Finite Group Databasebeta

← #14660424

Subgroups — #14660424

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×#10623356C211yesmaximal, characteristic
2C2×#10622845C211yesmaximal, characteristic
3C22×#66888C211yesmaximal, characteristic, complemented
4C2×#10622542C211yesmaximal, characteristic, complemented
5#13068336C211yesmaximal, characteristic, complemented
6C2×#10622161C211yesmaximal, characteristic, complemented
7C22×C11×#104C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12#10623356—22no—
13#10623356—22no—
14#10623356—22no—
15#10623356C414yescomplemented
16C2×#66997—21no—
17C2×#66989—21no—
18C2×#66988—22no—
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66977—22no—
22C22×#4318C2211yescharacteristic
23C2×C11×#104—22no—
24C2×C11×#104—22no—
25C2×C11×#104—22no—
26#10622845—22no—
27#10622845—22no—
28C2×#66899—21no—
29C2×#66896—21no—
30C2×C11⋊#95—22no—
31C2×#66888—22no—
32C2×#66888—22no—
33C2×#66888—22no—
34#10622542—22no—
35#10622542—22no—
36#10622189—22no—
37#10622161—22no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41C2×C412yes—
49C2×C11×#41D412yes—
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C23×Dic11D412yes—
58C22×Dic22—21no—
59C22×Dic22—21no—
60C22×Dic22—21no—
61C22×Dic22—21no—
62C22×Dic22—21no—
63C22×Dic22—21no—
64C22×Dic22—21no—
65C22×Dic22—21no—
66C22×Dic22—21no—
67C22×Dic22—21no—
68C22×Dic22—21no—
69C22×Dic22—21no—
70C22×Dic22C2×C412yes—
71C22×Dic22D412yes—
72C2×C11×M16—21no—
73C2×C11×M16—21no—
74C2×C11×M16—21no—
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C2×C11×M16D412yes—
78C22×C8×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11D412yes—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—21no—
87#66997—24no—
88#66997—24no—
89#66989—24no—
90#66989—24no—
91#66988—28no—
92#66988—28no—
93#66979—21no—
94#66979—21no—
95#66979C2×C412yes—
96#66979D412yes—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11D412yes—
103C2×C4⋊Dic11D412yes—
104#66977—28no—
105#66977—28no—
106C2×Dic11⋊C4—24no—
107C2×C4×Dic11—21no—
108C2×#4318—21no—
109C2×#4318—21no—
110C2×#4318—21no—
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318D412yes—
114C22×C11⋊C8—21no—
115C11×#104—28no—
116#66899—24no—
117#66896—24no—
118C11⋊#95—28no—
119#66888—28no—
120#10998—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—22no—
128C11×#41—22no—
129C11×#41—22no—
130C11×#41—22no—
131C11×#41—41no—
132C11×#41—41no—
133C11×#41—41no—
134C11×#41—41no—
135C11×#41—41no—
136C11×#41—41no—
137C11×#41—41no—
138C11×#41—41no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22⋊C412yes—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11C22⋊C412yes—
157C22×C4×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—42no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11C22×C411yescharacteristic
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×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11#4111yescharacteristic
180C22×C4×C11#4111yescharacteristic
181C22×C4×C11#4111yescharacteristic
182C22×C4×C11#4111yescharacteristic
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—44no—
192C22×Dic11—41no—
193C22×Dic11—41no—
194C22×Dic11C22⋊C414yes—
195C2×Dic22—22no—
196C2×Dic22—22no—
197C2×Dic22—22no—
198C2×Dic22—22no—
199C2×Dic22—22no—
200C2×Dic22—22no—
201C2×Dic22—22no—
202C2×Dic22—22no—
203C2×Dic22—22no—
204C2×Dic22—22no—
205C2×Dic22—22no—
206C2×Dic22—22no—
207C2×Dic22—41no—
208C2×Dic22—41no—
209C2×Dic22—41no—
210C2×Dic22—41no—
211C2×Dic22—41no—
212C2×Dic22—41no—
213C2×Dic22—41no—
214C2×Dic22—41no—
215C2×Dic22—41no—
216C2×Dic22—41no—
217C2×Dic22—41no—
218C2×Dic22—41no—
219C2×Dic22—41no—
220C2×Dic22—41no—
221C2×Dic22—41no—
222C2×Dic22—41no—
223C11×M16—22no—
224C11×M16—22no—
225C11×M16—41no—
226C11×M16—41no—
227C2×C8×C11—22no—
228C2×C8×C11—41no—
229C2×C8×C11—41no—
230C42×C11—22no—
231C42×C11—22no—
232C42×C11—41no—
233C42×C11—41no—
234C22⋊Dic11—216no—
235C22⋊Dic11—22no—
236C22⋊Dic11—22no—
237C4⋊Dic11—22no—
238C4⋊Dic11—22no—
239C4⋊Dic11—22no—
240C4⋊Dic11—41no—
241C4⋊Dic11—41no—
242C4⋊Dic11C22⋊C414yes—
243Dic11⋊C4—216no—
244C4×Dic11—22no—
245C4×Dic11—22no—
246#4318—22no—
247#4318—22no—
248#4318—41no—
249#4318—41no—
250C2×C11⋊C8—22no—
251C2×C11⋊C8—41no—
252C2×C11⋊C8—41no—
253C2×#536—111no—
254C22×#104D1111yescharacteristic
255C2×#417—111no—
256C22×#101—111no—
257C2×#391—111no—
258#1736—111no—
259C2×#339—111no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11C2×C22⋊C411yescharacteristic
268C23×C11#12011yescharacteristic
269C23×C11#12011yescharacteristic
270C23×C11#12011yescharacteristic
271C23×C11#12111yescharacteristic
272C23×C11#12111yescharacteristic
273C23×C11#12311yescharacteristic
274Q8×C11—22no—
275Q8×C11—22no—
276Q8×C11—41no—
277Q8×C11—41no—
278D4×C11—22no—
279D4×C11—22no—
280D4×C11—42no—
281D4×C11—42no—
282D4×C11—42no—
283D4×C11—42no—
284D4×C11—41no—
285D4×C11—41no—
286C2×C4×C11—24no—
287C2×C4×C11—22no—
288C2×C4×C11—44no—
289C2×C4×C11—42no—
290C2×C4×C11—44no—
291C2×C4×C11—42no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
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
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—44no—
337C2×Dic11—42no—
338C2×Dic11—82no—
339C2×Dic11—82no—
340Dic22—42no—
341Dic22—42no—
342Dic22—42no—
343Dic22—42no—
344Dic22—42no—
345Dic22—42no—
346Dic22—42no—
347Dic22—42no—
348C8×C11—42no—
349C11⋊C8—42no—
350C22×#41C2×D1111yescharacteristic
351C23×Q8—111no—
352C22×M16—111no—
353C22×M16C2×D1111yescharacteristic
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⋊C4—111no—
364C22×C42C2×D1111yescharacteristic
365C2×#104—22no—
366C2×#104—22no—
367C2×#104—22no—
368#417—222no—
369#417—222no—
370C2×#103—221no—
371C2×#102—221no—
372C2×#101—222no—
373C2×#101—222no—
374C2×#101—222no—
375#391—222no—
376#391—222no—
377C2×#95—222no—
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—44no—
389C22×C11—42no—
390C22×C11—81no—
391C22×C11—81no—
392C22×C11—82no—
393C22×C11#37911yescharacteristic
394C22×C11#38611yescharacteristic
395C22×C11#38611yescharacteristic
396C22×C11#39211yescharacteristic
397C22×C11#39211yescharacteristic
398C22×C11#39411yescharacteristic
399C22×C11#39411yescharacteristic
400C22×C11#45412yes—
401C22×C11#45612yes—
402C4×C11—44no—
403C4×C11—42no—
404C4×C11#38611yescharacteristic
405C4×C11#38611yescharacteristic
406C4×C11#39011yescharacteristic
407C4×C11#39011yescharacteristic
408C4×C11#39211yescharacteristic
409C4×C11#39211yescharacteristic
410C4×C11#39411yescharacteristic
411C4×C11#39411yescharacteristic
412Dic11—44no—
413Dic11—44no—
414Dic11—82no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41C4×D1112yes—
426C2×#41C22⋊D1112yes—
427C22×Q8—112no—
428C22×Q8—112no—
429C22×Q8—221no—
430C22×Q8—221no—
431C22×Q8—221no—
432C22×Q8—221no—
433C22×Q8—221no—
434C22×Q8—221no—
435C22×Q8—221no—
436C22×Q8—221no—
437C22×Q8—221no—
438C22×Q8—221no—
439C22×Q8—221no—
440C22×Q8—221no—
441C22×Q8D4411yescharacteristic
442C22×D4—21no—
443C22×D4D4411yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—112no—
447C23×C4—221no—
448C23×C4C22×D1111yescharacteristic
449C2×M16—21no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16—21no—
453C2×M16—21no—
454C2×M16—112no—
455C2×M16—221no—
456C2×M16—221no—
457C2×M16—221no—
458C2×M16—221no—
459C2×M16—221no—
460C2×M16C22⋊D1112yes—
461C22×C8—21no—
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—112no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—224no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
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—28no—
493#103—224no—
494#102—224no—
495#101—228no—
496#95—228no—
497C2×C11—21no—
498C2×C11—21no—
499C2×C11—21no—
500C2×C11—21no—
501C2×C11—82no—
502C2×C11#143811yescharacteristic
503C2×C11#179312yes—
504C2×C11#200311yescharacteristic
505C2×C11#200511yescharacteristic
506C2×C11#203812yes—
507C24—21no—
508C24D4×D1111yescharacteristic
509#41—22no—
510#41—22no—
511#41—22no—
512#41—22no—
513#41—22no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—41no—
518#41—41no—
519#41—41no—
520#41—41no—
521#41—41no—
522#41—41no—
523#41—41no—
524#41—41no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—222no—
531C2×Q8—222no—
532C2×Q8—222no—
533C2×Q8—222no—
534C2×Q8—222no—
535C2×Q8—222no—
536C2×Q8—222no—
537C2×Q8—222no—
538C2×Q8—222no—
539C2×Q8—222no—
540C2×Q8—222no—
541C2×Q8—222no—
542C2×Q8—441no—
543C2×Q8—441no—
544C2×Q8—441no—
545C2×Q8—441no—
546C2×Q8—441no—
547C2×Q8—441no—
548C2×Q8—441no—
549C2×Q8—441no—
550C2×Q8—441no—
551C2×Q8—441no—
552C2×Q8—441no—
553C2×Q8—441no—
554C2×Q8—441no—
555C2×Q8—441no—
556C2×Q8—441no—
557C2×Q8—441no—
558C2×Q8(C2×D11)⋊C412yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4(C2×D11)⋊C412yes—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—42no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—114no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—444no—
593C22×C4—441no—
594C22×C4—441no—
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×C4#434111yescharacteristic
605C22×C4#434111yescharacteristic
606C22×C4C2×C22⋊D1111yescharacteristic
607C22×C4C2×C22⋊D1111yescharacteristic
608C22×C4C2×C22⋊D1111yescharacteristic
609M16—22no—
610M16—22no—
611M16—41no—
612M16—41no—
613M16—222no—
614M16—222no—
615M16—441no—
616M16—441no—
617C2×C8—22no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—222no—
621C2×C8—441no—
622C2×C8—441no—
623C4⋊C4—114no—
624C4⋊C4—2216no—
625C4⋊C4—222no—
626C4⋊C4—222no—
627C4⋊C4—222no—
628C4⋊C4—441no—
629C4⋊C4—441no—
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—22no—
643C23—41no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23C22⋊C4×D1111yescharacteristic
648C23#6693511yescharacteristic
649C23#6693611yescharacteristic
650C23#6693711yescharacteristic
651C23#6699011yescharacteristic
652C23#6699011yescharacteristic
653C23#6699111yescharacteristic
654Q8—22no—
655Q8—22no—
656Q8—41no—
657Q8—41no—
658Q8—442no—
659Q8—442no—
660Q8—442no—
661Q8—442no—
662Q8—442no—
663Q8—442no—
664Q8—442no—
665Q8—442no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—224no—
687C2×C4—224no—
688C2×C4—224no—
689C2×C4—224no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4—442no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—444no—
697C2×C4—442no—
698C2×C4—882no—
699C2×C4—882no—
700C2×C4C22⋊C4×D1111yescharacteristic
701C2×C4(C22⋊D11)⋊C411yescharacteristic
702C2×C4(C22⋊D11)⋊C411yescharacteristic
703C2×C4#6693511yescharacteristic
704C2×C4#6693511yescharacteristic
705C2×C4#6693611yescharacteristic
706C2×C4#6693711yescharacteristic
707C2×C4#6693711yescharacteristic
708C2×C4#6693711yescharacteristic
709C2×C4#6693811yescharacteristic
710C2×C4#6693811yescharacteristic
711C2×C4#6693911yescharacteristic
712C2×C4C2×(C2×D11)⋊C411yescharacteristic
713C2×C4C4×C22⋊D1111yescharacteristic
714C2×C4C4×C22⋊D1111yescharacteristic
715C2×C4#6698211yescharacteristic
716C2×C4#6698311yescharacteristic
717C2×C4#6698311yescharacteristic
718C2×C4#6699011yescharacteristic
719C2×C4#6699011yescharacteristic
720C2×C4#6699111yescharacteristic
721C2×C4#6699211yescharacteristic
722C2×C4#6699211yescharacteristic
723C2×C4#6699211yescharacteristic
724C2×C4#6699211yescharacteristic
725C2×C4#6699311yescharacteristic
726C2×C4#6699311yescharacteristic
727C2×C4#6700611yescharacteristic
728C8—42no—
729C8—442no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—44no—
739C22—42no—
740C22—82no—
741C22—81no—
742C22—81no—
743C22#1062243912yes—
744C22#1062244012yes—
745C22#1062256811yescharacteristic
746C22#1062256911yescharacteristic
747C22#1062256911yescharacteristic
748C22#1062257211yescharacteristic
749C22#1062257311yescharacteristic
750C22#1062257411yescharacteristic
751C22#1062283611yescharacteristic
752C4—44no—
753C4—42no—
754C4—444no—
755C4—444no—
756C4—882no—
757C4#1062257011yescharacteristic
758C4#1062257011yescharacteristic
759C4#1062257111yescharacteristic
760C4#1062257211yescharacteristic
761C4#1062257311yescharacteristic
762C4#1062257411yescharacteristic
763C4#1062282611yescharacteristic
764C4#1062283611yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—82no—
770C2#1306685511yescharacteristic
771C2#1306857612yes—
772C2#1306963711yescharacteristic
773C2#1306965111yescharacteristic
774C2#1306983212yes—
subgroupG/H
centerC23#66935
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#104C2
socleC23×C11#120
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenterC22×#104D11
hypocenterC11#10998
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
3. C22×#66888C2semidirect
4. C2×#10622542C2semidirect
5. #13068336C2semidirect
6. C2×#10622161C2semidirect
15. #10623356C4semidirect
639. C11#10998semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
C2×#106228452
C22×#668882
C2×#106225422
#130683362
C2×#106221612
C22×C11×#1042
#1099811