Finite Group Databasebeta

← #14959847

Subgroups — #14959847

Order 2816.

2782 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
1C2×#10623001C211yesmaximal, characteristic, complemented
2#13076993C212yesmaximal, complemented
3#13076986C214yesmaximal, complemented
4#13076972C212yesmaximal, complemented
5#13076915C218yesmaximal, complemented
6C4×#66989C218yesmaximal, complemented
7#13071107C214yesmaximal, complemented
8C2×C42×Dic11C211yesmaximal, characteristic, complemented
9C2×C11×#532C211yesmaximal, characteristic
10C22×C11×#41C2212yes—
11C11×#532—28no—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×C11×#124C2212yes—
15C2×C11×#121C2214yes—
16C2×C4×D4×C11C2214yes—
17C22×C42×C11C2211yescharacteristic
18C2×#66989C2218yes—
19C2×#66979C2212yes—
20C2×#66977C2214yes—
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2214yes—
23#10623001—28no—
24C2×#66923C2212yes—
25C2×#66922C2212yes—
26C2×C4×Dic22C2214yes—
27#10622843C2218yes—
28#10622834C2218yes—
29#10622834C2218yes—
30#10622833C22116yes—
31C4×C22⋊Dic11C22116yes—
32#10622590C2218yes—
33#10622587C2218yes—
34#10622558C22132yes—
35C42×Dic11C2212yes—
36C42×Dic11C2214yes—
37C42×Dic11C2212yes—
38C2×C11×#41—28no—
39C2×C11×#41—216no—
40C22×Q8×C11C2312yes—
41C22×D4×C11C2314yes—
42C22×D4×C11C2314yes—
43C22×D4×C11C2312yes—
44C23×C4×C11C2314yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2314yes—
48C22×Dic22C2314yes—
49C11×C4⋊Q8—24no—
50C11×#127—24no—
51C11×#124—28no—
52C11×#121—216no—
53C4×D4×C11—216no—
54C2×C11×C4⋊C4C2314yes—
55C2×C11×C22⋊C4C2318yes—
56C2×C42×C11D418yes—
57C2×C42×C11C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11C2314yes—
61C2×C22⋊Dic11C23132yes—
62#66989—232no—
63#66979—28no—
64C2×C4⋊Dic11C2314yes—
65C2×C4⋊Dic11C2314yes—
66#66977—216no—
67C2×Dic11⋊C4C2318yes—
68C2×C4×Dic11—28no—
69C2×C4×Dic11—216no—
70C2×C4×Dic11C2314yes—
71C2×C4×Dic11C2318yes—
72C2×C4×Dic11C2314yes—
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C2314yes—
75C2×C4×Dic11C2314yes—
76#66923—28no—
77#66922—28no—
78C4×Dic22—216no—
79C11⋊#95C23132yes—
80#36639—111nomaximal, Sylow
81C24×C11C2414yes—
82C24×C11C2411yescharacteristic
83C11×#41—432no—
84C2×Q8×C11—24no—
85C2×Q8×C11—28no—
86C2×D4×C11—28no—
87C2×D4×C11—216no—
88C2×D4×C11—28no—
89C2×D4×C11—24no—
90C2×D4×C11—216no—
91C2×D4×C11—28no—
92C22×C4×C11—28no—
93C22×C4×C11—28no—
94C22×C4×C11—216no—
95C22×C4×C11C2×D418yes—
96C22×C4×C11C2×D414yes—
97C22×C4×C11#4118yes—
98C22×C4×C11C2414yes—
99C22×C4×C11C2412yes—
100C22×C4×C11C2411yescharacteristic
101C22×C4×C11C2412yes—
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—216no—
104C22×Dic11—28no—
105C22×Dic11C2418yes—
106C22×Dic11C2418yes—
107C2×Dic22—28no—
108C2×Dic22—216no—
109C11×C4⋊C4—28no—
110C11×C22⋊C4—216no—
111C42×C11C2×D418yes—
112C42×C11C2×D414yes—
113C42×C11C2×D414yes—
114C22⋊Dic11—264no—
115C22⋊Dic11—28no—
116C4⋊Dic11—28no—
117C4⋊Dic11—28no—
118Dic11⋊C4—216no—
119C4×Dic11—216no—
120C4×Dic11—28no—
121C4×Dic11—28no—
122C4×Dic11—28no—
123C4×Dic11—28no—
124C4×Dic11#41116yescomplemented
125C2×#533—111no—
126C2×#532D1111yescharacteristic
127#2862—112no—
128#2861—114no—
129#2858—112no—
130#2850—118no—
131C4×#124—118no—
132#2297—114no—
133C2×C43—111no—
134C23×C11—24no—
135C23×C11—24no—
136C23×C11—216no—
137C23×C11—28no—
138C23×C11C22×D412yes—
139C23×C11C2×#4114yes—
140C23×C11C2511yescharacteristic
141Q8×C11—48no—
142D4×C11—416no—
143D4×C11—48no—
144D4×C11—416no—
145C2×C4×C11—24no—
146C2×C4×C11—216no—
147C2×C4×C11—24no—
148C2×C4×C11—28no—
149C2×C4×C11—416no—
150C2×C4×C11#124116yescomplemented
151C2×C4×C11C22×D414yes—
152C2×C4×C11C22×D412yes—
153C2×C4×C11C22×D412yes—
154C2×C4×C11C22×D414yes—
155C2×C4×C11C2×#4114yes—
156C2×C4×C11C2×#4114yes—
157C2×C4×C11C2×#4118yes—
158C2×Dic11—232no—
159C2×Dic11—28no—
160C2×Dic11—28no—
161C2×Dic11—28no—
162C2×Dic11—216no—
163C2×Dic11C2×#41116yes—
164Dic22—416no—
165C22×#41C2×D1112yes—
166#533—228no—
167#532—28no—
168C2×C4⋊Q8—112no—
169C2×C4⋊Q8C2×D1111yescharacteristic
170C2×#127C2×D1111yescharacteristic
171C2×#125—112no—
172C2×#124—118no—
173C2×#124C2×D1112yes—
174C2×C22⋊Q8—114no—
175C2×#121C2×D1114yes—
176C2×C4×Q8—114no—
177C2×C4×D4C2×D1114yes—
178C2×#117—112no—
179C22×C42—114no—
180C22×C42—112no—
181C22×C42C2×D1111yescharacteristic
182#391—118no—
183#391—118no—
184#390—118no—
185#390—118no—
186#388—1132no—
187#386—1116no—
188#382—118no—
189C4×C22⋊C4—1116no—
190C43—112no—
191C43—112no—
192C43—114no—
193C22×C11—24no—
194C22×C11—28no—
195C22×C11—44no—
196C22×C11—48no—
197C22×C11—416no—
198C22×C11C2×#12414yes—
199C22×C11C23×D411yescharacteristic
200C22×C11C22×#4112yes—
201C22×C11C22×#4114yes—
202C4×C11—24no—
203C4×C11—44no—
204C4×C11C2×#12414yes—
205C4×C11C2×#12414yes—
206C4×C11#53218yes—
207Dic11—216no—
208Dic11—48no—
209C2×#41—216no—
210C2×#41—28no—
211C22×Q8—114no—
212C22×Q8C22×D1112yes—
213C22×D4C22×D1114yes—
214C22×D4C22×D1114yes—
215C22×D4C22×D1112yes—
216C23×C4—114no—
217C23×C4C22×D1114yes—
218C23×C4C22×D1112yes—
219C23×C4C22×D1111yescharacteristic
220C4⋊Q8—24no—
221C4⋊Q8—228no—
222#127—24no—
223#125—228no—
224#124—28no—
225#124—2232no—
226C22⋊Q8—2216no—
227#121—216no—
228C4×Q8—2216no—
229C4×D4—216no—
230#117—228no—
231C2×C4⋊C4—114no—
232C2×C4⋊C4—118no—
233C2×C4⋊C4—114no—
234C2×C4⋊C4C22×D1114yes—
235C2×C22⋊C4—114no—
236C2×C22⋊C4—1132no—
237C2×C22⋊C4C22×D1118yes—
238C2×C42—114no—
239C2×C42—118no—
240C2×C42—114no—
241C2×C42—114no—
242C2×C42—114no—
243C2×C42—114no—
244C2×C42—2216no—
245C2×C42—228no—
246C2×C42C22⋊D1118yes—
247C2×C42C22×D1111yescharacteristic
248C2×C42C22×D1111yescharacteristic
249C2×C42C22×D1112yes—
250#95—1132no—
251C2×C11—24no—
252C2×C11—84no—
253C2×C11C22×#12411yescharacteristic
254C2×C11C2×#53212yes—
255C2×C11#344414yes—
256C24C23×D1114yes—
257C24C23×D1111yescharacteristic
258#41—432no—
259C2×Q8—28no—
260C2×Q8—24no—
261C2×Q8—2216no—
262C2×Q8—228no—
263C2×D4—216no—
264C2×D4—28no—
265C2×D4—28no—
266C2×D4—216no—
267C2×D4—28no—
268C2×D4—24no—
269C22×C4—28no—
270C22×C4—216no—
271C22×C4—28no—
272C22×C4—118no—
273C22×C4—118no—
274C22×C4—2216no—
275C22×C4—228no—
276C22×C4#434118yes—
277C22×C4C2×C22⋊D1118yes—
278C22×C4C2×C22⋊D1114yes—
279C22×C4C23×D1114yes—
280C22×C4C23×D1112yes—
281C22×C4C23×D1111yescharacteristic
282C22×C4C23×D1112yes—
283C22×C4C23×D1111yescharacteristic
284C4⋊C4—28no—
285C4⋊C4—228no—
286C4⋊C4—2216no—
287C4⋊C4—228no—
288C22⋊C4—216no—
289C22⋊C4—2264no—
290C22⋊C4—228no—
291C42—1116no—
292C42—2216no—
293C42—228no—
294C42—228no—
295C42—228no—
296C42—228no—
297C42C2×C22⋊D1118yes—
298C42C2×C22⋊D1114yes—
299C42C2×C22⋊D1114yes—
300C11#3663911yescharacteristic, complemented, Sylow
301C23—24no—
302C23—28no—
303C23—216no—
304C23—24no—
305C23C2×#434114yes—
306C23C22×C22⋊D1112yes—
307C23C24×D1111yescharacteristic
308Q8—48no—
309Q8—4416no—
310D4—416no—
311D4—48no—
312D4—416no—
313C2×C4—24no—
314C2×C4—216no—
315C2×C4—28no—
316C2×C4—24no—
317C2×C4—416no—
318C2×C4—1116no—
319C2×C4—2232no—
320C2×C4—228no—
321C2×C4—228no—
322C2×C4—2216no—
323C2×C4—228no—
324C2×C4#66989116yescomplemented
325C2×C4C2×#434114yes—
326C2×C4C2×#434114yes—
327C2×C4#41×D1118yes—
328C2×C4C22×C22⋊D1114yes—
329C2×C4C22×C22⋊D1112yes—
330C2×C4C22×C22⋊D1112yes—
331C2×C4C22×C22⋊D1114yes—
332C22—24no—
333C22—28no—
334C22—44no—
335C22—48no—
336C22—416no—
337C22C2×#6698914yes—
338C22C22×#434112yes—
339C22C2×#41×D1114yes—
340C22C23×C22⋊D1111yescharacteristic
341C4—24no—
342C4—44no—
343C4—2216no—
344C4—448no—
345C4C2×#6698914yes—
346C4C2×#6698914yes—
347C4#1062336318yes—
348C2—24no—
349C2—84no—
350C2C22×#6698911yescharacteristic
351C2C2×#1062336312yes—
352C2#1308191114yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC2×C11×#532C2
hypercenterC2×#532D11
hypocenterC11#36639
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. #13076993C2semidirect
3. #13076986C2semidirect
4. #13076972C2semidirect
5. #13076915C2semidirect
6. C4×#66989C2semidirect
7. #13071107C2semidirect
8. C2×C42×Dic11C2semidirect
124. C4×Dic11#41semidirect
150. C2×C4×C11#124semidirect
300. C11#36639semidirect
324. C2×C4#66989semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130769932
#130769862
#130769722
#130769152
C4×#669892
#130711072
C2×C42×Dic112
C2×C11×#5322
#3663911