Finite Group Databasebeta

← #14657679

Subgroups — #14657679

Order 2816.

394 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 85 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#13069461C211yesmaximal, characteristic, complemented
2#13067404C211yesmaximal, characteristic, complemented
3#13067351C211yesmaximal, characteristic
4#13067297C211yesmaximal, characteristic, complemented
5#13067033C211yesmaximal, characteristic
6#13066507C211yesmaximal, characteristic, complemented
7C11×#3206C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#492—21no—
11C11×#487—21no—
12C11×#461—21no—
13C11×#461—21no—
14C11×#448—22no—
15C11×#431C2211yescharacteristic
16C2×#66900—22no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21#10622184—21no—
22#10622184—22no—
23#10622182—21no—
24D4⋊(C11⋊C8)—22no—
25#10622118—21no—
26#10622117—21no—
27C2×C11×#41—21no—
28C22×Q8×C11D412yes—
29C2×C11×SD16—22no—
30C2×C11×SD16—22no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×#127D411yescharacteristic
37C11×#124—21no—
38C11×#121—21no—
39C11×#121—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4318—21no—
46C2×#4318—21no—
47C2×#4318—21no—
48C11×C4⋊C8D411yescharacteristic
49C11×C4⋊C8D411yescharacteristic
50C11×#103—22no—
51C11×#103—22no—
52C11×C22⋊C8—21no—
53C4×C8×C11—21no—
54#66900—44no—
55C22⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61#66867—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10489—111nomaximal, Sylow
65C11×#41—82no—
66C2×Q8×C11—22no—
67C2×Q8×C11—22no—
68C2×Q8×C11—21no—
69C2×Q8×C11—42no—
70C2×Q8×C11—42no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—41no—
75C22×C4×C11—22no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C11×SD16—82no—
81C11×SD16—82no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96#4318—22no—
97#4318—41no—
98#4318—42no—
99#4318—81no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#3206D1111yescharacteristic
105#1966—111no—
106#1574—111no—
107#1560—111no—
108#1548—111no—
109#1484—111no—
110#1299—111no—
111C23×C11—41no—
112C23×C11#12311yescharacteristic
113Q8×C11—42no—
114Q8×C11—42no—
115Q8×C11—82no—
116Q8×C11—81no—
117D4×C11—41no—
118D4×C11—41no—
119D4×C11—41no—
120D4×C11—41no—
121D4×C11—81no—
122D4×C11—82no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—21no—
128C2×C4×C11—44no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—82no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11#12411yescharacteristic
138C8×C11—41no—
139C8×C11—41no—
140C11⋊C8—42no—
141C11⋊C8—42no—
142C11⋊C8—81no—
143C11⋊C8—81no—
144#532C2×D1111yescharacteristic
145C2×C4⋊Q8C2×D1111yescharacteristic
146#492—21no—
147#487—21no—
148#461—21no—
149#461—21no—
150#448—22no—
151#431—111no—
152#431C2×D1111yescharacteristic
153#423—111no—
154#423—111no—
155C2×#101—222no—
156C4×M16—111no—
157#335—221no—
158#334—221no—
159#333—222no—
160#333—221no—
161#331—221no—
162D4⋊C8—222no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11—81no—
169C22×C11#39411yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—82no—
174C4×C11—81no—
175C4×C11#45311yescharacteristic
176C4×C11#45511yescharacteristic
177C4×C11#47112yes—
178C4×C11#47111yescharacteristic
179C4×C11#47311yescharacteristic
180C2×#41—21no—
181C22×Q8C22⋊D1112yes—
182C2×SD16—22no—
183C2×SD16—22no—
184C2×M16—221no—
185C2×M16—221no—
186C2×M16—221no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8C22⋊D1111yescharacteristic
192#127C22⋊D1111yescharacteristic
193#124—21no—
194#121—21no—
195#121—21no—
196C4×D4—21no—
197C4×D4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—112no—
202C4⋊C8—221no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8C22⋊D1111yescharacteristic
207C4⋊C8C22⋊D1111yescharacteristic
208#103—22no—
209#103—22no—
210#101—444no—
211C22⋊C8—21no—
212C22⋊C8—221no—
213#97—221no—
214C4×C8—21no—
215C4×C8—221no—
216C4×C8—221no—
217C2×C11—41no—
218C2×C11—161no—
219C2×C11#203711yescharacteristic
220C2×C11#204611yescharacteristic
221C2×C11#205211yescharacteristic
222#41—82no—
223C2×Q8—21no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—42no—
227C2×Q8—42no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—41no—
232C22×C4—22no—
233C22×C4—41no—
234C22×C4#434111yescharacteristic
235C22×C4#434111yescharacteristic
236C22×C4C2×C22⋊D1111yescharacteristic
237SD16—82no—
238SD16—82no—
239M16—222no—
240M16—441no—
241M16—442no—
242M16—881no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—222no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C42D4×D1111yescharacteristic
258C42#434111yescharacteristic
259C42C2×C22⋊D1111yescharacteristic
260C42C2×C22⋊D1111yescharacteristic
261C11#1048911yescharacteristic, complemented, Sylow
262C23—41no—
263C23#6698811yescharacteristic
264Q8—42no—
265Q8—42no—
266Q8—82no—
267Q8—81no—
268D4—41no—
269D4—41no—
270D4—41no—
271D4—41no—
272D4—81no—
273D4—82no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—44no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—82no—
283C2×C4#6698811yescharacteristic
284C2×C4#6698911yescharacteristic
285C2×C4#6699111yescharacteristic
286C2×C4#6699211yescharacteristic
287C2×C4#6699211yescharacteristic
288C2×C4#6700611yescharacteristic
289C8—41no—
290C8—41no—
291C8—442no—
292C8—442no—
293C8—881no—
294C8—881no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—81no—
299C22—81no—
300C22—81no—
301C22#1062283511yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—81no—
306C4—82no—
307C4#1062279012yes—
308C4#1062281611yescharacteristic
309C4#1062281711yescharacteristic
310C4#1062285411yescharacteristic
311C4#1062285511yescharacteristic
312C2—41no—
313C2—161no—
314C2#1306982311yescharacteristic
315C2#1306987411yescharacteristic
316C2#1306991211yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3206C2
socleC22×C11#394
prime radicalC11×#532C22
hypercenter#3206D11
hypocenterC11#10489
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
1. #13069461C2semidirect
2. #13067404C2semidirect
4. #13067297C2semidirect
6. #13066507C2semidirect
261. C11#10489semidirect

Maximal subgroups

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

subgroupindex
#130694612
#130674042
#130673512
#130672972
#130670332
#130665072
C11×#32062
#1048911