Finite Group Databasebeta

← #14909825

Subgroups — #14909825

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079275C211yesmaximal, characteristic, complemented
2#13079102C211yesmaximal, characteristic
3#13070887C211yesmaximal, characteristic, complemented
4#13070872C211yesmaximal, characteristic, complemented
5#13070858C211yesmaximal, characteristic, complemented
6#13070848C211yesmaximal, characteristic, complemented
7#13070679C212yesmaximal, complemented
8#13070657C212yesmaximal, complemented
9#13070558C212yesmaximal, complemented
10#13070547C212yesmaximal, complemented
11C11×#2164C211yesmaximal, characteristic, complemented
12C2×#66961—21no—
13C2×#66957C2211yescharacteristic
14C22×D88C2211yescharacteristic
15#10623056—21no—
16#10623049—21no—
17C11×#405C2211yescharacteristic
18#10622750—21no—
19#10622729C2212yes—
20C2×Dic88C2212yescomplemented
21C2×#66864C2212yes—
22C2×#66864C2212yes—
23C2×#66864C2212yescomplemented
24#10622329—21no—
25#10622325—21no—
26#10622325—21no—
27#10622316—21no—
28#10622312C2211yescharacteristic, complemented
29C4×Dic44C2212yescomplemented
30#10622309C2211yescharacteristic
31#10622309C2211yescharacteristic
32#10622308C2211yescharacteristic
33#10622308C2211yescharacteristic
34#10622296C2211yescharacteristic, complemented
35C11×C4⋊C16C2212yescomplemented
36C11×C22⋊C16C2212yes—
37C11×#346C2211yescharacteristic, complemented
38C4×C11×C16C2211yescharacteristic, complemented
39#10622147C2212yes—
40#10622147C2212yes—
41#10622147C2212yescomplemented
42#10622141C2212yescomplemented
43C2×#4339—21no—
44C22×D44—21no—
45C2×C11×M16D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×#117D411yescharacteristic
48#66977—22no—
49#66961—44no—
50C2×Dic44—21no—
51C2×Dic44C2312yes—
52C2×Dic44C2311yescharacteristic
53#66957—42no—
54C2×D88—21no—
55C2×D88—21no—
56C2×D88—21no—
57C2×D88—42no—
58C2×D88C2311yescharacteristic
59C2×D88C2311yescharacteristic
60C2×D88C2311yescharacteristic
61C2×#4314—21no—
62C2×#4314—21no—
63C2×#4314—21no—
64#66948—42no—
65#66942—42no—
66#66935—42no—
67#66932—42no—
68#66928—21no—
69#66928—21no—
70#66927—21no—
71#66927—21no—
72#66923—21no—
73#66922—21no—
74C4×Dic22—22no—
75C2×C11×C16C2312yes—
76C2×C11×C16C2312yes—
77C11×#97D411yescharacteristic
78C11×#97D411yescharacteristic
79C4×C8×C11C2311yescharacteristic
80C4×C8×C11C2311yescharacteristic
81#66882C2312yes—
82#66881—21no—
83#66880—22no—
84#66880—22no—
85Dic88—42no—
86#66864—42no—
87#66864—42no—
88#66864—42no—
89#33788—111nomaximal, Sylow
90C23×D11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C2×C22⋊D11—41no—
93#4339—42no—
94#4339—42no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—42no—
99C2×D44—42no—
100C2×D44—41no—
101C2×D44—42no—
102C2×D44—42no—
103C2×C4×D11—41no—
104C2×Dic22—22no—
105C2×Dic22—21no—
106C11×M16—22no—
107C2×C8×C11—22no—
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2411yescharacteristic
112C11×C4⋊C4D812yes—
113C11×C22⋊C4D812yes—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C22⋊Dic11—42no—
117(C2×D11)⋊C4—42no—
118(C2×D11)⋊C4—42no—
119C4⋊Dic11—22no—
120C4⋊Dic11—42no—
121Dic11⋊C4—42no—
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124C4×Dic11—42no—
125Dic44—22no—
126Dic44—22no—
127Dic44—22no—
128Dic44—42no—
129D88—22no—
130D88—22no—
131D88—22no—
132D88—42no—
133D88—42no—
134D88—42no—
135#4314—42no—
136#4314—42no—
137#4314—42no—
138C11×C16—22no—
139C11×C16—22no—
140#3177—111no—
141#3155—111no—
142#2251—111no—
143#2248—111no—
144#2244—111no—
145#2242—111no—
146#2211—112no—
147#2207—112no—
148#2189—112no—
149#2187—112no—
150#2164D1111yescharacteristic, complemented
151C23×C11C2×D811yescharacteristic
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—82no—
156C22×D11—162no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11C2×D812yes—
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C2×D812yes—
162C2×C4×C11C22×D411yescharacteristic
163C22⋊D11—82no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167D44—41no—
168D44—41no—
169D44—41no—
170D44—41no—
171D44—41no—
172D44—41no—
173D44—82no—
174D44—162no—
175D44—162no—
176C4×D11—82no—
177Dic22—41no—
178Dic22—42no—
179Dic22—41no—
180Dic22—42no—
181C8×C11—21no—
182C8×C11—21no—
183C8×C11AGL(1,ℤ/8)12yes—
184C8×C11H(5,𝔽2)12yes—
185C2×AGL(1,ℤ/8)—221no—
186C2×#135—111no—
187C22×D8—111no—
188#541—221no—
189#535—221no—
190C2×Q32—112no—
191C2×SD32—112no—
192C2×SD32—112no—
193C2×SD32—112no—
194#499—111no—
195#496—221no—
196#496—221no—
197#495—111no—
198#495—111no—
199#494—111no—
200#493—111no—
201#493—111no—
202#491—221no—
203#470—221no—
204#467—112no—
205#441—221no—
206C4×Q16—112no—
207#405C2×D1111yescharacteristic
208C4⋊C16C2×D1112yescomplemented
209#358—112no—
210#357—112no—
211#357—112no—
212#357—112no—
213C22⋊C16C2×D1112yes—
214#346C2×D1111yescharacteristic, complemented
215C4×C16C2×D1111yescharacteristic, complemented
216C22×C11—22no—
217C22×C11—21no—
218C22×C11C22×D811yescharacteristic
219C2×D11—82no—
220C2×D11—82no—
221C2×D11—82no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—164no—
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—21no—
229C4×C11#53511yescharacteristic
230C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
231Dic11—82no—
232Dic11—81no—
233Dic11—82no—
234C2×#41—221no—
235C22×D4—221no—
236AGL(1,ℤ/8)—444no—
237#135—442no—
238C2×Q16—111no—
239C2×Q16—112no—
240C2×Q16—221no—
241C2×SD16—221no—
242C2×SD16—221no—
243C2×SD16—221no—
244C2×D8—111no—
245C2×D8—111no—
246C2×D8—111no—
247C2×D8—221no—
248C2×D8—221no—
249C2×D8—221no—
250C2×D8—442no—
251C2×M16D4411yescharacteristic
252C22×C8C22×D1111yescharacteristic
253C4⋊Q8—221no—
254#127—221no—
255#127—221no—
256#126—442no—
257#125—221no—
258#125—442no—
259#124—221no—
260#124—221no—
261C22⋊Q8—222no—
262#121—442no—
263#120—442no—
264C4×Q8—222no—
265#117D4411yescharacteristic
266Q32—442no—
267SD32—442no—
268SD32—442no—
269SD32—442no—
270C2×C16C22×D1112yes—
271C2×C16C22×D1112yes—
272#107—112no—
273#106—221no—
274#103—222no—
275#103—222no—
276#97D4411yescharacteristic
277#97D4411yescharacteristic
278C4×C8C22×D1111yescharacteristic
279C4×C8C22×D1111yescharacteristic
280C2×C11—41no—
281C2×C11#320511yescharacteristic
282C2×C11#341612yes—
283D11—161no—
284D11—161no—
285D11—161no—
286C24—441no—
287#41—442no—
288#41—442no—
289C2×Q8—222no—
290C2×Q8—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—442no—
295C2×D4—442no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—442no—
299C2×D4—442no—
300C22×C4—441no—
301C22×C4C2×D4411yescharacteristic
302Q16—222no—
303Q16—222no—
304Q16—222no—
305Q16—442no—
306SD16—442no—
307SD16—442no—
308SD16—442no—
309D8—222no—
310D8—222no—
311D8—222no—
312D8—442no—
313D8—442no—
314D8—442no—
315M16—22no—
316C2×C8—22no—
317C2×C8C2×D4411yescharacteristic
318C2×C8C2×D4411yescharacteristic
319C2×C8C2×D4411yescharacteristic
320C2×C8C23×D1111yescharacteristic
321C4⋊C4—222no—
322C4⋊C4—442no—
323C4⋊C4—442no—
324C4⋊C4—442no—
325C4⋊C4—442no—
326C4⋊C4D8812yes—
327C22⋊C4—442no—
328C22⋊C4—442no—
329C22⋊C4—442no—
330C22⋊C4D8812yes—
331C42—442no—
332C42C2×D4411yescharacteristic
333C42C2×D4411yescharacteristic
334C16—22no—
335C16—22no—
336C11#3378811yescharacteristic, complemented, Sylow
337C23—441no—
338C23—441no—
339C23—441no—
340C23—882no—
341C23—1762no—
342C23C2×D8811yescharacteristic
343Q8—441no—
344Q8—442no—
345Q8—441no—
346Q8—442no—
347D4—441no—
348D4—441no—
349D4—441no—
350D4—441no—
351D4—441no—
352D4—441no—
353D4—882no—
354D4—882no—
355D4—1762no—
356D4—1762no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—441no—
362C2×C4—882no—
363C2×C4C2×D8812yes—
364C2×C4C2×D8812yes—
365C2×C4C2×D8811yescharacteristic
366C2×C4C22×D4411yescharacteristic
367C8—21no—
368C8—21no—
369C8#6696112yes—
370C8#6704212yes—
371C22—22no—
372C22—21no—
373C22—882no—
374C22—882no—
375C22—882no—
376C22—881no—
377C22—881no—
378C22—881no—
379C22—1764no—
380C22C22×D8811yescharacteristic
381C4—22no—
382C4—22no—
383C4—21no—
384C4—882no—
385C4—881no—
386C4—882no—
387C4#1062305611yescharacteristic
388C4C2×#6696111yescharacteristic
389C2—41no—
390C2—1761no—
391C2—1761no—
392C2—1761no—
393C2#1307953611yescharacteristic
394C2#1308176412yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2164C2
socleC22×C11C22×D8
prime radical#13079102C2
hypercenter#2164D11
hypocenterC11#33788
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2164

Complements

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

NH ≅ G/Ntype
1. #13079275C2semidirect
3. #13070887C2semidirect
4. #13070872C2semidirect
5. #13070858C2semidirect
6. #13070848C2semidirect
7. #13070679C2semidirect
8. #13070657C2semidirect
9. #13070558C2semidirect
10. #13070547C2semidirect
11. C11×#2164C2semidirect
20. C2×Dic88C22semidirect
23. C2×#66864C22semidirect
28. #10622312C22semidirect
29. C4×Dic44C22semidirect
34. #10622296C22semidirect
35. C11×C4⋊C16C22semidirect
37. C11×#346C22semidirect
38. C4×C11×C16C22semidirect
41. #10622147C22semidirect
42. #10622141C22semidirect
150. #2164D11semidirect
208. C4⋊C16C2×D11semidirect
214. #346C2×D11semidirect
215. C4×C16C2×D11semidirect
336. C11#33788semidirect

Maximal subgroups

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

subgroupindex
#130792752
#130791022
#130708872
#130708722
#130708582
#130708482
#130706792
#130706572
#130705582
#130705472
C11×#21642
#3378811