Finite Group Databasebeta

← #14669296

Subgroups — #14669296

Order 2816.

962 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 962 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622186C214yesmaximal, complemented
2#13068544C212yesmaximal
3C2×C11×#536C211yesmaximal, characteristic
4C22×C11×#41C2211yescharacteristic
5C23×Q8×C11C411yescharacteristic
6C11×#536—28no—
7C2×C11×C4⋊Q8C2212yes—
8C2×C11×#124C412yes—
9C2×C11×#123—22no—
10C2×C11×C22⋊Q8—22no—
11C2×C11×#117C411yescharacteristic
12C2×#66900C2214yes—
13C2×#66897—22no—
14#10622820—22no—
15#10622186—28no—
16C2×C11×#41—24no—
17C2×C11×#41—42no—
18C2×C11×#41—42no—
19C22×Q8×C11—24no—
20C22×Q8×C11—21no—
21C22×Q8×C11—42no—
22C22×Q8×C11—42no—
23C22×Q8×C11C2×C412yes—
24C22×Q8×C11C2311yescharacteristic
25C22×D4×C11C2×C411yescharacteristic
26C22×D4×C11D412yes—
27C23×C4×C11—21no—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D412yes—
30C11×C4⋊Q8—24no—
31C11×C4⋊Q8D418yes—
32C11×#124—24no—
33C11×#124—24no—
34C11×#123—216no—
35C11×C22⋊Q8—216no—
36C11×#117—24no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—24no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—24no—
41C2×C42×C11C2×C412yes—
42C2×#4318—24no—
43#66900—28no—
44#66897—44no—
45C22⋊(C11⋊C8)—44no—
46#12704—111nomaximal, Sylow
47C24×C11C22⋊C412yes—
48C24×C11C22⋊C411yescharacteristic
49C11×#41—416no—
50C2×Q8×C11—24no—
51C2×Q8×C11—22no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11—416no—
55C2×Q8×C11—42no—
56C2×Q8×C11—42no—
57C2×Q8×C11—42no—
58C2×Q8×C11—42no—
59C2×Q8×C11C22⋊C414yes—
60C2×Q8×C11C2×D414yes—
61C2×D4×C11—24no—
62C2×D4×C11—22no—
63C2×D4×C11—24no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—42no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D412yes—
81C11×C4⋊C4—24no—
82C11×C4⋊C4—216no—
83C11×C22⋊C4—24no—
84C11×C22⋊C4—216no—
85C42×C11—22no—
86C42×C11C22⋊C414yes—
87#4318—44no—
88#4318—44no—
89C2×C11⋊C8—44no—
90C2×#536D1111yescharacteristic
91C2×#356—114no—
92#1785—112no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—22no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—42no—
99C23×C11—44no—
100C23×C11#9912yes—
101C23×C11C2×C22⋊C411yescharacteristic
102Q8×C11—44no—
103Q8×C11—44no—
104Q8×C11—48no—
105Q8×C11—44no—
106D4×C11—48no—
107D4×C11—44no—
108C2×C4×C11—28no—
109C2×C4×C11—21no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—24no—
116C2×C4×C11—24no—
117C2×C4×C11—48no—
118C2×C4×C11—44no—
119C2×C4×C11—48no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11#9912yes—
123C2×C4×C11C2×C22⋊C412yes—
124C2×C4×C11#12014yes—
125C11⋊C8—84no—
126C22×#41C2×D1111yescharacteristic
127C23×Q8Dic1111yescharacteristic
128#536—28no—
129C2×C4⋊Q8C2×D1112yes—
130C2×#124Dic1112yes—
131C2×#123—22no—
132C2×C22⋊Q8—22no—
133C2×#117Dic1111yescharacteristic
134C2×#101—114no—
135C2×#100—222no—
136#407—222no—
137#356—228no—
138C22×C11—22no—
139C22×C11—22no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11—44no—
143C22×C11—42no—
144C22×C11—44no—
145C22×C11—42no—
146C22×C11—82no—
147C22×C11#37911yescharacteristic
148C22×C11C2×#9911yescharacteristic
149C22×C11C2×#9911yescharacteristic
150C4×C11—22no—
151C4×C11—22no—
152C4×C11—24no—
153C4×C11—44no—
154C4×C11—44no—
155C2×#41—24no—
156C2×#41—42no—
157C2×#41—42no—
158C22×Q8—24no—
159C22×Q8—21no—
160C22×Q8—42no—
161C22×Q8—42no—
162C22×Q8C2×Dic1112yes—
163C22×Q8C22×D1111yescharacteristic
164C22×D4C2×Dic1111yescharacteristic
165C22×D4C22⋊D1112yes—
166C23×C4—21no—
167C23×C4C2×Dic1111yescharacteristic
168C23×C4C22⋊D1112yes—
169C2×M16—224no—
170C4⋊Q8—24no—
171C4⋊Q8C22⋊D1118yes—
172#124—24no—
173#124—24no—
174#123—216no—
175C22⋊Q8—216no—
176#117—24no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—24no—
179C2×C22⋊C4—21no—
180C2×C22⋊C4—24no—
181C2×C42C2×Dic1112yes—
182#101—228no—
183#100—444no—
184C22⋊C8—444no—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11—42no—
188C2×C11—82no—
189C2×C11#178111yescharacteristic
190C2×C11#213512yes—
191C24C22⋊Dic1112yes—
192C24C22⋊Dic1111yescharacteristic
193#41—416no—
194C2×Q8—24no—
195C2×Q8—22no—
196C2×Q8—41no—
197C2×Q8—41no—
198C2×Q8—416no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8C22⋊Dic1114yes—
204C2×Q8C2×C22⋊D1114yes—
205C2×D4—24no—
206C2×D4—22no—
207C2×D4—24no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—42no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4C22⋊Dic1111yescharacteristic
223C22×C4C22×Dic1111yescharacteristic
224C22×C4C2×C22⋊D1112yes—
225M16—444no—
226M16—444no—
227C2×C8—444no—
228C4⋊C4—24no—
229C4⋊C4—216no—
230C22⋊C4—24no—
231C22⋊C4—216no—
232C42—22no—
233C42C22⋊Dic1114yes—
234C11#1270411yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—42no—
241C23—44no—
242C23#6689812yes—
243C23C2×C22⋊Dic1111yescharacteristic
244Q8—44no—
245Q8—44no—
246Q8—48no—
247Q8—44no—
248D4—48no—
249D4—44no—
250C2×C4—28no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—48no—
260C2×C4—44no—
261C2×C4—48no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4#6689812yes—
265C2×C4C2×C22⋊Dic1112yes—
266C2×C4#6700614yes—
267C8—884no—
268C22—22no—
269C22—22no—
270C22—42no—
271C22—42no—
272C22—44no—
273C22—42no—
274C22—44no—
275C22—42no—
276C22—82no—
277C22C2×#6689811yescharacteristic
278C22C2×#6689811yescharacteristic
279C22#1062286011yescharacteristic
280C4—24no—
281C4—22no—
282C4—22no—
283C4—44no—
284C4—44no—
285C2—21no—
286C2—21no—
287C2—42no—
288C2—82no—
289C2#1306853111yescharacteristic
290C2#1307031112yes—
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC2×C11×#536C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C22
cosocleC22×Q8×C11C23
hypercenterC2×#536D11
hypocenterC11#12704
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#10622186C2semidirect
234. C11#12704semidirect

Maximal subgroups

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

subgroupindex
C2×#106221862
#130685442
C2×C11×#5362
#1270411