Finite Group Databasebeta

← #14769311

Subgroups — #14769311

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623140C211yesmaximal, characteristic
2C2×#10622343C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5#13071541C211yesmaximal, characteristic, complemented
6#13069541C211yesmaximal, characteristic, complemented
7#13069438C211yesmaximal, characteristic, complemented
8#13069053C211yesmaximal, characteristic, complemented
9#13069045C211yesmaximal, characteristic, complemented
10#13068937C211yesmaximal, characteristic, complemented
11#13068625C211yesmaximal, characteristic, complemented
12#13068548C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068440C211yesmaximal, characteristic, complemented
15C11×#1874C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C22×D4×D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic, complemented
21C2×#66993C2211yescharacteristic
22C2×#66990—21no—
23C2×C4×C22⋊D11C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic, complemented
25C22×#4313C2211yescharacteristic, complemented
26#10623140—24no—
27#10623140C418yescomplemented
28C2×#66948C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×#66945C2211yescharacteristic, complemented
31C2×#66937—21no—
32C2×#66935—21no—
33C2×C11×#102C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2211yescharacteristic, complemented
36C2×#66896C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic, complemented
38#10622826—21no—
39#10622825C2211yescharacteristic, complemented
40C4×C22⋊Dic11—21no—
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×#66885C2211yescharacteristic, complemented
44C2×#66885C2211yescharacteristic, complemented
45C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
46C2×#66879C2211yescharacteristic, complemented
47C2×Dic11⋊C8C2211yescharacteristic, complemented
48#10622603—21no—
49#10622600C2211yescharacteristic, complemented
50#10622591—21no—
51#10622590C2211yescharacteristic, complemented
52C4⋊C4×Dic11C2211yescharacteristic, complemented
53C2×#66873—24no—
54C2×#66873C2211yescharacteristic
55C2×#66873C2211yescharacteristic
56C2×#66873C2211yescharacteristic, complemented
57C2×#66873C2211yescharacteristic, complemented
58#10622383—24no—
59#10622343—24no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C24×D11—21no—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—21no—
71C22×C22⋊D11—21no—
72C22×C22⋊D11—21no—
73C22×C22⋊D11D411yescharacteristic
74C2×D4×D11—28no—
75C2×D4×D11—22no—
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—41no—
79C2×D4×D11—41no—
80C2×D4×D11—44no—
81C2×D4×D11—44no—
82C2×D4×D11C2×C414yescomplemented
83C22×D44—22no—
84C22×D44—22no—
85C22×D44—21no—
86C22×D44—21no—
87C22×D44—22no—
88C22×D44—41no—
89C22×D44—41no—
90C22×D44C2×C414yes—
91C22×D44C2311yescharacteristic
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×C4×D11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C11×#121—22no—
98C11×#121C2×C414yes—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—41no—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11D411yescharacteristic
108#66993—22no—
109#66993C2×C414yescomplemented
110#66990—28no—
111C4×C22⋊D11C2×C414yes—
112C4×C22⋊D11D414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4D411yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×Dic11⋊C4D411yescharacteristic
121C2×C4×Dic11—21no—
122C2×C4×Dic11—21no—
123C2×C4×Dic11C2311yescharacteristic
124C22×C11⋊C8—22no—
125C22×C11⋊C8—22no—
126C22×C11⋊C8—41no—
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C2×#4313—22no—
130C2×#4313—22no—
131C2×#4313—41no—
132#66948—22no—
133#66948C2×C414yescomplemented
134#66946—22no—
135#66946C2×C414yescomplemented
136#66945—22no—
137#66945—41no—
138#66937—28no—
139#66935—28no—
140C11×#102—22no—
141C11×#102—41no—
142C11×C22⋊C8—22no—
143#66896—22no—
144#66896—41no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150#66885—22no—
151#66885—22no—
152#66885—41no—
153#66885—41no—
154(C2×D11)⋊C8—22no—
155#66879—22no—
156Dic11⋊C8—22no—
157#66873—22no—
158#66873—22no—
159#66873—22no—
160#66873D414yescomplemented
161#22423—111nomaximal, Sylow
162C24×C11—21no—
163C24×C11C2×D411yescharacteristic
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—24no—
167C23×D11—24no—
168C23×D11—42no—
169C23×D11—42no—
170C23×D11—42no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11—42no—
174C23×D11—42no—
175C23×D11—42no—
176C23×D11—81no—
177C23×D11—81no—
178C23×D11—81no—
179C23×D11—81no—
180C23×D11C2×D411yescharacteristic
181C2×D4×C11—24no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—42no—
188C2×D4×C11—42no—
189C2×D4×C11C22×C412yes—
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×C11—21no—
197C22×C4×C11—42no—
198C22×C4×C11—42no—
199C22×C4×C11—81no—
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—24no—
207C2×C22⋊D11—22no—
208C2×C22⋊D11—22no—
209C2×C22⋊D11—42no—
210C2×C22⋊D11—42no—
211C2×C22⋊D11—42no—
212C2×C22⋊D11—42no—
213C2×C22⋊D11—81no—
214C2×C22⋊D11—81no—
215C2×C22⋊D11C22⋊C414yes—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221D4×D11—28no—
222D4×D11—44no—
223D4×D11—44no—
224D4×D11—44no—
225D4×D11—432no—
226C2×D44—24no—
227C2×D44—28no—
228C2×D44—24no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—21no—
236C2×D44—21no—
237C2×D44—42no—
238C2×D44—42no—
239C2×D44—44no—
240C2×D44—44no—
241C2×D44—44no—
242C2×D44—42no—
243C2×D44—42no—
244C2×D44C22×C412yes—
245C2×D44C22×C412yes—
246C2×D44C2×D412yes—
247C2×D44#4112yes—
248C2×C4×D11—24no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—42no—
254C2×C4×D11—42no—
255C2×C4×D11C22×C412yes—
256C2×C4×D11C2×D412yes—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—42no—
268C11×C4⋊C4C22×C412yes—
269C11×C4⋊C4C2×D412yescomplemented
270C11×C22⋊C4—24no—
271C22⋊Dic11—42no—
272C22⋊Dic11C22⋊C414yes—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—42no—
276(C2×D11)⋊C4—81no—
277(C2×D11)⋊C4C22⋊C414yes—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282Dic11⋊C4C22⋊C414yes—
283C4×Dic11—42no—
284C4×Dic11—81no—
285C4×Dic11C22×C412yes—
286C4×Dic11C2×D412yes—
287C2×C11⋊C8—21no—
288C2×C11⋊C8—21no—
289C2×C11⋊C8—21no—
290C2×C11⋊C8—21no—
291C2×C11⋊C8—21no—
292C2×C11⋊C8—44no—
293C2×C11⋊C8C2×D412yescomplemented
294#4313—44no—
295C2×D42—111no—
296C2×#435—111no—
297C2×#418—111no—
298C22×#102—111no—
299#2352—111no—
300#1982—111no—
301#1961—111no—
302#1895—111no—
303#1893—111no—
304#1875—111no—
305#1874D1111yescharacteristic, complemented
306#1804—111no—
307#1786—111no—
308#1786—111no—
309#1762—111no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—22no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11C2×C22⋊C412yes—
322C23×C11AGL(1,ℤ/8)12yes—
323C23×C11AGL(1,ℤ/8)12yes—
324C23×C11C22×D411yescharacteristic
325C22×D11—22no—
326C22×D11—21no—
327C22×D11—22no—
328C22×D11—21no—
329C22×D11—22no—
330C22×D11—21no—
331C22×D11—21no—
332C22×D11—21no—
333C22×D11—21no—
334C22×D11—22no—
335C22×D11—48no—
336C22×D11—48no—
337C22×D11—48no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—48no—
349C22×D11—84no—
350C22×D11—84no—
351C22×D11—84no—
352C22×D11—84no—
353C22×D11—84no—
354C22×D11—84no—
355C22×D11—84no—
356C22×D11—84no—
357C22×D11—84no—
358C22×D11—84no—
359C22×D11C2×C22⋊C412yes—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—48no—
363D4×C11—41no—
364D4×C11—41no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—84no—
381C2×C4×C11C2×C22⋊C412yes—
382C2×C4×C11C23×C411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C2×#4111yescharacteristic
386C2×C4×C11H(5,𝔽2)11yescharacteristic
387C2×C4×C11H(5,𝔽2)11yescharacteristic
388C22⋊D11—28no—
389C22⋊D11—48no—
390C22⋊D11—48no—
391C22⋊D11—84no—
392C2×Dic11—21no—
393C2×Dic11—21no—
394C2×Dic11—21no—
395C2×Dic11—21no—
396C2×Dic11—21no—
397C2×Dic11—21no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11C2×C22⋊C412yes—
405C2×Dic11C2×C22⋊C412yes—
406C2×Dic11C2×C22⋊C412yes—
407D44—22no—
408D44—22no—
409D44—22no—
410D44—22no—
411D44—22no—
412D44—48no—
413D44—48no—
414D44—41no—
415D44—41no—
416D44C4×D414yes—
417C4×D11—22no—
418C4×D11—22no—
419C4×D11—22no—
420C4×D11—22no—
421C4×D11—48no—
422C8×C11—41no—
423C8×C11—41no—
424C11⋊C8—22no—
425C11⋊C8—41no—
426C23×D4—111no—
427C23×D4—111no—
428C23×D4—221no—
429C22×M16—111no—
430C23×C8—111no—
431D42—118no—
432D42—224no—
433C2×#127—111no—
434C2×#121—111no—
435C2×#121—221no—
436C2×#121C2×D1111yescharacteristic
437C2×#120—221no—
438C2×#120—221no—
439C2×C4×D4—111no—
440C2×C4×D4—111no—
441C2×#117—111no—
442C22×C4⋊C4C2×D1111yescharacteristic, complemented
443#435—224no—
444C2×C4⋊C8—111no—
445#418—224no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—224no—
457C2×#102C2×D1111yescharacteristic, complemented
458C2×#102C2×D1111yescharacteristic, complemented
459C2×C22⋊C8—111no—
460C2×C22⋊C8C2×D1111yescharacteristic, complemented
461C2×#97—111no—
462#388—221no—
463#387—221no—
464#386—221no—
465#382—111no—
466#380—111no—
467#380—111no—
468C4×C4⋊C4—111no—
469C4×C22⋊C4—221no—
470#340—111no—
471#340—111no—
472#340C2×D1111yescharacteristic, complemented
473#340C2×D1111yescharacteristic, complemented
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11#41814yescomplemented
488C22×C11C22×C22⋊C411yescharacteristic
489C22×C11D4211yescharacteristic
490C22×C11#54611yescharacteristic
491C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
492C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
493C22×C11#57611yescharacteristic
494C22×C11#57711yescharacteristic
495C2×D11—24no—
496C2×D11—22no—
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—41no—
502C2×D11—42no—
503C2×D11—41no—
504C2×D11—42no—
505C2×D11—41no—
506C2×D11—42no—
507C2×D11—41no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—816no—
513C2×D11—816no—
514C2×D11—81no—
515C2×D11—81no—
516C2×D11—81no—
517C2×D11—81no—
518C4×C11—22no—
519C4×C11—42no—
520C4×C11—42no—
521C4×C11—81no—
522C4×C11C2×C4×D411yescharacteristic
523C4×C11#51811yescharacteristic
524C4×C11D4211yescharacteristic
525C4×C11#54611yescharacteristic
526Dic11—22no—
527Dic11—22no—
528Dic11—22no—
529Dic11—81no—
530Dic11—81no—
531C25—221no—
532C25—221no—
533C22×D4—21no—
534C22×D4—111no—
535C22×D4—114no—
536C22×D4—114no—
537C22×D4—111no—
538C22×D4—111no—
539C22×D4—222no—
540C22×D4—222no—
541C22×D4—221no—
542C22×D4—222no—
543C22×D4—221no—
544C22×D4—221no—
545C22×D4—221no—
546C22×D4—222no—
547C22×D4—222no—
548C22×D4—228no—
549C22×D4—221no—
550C22×D4—222no—
551C22×D4—441no—
552C22×D4—441no—
553C22×D4—441no—
554C22×D4—441no—
555C22×D4—444no—
556C22×D4—444no—
557C22×D4C22×D1111yescharacteristic
558C23×C4—21no—
559C23×C4—111no—
560C23×C4—221no—
561C23×C4C22×D1111yescharacteristic
562C2×M16—222no—
563C2×M16—222no—
564C2×M16—441no—
565C22×C8—111no—
566C22×C8—111no—
567C22×C8—222no—
568C22×C8—222no—
569C22×C8—441no—
570C22×C8C22×D1111yescharacteristic
571C22×C8C22×D1111yescharacteristic
572#127—114no—
573#127—222no—
574#121—22no—
575#121—114no—
576#121—228no—
577#121—222no—
578#121C4×D1114yes—
579#120—228no—
580#120—228no—
581C4×D4—114no—
582C4×D4—114no—
583C4×D4—114no—
584C4×D4—222no—
585#117—222no—
586#117—441no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—111no—
592C2×C4⋊C4—111no—
593C2×C4⋊C4C22×D1111yescharacteristic
594C2×C4⋊C4C22×D1111yescharacteristic
595C2×C4⋊C4C22×D1111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—111no—
598C2×C22⋊C4—111no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C42—111no—
605C2×C42—221no—
606C2×C42—221no—
607C4⋊C8—222no—
608#102—22no—
609#102—41no—
610#102—114no—
611#102—222no—
612#102—222no—
613#102—222no—
614#102—222no—
615#102—222no—
616#102—222no—
617#102—441no—
618#102—441no—
619#102—441no—
620C22⋊C8—22no—
621C22⋊C8—222no—
622#97—222no—
623#95—221no—
624#95—221no—
625#95—221no—
626#95—221no—
627#95—221no—
628C2×C11—24no—
629C2×C11—82no—
630C2×C11D4×C22⋊C411yescharacteristic
631C2×C11C2×#41811yescharacteristic
632C2×C11#289711yescharacteristic
633C2×C11#326411yescharacteristic
634C2×C11#326511yescharacteristic
635C2×C11#331011yescharacteristic
636C2×C11#331811yescharacteristic
637D11—42no—
638D11—44no—
639D11—82no—
640C24—21no—
641C24—111no—
642C24—224no—
643C24—221no—
644C24—221no—
645C24—224no—
646C24—442no—
647C24—442no—
648C24—442no—
649C24—442no—
650C24—442no—
651C24—442no—
652C24—442no—
653C24—442no—
654C24—881no—
655C24—881no—
656C24—881no—
657C24—881no—
658C24D4×D1111yescharacteristic
659C2×D4—24no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—114no—
668C2×D4—112no—
669C2×D4—112no—
670C2×D4—112no—
671C2×D4—112no—
672C2×D4—228no—
673C2×D4—224no—
674C2×D4—224no—
675C2×D4—224no—
676C2×D4—224no—
677C2×D4—228no—
678C2×D4—222no—
679C2×D4—222no—
680C2×D4—224no—
681C2×D4—221no—
682C2×D4—221no—
683C2×D4—221no—
684C2×D4—221no—
685C2×D4—221no—
686C2×D4—221no—
687C2×D4—221no—
688C2×D4—221no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—442no—
693C2×D4—442no—
694C2×D4—442no—
695C2×D4—442no—
696C2×D4—444no—
697C2×D4—444no—
698C2×D4—444no—
699C2×D4—442no—
700C2×D4—442no—
701C2×D4—442no—
702C2×D4—442no—
703C2×D4—4432no—
704C2×D4—881no—
705C2×D4—881no—
706C2×D4C2×C4×D1112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—81no—
717C22×C4—111no—
718C22×C4—111no—
719C22×C4—111no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—224no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—442no—
730C22×C4—442no—
731C22×C4C2×C4×D1112yes—
732C22×C4D4×D1111yescharacteristic
733C22×C4D4×D1112yes—
734C22×C4C23×D1111yescharacteristic
735M16—444no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—112no—
743C2×C8—221no—
744C2×C8—221no—
745C2×C8—221no—
746C2×C8—221no—
747C2×C8—221no—
748C2×C8—444no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—42no—
754C4⋊C4—114no—
755C4⋊C4—221no—
756C4⋊C4—221no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4C2×C4×D1112yes—
760C4⋊C4D4×D1112yescomplemented
761C22⋊C4—24no—
762C22⋊C4—114no—
763C22⋊C4—114no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4—442no—
767C22⋊C4—442no—
768C22⋊C4—881no—
769C42—112no—
770C42—112no—
771C42—442no—
772C42—881no—
773C11#2242311yescharacteristic, complemented, Sylow
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—112no—
786C23—222no—
787C23—221no—
788C23—221no—
789C23—221no—
790C23—221no—
791C23—221no—
792C23—222no—
793C23—221no—
794C23—222no—
795C23—222no—
796C23—448no—
797C23—448no—
798C23—448no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—441no—
808C23—448no—
809C23—441no—
810C23—884no—
811C23—884no—
812C23—884no—
813C23—884no—
814C23—884no—
815C23—884no—
816C23—884no—
817C23—884no—
818C23—884no—
819C23—884no—
820C23C22⋊C4×D1112yes—
821C23#6696412yes—
822C23#6696712yes—
823C23C2×D4×D1111yescharacteristic
824D4—22no—
825D4—22no—
826D4—48no—
827D4—41no—
828D4—41no—
829D4—114no—
830D4—228no—
831D4—222no—
832D4—222no—
833D4—222no—
834D4—222no—
835D4—222no—
836D4—448no—
837D4—448no—
838D4—448no—
839D4—448no—
840D4—441no—
841D4—441no—
842D4—884no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—84no—
859C2×C4—112no—
860C2×C4—112no—
861C2×C4—112no—
862C2×C4—221no—
863C2×C4—221no—
864C2×C4—221no—
865C2×C4—221no—
866C2×C4—221no—
867C2×C4—221no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—448no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4C22⋊C4×D1112yes—
880C2×C4C22×C4×D1111yescharacteristic
881C2×C4C2×D4×D1111yescharacteristic
882C2×C4C2×D4×D1111yescharacteristic
883C2×C4#6703711yescharacteristic
884C2×C4#41×D1111yescharacteristic
885C2×C4#6704211yescharacteristic
886C8—41no—
887C8—41no—
888C8—222no—
889C8—441no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—222no—
904C22—224no—
905C22—222no—
906C22—222no—
907C22—441no—
908C22—442no—
909C22—441no—
910C22—442no—
911C22—441no—
912C22—442no—
913C22—442no—
914C22—442no—
915C22—441no—
916C22—442no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—8816no—
921C22—8816no—
922C22—881no—
923C22—881no—
924C22—881no—
925C22—881no—
926C22#1062238314yescomplemented
927C22C2×C22⋊C4×D1111yescharacteristic
928C22#1062312111yescharacteristic
929C22#1062318511yescharacteristic
930C22C2×#6696411yescharacteristic
931C22C2×#6696711yescharacteristic
932C22#1062330511yescharacteristic
933C22#1062330911yescharacteristic
934C4—22no—
935C4—42no—
936C4—42no—
937C4—81no—
938C4—222no—
939C4—222no—
940C4—222no—
941C4—881no—
942C4—881no—
943C4C4×D4×D1111yescharacteristic
944C4#1062307611yescharacteristic
945C4#1062314011yescharacteristic
946C4#1062314111yescharacteristic
947C2—24no—
948C2—82no—
949C2—442no—
950C2—444no—
951C2—882no—
952C2#1307143411yescharacteristic
953C2C2×#1062238311yescharacteristic
954C2#1307714011yescharacteristic
955C2#1308008911yescharacteristic
956C2#1308010411yescharacteristic
957C2#1308063511yescharacteristic
958C2#1308075511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×#10623140C2
cosocleC22×C4×C11C24
hypercenter#1874D11
hypocenterC11#22423
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#10622343C2semidirect
3. C2×#10622383C2semidirect
4. C22×#66873C2semidirect
5. #13071541C2semidirect
6. #13069541C2semidirect
7. #13069438C2semidirect
8. #13069053C2semidirect
9. #13069045C2semidirect
10. #13068937C2semidirect
11. #13068625C2semidirect
12. #13068548C2semidirect
13. #13068545C2semidirect
14. #13068440C2semidirect
15. C11×#1874C2semidirect
20. C22×C11×C4⋊C4C22semidirect
24. C23×C11⋊C8C22semidirect
25. C22×#4313C22semidirect
27. #10623140C4semidirect
30. C2×#66945C22semidirect
33. C2×C11×#102C22semidirect
34. C2×C11×#102C22semidirect
35. C2×C11×C22⋊C8C22semidirect
36. C2×#66896C22semidirect
37. C2×#66896C22semidirect
39. #10622825C22semidirect
43. C2×#66885C22semidirect
44. C2×#66885C22semidirect
45. C2×(C2×D11)⋊C8C22semidirect
46. C2×#66879C22semidirect
47. C2×Dic11⋊C8C22semidirect
49. #10622600C22semidirect
51. #10622590C22semidirect
52. C4⋊C4×Dic11C22semidirect
56. C2×#66873C22semidirect
57. C2×#66873C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
82. C2×D4×D11C2×C4semidirect
109. #66993C2×C4semidirect
133. #66948C2×C4semidirect
135. #66946C2×C4semidirect
160. #66873D4semidirect
269. C11×C4⋊C4C2×D4semidirect
293. C2×C11⋊C8C2×D4semidirect
305. #1874D11semidirect
442. C22×C4⋊C4C2×D11semidirect
457. C2×#102C2×D11semidirect
458. C2×#102C2×D11semidirect
460. C2×C22⋊C8C2×D11semidirect
472. #340C2×D11semidirect
473. #340C2×D11semidirect
487. C22×C11#418semidirect
760. C4⋊C4D4×D11semidirect
773. C11#22423semidirect
926. C22#10622383semidirect

Maximal subgroups

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

subgroupindex
C2×#106231402
C2×#106223432
C2×#106223832
C22×#668732
#130715412
#130695412
#130694382
#130690532
#130690452
#130689372
#130686252
#130685482
#130685452
#130684402
C11×#18742
#2242311