Finite Group Databasebeta

← #32012785

Subgroups — #32012785

Order 18176.

1668 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985973C211yesmaximal, characteristic, complemented
2C22×#14556043C211yesmaximal, characteristic, complemented
3#22591189C212yesmaximal, complemented
4#22589177C212yesmaximal, complemented
5#22588799C212yesmaximal, complemented
6#22588794C212yesmaximal, complemented
7#22588328C211yesmaximal, characteristic, complemented
8#22588258C211yesmaximal, characteristic, complemented
9#22588255C211yesmaximal, characteristic, complemented
10C4×#14556043C211yesmaximal, characteristic, complemented
11C2×#546×C71C211yesmaximal, characteristic
12C2×#14556087C2212yescomplemented
13C22×C22⋊Dic71C2212yes—
14#17985973—24no—
15C2×#14556043—24no—
16C2×#14556043C2211yescharacteristic
17C2×#14556043C2211yescharacteristic
18C2×#14556043C2211yescharacteristic
19C2×#14556043C2212yes—
20C2×#14556043C2212yes—
21C2×#14556043C2211yescharacteristic
22C2×#14556043C2212yescomplemented
23C2×#14556043C2212yescomplemented
24#17985892—22no—
25#17985892—22no—
26#17985874—22no—
27#17985862C2212yescomplemented
28#17985859C2212yescomplemented
29#17985855C2212yes—
30C22⋊C4×Dic71—22no—
31C4×C22⋊Dic71C2212yescomplemented
32#17985766C2212yescomplemented
33#17985766C2212yescomplemented
34C22×#41×C71C2211yescharacteristic
35C23×D4×C71C2211yescharacteristic
36#546×C71—22no—
37#546×C71—22no—
38#546×C71—22no—
39#546×C71—22no—
40C2×#124×C71C411yescharacteristic, complemented
41C2×#123×C71C411yescharacteristic, complemented
42C2×#123×C71C2211yescharacteristic
43C2×C22⋊Q8×C71C411yescharacteristic, complemented
44C2×#121×C71C411yescharacteristic, complemented
45C2×#121×C71C411yescharacteristic, complemented
46C2×#121×C71C2211yescharacteristic
47C2×#120×C71C411yescharacteristic, complemented
48C2×#120×C71C2211yescharacteristic
49C2×C4×D4×C71C411yescharacteristic, complemented
50C2×C4×D4×C71C2211yescharacteristic
51C22×C22⋊C4×C71C411yescharacteristic, complemented
52C22×C22⋊C4×C71C2211yescharacteristic
53C23×Dic71—22no—
54#14556087—24no—
55#14556087—42no—
56C2×C4⋊Dic71—22no—
57C2×C4⋊Dic71—22no—
58C2×C22⋊Dic71—24no—
59C2×C22⋊Dic71—22no—
60C2×C22⋊Dic71—22no—
61C2×C22⋊Dic71—22no—
62C2×C22⋊Dic71—42no—
63C2×C22⋊Dic71C2312yes—
64C2×C22⋊Dic71C2312yes—
65C2×C22⋊Dic71C2312yes—
66C2×C22⋊Dic71C2312yes—
67C2×C4×Dic71—22no—
68C2×C4×Dic71—22no—
69#14556043—24no—
70#14556043—24no—
71#14556043—22no—
72#14556043—22no—
73#14556043—22no—
74#14556043—42no—
75#14556043—42no—
76#14556043D414yescomplemented
77C71⋊#95—22no—
78C71⋊#95—22no—
79C71⋊#95—22no—
80C71⋊#95—22no—
81C25×C71C2×C411yescharacteristic
82C25×C71C2311yescharacteristic
83C2×#41×C71—22no—
84C2×#41×C71—22no—
85C2×#41×C71—22no—
86C2×#41×C71—22no—
87C2×#41×C71—42no—
88C22×Q8×C71C2×C411yescharacteristic, complemented
89C22×D4×C71—22no—
90C22×D4×C71—22no—
91C22×D4×C71—22no—
92C22×D4×C71—22no—
93C22×D4×C71—42no—
94C22×D4×C71C2×C411yescharacteristic
95C22×D4×C71C2×C411yescharacteristic
96C22×D4×C71C2×C411yescharacteristic
97C22×D4×C71C2×C411yescharacteristic
98C22×D4×C71C2×C411yescharacteristic, complemented
99C22×D4×C71C2×C411yescharacteristic, complemented
100C22×D4×C71C2311yescharacteristic
101C22×D4×C71C2311yescharacteristic
102C22×D4×C71C2311yescharacteristic
103C23×C4×C71C2×C411yescharacteristic
104C23×C4×C71C2×C411yescharacteristic, complemented
105C23×C4×C71C2×C411yescharacteristic, complemented
106C23×C4×C71C2×C411yescharacteristic, complemented
107C23×C4×C71C2311yescharacteristic
108C23×C4×C71C2311yescharacteristic
109#124×C71—22no—
110#124×C71—22no—
111#123×C71—22no—
112#123×C71—22no—
113#123×C71—22no—
114#123×C71—22no—
115C22⋊Q8×C71—22no—
116C22⋊Q8×C71—22no—
117#121×C71—22no—
118#121×C71—22no—
119#121×C71—22no—
120#121×C71—22no—
121#121×C71—22no—
122#121×C71—22no—
123#120×C71—22no—
124#120×C71—22no—
125#120×C71—22no—
126#120×C71—22no—
127C4×D4×C71—22no—
128C4×D4×C71—22no—
129C4×D4×C71—21no—
130C4×D4×C71—21no—
131C4×D4×C71—21no—
132C4×D4×C71—21no—
133C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
134C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
135C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
136C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
137C2×C22⋊C4×C71—21no—
138C2×C22⋊C4×C71—21no—
139C2×C22⋊C4×C71—21no—
140C2×C22⋊C4×C71—21no—
141C2×C22⋊C4×C71C2×C411yescharacteristic
142C2×C22⋊C4×C71C2×C411yescharacteristic
143C2×C22⋊C4×C71C2×C411yescharacteristic
144C2×C22⋊C4×C71C2×C411yescharacteristic
145C2×C22⋊C4×C71C2×C411yescharacteristic
146C2×C22⋊C4×C71C2×C411yescharacteristic
147C2×C22⋊C4×C71C2×C411yescharacteristic, complemented
148C2×C22⋊C4×C71C2×C411yescharacteristic, complemented
149C2×C22⋊C4×C71C2×C411yescharacteristic, complemented
150C2×C22⋊C4×C71C2×C411yescharacteristic, complemented
151C2×C22⋊C4×C71C2×C411yescharacteristic, complemented
152C2×C22⋊C4×C71D412yes—
153C2×C22⋊C4×C71D412yes—
154C2×C22⋊C4×C71D412yes—
155C2×C22⋊C4×C71D412yes—
156C2×C22⋊C4×C71C2311yescharacteristic
157C2×C42×C71C2×C411yescharacteristic, complemented
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—44no—
163C22×Dic71—44no—
164C22×Dic71—82no—
165C4⋊Dic71—44no—
166C4⋊Dic71—82no—
167C22⋊Dic71—22no—
168C22⋊Dic71—22no—
169C22⋊Dic71—22no—
170C22⋊Dic71—22no—
171C22⋊Dic71—22no—
172C22⋊Dic71—22no—
173C22⋊Dic71—22no—
174C22⋊Dic71—44no—
175C22⋊Dic71—44no—
176C22⋊Dic71—82no—
177C22⋊Dic71C2×D414yes—
178C4×Dic71—44no—
179C4×Dic71—82no—
180C24×C71—21no—
181C24×C71—21no—
182C24×C71—22no—
183C24×C71—21no—
184C24×C71—21no—
185C24×C71—22no—
186C24×C71—41no—
187C24×C71—42no—
188C24×C71—42no—
189C24×C71—81no—
190C24×C71—81no—
191C24×C71C22×C411yescharacteristic
192C24×C71C22×C411yescharacteristic
193C24×C71C22×C411yescharacteristic
194C24×C71C22×C411yescharacteristic
195C24×C71C22×C411yescharacteristic
196C24×C71C2×D412yes—
197C24×C71C2×D412yes—
198C24×C71C2411yescharacteristic
199#41×C71—44no—
200#41×C71—44no—
201#41×C71—44no—
202#41×C71—44no—
203C2×Q8×C71—22no—
204C2×Q8×C71—22no—
205C2×Q8×C71—41no—
206C2×D4×C71—22no—
207C2×D4×C71—22no—
208C2×D4×C71—21no—
209C2×D4×C71—21no—
210C2×D4×C71—22no—
211C2×D4×C71—22no—
212C2×D4×C71—22no—
213C2×D4×C71—22no—
214C2×D4×C71—22no—
215C2×D4×C71—22no—
216C2×D4×C71—21no—
217C2×D4×C71—21no—
218C2×D4×C71—21no—
219C2×D4×C71—21no—
220C2×D4×C71—22no—
221C2×D4×C71—22no—
222C2×D4×C71—22no—
223C2×D4×C71—22no—
224C2×D4×C71—22no—
225C2×D4×C71—22no—
226C2×D4×C71—41no—
227C2×D4×C71—41no—
228C2×D4×C71—41no—
229C2×D4×C71—44no—
230C2×D4×C71—44no—
231C2×D4×C71—44no—
232C2×D4×C71—44no—
233C2×D4×C71—42no—
234C2×D4×C71—81no—
235C2×D4×C71—81no—
236C2×D4×C71C2×D412yes—
237C2×D4×C71#4112yes—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—22no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—22no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—22no—
249C22×C4×C71—22no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—41no—
253C22×C4×C71—41no—
254C22×C4×C71—41no—
255C22×C4×C71—81no—
256C22×C4×C71—81no—
257C22×C4×C71C22×C411yescharacteristic
258C22×C4×C71C22×C411yescharacteristic
259C22×C4×C71C22×C411yescharacteristic
260C22×C4×C71C22×C411yescharacteristic
261C22×C4×C71C22×C411yescharacteristic
262C22×C4×C71C22×C411yescharacteristic
263C22×C4×C71C22×C411yescharacteristic
264C22×C4×C71C22×C411yescharacteristic
265C22×C4×C71C22×C411yescharacteristic
266C22×C4×C71C2×D412yes—
267C22×C4×C71C2×D412yes—
268C22×C4×C71C2×D412yes—
269C22×C4×C71C2×D412yes—
270C4⋊C4×C71—22no—
271C4⋊C4×C71—21no—
272C4⋊C4×C71—21no—
273C4⋊C4×C71—22no—
274C4⋊C4×C71—22no—
275C22⋊C4×C71—21no—
276C22⋊C4×C71—21no—
277C22⋊C4×C71—22no—
278C22⋊C4×C71—22no—
279C22⋊C4×C71—21no—
280C22⋊C4×C71—21no—
281C22⋊C4×C71—21no—
282C22⋊C4×C71—21no—
283C22⋊C4×C71—22no—
284C22⋊C4×C71—21no—
285C22⋊C4×C71—21no—
286C22⋊C4×C71—22no—
287C22⋊C4×C71C22⋊C411yescharacteristic
288C22⋊C4×C71C22⋊C411yescharacteristic
289C22⋊C4×C71C22⋊C411yescharacteristic
290C22⋊C4×C71C22⋊C411yescharacteristic
291C22⋊C4×C71C22⋊C412yes—
292C22⋊C4×C71C22⋊C412yes—
293C22⋊C4×C71C22⋊C412yes—
294C22⋊C4×C71C22⋊C412yes—
295C22⋊C4×C71C22⋊C412yes—
296C22⋊C4×C71C22⋊C412yes—
297C42×C71—21no—
298C42×C71—21no—
299C23×C71—21no—
300C23×C71—21no—
301C23×C71—21no—
302C23×C71—21no—
303C23×C71—22no—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71—24no—
307C23×C71—21no—
308C23×C71—21no—
309C23×C71—22no—
310C23×C71—22no—
311C23×C71—21no—
312C23×C71—21no—
313C23×C71—21no—
314C23×C71—21no—
315C23×C71—21no—
316C23×C71—21no—
317C23×C71—41no—
318C23×C71—41no—
319C23×C71—41no—
320C23×C71—42no—
321C23×C71—41no—
322C23×C71—41no—
323C23×C71—42no—
324C23×C71—42no—
325C23×C71—42no—
326C23×C71—42no—
327C23×C71—41no—
328C23×C71—41no—
329C23×C71—42no—
330C23×C71—41no—
331C23×C71—41no—
332C23×C71—41no—
333C23×C71—41no—
334C23×C71—42no—
335C23×C71—81no—
336C23×C71—81no—
337C23×C71—82no—
338C23×C71—82no—
339C23×C71—84no—
340C23×C71—84no—
341C23×C71—84no—
342C23×C71C2×C22⋊C411yescharacteristic
343C23×C71C2×C22⋊C412yes—
344C23×C71C2×C22⋊C411yescharacteristic
345C23×C71C4×D412yes—
346C23×C71C23×C411yescharacteristic
347C23×C71C22×D411yescharacteristic
348C23×C71C22×D412yes—
349C23×C71C2×#4111yescharacteristic
350C23×C71H(5,𝔽2)12yes—
351Q8×C71—44no—
352D4×C71—24no—
353D4×C71—24no—
354D4×C71—44no—
355D4×C71—44no—
356D4×C71—44no—
357D4×C71—42no—
358D4×C71—42no—
359D4×C71—42no—
360D4×C71—42no—
361D4×C71—42no—
362D4×C71—42no—
363D4×C71—82no—
364D4×C71—82no—
365C2×C4×C71—21no—
366C2×C4×C71—21no—
367C2×C4×C71—21no—
368C2×C4×C71—21no—
369C2×C4×C71—21no—
370C2×C4×C71—21no—
371C2×C4×C71—22no—
372C2×C4×C71—22no—
373C2×C4×C71—22no—
374C2×C4×C71—22no—
375C2×C4×C71—21no—
376C2×C4×C71—21no—
377C2×C4×C71—21no—
378C2×C4×C71—21no—
379C2×C4×C71—21no—
380C2×C4×C71—21no—
381C2×C4×C71—21no—
382C2×C4×C71—21no—
383C2×C4×C71—41no—
384C2×C4×C71—41no—
385C2×C4×C71—42no—
386C2×C4×C71—42no—
387C2×C4×C71—42no—
388C2×C4×C71—42no—
389C2×C4×C71—42no—
390C2×C4×C71—42no—
391C2×C4×C71—42no—
392C2×C4×C71—42no—
393C2×C4×C71—41no—
394C2×C4×C71—41no—
395C2×C4×C71—81no—
396C2×C4×C71—81no—
397C2×C4×C71C2×C22⋊C411yescharacteristic
398C2×C4×C71C2×C22⋊C411yescharacteristic
399C2×C4×C71C2×C22⋊C412yes—
400C2×C4×C71C2×C22⋊C411yescharacteristic
401C2×C4×C71C2×C22⋊C411yescharacteristic
402C2×C4×C71C2×C22⋊C412yes—
403C2×C4×C71C4×D412yes—
404C2×Dic71—24no—
405C2×Dic71—42no—
406C2×Dic71—42no—
407C2×Dic71—42no—
408C2×Dic71—42no—
409C2×Dic71—42no—
410C2×Dic71—42no—
411C2×Dic71—42no—
412C2×Dic71—42no—
413C2×Dic71—42no—
414C2×Dic71—42no—
415C2×Dic71—42no—
416C2×Dic71—88no—
417C22×C71—21no—
418C22×C71—22no—
419C22×C71—21no—
420C22×C71—22no—
421C22×C71—21no—
422C22×C71—21no—
423C22×C71—22no—
424C22×C71—21no—
425C22×C71—22no—
426C22×C71—21no—
427C22×C71—22no—
428C22×C71—22no—
429C22×C71—21no—
430C22×C71—41no—
431C22×C71—41no—
432C22×C71—42no—
433C22×C71—44no—
434C22×C71—44no—
435C22×C71—42no—
436C22×C71—42no—
437C22×C71—42no—
438C22×C71—42no—
439C22×C71—41no—
440C22×C71—41no—
441C22×C71—41no—
442C22×C71—41no—
443C22×C71—41no—
444C22×C71—41no—
445C22×C71—41no—
446C22×C71—41no—
447C22×C71—82no—
448C22×C71—82no—
449C22×C71—81no—
450C22×C71—81no—
451C22×C71—84no—
452C22×C71—81no—
453C22×C71—81no—
454C22×C71—81no—
455C22×C71—81no—
456C22×C71—84no—
457C22×C71#41012yescomplemented
458C22×C71C22×C22⋊C411yescharacteristic
459C22×C71C2×C4×D411yescharacteristic
460C22×C71#51811yescharacteristic
461C22×C71D4212yes—
462C22×C71#54612yes—
463C4×C71—21no—
464C4×C71—21no—
465C4×C71—22no—
466C4×C71—22no—
467C4×C71—21no—
468C4×C71—21no—
469C4×C71—22no—
470C4×C71—41no—
471C4×C71—41no—
472C4×C71—41no—
473C4×C71—41no—
474Dic71—44no—
475Dic71—82no—
476Dic71—82no—
477Dic71—82no—
478#22405—711nomaximal, Sylow
479C2×C71—22no—
480C2×C71—22no—
481C2×C71—21no—
482C2×C71—21no—
483C2×C71—22no—
484C2×C71—42no—
485C2×C71—41no—
486C2×C71—42no—
487C2×C71—81no—
488C2×C71—81no—
489C2×C71D4×C22⋊C411yescharacteristic
490C2×C71C2×#41011yescharacteristic
491C2×C71#288311yescharacteristic
492C2×#546D7111yescharacteristic
493C2×#410—711no—
494C22×#99—711no—
495#2342—712no—
496#1964—712no—
497#1899—712no—
498#1898—712no—
499#1799—711no—
500#1782—711no—
501#1781—711no—
502C4×#99—711no—
503C71#2240511yescharacteristic, complemented, Sylow
504C22×#41C2×D7111yescharacteristic
505C23×D4C2×D7111yescharacteristic
506#546—22no—
507#546—22no—
508#546—22no—
509#546—22no—
510C2×#124Dic7111yescharacteristic, complemented
511C2×#123Dic7111yescharacteristic, complemented
512C2×#123C2×D7111yescharacteristic
513C2×C22⋊Q8Dic7111yescharacteristic, complemented
514C2×#121Dic7111yescharacteristic, complemented
515C2×#121Dic7111yescharacteristic, complemented
516C2×#121C2×D7111yescharacteristic
517C2×#120Dic7111yescharacteristic, complemented
518C2×#120C2×D7111yescharacteristic
519C2×C4×D4Dic7111yescharacteristic, complemented
520C2×C4×D4C2×D7111yescharacteristic
521C2×#117—712no—
522C22×C22⋊C4—712no—
523C22×C22⋊C4Dic7111yescharacteristic, complemented
524C22×C22⋊C4C2×D7111yescharacteristic
525#410—1424no—
526C2×#99—712no—
527C2×#99—712no—
528C2×#99—711no—
529C2×#99—711no—
530C2×#99—711no—
531C2×#99—712no—
532C2×#99—712no—
533C2×#99—711no—
534C2×#99—1424no—
535#388—1422no—
536#388—1422no—
537#385—1422no—
538#381—712no—
539#380—712no—
540#379—712no—
541C4×C22⋊C4—712no—
542C4×C22⋊C4—1422no—
543#342—712no—
544#342—712no—
545C25C2×Dic7111yescharacteristic
546C25C22×D7111yescharacteristic
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—42no—
552C22×Q8C2×Dic7111yescharacteristic, complemented
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—42no—
558C22×D4C2×Dic7111yescharacteristic
559C22×D4C2×Dic7111yescharacteristic
560C22×D4C2×Dic7111yescharacteristic
561C22×D4C2×Dic7111yescharacteristic
562C22×D4C2×Dic7111yescharacteristic, complemented
563C22×D4C2×Dic7111yescharacteristic, complemented
564C22×D4C22×D7111yescharacteristic
565C22×D4C22×D7111yescharacteristic
566C22×D4C22×D7111yescharacteristic
567C23×C4—1422no—
568C23×C4C2×Dic7111yescharacteristic
569C23×C4C2×Dic7111yescharacteristic, complemented
570C23×C4C2×Dic7111yescharacteristic, complemented
571C23×C4C2×Dic7111yescharacteristic, complemented
572C23×C4C22×D7111yescharacteristic
573C23×C4C22×D7111yescharacteristic
574#124—22no—
575#124—22no—
576#123—22no—
577#123—22no—
578#123—22no—
579#123—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#120—22no—
589#120—22no—
590#120—22no—
591#120—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598#117—2842no—
599#117—1424no—
600C2×C4⋊C4—1422no—
601C2×C4⋊C4—1422no—
602C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
603C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
604C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
605C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—2842no—
611C2×C22⋊C4—712no—
612C2×C22⋊C4—712no—
613C2×C22⋊C4—712no—
614C2×C22⋊C4—712no—
615C2×C22⋊C4—1422no—
616C2×C22⋊C4—1422no—
617C2×C22⋊C4—1424no—
618C2×C22⋊C4—1422no—
619C2×C22⋊C4C2×Dic7111yescharacteristic
620C2×C22⋊C4C2×Dic7111yescharacteristic
621C2×C22⋊C4C2×Dic7111yescharacteristic
622C2×C22⋊C4C2×Dic7111yescharacteristic
623C2×C22⋊C4C2×Dic7111yescharacteristic
624C2×C22⋊C4C2×Dic7111yescharacteristic
625C2×C22⋊C4C2×Dic7111yescharacteristic, complemented
626C2×C22⋊C4C2×Dic7111yescharacteristic, complemented
627C2×C22⋊C4C2×Dic7111yescharacteristic, complemented
628C2×C22⋊C4C2×Dic7111yescharacteristic, complemented
629C2×C22⋊C4C2×Dic7111yescharacteristic, complemented
630C2×C22⋊C4C22⋊D7112yes—
631C2×C22⋊C4C22⋊D7112yes—
632C2×C22⋊C4C22⋊D7112yes—
633C2×C22⋊C4C22⋊D7112yes—
634C2×C22⋊C4C22×D7111yescharacteristic
635C2×C42—1422no—
636C2×C42—1422no—
637C2×C42C2×Dic7111yescharacteristic, complemented
638#99—2842no—
639#99—2842no—
640#99—714no—
641#99—1424no—
642#99—1424no—
643#99—1422no—
644#99—1422no—
645#99—1422no—
646#95—1422no—
647#95—1422no—
648#95—1422no—
649#95—1422no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—41no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C22×Dic7111yescharacteristic
662C24C22×Dic7111yescharacteristic
663C24C22×Dic7111yescharacteristic
664C24C22×Dic7111yescharacteristic
665C24C22×Dic7111yescharacteristic
666C24C2×C22⋊D7112yes—
667C24C2×C22⋊D7112yes—
668C24C23×D7111yescharacteristic
669#41—44no—
670#41—44no—
671#41—44no—
672#41—44no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—41no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4—41no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4D4×D7112yes—
707C2×D4#1176586412yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—22no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4—41no—
725C22×C4—81no—
726C22×C4—81no—
727C22×C4—2844no—
728C22×C4—2844no—
729C22×C4—5682no—
730C22×C4—1422no—
731C22×C4—1422no—
732C22×C4—1422no—
733C22×C4—1422no—
734C22×C4C22×Dic7111yescharacteristic
735C22×C4C22×Dic7111yescharacteristic
736C22×C4C22×Dic7111yescharacteristic
737C22×C4C22×Dic7111yescharacteristic
738C22×C4C22×Dic7111yescharacteristic
739C22×C4C22×Dic7111yescharacteristic
740C22×C4C22×Dic7111yescharacteristic
741C22×C4C22×Dic7111yescharacteristic
742C22×C4C22×Dic7111yescharacteristic
743C22×C4C2×C22⋊D7112yes—
744C22×C4C2×C22⋊D7112yes—
745C22×C4C2×C22⋊D7112yes—
746C22×C4C2×C22⋊D7112yes—
747C4⋊C4—22no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—2844no—
753C4⋊C4—5682no—
754C22⋊C4—22no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—22no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—22no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—22no—
766C22⋊C4—2844no—
767C22⋊C4—2844no—
768C22⋊C4—5682no—
769C22⋊C4—714no—
770C22⋊C4—1422no—
771C22⋊C4—1422no—
772C22⋊C4—1422no—
773C22⋊C4—1422no—
774C22⋊C4—1422no—
775C22⋊C4—1422no—
776C22⋊C4—1422no—
777C22⋊C4C22⋊Dic7111yescharacteristic
778C22⋊C4C22⋊Dic7111yescharacteristic
779C22⋊C4C22⋊Dic7111yescharacteristic
780C22⋊C4C22⋊Dic7111yescharacteristic
781C22⋊C4C22⋊Dic7112yes—
782C22⋊C4C22⋊Dic7112yes—
783C22⋊C4C22⋊Dic7112yes—
784C22⋊C4C22⋊Dic7112yes—
785C22⋊C4C22⋊Dic7112yes—
786C22⋊C4C22⋊Dic7112yes—
787C42—21no—
788C42—21no—
789C42—2844no—
790C42—5682no—
791C23—22no—
792C23—22no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—24no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—41no—
810C23—42no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—41no—
815C23—41no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—41no—
820C23—41no—
821C23—42no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—42no—
827C23—81no—
828C23—81no—
829C23—82no—
830C23—82no—
831C23—84no—
832C23—84no—
833C23—84no—
834C23C2×C22⋊Dic7111yescharacteristic
835C23C2×C22⋊Dic7112yes—
836C23C2×C22⋊Dic7111yescharacteristic
837C23D4×Dic7112yes—
838C23C23×Dic7111yescharacteristic
839C23C2×D4×D7111yescharacteristic
840C23C22×C22⋊D7112yes—
841C23C2×#1176586411yescharacteristic
842C23#1455617312yes—
843Q8—44no—
844D4—24no—
845D4—24no—
846D4—44no—
847D4—44no—
848D4—44no—
849D4—42no—
850D4—42no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—82no—
856D4—82no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—2842no—
890C2×C4—2842no—
891C2×C4—2842no—
892C2×C4—2842no—
893C2×C4—2842no—
894C2×C4—2842no—
895C2×C4—2842no—
896C2×C4—2842no—
897C2×C4—2842no—
898C2×C4—2842no—
899C2×C4—2842no—
900C2×C4—5688no—
901C2×C4—1424no—
902C2×C4C2×C22⋊Dic7111yescharacteristic
903C2×C4C2×C22⋊Dic7111yescharacteristic
904C2×C4C2×C22⋊Dic7112yes—
905C2×C4C2×C22⋊Dic7111yescharacteristic
906C2×C4C2×C22⋊Dic7111yescharacteristic
907C2×C4C2×C22⋊Dic7112yes—
908C2×C4D4×Dic7112yes—
909C22—21no—
910C22—21no—
911C22—22no—
912C22—21no—
913C22—22no—
914C22—21no—
915C22—22no—
916C22—21no—
917C22—22no—
918C22—21no—
919C22—22no—
920C22—22no—
921C22—21no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—44no—
926C22—42no—
927C22—42no—
928C22—44no—
929C22—42no—
930C22—42no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—82no—
940C22—82no—
941C22—81no—
942C22—81no—
943C22—84no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22—84no—
949C22#1798597312yescomplemented
950C22C22×C22⋊Dic7111yescharacteristic
951C22C2×D4×Dic7111yescharacteristic
952C22#1798647411yescharacteristic
953C22D4×C22⋊D7112yes—
954C22#1798664312yes—
955C4—21no—
956C4—21no—
957C4—22no—
958C4—22no—
959C4—21no—
960C4—21no—
961C4—22no—
962C4—41no—
963C4—41no—
964C4—41no—
965C4—41no—
966C4—2844no—
967C4—5682no—
968C4—5682no—
969C4—5682no—
970C2—22no—
971C2—22no—
972C2—21no—
973C2—21no—
974C2—22no—
975C2—41no—
976C2—42no—
977C2—42no—
978C2—81no—
979C2—81no—
980C2D4×C22⋊Dic7111yescharacteristic
981C2C2×#1798597311yescharacteristic
982C2#2259680111yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic71
commutatorC23×C71C23×C4
FrattiniC24C23×D71
Fitting, prime radicalC2×#546×C71C2
socleC22×C71C22×C22⋊C4
cosocleC24×C71C24
hypercenterC2×#546D71
hypocenterC71#22405
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#17985973C2semidirect
2. C22×#14556043C2semidirect
3. #22591189C2semidirect
4. #22589177C2semidirect
5. #22588799C2semidirect
6. #22588794C2semidirect
7. #22588328C2semidirect
8. #22588258C2semidirect
9. #22588255C2semidirect
10. C4×#14556043C2semidirect
12. C2×#14556087C22semidirect
22. C2×#14556043C22semidirect
23. C2×#14556043C22semidirect
27. #17985862C22semidirect
28. #17985859C22semidirect
31. C4×C22⋊Dic71C22semidirect
32. #17985766C22semidirect
33. #17985766C22semidirect
40. C2×#124×C71C4semidirect
41. C2×#123×C71C4semidirect
43. C2×C22⋊Q8×C71C4semidirect
44. C2×#121×C71C4semidirect
45. C2×#121×C71C4semidirect
47. C2×#120×C71C4semidirect
49. C2×C4×D4×C71C4semidirect
51. C22×C22⋊C4×C71C4semidirect
76. #14556043D4semidirect
88. C22×Q8×C71C2×C4semidirect
98. C22×D4×C71C2×C4semidirect
99. C22×D4×C71C2×C4semidirect
104. C23×C4×C71C2×C4semidirect
105. C23×C4×C71C2×C4semidirect
106. C23×C4×C71C2×C4semidirect
133. C2×C4⋊C4×C71C2×C4semidirect
134. C2×C4⋊C4×C71C2×C4semidirect
135. C2×C4⋊C4×C71C2×C4semidirect
136. C2×C4⋊C4×C71C2×C4semidirect
147. C2×C22⋊C4×C71C2×C4semidirect
148. C2×C22⋊C4×C71C2×C4semidirect
149. C2×C22⋊C4×C71C2×C4semidirect
150. C2×C22⋊C4×C71C2×C4semidirect
151. C2×C22⋊C4×C71C2×C4semidirect
157. C2×C42×C71C2×C4semidirect
457. C22×C71#410semidirect
503. C71#22405semidirect
510. C2×#124Dic71semidirect
511. C2×#123Dic71semidirect
513. C2×C22⋊Q8Dic71semidirect
514. C2×#121Dic71semidirect
515. C2×#121Dic71semidirect
517. C2×#120Dic71semidirect
519. C2×C4×D4Dic71semidirect
523. C22×C22⋊C4Dic71semidirect
552. C22×Q8C2×Dic71semidirect
562. C22×D4C2×Dic71semidirect
563. C22×D4C2×Dic71semidirect
569. C23×C4C2×Dic71semidirect
570. C23×C4C2×Dic71semidirect
571. C23×C4C2×Dic71semidirect
602. C2×C4⋊C4C2×Dic71semidirect
603. C2×C4⋊C4C2×Dic71semidirect
604. C2×C4⋊C4C2×Dic71semidirect
605. C2×C4⋊C4C2×Dic71semidirect
625. C2×C22⋊C4C2×Dic71semidirect
626. C2×C22⋊C4C2×Dic71semidirect
627. C2×C22⋊C4C2×Dic71semidirect
628. C2×C22⋊C4C2×Dic71semidirect
629. C2×C22⋊C4C2×Dic71semidirect
637. C2×C42C2×Dic71semidirect
949. C22#17985973semidirect

Maximal subgroups

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

subgroupindex
C2×#179859732
C22×#145560432
#225911892
#225891772
#225887992
#225887942
#225883282
#225882582
#225882552
C4×#145560432
C2×#546×C712
#2240571