Finite Group Databasebeta

← #14736994

Subgroups — #14736994

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C212yesmaximal, complemented
2#13079044C211yesmaximal, characteristic
3#13068110C212yesmaximal, complemented
4#13068100C212yesmaximal, complemented
5#13067964C214yesmaximal, complemented
6C2×#10622095C211yesmaximal, characteristic, complemented
7#13067294C212yesmaximal, complemented
8C11×#2960C211yesmaximal, characteristic, complemented
9C11×#533C2211yescharacteristic
10C2×#66957—21no—
11C2×#66957—21no—
12#10623008C2212yes—
13C11×#446—21no—
14C11×#446C2212yes—
15C8×Q8×C11—21no—
16C8×Q8×C11C2212yes—
17C11×#424—21no—
18C11×#423C2211yescharacteristic
19C11×#405—21no—
20C2×C4×C8×C11C2211yescharacteristic
21#10622697—22no—
22#10622696—22no—
23#10622661—24no—
24#10622640C2214yes—
25#10622633C2214yes—
26C2×C4⋊(C11⋊C8)C2212yes—
27#10622312C2211yescharacteristic
28#10622309—21no—
29#10622309—21no—
30#10622308C2211yescharacteristic
31#10622306C2212yes—
32#10622123C2214yes—
33#10622120C2214yes—
34#10622095C2212yes—
35#10622095C2212yes—
36C2×#4339—22no—
37C2×C11×M16—21no—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11D411yescharacteristic
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8D412yes—
45C4×Q8×C11—21no—
46C4×Q8×C11C2312yes—
47C11×#117—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—24no—
50#66983—22no—
51#66983—22no—
52C22×C11⋊C8—22no—
53C2×Dic44—21no—
54C2×Dic44—21no—
55#66957—44no—
56#66957—44no—
57C2×D88—21no—
58C2×D88—21no—
59C2×#4314—22no—
60C2×#4314—22no—
61#66928—22no—
62#66927C2312yes—
63C4×D44—22no—
64C4×D44—22no—
65#66922C2312yes—
66C11×C4⋊C8—22no—
67C11×C4⋊C8—22no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×#97—22no—
71C4×C8×C11—22no—
72C4×C8×C11D411yescharacteristic
73C4×C8×C11D411yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76#66899—24no—
77#66873—24no—
78#66872—24no—
79C4⋊(C11⋊C8)—22no—
80C4⋊(C11⋊C8)C2314yes—
81#19205—111nomaximal, Sylow
82C2×Q8×C11—21no—
83C2×Q8×C11C2×D412yes—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C2×C22⋊D11—42no—
88#4339—44no—
89#4339—44no—
90C2×D44—22no—
91C2×D44—22no—
92C2×D44—22no—
93C2×C4×D11—42no—
94C2×Dic22—22no—
95C11×M16—42no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11SD1614yescomplemented
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4C2×D412yes—
109C11×C22⋊C4—22no—
110C42×C11—22no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11C2411yescharacteristic
115#4325—84no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—42no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C2×C11⋊C8—24no—
121C2×C11⋊C8—82no—
122Dic44—42no—
123Dic44—42no—
124D88—42no—
125D88—42no—
126#4314—44no—
127#4314—44no—
128#3246—112no—
129#3147—111no—
130#2960D1111yescharacteristic, complemented
131#1690—112no—
132#1688—112no—
133#1666—114no—
134C2×#334—111no—
135#1547—112no—
136C23×C11#12111yescharacteristic
137C22×D11—42no—
138Q8×C11—24no—
139Q8×C11—42no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11C2×SD1612yes—
148C2×C4×C11AGL(1,ℤ/8)12yes—
149C2×C4×C11C22×D411yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C2×#4111yescharacteristic
152C22⋊D11—84no—
153C2×Dic11—42no—
154D44—42no—
155D44—42no—
156D44—42no—
157D44—42no—
158D44—82no—
159C4×D11—84no—
160Dic22—42no—
161Dic22—42no—
162C8×C11—21no—
163C8×C11—21no—
164C8×C11—42no—
165C8×C11C2×SD1612yes—
166C8×C11C2×SD1612yes—
167C11⋊C8—44no—
168C2×#135—221no—
169C2×#135—221no—
170#533C2×D1111yescharacteristic
171#532—112no—
172#495—221no—
173#495—221no—
174#494—111no—
175#493—111no—
176#492—112no—
177#476—222no—
178#475—114no—
179#465—224no—
180#461—222no—
181#460—114no—
182#446—21no—
183#446C2×D1112yes—
184C8×Q8—21no—
185C8×Q8C2×D1112yes—
186#424—21no—
187#423C2×D1111yescharacteristic
188C2×C4⋊C8—112no—
189#405—21no—
190C2×C4×C8C2×D1111yescharacteristic
191#334—112no—
192#334—112no—
193#332—114no—
194#331—114no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11#46012yes—
198C22×C11C2×#12111yescharacteristic
199C2×D11—82no—
200C2×D11—82no—
201C2×D11—82no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—42no—
206C4×C11—42no—
207C4×C11#46012yes—
208C4×C11C22×SD1611yescharacteristic
209C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
210C4×C11#57712yes—
211Dic11—82no—
212C2×#41—222no—
213#135—444no—
214#135—444no—
215C2×Q16—221no—
216C2×Q16—221no—
217C2×SD16—224no—
218C2×SD16—222no—
219C2×SD16—222no—
220C2×D8—221no—
221C2×D8—221no—
222C2×M16—21no—
223C22×C8—222no—
224C22×C8C22⋊D1111yescharacteristic
225C22×C8C22⋊D1111yescharacteristic
226C4⋊Q8—112no—
227C4⋊Q8D4411yescharacteristic
228C4⋊Q8D4411yescharacteristic
229#127—112no—
230#125—21no—
231#124—222no—
232C22⋊Q8—21no—
233C22⋊Q8D4412yes—
234#121—222no—
235#121—222no—
236C4×Q8—21no—
237C4×Q8C22×D1112yes—
238C4×D4—222no—
239C4×D4—222no—
240#117—21no—
241C2×C42C22×D1111yescharacteristic
242#106—224no—
243C4⋊C8—22no—
244C4⋊C8—22no—
245C4⋊C8—21no—
246C4⋊C8—114no—
247C4⋊C8—222no—
248C4⋊C8C22×D1112yes—
249#103—224no—
250#102—224no—
251#97—22no—
252C4×C8—22no—
253C4×C8C22⋊D1111yescharacteristic
254C4×C8C22⋊D1111yescharacteristic
255C4×C8C22×D1111yescharacteristic
256C4×C8C22×D1111yescharacteristic
257C2×C11—22no—
258C2×C11C2×#46011yescharacteristic
259C2×C11#306011yescharacteristic
260C2×C11#306711yescharacteristic
261D11—162no—
262#41—444no—
263#41—444no—
264C2×Q8—21no—
265C2×Q8—222no—
266C2×Q8C2×D4412yes—
267C2×D4—222no—
268C2×D4—222no—
269C2×D4—222no—
270C2×D4—442no—
271C22×C4—442no—
272C22×C4C2×D4411yescharacteristic
273C22×C4#433911yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275Q16—442no—
276Q16—442no—
277SD16—444no—
278SD16—444no—
279SD16—884no—
280D8—442no—
281D8—442no—
282M16—42no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—224no—
286C2×C8—882no—
287C2×C8#432514yescomplemented
288C2×C8C2×C22⋊D1111yescharacteristic
289C2×C8C2×C22⋊D1111yescharacteristic
290C2×C8C2×C22⋊D1111yescharacteristic
291C2×C8C2×C22⋊D1111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—222no—
298C4⋊C4—222no—
299C4⋊C4C2×D4412yes—
300C22⋊C4—22no—
301C22⋊C4—442no—
302C22⋊C4—442no—
303C42—22no—
304C42C2×D4411yescharacteristic
305C42#433911yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C42C23×D1111yescharacteristic
308C11#1920511yescharacteristic, complemented, Sylow
309C23—442no—
310C23#6698311yescharacteristic
311Q8—24no—
312Q8—42no—
313Q8—442no—
314Q8—442no—
315D4—442no—
316D4—442no—
317D4—442no—
318D4—442no—
319D4—882no—
320D4—884no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—442no—
326C2×C4—884no—
327C2×C4#6698311yescharacteristic
328C2×C4#6698311yescharacteristic
329C2×C4#6698311yescharacteristic
330C2×C4C2×#432512yes—
331C2×C4#6700212yes—
332C2×C4C22×D4411yescharacteristic
333C2×C4C2×#433911yescharacteristic
334C2×C4C22×C22⋊D1111yescharacteristic
335C8—21no—
336C8—21no—
337C8—42no—
338C8—444no—
339C8C2×#432512yes—
340C8C2×#432512yes—
341C22—21no—
342C22—21no—
343C22—882no—
344C22—882no—
345C22—882no—
346C22#1062264012yes—
347C22C2×#6698311yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—42no—
352C4—42no—
353C4—882no—
354C4#1062264012yes—
355C4#1062328212yes—
356C4C22×#432511yescharacteristic
357C4C2×#6700211yescharacteristic
358C2—22no—
359C2—1762no—
360C2C2×#1062264011yescharacteristic
361C2#1307827811yescharacteristic
362C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×#121
prime radical#13079044C2
hypercenter#2960D11
hypocenterC11#19205
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960

Complements

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

NH ≅ G/Ntype
1. #13079928C2semidirect
3. #13068110C2semidirect
4. #13068100C2semidirect
5. #13067964C2semidirect
6. C2×#10622095C2semidirect
7. #13067294C2semidirect
8. C11×#2960C2semidirect
98. C2×C8×C11SD16semidirect
130. #2960D11semidirect
287. C2×C8#4325semidirect
308. C11#19205semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130790442
#130681102
#130681002
#130679642
C2×#106220952
#130672942
C11×#29602
#1920511