Finite Group Databasebeta

← #14769331

Subgroups — #14769331

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×#10623161C211yesmaximal, characteristic
2C2×#10622341C211yesmaximal, characteristic, complemented
3C2×#10622614C211yesmaximal, characteristic, complemented
4C2×#10622417C211yesmaximal, characteristic, complemented
5#13071566C211yesmaximal, characteristic, complemented
6#13069545C211yesmaximal, characteristic, complemented
7#13069429C211yesmaximal, characteristic, complemented
8#13069050C211yesmaximal, characteristic, complemented
9#13069043C211yesmaximal, characteristic, complemented
10#13068937C211yesmaximal, characteristic, complemented
11#13068615C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic, complemented
13#13068548C211yesmaximal, characteristic, complemented
14#13068440C211yesmaximal, characteristic, complemented
15C11×#1873C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic, complemented
24#10623161—24no—
25#10623161C418yescomplemented
26C2×#66948—21no—
27C2×#66948C2211yescharacteristic
28C2×#66947—21no—
29C2×#66946C2211yescharacteristic
30C2×#66945C2211yescharacteristic, complemented
31C2×#66935—21no—
32C2×C22⋊C4×D11—21no—
33C2×C11×#103C2211yescharacteristic, complemented
34C2×C11×#103C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×#66899C2211yescharacteristic, complemented
37C2×#66899C2211yescharacteristic, complemented
38#10622825C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
44C2×#66879C2211yescharacteristic, complemented
45C2×Dic11⋊C8C2211yescharacteristic, complemented
46#10622614—24no—
47#10622600C2211yescharacteristic, complemented
48#10622589C2211yescharacteristic, complemented
49C4⋊C4×Dic11C2211yescharacteristic, complemented
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54#10622570—21no—
55#10622557—21no—
56#10622553—21no—
57C4×Dic11⋊C4—21no—
58#10622417—24no—
59#10622341—24no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×Q8×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11D411yescharacteristic
68C2×#4343—22no—
69C2×#4343—22no—
70C2×#4343—22no—
71C2×#4343—41no—
72C2×#4343—41no—
73C2×#4343C2×C414yes—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—21no—
77C22×D44—21no—
78C22×D44—22no—
79C22×D44—21no—
80C22×D44—41no—
81C22×D44—41no—
82C22×D44C2×C414yes—
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8C2×C414yes—
92C11×#117—22no—
93C11×#117—41no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11D411yescharacteristic
103#67000—22no—
104#67000C2×C414yes—
105C4×C22⋊D11C2×C414yes—
106C4×C22⋊D11D414yes—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4D411yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4D411yescharacteristic
119C2×C4×Dic11—21no—
120C2×C4×Dic11—21no—
121C2×C4×Dic11C2311yescharacteristic
122C2×#4318—22no—
123C2×#4318—22no—
124C2×#4318—41no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C2×C8×D11—22no—
128C2×C8×D11—22no—
129C2×C8×D11—41no—
130#66948—22no—
131#66948—28no—
132#66948C2×C414yes—
133#66947—28no—
134#66946—22no—
135#66946C2×C414yes—
136#66945—22no—
137#66945—41no—
138#66935—28no—
139C22⋊C4×D11—28no—
140C11×#103—22no—
141C11×#103—41no—
142C11×C22⋊C8—22no—
143#66899—22no—
144#66899—41no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148#66885—22no—
149#66885—22no—
150#66885—41no—
151#66885—41no—
152(C2×D11)⋊C8—22no—
153#66879—22no—
154Dic11⋊C8—22no—
155#66873—22no—
156#66873—22no—
157#66873—22no—
158#66873D414yescomplemented
159#22424—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C23×D11—21no—
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
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11C22×C412yes—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11C22×C412yes—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2411yescharacteristic
189C2×C22⋊D11—41no—
190C2×C22⋊D11—41no—
191C2×C22⋊D11C22⋊C414yes—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11C2×D411yescharacteristic
195C22×Dic11C2×D411yescharacteristic
196C22×Dic11C2×D411yescharacteristic
197#4343—28no—
198#4343—44no—
199#4343—44no—
200#4343—44no—
201C2×D44—24no—
202C2×D44—24no—
203C2×D44—28no—
204C2×D44—24no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—42no—
214C2×D44—42no—
215C2×D44—44no—
216C2×D44—44no—
217C2×D44—44no—
218C2×D44—42no—
219C2×D44—42no—
220C2×D44—81no—
221C2×D44—81no—
222C2×D44C22×C412yes—
223C2×D44C22×C412yes—
224C2×D44C2×D412yes—
225C2×D44#4112yes—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—21no—
231C2×C4×D11—21no—
232C2×C4×D11—42no—
233C2×C4×D11—42no—
234C2×C4×D11—81no—
235C2×C4×D11—81no—
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—24no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4C22×C412yes—
250C11×C4⋊C4C2×D412yes—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—42no—
253C42×C11—42no—
254C22⋊Dic11—81no—
255C22⋊Dic11C22⋊C414yes—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—81no—
262(C2×D11)⋊C4C22⋊C414yes—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267Dic11⋊C4—42no—
268Dic11⋊C4—81no—
269Dic11⋊C4C22⋊C414yes—
270C4×Dic11—42no—
271C4×Dic11—42no—
272C4×Dic11C22×C412yes—
273C4×Dic11C2×D412yes—
274#4318—44no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8C2×D412yes—
281C8×D11—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#1873D1111yescharacteristic, complemented
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×C11C2×C22⋊C412yes—
304C23×C11C22×D411yescharacteristic
305C22×D11—22no—
306C22×D11—21no—
307C22×D11—22no—
308C22×D11—21no—
309C22×D11—22no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—22no—
315C22×D11—48no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
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—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11C2×C22⋊C412yes—
356C2×C4×C11C23×C411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C2×#4111yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C22⋊D11—44no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11C2×C22⋊C412yes—
376C2×Dic11C2×C22⋊C412yes—
377C2×Dic11C2×C22⋊C412yes—
378D44—22no—
379D44—22no—
380D44—22no—
381D44—22no—
382D44—22no—
383D44—48no—
384D44—48no—
385D44—41no—
386D44—41no—
387D44—84no—
388D44C4×D414yes—
389C4×D11—22no—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—48no—
394C4×D11—84no—
395C8×C11—41no—
396C8×C11—41no—
397C11⋊C8—22no—
398C11⋊C8—41no—
399C22×#41—111no—
400C23×D4—111no—
401C22×M16—111no—
402C23×C8—111no—
403#546—118no—
404#546—224no—
405C2×#124—111no—
406C2×#123—221no—
407C2×C22⋊Q8C2×D1111yescharacteristic
408C2×#121—111no—
409C2×#121—221no—
410C2×#120—221no—
411C2×C4×D4—111no—
412C2×C4×D4—111no—
413C2×#117—111no—
414C2×#117C2×D1111yescharacteristic
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×#102—111no—
431C2×#102—111no—
432C2×C22⋊C8—111no—
433C2×C22⋊C8C2×D1111yescharacteristic
434C2×#97—111no—
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#340C2×D1111yescharacteristic, complemented
446#340C2×D1111yescharacteristic, complemented
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11C22×C22⋊C411yescharacteristic
455C22×C11D4211yescharacteristic
456C22×C11#54611yescharacteristic
457C22×C11#57511yescharacteristic
458C22×C11#57511yescharacteristic
459C22×C11#57611yescharacteristic
460C22×C11#57711yescharacteristic
461C2×D11—24no—
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—41no—
468C2×D11—42no—
469C2×D11—41no—
470C2×D11—42no—
471C2×D11—41no—
472C2×D11—42no—
473C2×D11—41no—
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—42no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—81no—
488C4×C11C2×C4×D411yescharacteristic
489C4×C11#51811yescharacteristic
490C4×C11D4211yescharacteristic
491C4×C11#54611yescharacteristic
492Dic11—22no—
493Dic11—22no—
494Dic11—22no—
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×Q8C22×D1111yescharacteristic
505C22×D4—111no—
506C22×D4—114no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—222no—
510C22×D4—222no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4—222no—
515C22×D4—441no—
516C22×D4—441no—
517C23×C4—111no—
518C23×C4—221no—
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—22no—
535C22⋊Q8C4×D1114yes—
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—22no—
545#117—41no—
546#117—222no—
547#117—441no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—111no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—228no—
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—21no—
570C2×C42—111no—
571C2×C42—221no—
572C2×C42—221no—
573C4⋊C8—222no—
574#103—22no—
575#103—41no—
576#103—222no—
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—222no—
588#97—222no—
589#95—221no—
590#95—221no—
591#95—221no—
592C2×C11—42no—
593C2×C11D4×C22⋊C411yescharacteristic
594C2×C11#289611yescharacteristic
595C2×C11#289711yescharacteristic
596C2×C11#326711yescharacteristic
597C2×C11#326811yescharacteristic
598C2×C11#331111yescharacteristic
599C2×C11#331911yescharacteristic
600D11—42no—
601D11—44no—
602D11—82no—
603C24—111no—
604C24—221no—
605C24—221no—
606C24—224no—
607C24—442no—
608C24—442no—
609C24—442no—
610C24—442no—
611C24—881no—
612C24—881no—
613C24D4×D1111yescharacteristic
614#41—228no—
615#41—444no—
616#41—444no—
617#41—444no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8C2×C4×D1112yes—
624C2×D4—114no—
625C2×D4—112no—
626C2×D4—112no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—228no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—224no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—441no—
649C2×D4—441no—
650C2×D4—881no—
651C2×D4—881no—
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—111no—
661C22×C4—111no—
662C22×C4—111no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—224no—
666C22×C4—224no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—442no—
674C22×C4—442no—
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—24no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—114no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—442no—
706C4⋊C4—881no—
707C4⋊C4C2×C4×D1112yes—
708C4⋊C4D4×D1112yes—
709C22⋊C4—24no—
710C22⋊C4—42no—
711C22⋊C4—114no—
712C22⋊C4—114no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—442no—
718C22⋊C4—881no—
719C22⋊C4—881no—
720C42—42no—
721C42—112no—
722C42—112no—
723C42—442no—
724C42—442no—
725C11#2242411yescharacteristic, complemented, Sylow
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—112no—
733C23—222no—
734C23—221no—
735C23—221no—
736C23—221no—
737C23—221no—
738C23—221no—
739C23—222no—
740C23—221no—
741C23—222no—
742C23—222no—
743C23—448no—
744C23—448no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
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—114no—
767D4—222no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—448no—
773D4—448no—
774D4—444no—
775D4—441no—
776D4—441no—
777D4—884no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—112no—
797C2×C4—112no—
798C2×C4—112no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—221no—
804C2×C4—221no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—448no—
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×C4#6703711yescharacteristic
822C2×C4#41×D1111yescharacteristic
823C2×C4#6704211yescharacteristic
824C8—41no—
825C8—41no—
826C8—222no—
827C8—441no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—222no—
836C22—224no—
837C22—222no—
838C22—222no—
839C22—441no—
840C22—442no—
841C22—441no—
842C22—442no—
843C22—441no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—441no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—8816no—
853C22—881no—
854C22—881no—
855C22—881no—
856C22—881no—
857C22C2×C22⋊C4×D1111yescharacteristic
858C22#1062312111yescharacteristic
859C22#1062318511yescharacteristic
860C22#1062330011yescharacteristic
861C22#1062330111yescharacteristic
862C22#1062330811yescharacteristic
863C22#1062330811yescharacteristic
864C4—22no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—81no—
869C4—222no—
870C4—222no—
871C4—222no—
872C4—881no—
873C4—881no—
874C4C4×D4×D1111yescharacteristic
875C4#1062307611yescharacteristic
876C4#1062314011yescharacteristic
877C4#1062314111yescharacteristic
878C2—42no—
879C2—442no—
880C2—444no—
881C2—882no—
882C2#1307143411yescharacteristic
883C2#1307713411yescharacteristic
884C2#1307713811yescharacteristic
885C2#1308014411yescharacteristic
886C2#1308015911yescharacteristic
887C2#1308065511yescharacteristic
888C2#1308077511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC2×#10623161C2
cosocleC22×C4×C11C24
hypercenter#1873D11
hypocenterC11#22424
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. C2×#10622341C2semidirect
3. C2×#10622614C2semidirect
4. C2×#10622417C2semidirect
5. #13071566C2semidirect
6. #13069545C2semidirect
7. #13069429C2semidirect
8. #13069050C2semidirect
9. #13069043C2semidirect
10. #13068937C2semidirect
11. #13068615C2semidirect
12. #13068555C2semidirect
13. #13068548C2semidirect
14. #13068440C2semidirect
15. C11×#1873C2semidirect
23. C22×C8×D11C22semidirect
25. #10623161C4semidirect
30. C2×#66945C22semidirect
33. C2×C11×#103C22semidirect
34. C2×C11×#103C22semidirect
36. C2×#66899C22semidirect
37. C2×#66899C22semidirect
43. C2×(C2×D11)⋊C8C22semidirect
44. C2×#66879C22semidirect
45. C2×Dic11⋊C8C22semidirect
47. #10622600C22semidirect
48. #10622589C22semidirect
49. C4⋊C4×Dic11C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
158. #66873D4semidirect
292. #1873D11semidirect
422. C2×#103C2×D11semidirect
423. C2×#103C2×D11semidirect
445. #340C2×D11semidirect
446. #340C2×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×#106231612
C2×#106223412
C2×#106226142
C2×#106224172
#130715662
#130695452
#130694292
#130690502
#130690432
#130689372
#130686152
#130685552
#130685482
#130684402
C11×#18732
#2242411