Finite Group Databasebeta

← #14735636

Subgroups — #14735636

Order 2816.

840 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 171 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#13079830C212yesmaximal, complemented
2#13078961C211yesmaximal, characteristic
3#13067950C218yesmaximal, complemented
4#13067251C211yesmaximal, characteristic
5#13067231C212yesmaximal, complemented
6C11×#3550C211yesmaximal, characteristic
7C11×#563C2214yes—
8C11×#559—21no—
9Q82×C11—21no—
10C11×#556—22no—
11D4×Q8×C11—22no—
12C11×#542—24no—
13C11×#536—22no—
14C11×#533C2212yes—
15C11×#532C2211yescharacteristic
16#10623001C2211yescharacteristic
17#10622846—22no—
18#10622707—22no—
19#10622704—22no—
20#10622695—21no—
21#10622684—21no—
22#10622682C2214yes—
23#10622678C2214yes—
24#10622668C2214yes—
25#10622609—24no—
26#10622539C2212yes—
27C2×#66867C2211yescharacteristic
28#10622181C2218yes—
29#10622178C2214yes—
30C2×C11×#41D412yes—
31C22×Q8×C11—22no—
32C11×C4⋊Q8—24no—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D412yes—
36C11×C4⋊Q8D412yes—
37C11×#127D411yescharacteristic
38C11×#126—28no—
39C11×#125C2314yes—
40C11×#124—24no—
41C11×#124—24no—
42C11×#124C2312yes—
43C11×#123—24no—
44C11×#123—24no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—28no—
49C11×#121—22no—
50C4×Q8×C11—24no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×D4×C11—24no—
54C4×D4×C11—22no—
55C11×#117—22no—
56C11×#117D414yes—
57C2×C42×C11C2311yescharacteristic
58#66979—21no—
59#66977—22no—
60C22×C11⋊C8—21no—
61#66923—21no—
62#66922C2312yes—
63C4×Dic22—22no—
64#66899—24no—
65#66896—24no—
66C22⋊(C11⋊C8)—22no—
67#66874—24no—
68#66874—24no—
69#66872—24no—
70#66871—24no—
71C4⋊(C11⋊C8)—22no—
72#66867—21no—
73#66867C2312yes—
74#66867C2314yes—
75#19058—111nomaximal, Sylow
76C11×#41—44no—
77C2×Q8×C11—24no—
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11—84no—
81C2×Q8×C11C2×D412yes—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11C2×D412yes—
85C22×C4×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C2×Dic22—22no—
90C11×C4⋊C4—28no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4C2×D414yes—
97C11×C4⋊C4C2×D414yes—
98C11×C22⋊C4—24no—
99C11×C22⋊C4—28no—
100C11×C22⋊C4—24no—
101C11×C22⋊C4—24no—
102C42×C11—24no—
103C42×C11—24no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D412yes—
106C42×C11C2411yescharacteristic
107C22⋊Dic11—41no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110Dic11⋊C4—42no—
111C4×Dic11—41no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—42no—
115#3550D1111yescharacteristic
116#3237—112no—
117#3135—111no—
118#1664—118no—
119#1536—111no—
120#1531—112no—
121C23×C11—22no—
122C23×C11#12011yescharacteristic
123Q8×C11—42no—
124Q8×C11—44no—
125Q8×C11—44no—
126Q8×C11—84no—
127D4×C11—42no—
128D4×C11—44no—
129D4×C11—82no—
130C2×C4×C11—22no—
131C2×C4×C11—24no—
132C2×C4×C11—22no—
133C2×C4×C11—24no—
134C2×C4×C11—42no—
135C2×C4×C11—44no—
136C2×C4×C11—84no—
137C2×C4×C11#12012yes—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×C4×C11C22×D412yes—
141C2×Dic11—42no—
142Dic22—44no—
143C11⋊C8—44no—
144C11⋊C8—42no—
145#563C2×D1114yes—
146#559—21no—
147Q82—21no—
148#556—22no—
149D4×Q8—22no—
150#542—24no—
151#536—22no—
152#533—111no—
153#533C2×D1112yes—
154#532C2×D1111yescharacteristic
155#501—114no—
156#491—114no—
157#491—221no—
158#490—221no—
159#489—114no—
160#485—224no—
161#477—222no—
162#475—222no—
163#432—112no—
164#416—222no—
165C2×#97—111no—
166#330—118no—
167#329—114no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—42no—
171C22×C11—44no—
172C22×C11C2×#12011yescharacteristic
173C4×C11—21no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—42no—
177C4×C11—44no—
178C4×C11—44no—
179C4×C11#45512yes—
180Dic11—82no—
181C2×#41C22⋊D1112yes—
182C22×Q8—22no—
183C22×C8—221no—
184C4⋊Q8—24no—
185C4⋊Q8—24no—
186C4⋊Q8—112no—
187C4⋊Q8C22⋊D1111yescharacteristic
188C4⋊Q8C22⋊D1112yes—
189C4⋊Q8C22⋊D1112yes—
190#127C22⋊D1111yescharacteristic
191#126—28no—
192#125—221no—
193#125C22×D1114yes—
194#124—24no—
195#124—24no—
196#124C22×D1112yes—
197#123—24no—
198#123—24no—
199C22⋊Q8—24no—
200C22⋊Q8—22no—
201C22⋊Q8—22no—
202C22⋊Q8—28no—
203C22⋊Q8—222no—
204#121—22no—
205C4×Q8—24no—
206C4×Q8—22no—
207C4×Q8—22no—
208C4×Q8—222no—
209C4×D4—24no—
210C4×D4—22no—
211#117—22no—
212#117—221no—
213#117C22⋊D1114yes—
214C2×C42C22×D1111yescharacteristic
215#107—224no—
216#106—224no—
217C4⋊C8—222no—
218#103—224no—
219#103—224no—
220#103—224no—
221#102—224no—
222C22⋊C8—222no—
223#97—114no—
224#97—112no—
225#97—221no—
226C2×C11—41no—
227C2×C11—82no—
228C2×C11C2×#45511yescharacteristic
229C2×C11#302012yes—
230#41—44no—
231C2×Q8—24no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—84no—
235C2×Q8—222no—
236C2×Q8C2×C22⋊D1112yes—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4C2×C22⋊D1112yes—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4C2×C22⋊D1111yescharacteristic
243C22×C4C2×C22⋊D1112yes—
244C2×C8—222no—
245C2×C8—224no—
246C2×C8—442no—
247C4⋊C4—28no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—442no—
256C4⋊C4C2×C22⋊D1114yes—
257C4⋊C4C2×C22⋊D1114yes—
258C22⋊C4—24no—
259C22⋊C4—28no—
260C22⋊C4—24no—
261C22⋊C4—24no—
262C22⋊C4—441no—
263C42—24no—
264C42—24no—
265C42—441no—
266C42C2×C22⋊D1111yescharacteristic
267C42C2×C22⋊D1112yes—
268C42C23×D1111yescharacteristic
269C11#1905811yescharacteristic, complemented, Sylow
270C23—22no—
271C23#6700611yescharacteristic
272Q8—42no—
273Q8—44no—
274Q8—44no—
275Q8—84no—
276Q8—444no—
277D4—42no—
278D4—44no—
279D4—82no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—84no—
287C2×C4—442no—
288C2×C4#6700612yes—
289C2×C4#6700611yescharacteristic
290C2×C4C22×C22⋊D1112yes—
291C2×C4C22×C22⋊D1111yescharacteristic
292C8—442no—
293C8—444no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—44no—
298C22C2×#6700611yescharacteristic
299C4—21no—
300C4—22no—
301C4—22no—
302C4—42no—
303C4—44no—
304C4—44no—
305C4—882no—
306C4#1062285512yes—
307C2—41no—
308C2—82no—
309C2C2×#1062285511yescharacteristic
310C2#1307798012yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3550C2
socleC22×C11C2×#120
prime radicalC11×#532C22
hypercenter#3550D11
hypocenterC11#19058
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #13079830C2semidirect
3. #13067950C2semidirect
5. #13067231C2semidirect
269. C11#19058semidirect

Maximal subgroups

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

subgroupindex
#130798302
#130789612
#130679502
#130672512
#130672312
C11×#35502
#1905811