Finite Group Databasebeta

← #14769332

Subgroups — #14769332

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623360C211yesmaximal, characteristic
2C2×#10622343C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic, complemented
4C2×#10622846C211yesmaximal, characteristic, complemented
5#13071560C211yesmaximal, characteristic, complemented
6#13069545C211yesmaximal, characteristic, complemented
7#13069429C211yesmaximal, characteristic, complemented
8#13069046C211yesmaximal, characteristic, complemented
9#13069042C211yesmaximal, characteristic, complemented
10#13068936C211yesmaximal, characteristic, complemented
11#13068925C211yesmaximal, characteristic, complemented
12#13068614C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068443C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18#10623360—24no—
19#10623360C418yescomplemented
20C2×#67000C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66992—21no—
23C2×#66990—21no—
24C2×D4×Dic11C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66982—21no—
27C2×C4×C22⋊D11C2211yescharacteristic
28C22×(C2×D11)⋊C4—21no—
29C2×#66979C2211yescharacteristic, complemented
30C23×C11⋊C8C2211yescharacteristic, complemented
31C22×#4313C2211yescharacteristic
32C2×#66945C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic, complemented
34C2×C11×#103C2211yescharacteristic, complemented
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic, complemented
38C11×#380C2211yescharacteristic, complemented
39#10622846—24no—
40C2×#66899C2211yescharacteristic, complemented
41C2×#66899C2211yescharacteristic, complemented
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×#66879C2211yescharacteristic, complemented
48C2×Dic11⋊C8C2211yescharacteristic, complemented
49#10622600C2211yescharacteristic
50#10622589C2211yescharacteristic, complemented
51C4⋊C4×Dic11C2211yescharacteristic, complemented
52C2×#66873C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54#10622570—21no—
55#10622558—21no—
56#10622383—24no—
57#10622343—24no—
58#10622282—21no—
59#10622262—21no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41C2×C414yes—
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—21no—
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×C22⋊D11D411yescharacteristic
79C23×Dic11—21no—
80C2×D4×D11—22no—
81C2×D4×D11—22no—
82C2×D4×D11—22no—
83C2×D4×D11—41no—
84C2×D4×D11—41no—
85C2×D4×D11C2×C414yes—
86C22×D44C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11D411yescharacteristic
96#67000—22no—
97#67000C2×C414yes—
98#66999—22no—
99#66999C2×C414yes—
100#66992—28no—
101#66990—28no—
102D4×Dic11—22no—
103D4×Dic11C2×C414yes—
104#66983—22no—
105#66983C2×C414yes—
106#66982—28no—
107C4×C22⋊D11C2×C414yes—
108C4×C22⋊D11D414yes—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—28no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4D411yescharacteristic
117#66979—22no—
118#66979—41no—
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4D411yescharacteristic
126C2×C4×Dic11—21no—
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11C2311yescharacteristic
130C22×C11⋊C8—22no—
131C22×C11⋊C8—22no—
132C22×C11⋊C8—41no—
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×#4313—22no—
136C2×#4313—22no—
137C2×#4313—41no—
138#66945—22no—
139#66945—41no—
140C11×#103—41no—
141C11×#103—41no—
142C11×#102—22no—
143C11×#102—22no—
144C11×C22⋊C8—22no—
145C11×#95—21no—
146#66899—22no—
147#66899—22no—
148#66896—22no—
149#66896D414yescomplemented
150C11⋊#95—21no—
151C11⋊#95—21no—
152#66885—22no—
153#66885—41no—
154(C2×D11)⋊C8—22no—
155#66879—22no—
156Dic11⋊C8—22no—
157#66873—22no—
158#66873—41no—
159#22424—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11—24no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—81no—
169C23×D11—81no—
170C23×D11C2×D411yescharacteristic
171C11×#41—28no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11C22×C412yes—
181C2×D4×C11—24no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11C22×C412yes—
188C2×D4×C11C2×D412yes—
189C2×D4×C11#4112yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—24no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—42no—
199C22×C4×C11—42no—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—41no—
207C2×C22⋊D11—41no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—42no—
210C2×C22⋊D11—81no—
211C2×C22⋊D11—81no—
212C2×C22⋊D11C22⋊C414yes—
213C22×Dic11—24no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—81no—
218C22×Dic11—81no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222D4×D11—28no—
223D4×D11—44no—
224D4×D11—44no—
225D4×D11—44no—
226C2×D44—21no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44C22×C412yes—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×C4×D11—21no—
236C2×C4×D11C22×C412yes—
237C2×C4×D11C2×D412yes—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C22⋊C4—81no—
249C22⋊Dic11—24no—
250C22⋊Dic11—42no—
251C22⋊Dic11C22⋊C414yes—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—42no—
257(C2×D11)⋊C4—81no—
258(C2×D11)⋊C4C22⋊C414yes—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11C22×C412yes—
264C4⋊Dic11C2×D412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—42no—
267Dic11⋊C4—81no—
268Dic11⋊C4C22⋊C414yes—
269C4×Dic11—42no—
270C4×Dic11—42no—
271C4×Dic11—42no—
272C4×Dic11C22×C412yes—
273C4×Dic11C2×D412yes—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—44no—
280C2×C11⋊C8C2×D412yes—
281#4313—44no—
282C2×#546—111no—
283C2×#435—111no—
284C2×#418—111no—
285C2×#416—111no—
286#2354—111no—
287#1983—111no—
288#1959—111no—
289#1894—111no—
290#1893—111no—
291#1875—111no—
292#1873—111no—
293#1802—111no—
294#1788D1111yescharacteristic, complemented
295#1786—111no—
296#1762—111no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11C2×C22⋊C412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—22no—
319C22×D11—48no—
320C22×D11—48no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11C2×C22⋊C412yes—
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—41no—
336Q8×C11—41no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—48no—
341D4×C11C4×D414yes—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—48no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11C2×C22⋊C412yes—
359C2×C4×C11C23×C411yescharacteristic
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C2×#4111yescharacteristic
363C2×C4×C11H(5,𝔽2)11yescharacteristic
364C2×C4×C11H(5,𝔽2)11yescharacteristic
365C22⋊D11—44no—
366C22⋊D11—48no—
367C22⋊D11—84no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—84no—
384C2×Dic11C2×C22⋊C412yes—
385C2×Dic11C2×C22⋊C412yes—
386C2×Dic11C2×C22⋊C412yes—
387D44—22no—
388D44—22no—
389D44—41no—
390D44—41no—
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—22no—
395C8×C11—41no—
396C8×C11—41no—
397C11⋊C8—22no—
398C11⋊C8—41no—
399C22×#41C2×D1111yescharacteristic
400C23×D4—111no—
401C22×M16—111no—
402C23×C8—111no—
403#546—118no—
404#546—224no—
405C2×#124—111no—
406C2×#123—221no—
407C2×C22⋊Q8—111no—
408C2×#121—111no—
409C2×#121—221no—
410C2×#120—221no—
411C2×C4×D4—111no—
412C2×C4×D4—111no—
413C2×#117—111no—
414C2×#117—111no—
415C22×C22⋊C4—221no—
416#435—224no—
417C2×C4⋊C8—111no—
418#418—224no—
419#416—224no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103C2×D1111yescharacteristic, complemented
423C2×#103C2×D1111yescharacteristic, complemented
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102C2×D1111yescharacteristic
431C2×#102C2×D1111yescharacteristic
432C2×C22⋊C8—111no—
433C2×C22⋊C8C2×D1111yescharacteristic, complemented
434C2×#97—111no—
435#390—221no—
436#388—221no—
437#388—221no—
438#384—111no—
439#380—111no—
440#380C2×D1111yescharacteristic, complemented
441C4×C4⋊C4—111no—
442C4×C4⋊C4—221no—
443#340—111no—
444#340—111no—
445#340—111no—
446#340—111no—
447C22×C11—22no—
448C22×C11—24no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—41no—
459C22×C11—42no—
460C22×C11—41no—
461C22×C11C22×C22⋊C411yescharacteristic
462C22×C11D4211yescharacteristic
463C22×C11#54611yescharacteristic
464C22×C11#57511yescharacteristic
465C22×C11#57511yescharacteristic
466C22×C11#57611yescharacteristic
467C22×C11#57711yescharacteristic
468C2×D11—22no—
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—41no—
472C2×D11—41no—
473C2×D11—41no—
474C2×D11—41no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—816no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C4×C11—22no—
484C4×C11—42no—
485C4×C11—81no—
486C4×C11—81no—
487C4×C11C2×C4×D411yescharacteristic
488C4×C11#51811yescharacteristic
489C4×C11D4211yescharacteristic
490C4×C11#54611yescharacteristic
491Dic11—22no—
492Dic11—22no—
493Dic11—22no—
494Dic11—42no—
495Dic11—42no—
496Dic11—81no—
497C25—221no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41C4×D1114yes—
504C22×Q8C22×D1111yescharacteristic
505C22×D4—21no—
506C22×D4—111no—
507C22×D4—114no—
508C22×D4—111no—
509C22×D4—222no—
510C22×D4—221no—
511C22×D4—222no—
512C22×D4—222no—
513C22×D4—221no—
514C22×D4—441no—
515C22×D4—441no—
516C22×D4C22×D1111yescharacteristic
517C23×C4—21no—
518C23×C4—111no—
519C23×C4—221no—
520C23×C4C22×D1111yescharacteristic
521C2×M16—222no—
522C2×M16—222no—
523C2×M16—441no—
524C22×C8—111no—
525C22×C8—111no—
526C22×C8—222no—
527C22×C8—222no—
528C22×C8—441no—
529C22×C8C22×D1111yescharacteristic
530C22×C8C22×D1111yescharacteristic
531#124—114no—
532#124—222no—
533#123—228no—
534C22⋊Q8—114no—
535C22⋊Q8—222no—
536#121—114no—
537#121—228no—
538#121—222no—
539#120—228no—
540C4×D4—114no—
541C4×D4—114no—
542C4×D4—114no—
543C4×D4—222no—
544#117—222no—
545#117—222no—
546#117—441no—
547#117—441no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—111no—
559C2×C22⋊C4—111no—
560C2×C22⋊C4—228no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C42—111no—
570C2×C42—221no—
571C2×C42—221no—
572C2×C42—221no—
573C4⋊C8—222no—
574#103—41no—
575#103—41no—
576#103—222no—
577#103—222no—
578#102—22no—
579#102—22no—
580#102—114no—
581#102—222no—
582#102—222no—
583#102—222no—
584#102—441no—
585#102—441no—
586C22⋊C8—22no—
587C22⋊C8—222no—
588#97—222no—
589#95—21no—
590#95—221no—
591#95—221no—
592C2×C11—44no—
593C2×C11—42no—
594C2×C11D4×C22⋊C411yescharacteristic
595C2×C11#289611yescharacteristic
596C2×C11#289711yescharacteristic
597C2×C11#326711yescharacteristic
598C2×C11#326811yescharacteristic
599C2×C11#331111yescharacteristic
600C2×C11#331911yescharacteristic
601D11—42no—
602D11—82no—
603C24—21no—
604C24—111no—
605C24—224no—
606C24—221no—
607C24—442no—
608C24—442no—
609C24—442no—
610C24—442no—
611C24—881no—
612C24—881no—
613C24D4×D1111yescharacteristic
614#41—28no—
615#41—44no—
616#41—44no—
617#41—44no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8C2×C4×D1112yes—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—114no—
631C2×D4—112no—
632C2×D4—224no—
633C2×D4—228no—
634C2×D4—224no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—444no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—441no—
644C2×D4—441no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—881no—
648C2×D4—881no—
649C2×D4C2×C4×D1112yes—
650C2×D4D4×D1112yes—
651C2×D4#434112yes—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—111no—
663C22×C4—111no—
664C22×C4—111no—
665C22×C4—112no—
666C22×C4—112no—
667C22×C4—224no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—881no—
676C22×C4—881no—
677C22×C4C2×C4×D1112yes—
678C22×C4D4×D1111yescharacteristic
679C22×C4D4×D1112yes—
680C22×C4C23×D1111yescharacteristic
681M16—444no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—112no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—444no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—114no—
700C4⋊C4—112no—
701C4⋊C4—112no—
702C4⋊C4—224no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—442no—
708C4⋊C4—881no—
709C22⋊C4—81no—
710C22⋊C4—114no—
711C22⋊C4—114no—
712C22⋊C4—224no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—442no—
718C22⋊C4—442no—
719C22⋊C4—881no—
720C42—112no—
721C42—112no—
722C42—442no—
723C42—442no—
724C42—442no—
725C11#2242411yescharacteristic, complemented, Sylow
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—22no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—112no—
740C23—221no—
741C23—221no—
742C23—221no—
743C23—221no—
744C23—221no—
745C23—221no—
746C23—222no—
747C23—448no—
748C23—448no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—884no—
756C23—884no—
757C23—884no—
758C23—884no—
759C23—884no—
760C23C22⋊C4×D1112yes—
761C23C2×D4×D1111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—48no—
770D4—222no—
771D4—222no—
772D4—444no—
773D4—448no—
774D4—441no—
775D4—441no—
776D4—884no—
777D4(C22⋊D11)⋊C414yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—48no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—112no—
795C2×C4—112no—
796C2×C4—112no—
797C2×C4—221no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—884no—
817C2×C4C22⋊C4×D1112yes—
818C2×C4C22×C4×D1111yescharacteristic
819C2×C4C2×D4×D1111yescharacteristic
820C2×C4C2×D4×D1111yescharacteristic
821C2×C4C2×#434111yescharacteristic
822C2×C4#6703711yescharacteristic
823C2×C4#6703711yescharacteristic
824C8—41no—
825C8—41no—
826C8—222no—
827C8—441no—
828C22—22no—
829C22—24no—
830C22—22no—
831C22—22no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—222no—
843C22—222no—
844C22—222no—
845C22—441no—
846C22—441no—
847C22—441no—
848C22—441no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—8816no—
853C22—881no—
854C22—881no—
855C22—881no—
856C22—881no—
857C22C2×C22⋊C4×D1111yescharacteristic
858C22#1062312111yescharacteristic
859C22#1062312211yescharacteristic
860C22#1062329911yescharacteristic
861C22#1062329911yescharacteristic
862C22#1062330511yescharacteristic
863C22#1062330911yescharacteristic
864C4—22no—
865C4—42no—
866C4—81no—
867C4—81no—
868C4—222no—
869C4—222no—
870C4—222no—
871C4—442no—
872C4—442no—
873C4—881no—
874C4C2×(C22⋊D11)⋊C411yescharacteristic
875C4#1062301711yescharacteristic
876C4#1062312111yescharacteristic
877C4#1062312211yescharacteristic
878C2—42no—
879C2—44no—
880C2—442no—
881C2—882no—
882C2#1307143211yescharacteristic
883C2#1307713111yescharacteristic
884C2#1307714011yescharacteristic
885C2#1308014511yescharacteristic
886C2#1308016011yescharacteristic
887C2#1308065611yescharacteristic
888C2#1308077611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC2×#10623360C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#22424
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×#10622343C2semidirect
3. C2×#10622383C2semidirect
4. C2×#10622846C2semidirect
5. #13071560C2semidirect
6. #13069545C2semidirect
7. #13069429C2semidirect
8. #13069046C2semidirect
9. #13069042C2semidirect
10. #13068936C2semidirect
11. #13068925C2semidirect
12. #13068614C2semidirect
13. #13068545C2semidirect
14. #13068443C2semidirect
15. C11×#1788C2semidirect
19. #10623360C4semidirect
29. C2×#66979C22semidirect
30. C23×C11⋊C8C22semidirect
33. C2×C11×#103C22semidirect
34. C2×C11×#103C22semidirect
37. C2×C11×C22⋊C8C22semidirect
38. C11×#380C22semidirect
40. C2×#66899C22semidirect
41. C2×#66899C22semidirect
47. C2×#66879C22semidirect
48. C2×Dic11⋊C8C22semidirect
50. #10622589C22semidirect
51. C4⋊C4×Dic11C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
149. #66896D4semidirect
294. #1788D11semidirect
422. C2×#103C2×D11semidirect
423. C2×#103C2×D11semidirect
433. C2×C22⋊C8C2×D11semidirect
440. #380C2×D11semidirect
725. C11#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#106233602
C2×#106223432
C2×#106223832
C2×#106228462
#130715602
#130695452
#130694292
#130690462
#130690422
#130689362
#130689252
#130686142
#130685452
#130684432
C11×#17882
#2242411