Finite Group Databasebeta

← #14774086

Subgroups — #14774086

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×#10622627C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4#13071630C211yesmaximal, characteristic, complemented
5#13069491C211yesmaximal, characteristic, complemented
6#13069316C211yesmaximal, characteristic, complemented
7#13069240C211yesmaximal, characteristic, complemented
8#13069042C211yesmaximal, characteristic, complemented
9#13068967C211yesmaximal, characteristic, complemented
10#13068964C211yesmaximal, characteristic, complemented
11#13068877C211yesmaximal, characteristic, complemented
12#13068808C211yesmaximal, characteristic, complemented
13#13068441C211yesmaximal, characteristic, complemented
14#13068394C211yesmaximal, characteristic, complemented
15D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C22×#4323C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C2×(C22⋊D11)⋊C4—21no—
26C2×C4×D44C2211yescharacteristic, complemented
27C11×#390C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#386—21no—
30C11×#386—21no—
31C11×#380C2211yescharacteristic
32C11×#379—21no—
33C4×C11×C22⋊C4C2211yescharacteristic
34#10622830C418yescomplemented
35C2×#66896—24no—
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622627—24no—
44C2×#66873C2211yescharacteristic, complemented
45C2×#66873C2211yescharacteristic, complemented
46C2×#66872C2211yescharacteristic, complemented
47C2×#66872C2211yescharacteristic, complemented
48#10622571—21no—
49#10622552C2211yescharacteristic, complemented
50C4×C4⋊Dic11C2211yescharacteristic, complemented
51#10622541C2211yescharacteristic, complemented
52C2×#66867C2211yescharacteristic, complemented
53C2×#66867C2211yescharacteristic, complemented
54#10622283—21no—
55#10622281—21no—
56#10622167C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61#10622162C2211yescharacteristic, 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×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C23×Dic11—21no—
77C22×D44C2311yescharacteristic
78C22×C4×D11—21no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—41no—
82C4×D4×C11—41no—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—44no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×#4323—22no—
98C2×#4323—22no—
99C2×#4323—41no—
100C2×#4323—41no—
101C2×#4323C2×C414yescomplemented
102C2×#4323C2×C414yescomplemented
103#66983—22no—
104#66983C2×C414yescomplemented
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—41no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×Dic11⋊C4—21no—
116C2×C4×Dic11—21no—
117C22×C11⋊C8—22no—
118C22×C11⋊C8—22no—
119C22×C11⋊C8—41no—
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124(C22⋊D11)⋊C4—44no—
125C4×D44—22no—
126C4×D44—41no—
127C11×#95—21no—
128C11×#95D411yescharacteristic
129C11×#95D411yescharacteristic
130#66896—22no—
131#66896—22no—
132#66896—22no—
133#66896C2×C414yescomplemented
134#66896C2×C414yescomplemented
135#66896D414yescomplemented
136C11⋊#95—21no—
137C11⋊#95—21no—
138C22⋊(C11⋊C8)C2×C414yescomplemented
139#66873—22no—
140#66873—41no—
141#66872—22no—
142#66872—41no—
143#66867—22no—
144#66867—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—42no—
185C22×C4×C11—42no—
186C22×C4×C11—81no—
187C22×C4×C11—81no—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11#4112yes—
195C22×C4×C11C2411yescharacteristic
196C2×C22⋊D11—24no—
197C2×C22⋊D11—42no—
198C2×C22⋊D11—42no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—42no—
203C22×Dic11—42no—
204C22×Dic11—81no—
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—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231#4323—28no—
232#4323—44no—
233(C2×D11)⋊C4—24no—
234(C2×D11)⋊C4—42no—
235(C2×D11)⋊C4—42no—
236(C2×D11)⋊C4—81no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—42no—
242C4⋊Dic11C22×C412yes—
243C4⋊Dic11C2×D412yes—
244Dic11⋊C4—42no—
245C4×Dic11—42no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—44no—
256C2×C11⋊C8C22×C412yes—
257C2×C11⋊C8C22×C412yes—
258C2×C11⋊C8C2×D412yes—
259C2×#447—111no—
260C2×#442—111no—
261C22×#102—111no—
262#2361—111no—
263D4×C22⋊C4D1111yescharacteristic, complemented
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—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—84no—
344C2×C4×C11—84no—
345C2×C4×C11C4×D412yes—
346C2×C4×C11C23×C411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C2×#4111yescharacteristic
349C2×C4×C11C2×#4111yescharacteristic
350C2×C4×C11H(5,𝔽2)11yescharacteristic
351C2×C4×C11H(5,𝔽2)11yescharacteristic
352C22⋊D11—48no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—84no—
363D44—22no—
364D44—22no—
365D44—41no—
366D44—41no—
367C4×D11—84no—
368C11⋊C8—22no—
369C11⋊C8—22no—
370C11⋊C8—22no—
371C11⋊C8—41no—
372C23×D4C2×D1111yescharacteristic
373C22×D8—111no—
374C22×D8—111no—
375C23×C8—111no—
376C2×#121—111no—
377C2×C4×D4—111no—
378C2×C4×D4—221no—
379C2×C4×D4C2×D1111yescharacteristic
380C2×C4×D4C2×D1111yescharacteristic
381C22×C4⋊C4—111no—
382C22×C22⋊C4—21no—
383#447—118no—
384#442—224no—
385C2×#106—111no—
386C2×#106—111no—
387C2×#102—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—224no—
396C2×C22⋊C8—111no—
397C2×#97—111no—
398C2×#97—111no—
399#390—111no—
400#390C2×D1111yescharacteristic
401#390C2×D1111yescharacteristic
402#389—111no—
403#388—221no—
404#386—21no—
405#386—21no—
406#386—221no—
407#385—221no—
408#380C2×D1111yescharacteristic
409#379—21no—
410C4×C4⋊C4—111no—
411C4×C22⋊C4C2×D1111yescharacteristic
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—41no—
456C4×C11—41no—
457C4×C11—41no—
458C4×C11—41no—
459C4×C11—81no—
460C4×C11—81no—
461C4×C11C2×C4×D411yescharacteristic
462C4×C11#51811yescharacteristic
463C4×C11#54611yescharacteristic
464C4×C11#55111yescharacteristic
465Dic11—42no—
466Dic11—42no—
467Dic11—81no—
468C25—21no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
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—21no—
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—111no—
492C22×C8—111no—
493C22×C8—111no—
494C22×C8—111no—
495C22×C8—222no—
496C22×C8—222no—
497C22×C8—441no—
498#121—114no—
499#121—222no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—41no—
503C4×D4—41no—
504C4×D4—222no—
505C4×D4—441no—
506C4×D4—444no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—222no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—441no—
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—44no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4C22⋊D1111yescharacteristic
529C2×C22⋊C4C22⋊D1111yescharacteristic
530C2×C42—221no—
531C2×C42C22×D1111yescharacteristic
532C2×C42C22×D1111yescharacteristic
533#106—222no—
534#106—441no—
535#102—114no—
536#102—114no—
537#102—114no—
538#102—222no—
539#102—222no—
540#102—222no—
541#102—222no—
542#102—441no—
543C22⋊C8—114no—
544#97—222no—
545#97—441no—
546#95—21no—
547#95—221no—
548#95—221no—
549#95C22⋊D1111yescharacteristic
550#95C22⋊D1111yescharacteristic
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—
572C24C2×C22⋊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×D4D4×D1112yes—
600C2×D4#434112yes—
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—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—442no—
617C22×C4—442no—
618C22×C4—442no—
619C22×C4—442no—
620C22×C4—881no—
621C22×C4—881no—
622C22×C4C2×C4×D1112yes—
623C22×C4#433912yes—
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C2×C22⋊D1111yescharacteristic
627C22×C4C2×C22⋊D1111yescharacteristic
628C22×C4C2×C22⋊D1111yescharacteristic
629C22×C4C23×D1111yescharacteristic
630D8—228no—
631D8—444no—
632C2×C8—112no—
633C2×C8—112no—
634C2×C8—112no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—444no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—112no—
650C4⋊C4—112no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—221no—
655C4⋊C4—442no—
656C4⋊C4—442no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—224no—
667C22⋊C4—442no—
668C22⋊C4—442no—
669C22⋊C4—881no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
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—
708C23C4×C22⋊D1112yes—
709C23#6698512yes—
710C23#6700212yes—
711C23C22×C22⋊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—
725D4(C22⋊D11)⋊C414yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—884no—
762C2×C4—884no—
763C2×C4C4×C22⋊D1112yes—
764C2×C4C22×C4×D1111yescharacteristic
765C2×C4C2×#433911yescharacteristic
766C2×C4C2×D4×D1111yescharacteristic
767C2×C4C2×#434111yescharacteristic
768C2×C4#6703711yescharacteristic
769C2×C4#6703711yescharacteristic
770C8—222no—
771C8—222no—
772C8—222no—
773C8—441no—
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#1062262714yescomplemented
803C22C2×C4×C22⋊D1111yescharacteristic
804C22C2×#6698511yescharacteristic
805C22D4×C22⋊D1111yescharacteristic
806C22#1062333711yescharacteristic
807C22C2×#6700211yescharacteristic
808C22#1062336611yescharacteristic
809C22#1062336711yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—81no—
816C4—81no—
817C4—442no—
818C4—442no—
819C4—881no—
820C4C2×(C22⋊D11)⋊C411yescharacteristic
821C4#1062301711yescharacteristic
822C4#1062302111yescharacteristic
823C4#1062302611yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—882no—
828C2#1307159511yescharacteristic
829C2C2×#1062262711yescharacteristic
830C2#1307744811yescharacteristic
831C2#1308009711yescharacteristic
832C2#1308010711yescharacteristic
833C2#1308057711yescharacteristic
834C2#1308075711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
cosocleC22×C4×C11C24
hypercenterD4×C22⋊C4D11
hypocenterC11#22858
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622627C2semidirect
3. C22×#66896C2semidirect
4. #13071630C2semidirect
5. #13069491C2semidirect
6. #13069316C2semidirect
7. #13069240C2semidirect
8. #13069042C2semidirect
9. #13068967C2semidirect
10. #13068964C2semidirect
11. #13068877C2semidirect
12. #13068808C2semidirect
13. #13068441C2semidirect
14. #13068394C2semidirect
15. D4×C11×C22⋊C4C2semidirect
26. C2×C4×D44C22semidirect
34. #10622830C4semidirect
44. C2×#66873C22semidirect
45. C2×#66873C22semidirect
46. C2×#66872C22semidirect
47. C2×#66872C22semidirect
49. #10622552C22semidirect
50. C4×C4⋊Dic11C22semidirect
51. #10622541C22semidirect
52. C2×#66867C22semidirect
53. C2×#66867C22semidirect
56. #10622167C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622162C22semidirect
61. #10622162C22semidirect
69. C22×D4×C11C2×C4semidirect
101. C2×#4323C2×C4semidirect
102. C2×#4323C2×C4semidirect
104. #66983C2×C4semidirect
133. #66896C2×C4semidirect
134. #66896C2×C4semidirect
135. #66896D4semidirect
138. C22⋊(C11⋊C8)C2×C4semidirect
263. D4×C22⋊C4D11semidirect
318. D4×C11C4×D4semidirect
439. C22×C11#442semidirect
477. C22×D4C4×D11semidirect
675. C11#22858semidirect
725. D4(C22⋊D11)⋊C4semidirect
802. C22#10622627semidirect

Maximal subgroups

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

subgroupindex
C2×#106228302
C2×#106226272
C22×#668962
#130716302
#130694912
#130693162
#130692402
#130690422
#130689672
#130689642
#130688772
#130688082
#130684412
#130683942
D4×C11×C22⋊C42
#2285811