Finite Group Databasebeta

← #14775842

Subgroups — #14775842

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078406C211yesmaximal, characteristic
2#13077559C211yesmaximal, characteristic, complemented
3#13077181C211yesmaximal, characteristic
4#13069593C211yesmaximal, characteristic, complemented
5#13069392C211yesmaximal, characteristic, complemented
6#13069364C212yesmaximal, complemented
7#13069216C212yesmaximal, complemented
8#13068894C212yesmaximal
9#13068453C212yesmaximal
10C4×#66869C211yesmaximal, characteristic
11C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
12C2×#66954C2212yes—
13C4×#4339C2211yescharacteristic
14#10623001C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C4×C8×C11C2212yes—
18C43×C11C2211yescharacteristic
19#10622726C2212yes—
20C2×#66883C2212yes—
21#10622719C2212yes—
22#10622715C2212yes—
23#10622715C2212yes—
24#10622714C2212yes—
25C2×#66869C2211yescharacteristic
26C2×#66869C2211yescharacteristic
27#10622537C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29#10622464C411yescharacteristic, complemented
30#10622463C411yescharacteristic, complemented
31#10622460C412yescomplemented
32#10622459C411yescharacteristic, complemented
33#10622455C411yescharacteristic, complemented
34#10622452—22no—
35#10622450—21no—
36D11×C4⋊C8—21no—
37#10622444—21no—
38#10622443—21no—
39#10622442C412yescomplemented
40#10622441—22no—
41C11×#336C2212yes—
42#10622190C2212yes—
43#10622161C2212yes—
44#10622161C2212yes—
45#10622161C2211yescharacteristic
46#10622161C2211yescharacteristic
47C2×#4339C2311yescharacteristic
48C22×C8×C11C2312yes—
49C22×C8×C11C2312yes—
50C2×C42×C11—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C4×C22⋊D11—21no—
56C4×C22⋊D11—21no—
57#66979C2312yes—
58#66979C2311yescharacteristic
59#66977—21no—
60#66977—21no—
61C2×#4318C2311yescharacteristic
62C2×#4318C2312yes—
63C2×#4318C2311yescharacteristic
64#66954—24no—
65#66954—42no—
66C2×#4313—22no—
67C2×C8×D11—22no—
68C4×D44C2×C411yescharacteristic
69C4×D44C2×C411yescharacteristic
70#66925—21no—
71C42×D11—21no—
72#66923C2×C412yes—
73#66922C2×C411yescharacteristic
74#66922C2×C411yescharacteristic
75C4×Dic22—21no—
76C4×Dic22—21no—
77C4×Dic22C2×C411yescharacteristic
78C4×Dic22C2×C411yescharacteristic
79C11×C4⋊C8C2×C411yescharacteristic
80C11×C4⋊C8C2×C412yes—
81C11×C4⋊C8C2×C411yescharacteristic
82C11×C4⋊C8D412yes—
83C11×C4⋊C8D411yescharacteristic
84C11×C4⋊C8D411yescharacteristic
85C4×C8×C11—42no—
86#66885C2×C412yes—
87#66885C2×C412yes—
88#66883—42no—
89#66882C2×C412yes—
90#66882C2×C412yes—
91#66881C2×C412yes—
92#66881C2×C412yes—
93#66880C2×C412yes—
94#66880C2×C412yes—
95#66879—22no—
96Dic11⋊C8—22no—
97Dic11⋊C8—22no—
98Dic11⋊C8—22no—
99Dic11⋊C8—22no—
100C8×Dic11—22no—
101#66869—22no—
102#66869Q814yescomplemented
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105#66867—21no—
106C4×C11⋊C8—21no—
107#22982—111nomaximal, Sylow
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—21no—
114#4339—21no—
115#4339—21no—
116#4339C2×Q812yes—
117#4339#4112yes—
118C2×D44C22×C411yescharacteristic
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×C4×D11—21no—
122C2×Dic22—21no—
123C2×Dic22—21no—
124C2×Dic22C22×C411yescharacteristic
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C22×C412yes—
131C2×C8×C11C2×D412yes—
132C2×C8×C11C2×D412yes—
133C42×C11—24no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11—21no—
137C42×C11—42no—
138C42×C11C22×C411yescharacteristic
139C42×C11C22×C411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2×Q812yes—
143C22⋊Dic11—22no—
144C22⋊Dic11—21no—
145(C2×D11)⋊C4—21no—
146(C2×D11)⋊C4—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11C22×C412yes—
150C4⋊Dic11C22×C412yes—
151C4⋊Dic11C22×C411yescharacteristic
152C4⋊Dic11C22×C411yescharacteristic
153Dic11⋊C4—22no—
154Dic11⋊C4—22no—
155Dic11⋊C4—21no—
156Dic11⋊C4—21no—
157C4×Dic11—21no—
158C4×Dic11—21no—
159C4×Dic11—22no—
160C4×Dic11—21no—
161#4318—21no—
162#4318—22no—
163#4318—21no—
164#4318—22no—
165#4318—21no—
166#4318C2×Q812yes—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170#4313—44no—
171C8×D11—44no—
172#3076—111no—
173#2962—111no—
174#2906—111no—
175#1994—111no—
176#1950—111no—
177#1945—112no—
178#1922—112no—
179#1866—112no—
180C4×C4⋊C8D1111yescharacteristic, complemented
181#1764—112no—
182C4×#104—111no—
183C23×C11C2×#4111yescharacteristic
184C22×D11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11C4×D411yescharacteristic
194C2×C4×C11C4×D411yescharacteristic
195C2×C4×C11C4×D411yescharacteristic
196C2×C4×C11C4×D411yescharacteristic
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×Q811yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11H(5,𝔽2)11yescharacteristic
202C2×C4×C112−1+411yescharacteristic
203C22⋊D11—22no—
204C22⋊D11—22no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210D44—21no—
211D44C4×Q812yes—
212C4×D11—22no—
213C4×D11—22no—
214C4×D11—42no—
215C4×D11—81no—
216Dic22—21no—
217Dic22—42no—
218Dic22—81no—
219Dic22C4×Q812yes—
220C8×C11—22no—
221C8×C11—22no—
222C8×C11—22no—
223C8×C11—22no—
224C11⋊C8—22no—
225C11⋊C8—42no—
226C11⋊C8—41no—
227C2×#131—112no—
228#533—111no—
229C4×#41—111no—
230#479—112no—
231#478—112no—
232#477—111no—
233#476—111no—
234#475—111no—
235#474—111no—
236#446—222no—
237#446—221no—
238C8×Q8—221no—
239C2×#108—112no—
240#427—112no—
241#424—112no—
242#424—112no—
243#424—222no—
244#423—111no—
245#423—221no—
246C2×C4⋊C8—221no—
247C2×C4⋊C8C2×D1111yescharacteristic
248C2×C4⋊C8C2×D1111yescharacteristic
249C2×#104—111no—
250C2×#104—111no—
251#416—112no—
252#405—112no—
253C4×M16—111no—
254C2×C4×C8C2×D1112yes—
255C43C2×D1111yescharacteristic
256#341—112no—
257#339—112no—
258#339—111no—
259#339—111no—
260#339—112no—
261#336C2×D1112yes—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11C2×C4×D411yescharacteristic
265C22×C11#55211yescharacteristic
266C22×C11#55411yescharacteristic
267C2×D11—22no—
268C2×D11—41no—
269C2×D11—41no—
270C4×C11—24no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11#44312yes—
276C4×C11C2×C4×Q811yescharacteristic
277C4×C11#52011yescharacteristic
278C4×C11#54611yescharacteristic
279C4×C11D4×Q811yescharacteristic
280Dic11—22no—
281Dic11—42no—
282Dic11—41no—
283Dic11—42no—
284Dic11—41no—
285C2×#41—111no—
286#131—224no—
287#131—442no—
288C2×M16—111no—
289C2×M16—112no—
290C2×M16—111no—
291C2×M16—222no—
292C22×C8—222no—
293C22×C8C22×D1112yes—
294C22×C8C22×D1112yes—
295C4⋊Q8—111no—
296C4⋊Q8—111no—
297#125—112no—
298C22⋊Q8—221no—
299C22⋊Q8—221no—
300C4×Q8—111no—
301C4×Q8—111no—
302C4×Q8—221no—
303C4×Q8—221no—
304C4×D4—111no—
305C4×D4—111no—
306C4×D4—221no—
307C4×D4—221no—
308#117—111no—
309#117—112no—
310#117—221no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—221no—
314C2×C42C22×D1111yescharacteristic
315C2×C42C22×D1111yescharacteristic
316C2×C42C22×D1111yescharacteristic
317#108—442no—
318#107—112no—
319#107—112no—
320#106—112no—
321#106—112no—
322C4⋊C8—222no—
323C4⋊C8—222no—
324C4⋊C8—222no—
325C4⋊C8—222no—
326C4⋊C8—221no—
327C4⋊C8—221no—
328C4⋊C8C4×D1111yescharacteristic
329C4⋊C8C4×D1111yescharacteristic
330C4⋊C8C4×D1112yes—
331C4⋊C8D4411yescharacteristic
332C4⋊C8D4411yescharacteristic
333C4⋊C8D4412yes—
334#104—114no—
335#104—222no—
336#103—112no—
337#103—112no—
338#102—112no—
339#102—112no—
340#97—222no—
341#97—221no—
342C4×C8—42no—
343C4×C8—222no—
344C4×C8—221no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11#236011yescharacteristic
348C2×C11C2×#44311yescharacteristic
349C2×C11#295611yescharacteristic
350D11—42no—
351#41—112no—
352#41—112no—
353#41—221no—
354#41—221no—
355C2×Q8—111no—
356C2×Q8—221no—
357C2×Q8—221no—
358C2×D4—111no—
359C2×D4—221no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4#433911yescharacteristic
366C22×C4#433911yescharacteristic
367C22×C4C23×D1111yescharacteristic
368M16—112no—
369M16—221no—
370M16—221no—
371M16—222no—
372M16—221no—
373M16—222no—
374M16—444no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—222no—
382C2×C8—444no—
383C2×C8C2×C4×D1112yes—
384C2×C8C2×C4×D1112yes—
385C2×C8C2×D4412yes—
386C2×C8C2×D4412yes—
387C4⋊C4—112no—
388C4⋊C4—112no—
389C4⋊C4—111no—
390C4⋊C4—111no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—222no—
394C4⋊C4—222no—
395C4⋊C4—221no—
396C4⋊C4—221no—
397C22⋊C4—221no—
398C22⋊C4—222no—
399C22⋊C4—221no—
400C22⋊C4—221no—
401C42—24no—
402C42—21no—
403C42—21no—
404C42—21no—
405C42—42no—
406C42—221no—
407C42—221no—
408C42—222no—
409C42—221no—
410C42C2×C4×D1111yescharacteristic
411C42C2×C4×D1111yescharacteristic
412C42C2×D4411yescharacteristic
413C42C2×D4411yescharacteristic
414C42Q8×D1112yes—
415C11#2298211yescharacteristic, complemented, Sylow
416C23—221no—
417C23C2×#433911yescharacteristic
418Q8—112no—
419Q8—221no—
420Q8—442no—
421Q8—881no—
422D4—112no—
423D4—222no—
424D4—222no—
425D4—221no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—221no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—442no—
442C2×C4—881no—
443C2×C4C4×D4411yescharacteristic
444C2×C4C4×D4411yescharacteristic
445C2×C4C4×D4411yescharacteristic
446C2×C4C4×D4411yescharacteristic
447C2×C4C22×C4×D1111yescharacteristic
448C2×C4C22×D4411yescharacteristic
449C2×C4#6703711yescharacteristic
450C2×C4C2×Q8×D1111yescharacteristic
451C2×C4#41×D1111yescharacteristic
452C2×C4#6704311yescharacteristic
453C8—22no—
454C8—22no—
455C8—22no—
456C8—22no—
457C8—222no—
458C8—442no—
459C8—441no—
460C22—21no—
461C22—21no—
462C22—222no—
463C22—441no—
464C22—441no—
465C22C2×C4×D4411yescharacteristic
466C22#1062304211yescharacteristic
467C22#1062306011yescharacteristic
468C4—24no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—42no—
473C4—222no—
474C4—441no—
475C4—442no—
476C4—441no—
477C4—442no—
478C4#1062231312yes—
479C4#1062307711yescharacteristic
480C4#1062308511yescharacteristic
481C4C4×Q8×D1111yescharacteristic
482C4Q8×D4411yescharacteristic
483C2—21no—
484C2—21no—
485C2—442no—
486C2#1307162311yescharacteristic
487C2C2×#1062231311yescharacteristic
488C2#1307752711yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C4⋊C8C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenterC4×C4⋊C8D11
hypocenterC11#22982
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13077559C2semidirect
4. #13069593C2semidirect
5. #13069392C2semidirect
6. #13069364C2semidirect
7. #13069216C2semidirect
11. C4×C11×C4⋊C8C2semidirect
29. #10622464C4semidirect
30. #10622463C4semidirect
31. #10622460C4semidirect
32. #10622459C4semidirect
33. #10622455C4semidirect
39. #10622442C4semidirect
102. #66869Q8semidirect
180. C4×C4⋊C8D11semidirect
415. C11#22982semidirect

Maximal subgroups

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

subgroupindex
#130784062
#130775592
#130771812
#130695932
#130693922
#130693642
#130692162
#130688942
#130684532
C4×#668692
C4×C11×C4⋊C82
#2298211