Finite Group Databasebeta

← #14774090

Subgroups — #14774090

Order 2816.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622830C211yesmaximal, characteristic
2C2×#10622398C211yesmaximal, characteristic, complemented
3#13071632C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13069489C211yesmaximal, characteristic, complemented
6#13069310C211yesmaximal, characteristic, complemented
7#13069246C211yesmaximal, characteristic, complemented
8#13069044C211yesmaximal, characteristic, complemented
9#13068962C211yesmaximal, characteristic, complemented
10#13068961C211yesmaximal, characteristic, complemented
11#13068875C211yesmaximal, characteristic, complemented
12#13068809C211yesmaximal, characteristic, complemented
13#13068443C211yesmaximal, characteristic, complemented
14#13068392C211yesmaximal, characteristic, complemented
15C22×C11×#102C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C22⋊Dic11—21no—
20C2×D4×Dic11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C2×#66946C2211yescharacteristic, complemented
27C2×C11×#102—24no—
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32#10622860—21no—
33#10622834C2211yescharacteristic
34#10622834C2211yescharacteristic
35#10622833—21no—
36#10622833—21no—
37#10622830C418yescomplemented
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40#10622826—21no—
41#10622825C2211yescharacteristic
42C4×C22⋊Dic11C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×#66885C2211yescharacteristic, complemented
45C2×#66885C2211yescharacteristic, complemented
46C2×#66879C2211yescharacteristic, complemented
47C2×#66879C2211yescharacteristic, complemented
48#10622603—21no—
49#10622602—21no—
50#10622601C2211yescharacteristic, complemented
51C4⋊C4×Dic11C2211yescharacteristic, complemented
52#10622586C2211yescharacteristic, complemented
53C2×#66872C2211yescharacteristic, complemented
54C2×#66872C2211yescharacteristic, complemented
55#10622398—24no—
56#10622189C2211yescharacteristic, complemented
57#10622189C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62C25×C11—21no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—41no—
68C22×D4×C11—41no—
69C22×D4×C11C2×C414yescomplemented
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11—21no—
75C23×Dic11—21no—
76C23×Dic11—21no—
77C22×D44C2311yescharacteristic
78C22×C4×D11—21no—
79C22×C8×C11—22no—
80C22×C8×C11—22no—
81C22×C8×C11—41no—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—41no—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—44no—
97C2×C22⋊Dic11D411yescharacteristic
98C2×C22⋊Dic11D411yescharacteristic
99D4×Dic11—22no—
100D4×Dic11—22no—
101D4×Dic11—41no—
102D4×Dic11—41no—
103C2×#4323—22no—
104C2×#4323—22no—
105C2×#4323—41no—
106C2×#4323—41no—
107C2×#4323C2×C414yescomplemented
108C2×#4323C2×C414yescomplemented
109#66983—22no—
110#66983C2×C414yescomplemented
111C4×C22⋊D11—44no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×C4×Dic11—21no—
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125#66946—22no—
126#66946—41no—
127C11×#102—22no—
128C11×#102—22no—
129C11×#102—22no—
130C11×#102D414yescomplemented
131#66896C2×C414yescomplemented
132#66896C2×C414yescomplemented
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95D411yescharacteristic
137C11⋊#95D411yescharacteristic
138C22⋊(C11⋊C8)C2×C414yescomplemented
139#66885—22no—
140#66885—41no—
141#66879—22no—
142#66879—41no—
143#66872—22no—
144#66872—41no—
145#22858—111nomaximal, Sylow
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—24no—
149C24×C11—42no—
150C24×C11—42no—
151C24×C11—42no—
152C24×C11—42no—
153C24×C11—81no—
154C24×C11—81no—
155C24×C11C2×D411yescharacteristic
156C23×D11—21no—
157C2×D4×C11—28no—
158C2×D4×C11—24no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—44no—
168C2×D4×C11—44no—
169C2×D4×C11—44no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11C22×C412yes—
173C2×D4×C11C22×C412yes—
174C2×D4×C11C2×D412yes—
175C2×D4×C11#4112yes—
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×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—81no—
185C22×C4×C11C22×C412yes—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11#4112yes—
188C22×C4×C11C2411yescharacteristic
189C2×C22⋊D11—24no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—42no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11—42no—
199C22×Dic11—81no—
200C22×Dic11—81no—
201C22×Dic11C2×D411yescharacteristic
202C22×Dic11C2×D411yescharacteristic
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44C22×C412yes—
211C2×C4×D11—42no—
212C2×C4×D11—42no—
213C2×C4×D11—81no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—44no—
220C2×C8×C11C2×D412yes—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—42no—
225C11×C4⋊C4C2×D412yes—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11—42no—
229C22⋊Dic11—42no—
230C22⋊Dic11—42no—
231C22⋊Dic11—42no—
232C22⋊Dic11—42no—
233C22⋊Dic11—81no—
234C22⋊Dic11—81no—
235#4323—28no—
236#4323—44no—
237(C2×D11)⋊C4—24no—
238(C2×D11)⋊C4—42no—
239(C2×D11)⋊C4—42no—
240(C2×D11)⋊C4—81no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11C22×C412yes—
247Dic11⋊C4—42no—
248C4×Dic11—21no—
249C4×Dic11—21no—
250C4×Dic11—21no—
251C4×Dic11—21no—
252C4×Dic11—42no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8C22×C412yes—
258C2×C11⋊C8C22×C412yes—
259C2×#447—111no—
260C2×#442—111no—
261C22×#102D1111yescharacteristic, complemented
262#2361—111no—
263D4×C22⋊C4—111no—
264#1972—111no—
265#1936—111no—
266#1926—111no—
267#1893—111no—
268#1879—111no—
269#1879—111no—
270#1864—111no—
271#1853—111no—
272#1762—111no—
273#1752—111no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—48no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—48no—
294C23×C11—84no—
295C23×C11—84no—
296C23×C11—84no—
297C23×C11—84no—
298C23×C11—84no—
299C23×C11C4×D412yes—
300C23×C11AGL(1,ℤ/8)12yes—
301C23×C11AGL(1,ℤ/8)12yes—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—48no—
316D4×C11—41no—
317D4×C11—41no—
318D4×C11C4×D414yescomplemented
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—84no—
332C2×C4×C11C4×D412yes—
333C2×C4×C11C23×C411yescharacteristic
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C22⋊D11—48no—
340C2×Dic11—22no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—84no—
362C2×Dic11—84no—
363D44—22no—
364D44—22no—
365D44—41no—
366D44—41no—
367C4×D11—84no—
368C8×C11—22no—
369C8×C11—41no—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C23×D4C2×D1111yescharacteristic
373C22×D8—111no—
374C22×D8—111no—
375C23×C8C2×D1111yescharacteristic
376C2×#121—111no—
377C2×C4×D4—111no—
378C2×C4×D4—111no—
379C2×C4×D4—111no—
380C2×C4×D4—221no—
381C22×C4⋊C4C2×D1111yescharacteristic
382C22×C22⋊C4—221no—
383#447—118no—
384#442—224no—
385C2×#106—111no—
386C2×#106—111no—
387C2×#102—24no—
388C2×#102—111no—
389C2×#102—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×#102C2×D1111yescharacteristic
393C2×#102C2×D1111yescharacteristic
394C2×#102C2×D1111yescharacteristic
395C2×#102C2×D1111yescharacteristic
396C2×C22⋊C8—111no—
397C2×#97—111no—
398C2×#97—111no—
399#390—111no—
400#390—111no—
401#390—111no—
402#389—111no—
403#388—221no—
404#386—221no—
405#386—221no—
406#386—221no—
407#385—221no—
408#380—111no—
409#379—221no—
410C4×C4⋊C4—111no—
411C4×C22⋊C4—111no—
412#340—111no—
413#340—111no—
414#340—111no—
415#340—111no—
416#336—111no—
417#336—111no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—24no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—816no—
435C22×C11—81no—
436C22×C11—81no—
437C22×C11—81no—
438C22×C11—81no—
439C22×C11#44214yescomplemented
440C22×C11C2×C4×D411yescharacteristic
441C22×C11D4211yescharacteristic
442C22×C11#54611yescharacteristic
443C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
444C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
445C22×C11#57611yescharacteristic
446C22×C11#57711yescharacteristic
447C2×D11—42no—
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—81no—
451C2×D11—81no—
452C2×D11—81no—
453C2×D11—81no—
454C4×C11—22no—
455C4×C11—42no—
456C4×C11—81no—
457C4×C11C2×C4×D411yescharacteristic
458C4×C11#51811yescharacteristic
459C4×C11#54611yescharacteristic
460C4×C11#55111yescharacteristic
461Dic11—42no—
462Dic11—41no—
463Dic11—41no—
464Dic11—41no—
465Dic11—41no—
466Dic11—81no—
467Dic11—81no—
468C25—21no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4—111no—
476C22×D4—221no—
477C22×D4C4×D1114yescomplemented
478C22×D4C22×D1111yescharacteristic
479C22×D4C22×D1111yescharacteristic
480C23×C4—21no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4—221no—
484C23×C4C22×D1111yescharacteristic
485C2×D8—114no—
486C2×D8—114no—
487C2×D8—222no—
488C2×D8—222no—
489C2×D8—441no—
490C2×D8—441no—
491C22×C8—22no—
492C22×C8—22no—
493C22×C8—41no—
494C22×C8—111no—
495C22×C8—111no—
496C22×C8C22×D1111yescharacteristic
497C22×C8C22×D1111yescharacteristic
498#121—114no—
499#121—222no—
500C4×D4—222no—
501C4×D4—222no—
502C4×D4—222no—
503C4×D4—441no—
504C4×D4—441no—
505C4×D4—441no—
506C4×D4—444no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—41no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—111no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—444no—
530C2×C42—111no—
531C2×C42—111no—
532C2×C42—221no—
533#106—222no—
534#106—441no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—114no—
539#102—114no—
540#102—222no—
541#102—441no—
542#102C22⋊D1114yescomplemented
543C22⋊C8—114no—
544#97—222no—
545#97—441no—
546#95—111no—
547#95—111no—
548#95—221no—
549#95—221no—
550#95—221no—
551C2×C11—24no—
552C2×C11—44no—
553C2×C11—82no—
554C2×C11#235811yescharacteristic
555C2×C11C2×#44211yescharacteristic
556C2×C11#294611yescharacteristic
557C2×C11#326411yescharacteristic
558C2×C11#326511yescharacteristic
559C2×C11#330611yescharacteristic
560C2×C11#331811yescharacteristic
561D11—82no—
562C24—21no—
563C24—21no—
564C24—24no—
565C24—42no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—81no—
570C24—81no—
571C24—221no—
572C24D4×D1111yescharacteristic
573C2×D4—28no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—44no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—112no—
589C2×D4—224no—
590C2×D4—221no—
591C2×D4—221no—
592C2×D4—221no—
593C2×D4—221no—
594C2×D4—221no—
595C2×D4—442no—
596C2×D4—442no—
597C2×D4C2×C4×D1112yes—
598C2×D4C2×C4×D1112yes—
599C2×D4#433912yes—
600C2×D4C2×C22⋊D1112yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—442no—
618C22×C4—442no—
619C22×C4—442no—
620C22×C4—442no—
621C22×C4—442no—
622C22×C4—442no—
623C22×C4—881no—
624C22×C4—881no—
625C22×C4—881no—
626C22×C4C2×C4×D1112yes—
627C22×C4D4×D1111yescharacteristic
628C22×C4#434112yes—
629C22×C4C23×D1111yescharacteristic
630D8—228no—
631D8—444no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—44no—
638C2×C8—112no—
639C2×C8—112no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8C2×C22⋊D1112yes—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—112no—
650C4⋊C4—221no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—221no—
655C4⋊C4—442no—
656C4⋊C4C2×C22⋊D1112yes—
657C22⋊C4—222no—
658C22⋊C4—222no—
659C22⋊C4—224no—
660C22⋊C4—442no—
661C22⋊C4—442no—
662C22⋊C4—442no—
663C22⋊C4—442no—
664C22⋊C4—442no—
665C22⋊C4—442no—
666C22⋊C4—442no—
667C22⋊C4—881no—
668C22⋊C4—881no—
669C22⋊C4—881no—
670C42—221no—
671C42—221no—
672C42—221no—
673C42—221no—
674C42—442no—
675C11#2285811yescharacteristic, complemented, Sylow
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—48no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—48no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—222no—
702C23—441no—
703C23—441no—
704C23—441no—
705C23—441no—
706C23—441no—
707C23—441no—
708C23(C22⋊D11)⋊C412yes—
709C23#6696412yes—
710C23#6696712yes—
711C23C2×D4×D1111yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—222no—
721D4—222no—
722D4—448no—
723D4—441no—
724D4—441no—
725D4C4×C22⋊D1114yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—222no—
740C2×C4—221no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—884no—
761C2×C4—884no—
762C2×C4—884no—
763C2×C4(C22⋊D11)⋊C412yes—
764C2×C4C22×C4×D1111yescharacteristic
765C2×C4C2×#433911yescharacteristic
766C2×C4C2×#434111yescharacteristic
767C2×C4#6703711yescharacteristic
768C2×C4#6703711yescharacteristic
769C2×C4C22×C22⋊D1111yescharacteristic
770C8—22no—
771C8—41no—
772C8—222no—
773C8—222no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—816no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—442no—
796C22—442no—
797C22—442no—
798C22—881no—
799C22—881no—
800C22—881no—
801C22—881no—
802C22#1062239814yescomplemented
803C22C2×(C22⋊D11)⋊C411yescharacteristic
804C22#1062302111yescharacteristic
805C22C2×#6696411yescharacteristic
806C22#1062328811yescharacteristic
807C22C2×#6696711yescharacteristic
808C22#1062329311yescharacteristic
809C22D4×C22⋊D1111yescharacteristic
810C4—22no—
811C4—42no—
812C4—81no—
813C4—441no—
814C4—441no—
815C4—442no—
816C4—441no—
817C4—441no—
818C4—881no—
819C4—881no—
820C4#1062301711yescharacteristic
821C4#1062302611yescharacteristic
822C4C2×C4×C22⋊D1111yescharacteristic
823C4#1062333711yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—882no—
828C2#1307159511yescharacteristic
829C2C2×#1062239811yescharacteristic
830C2#1307744211yescharacteristic
831C2#1308009611yescharacteristic
832C2#1308011111yescharacteristic
833C2#1308057311yescharacteristic
834C2#1308075311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
cosocleC22×C4×C11C24
hypercenterC22×#102D11
hypocenterC11#22858
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#10622398C2semidirect
3. #13071632C2semidirect
4. D4×C22⋊Dic11C2semidirect
5. #13069489C2semidirect
6. #13069310C2semidirect
7. #13069246C2semidirect
8. #13069044C2semidirect
9. #13068962C2semidirect
10. #13068961C2semidirect
11. #13068875C2semidirect
12. #13068809C2semidirect
13. #13068443C2semidirect
14. #13068392C2semidirect
15. C22×C11×#102C2semidirect
26. C2×#66946C22semidirect
37. #10622830C4semidirect
44. C2×#66885C22semidirect
45. C2×#66885C22semidirect
46. C2×#66879C22semidirect
47. C2×#66879C22semidirect
50. #10622601C22semidirect
51. C4⋊C4×Dic11C22semidirect
52. #10622586C22semidirect
53. C2×#66872C22semidirect
54. C2×#66872C22semidirect
56. #10622189C22semidirect
57. #10622189C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
69. C22×D4×C11C2×C4semidirect
107. C2×#4323C2×C4semidirect
108. C2×#4323C2×C4semidirect
110. #66983C2×C4semidirect
130. C11×#102D4semidirect
131. #66896C2×C4semidirect
132. #66896C2×C4semidirect
138. C22⋊(C11⋊C8)C2×C4semidirect
261. C22×#102D11semidirect
318. D4×C11C4×D4semidirect
439. C22×C11#442semidirect
477. C22×D4C4×D11semidirect
542. #102C22⋊D11semidirect
675. C11#22858semidirect
725. D4C4×C22⋊D11semidirect
802. C22#10622398semidirect

Maximal subgroups

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

subgroupindex
C2×#106228302
C2×#106223982
#130716322
D4×C22⋊Dic112
#130694892
#130693102
#130692462
#130690442
#130689622
#130689612
#130688752
#130688092
#130684432
#130683922
C22×C11×#1022
#2285811