Finite Group Databasebeta

← #14769369

Subgroups — #14769369

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623337C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3C2×#10622384C211yesmaximal, characteristic, complemented
4#13071546C211yesmaximal, characteristic, complemented
5#13069547C211yesmaximal, characteristic, complemented
6#13069426C211yesmaximal, characteristic, complemented
7#13069051C211yesmaximal, characteristic, complemented
8#13069049C211yesmaximal, characteristic, complemented
9#13068930C211yesmaximal, characteristic, complemented
10#13068928C211yesmaximal, characteristic, complemented
11#13068624C211yesmaximal, characteristic, complemented
12#13068553C211yesmaximal, characteristic, complemented
13#13068547C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#418C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×#4341C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#67006—21no—
21C22×C22⋊Dic11—21no—
22#10623337—24no—
23#10623337C418yescomplemented
24C2×#66992—21no—
25C2×#66991C2211yescharacteristic
26C2×#66989C2211yescharacteristic
27C2×#66988—21no—
28C2×D4×Dic11C2211yescharacteristic
29C2×C4×C22⋊D11C2211yescharacteristic
30C2×#66977C2211yescharacteristic
31C22×#4313C2211yescharacteristic, complemented
32C2×C4⋊C4×D11C2211yescharacteristic, complemented
33C11×#418—24no—
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622825C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622741—24no—
45C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
46C2×#66880C2211yescharacteristic, complemented
47C2×#66880C2211yescharacteristic, complemented
48C2×Dic11⋊C8C2211yescharacteristic, complemented
49C2×C8×Dic11C2211yescharacteristic, complemented
50#10622600C2211yescharacteristic, complemented
51#10622590C2211yescharacteristic, complemented
52C4⋊C4×Dic11C2211yescharacteristic, complemented
53C2×#66874C2211yescharacteristic, complemented
54C2×#66874C2211yescharacteristic, complemented
55#10622569—21no—
56#10622558—21no—
57C4×(C2×D11)⋊C4—21no—
58#10622546—21no—
59#10622384—24no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C25×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—21no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2×C414yescomplemented
72C22×D4×C11C2311yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C22×C22⋊D11—21no—
77C22×C22⋊D11D411yescharacteristic
78C23×Dic11—21no—
79C23×Dic11—21no—
80C2×#4341—22no—
81C2×#4341—22no—
82C2×#4341—22no—
83C2×#4341—41no—
84C2×#4341—41no—
85C2×#4341C2×C414yes—
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C2×C11×M16—22no—
90C2×C11×M16—22no—
91C2×C11×M16—41no—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×#117—22no—
95C11×#117—41no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C42×C11—21no—
100#67006—28no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—28no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11D411yescharacteristic
109#66992—28no—
110#66991—22no—
111#66991C2×C414yes—
112#66989—22no—
113#66989C2×C414yescomplemented
114#66988—28no—
115D4×Dic11—22no—
116D4×Dic11C2×C414yescomplemented
117C4×C22⋊D11C2×C414yes—
118C4×C22⋊D11D414yes—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4D411yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124#66977—22no—
125#66977C2×C414yescomplemented
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4D411yescharacteristic
129C2×C4×Dic11—21no—
130C2×C4×Dic11C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C2×#4313—22no—
134C2×#4313—22no—
135C2×#4313—41no—
136C4⋊C4×D11—22no—
137C4⋊C4×D11—41no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—22no—
141C11×#102D414yescomplemented
142#66896—22no—
143#66896—22no—
144#66896—41no—
145#66896—41no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C22⋊(C11⋊C8)—22no—
152(C2×D11)⋊C8—22no—
153#66880—22no—
154#66880—41no—
155Dic11⋊C8—22no—
156C8×Dic11—22no—
157#66874—22no—
158#66874—41no—
159#22427—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—24no—
163C24×C11—42no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11—81no—
168C24×C11—81no—
169C24×C11C2×D411yescharacteristic
170C23×D11C2×D411yescharacteristic
171C2×D4×C11—28no—
172C2×D4×C11—24no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—44no—
182C2×D4×C11—44no—
183C2×D4×C11—44no—
184C2×D4×C11—42no—
185C2×D4×C11—42no—
186C2×D4×C11C22×C412yes—
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—21no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—41no—
203C2×C22⋊D11—41no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—81no—
207C2×C22⋊D11—81no—
208C2×C22⋊D11C22⋊C414yes—
209C22×Dic11—24no—
210C22×Dic11—24no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—42no—
216C22×Dic11—42no—
217C22×Dic11—81no—
218C22×Dic11—81no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222#4341—28no—
223#4341—44no—
224#4341—44no—
225#4341—44no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—42no—
231C2×C4×D11—42no—
232C2×C4×D11—81no—
233C2×C4×D11C22×C412yes—
234C2×C4×D11C2×D412yes—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—21no—
240C2×Dic22C22×C412yes—
241C11×M16—44no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11C2×D412yes—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4C2×D412yes—
252C11×C22⋊C4—42no—
253C42×C11—42no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—81no—
260C22⋊Dic11C22⋊C414yes—
261(C2×D11)⋊C4—42no—
262(C2×D11)⋊C4C22⋊C414yes—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11C22×C412yes—
269Dic11⋊C4—24no—
270Dic11⋊C4—42no—
271Dic11⋊C4C22⋊C414yes—
272C4×Dic11—81no—
273C4×Dic11C22×C412yes—
274C4×Dic11C2×D412yes—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281#4313—44no—
282C2×#546—111no—
283C2×#436—111no—
284C2×#417—111no—
285C2×#418D1111yescharacteristic, complemented
286#2352—111no—
287#1983—111no—
288#1958—111no—
289#1895—111no—
290#1894—111no—
291#1874—111no—
292#1873—111no—
293#1804—111no—
294#1788—111no—
295#1786—111no—
296C4×#102—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—22no—
307C23×C11—48no—
308C23×C11—48no—
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—41no—
318C23×C11—41no—
319C23×C11—84no—
320C23×C11—84no—
321C23×C11—84no—
322C23×C11—84no—
323C23×C11—84no—
324C23×C11C2×C22⋊C412yes—
325C23×C11C22×D411yescharacteristic
326C22×D11—21no—
327C22×D11—21no—
328C22×D11—21no—
329C22×D11—21no—
330C22×D11—21no—
331C22×D11—21no—
332C22×D11C2×C22⋊C412yes—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—48no—
339D4×C11—41no—
340D4×C11—41no—
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—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11C2×C22⋊C412yes—
355C2×C4×C11C23×C411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C2×#4111yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C22⋊D11—44no—
362C22⋊D11—48no—
363C22⋊D11—84no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—48no—
373C2×Dic11—41no—
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—84no—
384C2×Dic11C2×C22⋊C412yes—
385C2×Dic11C2×C22⋊C412yes—
386C2×Dic11C2×C22⋊C412yes—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—22no—
391C4×D11—84no—
392Dic22—22no—
393Dic22—22no—
394Dic22—41no—
395Dic22—41no—
396C8×C11—22no—
397C8×C11—41no—
398C11⋊C8—41no—
399C11⋊C8—41no—
400C22×#41—111no—
401C23×D4C2×D1111yescharacteristic
402C22×M16—111no—
403C22×M16C2×D1111yescharacteristic
404#546—118no—
405#546—224no—
406C2×#124—111no—
407C2×#123—221no—
408C2×C22⋊Q8—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×#120—221no—
412C2×C4×D4—111no—
413C2×C4×D4—111no—
414C2×#117C2×D1111yescharacteristic
415C22×C4⋊C4—111no—
416C22×C22⋊C4—221no—
417#436—224no—
418C2×C4⋊C8—111no—
419#418—24no—
420#417—224no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102C2×D1111yescharacteristic
430C2×#102C2×D1111yescharacteristic
431C2×#102C2×D1111yescharacteristic
432C2×#102C2×D1111yescharacteristic
433C2×C22⋊C8—111no—
434C2×C22⋊C8—111no—
435C2×C4×C8—111no—
436#388—221no—
437#387—221no—
438#386—221no—
439#382—111no—
440#380—111no—
441#380—111no—
442C4×C4⋊C4—111no—
443C4×C22⋊C4—221no—
444#340—111no—
445#340—111no—
446#340—111no—
447#340—111no—
448C22×C11—22no—
449C22×C11—24no—
450C22×C11—22no—
451C22×C11—22no—
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×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—816no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11C22×C22⋊C411yescharacteristic
471C22×C11D4211yescharacteristic
472C22×C11#54611yescharacteristic
473C22×C11#57511yescharacteristic
474C22×C11#57511yescharacteristic
475C22×C11#57611yescharacteristic
476C22×C11#57711yescharacteristic
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—41no—
481C2×D11—41no—
482C2×D11—41no—
483C2×D11—41no—
484C4×C11—22no—
485C4×C11—42no—
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—
497Dic11—81no—
498C25—21no—
499C2×#41—114no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—222no—
503C2×#41—441no—
504C2×#41—441no—
505C22×Q8—111no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—111no—
513C22×D4—221no—
514C22×D4—221no—
515C22×D4C4×D1114yescomplemented
516C22×D4C22×D1111yescharacteristic
517C22×D4C22×D1111yescharacteristic
518C23×C4—111no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4—221no—
522C23×C4C22×D1111yescharacteristic
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—222no—
527C2×M16—222no—
528C2×M16—441no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533#124—114no—
534#124—222no—
535#123—228no—
536C22⋊Q8—114no—
537C22⋊Q8—222no—
538#121—114no—
539#121—228no—
540#121—222no—
541#120—228no—
542C4×D4—114no—
543C4×D4—114no—
544C4×D4—114no—
545C4×D4—222no—
546#117—22no—
547#117—41no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—222no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—441no—
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
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—
572C4⋊C8—222no—
573#103—222no—
574#103—222no—
575#103—441no—
576#103—441no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—222no—
581#102—222no—
582#102—441no—
583#102—441no—
584#102C22⋊D1114yescomplemented
585C22⋊C8—222no—
586C22⋊C8—222no—
587C4×C8—222no—
588#95—221no—
589#95—221no—
590#95—221no—
591#95—221no—
592#95—221no—
593C2×C11—42no—
594C2×C11—44no—
595C2×C11—82no—
596C2×C11D4×C22⋊C411yescharacteristic
597C2×C11#289611yescharacteristic
598C2×C11#289711yescharacteristic
599C2×C11#327311yescharacteristic
600C2×C11#327511yescharacteristic
601C2×C11#332211yescharacteristic
602C2×C11#332311yescharacteristic
603D11—42no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24—111no—
614C24D4×D1111yescharacteristic
615#41—228no—
616#41—444no—
617#41—444no—
618#41—444no—
619C2×Q8—112no—
620C2×Q8—221no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—221no—
624C2×Q8—221no—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—114no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—441no—
644C2×D4—441no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—881no—
648C2×D4—881no—
649C2×D4C2×C4×D1112yes—
650C2×D4C2×C4×D1112yes—
651C2×D4#433912yes—
652C2×D4C2×C22⋊D1112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—224no—
665C22×C4—224no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—442no—
675C22×C4—442no—
676C22×C4—442no—
677C22×C4—442no—
678C22×C4—881no—
679C22×C4—881no—
680C22×C4—881no—
681C22×C4C2×C4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4D4×D1112yes—
684C22×C4C23×D1111yescharacteristic
685M16—44no—
686M16—444no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8C2×C22⋊D1112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—114no—
703C4⋊C4—112no—
704C4⋊C4—224no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—442no—
711C4⋊C4C2×C22⋊D1112yes—
712C22⋊C4—42no—
713C22⋊C4—114no—
714C22⋊C4—114no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4—442no—
721C22⋊C4—881no—
722C42—42no—
723C42—112no—
724C42—112no—
725C42—881no—
726C11#2242711yescharacteristic, complemented, Sylow
727C23—22no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—22no—
737C23—48no—
738C23—48no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—112no—
755C23—221no—
756C23—221no—
757C23—221no—
758C23—221no—
759C23—221no—
760C23—221no—
761C23C22⋊C4×D1112yes—
762C23C2×D4×D1111yescharacteristic
763Q8—222no—
764Q8—222no—
765Q8—441no—
766Q8—441no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4—444no—
776D4—448no—
777D4—884no—
778D4C4×C22⋊D1114yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—112no—
792C2×C4—112no—
793C2×C4—112no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—448no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—884no—
818C2×C4—884no—
819C2×C4C22⋊C4×D1112yes—
820C2×C4C22×C4×D1111yescharacteristic
821C2×C4C2×#433911yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4#6703711yescharacteristic
824C2×C4#6703711yescharacteristic
825C2×C4C22×C22⋊D1111yescharacteristic
826C8—22no—
827C8—41no—
828C8—441no—
829C8—441no—
830C22—22no—
831C22—24no—
832C22—22no—
833C22—22no—
834C22—42no—
835C22—42no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—816no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—222no—
853C22—222no—
854C22—222no—
855C22—441no—
856C22—441no—
857C22—441no—
858C22—441no—
859C22C2×C22⋊C4×D1111yescharacteristic
860C22#1062302111yescharacteristic
861C22#1062330411yescharacteristic
862C22#1062330411yescharacteristic
863C22#1062330511yescharacteristic
864C22#1062330611yescharacteristic
865C22D4×C22⋊D1111yescharacteristic
866C4—22no—
867C4—42no—
868C4—81no—
869C4—222no—
870C4—222no—
871C4—222no—
872C4—442no—
873C4—442no—
874C4—881no—
875C4—881no—
876C4#1062301711yescharacteristic
877C4#1062302111yescharacteristic
878C4C2×C4×C22⋊D1111yescharacteristic
879C4D4×C22⋊D1111yescharacteristic
880C2—42no—
881C2—44no—
882C2—82no—
883C2—442no—
884C2C22⋊C4×C22⋊D1111yescharacteristic
885C2#1307713011yescharacteristic
886C2#1307714111yescharacteristic
887C2#1308022111yescharacteristic
888C2#1308024711yescharacteristic
889C2#1308081311yescharacteristic
890C2#1308082811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC23×C11C22×D4
prime radicalC2×#10623337C2
cosocleC22×C4×C11C24
hypercenterC2×#418D11
hypocenterC11#22427
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. C2×#10622384C2semidirect
4. #13071546C2semidirect
5. #13069547C2semidirect
6. #13069426C2semidirect
7. #13069051C2semidirect
8. #13069049C2semidirect
9. #13068930C2semidirect
10. #13068928C2semidirect
11. #13068624C2semidirect
12. #13068553C2semidirect
13. #13068547C2semidirect
14. #102×Dic11C2semidirect
15. C2×C11×#418C2semidirect
23. #10623337C4semidirect
31. C22×#4313C22semidirect
32. C2×C4⋊C4×D11C22semidirect
45. C2×(C2×D11)⋊C8C22semidirect
46. C2×#66880C22semidirect
47. C2×#66880C22semidirect
48. C2×Dic11⋊C8C22semidirect
49. C2×C8×Dic11C22semidirect
50. #10622600C22semidirect
51. #10622590C22semidirect
52. C4⋊C4×Dic11C22semidirect
53. C2×#66874C22semidirect
54. C2×#66874C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
71. C22×D4×C11C2×C4semidirect
113. #66989C2×C4semidirect
116. D4×Dic11C2×C4semidirect
125. #66977C2×C4semidirect
141. C11×#102D4semidirect
285. C2×#418D11semidirect
515. C22×D4C4×D11semidirect
584. #102C22⋊D11semidirect
726. C11#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#106233372
C2×#106227412
C2×#106223842
#130715462
#130695472
#130694262
#130690512
#130690492
#130689302
#130689282
#130686242
#130685532
#130685472
#102×Dic112
C2×C11×#4182
#2242711