Finite Group Databasebeta

← #14736995

Subgroups — #14736995

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#13079933C212yesmaximal, complemented
2#13079044C211yesmaximal, characteristic
3#13077550C211yesmaximal, characteristic, complemented
4#13068111C212yesmaximal, complemented
5#13068101C212yesmaximal, complemented
6#13067965C214yesmaximal, complemented
7#13067291C212yesmaximal, complemented
8C2×C11×#334C211yesmaximal, characteristic, complemented
9C2×#66957—21no—
10C2×#66957—21no—
11#10623008C2212yes—
12#10623001C2211yescharacteristic
13C2×C11×C4⋊C8C2212yes—
14C2×C4×C8×C11C2211yescharacteristic
15#10622727—24no—
16#10622715—21no—
17#10622714—21no—
18#10622537C2211yescharacteristic
19#10622464C2214yes—
20#10622461C2214yes—
21#10622455—22no—
22#10622454—22no—
23#10622312C2211yescharacteristic
24#10622309—21no—
25#10622309—21no—
26#10622308C2211yescharacteristic
27#10622306C2212yes—
28#10622292—21no—
29#10622292C2212yes—
30C8×Dic22—21no—
31C8×Dic22C2212yes—
32C11×#334C2212yes—
33C11×#334C2212yes—
34#10622124C2214yes—
35#10622123C2214yes—
36C2×#4339—22no—
37C22×C8×C11—22no—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11D411yescharacteristic
40C2×C42×C11C2311yescharacteristic
41#66983—22no—
42#66983—22no—
43#66979—21no—
44#66977—21no—
45#66977D412yes—
46C2×#4318—21no—
47C2×Dic44—21no—
48C2×Dic44—21no—
49#66957—44no—
50#66957—44no—
51C2×D88—21no—
52C2×D88—21no—
53C2×#4314—22no—
54C2×#4314—22no—
55C2×#4314—24no—
56#66928—22no—
57#66927C2312yes—
58C4×D44—22no—
59C4×D44—22no—
60#66923—21no—
61#66922D411yescharacteristic
62#66922D411yescharacteristic
63#66922C2312yes—
64C4×Dic22—21no—
65C4×Dic22C2312yes—
66C11×C4⋊C8—22no—
67C11×C4⋊C8C2314yes—
68C4×C8×C11D411yescharacteristic
69C4×C8×C11D411yescharacteristic
70C4×C8×C11C2311yescharacteristic
71C4×C8×C11C2311yescharacteristic
72#66885—24no—
73#66881—24no—
74#66880—24no—
75#66879—22no—
76Dic11⋊C8—22no—
77Dic11⋊C8—22no—
78C8×Dic11—22no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)C2312yes—
81#19205—111nomaximal, Sylow
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C2×C22⋊D11—42no—
86#4339—44no—
87#4339—44no—
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—22no—
91C2×C4×D11—42no—
92C2×Dic22—21no—
93C2×Dic22—22no—
94C2×Dic22C2×D412yes—
95C2×C8×C11—22no—
96C2×C8×C11—24no—
97C2×C8×C11—82no—
98C2×C8×C11SD1614yescomplemented
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11C2411yescharacteristic
107C22⋊Dic11—22no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11C2×D412yes—
116Dic11⋊C4—22no—
117Dic11⋊C4—22no—
118C4×Dic11—22no—
119#4318—42no—
120C2×C11⋊C8—22no—
121Dic44—42no—
122Dic44—42no—
123D88—42no—
124D88—42no—
125#4314—44no—
126#4314—44no—
127#4314—84no—
128#3246—112no—
129#3147—111no—
130#2960—111no—
131#1690—112no—
132#1688—112no—
133#1666—114no—
134C2×#334D1111yescharacteristic, complemented
135#1547—112no—
136C23×C11#12111yescharacteristic
137C22×D11—42no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11C2×SD1612yes—
144C2×C4×C11AGL(1,ℤ/8)12yes—
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C22⋊D11—84no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—42no—
152D44—42no—
153D44—42no—
154D44—42no—
155D44—42no—
156D44—82no—
157C4×D11—84no—
158Dic22—24no—
159Dic22—42no—
160Dic22—42no—
161Dic22—42no—
162C8×C11—21no—
163C8×C11—21no—
164C8×C11—44no—
165C8×C11C2×SD1612yes—
166C8×C11C2×SD1612yes—
167C11⋊C8—42no—
168C2×#135—221no—
169C2×#135—221no—
170#533—111no—
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—112no—
183#446—221no—
184C8×Q8—112no—
185C8×Q8—221no—
186#424—221no—
187#423—111no—
188C2×C4⋊C8C2×D1112yes—
189#405—221no—
190C2×C4×C8C2×D1111yescharacteristic
191#334C2×D1112yes—
192#334C2×D1112yes—
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#46012yes—
206C4×C11C22×SD1611yescharacteristic
207C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
208C4×C11#57712yes—
209Dic11—42no—
210Dic11—42no—
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—221no—
223C22×C8—22no—
224C22×C8D4411yescharacteristic
225C22×C8D4411yescharacteristic
226C4⋊Q8—111no—
227C4⋊Q8—111no—
228C4⋊Q8—112no—
229#127—112no—
230#125—221no—
231#124—222no—
232C22⋊Q8—112no—
233C22⋊Q8—221no—
234#121—222no—
235#121—222no—
236C4×Q8—112no—
237C4×Q8—221no—
238C4×D4—222no—
239C4×D4—222no—
240#117—221no—
241C2×C42C22×D1111yescharacteristic
242#106—224no—
243C4⋊C8—22no—
244C4⋊C8—112no—
245C4⋊C8—222no—
246C4⋊C8—222no—
247C4⋊C8—221no—
248C4⋊C8C22×D1114yes—
249#103—224no—
250#102—224no—
251#97—222no—
252C4×C8—222no—
253C4×C8D4411yescharacteristic
254C4×C8D4411yescharacteristic
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—112no—
265C2×Q8—221no—
266C2×Q8—222no—
267C2×D4—222no—
268C2×D4—222no—
269C2×D4—222no—
270C2×D4—442no—
271C22×C4—442no—
272C22×C4C2×D4411yescharacteristic
273C22×C4D4×D1111yescharacteristic
274C22×C4#434311yescharacteristic
275Q16—442no—
276Q16—442no—
277SD16—444no—
278SD16—444no—
279SD16—884no—
280D8—442no—
281D8—442no—
282M16—442no—
283C2×C8—22no—
284C2×C8—24no—
285C2×C8—82no—
286C2×C8—222no—
287C2×C8#431414yescomplemented
288C2×C8C2×D4411yescharacteristic
289C2×C8C2×D4411yescharacteristic
290C2×C8C2×D4411yescharacteristic
291C2×C8C2×D4411yescharacteristic
292C4⋊C4—112no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—222no—
296C4⋊C4—221no—
297C4⋊C4—222no—
298C4⋊C4—222no—
299C4⋊C4—222no—
300C22⋊C4—222no—
301C22⋊C4—442no—
302C22⋊C4—442no—
303C42—222no—
304C42C2×D4411yescharacteristic
305C42D4×D1111yescharacteristic
306C42#434311yescharacteristic
307C42C23×D1111yescharacteristic
308C11#1920511yescharacteristic, complemented, Sylow
309C23—442no—
310C23#6694811yescharacteristic
311Q8—224no—
312Q8—442no—
313Q8—442no—
314Q8—442no—
315D4—442no—
316D4—442no—
317D4—442no—
318D4—442no—
319D4—882no—
320D4—884no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—222no—
324C2×C4—222no—
325C2×C4—442no—
326C2×C4—884no—
327C2×C4#6694811yescharacteristic
328C2×C4#6694811yescharacteristic
329C2×C4#6694811yescharacteristic
330C2×C4C2×#431412yes—
331C2×C4#6696112yes—
332C2×C4C22×D4411yescharacteristic
333C2×C4C2×D4×D1111yescharacteristic
334C2×C4C2×#434311yescharacteristic
335C8—21no—
336C8—21no—
337C8—44no—
338C8—442no—
339C8C2×#431412yes—
340C8C2×#431412yes—
341C22—21no—
342C22—21no—
343C22—882no—
344C22—882no—
345C22—882no—
346C22#1062246112yes—
347C22C2×#6694811yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—442no—
352C4—442no—
353C4—882no—
354C4#1062246112yes—
355C4C22×#431411yescharacteristic
356C4C2×#6696111yescharacteristic
357C4#1062329312yes—
358C2—22no—
359C2—1762no—
360C2C2×#1062246111yescharacteristic
361C2#1307827911yescharacteristic
362C2#1307833711yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#334C2
socleC22×C11C2×#121
prime radical#13079044C2
hypercenterC2×#334D11
hypocenterC11#19205
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
1. #13079933C2semidirect
3. #13077550C2semidirect
4. #13068111C2semidirect
5. #13068101C2semidirect
6. #13067965C2semidirect
7. #13067291C2semidirect
8. C2×C11×#334C2semidirect
98. C2×C8×C11SD16semidirect
134. C2×#334D11semidirect
287. C2×C8#4314semidirect
308. C11#19205semidirect

Maximal subgroups

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

subgroupindex
#130799332
#130790442
#130775502
#130681112
#130681012
#130679652
#130672912
C2×C11×#3342
#1920511