Finite Group Databasebeta

← #13071883

Subgroups — #13071883

Order 1408.

528 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 155 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
1C2×Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×#66930C211yesmaximal, characteristic
3C11×#393C211yesmaximal, characteristic
4#10622842C211yesmaximal, characteristic, complemented
5#10622562C211yesmaximal, characteristic
6#10622561C212yesmaximal
7C22⋊C4×Dic11C212yesmaximal
8#10622272C211yesmaximal, characteristic, complemented
9#10622270C212yesmaximal, complemented
10#10622262C212yesmaximal, complemented
11#10622262C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C22⋊Dic11C2212yes—
18Q8×Dic11—24no—
19C2×C4⋊Dic11C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2211yescharacteristic
22C2×Dic11⋊C4C2211yescharacteristic
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2212yes—
28C2×C4×Dic11C2212yes—
29C2×C4×Dic11C2211yescharacteristic
30#66930—24no—
31C11×#95C2212yes—
32C11×#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C2×Q8×C11—22no—
39C2×Q8×C11—24no—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×Dic11—22no—
45C22×Dic11—22no—
46C22×Dic11Q814yescomplemented
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C11×C22⋊C4—22no—
54C11×C22⋊C4—24no—
55C22⋊Dic11—22no—
56C22⋊Dic11—24no—
57C4⋊Dic11—24no—
58C4⋊Dic11—22no—
59Dic11⋊C4—22no—
60Dic11⋊C4—24no—
61Dic11⋊C4—24no—
62Dic11⋊C4—22no—
63Dic11⋊C4—24no—
64C4×Dic11—22no—
65C4×Dic11—24no—
66C4×Dic11—24no—
67C4×Dic11D414yes—
68#2396—111nomaximal, Sylow
69C23×C11—21no—
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—21no—
73C23×C11C2×Q812yes—
74C23×C11C2411yescharacteristic
75Q8×C11—28no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11C2×D412yes—
85C2×C4×C11#4114yes—
86C2×Dic11—21no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—21no—
91C2×Dic11—28no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11C2×D412yes—
98C2×Dic11C2×D412yes—
99C2×Dic11C2×Q812yes—
100C2×Dic11C2×Q812yes—
101C2×Dic11#4114yes—
102C2×Dic11#4112yes—
103C2×C4×Q8—111no—
104C2×#117—111no—
105#400—111no—
106#399—111no—
107#398—112no—
108#396—112no—
109#395—111no—
110#393D1111yescharacteristic
111C4×C4⋊C4—111no—
112C4×C4⋊C4—112no—
113C4×C22⋊C4—112no—
114C22×C11—22no—
115C22×C11—24no—
116C22×C11—41no—
117C22×C11—42no—
118C22×C11—41no—
119C22×C11C22×D411yescharacteristic
120C22×C11C22×Q811yescharacteristic
121C22×C11C2×#4112yes—
122C22×C11C2×#4111yescharacteristic
123C22×C11C2×#4112yes—
124C4×C11—22no—
125C4×C11—24no—
126C4×C11—42no—
127C4×C11—41no—
128Dic11—22no—
129Dic11—24no—
130Dic11—22no—
131Dic11—41no—
132Dic11—42no—
133Dic11C22⋊Q814yes—
134C22×Q8C2×D1111yescharacteristic
135C23×C4—111no—
136C4×Q8—224no—
137#117—224no—
138C2×C4⋊C4—111no—
139C2×C4⋊C4—111no—
140C2×C4⋊C4—112no—
141C2×C4⋊C4—111no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—112no—
145C2×C22⋊C4—111no—
146C2×C22⋊C4—112no—
147C2×C22⋊C4C2×D1111yescharacteristic
148C2×C22⋊C4C2×D1112yes—
149C2×C42—111no—
150C2×C42—111no—
151C2×C42—112no—
152C2×C42—112no—
153#95—112no—
154#95—112no—
155#95—111no—
156#95—112no—
157#95C2×D1112yes—
158#95C2×D1111yescharacteristic
159C2×C11—42no—
160C2×C11C2×C22⋊Q811yescharacteristic
161C2×C11#52511yescharacteristic
162C2×C11#52912yes—
163C2×C11#53211yescharacteristic
164C2×C11#53312yes—
165C24C22×D1111yescharacteristic
166C2×Q8—22no—
167C2×Q8—24no—
168C22×C4—111no—
169C22×C4—114no—
170C22×C4—111no—
171C22×C4—112no—
172C22×C4—111no—
173C22×C4—111no—
174C22×C4—112no—
175C22×C4—222no—
176C22×C4—222no—
177C22×C4C22×D1112yes—
178C22×C4C22×D1111yescharacteristic
179C22×C4C22×D1111yescharacteristic
180C22×C4C22×D1112yes—
181C4⋊C4—222no—
182C4⋊C4—224no—
183C4⋊C4—224no—
184C4⋊C4—224no—
185C4⋊C4—222no—
186C4⋊C4—222no—
187C4⋊C4—224no—
188C22⋊C4—22no—
189C22⋊C4—24no—
190C22⋊C4—222no—
191C22⋊C4—224no—
192C42—114no—
193C42—222no—
194C42—224no—
195C42—224no—
196C11#239611yescharacteristic, complemented, Sylow
197C23—21no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23Q8×D1112yes—
202C23C23×D1111yescharacteristic
203Q8—28no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—112no—
213C2×C4—112no—
214C2×C4—112no—
215C2×C4—112no—
216C2×C4—112no—
217C2×C4—114no—
218C2×C4—228no—
219C2×C4—221no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4D4×D1112yes—
230C2×C4#434114yes—
231C22—24no—
232C22—22no—
233C22—41no—
234C22—41no—
235C22—42no—
236C22C2×D4×D1111yescharacteristic
237C22C2×#434112yes—
238C22C2×Q8×D1111yescharacteristic
239C22#41×D1112yes—
240C22#41×D1111yescharacteristic
241C4—22no—
242C4—24no—
243C4—41no—
244C4—42no—
245C4—114no—
246C4—222no—
247C4—222no—
248C4—224no—
249C4—441no—
250C4—442no—
251C2—42no—
252C2#1062311711yescharacteristic
253C2#1062315312yes—
254C2D11×C22⋊Q811yescharacteristic
255C2#1062319911yescharacteristic
256C2#1062321112yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC24×C11C23
hypercenter#393D11
hypocenterC11#2396
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic11C2semidirect
4. #10622842C2semidirect
8. #10622272C2semidirect
9. #10622270C2semidirect
10. #10622262C2semidirect
11. #10622262C2semidirect
46. C22×Dic11Q8semidirect
196. C11#2396semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic112
C2×#669302
C11×#3932
#106228422
#106225622
#106225612
C22⋊C4×Dic112
#106222722
#106222702
#106222622
#239611