Finite Group Databasebeta

← #14772119

Subgroups — #14772119

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622631C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic
3C2×C4×#4324C211yesmaximal, characteristic
4#13071536C211yesmaximal, characteristic, complemented
5#13069351C211yesmaximal, characteristic, complemented
6#13069346C211yesmaximal, characteristic, complemented
7#13068883C211yesmaximal, characteristic, complemented
8#13068877C211yesmaximal, characteristic
9#13068869C211yesmaximal, characteristic, complemented
10#13068863C211yesmaximal, characteristic
11#13068782C211yesmaximal, characteristic, complemented
12#13068626C211yesmaximal, characteristic
13#13068618C211yesmaximal, characteristic, complemented
14#13068491C211yesmaximal, characteristic, complemented
15D4×C11×C4⋊C4C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4—21no—
20C22×#4324C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#385—21no—
27C11×#385—21no—
28C11×#384C2211yescharacteristic
29C11×#380—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622631—24no—
35#10622631C418yescomplemented
36C4×#4324—24no—
37#10622585—21no—
38#10622585—21no—
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622549C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622541C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622263—21no—
55#10622262—21no—
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C22×Dic22C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—41no—
71C4×D4×C11—41no—
72C4×D4×C11C2×C414yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—44no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×#4324C2×C414yes—
90C2×#4324D414yes—
91C2×#4324Q814yes—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C4×Dic22—41no—
111C4×Dic22—41no—
112C4×Dic22C2×C414yescomplemented
113C11×#95—21no—
114C11×#95—21no—
115C11×#95D411yescharacteristic
116C11×#95D411yescharacteristic
117#66896—22no—
118#66896—22no—
119#66896C2×C414yes—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66874—22no—
125#66874—22no—
126#66874C2×C414yescomplemented
127#66872—22no—
128#66872—41no—
129#66871—22no—
130#66871—41no—
131#66871C2×C414yescomplemented
132C4⋊(C11⋊C8)—22no—
133#66867—22no—
134#66867C2×C414yescomplemented
135C4×C11⋊C8—22no—
136#22677—111nomaximal, Sylow
137C24×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11C22×C412yes—
142C2×D4×C11C2×D412yes—
143C2×D4×C11C2×Q812yes—
144C22×C4×C11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—81no—
155C22×C4×C11—81no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C2×Dic22C2×D412yes—
172C2×Dic22C2×Q812yes—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4C22×C412yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11C22×C412yes—
193C42×C11#4112yes—
194#4324C4⋊C4116yescomplemented
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C22×C412yes—
201Dic11⋊C4—24no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206C4×Dic11—24no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C22×C412yes—
218C2×C11⋊C8C22×C412yes—
219C2×C11⋊C8C2×D412yes—
220C2×C11⋊C8C2×Q812yes—
221C2×#440—111no—
222C2×#440—111no—
223C2×C4×SD16—111no—
224#2351—111no—
225D4×C4⋊C4D1111yescharacteristic
226#1943—111no—
227#1942—111no—
228#1865—111no—
229#1864—111no—
230#1863—111no—
231#1862—111no—
232#1847—111no—
233#1804—111no—
234#1803—111no—
235#1771—111no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11C22×D411yescharacteristic
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11C2×C4⋊C414yes—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—48no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—84no—
274C2×C4×C11—84no—
275C2×C4×C11C4×D412yes—
276C2×C4×C11C4×D412yes—
277C2×C4×C11AGL(1,ℤ/8)12yes—
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×Q811yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C112−1+411yescharacteristic
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296Dic22—22no—
297Dic22—22no—
298Dic22—22no—
299Dic22C2×C4⋊C414yescomplemented
300C11⋊C8—22no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8C2×C4⋊C414yescomplemented
304C22×SD16—111no—
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×Q8—111no—
308C2×C4×D4C2×D1111yescharacteristic
309C2×C4×D4C2×D1111yescharacteristic
310C2×C4×D4C2×D1111yescharacteristic
311C22×C4⋊C4—21no—
312#440—118no—
313#440—224no—
314C4×SD16—224no—
315C2×#107—111no—
316C2×#107—111no—
317C2×#107—111no—
318C2×#106—111no—
319C2×#106—111no—
320C2×C4⋊C8—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#97—111no—
328C2×#97—111no—
329C2×C4×C8—111no—
330#389—111no—
331#389—111no—
332#389—221no—
333#389—221no—
334#389C2×D1111yescharacteristic
335#389C2×D1111yescharacteristic
336#385—21no—
337#385—21no—
338#384C2×D1111yescharacteristic
339#382—111no—
340#382—221no—
341#380—21no—
342C4×C4⋊C4—221no—
343C4×C4⋊C4C2×D1111yescharacteristic
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#336—111no—
349#336—111no—
350C22×C11—24no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11C2×C4×D411yescharacteristic
358C22×C11D4211yescharacteristic
359C22×C11D4×Q811yescharacteristic
360C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57711yescharacteristic
363C22×C11#57811yescharacteristic
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—22no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11C22×C4⋊C411yescharacteristic
374C4×C11#52011yescharacteristic
375C4×C11#54711yescharacteristic
376C4×C11#55411yescharacteristic
377Dic11—24no—
378Dic11—42no—
379Dic11—81no—
380Dic11—81no—
381C22×Q8—111no—
382C22×D4C22×D1111yescharacteristic
383C23×C4—21no—
384C23×C4—21no—
385C23×C4—21no—
386C2×SD16—114no—
387C2×SD16—114no—
388C2×SD16—114no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C4×Q8—114no—
394C4×Q8—222no—
395C4×Q8—222no—
396C4×Q8—222no—
397C4×Q8—441no—
398C4×Q8—441no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—41no—
403C4×D4—41no—
404C4×D4C4×D1114yes—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22⋊D1111yescharacteristic
419C2×C4⋊C4C22⋊D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432#107—114no—
433#107—222no—
434#107—441no—
435#106—222no—
436#106—441no—
437C4⋊C8—222no—
438#103—114no—
439#103—222no—
440#103—222no—
441#102—114no—
442#102—222no—
443#102—222no—
444#97—114no—
445#97—222no—
446C4×C8—222no—
447#95—21no—
448#95—21no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95C22⋊D1111yescharacteristic
454#95C22⋊D1111yescharacteristic
455C2×C11—44no—
456C2×C11D4×C4⋊C411yescharacteristic
457C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
458C2×C11#294711yescharacteristic
459C2×C11#326511yescharacteristic
460C2×C11#326911yescharacteristic
461C2×C11#338611yescharacteristic
462C2×C11#338811yescharacteristic
463C24—21no—
464C2×Q8—112no—
465C2×Q8—112no—
466C2×Q8—112no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4C2×C4×D1112yes—
474C2×D4D4×D1112yes—
475C2×D4Q8×D1112yes—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499SD16—1116no—
500C2×C8—112no—
501C2×C8—112no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—41no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—112no—
524C4⋊C4—224no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4C2×C4×D1112yes—
535C22⋊C4—24no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—224no—
543C42—442no—
544C42—442no—
545C42C2×C4×D1112yes—
546C42#433912yes—
547C11#2267711yescharacteristic, complemented, Sylow
548C23—22no—
549C23—22no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C22×C22⋊D1111yescharacteristic
556Q8—114no—
557Q8—222no—
558Q8—222no—
559Q8—222no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4C4⋊C4×D1114yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—48no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4C4×C22⋊D1112yes—
604C2×C4C4×C22⋊D1112yes—
605C2×C4#6698512yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4C2×Q8×D1111yescharacteristic
611C2×C4#6704011yescharacteristic
612C8—114no—
613C8—222no—
614C8—441no—
615C8—441no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22C2×C4×C22⋊D1111yescharacteristic
624C22C2×#6698511yescharacteristic
625C22D4×C22⋊D1111yescharacteristic
626C22Q8×C22⋊D1111yescharacteristic
627C22#1062335311yescharacteristic
628C22#1062336711yescharacteristic
629C22#1062336911yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—42no—
637C4—81no—
638C4—81no—
639C4—224no—
640C4—442no—
641C4—881no—
642C4—881no—
643C4C2×C4⋊C4×D1111yescharacteristic
644C4#1062303511yescharacteristic
645C4#1062303811yescharacteristic
646C4#1062304211yescharacteristic
647C2—44no—
648C2C4⋊C4×C22⋊D1111yescharacteristic
649C2C4×#6698511yescharacteristic
650C2#1307745511yescharacteristic
651C2#1308010711yescharacteristic
652C2#1308016711yescharacteristic
653C2#1308153711yescharacteristic
654C2#1308156111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11#22677
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #13071536C2semidirect
5. #13069351C2semidirect
6. #13069346C2semidirect
7. #13068883C2semidirect
9. #13068869C2semidirect
11. #13068782C2semidirect
13. #13068618C2semidirect
14. #13068491C2semidirect
35. #10622631C4semidirect
112. C4×Dic22C2×C4semidirect
126. #66874C2×C4semidirect
131. #66871C2×C4semidirect
134. #66867C2×C4semidirect
194. #4324C4⋊C4semidirect
299. Dic22C2×C4⋊C4semidirect
303. C11⋊C8C2×C4⋊C4semidirect
547. C11#22677semidirect

Maximal subgroups

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

subgroupindex
C2×#106226312
C2×C4×#43242
#130715362
#130693512
#130693462
#130688832
#130688772
#130688692
#130688632
#130687822
#130686262
#130686182
#130684912
D4×C11×C4⋊C42
#2267711