Finite Group Databasebeta

← #14787819

Subgroups — #14787819

Order 2816.

1204 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2C2×#10622627C211yesmaximal, characteristic, complemented
3#13073517C211yesmaximal, characteristic, complemented
4#13069795C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069590C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068938C212yesmaximal, complemented
9#13068815C212yesmaximal, complemented
10#13068626C211yesmaximal, characteristic, complemented
11C2×C11×#555C211yesmaximal, characteristic, complemented
12C11×#555—24no—
13C11×#555—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124—22no—
16C2×C11×#121—21no—
17C2×C11×#121C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117—21no—
21C2×C11×#117C2212yes—
22C22×#4323C2211yescharacteristic
23C2×#66983C2212yes—
24C2×C4×D44C2211yescharacteristic
25#10622836—21no—
26C2×#66896C2211yescharacteristic
27C2×#66896C2212yes—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622700—24no—
32#10622627—24no—
33#10622606—21no—
34C2×#66873C2212yes—
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2212yes—
38#10622569—22no—
39#10622549C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11D411yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2312yes—
51C22×C22⋊D11—22no—
52C22×D44C2311yescharacteristic
53C22×C4×D11—21no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8D414yescomplemented
56C11×#124—216no—
57C11×#121—28no—
58C11×#121—24no—
59C11×#121—24no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11D414yescomplemented
64C11×#117—28no—
65C11×#117—24no—
66C11×#117—24no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—22no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—22no—
78C2×#4323—22no—
79C2×#4323—22no—
80C2×#4323—22no—
81#66983—24no—
82#66983—42no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90C4×D44—22no—
91C4×D44—22no—
92#66896—22no—
93#66896—42no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—22no—
97C22⋊(C11⋊C8)—24no—
98C22⋊(C11⋊C8)—42no—
99#66873—22no—
100#66873—24no—
101#66872—22no—
102#66871—24no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#24129—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11C2×D412yes—
108C23×D11—21no—
109C2×Q8×C11—24no—
110C2×Q8×C11—82no—
111C2×D4×C11—28no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—42no—
119C2×D4×C11—82no—
120C2×D4×C11—82no—
121C2×D4×C11C2×D412yes—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—44no—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—44no—
137C2×C22⋊D11—44no—
138C2×C22⋊D11—82no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44#4112yes—
147C2×C4×D11—42no—
148C2×C4×D11—82no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C2×D414yes—
154C11×C4⋊C4C2×D412yes—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—28no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C42×C11—28no—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—82no—
163#4323—28no—
164(C2×D11)⋊C4—44no—
165(C2×D11)⋊C4—42no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8#4112yes—
179C2×#555D1111yescharacteristic, complemented
180C2×#474—111no—
181C2×#442—111no—
182#2535—111no—
183#2033—112no—
184#1999—112no—
185#1993—111no—
186#1955—111no—
187#1875—112no—
188#1854—112no—
189#1804—111no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—42no—
207C22×D11—42no—
208Q8×C11—84no—
209D4×C11—22no—
210D4×C11—22no—
211D4×C11—44no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—88no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—48no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11#12012yes—
231C2×C4×C11#12012yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C22⋊D11—88no—
239C2×Dic11—41no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244D44—22no—
245D44—22no—
246D44—41no—
247D44—41no—
248C4×D11—84no—
249C11⋊C8—22no—
250C11⋊C8—41no—
251C11⋊C8—42no—
252C22×D8—111no—
253#555—24no—
254#555—24no—
255C2×C4⋊Q8C2×D1111yescharacteristic
256C2×#124—22no—
257C2×#121—21no—
258C2×#121—112no—
259C2×#121C2×D1112yes—
260C2×C4×D4—111no—
261C2×C4×D4C2×D1111yescharacteristic
262C2×C4×D4C2×D1111yescharacteristic
263C2×#117—21no—
264C2×#117C2×D1112yes—
265#474—224no—
266#442—224no—
267C2×#107—112no—
268C2×#106—111no—
269C2×C4⋊C8—111no—
270C2×#102—111no—
271C2×#102—111no—
272C2×#102—112no—
273C2×#102—112no—
274C2×C22⋊C8—112no—
275C2×C22⋊C8—112no—
276C2×#97—111no—
277#397—221no—
278#392—221no—
279#386—222no—
280#382—111no—
281#380—112no—
282#340—112no—
283#340—112no—
284#340—112no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11C2×#12011yescharacteristic
298C22×C11#54611yescharacteristic
299C22×C11#54711yescharacteristic
300C22×C11#57512yes—
301C22×C11#57612yes—
302C2×D11—42no—
303C2×D11—44no—
304C2×D11—82no—
305C2×D11—81no—
306C2×D11—81no—
307C4×C11—22no—
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—44no—
312C4×C11#52511yescharacteristic
313C4×C11#53711yescharacteristic
314C4×C11#54811yescharacteristic
315C4×C11#55011yescharacteristic
316Dic11—81no—
317Dic11—82no—
318C22×Q8—21no—
319C22×D4—22no—
320C22×D4—111no—
321C22×D4—222no—
322C22×D4C22⋊D1111yescharacteristic
323C22×D4C22×D1111yescharacteristic
324C23×C4—21no—
325C23×C4—221no—
326C23×C4C22×D1112yes—
327C2×D8—222no—
328C2×D8—222no—
329C2×D8—222no—
330C22×C8—111no—
331C22×C8—111no—
332C22×C8—112no—
333C4⋊Q8—22no—
334C4⋊Q8C22⋊D1114yescomplemented
335#124—216no—
336#121—28no—
337#121—24no—
338#121—24no—
339#121—224no—
340#121—442no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—222no—
345C4×D4—222no—
346C4×D4C22⋊D1114yescomplemented
347#117—28no—
348#117—24no—
349#117—24no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4C22⋊D1111yescharacteristic
354C2×C4⋊C4C22×D1111yescharacteristic
355C2×C4⋊C4C22×D1112yes—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—221no—
360C2×C22⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4C22⋊D1112yes—
363C2×C42—22no—
364C2×C42C22×D1111yescharacteristic
365#107—224no—
366#106—222no—
367C4⋊C8—222no—
368#102—222no—
369#102—222no—
370#102—224no—
371#102—442no—
372C22⋊C8—224no—
373C22⋊C8—442no—
374#97—222no—
375#95—222no—
376#95—221no—
377#95—221no—
378C2×C11—82no—
379C2×C11—82no—
380C2×C11#240711yescharacteristic
381C2×C11#300511yescharacteristic
382C2×C11#300811yescharacteristic
383C2×C11#331912yes—
384C2×C11#334712yes—
385D11—82no—
386C24—21no—
387C24—221no—
388C24C2×C22⋊D1112yes—
389C2×Q8—24no—
390C2×Q8—82no—
391C2×D4—28no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—42no—
399C2×D4—82no—
400C2×D4—82no—
401C2×D4—112no—
402C2×D4—221no—
403C2×D4—221no—
404C2×D4—221no—
405C2×D4—221no—
406C2×D4—221no—
407C2×D4—444no—
408C2×D4—444no—
409C2×D4—882no—
410C2×D4C2×C22⋊D1112yes—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—44no—
421C22×C4—222no—
422C22×C4—221no—
423C22×C4—442no—
424C22×C4—882no—
425C22×C4C2×C22⋊D1112yes—
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429D8—228no—
430C2×C8—112no—
431C2×C8—221no—
432C2×C8—221no—
433C2×C8—222no—
434C2×C8—221no—
435C2×C8—222no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—222no—
439C4⋊C4—24no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4—221no—
446C4⋊C4—221no—
447C4⋊C4C2×C22⋊D1112yes—
448C4⋊C4C2×C22⋊D1114yes—
449C22⋊C4—28no—
450C22⋊C4—28no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—444no—
454C22⋊C4—442no—
455C22⋊C4—882no—
456C42—28no—
457C42C2×C22⋊D1112yes—
458C42C2×C22⋊D1112yes—
459C11#2412911yescharacteristic, complemented, Sylow
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—42no—
469C23—41no—
470C23—41no—
471C23—42no—
472C23—222no—
473C23—442no—
474C23—441no—
475C23—442no—
476C23—441no—
477C23C22×C22⋊D1111yescharacteristic
478Q8—84no—
479D4—22no—
480D4—22no—
481D4—44no—
482D4—41no—
483D4—41no—
484D4—88no—
485D4—222no—
486D4—222no—
487D4—441no—
488D4—441no—
489D4—888no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—48no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—441no—
510C2×C4—884no—
511C2×C4#6700612yes—
512C2×C4#6700612yes—
513C2×C4#41×D1111yescharacteristic
514C2×C4#41×D1111yescharacteristic
515C2×C4#6704211yescharacteristic
516C2×C4#6704311yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C2×C4C22×C22⋊D1111yescharacteristic
519C8—222no—
520C8—441no—
521C8—442no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—82no—
533C22—82no—
534C22—442no—
535C22—444no—
536C22—882no—
537C22—881no—
538C22—881no—
539C22#1062335312yes—
540C22#1062335511yescharacteristic
541C22#1062336011yescharacteristic
542C22#1062336612yes—
543C22C2×#6700611yescharacteristic
544C4—22no—
545C4—22no—
546C4—42no—
547C4—42no—
548C4—44no—
549C4—881no—
550C4—882no—
551C4#1062335911yescharacteristic
552C4#1062336211yescharacteristic
553C4#1062336411yescharacteristic
554C4#1062336511yescharacteristic
555C2—82no—
556C2—82no—
557C2—882no—
558C2#1307195511yescharacteristic
559C2#1307785811yescharacteristic
560C2#1307788411yescharacteristic
561C2#1308076612yes—
562C2#1308111612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#555C2
socleC23×C11C22×D4
hypercenterC2×#555D11
hypocenterC11#24129
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
2. C2×#10622627C2semidirect
3. #13073517C2semidirect
4. #13069795C2semidirect
5. #13069612C2semidirect
6. #13069590C2semidirect
7. #13069415C2semidirect
8. #13068938C2semidirect
9. #13068815C2semidirect
10. #13068626C2semidirect
11. C2×C11×#555C2semidirect
55. C11×C4⋊Q8D4semidirect
63. C4×D4×C11D4semidirect
179. C2×#555D11semidirect
334. C4⋊Q8C22⋊D11semidirect
346. C4×D4C22⋊D11semidirect
459. C11#24129semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×#106226272
#130735172
#130697952
#130696122
#130695902
#130694152
#130689382
#130688152
#130686262
C2×C11×#5552
#2412911