Finite Group Databasebeta

← #14670053

Subgroups — #14670053

Order 2816.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#13077256C211yesmaximal, characteristic
2#13068721C212yesmaximal
3#13066746C212yesmaximal
4#13066737C211yesmaximal, characteristic
5C11×#1392C211yesmaximal, characteristic
6#41×Dic11C2211yescharacteristic
7C11×#413C2212yes—
8C11×#408C2211yescharacteristic
9#10622853C2212yes—
10#10622847C2211yescharacteristic
11#10622732C411yescharacteristic, complemented
12M16×Dic11C411yescharacteristic, complemented
13#10622715C411yescharacteristic, complemented
14C2×C8×Dic11C411yescharacteristic, complemented
15#10622333—22no—
16#10622331—22no—
17#10622195—22no—
18#10622193—22no—
19C2×C11×#41C2311yescharacteristic
20C2×C11×M16—22no—
21C2×C11×M16C2×C411yescharacteristic
22C22×C8×C11C2×C411yescharacteristic
23Q8×Dic11—21no—
24D4×Dic11—22no—
25D4×Dic11—21no—
26#66979—22no—
27#66979C2×C411yescharacteristic
28#66979D412yes—
29C2×C4×Dic11C2×C411yescharacteristic
30C2×C4×Dic11D412yes—
31C2×#4318C2×C411yescharacteristic
32C22×C11⋊C8C2×C411yescharacteristic
33C11×#101—22no—
34C11×#100—22no—
35C11×C22⋊C8—22no—
36#66898—22no—
37#66898—22no—
38C22⋊(C11⋊C8)—22no—
39#66879—21no—
40Dic11⋊C8—22no—
41Dic11⋊C8—22no—
42C8×Dic11—21no—
43C8×Dic11—21no—
44C8×Dic11—21no—
45#12864—111nomaximal, Sylow
46C11×#41—41no—
47C11×#41—41no—
48C2×Q8×C11#4111yescharacteristic
49C2×D4×C11#4111yescharacteristic
50C2×D4×C11#4112yes—
51C22×C4×C11C22×C411yescharacteristic
52C22×C4×C11C2×D412yes—
53C22×Dic11—21no—
54C22×Dic11—22no—
55C11×M16—41no—
56C11×M16—42no—
57C11×M16—42no—
58C2×C8×C11—21no—
59C2×C8×C11—21no—
60C2×C8×C11—41no—
61C2×C8×C11—42no—
62C22⋊Dic11—21no—
63C22⋊Dic11—22no—
64C22⋊Dic11—42no—
65C4⋊Dic11—21no—
66C4⋊Dic11—22no—
67C4⋊Dic11—42no—
68C4×Dic11—21no—
69C4×Dic11—22no—
70C4×Dic11—42no—
71C4×Dic11C22⋊C411yescharacteristic
72C4×Dic11C22⋊C411yescharacteristic
73C4×Dic11C22⋊C412yes—
74#4318—41no—
75C2×C11⋊C8—21no—
76C2×C11⋊C8—21no—
77C2×C11⋊C8—41no—
78#2922—111no—
79#1827—112no—
80#1395—112no—
81#1392D1111yescharacteristic
82#1391—111no—
83C23×C11#11711yescharacteristic
84C23×C11#12312yes—
85Q8×C11—41no—
86D4×C11—42no—
87D4×C11—41no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11C2×C22⋊C411yescharacteristic
93C2×C4×C11#11711yescharacteristic
94C2×C4×C11#12312yes—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—42no—
99C2×Dic11—44no—
100C2×Dic11—82no—
101C8×C11—41no—
102C8×C11—41no—
103C8×C11—82no—
104C11⋊C8—41no—
105C11⋊C8—41no—
106C4×#41—111no—
107#433—222no—
108#431—222no—
109#424—111no—
110#424—111no—
111#413C2×D1112yes—
112#410—112no—
113#408—111no—
114#408C2×D1111yescharacteristic
115C4×M16—111no—
116C2×C4×C8—111no—
117#339—222no—
118H(3,ℤ/4)—222no—
119C22×C11—21no—
120C22×C11—22no—
121C22×C11—41no—
122C22×C11—42no—
123C22×C11#38111yescharacteristic
124C4×C11—21no—
125C4×C11—22no—
126C4×C11#41011yescharacteristic
127C4×C11#41011yescharacteristic
128Dic11—22no—
129Dic11—41no—
130Dic11—42no—
131Dic11—162no—
132C2×#41C22×D1111yescharacteristic
133C2×M16—22no—
134C2×M16—111no—
135C2×M16C4×D1111yescharacteristic
136C22×C8—111no—
137C22×C8C4×D1111yescharacteristic
138C4×Q8—221no—
139C4×D4—222no—
140C4×D4—221no—
141#117—111no—
142#117—112no—
143#117—222no—
144C2×C42—111no—
145C2×C42—112no—
146C4⋊C8—222no—
147C4⋊C8—222no—
148#101—22no—
149#100—22no—
150#99—222no—
151#99—222no—
152C22⋊C8—22no—
153C22⋊C8—222no—
154#97—221no—
155C4×C8—221no—
156C4×C8—221no—
157C4×C8—221no—
158C2×C11—21no—
159C2×C11—42no—
160C2×C11—41no—
161C2×C11#182011yescharacteristic
162#41—41no—
163#41—41no—
164C2×Q8#434111yescharacteristic
165C2×D4#433912yes—
166C2×D4#434311yescharacteristic
167C22×C4—221no—
168C22×C4—222no—
169C22×C4C2×C4×D1111yescharacteristic
170C22×C4D4×D1112yes—
171M16—41no—
172M16—42no—
173M16—42no—
174M16—441no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—221no—
180C2×C8—221no—
181C2×C8—441no—
182C4⋊C4—222no—
183C4⋊C4—221no—
184C4⋊C4—442no—
185C22⋊C4—221no—
186C22⋊C4—222no—
187C22⋊C4—442no—
188C42—111no—
189C42—111no—
190C42—112no—
191C42—222no—
192C42—221no—
193C42—442no—
194C11#1286411yescharacteristic, complemented, Sylow
195C23#6692511yescharacteristic
196C23#6694712yes—
197Q8—41no—
198D4—42no—
199D4—41no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—221no—
205C2×C4—221no—
206C2×C4—222no—
207C2×C4—442no—
208C2×C4—444no—
209C2×C4—882no—
210C2×C4C22⋊C4×D1111yescharacteristic
211C2×C4#6693612yes—
212C2×C4#6694511yescharacteristic
213C8—41no—
214C8—41no—
215C8—82no—
216C8—441no—
217C8—441no—
218C22—22no—
219C22—21no—
220C22—41no—
221C22—42no—
222C22#1062227711yescharacteristic
223C4—22no—
224C4—21no—
225C4—222no—
226C4—441no—
227C4—442no—
228C4—1762no—
229C4#1062235311yescharacteristic
230C4#1062235311yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1306869211yescharacteristic
subgroupG/H
centerC4#10622353
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#1392C2
socleC2×C11#1820
prime radical, cosocleC2×C11×#41C23
hypercenter#1392D11
hypocenterC11#12864
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1392

Complements

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

NH ≅ G/Ntype
11. #10622732C4semidirect
12. M16×Dic11C4semidirect
13. #10622715C4semidirect
14. C2×C8×Dic11C4semidirect
194. C11#12864semidirect

Maximal subgroups

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

subgroupindex
#130772562
#130687212
#130667462
#130667372
C11×#13922
#1286411