Finite Group Databasebeta

← #14653227

Subgroups — #14653227

Order 2816.

398 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 127 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#13068754C211yesmaximal, characteristic
2#13067301C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic
4#13067288C211yesmaximal, characteristic
5#13067288C211yesmaximal, characteristic
6#13066899C211yesmaximal, characteristic
7C2×C11×#487C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#487—21no—
11C11×#487—21no—
12C11×#487C414yes—
13C2×C11×#103—22no—
14C2×C4×C8×C11C2211yescharacteristic
15#10622538C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622190—22no—
20#10622185—22no—
21#10622185—22no—
22#10622185—22no—
23#10622184—22no—
24#10622093—21no—
25C8×C11⋊C8—21no—
26C22×Q8×C11—21no—
27C22×Q8×C11—21no—
28C22×C8×C11D412yes—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8C2×C412yes—
36C11×C4⋊Q8C2×C412yes—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4318—21no—
43C2×#4318—21no—
44C11×#103—24no—
45C11×#103—24no—
46C4×C8×C11C2×C412yes—
47C4×C8×C11D411yescharacteristic
48C4×C8×C11D411yescharacteristic
49C22⋊(C11⋊C8)—21no—
50C22⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)D412yes—
56C4⋊(C11⋊C8)D412yes—
57C4×C11⋊C8—21no—
58C4×C11⋊C8—21no—
59#9770—111nomaximal, Sylow
60C2×Q8×C11—22no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×Q8×C11—42no—
65C2×Q8×C11—42no—
66C2×Q8×C11—82no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C2×C8×C11—22no—
73C2×C8×C11—22no—
74C2×C8×C11C22⋊C412yes—
75C2×C8×C11C22⋊C412yes—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C42×C11C22×C411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88#4318—42no—
89#4318—42no—
90C2×C11⋊C8—22no—
91C2×C11⋊C8—22no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8—41no—
94C2×#487D1111yescharacteristic
95#1837—111no—
96#1549—111no—
97#1548—111no—
98#1546—111no—
99#1546—111no—
100#1450—111no—
101C23×C11#12411yescharacteristic
102Q8×C11—44no—
103Q8×C11—82no—
104Q8×C11—82no—
105Q8×C11—81no—
106Q8×C11—81no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—82no—
112C2×C4×C11—82no—
113C2×C4×C11C2×C22⋊C411yescharacteristic
114C2×C4×C11C4×D411yescharacteristic
115C2×C4×C11C4×D411yescharacteristic
116C2×C4×C11#12111yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12711yescharacteristic
119C2×C4×C11#13512yes—
120C2×C4×C11#13512yes—
121C8×C11—22no—
122C8×C11—22no—
123C11⋊C8—42no—
124C11⋊C8—42no—
125C11⋊C8—81no—
126C11⋊C8—81no—
127C2×C4⋊Q8C2×D1111yescharacteristic
128C2×C4⋊Q8C2×D1111yescharacteristic
129#487—21no—
130#487—21no—
131#487Dic1114yes—
132#431—111no—
133#431—111no—
134#423—111no—
135#423—111no—
136C2×#103—22no—
137C2×C4×C8C2×D1111yescharacteristic
138#341—222no—
139#333—222no—
140#332—222no—
141#332—222no—
142#332—222no—
143#322—221no—
144C82—221no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11#39011yescharacteristic
148C22×C11#48812yes—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—82no—
152C4×C11—82no—
153C4×C11#41612yes—
154C4×C11#47112yes—
155C4×C11#47312yes—
156C4×C11#49511yescharacteristic
157C4×C11#49511yescharacteristic
158C22×Q8—21no—
159C22×Q8—21no—
160C2×M16—221no—
161C2×M16—221no—
162C22×C8C22⋊D1112yes—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—21no—
168C4⋊Q8—21no—
169C4⋊Q8C2×Dic1112yes—
170C4⋊Q8C2×Dic1112yes—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C42C22×D1111yescharacteristic
176C4⋊C8—112no—
177C4⋊C8—112no—
178C4⋊C8—221no—
179C4⋊C8—221no—
180C4⋊C8—221no—
181C4⋊C8—221no—
182#103—24no—
183#103—24no—
184C22⋊C8—221no—
185C22⋊C8—221no—
186C4×C8—221no—
187C4×C8—221no—
188C4×C8C2×Dic1112yes—
189C4×C8C22⋊D1111yescharacteristic
190C4×C8C22⋊D1111yescharacteristic
191C2×C11—22no—
192C2×C11#195811yescharacteristic
193C2×C11#197711yescharacteristic
194C2×C11#197911yescharacteristic
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—82no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4#434111yescharacteristic
205C22×C4#434111yescharacteristic
206C22×C4C2×C22⋊D1111yescharacteristic
207M16—442no—
208M16—442no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—222no—
212C2×C8—222no—
213C2×C8—441no—
214C2×C8—441no—
215C2×C8C22⋊Dic1112yes—
216C2×C8C22⋊Dic1112yes—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C42D4×D1111yescharacteristic
226C42D4×D1111yescharacteristic
227C42C22×Dic1111yescharacteristic
228C42C2×C22⋊D1111yescharacteristic
229C11#977011yescharacteristic, complemented, Sylow
230C23#6698911yescharacteristic
231Q8—44no—
232Q8—82no—
233Q8—82no—
234Q8—81no—
235Q8—81no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4D4×Dic1111yescharacteristic
243C2×C4D4×Dic1111yescharacteristic
244C2×C4#6699111yescharacteristic
245C2×C4#6699111yescharacteristic
246C2×C4#6699311yescharacteristic
247C2×C4#6700312yes—
248C2×C4#6700312yes—
249C2×C4C2×C22⋊Dic1111yescharacteristic
250C8—22no—
251C8—22no—
252C8—442no—
253C8—442no—
254C8—881no—
255C8—881no—
256C22—21no—
257C22—21no—
258C22#1062266912yes—
259C22#1062283411yescharacteristic
260C4—21no—
261C4—21no—
262C4—82no—
263C4—82no—
264C4#1062267211yescharacteristic
265C4#1062267211yescharacteristic
266C4#1062279012yes—
267C4#1062280512yes—
268C4#1062284612yes—
269C2—22no—
270C2#1306942811yescharacteristic
271C2#1306952111yescharacteristic
272C2#1306953211yescharacteristic
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#487C2
socleC22×C11#390
prime radicalC23×C11#124
cosocleC2×C42×C11C23
hypercenterC2×#487D11
hypocenterC11#9770
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
229. C11#9770semidirect

Maximal subgroups

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

subgroupindex
#130687542
#130673012
#130672972
#130672882
#130668992
C2×C11×#4872
#977011