Finite Group Databasebeta

← #13073995

Subgroups — #13073995

Order 1408.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C22×Dic11⋊C4C211yesmaximal, characteristic
2C2×#66931C211yesmaximal, characteristic
3C11×#385C211yesmaximal, characteristic
4#10622823C211yesmaximal, characteristic
5#10622592C212yesmaximal, complemented
6#10622586C212yesmaximal, complemented
7#10622563C211yesmaximal, characteristic
8#10622559C211yesmaximal, characteristic
9C22⋊C4×Dic11C211yesmaximal, characteristic
10#10622270C212yesmaximal, complemented
11#10622260C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C22×Dic22C2211yescharacteristic
16C2×C11×C4⋊C4C2212yes—
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2212yes—
23C2×Dic11⋊C4—24no—
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2212yes—
31#66931—24no—
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C22×C4×C11—22no—
39C22×C4×C11—42no—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×Dic11—24no—
45C22×Dic11—22no—
46C22×Dic11—42no—
47C22×Dic11D414yes—
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2312yes—
53C22×Dic11C2312yes—
54C2×Dic22—22no—
55C2×Dic22—42no—
56C11×C4⋊C4—42no—
57C11×C22⋊C4—22no—
58C11×C22⋊C4Q814yescomplemented
59C22⋊Dic11—22no—
60C22⋊Dic11Q814yescomplemented
61C4⋊Dic11—22no—
62C4⋊Dic11—24no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—24no—
66Dic11⋊C4—24no—
67Dic11⋊C4—24no—
68Dic11⋊C4—42no—
69C4×Dic11—42no—
70#2583—111nomaximal, Sylow
71C23×C11—22no—
72C23×C11—22no—
73C23×C11C2×D412yes—
74C23×C11C2×Q812yes—
75C23×C11C2×Q812yes—
76C23×C11C2411yescharacteristic
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—44no—
87C2×C4×C11C2×Q814yes—
88C2×Dic11—28no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—44no—
100C2×Dic11C2×D412yes—
101C2×Dic11C2×D412yes—
102C2×Dic11C2×Q814yes—
103C2×Dic11#4114yes—
104Dic22—44no—
105C2×C22⋊Q8—111no—
106C22×C4⋊C4—111no—
107#398—112no—
108#395—112no—
109#389—112no—
110#389—112no—
111#385—111no—
112#385—111no—
113#385—111no—
114#385D1111yescharacteristic
115C4×C22⋊C4—111no—
116C22×C11—22no—
117C22×C11—22no—
118C22×C11—24no—
119C22×C11—24no—
120C22×C11C4⋊Q814yes—
121C22×C11C22×D411yescharacteristic
122C22×C11C22×Q811yescharacteristic
123C22×C11C22×Q811yescharacteristic
124C22×C11C2×#4112yes—
125C22×C11H(5,𝔽2)12yes—
126C4×C11—24no—
127C4×C11—41no—
128C4×C11—42no—
129C4×C11—41no—
130Dic11—24no—
131Dic11—22no—
132Dic11—22no—
133Dic11—24no—
134Dic11—41no—
135Dic11—41no—
136C22×Q8—111no—
137C23×C4—111no—
138C23×C4—111no—
139C23×C4C2×D1111yescharacteristic
140C22⋊Q8—224no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—111no—
144C2×C4⋊C4—111no—
145C2×C4⋊C4—111no—
146C2×C4⋊C4—112no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—224no—
150C2×C4⋊C4C2×D1112yes—
151C2×C22⋊C4—111no—
152C2×C22⋊C4—111no—
153C2×C22⋊C4C2×D1111yescharacteristic
154C2×C22⋊C4C2×D1111yescharacteristic
155C2×C42—112no—
156#95—112no—
157#95—112no—
158#95—112no—
159#95—112no—
160#95C2×D1112yes—
161C2×C11—24no—
162C2×C11#52511yescharacteristic
163C2×C11C2×C4⋊Q811yescharacteristic
164C2×C11#53411yescharacteristic
165C2×C11#55412yes—
166C2×C11#55412yes—
167C24C22×D1111yescharacteristic
168C2×Q8—222no—
169C2×Q8—442no—
170C22×C4—22no—
171C22×C4—42no—
172C22×C4—112no—
173C22×C4—112no—
174C22×C4—111no—
175C22×C4—111no—
176C22×C4—114no—
177C22×C4—111no—
178C22×C4—111no—
179C22×C4—224no—
180C22×C4—222no—
181C22×C4—442no—
182C22×C4C22×D1111yescharacteristic
183C22×C4C22×D1112yes—
184C22×C4C22×D1111yescharacteristic
185C22×C4C22×D1112yes—
186C4⋊C4—42no—
187C4⋊C4—224no—
188C4⋊C4—224no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—222no—
192C4⋊C4—224no—
193C4⋊C4—224no—
194C4⋊C4—442no—
195C22⋊C4—22no—
196C22⋊C4—114no—
197C22⋊C4—222no—
198C22⋊C4Dic2214yescomplemented
199C42—442no—
200C11#258311yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23C2×Dic2212yes—
204C23D4×D1112yes—
205C23Q8×D1112yes—
206C23C23×D1111yescharacteristic
207Q8—444no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—44no—
218C2×C4—112no—
219C2×C4—112no—
220C2×C4—114no—
221C2×C4—114no—
222C2×C4—228no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—221no—
230C2×C4—221no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—444no—
234C2×C4C2×Dic2214yes—
235C22—24no—
236C22—22no—
237C22—24no—
238C22—22no—
239C22#6694114yes—
240C22C22×Dic2211yescharacteristic
241C22C2×D4×D1111yescharacteristic
242C22#6703712yes—
243C22C2×Q8×D1111yescharacteristic
244C22#41×D1112yes—
245C4—24no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—222no—
250C4—222no—
251C4—224no—
252C4—224no—
253C4—441no—
254C4—441no—
255C2—24no—
256C2C2×#6694111yescharacteristic
257C2#1062307012yes—
258C2#1062312011yescharacteristic
259C2#1062316712yes—
260C2#1062318711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#385C2
prime radicalC24×C11C23
hypercenter#385D11
hypocenterC11#2583
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
5. #10622592C2semidirect
6. #10622586C2semidirect
10. #10622270C2semidirect
11. #10622260C2semidirect
58. C11×C22⋊C4Q8semidirect
60. C22⋊Dic11Q8semidirect
198. C22⋊C4Dic22semidirect
200. C11#2583semidirect

Maximal subgroups

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

subgroupindex
C22×Dic11⋊C42
C2×#669312
C11×#3852
#106228232
#106225922
#106225862
#106225632
#106225592
C22⋊C4×Dic112
#106222702
#106222602
#258311