Finite Group Databasebeta

← #14913910

Subgroups — #14913910

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071581C218yesmaximal, complemented
2#13071573C218yesmaximal, complemented
3#13071219C214yesmaximal
4#13071202C212yesmaximal
5#13071023C212yesmaximal
6#13071014C214yesmaximal
7#13070973C212yesmaximal
8C22×C4×Q8×C11C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C2×C4×Q8×C11C4116yescomplemented
11C2×C4×Q8×C11C2214yes—
12C2×C4×Q8×C11C2214yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2212yes—
16C22×C42×C11C2211yescharacteristic
17C2×#66979C2214yes—
18#10622843C22116yes—
19#10622825C2214yes—
20#10622825C2214yes—
21#10622824C2218yes—
22C4×C22⋊Dic11C2218yes—
23#10622594C22132yes—
24C4⋊C4×Dic11C22116yes—
25#10622550C2218yes—
26#10622549C2218yes—
27#10622549C2214yes—
28#10622548C2214yes—
29C4×C4⋊Dic11C2218yes—
30C4×C4⋊Dic11C2214yes—
31C4×C4⋊Dic11C2214yes—
32#10622545C2218yes—
33C22×Q8×C11—28no—
34C22×Q8×C11C2×C418yes—
35C22×Q8×C11C2314yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C4×Q8×C11C2×C4132yes—
42C4×Q8×C11C2×C4132yes—
43C2×C11×C4⋊C4C2×C4116yes—
44C2×C11×C4⋊C4C2×C418yes—
45C2×C11×C4⋊C4C2314yes—
46C2×C11×C4⋊C4C2318yes—
47C2×C42×C11C2×C4116yes—
48C2×C42×C11C2×C418yes—
49C2×C42×C11C2314yes—
50C2×C42×C11C2312yes—
51C2×C42×C11C2312yes—
52C2×C42×C11C2314yes—
53C2×C22⋊Dic11C2318yes—
54#66979—216no—
55C2×C4⋊Dic11C2318yes—
56C2×C4⋊Dic11C2318yes—
57C2×C4⋊Dic11C2318yes—
58C2×C4×Dic11C2318yes—
59C2×C4×Dic11C23116yes—
60C11⋊#95C2318yes—
61C11⋊#95C23116yes—
62C11⋊#95C2318yes—
63C11⋊#95C23116yes—
64C11⋊#95C23116yes—
65#34187—111nomaximal, Sylow
66C24×C11C2411yescharacteristic
67C2×Q8×C11—232no—
68C2×Q8×C11—28no—
69C2×Q8×C11—28no—
70C2×Q8×C11C22×C4116yes—
71C22×C4×C11—28no—
72C22×C4×C11—24no—
73C22×C4×C11—44no—
74C22×C4×C11—42no—
75C22×C4×C11C22×C414yes—
76C22×C4×C11C22×C418yes—
77C22×C4×C11C22×C418yes—
78C22×C4×C11C22×C414yes—
79C22×C4×C11C22×C414yes—
80C22×C4×C11#4118yes—
81C22×C4×C11C2411yescharacteristic
82C22×C4×C11C2414yes—
83C22×C4×C11C2414yes—
84C22×C4×C11C2412yes—
85C22×C4×C11C2412yes—
86C22×C4×C11C2411yescharacteristic
87C22×Dic11C24116yes—
88C11×C4⋊C4C22×C4132yes—
89C11×C4⋊C4C22×C4116yes—
90C42×C11C22×C4116yes—
91C42×C11C22×C418yes—
92C42×C11C22×C4116yes—
93C42×C11C22×C418yes—
94C22⋊Dic11—216no—
95C4⋊Dic11—216no—
96C4⋊Dic11—216no—
97C4⋊Dic11—48no—
98C4×Dic11—216no—
99C4×Dic11—416no—
100C22×C4×Q8D1111yescharacteristic
101#2356—118no—
102#2355—118no—
103#2313—114no—
104#2310—112no—
105#2285—112no—
106#2283—114no—
107#2274—112no—
108C23×C11—22no—
109C23×C11—22no—
110C23×C11C23×C412yes—
111C23×C11C2×#4114yes—
112C23×C11C2511yescharacteristic
113Q8×C11—232no—
114C2×C4×C11—216no—
115C2×C4×C11—28no—
116C2×C4×C11—22no—
117C2×C4×C11—28no—
118C2×C4×C11—24no—
119C2×C4×C11—28no—
120C2×C4×C11—48no—
121C2×C4×C11—44no—
122C2×C4×C11#117116yes—
123C2×C4×C11C23×C412yes—
124C2×C4×C11C23×C418yes—
125C2×C4×C11C23×C414yes—
126C2×C4×C11C23×C418yes—
127C2×C4×C11C23×C414yes—
128C2×C4×C11C23×C412yes—
129C2×C4×C11C2×#4114yes—
130C2×C4×C11C2×#4114yes—
131C2×C4×C112−1+414yes—
132C2×Dic11—216no—
133C2×Dic11—216no—
134C2×Dic11—216no—
135C23×Q8C2×D1111yescharacteristic
136C2×C4×Q8Dic11116yescomplemented
137C2×C4×Q8C2×D1114yes—
138C2×C4×Q8C2×D1114yes—
139C2×#117—114no—
140C22×C4⋊C4C2×D1112yes—
141C22×C4⋊C4C2×D1111yescharacteristic
142C22×C42C2×D1112yes—
143C22×C42C2×D1111yescharacteristic
144#391—1116no—
145#387—1132no—
146#384—114no—
147#383—118no—
148#382—118no—
149#382—114no—
150#381—118no—
151#380—114no—
152#380—114no—
153C4×C4⋊C4—1116no—
154C4×C4⋊C4—118no—
155C4×C4⋊C4—114no—
156C4×C4⋊C4—114no—
157C4×C22⋊C4—118no—
158#376—118no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—28no—
162C22×C11C2×#11714yes—
163C22×C11C24×C411yescharacteristic
164C22×C11C22×#4112yes—
165C22×C11C2×2−1+412yes—
166C22×C11#58512yes—
167C4×C11—28no—
168C4×C11—22no—
169C4×C11—28no—
170C4×C11—24no—
171C4×C11C2×#11718yes—
172C4×C11#51914yes—
173Dic11—416no—
174C22×Q8—28no—
175C22×Q8C2×Dic1118yes—
176C22×Q8C22×D1114yes—
177C23×C4C22×D1112yes—
178C23×C4C22×D1111yescharacteristic
179C23×C4C22×D1112yes—
180C23×C4C22×D1111yescharacteristic
181C23×C4C22×D1111yescharacteristic
182C4×Q8C2×Dic11132yes—
183C4×Q8C2×Dic11132yes—
184#117—2216no—
185C2×C4⋊C4—118no—
186C2×C4⋊C4—118no—
187C2×C4⋊C4—118no—
188C2×C4⋊C4C2×Dic11116yes—
189C2×C4⋊C4C2×Dic1118yes—
190C2×C4⋊C4C22×D1114yes—
191C2×C4⋊C4C22×D1118yes—
192C2×C22⋊C4—118no—
193C2×C42—118no—
194C2×C42—1116no—
195C2×C42C2×Dic11116yes—
196C2×C42C2×Dic1118yes—
197C2×C42C22×D1114yes—
198C2×C42C22×D1112yes—
199C2×C42C22×D1114yes—
200C2×C42C22×D1112yes—
201#95—118no—
202#95—1116no—
203#95—1116no—
204#95—118no—
205#95—1116no—
206C2×C11—24no—
207C2×C11C22×#11711yescharacteristic
208C2×C11C2×#51911yescharacteristic
209C2×C11#342811yescharacteristic
210C2×C11#350714yes—
211C24C23×D1111yescharacteristic
212C2×Q8—232no—
213C2×Q8—28no—
214C2×Q8—28no—
215C2×Q8C22×Dic11116yes—
216C22×C4—28no—
217C22×C4—24no—
218C22×C4—44no—
219C22×C4—42no—
220C22×C4—1116no—
221C22×C4#433918yes—
222C22×C4C22×Dic1114yes—
223C22×C4C22×Dic1118yes—
224C22×C4C22×Dic1118yes—
225C22×C4C22×Dic1114yes—
226C22×C4C22×Dic1114yes—
227C22×C4C23×D1111yescharacteristic
228C22×C4C23×D1114yes—
229C22×C4C23×D1114yes—
230C22×C4C23×D1112yes—
231C22×C4C23×D1112yes—
232C22×C4C23×D1111yescharacteristic
233C4⋊C4—2216no—
234C4⋊C4—2216no—
235C4⋊C4—448no—
236C4⋊C4C22×Dic11132yes—
237C4⋊C4C22×Dic11116yes—
238C22⋊C4—2216no—
239C42—2216no—
240C42—4416no—
241C42C22×Dic11116yes—
242C42C22×Dic1118yes—
243C42C22×Dic11116yes—
244C42C22×Dic1118yes—
245C11#3418711yescharacteristic, complemented, Sylow
246C23—22no—
247C23—22no—
248C23C2×#433914yes—
249C23C23×Dic1112yes—
250C23C24×D1111yescharacteristic
251Q8—232no—
252C2×C4—216no—
253C2×C4—28no—
254C2×C4—22no—
255C2×C4—28no—
256C2×C4—24no—
257C2×C4—28no—
258C2×C4—48no—
259C2×C4—44no—
260C2×C4—2216no—
261C2×C4—2216no—
262C2×C4—2216no—
263C2×C4#66979116yes—
264C2×C4C2×#433914yes—
265C2×C4C2×#433914yes—
266C2×C4#6704014yes—
267C2×C4C23×Dic1112yes—
268C2×C4C23×Dic1118yes—
269C2×C4C23×Dic1114yes—
270C2×C4C23×Dic1118yes—
271C2×C4C23×Dic1114yes—
272C2×C4C23×Dic1112yes—
273C22—28no—
274C22—22no—
275C22—22no—
276C22C2×#6697914yes—
277C22C22×#433912yes—
278C22C2×#6704012yes—
279C22#1062345312yes—
280C22C24×Dic1111yescharacteristic
281C4—28no—
282C4—22no—
283C4—28no—
284C4—24no—
285C4—4416no—
286C4C2×#6697918yes—
287C4#1062334314yes—
288C2—24no—
289C2C22×#6697911yescharacteristic
290C2C2×#1062334311yescharacteristic
291C2#1308181911yescharacteristic
292C2#1308248114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC22×C4×Q8×C11C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11#34187
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #13071581C2semidirect
2. #13071573C2semidirect
10. C2×C4×Q8×C11C4semidirect
136. C2×C4×Q8Dic11semidirect
245. C11#34187semidirect

Maximal subgroups

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

subgroupindex
#130715812
#130715732
#130712192
#130712022
#130710232
#130710142
#130709732
C22×C4×Q8×C112
#3418711