Finite Group Databasebeta

← #13075575

Subgroups — #13075575

Order 1408.

476 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 133 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×#66932C212yesmaximal, complemented
2C11×#390C211yesmaximal, characteristic
3#10622835C212yesmaximal
4#10622585C212yesmaximal, complemented
5#10622564C212yesmaximal, complemented
6#10622562C212yesmaximal, complemented
7#10622561C212yesmaximal, complemented
8#10622541C211yesmaximal, characteristic, complemented
9#10622541C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C22⋊C4C2212yes—
13C2×C11×C22⋊C4C2212yes—
14C2×C42×C11C2211yescharacteristic
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2212yes—
28#66932—28no—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C24×C11C2312yes—
33C2×D4×C11—22no—
34C2×D4×C11—41no—
35C2×D4×C11—41no—
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C11×C4⋊C4—41no—
45C11×C22⋊C4—24no—
46C11×C22⋊C4—24no—
47C42×C11—41no—
48C22⋊Dic11—24no—
49C22⋊Dic11—24no—
50C22⋊Dic11—42no—
51C22⋊Dic11—42no—
52C4⋊Dic11—22no—
53C4⋊Dic11—41no—
54C4⋊Dic11—41no—
55C4⋊Dic11D414yescomplemented
56Dic11⋊C4—24no—
57Dic11⋊C4—24no—
58Dic11⋊C4—24no—
59Dic11⋊C4—42no—
60C4×Dic11—24no—
61#2727—111nomaximal, Sylow
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—22no—
69C23×C11C2411yescharacteristic
70D4×C11—44no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11C2×D412yes—
81C2×C4×C11#4112yes—
82C2×C4×C11#4112yes—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11C2×D414yes—
95C2×#126—112no—
96#399—112no—
97#396—112no—
98#394—112no—
99#390D1111yescharacteristic
100#389—112no—
101#389—111no—
102#389—111no—
103#388—112no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11—42no—
107C22×C11—42no—
108C22×C11—42no—
109C22×C11—42no—
110C22×C11—42no—
111C22×C11C22×D411yescharacteristic
112C22×C11C2×#4111yescharacteristic
113C22×C11C2×#4111yescharacteristic
114C22×C11H(5,𝔽2)11yescharacteristic
115C22×C11H(5,𝔽2)11yescharacteristic
116C22×C112−1+411yescharacteristic
117C22×C112−1+411yescharacteristic
118C4×C11—22no—
119C4×C11—22no—
120C4×C11—22no—
121C4×C11—42no—
122Dic11—24no—
123Dic11—42no—
124Dic11—42no—
125Dic11—42no—
126C22×D4C2×D1111yescharacteristic
127#126—228no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4—112no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4—111no—
133C2×C4⋊C4—111no—
134C2×C4⋊C4—111no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4C2×D1111yescharacteristic
137C2×C22⋊C4—112no—
138C2×C22⋊C4—112no—
139C2×C22⋊C4—112no—
140C2×C22⋊C4—112no—
141C2×C22⋊C4C2×D1112yes—
142C2×C22⋊C4C2×D1112yes—
143C2×C42—112no—
144C2×C42C2×D1111yescharacteristic
145#95—112no—
146#95—112no—
147#95—112no—
148C2×C11—82no—
149C2×C11#53711yescharacteristic
150C2×C11#53811yescharacteristic
151C2×C11#53911yescharacteristic
152C2×C11#54711yescharacteristic
153C2×C11#55011yescharacteristic
154C2×C11#55611yescharacteristic
155C2×C11#56311yescharacteristic
156C24C22×D1112yes—
157C2×D4—22no—
158C2×D4—41no—
159C2×D4—41no—
160C22×C4—112no—
161C22×C4—112no—
162C22×C4—112no—
163C22×C4—112no—
164C22×C4C22×D1112yes—
165C22×C4C22×D1111yescharacteristic
166C22×C4C22×D1111yescharacteristic
167C22×C4C22×D1111yescharacteristic
168C4⋊C4—41no—
169C4⋊C4—114no—
170C4⋊C4—224no—
171C4⋊C4—224no—
172C4⋊C4—224no—
173C4⋊C4—222no—
174C4⋊C4—442no—
175C4⋊C4—441no—
176C4⋊C4—441no—
177C22⋊C4—24no—
178C22⋊C4—24no—
179C22⋊C4—224no—
180C22⋊C4—224no—
181C22⋊C4—442no—
182C22⋊C4—442no—
183C42—41no—
184C42—224no—
185C11#272711yescharacteristic, complemented, Sylow
186C23—22no—
187C23—22no—
188C23—22no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23C23×D1111yescharacteristic
194D4—44no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—114no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4#433912yes—
217C2×C4D4×D1112yes—
218C2×C4#434112yes—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—42no—
226C22C2×#433911yescharacteristic
227C22C2×D4×D1111yescharacteristic
228C22C2×#434111yescharacteristic
229C22#6703711yescharacteristic
230C22#6703711yescharacteristic
231C22#6704311yescharacteristic
232C22#6704311yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—42no—
237C4—224no—
238C4—442no—
239C4—442no—
240C4—442no—
241C2—82no—
242C2#1062302511yescharacteristic
243C2#1062307311yescharacteristic
244C2#1062308211yescharacteristic
245C2#1062312811yescharacteristic
246C2#1062313311yescharacteristic
247C2#1062320311yescharacteristic
248C2#1062324911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2727
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#66932C2semidirect
4. #10622585C2semidirect
5. #10622564C2semidirect
6. #10622562C2semidirect
7. #10622561C2semidirect
8. #10622541C2semidirect
9. #10622541C2semidirect
55. C4⋊Dic11D4semidirect
185. C11#2727semidirect

Maximal subgroups

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

subgroupindex
C2×#669322
C11×#3902
#106228352
#106225852
#106225642
#106225622
#106225612
#106225412
#272711