Finite Group Databasebeta

← #13076700

Subgroups — #13076700

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×#393C211yesmaximal, characteristic, complemented
2#10622844C212yesmaximal, complemented
3#10622574C212yesmaximal, complemented
4#10622573C211yesmaximal, characteristic
5#10622571C212yesmaximal, complemented
6#10622559C211yesmaximal, characteristic, complemented
7#10622287C212yesmaximal, complemented
8#10622285C212yesmaximal, complemented
9#10622273C212yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C23×Dic11C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×C4⋊Dic11C2212yes—
23C2×Dic11⋊C4C2212yes—
24C11×#95C2212yes—
25C11×#95C2211yescharacteristic
26C11⋊#95C2211yescharacteristic
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C24×C11C2311yescharacteristic
32C23×D11C2312yes—
33C2×Q8×C11—42no—
34C2×Q8×C11—41no—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C2×C22⋊D11—24no—
40C2×C22⋊D11—42no—
41C2×C22⋊D11—42no—
42C22×Dic11—41no—
43C22×Dic11—42no—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C2×D44—42no—
48C2×D44—41no—
49C11×C22⋊C4—42no—
50C11×C22⋊C4—41no—
51C22⋊Dic11—22no—
52(C2×D11)⋊C4—42no—
53(C2×D11)⋊C4—42no—
54(C2×D11)⋊C4—42no—
55(C2×D11)⋊C4—42no—
56(C2×D11)⋊C4—42no—
57C4⋊Dic11—42no—
58Dic11⋊C4—42no—
59#2824—111nomaximal, Sylow
60C23×C11—21no—
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—21no—
64C23×C11#4112yes—
65C23×C11C2411yescharacteristic
66C22×D11—22no—
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—22no—
70C22×D11—22no—
71C22×D11—22no—
72C22×D11—22no—
73Q8×C11—44no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C22⋊D11—48no—
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—
95D44—44no—
96#400—112no—
97#397—112no—
98#394—112no—
99#394—112no—
100#393—112no—
101#393D1111yescharacteristic, complemented
102#392—111no—
103#386—112no—
104#385—111no—
105C22×C11—24no—
106C22×C11—22no—
107C22×C11—41no—
108C22×C11—41no—
109C22×C11—42no—
110C22×C11C2×#4111yescharacteristic
111C22×C11H(5,𝔽2)12yes—
112C22×C11H(5,𝔽2)11yescharacteristic
113C22×C11H(5,𝔽2)12yes—
114C22×C112−1+411yescharacteristic
115C2×D11—42no—
116C2×D11—42no—
117C2×D11—42no—
118C2×D11—42no—
119C2×D11—42no—
120C2×D11—42no—
121C2×D11—42no—
122C4×C11—41no—
123C4×C11—42no—
124C4×C11—41no—
125C4×C11—42no—
126Dic11—42no—
127Dic11—42no—
128Dic11—42no—
129C22×Q8C2×D1111yescharacteristic
130C22×D4—112no—
131C22×D4—111no—
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—111no—
147#95—112no—
148#95C2×D1112yes—
149#95C2×D1111yescharacteristic
150C2×C11—42no—
151C2×C11#53812yes—
152C2×C11#53911yescharacteristic
153C2×C11#56011yescharacteristic
154C2×C11H(3,𝔽4)11yescharacteristic
155C2×C11#56212yes—
156D11—82no—
157C24—112no—
158C24C22×D1111yescharacteristic
159C2×Q8—42no—
160C2×Q8—41no—
161C2×D4—224no—
162C2×D4—441no—
163C2×D4—442no—
164C2×D4—442no—
165C2×D4—442no—
166C22×C4—112no—
167C22×C4—112no—
168C22×C4—112no—
169C22×C4—441no—
170C22×C4—442no—
171C22×C4C22×D1111yescharacteristic
172C22×C4C22×D1112yes—
173C22×C4C22×D1112yes—
174C22×C4C22×D1111yescharacteristic
175C4⋊C4—442no—
176C4⋊C4—442no—
177C22⋊C4—42no—
178C22⋊C4—41no—
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—222no—
191C23—222no—
192C23—222no—
193C23—222no—
194C23—222no—
195C23—222no—
196C23—222no—
197C23#434312yes—
198C23C23×D1111yescharacteristic
199Q8—44no—
200D4—444no—
201D4—448no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
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—442no—
228C22—442no—
229C22—442no—
230C22—442no—
231C22—442no—
232C22—442no—
233C22—442no—
234C22#6703712yes—
235C22#6703711yescharacteristic
236C22C2×#434311yescharacteristic
237C22#6704212yes—
238C22#6704311yescharacteristic
239C4—42no—
240C4—41no—
241C4—41no—
242C4—42no—
243C4—442no—
244C4—442no—
245C4—442no—
246C2—42no—
247C2—882no—
248C2#1062312611yescharacteristic
249C2#1062317512yes—
250C2#1062317611yescharacteristic
251C2#1062321411yescharacteristic
252C2#1062321512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radical#10622573C2
hypercenter#393D11
hypocenterC11#2824
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C11×#393C2semidirect
2. #10622844C2semidirect
3. #10622574C2semidirect
5. #10622571C2semidirect
6. #10622559C2semidirect
7. #10622287C2semidirect
8. #10622285C2semidirect
9. #10622273C2semidirect
101. #393D11semidirect
185. C11#2824semidirect

Maximal subgroups

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

subgroupindex
C11×#3932
#106228442
#106225742
#106225732
#106225712
#106225592
#106222872
#106222852
#106222732
#282411