22⋊Dic7111yescharacteristic
581C22×C4C22⋊Dic7111yescharacteristic
582C22×C4C22⋊Dic7111yescharacteristic
583C22×C4C22×Dic7111yescharacteristic
584C22×C4C22×Dic7111yescharacteristic
585C22×C4C22×Dic7111yescharacteristic
586C22×C4C22×Dic7111yescharacteristic
587C22×C4C22×Dic7111yescharacteristic
588C22×C4C22×Dic7111yescharacteristic
589C22×C4C2×C22⋊D7111yescharacteristic
590C22×C4C2×C22⋊D7111yescharacteristic
591C22×C4C2×C22⋊D7111yescharacteristic
592C22×C4C2×C22⋊D7111yescharacteristic
593C22×C4C2×C22⋊D7111yescharacteristic
594C22×C4C2×C22⋊D7111yescharacteristic
595C22×C4C2×C22⋊D7111yescharacteristic
596C22×C4C2×C22⋊D7111yescharacteristic
597C22×C4C2×C22⋊D7111yescharacteristic
598C22×C4C23×D7111yescharacteristic
599C2×C8—2844no—
600C2×C8—2844no—
601C2×C8—2844no—
602C2×C8—1424no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—2844no—
610C4⋊C4C22×Dic7112yes—
611C4⋊C4C22×Dic7112yes—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—2844no—
623C22⋊C4—2844no—
624C22⋊C4—2844no—
625C42—22no—
626C42—22no—
627C42—2844no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—416no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23C2×C22⋊Dic7111yescharacteristic
654C23C2×C22⋊Dic7111yescharacteristic
655C23C2×C22⋊Dic7111yescharacteristic
656C23C2×C22⋊Dic7111yescharacteristic
657C23C2×C22⋊Dic7111yescharacteristic
658C23C2×C22⋊Dic7111yescharacteristic
659C23#1455614814yes—
660C23C22×C22⋊D7111yescharacteristic
661Q8—42no—
662Q8—42no—
663D4—42no—
664D4—44no—
665D4—44no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—42no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—2844no—
707C2×C4—2844no—
708C2×C4—2844no—
709C2×C4#1455604314yes—
710C2×C4C2×C22⋊Dic7111yescharacteristic
711C2×C4C2×C22⋊Dic7111yescharacteristic
712C2×C4C2×C22⋊Dic7111yescharacteristic
713C2×C4C2×C22⋊Dic7111yescharacteristic
714C2×C4C2×C22⋊Dic7111yescharacteristic
715C2×C4C2×C22⋊Dic7111yescharacteristic
716C2×C4C23×Dic7111yescharacteristic
717C2×C4C22×C22⋊D7111yescharacteristic
718C8—2844no—
719C22—28no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22C2×#1455604312yes—
747C22#1798599512yes—
748C22#1798599512yes—
749C22#1798601612yes—
750C22C22×C22⋊Dic7111yescharacteristic
751C22C2×#1455614812yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—5684no—
762C4C2×#1455604312yes—
763C4C2×#1455604312yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—82no—
772C2C22×#1455604311yescharacteristic
773C2C2×#1798599511yescharacteristic
774C2C2×#1798601611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC2×#525×C71C2
socleC22×C71C22×C22⋊C4
cosocleC22×C4×C71C24
hypercenterC2×#525D71
hypocenterC71#17572
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊(C71⋊C8)C2semidirect
2. #22590723C2semidirect
3. #22586912C2semidirect
4. #22586908C2semidirect
5. #22586896C2semidirect
6. #22586831C2semidirect
14. C2×C22⋊(C71⋊C8)C22semidirect
15. C2×C22⋊(C71⋊C8)C22semidirect
16. #17985862C22semidirect
21. C4×C22⋊Dic71C22semidirect
22. #17985736C22semidirect
23. #17985733C22semidirect
24. C22×#41×C71C4semidirect
30. #525×C71C4semidirect
31. #525×C71C4semidirect
35. C2×C22⋊Q8×C71C4semidirect
37. C2×#121×C71C4semidirect
42. C2×#117×C71C4semidirect
395. C71#17572semidirect
396. C22×#41Dic71semidirect
403. #525Dic71semidirect
404. #525Dic71semidirect
408. C2×C22⋊Q8Dic71semidirect
410. C2×#121Dic71semidirect
416. C2×#117Dic71semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊(C71⋊C8)2
#225907232
#225869122
#225869082
#225868962
#225868312
C2×#525×C712
#1757271