Finite Group Databasebeta

← #14769576

Subgroups — #14769576

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic
2C2×#10622402C211yesmaximal, characteristic, complemented
3C2×#10622403C211yesmaximal, characteristic, complemented
4#13071457C211yesmaximal, characteristic
5#13071448C211yesmaximal, characteristic, complemented
6#13069498C211yesmaximal, characteristic, complemented
7#13069471C211yesmaximal, characteristic, complemented
8#13068968C211yesmaximal, characteristic, complemented
9#13068968C211yesmaximal, characteristic, complemented
10#13068955C211yesmaximal, characteristic, complemented
11#13068955C211yesmaximal, characteristic, complemented
12#13068647C211yesmaximal, characteristic, complemented
13#13068552C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×#67004—24no—
19C2×#67004—24no—
20C2×#67004C418yescomplemented
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C22×#4324C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C2×#66940C2211yescharacteristic
29C2×#66940C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C11×#380C2211yescharacteristic
36#10622834—21no—
37#10622834—21no—
38#10622834C2211yescharacteristic
39#10622834C2211yescharacteristic
40#10622825—21no—
41#10622825C2211yescharacteristic
42C4×C22⋊Dic11—21no—
43C4×C22⋊Dic11C2211yescharacteristic
44C2×#66880C2211yescharacteristic
45C2×#66880C2211yescharacteristic
46C2×#66880C2211yescharacteristic
47C2×#66880C2211yescharacteristic
48C2×#66879C2211yescharacteristic
49C2×C8×Dic11C2211yescharacteristic
50#10622587C2211yescharacteristic
51#10622587C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54#10622555—21no—
55C22⋊C4×Dic11—21no—
56#10622403—24no—
57#10622402—24no—
58#10622259—21no—
59#10622259—21no—
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C2×C11×#41C2×C414yes—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C23×Dic11—21no—
76C22×Dic22—22no—
77C22×Dic22—22no—
78C22×Dic22—21no—
79C22×Dic22—22no—
80C22×Dic22—41no—
81C22×Dic22—41no—
82C22×Dic22C2×C414yes—
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11D411yescharacteristic
96C2×C22⋊Dic11D411yescharacteristic
97#67004—232no—
98Q8×Dic11—22no—
99Q8×Dic11—22no—
100Q8×Dic11—41no—
101Q8×Dic11—41no—
102C2×#4326—22no—
103C2×#4326—22no—
104C2×#4326C2×C414yes—
105C2×#4326C2×C414yes—
106C2×#4326D414yes—
107C2×#4326D414yes—
108C2×#4324—22no—
109C2×#4324—22no—
110C2×#4324—22no—
111C2×#4324—22no—
112C2×#4324C2×C414yes—
113C2×#4324C2×C414yes—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×C4×Dic11—21no—
121C2×C4×Dic11—21no—
122C2×C4×Dic11—21no—
123C2×C4×Dic11—21no—
124C2×C4×Dic11C2311yescharacteristic
125C2×C4×Dic11C2311yescharacteristic
126C2×#4318—22no—
127C2×#4318—22no—
128C2×#4318C2×C414yes—
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131#66940—22no—
132#66940—22no—
133#66940—41no—
134#66940—41no—
135C11×#103—22no—
136C11×#103—22no—
137C11×#102—41no—
138C11×#102—41no—
139C11×C22⋊C8—22no—
140C11×#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95D411yescharacteristic
147C11⋊#95D411yescharacteristic
148#66880—22no—
149#66880—22no—
150#66880—41no—
151#66880—41no—
152#66879—22no—
153C8×Dic11—22no—
154#66872—22no—
155#66871—22no—
156#22445—111nomaximal, Sylow
157C24×C11—21no—
158C24×C11C2×D411yescharacteristic
159C11×#41—28no—
160C11×#41—44no—
161C11×#41—44no—
162C11×#41—44no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11C22×C412yes—
167C2×Q8×C11C2×D412yes—
168C2×Q8×C11C2×D412yes—
169C2×D4×C11—24no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—42no—
176C2×D4×C11—42no—
177C2×D4×C11C22×C412yes—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—24no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11#4112yes—
191C22×C4×C11C2411yescharacteristic
192C22×Dic11—24no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—42no—
198C22×Dic11—42no—
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201C22×Dic11C2×D411yescharacteristic
202C22×Dic11C2×D411yescharacteristic
203C2×Dic22—28no—
204C2×Dic22—24no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C2×Dic22—21no—
213C2×Dic22—44no—
214C2×Dic22—44no—
215C2×Dic22—44no—
216C2×Dic22—42no—
217C2×Dic22—42no—
218C2×Dic22C22×C412yes—
219C2×Dic22C22×C412yes—
220C2×Dic22C2×D412yes—
221C2×Dic22C2×D412yes—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C22⋊C4—42no—
233C22⋊Dic11—22no—
234C22⋊Dic11—41no—
235C22⋊Dic11—42no—
236C22⋊Dic11—42no—
237C22⋊Dic11—81no—
238C22⋊Dic11—81no—
239C22⋊Dic11—81no—
240#4326—28no—
241#4326C22⋊C4116yescomplemented
242#4324—28no—
243#4324—28no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—42no—
249C4⋊Dic11—42no—
250Dic11⋊C4—42no—
251Dic11⋊C4—42no—
252C4×Dic11—21no—
253C4×Dic11—21no—
254C4×Dic11—21no—
255C4×Dic11—21no—
256C4×Dic11—42no—
257C4×Dic11—42no—
258C4×Dic11—42no—
259C4×Dic11—42no—
260#4318—28no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8C22×C412yes—
264C2×C11⋊C8C22×C412yes—
265C2×C11⋊C8C2×D412yes—
266C2×C11⋊C8C2×D412yes—
267C22×#137—111no—
268C2×#441—111no—
269C2×C4×Q16—111no—
270#2341—111no—
271Q8×C22⋊C4—111no—
272#1973—111no—
273#1968—111no—
274#1880—111no—
275#1880—111no—
276#1878—111no—
277#1878—111no—
278#1809—111no—
279#1788D1111yescharacteristic
280#1787—111no—
281#1753—111no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—22no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11C4×D412yes—
296C23×C11C22×D411yescharacteristic
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11C2×C22⋊C414yes—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—48no—
304D4×C11—41no—
305D4×C11—41no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—48no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11C4×D412yes—
323C2×C4×C11C23×C411yescharacteristic
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×Dic11—22no—
330C2×Dic11—21no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—21no—
334C2×Dic11—22no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—48no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11#13712yescomplemented
354Dic22—22no—
355Dic22—22no—
356Dic22—22no—
357Dic22—22no—
358Dic22—22no—
359Dic22—48no—
360Dic22—41no—
361Dic22—41no—
362Dic22C2×C22⋊C414yes—
363C8×C11—41no—
364C8×C11—41no—
365C11⋊C8—22no—
366C11⋊C8C2×C22⋊C414yes—
367C22×#41C2×D1111yescharacteristic
368C23×Q8—111no—
369C2×#137—118no—
370C2×#137—224no—
371C2×#137—224no—
372C22×Q16—111no—
373C22×Q16—111no—
374C22×SD16—111no—
375C22×SD16—111no—
376C22×M16—111no—
377C2×C4×Q8—111no—
378C2×C4×Q8—111no—
379C2×C4×Q8—111no—
380C2×C4×Q8—111no—
381#441—224no—
382C4×Q16—224no—
383C2×#107—111no—
384C2×#106—111no—
385C2×#103—111no—
386C2×#103—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103C2×D1111yescharacteristic
390C2×#103C2×D1111yescharacteristic
391C2×#102C2×D1111yescharacteristic
392C2×#102C2×D1111yescharacteristic
393C2×C22⋊C8C2×D1111yescharacteristic
394C2×#97—111no—
395C2×C4×C8—111no—
396#391—111no—
397#391—111no—
398#391—221no—
399#391—221no—
400#390—111no—
401#390—111no—
402#390—221no—
403#390—221no—
404#380—111no—
405#380—221no—
406#380—221no—
407#380C2×D1111yescharacteristic
408C4×C22⋊C4—111no—
409C4×C22⋊C4—221no—
410C4×C22⋊C4—221no—
411#340—111no—
412#340—111no—
413#336—111no—
414#336—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11C2×C4×D411yescharacteristic
430C22×C11D4211yescharacteristic
431C22×C11D4211yescharacteristic
432C22×C11C2×#13711yescharacteristic
433C22×C11#57511yescharacteristic
434C22×C11#57711yescharacteristic
435C22×C11#57811yescharacteristic
436C4×C11—22no—
437C4×C11—24no—
438C4×C11—81no—
439C4×C11—81no—
440C4×C11C22×C22⋊C411yescharacteristic
441C4×C11#51811yescharacteristic
442C4×C11#54611yescharacteristic
443C4×C11#54611yescharacteristic
444Dic11—24no—
445Dic11—22no—
446Dic11—42no—
447Dic11—41no—
448Dic11—41no—
449Dic11—41no—
450Dic11—81no—
451Dic11—81no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—41no—
456C2×#41—41no—
457C2×#41C4×D1114yes—
458C22×Q8—114no—
459C22×Q8—111no—
460C22×Q8—111no—
461C22×Q8—222no—
462C22×Q8—222no—
463C22×Q8—221no—
464C22×Q8—222no—
465C22×Q8—441no—
466C22×Q8—441no—
467C22×Q8C22×D1111yescharacteristic
468C22×D4—21no—
469C22×D4C22×D1111yescharacteristic
470C23×C4—21no—
471C23×C4—221no—
472C23×C4C22×D1111yescharacteristic
473#137—2232no—
474C2×Q16—114no—
475C2×Q16—114no—
476C2×Q16—114no—
477C2×Q16—114no—
478C2×Q16—222no—
479C2×Q16—222no—
480C2×SD16—114no—
481C2×SD16—114no—
482C2×SD16—222no—
483C2×SD16—222no—
484C2×SD16—222no—
485C2×SD16—222no—
486C2×M16—114no—
487C2×M16—222no—
488C2×M16—222no—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8C22×D1111yescharacteristic
492C22×C8C22×D1111yescharacteristic
493C4×Q8—222no—
494C4×Q8—222no—
495C4×Q8—222no—
496C4×Q8—222no—
497C4×Q8—441no—
498C4×Q8—441no—
499C4×Q8—441no—
500C4×Q8—441no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4C22×D1111yescharacteristic
508C2×C4⋊C4C22×D1111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—111no—
511C2×C22⋊C4—111no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C42—111no—
518C2×C42—111no—
519C2×C42—221no—
520C2×C42—221no—
521C2×C42—221no—
522C2×C42—221no—
523#107—222no—
524#106—222no—
525#103—22no—
526#103—22no—
527#103—222no—
528#103—222no—
529#103—441no—
530#103—441no—
531#102—41no—
532#102—41no—
533C22⋊C8—22no—
534#97—222no—
535C4×C8—222no—
536#95—21no—
537#95—111no—
538#95—111no—
539#95—221no—
540#95—221no—
541#95—221no—
542#95—221no—
543#95—221no—
544C2×C11—42no—
545C2×C11—82no—
546C2×C11D4×C22⋊C411yescharacteristic
547C2×C11C4×#13711yescharacteristic
548C2×C11#294711yescharacteristic
549C2×C11#327011yescharacteristic
550C2×C11#327111yescharacteristic
551C2×C11#327711yescharacteristic
552C2×C11#327811yescharacteristic
553C24—21no—
554C24D4×D1111yescharacteristic
555#41—28no—
556#41—44no—
557#41—44no—
558#41—44no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—112no—
563C2×Q8—112no—
564C2×Q8—112no—
565C2×Q8—112no—
566C2×Q8—228no—
567C2×Q8—224no—
568C2×Q8—221no—
569C2×Q8—221no—
570C2×Q8—221no—
571C2×Q8—221no—
572C2×Q8—221no—
573C2×Q8—221no—
574C2×Q8—221no—
575C2×Q8—221no—
576C2×Q8—442no—
577C2×Q8—442no—
578C2×Q8—444no—
579C2×Q8—444no—
580C2×Q8—444no—
581C2×Q8C2×C4×D1112yes—
582C2×Q8D4×D1112yes—
583C2×Q8D4×D1112yes—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4C2×C4×D1112yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—111no—
606C22×C4—111no—
607C22×C4—221no—
608C22×C4—224no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—442no—
613C22×C4—442no—
614C22×C4C2×C4×D1112yes—
615C22×C4D4×D1111yescharacteristic
616C22×C4#434112yes—
617C22×C4C23×D1111yescharacteristic
618Q16—1116no—
619Q16—228no—
620SD16—228no—
621SD16—228no—
622M16—228no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—112no—
630C2×C8—112no—
631C2×C8—112no—
632C2×C8—112no—
633C2×C8—221no—
634C2×C8—221no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—442no—
644C4⋊C4—442no—
645C4⋊C4—442no—
646C4⋊C4—442no—
647C22⋊C4—42no—
648C22⋊C4—222no—
649C22⋊C4—442no—
650C22⋊C4—441no—
651C22⋊C4—442no—
652C22⋊C4—881no—
653C22⋊C4—881no—
654C22⋊C4—881no—
655C42—221no—
656C42—221no—
657C42—221no—
658C42—221no—
659C42—442no—
660C42—442no—
661C42—442no—
662C42—442no—
663C11#2244511yescharacteristic, complemented, Sylow
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23(C22⋊D11)⋊C412yes—
678C23C2×D4×D1111yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—114no—
683Q8—222no—
684Q8—222no—
685Q8—222no—
686Q8—222no—
687Q8—222no—
688Q8—448no—
689Q8—441no—
690Q8—441no—
691Q8C22⋊C4×D1114yes—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—41no—
696D4—41no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—48no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—112no—
714C2×C4—222no—
715C2×C4—221no—
716C2×C4—221no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—221no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—448no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4(C22⋊D11)⋊C412yes—
739C2×C4C22×C4×D1111yescharacteristic
740C2×C4C2×D4×D1111yescharacteristic
741C2×C4C2×D4×D1111yescharacteristic
742C2×C4C2×#434111yescharacteristic
743C2×C4#6703711yescharacteristic
744C2×C4#6703711yescharacteristic
745C8—41no—
746C8—41no—
747C8—114no—
748C8—222no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22C2×(C22⋊D11)⋊C411yescharacteristic
764C22#1062312111yescharacteristic
765C22#1062312111yescharacteristic
766C22#1062330111yescharacteristic
767C22#1062330211yescharacteristic
768C22#1062330411yescharacteristic
769C22D11×#13711yescharacteristic
770C4—22no—
771C4—24no—
772C4—81no—
773C4—81no—
774C4—224no—
775C4—222no—
776C4—442no—
777C4—441no—
778C4—441no—
779C4—441no—
780C4—881no—
781C4—881no—
782C4C2×C22⋊C4×D1111yescharacteristic
783C4#1062301711yescharacteristic
784C4#1062312211yescharacteristic
785C4#1062312211yescharacteristic
786C2—42no—
787C2—82no—
788C2#1307143211yescharacteristic
789C2#1307744011yescharacteristic
790C2#1307746211yescharacteristic
791C2#1308018411yescharacteristic
792C2#1308019911yescharacteristic
793C2#1308026611yescharacteristic
794C2#1308027511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#22445
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622402C2semidirect
3. C2×#10622403C2semidirect
5. #13071448C2semidirect
6. #13069498C2semidirect
7. #13069471C2semidirect
8. #13068968C2semidirect
9. #13068968C2semidirect
10. #13068955C2semidirect
11. #13068955C2semidirect
12. #13068647C2semidirect
13. #13068552C2semidirect
14. #13068402C2semidirect
20. C2×#67004C4semidirect
241. #4326C22⋊C4semidirect
353. C2×Dic11#137semidirect
663. C11#22445semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106224022
C2×#106224032
#130714572
#130714482
#130694982
#130694712
#130689682
#130689552
#130686472
#130685522
#130684022
C11×#17882
#2244511