Finite Group Databasebeta

← #14669293

Subgroups — #14669293

Order 2816.

1154 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1154 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×#10622180C214yesmaximal, complemented
2#13068544C212yesmaximal, complemented
3C2×C11×#535C211yesmaximal, characteristic
4C22×C11×#41C2211yescharacteristic
5C23×D4×C11C411yescharacteristic
6C11×#535—28no—
7C2×C11×#127C412yes—
8C2×C11×#124C2212yes—
9C2×C11×#121—22no—
10C2×C11×#120—22no—
11C2×C11×#117C411yescharacteristic
12C2×#66900C2214yescomplemented
13C2×#66897—22no—
14#10622820—22no—
15#10622180—28no—
16C25×C11—21no—
17C2×C11×#41—24no—
18C2×C11×#41—42no—
19C2×C11×#41—42no—
20C22×Q8×C11C2311yescharacteristic
21C22×D4×C11—24no—
22C22×D4×C11—24no—
23C22×D4×C11—21no—
24C22×D4×C11—42no—
25C22×D4×C11—42no—
26C22×D4×C11C2×C411yescharacteristic
27C22×D4×C11C2×C412yes—
28C22×D4×C11D412yes—
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11D412yes—
31C11×#127—24no—
32C11×#127—24no—
33C11×#124—24no—
34C11×#124D418yes—
35C11×#121—216no—
36C11×#120—216no—
37C11×#117—24no—
38C2×C11×C4⋊C4—21no—
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#12703—111nomaximal, Sylow
47C24×C11—24no—
48C24×C11—22no—
49C24×C11—42no—
50C24×C11—42no—
51C24×C11—84no—
52C24×C11C22⋊C412yes—
53C24×C11C22⋊C411yescharacteristic
54C11×#41—416no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11C2×D414yes—
58C2×D4×C11—24no—
59C2×D4×C11—24no—
60C2×D4×C11—216no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—24no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—42no—
67C2×D4×C11—416no—
68C2×D4×C11—42no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—88no—
73C2×D4×C11C22⋊C414yes—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—42no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D412yes—
84C11×C4⋊C4—24no—
85C11×C22⋊C4—24no—
86C11×C22⋊C4—216no—
87C42×C11—22no—
88C42×C11C22⋊C414yes—
89#4318—44no—
90#4318—44no—
91C2×C11⋊C8—44no—
92C2×#535D1111yescharacteristic
93C2×#355—114no—
94#1785—112no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—24no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—42no—
102C23×C11—44no—
103C23×C11—48no—
104C23×C11—48no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11—88no—
108C23×C11—88no—
109C23×C11—88no—
110C23×C11#9912yes—
111C23×C11C2×C22⋊C411yescharacteristic
112Q8×C11—44no—
113D4×C11—48no—
114D4×C11—44no—
115D4×C11—48no—
116D4×C11—44no—
117D4×C11—44no—
118D4×C11—816no—
119C2×C4×C11—28no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—24no—
127C2×C4×C11—48no—
128C2×C4×C11—44no—
129C2×C4×C11#9912yes—
130C2×C4×C11C2×C22⋊C412yes—
131C2×C4×C11#12014yes—
132C11⋊C8—84no—
133C22×#41C2×D1111yescharacteristic
134C23×D4Dic1111yescharacteristic
135#535—28no—
136C2×#127Dic1112yes—
137C2×#124C2×D1112yes—
138C2×#121—22no—
139C2×#120—22no—
140C2×#117Dic1111yescharacteristic
141C2×#101—114no—
142C2×#100—222no—
143#407—222no—
144#355—228no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—42no—
148C22×C11—42no—
149C22×C11—44no—
150C22×C11—48no—
151C22×C11—42no—
152C22×C11—44no—
153C22×C11—42no—
154C22×C11—44no—
155C22×C11—82no—
156C22×C11—84no—
157C22×C11—816no—
158C22×C11—84no—
159C22×C11#37911yescharacteristic
160C22×C11C2×#9911yescharacteristic
161C22×C11C2×#9911yescharacteristic
162C4×C11—22no—
163C4×C11—22no—
164C4×C11—24no—
165C4×C11—44no—
166C25—21no—
167C2×#41—24no—
168C2×#41—42no—
169C2×#41—42no—
170C22×Q8C22×D1111yescharacteristic
171C22×D4—24no—
172C22×D4—24no—
173C22×D4—21no—
174C22×D4—42no—
175C22×D4—42no—
176C22×D4C2×Dic1111yescharacteristic
177C22×D4C2×Dic1112yes—
178C22×D4C22⋊D1112yes—
179C23×C4C2×Dic1111yescharacteristic
180C23×C4C22⋊D1112yes—
181C2×M16—224no—
182#127—24no—
183#127—24no—
184#124—24no—
185#124C22⋊D1118yes—
186#121—216no—
187#120—216no—
188#117—24no—
189C2×C4⋊C4—21no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4—24no—
192C2×C42C2×Dic1112yes—
193#101—228no—
194#100—444no—
195C22⋊C8—444no—
196C2×C11—21no—
197C2×C11—21no—
198C2×C11—42no—
199C2×C11—82no—
200C2×C11—84no—
201C2×C11#178111yescharacteristic
202C2×C11#213412yes—
203C24—24no—
204C24—22no—
205C24—42no—
206C24—42no—
207C24—84no—
208C24C22⋊Dic1112yes—
209C24C22⋊Dic1111yescharacteristic
210#41—416no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8C2×C22⋊D1114yes—
214C2×D4—24no—
215C2×D4—24no—
216C2×D4—216no—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—24no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—42no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—416no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—88no—
229C2×D4C22⋊Dic1114yes—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—42no—
237C22×C4C22⋊Dic1111yescharacteristic
238C22×C4C22×Dic1111yescharacteristic
239C22×C4C2×C22⋊D1112yes—
240M16—444no—
241M16—444no—
242C2×C8—444no—
243C4⋊C4—24no—
244C22⋊C4—24no—
245C22⋊C4—216no—
246C42—22no—
247C42C22⋊Dic1114yes—
248C11#1270311yescharacteristic, complemented, Sylow
249C23—21no—
250C23—21no—
251C23—22no—
252C23—24no—
253C23—22no—
254C23—22no—
255C23—42no—
256C23—44no—
257C23—48no—
258C23—48no—
259C23—42no—
260C23—42no—
261C23—88no—
262C23—88no—
263C23—88no—
264C23#6689812yes—
265C23C2×C22⋊Dic1111yescharacteristic
266Q8—44no—
267D4—48no—
268D4—44no—
269D4—48no—
270D4—44no—
271D4—44no—
272D4—816no—
273C2×C4—28no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—24no—
281C2×C4—48no—
282C2×C4—44no—
283C2×C4#6689812yes—
284C2×C4C2×C22⋊Dic1112yes—
285C2×C4#6700614yes—
286C8—884no—
287C22—22no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—44no—
292C22—48no—
293C22—42no—
294C22—44no—
295C22—42no—
296C22—44no—
297C22—82no—
298C22—84no—
299C22—816no—
300C22—84no—
301C22C2×#6689811yescharacteristic
302C22C2×#6689811yescharacteristic
303C22#1062286011yescharacteristic
304C4—24no—
305C4—22no—
306C4—22no—
307C4—44no—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—82no—
312C2—84no—
313C2#1306853111yescharacteristic
314C2#1307030812yes—
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
Fitting, prime radicalC2×C11×#535C2
socleC22×C11C2×#99
cosocleC22×Q8×C11C23
hypercenterC2×#535D11
hypocenterC11#12703
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#10622180C2semidirect
2. #13068544C2semidirect
12. C2×#66900C22semidirect
248. C11#12703semidirect

Maximal subgroups

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

subgroupindex
C2×#106221802
#130685442
C2×C11×#5352
#1270311