Finite Group Databasebeta

← #14653197

Subgroups — #14653197

Order 2816.

374 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 107 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#13068367C211yesmaximal, characteristic
2#13067379C211yesmaximal, characteristic
3#13067231C212yesmaximal
4#13067128C212yesmaximal
5C11×#3170C211yesmaximal, characteristic
6C11×#533C2212yes—
7C11×#500C411yescharacteristic, complemented
8C11×#494C411yescharacteristic, complemented
9C11×#487C412yescomplemented
10C11×#467—21no—
11C11×#467—21no—
12C4×C11×Q16—21no—
13C4×C11×Q16—21no—
14C2×C4×C8×C11C2211yescharacteristic
15#10622545C2211yescharacteristic
16#10622539C2212yes—
17C2×#66867C2211yescharacteristic
18#10622188—21no—
19#10622188—21no—
20#10622181—24no—
21#10622176—24no—
22#10622096—21no—
23#10622095—21no—
24C2×C11×Q16—21no—
25C2×C11×Q16—21no—
26C22×C8×C11D411yescharacteristic
27C22×C8×C11D411yescharacteristic
28C11×C4⋊Q8C2×C412yes—
29C11×C4⋊Q8C2×C412yes—
30C11×#125—22no—
31C11×C22⋊Q8—22no—
32C11×C22⋊Q8—22no—
33C4×Q8×C11—22no—
34C4×Q8×C11—22no—
35C11×#117—22no—
36C2×C42×C11C2311yescharacteristic
37C2×C4×Dic11—21no—
38C22×C11⋊C8—21no—
39C11×#107—21no—
40C11×#107—21no—
41C11×#103—22no—
42C11×#103—22no—
43C4×C8×C11C2×C411yescharacteristic
44C4×C8×C11C2×C411yescharacteristic
45C4×C8×C11D411yescharacteristic
46C4×C8×C11D411yescharacteristic
47C11⋊#95—21no—
48C11⋊#95D412yes—
49C22⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—22no—
51#66867—21no—
52#66867—22no—
53#66867D412yes—
54#9765—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×Q8×C11—22no—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C22×Dic11—22no—
61C11×Q16—42no—
62C11×Q16—42no—
63C2×C8×C11—41no—
64C2×C8×C11—41no—
65C2×C8×C11C22⋊C411yescharacteristic
66C2×C8×C11C22⋊C411yescharacteristic
67C2×C8×C11C22⋊C411yescharacteristic
68C2×C8×C11C22⋊C411yescharacteristic
69C11×C4⋊C4—22no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C11×C22⋊C4—42no—
76C42×C11—42no—
77C42×C11C22×C411yescharacteristic
78C42×C11C2×D411yescharacteristic
79C42×C11C2×D411yescharacteristic
80C42×C11#4111yescharacteristic
81C4×Dic11—41no—
82C4×Dic11—41no—
83C2×C11⋊C8—22no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—42no—
87#3170D1111yescharacteristic
88#1746—111no—
89#1568—111no—
90#1531—112no—
91#1506—112no—
92C23×C11#12111yescharacteristic
93Q8×C11—42no—
94Q8×C11—42no—
95Q8×C11—82no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11C2×C22⋊C411yescharacteristic
103C2×C4×C11C4×D411yescharacteristic
104C2×C4×C11C4×D411yescharacteristic
105C2×C4×C11#12111yescharacteristic
106C2×C4×C11#12411yescharacteristic
107C2×C4×C11#12711yescharacteristic
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C8×C11—21no—
112C8×C11—21no—
113C8×C11—21no—
114C8×C11—21no—
115C11⋊C8—42no—
116C11⋊C8—82no—
117#533C2×D1112yes—
118#500Dic1111yescharacteristic, complemented
119#494Dic1111yescharacteristic, complemented
120#487Dic1112yescomplemented
121#467—21no—
122#467—21no—
123C4×Q16—21no—
124C4×Q16—21no—
125#432—112no—
126C2×#97—111no—
127C2×C4×C8C2×D1111yescharacteristic
128#376—111no—
129#336—221no—
130#336—221no—
131#335—221no—
132#334—221no—
133#330—224no—
134#328—224no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11#39011yescharacteristic
138C22×C11#47312yes—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—82no—
145C4×C11—82no—
146C4×C11#42111yescharacteristic
147C4×C11#42111yescharacteristic
148Dic11—82no—
149C2×Q16—21no—
150C2×Q16—21no—
151C22×C8—221no—
152C22×C8C22⋊D1111yescharacteristic
153C22×C8C22⋊D1111yescharacteristic
154C4⋊Q8C2×Dic1112yes—
155C4⋊Q8C2×Dic1112yes—
156#125—22no—
157C22⋊Q8—22no—
158C22⋊Q8—22no—
159C4×Q8—22no—
160C4×Q8—22no—
161#117—22no—
162C2×C42—221no—
163C2×C42C22×D1111yescharacteristic
164#107—21no—
165#107—21no—
166C4⋊C8—222no—
167#103—22no—
168#103—22no—
169C22⋊C8—222no—
170#97—112no—
171#97—222no—
172#97—221no—
173C4×C8C2×Dic1111yescharacteristic
174C4×C8C2×Dic1111yescharacteristic
175C4×C8C22⋊D1111yescharacteristic
176C4×C8C22⋊D1111yescharacteristic
177#95—112no—
178#95—221no—
179C2×C11—22no—
180C2×C11#196311yescharacteristic
181C2×C11#197611yescharacteristic
182C2×C11#197911yescharacteristic
183C2×Q8—22no—
184C2×Q8—22no—
185C22×C4—222no—
186C22×C4D4×D1111yescharacteristic
187C22×C4#434111yescharacteristic
188C22×C4C2×C22⋊D1111yescharacteristic
189Q16—42no—
190Q16—42no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—222no—
194C2×C8—441no—
195C2×C8—441no—
196C2×C8—442no—
197C2×C8C22⋊Dic1111yescharacteristic
198C2×C8C22⋊Dic1111yescharacteristic
199C2×C8C22⋊Dic1111yescharacteristic
200C2×C8C22⋊Dic1111yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C22⋊C4—42no—
208C42—42no—
209C42—441no—
210C42—441no—
211C42D4×D1111yescharacteristic
212C42#434111yescharacteristic
213C42C22×Dic1111yescharacteristic
214C42C2×C22⋊D1111yescharacteristic
215C11#976511yescharacteristic, complemented, Sylow
216C23#6699111yescharacteristic
217Q8—42no—
218Q8—42no—
219Q8—82no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4D4×Dic1111yescharacteristic
230C2×C4D4×Dic1111yescharacteristic
231C2×C4#6698911yescharacteristic
232C2×C4#6699111yescharacteristic
233C2×C4#6699311yescharacteristic
234C2×C4C2×C22⋊Dic1111yescharacteristic
235C8—21no—
236C8—21no—
237C8—21no—
238C8—21no—
239C8—442no—
240C8—882no—
241C22—21no—
242C22—21no—
243C22#1062280512yes—
244C22#1062283411yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—21no—
249C4—21no—
250C4—82no—
251C4—82no—
252C4—882no—
253C4#1062284911yescharacteristic
254C4#1062284911yescharacteristic
255C2—22no—
256C2#1306944911yescharacteristic
257C2#1306951511yescharacteristic
258C2#1306953211yescharacteristic
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3170C2
socleC22×C11#390
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#3170D11
hypocenterC11#9765
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
7. C11×#500C4semidirect
8. C11×#494C4semidirect
9. C11×#487C4semidirect
118. #500Dic11semidirect
119. #494Dic11semidirect
120. #487Dic11semidirect
215. C11#9765semidirect

Maximal subgroups

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

subgroupindex
#130683672
#130673792
#130672312
#130671282
C11×#31702
#976511