Finite Group Databasebeta

← #14669316

Subgroups — #14669316

Order 2816.

952 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 952 conjugacy classes of subgroups — too many to draw. Only its 135 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
1#13070305C214yesmaximal, complemented
2#13068540C212yesmaximal, complemented
3C11×#3486C211yesmaximal, characteristic
4C2×C11×2−1+4C411yescharacteristic
5C23×Q8×C11C2211yescharacteristic
6D4×Q8×C11—24no—
7C11×#548—24no—
8C11×#536—22no—
9C11×#536C2212yes—
10C11×#525—22no—
11C11×#525C412yes—
12C11×#519C411yescharacteristic
13C2×#66900—22no—
14C2×#66900C2214yes—
15#10622820—22no—
16#10622186—24no—
17#10622180—24no—
18C11×2−1+4—44no—
19C2×C11×#41—22no—
20C2×C11×#41—22no—
21C2×C11×#41C2×C412yes—
22C22×Q8×C11—22no—
23C22×Q8×C11—24no—
24C22×Q8×C11—44no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×Q8×C11D412yes—
27C22×Q8×C11C2311yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D412yes—
30C11×C4⋊Q8—24no—
31C11×C4⋊Q8D414yes—
32C11×#124—24no—
33C11×#124D414yes—
34C11×#123—22no—
35C11×#123—24no—
36C11×C22⋊Q8—24no—
37C11×C22⋊Q8—28no—
38C11×C22⋊Q8—22no—
39C11×C22⋊Q8—24no—
40C11×#121—24no—
41C11×#121—22no—
42C11×#120—22no—
43C4×Q8×C11—24no—
44C4×D4×C11—28no—
45C4×D4×C11—24no—
46C11×#117—22no—
47C11×#117C2×C412yes—
48C2×#4318—24no—
49#66900—28no—
50#66900—44no—
51C22⋊(C11⋊C8)—44no—
52#12710—111nomaximal, Sylow
53C24×C11C22⋊C411yescharacteristic
54C11×#41—44no—
55C11×#41—44no—
56C11×#41—48no—
57C11×#41—44no—
58C2×Q8×C11—22no—
59C2×Q8×C11—24no—
60C2×Q8×C11—24no—
61C2×Q8×C11—22no—
62C2×Q8×C11—24no—
63C2×Q8×C11—42no—
64C2×Q8×C11—42no—
65C2×Q8×C11—416no—
66C2×Q8×C11—48no—
67C2×Q8×C11C22⋊C412yes—
68C2×Q8×C11C2×D414yes—
69C2×D4×C11—24no—
70C2×D4×C11—22no—
71C2×D4×C11—22no—
72C2×D4×C11C22⋊C412yes—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—24no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C412yes—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D412yes—
84C11×C4⋊C4—24no—
85C11×C4⋊C4—24no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—28no—
88C11×C22⋊C4—24no—
89C11×C22⋊C4—24no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—28no—
92C42×C11—24no—
93C42×C11C22⋊C414yes—
94#4318—44no—
95#4318—44no—
96C2×C11⋊C8—44no—
97#3486D1111yescharacteristic
98#2133—114no—
99#1784—112no—
100C23×C11—21no—
101C23×C11—22no—
102C23×C11—22no—
103C23×C11—42no—
104C23×C11C2×C22⋊C411yescharacteristic
105Q8×C11—28no—
106Q8×C11—44no—
107Q8×C11—48no—
108Q8×C11—42no—
109Q8×C11—44no—
110D4×C11—42no—
111D4×C11—44no—
112D4×C11—48no—
113D4×C11—44no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—24no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—48no—
124C2×C4×C11—44no—
125C2×C4×C11—48no—
126C2×C4×C11—44no—
127C2×C4×C11#9914yes—
128C2×C4×C11C2×C22⋊C412yes—
129C2×C4×C11#12014yes—
130C11⋊C8—84no—
131C2×2−1+4Dic1111yescharacteristic
132C23×Q8C2×D1111yescharacteristic
133D4×Q8—24no—
134#548—24no—
135#536—22no—
136#536C2×D1112yes—
137#525—22no—
138#525Dic1112yes—
139#519Dic1111yescharacteristic
140C2×#101—114no—
141C2×#101—222no—
142#407—222no—
143#356—224no—
144#355—224no—
145C22×C11—22no—
146C22×C11—24no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11—42no—
150C22×C11—44no—
151C22×C11—41no—
152C22×C11—42no—
153C22×C11#37911yescharacteristic
154C22×C11C2×#9912yes—
155C4×C11—24no—
156C4×C11—22no—
157C4×C11—24no—
158C4×C11—44no—
159C4×C11—41no—
160C4×C11—42no—
1612−1+4—44no—
162C2×#41—22no—
163C2×#41—22no—
164C2×#41C2×Dic1112yes—
165C22×Q8—22no—
166C22×Q8—24no—
167C22×Q8—44no—
168C22×Q8C2×Dic1111yescharacteristic
169C22×Q8C22⋊D1112yes—
170C22×Q8C22×D1111yescharacteristic
171C23×C4C2×Dic1111yescharacteristic
172C23×C4C22⋊D1112yes—
173C2×M16—224no—
174C4⋊Q8—24no—
175C4⋊Q8C22⋊D1114yes—
176#124—24no—
177#124C22⋊D1114yes—
178#123—22no—
179#123—24no—
180C22⋊Q8—24no—
181C22⋊Q8—28no—
182C22⋊Q8—22no—
183C22⋊Q8—24no—
184#121—24no—
185#121—22no—
186#120—22no—
187C4×Q8—24no—
188C4×D4—28no—
189C4×D4—24no—
190#117—22no—
191#117C2×Dic1112yes—
192#101—228no—
193#101—444no—
194C22⋊C8—444no—
195C2×C11—21no—
196C2×C11—22no—
197C2×C11—42no—
198C2×C11—82no—
199C2×C11#178111yescharacteristic
200C24C22⋊Dic1111yescharacteristic
201#41—44no—
202#41—44no—
203#41—48no—
204#41—44no—
205C2×Q8—22no—
206C2×Q8—24no—
207C2×Q8—24no—
208C2×Q8—22no—
209C2×Q8—24no—
210C2×Q8—42no—
211C2×Q8—42no—
212C2×Q8—416no—
213C2×Q8—48no—
214C2×Q8C22⋊Dic1112yes—
215C2×Q8C2×C22⋊D1114yes—
216C2×D4—24no—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4C22⋊Dic1112yes—
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4C22⋊Dic1111yescharacteristic
228C22×C4C22⋊Dic1112yes—
229C22×C4C22×Dic1111yescharacteristic
230C22×C4C2×C22⋊D1112yes—
231M16—444no—
232M16—444no—
233C2×C8—444no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—22no—
237C4⋊C4—28no—
238C22⋊C4—24no—
239C22⋊C4—24no—
240C22⋊C4—22no—
241C22⋊C4—28no—
242C42—24no—
243C42C22⋊Dic1114yes—
244C11#1271011yescharacteristic, complemented, Sylow
245C23—22no—
246C23—21no—
247C23—22no—
248C23—42no—
249C23C2×C22⋊Dic1111yescharacteristic
250Q8—28no—
251Q8—44no—
252Q8—48no—
253Q8—42no—
254Q8—44no—
255D4—42no—
256D4—44no—
257D4—48no—
258D4—44no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—48no—
269C2×C4—44no—
270C2×C4—48no—
271C2×C4—44no—
272C2×C4#6689814yes—
273C2×C4C2×C22⋊Dic1112yes—
274C2×C4#6700614yes—
275C8—884no—
276C22—22no—
277C22—24no—
278C22—41no—
279C22—41no—
280C22—42no—
281C22—44no—
282C22—41no—
283C22—42no—
284C22C2×#6689812yes—
285C22#1062286011yescharacteristic
286C4—24no—
287C4—24no—
288C4—22no—
289C4—44no—
290C4—41no—
291C4—42no—
292C2—21no—
293C2—22no—
294C2—42no—
295C2—82no—
296C2#1306853111yescharacteristic
subgroupG/H
centerC2#13068531
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
Fitting, prime radicalC11×#3486C2
socleC2×C11#1781
cosocleC22×Q8×C11C23
hypercenter#3486D11
hypocenterC11#12710
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C23×Q8 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #13070305C2semidirect
2. #13068540C2semidirect
244. C11#12710semidirect

Maximal subgroups

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

subgroupindex
#130703052
#130685402
C11×#34862
#1271011