Finite Group Databasebeta

← #14810252

Subgroups — #14810252

Order 2816.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622669C211yesmaximal, characteristic, complemented
2C2×#10622622C211yesmaximal, characteristic, complemented
3#13073782C211yesmaximal, characteristic, complemented
4#13069816C211yesmaximal, characteristic, complemented
5#13069809C211yesmaximal, characteristic, complemented
6#13069802C211yesmaximal, characteristic, complemented
7#13069795C211yesmaximal, characteristic, complemented
8#13069549C211yesmaximal, characteristic, complemented
9#13069411C211yesmaximal, characteristic, complemented
10#13068556C211yesmaximal, characteristic, complemented
11#13068556C211yesmaximal, characteristic, complemented
12#13068547C211yesmaximal, characteristic, complemented
13#13068547C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C2×C11×#546C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C11×#546—24no—
19C11×#546—24no—
20C2×C11×#124C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#120—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C22⋊C4—21no—
29C2×#66923C2211yescharacteristic, complemented
30C2×#66899C2211yescharacteristic, complemented
31C2×#66899C2211yescharacteristic, complemented
32C2×#66899C2211yescharacteristic, complemented
33C2×#66899C2211yescharacteristic, complemented
34#10622835—21no—
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic
44#10622825C2211yescharacteristic
45#10622825C2211yescharacteristic, complemented
46#10622825C2211yescharacteristic, complemented
47C2×C22⋊(C11⋊C8)C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
50C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
51#10622669—24no—
52#10622622—24no—
53#10622595—21no—
54C2×#66872C2211yescharacteristic, complemented
55C2×#66871C2211yescharacteristic, complemented
56#10622558—21no—
57#10622558—21no—
58C4×C4⋊Dic11C2211yescharacteristic, complemented
59C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
60C2×C4×C11⋊C8C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C25×C11—21no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11—21no—
73C22×D4×C11—22no—
74C22×D4×C11—22no—
75C22×D4×C11—22no—
76C22×D4×C11—22no—
77C22×D4×C11—21no—
78C22×D4×C11—41no—
79C22×D4×C11—41no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C11×#124—22no—
88C11×#124D414yes—
89C11×#123—28no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×#121—28no—
93C11×#121—22no—
94C11×#121—22no—
95C11×#120—28no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11D414yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—28no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×C4×Dic11—21no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127#66923—22no—
128#66923—22no—
129#66899—22no—
130#66899—22no—
131#66899—41no—
132#66899—41no—
133#66896—22no—
134#66896—22no—
135#66896—22no—
136#66896—22no—
137#66896—22no—
138#66896—22no—
139#66896—41no—
140#66896—41no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C22⋊(C11⋊C8)—41no—
147C22⋊(C11⋊C8)—41no—
148C22⋊(C11⋊C8)—41no—
149C22⋊(C11⋊C8)—41no—
150#66872—22no—
151#66871—22no—
152C4⋊(C11⋊C8)—22no—
153C4×C11⋊C8—22no—
154#25890—111nomaximal, Sylow
155C24×C11—21no—
156C24×C11—24no—
157C24×C11—21no—
158C24×C11—42no—
159C24×C11—42no—
160C24×C11—42no—
161C24×C11—42no—
162C24×C11—81no—
163C24×C11—81no—
164C24×C11C2×D411yescharacteristic
165C24×C11C2×D411yescharacteristic
166C11×#41—44no—
167C11×#41—44no—
168C11×#41—44no—
169C11×#41—44no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11C2×D412yes—
176C2×D4×C11—24no—
177C2×D4×C11—24no—
178C2×D4×C11—22no—
179C2×D4×C11—24no—
180C2×D4×C11—22no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—41no—
190C2×D4×C11—42no—
191C2×D4×C11—42no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—42no—
196C2×D4×C11—42no—
197C2×D4×C11—44no—
198C2×D4×C11—81no—
199C2×D4×C11—81no—
200C2×D4×C11C2×D412yes—
201C2×D4×C11C2×D412yes—
202C2×D4×C11#4112yes—
203C2×D4×C11#4112yes—
204C22×C4×C11—24no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—24no—
220C22×C4×C11—42no—
221C22×C4×C11—42no—
222C22×C4×C11—81no—
223C22×C4×C11—81no—
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2411yescharacteristic
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C2×D412yes—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—22no—
244C42×C11C2×D412yes—
245C42×C11C2×D412yes—
246C22⋊Dic11—42no—
247C22⋊Dic11—42no—
248C22⋊Dic11—81no—
249C22⋊Dic11—81no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258Dic11⋊C4—42no—
259Dic11⋊C4—42no—
260C4×Dic11—81no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×#546D1111yescharacteristic
274C2×#488—111no—
275C2×#478—111no—
276#2562—111no—
277#2036—111no—
278#2035—111no—
279#2034—111no—
280#2033—111no—
281#1983—111no—
282#1954—111no—
283#1788—111no—
284#1788—111no—
285#1786—111no—
286#1786—111no—
287C4×#102—111no—
288C23×C11—21no—
289C23×C11—22no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—48no—
306C23×C11—48no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—84no—
318C23×C11—84no—
319C23×C11—84no—
320C23×C11—84no—
321C23×C11—84no—
322C23×C11#13512yes—
323C23×C11C22×D411yescharacteristic
324Q8×C11—22no—
325Q8×C11—22no—
326Q8×C11—41no—
327Q8×C11—41no—
328D4×C11—22no—
329D4×C11—22no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—44no—
334D4×C11—48no—
335D4×C11—48no—
336D4×C11—41no—
337D4×C11—41no—
338D4×C11—84no—
339D4×C11#12414yes—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—21no—
346C2×C4×C11—22no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—48no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—84no—
366C2×C4×C11#12012yes—
367C2×C4×C11#12012yes—
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C2×#4111yescharacteristic
371C2×C4×C11C2×#4111yescharacteristic
372C2×C4×C11H(5,𝔽2)11yescharacteristic
373C2×C4×C11H(5,𝔽2)11yescharacteristic
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C11⋊C8—41no—
387C11⋊C8—41no—
388C11⋊C8—41no—
389C11⋊C8—41no—
390C22×#41C2×D1111yescharacteristic
391C23×D4C2×D1111yescharacteristic
392#546—24no—
393#546—24no—
394C2×#125—111no—
395C2×#124C2×D1111yescharacteristic
396C2×#123—21no—
397C2×C22⋊Q8C2×D1111yescharacteristic
398C2×#121—21no—
399C2×#121C2×D1111yescharacteristic
400C2×#120—21no—
401C2×C4×D4C2×D1111yescharacteristic
402C2×C4×D4C2×D1111yescharacteristic
403C22×C22⋊C4—21no—
404#488—224no—
405#478—224no—
406C2×#107—111no—
407C2×#106—111no—
408C2×C4⋊C8—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×C22⋊C8—111no—
422C2×C22⋊C8—111no—
423C2×C22⋊C8—111no—
424C2×C22⋊C8—111no—
425C2×C4×C8—111no—
426#400—221no—
427#394—221no—
428#388—221no—
429#388—221no—
430#380—111no—
431#380—111no—
432#380—111no—
433#380—111no—
434C4×C4⋊C4—111no—
435#340—111no—
436#340—111no—
437C22×C11—24no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—41no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—41no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—41no—
448C22×C11—42no—
449C22×C11—41no—
450C22×C11—42no—
451C22×C11—41no—
452C22×C11—42no—
453C22×C11—41no—
454C22×C11—42no—
455C22×C11—41no—
456C22×C11—42no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—816no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11C2×#12011yescharacteristic
467C22×C11#54611yescharacteristic
468C22×C11#54611yescharacteristic
469C22×C11C2×#13511yescharacteristic
470C22×C11#57511yescharacteristic
471C22×C11#57611yescharacteristic
472C22×C11#57711yescharacteristic
473C4×C11—22no—
474C4×C11—22no—
475C4×C11—41no—
476C4×C11—41no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11C2×#12411yescharacteristic
480C4×C11#53511yescharacteristic
481C4×C11#54611yescharacteristic
482C4×C11#54611yescharacteristic
483Dic11—81no—
484Dic11—81no—
485Dic11—81no—
486Dic11—81no—
487C25—21no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C22×D1111yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4C22⋊D1111yescharacteristic
505C22×D4C22×D1111yescharacteristic
506C22×D4C22×D1111yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511C22×C8—111no—
512C22×C8—111no—
513C22×C8—111no—
514C22×C8—111no—
515#125—222no—
516#125—222no—
517#124—22no—
518#124C22⋊D1114yes—
519#123—28no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—28no—
523#121—22no—
524#121—22no—
525#120—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4C22⋊D1114yes—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—111no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4C22⋊D1111yescharacteristic
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C22⋊C4—28no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4C22⋊D1111yescharacteristic
550C2×C22⋊C4C22⋊D1111yescharacteristic
551C2×C42—221no—
552C2×C42C22×D1111yescharacteristic
553#107—222no—
554#106—222no—
555C4⋊C8—222no—
556#103—222no—
557#103—222no—
558#103—441no—
559#103—441no—
560#102—222no—
561#102—222no—
562#102—222no—
563#102—222no—
564#102—222no—
565#102—222no—
566#102—441no—
567#102—441no—
568C22⋊C8—441no—
569C22⋊C8—441no—
570C22⋊C8—441no—
571C22⋊C8—441no—
572C4×C8—222no—
573#95—221no—
574#95—221no—
575#95—221no—
576#95—221no—
577#95—221no—
578C2×C11—42no—
579C2×C11—44no—
580C2×C11—81no—
581C2×C11—82no—
582C2×C11#243511yescharacteristic
583C2×C11#300211yescharacteristic
584C2×C11#301211yescharacteristic
585C2×C11#329611yescharacteristic
586C2×C11#329711yescharacteristic
587C2×C11#332211yescharacteristic
588C2×C11#332311yescharacteristic
589C24—21no—
590C24—24no—
591C24—21no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—81no—
597C24—81no—
598C24C2×C22⋊D1111yescharacteristic
599C24C2×C22⋊D1111yescharacteristic
600#41—44no—
601#41—44no—
602#41—44no—
603#41—44no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8C2×C22⋊D1112yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—22no—
613C2×D4—24no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—44no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4#434112yes—
635C2×D4#434112yes—
636C2×D4C2×C22⋊D1112yes—
637C2×D4C2×C22⋊D1112yes—
638C22×C4—24no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4—81no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4C2×C22⋊D1111yescharacteristic
663C22×C4C2×C22⋊D1111yescharacteristic
664C22×C4C2×C22⋊D1111yescharacteristic
665C22×C4C2×C22⋊D1111yescharacteristic
666C22×C4C23×D1111yescharacteristic
667C2×C8—221no—
668C2×C8—221no—
669C2×C8—221no—
670C2×C8—221no—
671C2×C8—221no—
672C2×C8—221no—
673C2×C8—221no—
674C2×C8—221no—
675C2×C8—221no—
676C2×C8—221no—
677C2×C8—221no—
678C2×C8—221no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—221no—
683C4⋊C4—221no—
684C4⋊C4—221no—
685C4⋊C4—221no—
686C4⋊C4—221no—
687C4⋊C4—221no—
688C4⋊C4—221no—
689C4⋊C4—221no—
690C4⋊C4—442no—
691C4⋊C4—442no—
692C4⋊C4C2×C22⋊D1112yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—22no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—22no—
700C22⋊C4—442no—
701C22⋊C4—442no—
702C22⋊C4—881no—
703C22⋊C4—881no—
704C42—881no—
705C42C2×C22⋊D1112yes—
706C42C2×C22⋊D1112yes—
707C11#2589011yescharacteristic, complemented, Sylow
708C23—21no—
709C23—21no—
710C23—22no—
711C23—22no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—22no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23#6700312yes—
743C23C22×C22⋊D1111yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4#6698914yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—84no—
786C2×C4—441no—
787C2×C4—441no—
788C2×C4—441no—
789C2×C4—441no—
790C2×C4—441no—
791C2×C4—441no—
792C2×C4—441no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4#6700612yes—
799C2×C4#6700612yes—
800C2×C4C2×#434111yescharacteristic
801C2×C4C2×#434111yescharacteristic
802C2×C4#6703711yescharacteristic
803C2×C4#6703711yescharacteristic
804C2×C4C22×C22⋊D1111yescharacteristic
805C2×C4C22×C22⋊D1111yescharacteristic
806C8—441no—
807C8—441no—
808C8—441no—
809C8—441no—
810C22—22no—
811C22—22no—
812C22—24no—
813C22—22no—
814C22—41no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—41no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22#1062333711yescharacteristic
840C22#1062333711yescharacteristic
841C22C2×#6700311yescharacteristic
842C22#1062335311yescharacteristic
843C22#1062336611yescharacteristic
844C22#1062336711yescharacteristic
845C22C2×#6700611yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—881no—
853C4—881no—
854C4—881no—
855C4—881no—
856C4C2×#6698911yescharacteristic
857C4#1062333611yescharacteristic
858C4#1062333711yescharacteristic
859C4#1062333711yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2#1307226311yescharacteristic
865C2#1307783411yescharacteristic
866C2#1307792011yescharacteristic
867C2#1308045111yescharacteristic
868C2#1308046611yescharacteristic
869C2#1308081711yescharacteristic
870C2#1308083211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11#25890
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#10622669C2semidirect
2. C2×#10622622C2semidirect
3. #13073782C2semidirect
4. #13069816C2semidirect
5. #13069809C2semidirect
6. #13069802C2semidirect
7. #13069795C2semidirect
8. #13069549C2semidirect
9. #13069411C2semidirect
10. #13068556C2semidirect
11. #13068556C2semidirect
12. #13068547C2semidirect
13. #13068547C2semidirect
14. C4×#66896C2semidirect
29. C2×#66923C22semidirect
30. C2×#66899C22semidirect
31. C2×#66899C22semidirect
32. C2×#66899C22semidirect
33. C2×#66899C22semidirect
45. #10622825C22semidirect
46. #10622825C22semidirect
49. C2×C22⋊(C11⋊C8)C22semidirect
50. C2×C22⋊(C11⋊C8)C22semidirect
54. C2×#66872C22semidirect
55. C2×#66871C22semidirect
58. C4×C4⋊Dic11C22semidirect
59. C2×C4⋊(C11⋊C8)C22semidirect
60. C2×C4×C11⋊C8C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
707. C11#25890semidirect

Maximal subgroups

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

subgroupindex
C2×#106226692
C2×#106226222
#130737822
#130698162
#130698092
#130698022
#130697952
#130695492
#130694112
#130685562
#130685472
C4×#668962
C2×C11×#5462
#2589011