Finite Group Databasebeta

← #14660421

Subgroups — #14660421

Order 2816.

1350 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
1C2×#10623347C211yesmaximal, characteristic
2C22×#66869C211yesmaximal, characteristic
3C2×#10622579C211yesmaximal, characteristic
4C22×#66900C211yesmaximal, characteristic, complemented
5#13068335C211yesmaximal, characteristic, complemented
6C2×#10622161C211yesmaximal, characteristic, complemented
7C2×C11×#391C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12#10623347—22no—
13#10623347—22no—
14#10623347—22no—
15#10623347C414yescomplemented
16C2×#67000—21no—
17C2×#66999—22no—
18C2×#66997—21no—
19C2×#66982—22no—
20C2×#66979C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C11×#391—22no—
24C11×#391—22no—
25C2×C11×#95—22no—
26C2×#66900—22no—
27C2×#66900—22no—
28C2×#66900—22no—
29C2×#66874—21no—
30#10622579—22no—
31#10622579—22no—
32C2×#66873—21no—
33C2×#66869—22no—
34C2×#66869—22no—
35C2×#66869—22no—
36#10622167—22no—
37#10622161—22no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11—21no—
50C22×Q8×C11C2×C412yes—
51C22×Q8×C11D412yes—
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11D412yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—21no—
57C2×#4339—21no—
58C2×#4339—21no—
59C2×#4339—21no—
60C2×#4339—21no—
61C2×#4339—21no—
62C2×#4339—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339C2×C412yes—
68C2×#4339D412yes—
69C22×D44D411yescharacteristic
70C22×C4×D11—21no—
71C22×Dic22D411yescharacteristic
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D412yes—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11D412yes—
84C2×C22⋊Dic11—21no—
85#67000—24no—
86#67000—24no—
87#66999—28no—
88#66999—28no—
89#66997—24no—
90#66997—24no—
91#66982—28no—
92#66982—28no—
93C2×(C2×D11)⋊C4—24no—
94#66979—21no—
95#66979—21no—
96#66979C2×C412yes—
97#66979D412yes—
98C2×C4⋊Dic11D412yes—
99C2×Dic11⋊C4—24no—
100C2×C4×Dic11—21no—
101C2×#4318—21no—
102C2×#4318—21no—
103C2×#4318—21no—
104C2×#4318—21no—
105C2×#4318—21no—
106C2×#4318—21no—
107C2×#4318—21no—
108C2×#4318—21no—
109C2×#4318—21no—
110C2×#4318—21no—
111C2×#4318D412yes—
112C2×#4318D412yes—
113C22×C11⋊C8—21no—
114C22×C11⋊C8—21no—
115C11×#95—28no—
116#66900—28no—
117#66874—24no—
118#66873—24no—
119#66869—28no—
120#10998—111nomaximal, Sylow
121C24×C11C2×D411yescharacteristic
122C23×D11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—41no—
136C2×Q8×C11—41no—
137C2×Q8×C11—41no—
138C2×Q8×C11—41no—
139C2×Q8×C11—41no—
140C2×Q8×C11—41no—
141C2×Q8×C11—41no—
142C2×Q8×C11—41no—
143C2×Q8×C11—41no—
144C2×Q8×C11—41no—
145C2×Q8×C11—41no—
146C2×Q8×C11—41no—
147C2×Q8×C11—41no—
148C2×Q8×C11—41no—
149C2×Q8×C11—41no—
150C2×Q8×C11—41no—
151C22×C4×C11—24no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—42no—
161C22×C4×C11—41no—
162C22×C4×C11—41no—
163C22×C4×C11—44no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C22×C4×C11C22⋊C414yes—
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11#4111yescharacteristic
178C22×C4×C11#4111yescharacteristic
179C22×C4×C11#4111yescharacteristic
180C22×C4×C11#4111yescharacteristic
181C2×C22⋊D11—22no—
182C2×C22⋊D11—22no—
183C2×C22⋊D11—41no—
184C2×C22⋊D11—41no—
185C2×C22⋊D11—41no—
186C2×C22⋊D11—41no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189#4339—22no—
190#4339—22no—
191#4339—22no—
192#4339—22no—
193#4339—22no—
194#4339—22no—
195#4339—22no—
196#4339—22no—
197#4339—41no—
198#4339—41no—
199#4339—41no—
200#4339—41no—
201#4339—41no—
202#4339—41no—
203#4339—41no—
204#4339—41no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44C22⋊C412yes—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11—41no—
214C2×C4×D11—41no—
215C2×C4×D11—41no—
216C2×C4×D11—41no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C2×Dic22—21no—
221C2×Dic22—21no—
222C2×Dic22C22⋊C412yes—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—41no—
226C11×C4⋊C4—41no—
227C42×C11—22no—
228C42×C11—22no—
229C42×C11—41no—
230C42×C11—41no—
231C22⋊Dic11—22no—
232C22⋊Dic11—22no—
233(C2×D11)⋊C4—216no—
234C4⋊Dic11—22no—
235C4⋊Dic11C22⋊C414yes—
236Dic11⋊C4—216no—
237C4×Dic11—22no—
238C4×Dic11—22no—
239#4318—22no—
240#4318—22no—
241#4318—22no—
242#4318—22no—
243#4318—41no—
244#4318—41no—
245#4318—41no—
246#4318—41no—
247C2×C11⋊C8—22no—
248C2×C11⋊C8—22no—
249C2×C11⋊C8—41no—
250C2×C11⋊C8—41no—
251C2×C11⋊C8—41no—
252C2×C11⋊C8—41no—
253C2×#536—111no—
254C22×#104—111no—
255C2×#417—111no—
256C22×#101—111no—
257C2×#391D1111yescharacteristic, complemented
258#1736—111no—
259C2×#339—111no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11C2×C22⋊C411yescharacteristic
263C23×C11#12011yescharacteristic
264C23×C11#12011yescharacteristic
265C23×C11#12011yescharacteristic
266C23×C11#12111yescharacteristic
267C23×C11#12111yescharacteristic
268C23×C11#12311yescharacteristic
269C22×D11—22no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—42no—
273C22×D11—42no—
274Q8×C11—42no—
275Q8×C11—42no—
276Q8×C11—42no—
277Q8×C11—42no—
278Q8×C11—42no—
279Q8×C11—42no—
280Q8×C11—42no—
281Q8×C11—42no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—44no—
287C2×C4×C11—42no—
288C2×C4×C11—44no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—44no—
295C2×C4×C11—42no—
296C2×C4×C11—82no—
297C2×C4×C11—82no—
298C2×C4×C11C2×C22⋊C411yescharacteristic
299C2×C4×C11C2×C22⋊C411yescharacteristic
300C2×C4×C11C4×D411yescharacteristic
301C2×C4×C11C4×D411yescharacteristic
302C2×C4×C11C4×D411yescharacteristic
303C2×C4×C11C4×D411yescharacteristic
304C2×C4×C11#12011yescharacteristic
305C2×C4×C11#12011yescharacteristic
306C2×C4×C11#12011yescharacteristic
307C2×C4×C11#12011yescharacteristic
308C2×C4×C11#12011yescharacteristic
309C2×C4×C11#12111yescharacteristic
310C2×C4×C11#12111yescharacteristic
311C2×C4×C11#12111yescharacteristic
312C2×C4×C11#12111yescharacteristic
313C2×C4×C11#12111yescharacteristic
314C2×C4×C11#12111yescharacteristic
315C2×C4×C11#12111yescharacteristic
316C2×C4×C11#12111yescharacteristic
317C2×C4×C11#12111yescharacteristic
318C2×C4×C11#12111yescharacteristic
319C2×C4×C11#12311yescharacteristic
320C2×C4×C11#12311yescharacteristic
321C2×C4×C11#12311yescharacteristic
322C2×C4×C11#12411yescharacteristic
323C2×C4×C11#12411yescharacteristic
324C2×C4×C11#12711yescharacteristic
325C2×C4×C11#12711yescharacteristic
326C22⋊D11—42no—
327C22⋊D11—42no—
328C22⋊D11—42no—
329C22⋊D11—42no—
330C2×Dic11—24no—
331C2×Dic11—22no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336D44—22no—
337D44—22no—
338D44—41no—
339D44—41no—
340C4×D11—42no—
341C4×D11—42no—
342C4×D11—42no—
343C4×D11—42no—
344Dic22—22no—
345Dic22—22no—
346Dic22—41no—
347Dic22—41no—
348C11⋊C8—42no—
349C11⋊C8—42no—
350C22×#41—111no—
351C23×Q8C2×D1111yescharacteristic
352C22×M16—111no—
353C22×M16—111no—
354#536—114no—
355#536—222no—
356#536—222no—
357#536—222no—
358C2×C4⋊Q8—221no—
359C2×#124—221no—
360C2×#123—222no—
361C2×C22⋊Q8—222no—
362C2×#117—111no—
363C22×C4⋊C4C2×D1111yescharacteristic
364C22×C42C2×D1111yescharacteristic
365C2×#104—222no—
366C2×#104—222no—
367C2×#104—222no—
368#417—222no—
369#417—222no—
370C2×#103—221no—
371C2×#102—221no—
372C2×#101—222no—
373C2×#101—222no—
374C2×#101—222no—
375#391—22no—
376#391—22no—
377C2×#95—22no—
378#340—222no—
379#339—222no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—21no—
385C22×C11—21no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11#37911yescharacteristic
389C22×C11#38611yescharacteristic
390C22×C11#38611yescharacteristic
391C22×C11#39211yescharacteristic
392C22×C11#39211yescharacteristic
393C22×C11#39411yescharacteristic
394C22×C11#39411yescharacteristic
395C22×C11#45412yes—
396C22×C11#45612yes—
397C2×D11—44no—
398C2×D11—42no—
399C2×D11—81no—
400C2×D11—81no—
401C2×D11—82no—
402C4×C11—44no—
403C4×C11—44no—
404C4×C11—82no—
405C4×C11#38611yescharacteristic
406C4×C11#38611yescharacteristic
407C4×C11#39011yescharacteristic
408C4×C11#39011yescharacteristic
409C4×C11#39211yescharacteristic
410C4×C11#39211yescharacteristic
411C4×C11#39411yescharacteristic
412C4×C11#39411yescharacteristic
413Dic11—44no—
414Dic11—42no—
415C2×#41—112no—
416C2×#41—112no—
417C2×#41—221no—
418C2×#41—221no—
419C2×#41—221no—
420C2×#41—221no—
421C2×#41—221no—
422C2×#41—221no—
423C2×#41—221no—
424C2×#41—221no—
425C2×#41—221no—
426C2×#41—221no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8—21no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—111no—
440C22×Q8C4×D1112yes—
441C22×Q8D4412yes—
442C22×D4—111no—
443C22×D4—221no—
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—221no—
447C23×C4C22⋊D1112yes—
448C23×C4C22×D1111yescharacteristic
449C2×M16—112no—
450C2×M16—112no—
451C2×M16—221no—
452C2×M16—221no—
453C2×M16—221no—
454C2×M16—221no—
455C2×M16—221no—
456C2×M16—221no—
457C2×M16—221no—
458C2×M16—221no—
459C2×M16—221no—
460C2×M16—221no—
461C22×C8—221no—
462C22×C8—221no—
463C4⋊Q8—224no—
464C4⋊Q8—224no—
465#124—224no—
466#124—224no—
467#123—228no—
468#123—228no—
469C22⋊Q8—228no—
470C22⋊Q8—228no—
471#117—112no—
472#117—112no—
473#117—221no—
474#117—221no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—112no—
481C2×C4⋊C4—224no—
482C2×C4⋊C4C22⋊D1112yes—
483C2×C22⋊C4—224no—
484C2×C22⋊C4—221no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—221no—
491C2×C42C22⋊D1112yes—
492#104—228no—
493#103—224no—
494#102—224no—
495#101—228no—
496#95—28no—
497C2×C11—21no—
498C2×C11—21no—
499C2×C11—21no—
500C2×C11—21no—
501C2×C11#143811yescharacteristic
502C2×C11#179312yes—
503C2×C11#200311yescharacteristic
504C2×C11#200511yescharacteristic
505C2×C11#203812yes—
506D11—82no—
507C24—221no—
508C24C2×C22⋊D1111yescharacteristic
509#41—222no—
510#41—222no—
511#41—222no—
512#41—222no—
513#41—222no—
514#41—222no—
515#41—222no—
516#41—222no—
517#41—441no—
518#41—441no—
519#41—441no—
520#41—441no—
521#41—441no—
522#41—441no—
523#41—441no—
524#41—441no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—112no—
554C2×Q8—221no—
555C2×Q8—221no—
556C2×Q8—221no—
557C2×Q8—221no—
558C2×Q8—221no—
559C2×D4—112no—
560C2×D4—222no—
561C2×D4—222no—
562C2×D4—221no—
563C2×D4—221no—
564C2×D4—221no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—441no—
568C2×D4—441no—
569C2×D4—441no—
570C2×D4—441no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—44no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—222no—
587C22×C4—221no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—441no—
591C22×C4—441no—
592C22×C4—441no—
593C22×C4—441no—
594C22×C4(C2×D11)⋊C414yes—
595C22×C4C2×C4×D1111yescharacteristic
596C22×C4C2×D4411yescharacteristic
597C22×C4#433911yescharacteristic
598C22×C4#433911yescharacteristic
599C22×C4D4×D1111yescharacteristic
600C22×C4D4×D1111yescharacteristic
601C22×C4D4×D1111yescharacteristic
602C22×C4D4×D1111yescharacteristic
603C22×C4D4×D1111yescharacteristic
604C22×C4D4×D1111yescharacteristic
605C22×C4#434111yescharacteristic
606C22×C4#434111yescharacteristic
607C22×C4C2×C22⋊D1111yescharacteristic
608C22×C4C2×C22⋊D1111yescharacteristic
609M16—222no—
610M16—222no—
611M16—222no—
612M16—222no—
613M16—441no—
614M16—441no—
615M16—441no—
616M16—441no—
617C2×C8—222no—
618C2×C8—222no—
619C2×C8—441no—
620C2×C8—441no—
621C2×C8—441no—
622C2×C8—441no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—114no—
628C4⋊C4—2216no—
629C4⋊C4—222no—
630C22⋊C4—2216no—
631C22⋊C4—222no—
632C22⋊C4—222no—
633C42—22no—
634C42—22no—
635C42—41no—
636C42—41no—
637C42—222no—
638C42—222no—
639C11#1099811yescharacteristic, complemented, Sylow
640C23—22no—
641C23—22no—
642C23—222no—
643C23—441no—
644C23—441no—
645C23—442no—
646C23—442no—
647C23C2×(C2×D11)⋊C411yescharacteristic
648C23#6698211yescharacteristic
649C23#6699011yescharacteristic
650C23#6699011yescharacteristic
651C23#6699211yescharacteristic
652C23#6699211yescharacteristic
653C23#6700611yescharacteristic
654Q8—42no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—222no—
663Q8—222no—
664Q8—441no—
665Q8—441no—
666D4—222no—
667D4—222no—
668D4—442no—
669D4—442no—
670D4—442no—
671D4—442no—
672D4—441no—
673D4—441no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4—224no—
691C2×C4—222no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4C22⋊C4×D1111yescharacteristic
701C2×C4C22⋊C4×D1111yescharacteristic
702C2×C4(C22⋊D11)⋊C411yescharacteristic
703C2×C4(C22⋊D11)⋊C411yescharacteristic
704C2×C4#6693511yescharacteristic
705C2×C4#6693511yescharacteristic
706C2×C4#6693511yescharacteristic
707C2×C4#6693611yescharacteristic
708C2×C4#6693611yescharacteristic
709C2×C4#6693711yescharacteristic
710C2×C4#6693711yescharacteristic
711C2×C4#6693711yescharacteristic
712C2×C4#6693711yescharacteristic
713C2×C4#6693811yescharacteristic
714C2×C4#6693811yescharacteristic
715C2×C4#6693911yescharacteristic
716C2×C4C4×C22⋊D1111yescharacteristic
717C2×C4C4×C22⋊D1111yescharacteristic
718C2×C4#6698311yescharacteristic
719C2×C4#6698311yescharacteristic
720C2×C4#6699011yescharacteristic
721C2×C4#6699011yescharacteristic
722C2×C4#6699111yescharacteristic
723C2×C4#6699111yescharacteristic
724C2×C4#6699211yescharacteristic
725C2×C4#6699211yescharacteristic
726C2×C4#6699311yescharacteristic
727C2×C4#6699311yescharacteristic
728C8—442no—
729C8—442no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—444no—
739C22—442no—
740C22—882no—
741C22—881no—
742C22—881no—
743C22#1062256811yescharacteristic
744C22#1062257111yescharacteristic
745C22#1062257211yescharacteristic
746C22#1062257211yescharacteristic
747C22#1062267512yes—
748C22#1062270812yes—
749C22#1062282611yescharacteristic
750C22#1062283611yescharacteristic
751C22#1062283611yescharacteristic
752C4—44no—
753C4—44no—
754C4—82no—
755C4—444no—
756C4—442no—
757C4#1062256911yescharacteristic
758C4#1062256911yescharacteristic
759C4#1062257011yescharacteristic
760C4#1062257011yescharacteristic
761C4#1062257311yescharacteristic
762C4#1062257311yescharacteristic
763C4#1062257411yescharacteristic
764C4#1062257411yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—882no—
770C2#1306685511yescharacteristic
771C2#1306857412yes—
772C2#1306963811yescharacteristic
773C2#1306965211yescharacteristic
774C2#1306983312yes—
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#391C2
socleC23×C11#120
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenterC2×#391D11
hypocenterC11#10998
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
4. C22×#66900C2semidirect
5. #13068335C2semidirect
6. C2×#10622161C2semidirect
7. C2×C11×#391C2semidirect
15. #10623347C4semidirect
257. C2×#391D11semidirect
639. C11#10998semidirect

Maximal subgroups

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

subgroupindex
C2×#106233472
C22×#668692
C2×#106225792
C22×#669002
#130683352
C2×#106221612
C2×C11×#3912
#1099811