Finite Group Databasebeta

← #14769330

Subgroups — #14769330

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×#10623081C211yesmaximal, characteristic
2C2×#10622744C211yesmaximal, characteristic, complemented
3C2×#10622726C211yesmaximal, characteristic, complemented
4#13071565C211yesmaximal, characteristic, complemented
5#13069546C211yesmaximal, characteristic, complemented
6#13069432C211yesmaximal, characteristic, complemented
7#13069049C211yesmaximal, characteristic, complemented
8#13069044C211yesmaximal, characteristic, complemented
9#13068936C211yesmaximal, characteristic, complemented
10#13068926C211yesmaximal, characteristic, complemented
11#13068617C211yesmaximal, characteristic, complemented
12#13068557C211yesmaximal, characteristic, complemented
13#13068548C211yesmaximal, characteristic, complemented
14#13068442C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66990—21no—
22C2×#66983C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C2×#66979C2211yescharacteristic, complemented
25C2×#66977C2211yescharacteristic
26#10623081—24no—
27#10623081C418yescomplemented
28C2×#66947—21no—
29C2×#66937—21no—
30C2×C22⋊C4×D11—21no—
31C2×#66928C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C11×#435—24no—
34C2×C11×C4⋊C8C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic, complemented
37C2×C11×#97C2211yescharacteristic, complemented
38#10622834—21no—
39#10622825C2211yescharacteristic
40#10622825C2211yescharacteristic, complemented
41#10622744—24no—
42#10622726—24no—
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×#66885C2211yescharacteristic
48C2×#66885C2211yescharacteristic
49C2×#66885C2211yescharacteristic
50C2×#66885C2211yescharacteristic
51C2×#66880C2211yescharacteristic, complemented
52C2×#66880C2211yescharacteristic, complemented
53C2×#66880C2211yescharacteristic, complemented
54C2×#66880C2211yescharacteristic, complemented
55C4⋊C4×Dic11—21no—
56#10622564—21no—
57#10622564—21no—
58#10622548C2211yescharacteristic, complemented
59C4×C4⋊Dic11C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63#10622189C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11D411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—41no—
74C2×#4339—41no—
75C2×#4339C2×C414yes—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—21no—
79C22×D44—22no—
80C22×D44—41no—
81C22×D44—41no—
82C22×D44C2×C414yes—
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×Dic22C2311yescharacteristic
88C2×C11×M16—22no—
89C2×C11×M16—22no—
90C2×C11×M16—41no—
91C22×C8×C11—22no—
92C22×C8×C11—22no—
93C22×C8×C11—41no—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C4×D4×C11C2×C414yes—
99C4×D4×C11D414yes—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109#66990—28no—
110#66983—22no—
111#66983C2×C414yes—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116#66979—22no—
117#66979—22no—
118#66979—41no—
119#66979—41no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127#66977—22no—
128#66977C2×C414yes—
129C2×Dic11⋊C4—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133#66947—28no—
134#66937—28no—
135C22⋊C4×D11—28no—
136#66928—22no—
137#66928C2×C414yes—
138C4×D44—22no—
139C4×D44C2×C414yes—
140C11×C4⋊C8—22no—
141C11×C22⋊C8—22no—
142C11×C22⋊C8—22no—
143C11×#97—22no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147#66885—22no—
148#66885—22no—
149#66885—22no—
150#66885—22no—
151#66885—22no—
152#66885—41no—
153#66885—41no—
154#66885D414yescomplemented
155#66880—22no—
156#66880—22no—
157#66880—41no—
158#66880—41no—
159#22424—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—24no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—81no—
170C23×D11—81no—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11C22⋊C414yes—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C22×C412yes—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2411yescharacteristic
191C2×C22⋊D11—24no—
192C2×C22⋊D11—24no—
193C2×C22⋊D11—42no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—81no—
196C2×C22⋊D11—81no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203#4339—28no—
204#4339—44no—
205#4339—44no—
206#4339—44no—
207C2×D44—28no—
208C2×D44—24no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—42no—
218C2×D44—42no—
219C2×D44—44no—
220C2×D44—44no—
221C2×D44—44no—
222C2×D44C22×C412yes—
223C2×D44C22×C412yes—
224C2×D44C2×D412yes—
225C2×D44#4112yes—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—42no—
229C2×C4×D11—42no—
230C2×C4×D11—81no—
231C2×C4×D11—81no—
232C2×Dic22—21no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22C22×C412yes—
238C11×M16—44no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—44no—
251C2×C8×C11C2×D412yes—
252C11×C4⋊C4C22⋊C414yes—
253C11×C22⋊C4C22⋊C414yes—
254C11×C22⋊C4C22⋊C414yes—
255C42×C11C22×C412yes—
256C42×C11C2×D412yes—
257C22⋊Dic11—24no—
258C22⋊Dic11—42no—
259C22⋊Dic11—42no—
260C22⋊Dic11—81no—
261C22⋊Dic11—81no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—42no—
275C4⋊Dic11—81no—
276C4⋊Dic11C22×C412yes—
277C4⋊Dic11C2×D412yes—
278Dic11⋊C4—24no—
279C4×Dic11—42no—
280C4×Dic11—42no—
281C4×Dic11—42no—
282C2×#546—111no—
283C2×#435D1111yescharacteristic, complemented
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#1788—111no—
295#1786—111no—
296#1762—111no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11C2×C22⋊C412yes—
310C23×C11C2×C22⋊C412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—48no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—48no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11—84no—
333D4×C11—44no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11C2×C22⋊C412yes—
351C2×C4×C11C2×C22⋊C412yes—
352C2×C4×C11C2×C22⋊C412yes—
353C2×C4×C11C2×C22⋊C412yes—
354C2×C4×C11C23×C411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C22⋊D11—48no—
361C22⋊D11—84no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380D44—22no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—22no—
385D44—48no—
386D44—41no—
387D44—41no—
388D44C4×D414yes—
389C4×D11—48no—
390C4×D11—84no—
391Dic22—22no—
392Dic22—22no—
393Dic22—41no—
394Dic22—41no—
395C8×C11—22no—
396C8×C11—41no—
397C8×C11—41no—
398C8×C11—41no—
399C22×#41—111no—
400C23×D4—111no—
401C22×M16C2×D1111yescharacteristic
402C23×C8C2×D1111yescharacteristic, complemented
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×D4C2×D1111yescharacteristic
413C2×#117—111no—
414C2×#117—111no—
415C22×C22⋊C4—221no—
416#435—24no—
417C2×C4⋊C8C2×D1111yescharacteristic, complemented
418#418—224no—
419#416—224no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×C22⋊C8C2×D1111yescharacteristic
433C2×C22⋊C8C2×D1111yescharacteristic, complemented
434C2×#97C2×D1111yescharacteristic, complemented
435#390—221no—
436#388—221no—
437#388—221no—
438#384—111no—
439#380—111no—
440#380—111no—
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—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
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—24no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
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—22no—
485C4×C11—22no—
486C4×C11—22no—
487C4×C11C2×C4×D411yescharacteristic
488C4×C11#51811yescharacteristic
489C4×C11D4211yescharacteristic
490C4×C11#54611yescharacteristic
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494Dic11—81no—
495Dic11—81no—
496Dic11—81no—
497C25—221no—
498C2×#41—114no—
499C2×#41—222no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—441no—
503C2×#41—441no—
504C22×Q8—111no—
505C22×D4—114no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—222no—
509C22×D4—222no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—222no—
514C22×D4—441no—
515C22×D4—441no—
516C22×D4D4411yescharacteristic
517C23×C4—221no—
518C23×C4—221no—
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C2×M16—22no—
522C2×M16—22no—
523C2×M16—41no—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—41no—
527C22×C8C22×D1111yescharacteristic
528C22×C8C22×D1111yescharacteristic
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—222no—
538#121—228no—
539#120—228no—
540C4×D4—114no—
541C4×D4—222no—
542C4×D4C4×D1114yes—
543C4×D4C22⋊D1114yes—
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—111no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4D4411yescharacteristic
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—228no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4D4411yescharacteristic
568C2×C22⋊C4D4411yescharacteristic
569C2×C42—221no—
570C2×C42—221no—
571C2×C42—221no—
572C2×C42C22×D1111yescharacteristic
573C4⋊C8—22no—
574#103—222no—
575#103—222no—
576#103—441no—
577#103—441no—
578#102—114no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—222no—
584#102—441no—
585#102—441no—
586C22⋊C8—22no—
587C22⋊C8—22no—
588#97—22no—
589#95—221no—
590#95—221no—
591#95—221no—
592C2×C11—42no—
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—44no—
602D11—82no—
603C24—221no—
604C24—221no—
605C24—224no—
606C24—442no—
607C24—442no—
608C24—442no—
609C24—442no—
610C24—881no—
611C24—881no—
612C24C2×D4411yescharacteristic
613C24C2×D4411yescharacteristic
614#41—228no—
615#41—444no—
616#41—444no—
617#41—444no—
618C2×Q8—112no—
619C2×Q8—221no—
620C2×Q8—221no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—221no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—112no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—228no—
631C2×D4—224no—
632C2×D4—224no—
633C2×D4—224no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—881no—
650C2×D4—881no—
651C2×D4(C2×D11)⋊C414yes—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—224no—
664C22×C4—224no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—881no—
671C22×C4—881no—
672C22×C4C2×C4×D1112yes—
673C22×C4C2×C4×D1112yes—
674C22×C4C2×D4411yescharacteristic
675C22×C4C2×D4411yescharacteristic
676C22×C4C2×D4411yescharacteristic
677C22×C4C2×D4411yescharacteristic
678C22×C4C2×C22⋊D1112yes—
679C22×C4C2×C22⋊D1112yes—
680C22×C4C23×D1111yescharacteristic
681M16—44no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—44no—
694C2×C8D4×D1112yes—
695C4⋊C4—112no—
696C4⋊C4—112no—
697C4⋊C4—224no—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—442no—
707C4⋊C4—881no—
708C4⋊C4(C2×D11)⋊C414yes—
709C22⋊C4—224no—
710C22⋊C4—224no—
711C22⋊C4—224no—
712C22⋊C4—224no—
713C22⋊C4—224no—
714C22⋊C4—442no—
715C22⋊C4—442no—
716C22⋊C4—881no—
717C22⋊C4—881no—
718C22⋊C4(C2×D11)⋊C414yes—
719C22⋊C4(C2×D11)⋊C414yes—
720C42—442no—
721C42—442no—
722C42—442no—
723C42C2×C4×D1112yes—
724C42C2×C22⋊D1112yes—
725C11#2242411yescharacteristic, complemented, Sylow
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—448no—
743C23—448no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—884no—
755C23—884no—
756C23—884no—
757C23—884no—
758C23—884no—
759C23C2×(C2×D11)⋊C412yes—
760C23C2×(C2×D11)⋊C412yes—
761C23C22×D4411yescharacteristic
762Q8—222no—
763Q8—222no—
764Q8—441no—
765Q8—441no—
766D4—44no—
767D4—114no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—448no—
774D4—448no—
775D4—441no—
776D4—441no—
777D4—884no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—448no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
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—441no—
813C2×C4—884no—
814C2×C4C2×(C2×D11)⋊C412yes—
815C2×C4C2×(C2×D11)⋊C412yes—
816C2×C4C2×(C2×D11)⋊C412yes—
817C2×C4C2×(C2×D11)⋊C412yes—
818C2×C4C22×C4×D1111yescharacteristic
819C2×C4C2×D4×D1111yescharacteristic
820C2×C4#6703711yescharacteristic
821C2×C4#41×D1111yescharacteristic
822C2×C4#6704211yescharacteristic
823C2×C4C22×C22⋊D1111yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—224no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—8816no—
853C22—881no—
854C22—881no—
855C22—881no—
856C22—881no—
857C22D4×D4411yescharacteristic
858C22#1062308511yescharacteristic
859C22#1062327911yescharacteristic
860C22#1062327911yescharacteristic
861C22#1062328211yescharacteristic
862C22#1062328311yescharacteristic
863C22C22×(C2×D11)⋊C411yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—442no—
869C4—442no—
870C4—442no—
871C4—881no—
872C4—881no—
873C4—881no—
874C4C4×D4×D1111yescharacteristic
875C4#1062307611yescharacteristic
876C4D4×C22⋊D1111yescharacteristic
877C4#1062336011yescharacteristic
878C2—42no—
879C2—42no—
880C2—444no—
881C2—882no—
882C2D4×(C2×D11)⋊C411yescharacteristic
883C2#1307713611yescharacteristic
884C2#1307714311yescharacteristic
885C2#1308014611yescharacteristic
886C2#1308016111yescharacteristic
887C2#1308065411yescharacteristic
888C2#1308077411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC2×#10623081C2
cosocleC22×C4×C11C24
hypercenterC2×#435D11
hypocenterC11#22424
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#10622744C2semidirect
3. C2×#10622726C2semidirect
4. #13071565C2semidirect
5. #13069546C2semidirect
6. #13069432C2semidirect
7. #13069049C2semidirect
8. #13069044C2semidirect
9. #13068936C2semidirect
10. #13068926C2semidirect
11. #13068617C2semidirect
12. #13068557C2semidirect
13. #13068548C2semidirect
14. #13068442C2semidirect
15. C2×C11×#435C2semidirect
19. C23×C8×C11C22semidirect
24. C2×#66979C22semidirect
27. #10623081C4semidirect
34. C2×C11×C4⋊C8C22semidirect
36. C2×C11×C22⋊C8C22semidirect
37. C2×C11×#97C22semidirect
40. #10622825C22semidirect
51. C2×#66880C22semidirect
52. C2×#66880C22semidirect
53. C2×#66880C22semidirect
54. C2×#66880C22semidirect
58. #10622548C22semidirect
59. C4×C4⋊Dic11C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622189C22semidirect
63. #10622189C22semidirect
154. #66885D4semidirect
283. C2×#435D11semidirect
402. C23×C8C2×D11semidirect
417. C2×C4⋊C8C2×D11semidirect
433. C2×C22⋊C8C2×D11semidirect
434. C2×#97C2×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×#106230812
C2×#106227442
C2×#106227262
#130715652
#130695462
#130694322
#130690492
#130690442
#130689362
#130689262
#130686172
#130685572
#130685482
#130684422
C2×C11×#4352
#2242411