Finite Group Databasebeta

← #13076698

Subgroups — #13076698

Order 1408.

472 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C11×#392C211yesmaximal, characteristic
2#10622835C212yesmaximal, complemented
3#10622835C212yesmaximal, complemented
4#10622833C212yesmaximal, complemented
5#10622565C212yesmaximal, complemented
6#10622560C212yesmaximal, complemented
7#10622560C211yesmaximal, characteristic, complemented
8#10622559C211yesmaximal, characteristic, complemented
9#10622271C212yesmaximal, complemented
10C22×D4×C11C2212yes—
11C22×D4×C11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C11×#95C2211yescharacteristic
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C24×C11C2312yes—
32C24×C11C2311yescharacteristic
33C2×D4×C11—24no—
34C2×D4×C11—42no—
35C2×D4×C11—42no—
36C2×D4×C11—42no—
37C2×D4×C11—41no—
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×Dic11—41no—
42C22×Dic11—42no—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C2×Dic22—42no—
48C2×Dic22—41no—
49C11×C22⋊C4—41no—
50C11×C22⋊C4—42no—
51C22⋊Dic11—22no—
52C22⋊Dic11—42no—
53C22⋊Dic11—42no—
54C22⋊Dic11—42no—
55C22⋊Dic11—42no—
56C22⋊Dic11—42no—
57Dic11⋊C4—42no—
58Dic11⋊C4—42no—
59#2824—111nomaximal, Sylow
60C23×C11—22no—
61C23×C11—21no—
62C23×C11—22no—
63C23×C11—21no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—22no—
69C23×C11—22no—
70C23×C11—22no—
71C23×C11#4112yes—
72C23×C11C2411yescharacteristic
73D4×C11—48no—
74D4×C11—44no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×Dic11—22no—
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×Dic11—44no—
95Dic22—44no—
96#400—112no—
97#397—112no—
98#394—112no—
99#394—112no—
100#393—112no—
101#393—111no—
102#392D1111yescharacteristic
103#386—112no—
104#385—111no—
105C22×C11—24no—
106C22×C11—22no—
107C22×C11—41no—
108C22×C11—41no—
109C22×C11—42no—
110C22×C11—42no—
111C22×C11—42no—
112C22×C11—42no—
113C22×C11—42no—
114C22×C11—42no—
115C22×C11—42no—
116C22×C11—42no—
117C22×C11C2×#4111yescharacteristic
118C22×C11H(5,𝔽2)12yes—
119C22×C11H(5,𝔽2)12yes—
120C22×C11H(5,𝔽2)11yescharacteristic
121C22×C112−1+411yescharacteristic
122C4×C11—42no—
123C4×C11—41no—
124C4×C11—41no—
125Dic11—42no—
126Dic11—42no—
127Dic11—42no—
128Dic11—42no—
129C22×Q8—111no—
130C22×D4C2×D1112yes—
131C22×D4C2×D1111yescharacteristic
132C23×C4—111no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—112no—
135C2×C22⋊C4—111no—
136C2×C22⋊C4—112no—
137C2×C22⋊C4—112no—
138C2×C22⋊C4—112no—
139C2×C22⋊C4—112no—
140C2×C22⋊C4—112no—
141C2×C22⋊C4C2×D1111yescharacteristic
142C2×C22⋊C4C2×D1112yes—
143#95—112no—
144#95—112no—
145#95—112no—
146#95—112no—
147#95—112no—
148#95—111no—
149#95C2×D1111yescharacteristic
150C2×C11—42no—
151C2×C11—82no—
152C2×C11#53812yes—
153C2×C11#53911yescharacteristic
154C2×C11#56011yescharacteristic
155C2×C11H(3,𝔽4)11yescharacteristic
156C2×C11#56212yes—
157C24C22×D1112yes—
158C24C22×D1111yescharacteristic
159C2×Q8—442no—
160C2×Q8—441no—
161C2×D4—24no—
162C2×D4—42no—
163C2×D4—41no—
164C2×D4—42no—
165C2×D4—42no—
166C22×C4—112no—
167C22×C4—112no—
168C22×C4—112no—
169C22×C4—112no—
170C22×C4—441no—
171C22×C4—442no—
172C22×C4C22×D1112yes—
173C22×C4C22×D1111yescharacteristic
174C22×C4C22×D1111yescharacteristic
175C4⋊C4—442no—
176C4⋊C4—442no—
177C22⋊C4—41no—
178C22⋊C4—42no—
179C22⋊C4—222no—
180C22⋊C4—442no—
181C22⋊C4—442no—
182C22⋊C4—442no—
183C22⋊C4—442no—
184C22⋊C4—442no—
185C11#282411yescharacteristic, complemented, Sylow
186C23—21no—
187C23—22no—
188C23—22no—
189C23—21no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23#434112yes—
198C23C23×D1111yescharacteristic
199Q8—444no—
200D4—48no—
201D4—44no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—444no—
222C22—24no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22C2×#434111yescharacteristic
235C22#6703712yes—
236C22#6703711yescharacteristic
237C22#6703712yes—
238C22#6704311yescharacteristic
239C4—41no—
240C4—42no—
241C4—41no—
242C4—442no—
243C4—442no—
244C4—442no—
245C4—442no—
246C2—42no—
247C2—82no—
248C2#1062312412yes—
249C2#1062312511yescharacteristic
250C2#1062313311yescharacteristic
251C2#1062315212yes—
252C2#1062325111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC11×#392C2
hypercenter#392D11
hypocenterC11#2824
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
2. #10622835C2semidirect
3. #10622835C2semidirect
4. #10622833C2semidirect
5. #10622565C2semidirect
6. #10622560C2semidirect
7. #10622560C2semidirect
8. #10622559C2semidirect
9. #10622271C2semidirect
185. C11#2824semidirect

Maximal subgroups

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

subgroupindex
C11×#3922
#106228352
#106228332
#106225652
#106225602
#106225592
#106222712
#282411