Finite Group Databasebeta

← #14791439

Subgroups — #14791439

Order 2816.

1464 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622654C211yesmaximal, characteristic, complemented
2C2×#10622852C211yesmaximal, characteristic, complemented
3C2×#10622841C211yesmaximal, characteristic, complemented
4C22×#66899C211yesmaximal, characteristic, complemented
5#13072067C211yesmaximal, characteristic, complemented
6#13069852C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic, complemented
8#13069710C211yesmaximal, characteristic, complemented
9#13069624C211yesmaximal, characteristic, complemented
10#13068957C211yesmaximal, characteristic, complemented
11#13068934C211yesmaximal, characteristic, complemented
12#13068909C211yesmaximal, characteristic, complemented
13#13068884C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic, complemented
15C2×C11×#548C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C11×#548—24no—
19C11×#548—24no—
20C2×C11×#124—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4324C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C23×C11⋊C8C2211yescharacteristic
36#10622852—24no—
37#10622841—24no—
38C2×#66899—24no—
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44C2×#66899C2211yescharacteristic
45#10622833—21no—
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49#10622825C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53#10622654—24no—
54#10622597—21no—
55C2×#66874C2211yescharacteristic
56C2×#66872C2211yescharacteristic
57#10622561—21no—
58#10622555—21no—
59#10622542C2211yescharacteristic
60#10622541C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622162C2211yescharacteristic
64#10622162C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C22×Q8×C11—21no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—22no—
75C22×Q8×C11—41no—
76C22×Q8×C11—41no—
77C22×Q8×C11D414yes—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11D411yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×Dic11—21no—
89C22×Dic22C2311yescharacteristic
90C11×#124—28no—
91C11×#124—22no—
92C11×#124—22no—
93C11×C22⋊Q8—28no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—22no—
96C11×#121—28no—
97C11×#121—22no—
98C11×#121D414yes—
99C4×Q8×C11—22no—
100C4×Q8×C11—22no—
101C4×D4×C11—28no—
102C4×D4×C11—22no—
103C4×D4×C11—22no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C42×C11—21no—
115C2×C42×C11C2311yescharacteristic
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×#4326—22no—
120C2×#4326—22no—
121C2×#4326—22no—
122C2×#4326—22no—
123C2×#4326—41no—
124C2×#4326—41no—
125C2×#4324—22no—
126C2×#4324—22no—
127C2×#4324—41no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—41no—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134#66977—22no—
135#66977—22no—
136#66977—22no—
137#66977—41no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C22×C11⋊C8—22no—
142C22×C11⋊C8—22no—
143C22×C11⋊C8—41no—
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148#66899—22no—
149#66899—22no—
150#66899—22no—
151#66899—22no—
152#66899—22no—
153#66899D414yescomplemented
154#66896—22no—
155#66896—22no—
156#66896—41no—
157C11⋊#95—21no—
158C11⋊#95—21no—
159C11⋊#95—21no—
160C11⋊#95—21no—
161C22⋊(C11⋊C8)—22no—
162C22⋊(C11⋊C8)—22no—
163C22⋊(C11⋊C8)—41no—
164#66874—22no—
165#66872—22no—
166#24431—111nomaximal, Sylow
167C24×C11—21no—
168C24×C11C2×D411yescharacteristic
169C24×C11C2×D411yescharacteristic
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—44no—
174C2×Q8×C11—24no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—28no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—42no—
185C2×Q8×C11—42no—
186C2×Q8×C11—44no—
187C2×Q8×C11—44no—
188C2×Q8×C11—44no—
189C2×Q8×C11C2×D412yes—
190C2×Q8×C11C2×D412yes—
191C2×Q8×C11C2×D412yes—
192C2×Q8×C11#4112yes—
193C2×D4×C11—24no—
194C2×D4×C11—22no—
195C2×D4×C11—24no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—42no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11C2×D412yes—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—24no—
214C22×C4×C11—24no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—42no—
224C22×C4×C11—42no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2411yescharacteristic
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—42no—
239C22×Dic11—42no—
240C22×Dic11—81no—
241C2×Dic22—21no—
242C2×Dic22—21no—
243C2×Dic22—21no—
244C2×Dic22—21no—
245C2×Dic22—21no—
246C2×Dic22—21no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—22no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4C2×D412yes—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—22no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—22no—
258C42×C11—24no—
259C42×C11—21no—
260C42×C11—21no—
261C22⋊Dic11—42no—
262C22⋊Dic11—42no—
263C22⋊Dic11—81no—
264#4326—44no—
265#4326—44no—
266#4324—44no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—42no—
273C4⋊Dic11C2×D412yes—
274Dic11⋊C4—42no—
275Dic11⋊C4—42no—
276Dic11⋊C4—81no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—21no—
286C2×C11⋊C8—21no—
287C2×C11⋊C8—21no—
288C2×C11⋊C8—44no—
289C2×C11⋊C8C2×D412yes—
290C2×#548D1111yescharacteristic
291C2×#465—111no—
292C2×#452—111no—
293C2×#451—111no—
294C22×#103—111no—
295#2417—111no—
296#2042—111no—
297#2035—111no—
298#2015—111no—
299#2001—111no—
300#1878—111no—
301#1874—111no—
302#1869—111no—
303#1865—111no—
304#1788—111no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—22no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11#12012yes—
324C23×C11#13512yes—
325C23×C11#13712yes—
326C23×C11C22×D411yescharacteristic
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—48no—
333Q8×C11—41no—
334Q8×C11—41no—
335Q8×C11#12114yes—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—48no—
339D4×C11—44no—
340D4×C11—48no—
341D4×C11—41no—
342D4×C11—41no—
343C2×C4×C11—22no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—21no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—48no—
364C2×C4×C11—48no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11#12012yes—
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C2×#4111yescharacteristic
378C2×C4×C11H(5,𝔽2)11yescharacteristic
379C2×C4×C11H(5,𝔽2)11yescharacteristic
380C2×Dic11—22no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—84no—
393Dic22—41no—
394Dic22—41no—
395Dic22—41no—
396Dic22—41no—
397C11⋊C8—22no—
398C11⋊C8—41no—
399C11⋊C8—41no—
400C11⋊C8—41no—
401C22×#41C2×D1111yescharacteristic
402C23×Q8C2×D1111yescharacteristic
403C22×Q16—111no—
404C22×Q16—111no—
405C22×SD16—111no—
406C23×C8—111no—
407#548—24no—
408#548—24no—
409C2×#124—21no—
410C2×#124C2×D1111yescharacteristic
411C2×C22⋊Q8—21no—
412C2×C22⋊Q8—111no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8C2×D1111yescharacteristic
415C2×#121—21no—
416C2×#121C2×D1111yescharacteristic
417C2×C4×Q8C2×D1111yescharacteristic
418C2×C4×D4—21no—
419C2×C4×D4C2×D1111yescharacteristic
420C22×C4⋊C4—111no—
421#465—224no—
422#452—224no—
423#451—224no—
424C2×#106—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—224no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×C22⋊C8—111no—
437C2×C22⋊C8—111no—
438C2×C22⋊C8—111no—
439#398—221no—
440#396—221no—
441#391—111no—
442#389—111no—
443#386—221no—
444#380—111no—
445#380—221no—
446#340—111no—
447#340—111no—
448#336—111no—
449#336—111no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—42no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—42no—
460C22×C11—41no—
461C22×C11—42no—
462C22×C11—41no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11#45214yescomplemented
471C22×C11C2×#12011yescharacteristic
472C22×C11D4211yescharacteristic
473C22×C11#54611yescharacteristic
474C22×C11C2×#13511yescharacteristic
475C22×C11C2×#13711yescharacteristic
476C22×C11#57711yescharacteristic
477C22×C11#57811yescharacteristic
478C4×C11—22no—
479C4×C11—24no—
480C4×C11—41no—
481C4×C11—42no—
482C4×C11—41no—
483C4×C11—42no—
484C4×C11—41no—
485C4×C11C2×#12111yescharacteristic
486C4×C11#53411yescharacteristic
487C4×C11D4211yescharacteristic
488C4×C11#54611yescharacteristic
489Dic11—42no—
490Dic11—81no—
491Dic11—81no—
492Dic11—81no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C22×Q8—21no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8—111no—
506C22×Q8C22⋊D1114yes—
507C22×Q8C22×D1111yescharacteristic
508C22×Q8C22×D1111yescharacteristic
509C22×D4—21no—
510C22×D4—21no—
511C22×D4C22⋊D1111yescharacteristic
512C22×D4C22×D1111yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—221no—
516C23×C4C22×D1111yescharacteristic
517C23×C4C22×D1111yescharacteristic
518C2×Q16—222no—
519C2×Q16—222no—
520C2×Q16—222no—
521C2×Q16—222no—
522C2×Q16—441no—
523C2×Q16—441no—
524C2×SD16—222no—
525C2×SD16—222no—
526C2×SD16—441no—
527C22×C8—111no—
528C22×C8—111no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8—222no—
532C22×C8—222no—
533C22×C8—441no—
534#124—28no—
535#124—22no—
536#124—22no—
537C22⋊Q8—28no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—222no—
541C22⋊Q8—222no—
542C22⋊Q8—222no—
543C22⋊Q8—441no—
544#121—28no—
545#121—22no—
546#121C22⋊D1114yes—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×D4—28no—
550C4×D4—22no—
551C4×D4—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—222no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—441no—
563C2×C4⋊C4C22⋊D1111yescharacteristic
564C2×C4⋊C4C22×D1111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4C22⋊D1111yescharacteristic
573C2×C22⋊C4C22⋊D1111yescharacteristic
574C2×C42—21no—
575C2×C42C22×D1111yescharacteristic
576#106—222no—
577#103—114no—
578#103—222no—
579#103—222no—
580#103—222no—
581#103—222no—
582#103—222no—
583#103—222no—
584#102—222no—
585#102—222no—
586#102—441no—
587C22⋊C8—222no—
588C22⋊C8—222no—
589C22⋊C8—441no—
590#95—221no—
591#95—221no—
592#95—221no—
593#95—221no—
594C2×C11—24no—
595C2×C11—81no—
596C2×C11—82no—
597C2×C11#241011yescharacteristic
598C2×C11C2×#45211yescharacteristic
599C2×C11#301311yescharacteristic
600C2×C11#327011yescharacteristic
601C2×C11#328211yescharacteristic
602C2×C11#330011yescharacteristic
603C2×C11#331611yescharacteristic
604C24—21no—
605C24C2×C22⋊D1111yescharacteristic
606C24C2×C22⋊D1111yescharacteristic
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611C2×Q8—24no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—28no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—42no—
622C2×Q8—42no—
623C2×Q8—44no—
624C2×Q8—44no—
625C2×Q8—44no—
626C2×Q8—221no—
627C2×Q8—221no—
628C2×Q8—221no—
629C2×Q8—221no—
630C2×Q8—221no—
631C2×Q8—221no—
632C2×Q8D4×D1112yes—
633C2×Q8#434112yes—
634C2×Q8C2×C22⋊D1112yes—
635C2×Q8C2×C22⋊D1112yes—
636C2×D4—24no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—24no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4C2×C22⋊D1112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—442no—
675C22×C4—442no—
676C22×C4—881no—
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1112yes—
682C22×C4C2×C22⋊D1112yes—
683C22×C4C23×D1111yescharacteristic
684Q16—444no—
685Q16—444no—
686SD16—444no—
687C2×C8—112no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8—221no—
699C2×C8—444no—
700C4⋊C4—24no—
701C4⋊C4—24no—
702C4⋊C4—22no—
703C4⋊C4—21no—
704C4⋊C4—112no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—442no—
711C4⋊C4—442no—
712C4⋊C4—442no—
713C4⋊C4—881no—
714C4⋊C4C2×C22⋊D1112yes—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—22no—
721C22⋊C4—442no—
722C22⋊C4—442no—
723C22⋊C4—881no—
724C42—24no—
725C42—21no—
726C42—21no—
727C11#2443111yescharacteristic, complemented, Sylow
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23#6700312yes—
747C23#6700412yes—
748C23#6700612yes—
749C23C22×C22⋊D1111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—22no—
755Q8—48no—
756Q8—41no—
757Q8—41no—
758Q8—441no—
759Q8—441no—
760Q8—441no—
761Q8—441no—
762Q8#6699214yes—
763D4—22no—
764D4—22no—
765D4—48no—
766D4—44no—
767D4—48no—
768D4—41no—
769D4—41no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—222no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—884no—
813C2×C4#6700612yes—
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4C2×#434111yescharacteristic
816C2×C4#6703711yescharacteristic
817C2×C4#6703711yescharacteristic
818C2×C4C22×C22⋊D1111yescharacteristic
819C2×C4C22×C22⋊D1111yescharacteristic
820C8—222no—
821C8—441no—
822C8—441no—
823C8—441no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22#1062285214yescomplemented
845C22D4×C22⋊D1111yescharacteristic
846C22#1062333711yescharacteristic
847C22C2×#6700311yescharacteristic
848C22C2×#6700411yescharacteristic
849C22#1062336811yescharacteristic
850C22#1062336911yescharacteristic
851C22C2×#6700611yescharacteristic
852C4—22no—
853C4—24no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—42no—
858C4—41no—
859C4—442no—
860C4—881no—
861C4—881no—
862C4—881no—
863C4D4×C22⋊D1111yescharacteristic
864C4C2×#6699211yescharacteristic
865C4#1062333511yescharacteristic
866C4#1062333711yescharacteristic
867C2—24no—
868C2—81no—
869C2—82no—
870C2#1307199011yescharacteristic
871C2C2×#1062285211yescharacteristic
872C2#1307793111yescharacteristic
873C2#1308018211yescharacteristic
874C2#1308032411yescharacteristic
875C2#1308050311yescharacteristic
876C2#1308072711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#548C2
socleC23×C11C22×D4
hypercenterC2×#548D11
hypocenterC11#24431
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#10622654C2semidirect
2. C2×#10622852C2semidirect
3. C2×#10622841C2semidirect
4. C22×#66899C2semidirect
5. #13072067C2semidirect
6. #13069852C2semidirect
7. #13069809C2semidirect
8. #13069710C2semidirect
9. #13069624C2semidirect
10. #13068957C2semidirect
11. #13068934C2semidirect
12. #13068909C2semidirect
13. #13068884C2semidirect
14. #13068556C2semidirect
153. #66899D4semidirect
470. C22×C11#452semidirect
727. C11#24431semidirect
844. C22#10622852semidirect

Maximal subgroups

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

subgroupindex
C2×#106226542
C2×#106228522
C2×#106228412
C22×#668992
#130720672
#130698522
#130698092
#130697102
#130696242
#130689572
#130689342
#130689092
#130688842
#130685562
C2×C11×#5482
#2443111