Finite Group Databasebeta

← #14729753

Subgroups — #14729753

Order 2816.

968 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079176C211yesmaximal, characteristic, complemented
2#13078647C211yesmaximal, characteristic, complemented
3#13078071C211yesmaximal, characteristic
4#13067893C211yesmaximal, characteristic, complemented
5#13067879C211yesmaximal, characteristic, complemented
6#13067837C211yesmaximal, characteristic, complemented
7#13067823C211yesmaximal, characteristic, complemented
8#13067719C211yesmaximal, characteristic, complemented
9#13067712C211yesmaximal, characteristic, complemented
10#13067694C211yesmaximal, characteristic, complemented
11#13067688C211yesmaximal, characteristic, complemented
12#13067273C211yesmaximal, characteristic, complemented
13#13066998C211yesmaximal, characteristic, complemented
14C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15Q8×C11×#41C211yesmaximal, characteristic, complemented
16Q82×C11C2211yescharacteristic
17C11×#557—21no—
18C11×#557C2211yescharacteristic
19C11×#554—22no—
20C11×#554—21no—
21C11×#554—21no—
22C11×#554C2211yescharacteristic
23D4×Q8×C11—21no—
24D4×Q8×C11C2211yescharacteristic
25C11×#533—22no—
26C11×#533—21no—
27C11×#533—21no—
28C11×#533C2211yescharacteristic
29C4×C11×#41—21no—
30C4×C11×#41C2211yescharacteristic
31C2×C4×Q8×C11—21no—
32C2×C4×Q8×C11C2211yescharacteristic
33C2×#67003—21no—
34#10623008C2211yescharacteristic
35#10622840—21no—
36#10622701C2211yescharacteristic
37#10622698C2211yescharacteristic
38#10622694C2211yescharacteristic
39#10622692C2211yescharacteristic
40#10622661—22no—
41#10622644C2211yescharacteristic
42#10622641—21no—
43#10622640C2211yescharacteristic
44#10622640C2211yescharacteristic
45#10622640C2211yescharacteristic
46C4×#4325—21no—
47C4×#4325—21no—
48C4×#4325—22no—
49#10622633C2211yescharacteristic
50#10622633C2211yescharacteristic
51#10622632C2211yescharacteristic
52#10622629—21no—
53#10622628C2211yescharacteristic
54#10622615—21no—
55#10622581—21no—
56#10622538C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59#10622185C2211yescharacteristic
60#10622185C2211yescharacteristic
61#10622184C2211yescharacteristic
62#10622184C2211yescharacteristic
63Q8⋊(C11⋊C8)C2211yescharacteristic
64Q8⋊(C11⋊C8)C2211yescharacteristic
65Q8⋊(C11⋊C8)C2211yescharacteristic
66Q8⋊(C11⋊C8)C2211yescharacteristic
67Q8⋊(C11⋊C8)C2211yescharacteristic
68Q8⋊(C11⋊C8)C2211yescharacteristic
69D4⋊(C11⋊C8)C2211yescharacteristic
70D4⋊(C11⋊C8)C2211yescharacteristic
71C2×C11×#41D411yescharacteristic
72C22×Q8×C11—21no—
73C22×Q8×C11D411yescharacteristic
74C2×#4339—21no—
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8—21no—
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8—21no—
79C11×C4⋊Q8—21no—
80C11×C4⋊Q8—21no—
81C11×C4⋊Q8C2311yescharacteristic
82C11×C4⋊Q8C2311yescharacteristic
83C11×#125—22no—
84C11×#125—22no—
85C11×#125—22no—
86C11×#125—21no—
87C11×#125—21no—
88C11×#125—21no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8—21no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8D412yes—
100C4×Q8×C11—22no—
101C4×Q8×C11—22no—
102C4×Q8×C11—22no—
103C4×Q8×C11—21no—
104C4×Q8×C11—21no—
105C4×Q8×C11—21no—
106C4×Q8×C11—21no—
107C4×Q8×C11—21no—
108C4×Q8×C11—21no—
109C4×Q8×C11—21no—
110C4×Q8×C11D411yescharacteristic
111C4×Q8×C11D411yescharacteristic
112C4×Q8×C11D411yescharacteristic
113C4×Q8×C11D412yes—
114C4×Q8×C11C2311yescharacteristic
115C4×Q8×C11C2311yescharacteristic
116C4×Q8×C11C2311yescharacteristic
117C4×D4×C11—22no—
118C4×D4×C11—22no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11D411yescharacteristic
124C4×D4×C11C2311yescharacteristic
125C11×#117—22no—
126C11×#117—21no—
127C11×#117—21no—
128C11×#117D411yescharacteristic
129C2×C11×C4⋊C4—22no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4D411yescharacteristic
133C2×C42×C11—22no—
134C2×C42×C11—21no—
135C2×C42×C11—21no—
136C2×C42×C11C2311yescharacteristic
137#67003—44no—
138C2×#4326—21no—
139C2×#4325—21no—
140C2×#4325—21no—
141C2×#4325—21no—
142C2×#4325—22no—
143C2×#4324—21no—
144C2×#4323—21no—
145#66983—21no—
146#66983—21no—
147C22×C11⋊C8—21no—
148C22×C11⋊C8—21no—
149#66928—21no—
150#66927C2311yescharacteristic
151C4×D44—21no—
152C4×D44—21no—
153#66922C2311yescharacteristic
154#66899—21no—
155#66899—21no—
156#66899—22no—
157C22⋊(C11⋊C8)—21no—
158#66874—21no—
159#66874—21no—
160#66873—21no—
161#66873—21no—
162#66873—21no—
163#66873—21no—
164#66873—22no—
165#66872—21no—
166#66872—21no—
167#66872—22no—
168C4⋊(C11⋊C8)—21no—
169C4⋊(C11⋊C8)C2311yescharacteristic
170C4⋊(C11⋊C8)C2311yescharacteristic
171C4⋊(C11⋊C8)C2311yescharacteristic
172C4⋊(C11⋊C8)C2311yescharacteristic
173C4×C11⋊C8—21no—
174C4×C11⋊C8—21no—
175C4×C11⋊C8C2311yescharacteristic
176C4×C11⋊C8C2311yescharacteristic
177#18518—111nomaximal, Sylow
178C11×#41—22no—
179C11×#41SD1614yescomplemented
180C2×Q8×C11—22no—
181C2×Q8×C11—22no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—41no—
186C2×Q8×C11—42no—
187C2×Q8×C11—42no—
188C2×Q8×C11C2×D411yescharacteristic
189C2×Q8×C11C2×D411yescharacteristic
190C2×Q8×C11C2×D411yescharacteristic
191C2×Q8×C11C2×D412yes—
192C2×D4×C11—21no—
193C2×D4×C11C2×D411yescharacteristic
194C22×C4×C11—21no—
195C22×C4×C11—22no—
196C22×C4×C11—21no—
197C22×C4×C11—22no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C2×C22⋊D11—41no—
205#4339—42no—
206#4339—42no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×C4×D11—41no—
211C2×Dic22—21no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—22no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4C2×D411yescharacteristic
233C11×C4⋊C4C2×D411yescharacteristic
234C11×C4⋊C4C2×D412yes—
235C11×C4⋊C4C2×D411yescharacteristic
236C11×C4⋊C4C2×D411yescharacteristic
237C11×C22⋊C4—22no—
238C11×C22⋊C4—22no—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—21no—
241C11×C22⋊C4—21no—
242C11×C22⋊C4—21no—
243C42×C11—22no—
244C42×C11—22no—
245C42×C11—21no—
246C42×C11—22no—
247C42×C11—21no—
248C42×C11—21no—
249C42×C11—21no—
250C42×C11—21no—
251C42×C11—21no—
252C42×C11—21no—
253C42×C11C2×D411yescharacteristic
254C42×C11C2×D411yescharacteristic
255C42×C11C2×D411yescharacteristic
256C42×C11C2411yescharacteristic
257#4326—42no—
258#4325—42no—
259#4325—44no—
260#4325—42no—
261#4325—42no—
262#4324—42no—
263#4323—42no—
264(C2×D11)⋊C4—41no—
265(C2×D11)⋊C4—41no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—42no—
275C2×C11⋊C8—42no—
276Q8×#41D1111yescharacteristic, complemented
277#3167—111no—
278#3103—111no—
279#3035—111no—
280#1653—111no—
281#1651—111no—
282#1645—111no—
283#1643—111no—
284#1627—111no—
285#1626—111no—
286#1623—111no—
287#1622—111no—
288#1542—111no—
289#1476—111no—
290C2×Q8⋊C8—111no—
291C23×C11—21no—
292C23×C11#12011yescharacteristic
293C22×D11—41no—
294Q8×C11—21no—
295Q8×C11—21no—
296Q8×C11—21no—
297Q8×C11—21no—
298Q8×C11—42no—
299Q8×C11—42no—
300Q8×C11—44no—
301Q8×C11—41no—
302Q8×C11—41no—
303Q8×C11—82no—
304Q8×C11C2×SD1612yes—
305Q8×C11#13512yescomplemented
306D4×C11—24no—
307D4×C11—21no—
308D4×C11C2×SD1612yes—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—24no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—41no—
322C2×C4×C11—42no—
323C2×C4×C11—44no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—81no—
327C2×C4×C11—81no—
328C2×C4×C11—82no—
329C2×C4×C11#12011yescharacteristic
330C2×C4×C11#12011yescharacteristic
331C2×C4×C11#12011yescharacteristic
332C2×C4×C11C2×SD1612yes—
333C2×C4×C11#13712yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C22⋊D11—82no—
338C2×Dic11—41no—
339D44—42no—
340D44—41no—
341D44—41no—
342D44—41no—
343D44—41no—
344C4×D11—82no—
345Dic22—41no—
346Dic22—41no—
347C11⋊C8—22no—
348C11⋊C8—41no—
349C11⋊C8—41no—
350C11⋊C8—41no—
351C11⋊C8—41no—
352C11⋊C8—41no—
353C2×#135—221no—
354Q82C2×D1111yescharacteristic
355#557—21no—
356#557C2×D1111yescharacteristic
357#554—22no—
358#554—21no—
359#554—21no—
360#554C2×D1111yescharacteristic
361D4×Q8—21no—
362D4×Q8C2×D1111yescharacteristic
363#533—22no—
364#533—21no—
365#533—21no—
366#533C2×D1111yescharacteristic
367#532—111no—
368C4×#41—21no—
369C4×#41C2×D1111yescharacteristic
370C2×C4×Q8—21no—
371C2×C4×Q8C2×D1111yescharacteristic
372#498—111no—
373#492—111no—
374#487—111no—
375#486—111no—
376#481—221no—
377#475—111no—
378#475—111no—
379#465—222no—
380#464—221no—
381#463—221no—
382#462—111no—
383#461—111no—
384#460—111no—
385#460—111no—
386#460—111no—
387#459—111no—
388#448—221no—
389C4×SD16—221no—
390C4×SD16—221no—
391C4×SD16—222no—
392#431—111no—
393C2×C4⋊C8—111no—
394#416—221no—
395C2×C4×C8—111no—
396#333—111no—
397#333—111no—
398#332—111no—
399#332—111no—
400Q8⋊C8—111no—
401Q8⋊C8—111no—
402Q8⋊C8—111no—
403Q8⋊C8—111no—
404Q8⋊C8—111no—
405Q8⋊C8—111no—
406D4⋊C8—111no—
407D4⋊C8—111no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—22no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11#44812yes—
414C22×C11C2×#12011yescharacteristic
415C2×D11—81no—
416C2×D11—81no—
417C2×D11—81no—
418C4×C11—22no—
419C4×C11—21no—
420C4×C11—22no—
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—41no—
424C4×C11—42no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—42no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11#44812yes—
431C4×C11C22×SD1611yescharacteristic
432C4×C11C2×#13511yescharacteristic
433C4×C11C2×#13711yescharacteristic
434C4×C11#57511yescharacteristic
435Dic11—81no—
436C2×#41—221no—
437C2×#41C22⋊D1111yescharacteristic
438C22×Q8—21no—
439C22×Q8C22⋊D1111yescharacteristic
440#135—444no—
441C2×Q16—221no—
442C2×SD16—221no—
443C2×SD16—221no—
444C2×SD16—221no—
445C2×SD16—222no—
446C2×SD16—221no—
447C2×D8—221no—
448C22×C8—221no—
449C22×C8—221no—
450C4⋊Q8—22no—
451C4⋊Q8—21no—
452C4⋊Q8—22no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8—21no—
456C4⋊Q8—111no—
457C4⋊Q8C22×D1111yescharacteristic
458C4⋊Q8C22×D1111yescharacteristic
459#127—111no—
460#125—22no—
461#125—22no—
462#125—22no—
463#125—21no—
464#125—21no—
465#125—21no—
466#124—221no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—22no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—22no—
477C22⋊Q8C22⋊D1112yes—
478#121—221no—
479#121—221no—
480C4×Q8—22no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—21no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8C22⋊D1111yescharacteristic
491C4×Q8C22⋊D1111yescharacteristic
492C4×Q8C22⋊D1111yescharacteristic
493C4×Q8C22⋊D1112yes—
494C4×Q8C22×D1111yescharacteristic
495C4×Q8C22×D1111yescharacteristic
496C4×Q8C22×D1111yescharacteristic
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—221no—
504C4×D4—221no—
505C4×D4C22⋊D1111yescharacteristic
506C4×D4C22×D1111yescharacteristic
507#117—22no—
508#117—21no—
509#117—21no—
510#117C22⋊D1111yescharacteristic
511C2×C4⋊C4—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4C22⋊D1111yescharacteristic
515C2×C42—22no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42C22×D1111yescharacteristic
519#106—222no—
520#106—221no—
521#106—221no—
522C4⋊C8—111no—
523C4⋊C8—111no—
524C4⋊C8—111no—
525C4⋊C8—111no—
526C4⋊C8—221no—
527#103—221no—
528#103—221no—
529#103—222no—
530#103—221no—
531#103—221no—
532#102—221no—
533#102—221no—
534#102—221no—
535#102—221no—
536#102—222no—
537C22⋊C8—221no—
538C4×C8—111no—
539C4×C8—111no—
540C4×C8—221no—
541C4×C8—221no—
542C2×C11—22no—
543C2×C11—42no—
544C2×C11C2×#44811yescharacteristic
545C2×C11#300211yescharacteristic
546C2×C11#301811yescharacteristic
547D11—161no—
548#41—22no—
549#41—442no—
550#41—442no—
551#41#432514yescomplemented
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—41no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—221no—
561C2×Q8C2×C22⋊D1111yescharacteristic
562C2×Q8C2×C22⋊D1111yescharacteristic
563C2×Q8C2×C22⋊D1111yescharacteristic
564C2×Q8C2×C22⋊D1112yes—
565C2×D4—21no—
566C2×D4—221no—
567C2×D4—221no—
568C2×D4—221no—
569C2×D4—441no—
570C2×D4C2×C22⋊D1111yescharacteristic
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—441no—
579C22×C4C2×C22⋊D1111yescharacteristic
580C22×C4C2×C22⋊D1111yescharacteristic
581C22×C4C2×C22⋊D1111yescharacteristic
582Q16—442no—
583SD16—444no—
584SD16—442no—
585SD16—442no—
586SD16—442no—
587SD16—442no—
588D8—442no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—442no—
596C2×C8—442no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4C2×C22⋊D1111yescharacteristic
620C4⋊C4C2×C22⋊D1111yescharacteristic
621C4⋊C4C2×C22⋊D1111yescharacteristic
622C4⋊C4C2×C22⋊D1111yescharacteristic
623C4⋊C4C2×C22⋊D1112yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—441no—
631C22⋊C4—441no—
632C42—22no—
633C42—22no—
634C42—21no—
635C42—21no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42C2×C22⋊D1111yescharacteristic
643C42C2×C22⋊D1111yescharacteristic
644C42C2×C22⋊D1111yescharacteristic
645C42C23×D1111yescharacteristic
646C11#1851811yescharacteristic, complemented, Sylow
647C23—21no—
648C23—441no—
649C23#6700611yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—42no—
655Q8—42no—
656Q8—44no—
657Q8—41no—
658Q8—41no—
659Q8—82no—
660Q8—441no—
661Q8—441no—
662Q8C2×#432512yes—
663Q8#6700312yescomplemented
664D4—24no—
665D4—21no—
666D4—442no—
667D4—441no—
668D4—441no—
669D4—441no—
670D4—441no—
671D4—882no—
672D4C2×#432512yes—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—24no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—82no—
693C2×C4—441no—
694C2×C4—882no—
695C2×C4C2×#432512yes—
696C2×C4#6699512yes—
697C2×C4#6700611yescharacteristic
698C2×C4#6700611yescharacteristic
699C2×C4#6700611yescharacteristic
700C2×C4C22×C22⋊D1111yescharacteristic
701C2×C4C22×C22⋊D1111yescharacteristic
702C2×C4C22×C22⋊D1111yescharacteristic
703C8—222no—
704C8—441no—
705C8—441no—
706C8—441no—
707C8—441no—
708C8—441no—
709C22—21no—
710C22—21no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—881no—
715C22—881no—
716C22—881no—
717C22#1062284012yes—
718C22C2×#6700611yescharacteristic
719C4—22no—
720C4—21no—
721C4—22no—
722C4—21no—
723C4—21no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—881no—
732C4#1062284012yes—
733C4C22×#432511yescharacteristic
734C4C2×#6699511yescharacteristic
735C4C2×#6700311yescharacteristic
736C4#1062335311yescharacteristic
737C2—22no—
738C2—42no—
739C2—1761no—
740C2C2×#1062284011yescharacteristic
741C2#1307783411yescharacteristic
742C2#1307796511yescharacteristic
subgroupG/H
centerC2×C4#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingQ8×C11×#41C2
socleC22×C11C2×#120
prime radical#13078071C2
hypercenterQ8×#41D11
hypocenterC11#18518
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #13079176C2semidirect
2. #13078647C2semidirect
4. #13067893C2semidirect
5. #13067879C2semidirect
6. #13067837C2semidirect
7. #13067823C2semidirect
8. #13067719C2semidirect
9. #13067712C2semidirect
10. #13067694C2semidirect
11. #13067688C2semidirect
12. #13067273C2semidirect
13. #13066998C2semidirect
14. C2×Q8⋊(C11⋊C8)C2semidirect
15. Q8×C11×#41C2semidirect
179. C11×#41SD16semidirect
276. Q8×#41D11semidirect
305. Q8×C11#135semidirect
551. #41#4325semidirect
646. C11#18518semidirect
663. Q8#67003semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130786472
#130780712
#130678932
#130678792
#130678372
#130678232
#130677192
#130677122
#130676942
#130676882
#130672732
#130669982
C2×Q8⋊(C11⋊C8)2
Q8×C11×#412
#1851811