Finite Group Databasebeta

← #14738416

Subgroups — #14738416

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079627C212yesmaximal, complemented
2#13077550C211yesmaximal, characteristic, complemented
3#13068181C214yesmaximal, complemented
4#13068007C212yesmaximal, complemented
5#13067973C212yesmaximal, complemented
6#13067379C211yesmaximal, characteristic, complemented
7#13067338C212yesmaximal, 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#10622852—24no—
20#10622715—21no—
21#10622714—21no—
22#10622703C2214yes—
23#10622688C2214yes—
24#10622673—22no—
25#10622668—22no—
26#10622539C2212yes—
27#10622537C2211yescharacteristic
28#10622292—21no—
29#10622292C2212yes—
30C8×Dic22—21no—
31C8×Dic22C2212yes—
32#10622185C2214yes—
33#10622182C2214yes—
34#10622096C2212yes—
35#10622095C2212yes—
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×#4326—24no—
50C2×#4324—24no—
51#66979—21no—
52#66977—21no—
53#66977D412yes—
54C2×#4318—21no—
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#66899—24no—
69#66896—24no—
70C22⋊(C11⋊C8)—22no—
71#66879—22no—
72Dic11⋊C8—22no—
73Dic11⋊C8—22no—
74C8×Dic11—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)C2312yes—
77C4⋊(C11⋊C8)C2314yes—
78#66867—22no—
79#19341—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#4326—84no—
110#4324—84no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11C2×D412yes—
115Dic11⋊C4—22no—
116Dic11⋊C4—22no—
117C4×Dic11—22no—
118#4318—42no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—22no—
121#3216—112no—
122#3169D1111yescharacteristic
123#2960—111no—
124#1702—114no—
125#1674—112no—
126#1668—112no—
127#1568—111no—
128#1557—112no—
129C23×C11—42no—
130C23×C11#12111yescharacteristic
131Q8×C11—44no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—44no—
135D4×C11—82no—
136D4×C11—84no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—84no—
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C2×#4111yescharacteristic
149C2×Dic11—22no—
150C2×Dic11—22no—
151Dic22—22no—
152Dic22—22no—
153Dic22—42no—
154C8×C11—21no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11#13712yes—
158C11⋊C8—42no—
159C11⋊C8—44no—
160#533—111no—
161#532C2×D1112yes—
162#500C2×D1111yescharacteristic
163#497—222no—
164#493C2×D1111yescharacteristic
165#489—222no—
166#486C2×D1112yes—
167#466—21no—
168#466—21no—
169#462—114no—
170#460—114no—
171#452—224no—
172#446—112no—
173#446—221no—
174C8×Q8—112no—
175C8×Q8—221no—
176C4×D8—21no—
177C4×D8—21no—
178#432—112no—
179#424—221no—
180#423—111no—
181#405—221no—
182C2×C4×C8C2×D1111yescharacteristic
183#335—112no—
184#334—112no—
185#332—114no—
186#331—114no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—82no—
193C22×C11C2×#12111yescharacteristic
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—82no—
199C4×C11C2×#13711yescharacteristic
200C4×C11#57511yescharacteristic
201C4×C11#57612yes—
202Dic11—42no—
203Dic11—42no—
204C2×#41—22no—
205C2×Q16—224no—
206C2×SD16—224no—
207C2×D8—21no—
208C2×D8—21no—
209C2×M16—221no—
210C22×C8C22⋊D1111yescharacteristic
211C22×C8C22⋊D1111yescharacteristic
212C4⋊Q8—111no—
213C4⋊Q8—111no—
214C4⋊Q8C22×D1112yes—
215#127C22×D1112yes—
216#125—221no—
217#124—22no—
218C22⋊Q8—112no—
219C22⋊Q8—221no—
220#121—22no—
221#121—22no—
222C4×Q8—112no—
223C4×Q8—221no—
224C4×D4—22no—
225C4×D4—22no—
226#117—221no—
227C2×C42C22×D1111yescharacteristic
228#107—21no—
229#107—21no—
230C4⋊C8—112no—
231C4⋊C8—114no—
232C4⋊C8—222no—
233C4⋊C8—222no—
234C4⋊C8—221no—
235#103—224no—
236#102—22no—
237#102—22no—
238#102—224no—
239C22⋊C8—222no—
240#97—222no—
241#97—222no—
242C4×C8—222no—
243C4×C8C22⋊D1111yescharacteristic
244C4×C8C22⋊D1111yescharacteristic
245C4×C8C22×D1111yescharacteristic
246C4×C8C22×D1111yescharacteristic
247C2×C11—41no—
248C2×C11—162no—
249C2×C11#303711yescharacteristic
250C2×C11#305811yescharacteristic
251C2×C11#306711yescharacteristic
252#41—84no—
253C2×Q8—22no—
254C2×Q8—112no—
255C2×Q8—221no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—42no—
260C22×C4—42no—
261C22×C4D4×D1111yescharacteristic
262C22×C4#434111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264Q16—884no—
265SD16—884no—
266D8—42no—
267D8—42no—
268M16—442no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—224no—
272C2×C8—222no—
273C2×C8C2×C22⋊D1111yescharacteristic
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C2×C22⋊D1111yescharacteristic
276C2×C8C2×C22⋊D1111yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—112no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—222no—
283C4⋊C4—221no—
284C4⋊C4—222no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—222no—
288C42—222no—
289C42D4×D1111yescharacteristic
290C42#434111yescharacteristic
291C42C2×C22⋊D1111yescharacteristic
292C42C23×D1111yescharacteristic
293C11#1934111yescharacteristic, complemented, Sylow
294C23—42no—
295C23#6699111yescharacteristic
296Q8—44no—
297Q8—222no—
298Q8—222no—
299Q8—442no—
300D4—44no—
301D4—42no—
302D4—42no—
303D4—82no—
304D4—84no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—84no—
311C2×C4—222no—
312C2×C4—222no—
313C2×C4#6699111yescharacteristic
314C2×C4#6699111yescharacteristic
315C2×C4#6699111yescharacteristic
316C2×C4C2×D4×D1111yescharacteristic
317C2×C4C2×#434111yescharacteristic
318C2×C4C22×C22⋊D1111yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—444no—
323C8—442no—
324C8#6700412yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22C2×#6699111yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—442no—
338C4—442no—
339C4#1062328812yes—
340C4#1062335311yescharacteristic
341C4C2×#6700411yescharacteristic
342C2—41no—
343C2—162no—
344C2#1307808411yescharacteristic
345C2#1307826011yescharacteristic
346C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19341
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. #13079627C2semidirect
2. #13077550C2semidirect
3. #13068181C2semidirect
4. #13068007C2semidirect
5. #13067973C2semidirect
6. #13067379C2semidirect
7. #13067338C2semidirect
293. C11#19341semidirect

Maximal subgroups

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

subgroupindex
#130796272
#130775502
#130681812
#130680072
#130679732
#130673792
#130673382
C11×#31692
#1934111