Finite Group Databasebeta

← #14738443

Subgroups — #14738443

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080003C212yesmaximal, complemented
2#13077550C211yesmaximal, characteristic, complemented
3#13068153C214yesmaximal, complemented
4#13068017C212yesmaximal, complemented
5#13067973C212yesmaximal, complemented
6#13067375C211yesmaximal, characteristic, complemented
7#13067351C212yesmaximal, complemented
8C11×#3169C211yesmaximal, characteristic
9C11×#532C2212yes—
10#10623001C2211yescharacteristic
11C11×#500C2211yescharacteristic
12C11×#493C2211yescharacteristic
13C11×#486C2212yes—
14C11×#466—21no—
15C11×#466—21no—
16C4×C11×D8—21no—
17C4×C11×D8—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622715—21no—
20#10622714—21no—
21#10622704C2214yes—
22#10622688C2214yes—
23#10622655—24no—
24#10622632—22no—
25#10622620—22no—
26#10622537C2211yescharacteristic
27#10622537C2212yes—
28#10622292—21no—
29#10622292C2212yes—
30C8×Dic22—21no—
31C8×Dic22C2212yes—
32#10622184C2214yes—
33#10622182C2214yes—
34#10622096C2212yes—
35#10622096C2212yes—
36C2×C11×#41—22no—
37C2×C11×D8—21no—
38C2×C11×D8—21no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C11×C4⋊Q8C2312yes—
42C11×#127C2312yes—
43C11×#124—22no—
44C11×#121—22no—
45C11×#121—22no—
46C4×D4×C11—22no—
47C4×D4×C11—22no—
48C2×C42×C11C2311yescharacteristic
49C2×#4324—24no—
50#66979—21no—
51#66977—21no—
52#66977D412yes—
53C2×#4318—21no—
54C2×#4318—22no—
55#66923—21no—
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22C2312yes—
60C11×#107—21no—
61C11×#107—21no—
62C11×#102—22no—
63C11×#102—22no—
64C4×C8×C11D411yescharacteristic
65C4×C8×C11D411yescharacteristic
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2311yescharacteristic
68#66896—24no—
69#66879—22no—
70Dic11⋊C8—22no—
71Dic11⋊C8—22no—
72C8×Dic11—22no—
73#66874—24no—
74#66871—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—22no—
77C4⋊(C11⋊C8)C2312yes—
78C4⋊(C11⋊C8)C2314yes—
79#19344—111nomaximal, Sylow
80C11×#41—84no—
81C2×Q8×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×Dic22—21no—
91C2×Dic22C2×D412yes—
92C11×D8—42no—
93C11×D8—42no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11C2411yescharacteristic
108C22⋊Dic11—22no—
109#4324—84no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11C2×D412yes—
114Dic11⋊C4—22no—
115Dic11⋊C4—22no—
116C4×Dic11—22no—
117#4318—42no—
118#4318—82no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—22no—
121#3254—112no—
122#3169D1111yescharacteristic
123#2960—111no—
124#1698—114no—
125#1676—112no—
126#1668—112no—
127#1567—111no—
128#1560—112no—
129C23×C11—42no—
130C23×C11#12111yescharacteristic
131Q8×C11—82no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—42no—
136D4×C11—82no—
137D4×C11—84no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—42no—
144C2×C4×C11—84no—
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C2×C4×C11C2×#4111yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—22no—
153Dic22—22no—
154Dic22—22no—
155Dic22—42no—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11—21no—
159C8×C11#13712yes—
160C11⋊C8—42no—
161C11⋊C8—44no—
162#533—111no—
163#532C2×D1112yes—
164#500C2×D1111yescharacteristic
165#493C2×D1111yescharacteristic
166#486C2×D1112yes—
167#477—114no—
168#474—222no—
169#468—224no—
170#466—21no—
171#466—21no—
172#461—222no—
173#460—114no—
174#446—112no—
175#446—221no—
176C8×Q8—112no—
177C8×Q8—221no—
178C4×D8—21no—
179C4×D8—21no—
180#424—221no—
181#423—111no—
182#423—112no—
183#405—221no—
184C2×C4×C8C2×D1111yescharacteristic
185#335—112no—
186#335—112no—
187#333—114no—
188#331—114no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11C2×#12111yescharacteristic
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—82no—
200C4×C11#47212yes—
201C4×C11C2×#13711yescharacteristic
202C4×C11#57511yescharacteristic
203C4×C11#57611yescharacteristic
204C4×C11#57811yescharacteristic
205Dic11—42no—
206Dic11—42no—
207C2×#41—22no—
208C2×SD16—224no—
209C2×D8—21no—
210C2×D8—21no—
211C2×M16—221no—
212C2×M16—222no—
213C22×C8C22⋊D1111yescharacteristic
214C22×C8C22⋊D1111yescharacteristic
215C4⋊Q8—111no—
216C4⋊Q8—111no—
217C4⋊Q8C22×D1112yes—
218#127C22×D1112yes—
219#125—221no—
220#124—22no—
221C22⋊Q8—112no—
222C22⋊Q8—221no—
223#121—22no—
224#121—22no—
225C4×Q8—112no—
226C4×Q8—221no—
227C4×D4—22no—
228C4×D4—22no—
229#117—221no—
230C2×C42C22×D1111yescharacteristic
231#107—21no—
232#107—21no—
233#107—224no—
234C4⋊C8—112no—
235C4⋊C8—114no—
236C4⋊C8—222no—
237C4⋊C8—222no—
238C4⋊C8—222no—
239C4⋊C8—221no—
240#103—224no—
241#102—22no—
242#102—22no—
243#102—224no—
244#97—222no—
245C4×C8—222no—
246C4×C8C22⋊D1111yescharacteristic
247C4×C8C22⋊D1111yescharacteristic
248C4×C8C22×D1111yescharacteristic
249C4×C8C22×D1111yescharacteristic
250C2×C11—41no—
251C2×C11—162no—
252C2×C11#303711yescharacteristic
253C2×C11#306111yescharacteristic
254C2×C11C2×#47211yescharacteristic
255#41—84no—
256C2×Q8—22no—
257C2×Q8—112no—
258C2×Q8—221no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—42no—
263C22×C4—42no—
264C22×C4D4×D1111yescharacteristic
265C22×C4#434111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267SD16—884no—
268D8—42no—
269D8—42no—
270M16—442no—
271M16—882no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—224no—
275C2×C8—222no—
276C2×C8C2×C22⋊D1111yescharacteristic
277C2×C8C2×C22⋊D1111yescharacteristic
278C2×C8C2×C22⋊D1111yescharacteristic
279C2×C8C2×C22⋊D1111yescharacteristic
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—112no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—222no—
286C4⋊C4—221no—
287C4⋊C4—222no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—222no—
291C42—222no—
292C42D4×D1111yescharacteristic
293C42#434111yescharacteristic
294C42C2×C22⋊D1111yescharacteristic
295C42C23×D1111yescharacteristic
296C11#1934411yescharacteristic, complemented, Sylow
297C23—42no—
298C23#6699111yescharacteristic
299Q8—82no—
300Q8—222no—
301Q8—222no—
302Q8—442no—
303D4—42no—
304D4—42no—
305D4—42no—
306D4—42no—
307D4—82no—
308D4—84no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—84no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4#6699111yescharacteristic
319C2×C4#6699111yescharacteristic
320C2×C4#6699111yescharacteristic
321C2×C4C2×D4×D1111yescharacteristic
322C2×C4C2×#434111yescharacteristic
323C2×C4C22×C22⋊D1111yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—444no—
328C8—442no—
329C8#6700412yes—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—82no—
334C22—82no—
335C22—82no—
336C22C2×#6699111yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—442no—
342C4—442no—
343C4#1062277312yes—
344C4#1062330011yescharacteristic
345C4#1062330211yescharacteristic
346C4#1062335311yescharacteristic
347C4C2×#6700411yescharacteristic
348C2—41no—
349C2—162no—
350C2#1307808411yescharacteristic
351C2#1307828211yescharacteristic
352C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19344
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13080003C2semidirect
2. #13077550C2semidirect
3. #13068153C2semidirect
4. #13068017C2semidirect
5. #13067973C2semidirect
6. #13067375C2semidirect
7. #13067351C2semidirect
296. C11#19344semidirect

Maximal subgroups

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

subgroupindex
#130800032
#130775502
#130681532
#130680172
#130679732
#130673752
#130673512
C11×#31692
#1934411