Finite Group Databasebeta

← #14660423

Subgroups — #14660423

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
1C22×#66901C211yesmaximal, characteristic
2C2×#10622845C211yesmaximal, characteristic
3C22×#66900C211yesmaximal, characteristic, complemented
4C2×#10622843C211yesmaximal, characteristic, complemented
5#13068337C211yesmaximal, characteristic, complemented
6C2×#10622170C211yesmaximal, characteristic, complemented
7C2×C11×#536C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C23×Q8×C11C2211yescharacteristic
10C11×#536—22no—
11C11×#536—22no—
12C11×#536—22no—
13C11×#536C414yescomplemented
14C2×C11×C4⋊Q8—21no—
15C2×C11×#124—21no—
16C2×C11×#123—22no—
17C2×C11×C22⋊Q8—22no—
18C2×C11×#117C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C2×#66901—22no—
24C2×#66901—22no—
25C2×#66901—22no—
26#10622845—22no—
27#10622845—22no—
28#10622843—22no—
29#10622843—22no—
30C2×#66900—22no—
31C2×#66900—22no—
32C2×#66900—22no—
33C2×#66899—21no—
34C2×#66896—21no—
35C2×C11⋊#95—22no—
36#10622170—22no—
37#10622167—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×C11—21no—
51C22×Q8×C11—21no—
52C22×Q8×C11—21no—
53C22×Q8×C11—21no—
54C22×Q8×C11—21no—
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×Q8×C11—21no—
58C22×Q8×C11—21no—
59C22×Q8×C11—21no—
60C22×Q8×C11—21no—
61C22×Q8×C11—21no—
62C22×Q8×C11C2×C412yes—
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11D412yes—
65C22×D4×C11—21no—
66C22×D4×C11D411yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11D412yes—
69C23×C4×C11C2311yescharacteristic
70C23×Dic11—21no—
71C23×Dic11—21no—
72C11×C4⋊Q8—24no—
73C11×C4⋊Q8—24no—
74C11×#124—24no—
75C11×#124—24no—
76C11×#123—28no—
77C11×#123—28no—
78C11×C22⋊Q8—28no—
79C11×C22⋊Q8—28no—
80C11×#117—21no—
81C11×#117—21no—
82C11×#117C2×C412yes—
83C11×#117D412yes—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D412yes—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11D412yes—
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—
115#66901—28no—
116#66900—28no—
117#66899—24no—
118#66896—24no—
119C11⋊#95—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—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11—22no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—21no—
149C2×Q8×C11—22no—
150C2×Q8×C11—22no—
151C2×Q8×C11—22no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—41no—
157C2×Q8×C11—41no—
158C2×Q8×C11—41no—
159C2×Q8×C11—41no—
160C2×Q8×C11—41no—
161C2×Q8×C11—41no—
162C2×Q8×C11—41no—
163C2×Q8×C11—41no—
164C2×Q8×C11—41no—
165C2×Q8×C11—41no—
166C2×Q8×C11—41no—
167C2×Q8×C11—41no—
168C2×Q8×C11—41no—
169C2×Q8×C11—41no—
170C2×Q8×C11—41no—
171C2×Q8×C11—41no—
172C2×Q8×C11C22⋊C412yes—
173C2×D4×C11—22no—
174C2×D4×C11—22no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—41no—
181C2×D4×C11—41no—
182C2×D4×C11—41no—
183C2×D4×C11—41no—
184C2×D4×C11C22⋊C412yes—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—21no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—41no—
196C22×C4×C11—41no—
197C22×C4×C11—41no—
198C22×C4×C11—41no—
199C22×C4×C11C22⋊C414yes—
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11#4111yescharacteristic
211C22×C4×C11#4111yescharacteristic
212C22×C4×C11#4111yescharacteristic
213C22×C4×C11#4111yescharacteristic
214C22×Dic11—24no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—42no—
218C22×Dic11—44no—
219C22×Dic11—41no—
220C22×Dic11—41no—
221C22×Dic11—41no—
222C22×Dic11—41no—
223C11×C4⋊C4—216no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4C22⋊C414yes—
226C11×C22⋊C4—216no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—22no—
229C42×C11—22no—
230C42×C11—22no—
231C4⋊Dic11—22no—
232C4⋊Dic11—22no—
233C4⋊Dic11—41no—
234C4⋊Dic11—41no—
235C4×Dic11—22no—
236C4×Dic11—22no—
237C4×Dic11—41no—
238C4×Dic11—41no—
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×#536D1111yescharacteristic
254C22×#104—111no—
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—42no—
277Q8×C11—42no—
278Q8×C11—42no—
279Q8×C11—42no—
280Q8×C11—42no—
281Q8×C11—42no—
282Q8×C11—41no—
283Q8×C11—42no—
284Q8×C11—42no—
285Q8×C11—41no—
286D4×C11—22no—
287D4×C11—22no—
288D4×C11—42no—
289D4×C11—42no—
290D4×C11—42no—
291D4×C11—42no—
292D4×C11—41no—
293D4×C11—41no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—22no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—41no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—41no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11C2×C22⋊C411yescharacteristic
312C2×C4×C11C2×C22⋊C411yescharacteristic
313C2×C4×C11C4×D411yescharacteristic
314C2×C4×C11C4×D411yescharacteristic
315C2×C4×C11C4×D411yescharacteristic
316C2×C4×C11C4×D411yescharacteristic
317C2×C4×C11#12011yescharacteristic
318C2×C4×C11#12011yescharacteristic
319C2×C4×C11#12011yescharacteristic
320C2×C4×C11#12011yescharacteristic
321C2×C4×C11#12011yescharacteristic
322C2×C4×C11#12111yescharacteristic
323C2×C4×C11#12111yescharacteristic
324C2×C4×C11#12111yescharacteristic
325C2×C4×C11#12111yescharacteristic
326C2×C4×C11#12111yescharacteristic
327C2×C4×C11#12111yescharacteristic
328C2×C4×C11#12111yescharacteristic
329C2×C4×C11#12111yescharacteristic
330C2×C4×C11#12111yescharacteristic
331C2×C4×C11#12111yescharacteristic
332C2×C4×C11#12311yescharacteristic
333C2×C4×C11#12311yescharacteristic
334C2×C4×C11#12311yescharacteristic
335C2×C4×C11#12411yescharacteristic
336C2×C4×C11#12411yescharacteristic
337C2×C4×C11#12711yescharacteristic
338C2×C4×C11#12711yescharacteristic
339C2×Dic11—24no—
340C2×Dic11—44no—
341C2×Dic11—42no—
342C2×Dic11—44no—
343C2×Dic11—42no—
344C2×Dic11—44no—
345C2×Dic11—42no—
346C2×Dic11—82no—
347C2×Dic11—82no—
348C11⋊C8—42no—
349C11⋊C8—42no—
350C22×#41C2×D1111yescharacteristic
351C23×Q8C2×D1111yescharacteristic
352C22×M16—111no—
353C22×M16—111no—
354#536—22no—
355#536—22no—
356#536—22no—
357#536Dic1114yescomplemented
358C2×C4⋊Q8—21no—
359C2×#124—21no—
360C2×#123—22no—
361C2×C22⋊Q8—22no—
362C2×#117C2×D1111yescharacteristic
363C22×C4⋊C4—111no—
364C22×C42—111no—
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—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—44no—
404C4×C11—42no—
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—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×#41C2×Dic1112yes—
426C2×#41C22⋊D1112yes—
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×Q8C2×Dic1112yes—
440C22×Q8C22⋊D1111yescharacteristic
441C22×Q8C22⋊D1112yes—
442C22×D4—21no—
443C22×D4C22⋊D1111yescharacteristic
444C23×C4—21no—
445C23×C4—221no—
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—24no—
464C4⋊Q8—24no—
465#124—24no—
466#124—24no—
467#123—28no—
468#123—28no—
469C22⋊Q8—28no—
470C22⋊Q8—28no—
471#117—21no—
472#117—21no—
473#117C2×Dic1112yes—
474#117C22⋊D1112yes—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4C22⋊D1112yes—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—21no—
485C2×C42—21no—
486C2×C42—112no—
487C2×C42—221no—
488C2×C42—221no—
489C2×C42—221no—
490C2×C42—221no—
491C2×C42—221no—
492#104—228no—
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—
508C24C2×C22⋊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—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—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
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—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8C22⋊Dic1112yes—
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×D4C22⋊Dic1112yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—224no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—442no—
589C22×C4—441no—
590C22×C4—441no—
591C22×C4—444no—
592C22×C4—441no—
593C22×C4—441no—
594C22×C4C22⋊Dic1114yes—
595C22×C4D4×D1111yescharacteristic
596C22×C4D4×D1111yescharacteristic
597C22×C4D4×D1111yescharacteristic
598C22×C4D4×D1111yescharacteristic
599C22×C4#434111yescharacteristic
600C22×C4#434111yescharacteristic
601C22×C4#434111yescharacteristic
602C22×C4#434111yescharacteristic
603C22×C4C22×Dic1111yescharacteristic
604C22×C4C2×C22⋊D1111yescharacteristic
605C22×C4C2×C22⋊D1111yescharacteristic
606C22×C4C2×C22⋊D1111yescharacteristic
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—216no—
624C4⋊C4—22no—
625C4⋊C4—222no—
626C4⋊C4—222no—
627C4⋊C4—441no—
628C4⋊C4—441no—
629C4⋊C4C22⋊Dic1114yes—
630C22⋊C4—216no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C42—22no—
634C42—22no—
635C42—222no—
636C42—222no—
637C42—441no—
638C42—441no—
639C11#1099811yescharacteristic, complemented, Sylow
640C23—22no—
641C23—22no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23#6698811yescharacteristic
648C23#6699011yescharacteristic
649C23#6699211yescharacteristic
650C23#6699211yescharacteristic
651C23C2×C22⋊Dic1111yescharacteristic
652C23#6700611yescharacteristic
653C23#6700611yescharacteristic
654Q8—22no—
655Q8—22no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—41no—
663Q8—42no—
664Q8—42no—
665Q8—41no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—224no—
692C2×C4—444no—
693C2×C4—444no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—444no—
697C2×C4—442no—
698C2×C4—882no—
699C2×C4—882no—
700C2×C4D4×Dic1111yescharacteristic
701C2×C4D4×Dic1111yescharacteristic
702C2×C4D4×Dic1111yescharacteristic
703C2×C4D4×Dic1111yescharacteristic
704C2×C4#6698811yescharacteristic
705C2×C4#6698811yescharacteristic
706C2×C4#6698811yescharacteristic
707C2×C4#6698911yescharacteristic
708C2×C4#6698911yescharacteristic
709C2×C4#6699011yescharacteristic
710C2×C4#6699011yescharacteristic
711C2×C4#6699011yescharacteristic
712C2×C4#6699111yescharacteristic
713C2×C4#6699111yescharacteristic
714C2×C4#6699111yescharacteristic
715C2×C4#6699111yescharacteristic
716C2×C4#6699211yescharacteristic
717C2×C4#6699211yescharacteristic
718C2×C4#6699211yescharacteristic
719C2×C4#6699211yescharacteristic
720C2×C4#6699211yescharacteristic
721C2×C4#6699211yescharacteristic
722C2×C4#6699311yescharacteristic
723C2×C4#6699311yescharacteristic
724C2×C4C2×C22⋊Dic1111yescharacteristic
725C2×C4C2×C22⋊Dic1111yescharacteristic
726C2×C4#6700611yescharacteristic
727C2×C4#6700611yescharacteristic
728C8—442no—
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#1062283311yescharacteristic
744C22#1062283311yescharacteristic
745C22#1062283511yescharacteristic
746C22#1062283511yescharacteristic
747C22#1062283611yescharacteristic
748C22#1062283611yescharacteristic
749C22#1062285812yes—
750C22#1062285912yes—
751C22#1062286011yescharacteristic
752C4—44no—
753C4—44no—
754C4—42no—
755C4—444no—
756C4—882no—
757C4#1062283311yescharacteristic
758C4#1062283311yescharacteristic
759C4#1062283411yescharacteristic
760C4#1062283411yescharacteristic
761C4#1062283511yescharacteristic
762C4#1062283511yescharacteristic
763C4#1062283611yescharacteristic
764C4#1062283611yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—82no—
770C2#1306685711yescharacteristic
771C2#1306857512yes—
772C2#1306963611yescharacteristic
773C2#1306965011yescharacteristic
774C2#1306983012yes—
subgroupG/H
centerC23#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#536C2
socleC23×C11#120
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenterC2×#536D11
hypocenterC11#10998
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
3. C22×#66900C2semidirect
4. C2×#10622843C2semidirect
5. #13068337C2semidirect
6. C2×#10622170C2semidirect
13. C11×#536C4semidirect
357. #536Dic11semidirect
639. C11#10998semidirect

Maximal subgroups

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

subgroupindex
C22×#669012
C2×#106228452
C22×#669002
C2×#106228432
#130683372
C2×#106221702
C2×C11×#5362
#1099811