Finite Group Databasebeta

← #13073609

Subgroups — #13073609

Order 1408.

604 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 165 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×C11×#124C211yesmaximal, characteristic
2C2×#66997C211yesmaximal, characteristic, complemented
3C2×#66989C211yesmaximal, characteristic
4C2×D4×Dic11C211yesmaximal, characteristic
5#10622843C211yesmaximal, characteristic, complemented
6#10622565C214yesmaximal, complemented
7#10622555C214yesmaximal, complemented
8C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
9#10622542C211yesmaximal, characteristic, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D4×C11C2211yescharacteristic
12C23×Dic11C2212yes—
13C22×Dic22C2211yescharacteristic
14C11×#124—24no—
15C2×C11×C22⋊C4C2214yes—
16C2×C42×C11C2211yescharacteristic
17C2×C22⋊Dic11C2214yes—
18C2×C22⋊Dic11C2212yes—
19#66997—24no—
20#66989—24no—
21D4×Dic11—24no—
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2211yescharacteristic
28C11⋊#95C2214yes—
29C11⋊#95C2212yes—
30C11⋊#95C2214yes—
31C24×C11C2312yes—
32C2×Q8×C11—22no—
33C2×Q8×C11—22no—
34C2×Q8×C11—22no—
35C2×D4×C11—22no—
36C2×D4×C11—22no—
37C2×D4×C11D414yes—
38C22×C4×C11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×Dic11—24no—
42C22×Dic11—28no—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×Dic22—22no—
49C2×Dic22—22no—
50C2×Dic22—22no—
51C11×C22⋊C4—28no—
52C42×C11—22no—
53C22⋊Dic11—24no—
54C22⋊Dic11—28no—
55C4⋊Dic11—22no—
56Dic11⋊C4—24no—
57Dic11⋊C4—24no—
58Dic11⋊C4—24no—
59C4×Dic11—22no—
60C4×Dic11D414yes—
61#2547—111nomaximal, Sylow
62C23×C11—22no—
63C23×C11—24no—
64C23×C11—22no—
65C23×C11—24no—
66C23×C11C2×D414yes—
67C23×C11C2411yescharacteristic
68Q8×C11—44no—
69D4×C11—28no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2×D412yes—
78C2×C4×C11#4112yes—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—24no—
87C2×Dic11—22no—
88C2×Dic11—48no—
89C2×Dic11C2×D412yes—
90C2×Dic11C2×D412yes—
91C2×Dic11#4114yes—
92Dic22—44no—
93C2×C4⋊Q8—111no—
94C2×#124—111no—
95C2×#124D1111yescharacteristic
96C2×C4×D4—111no—
97#397—114no—
98#391—111no—
99#391—111no—
100#380—114no—
101C4×C4⋊C4—111no—
102C22×C11—24no—
103C22×C11—28no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11—44no—
107C22×C11C22×D411yescharacteristic
108C22×C11C22×D411yescharacteristic
109C22×C11C2×#4111yescharacteristic
110C22×C11C2×#4112yes—
111C22×C112−1+412yes—
112C4×C11—42no—
113C4×C11—42no—
114C4×C11#12114yes—
115Dic11—22no—
116Dic11—42no—
117Dic11—42no—
118Dic11—42no—
119Dic11#12414yescomplemented
120C22×Q8—111no—
121C22×Q8C2×D1111yescharacteristic
122C22×D4C2×D1111yescharacteristic
123C23×C4—112no—
124C4⋊Q8—224no—
125#124—24no—
126#124—224no—
127C4×D4—224no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4—112no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4—112no—
132C2×C22⋊C4—112no—
133C2×C22⋊C4—114no—
134C2×C22⋊C4C2×D1114yes—
135C2×C42—111no—
136C2×C42—111no—
137C2×C42C2×D1111yescharacteristic
138#95—112no—
139#95—114no—
140#95—114no—
141C2×C11—44no—
142C2×C11C2×#12111yescharacteristic
143C2×C11C2×#12411yescharacteristic
144C2×C11#53611yescharacteristic
145C2×C11#54712yes—
146C2×C11#55612yes—
147C24C22×D1112yes—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—222no—
152C2×Q8—222no—
153C2×Q8—222no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4C22⋊D1114yes—
157C22×C4—111no—
158C22×C4—111no—
159C22×C4—112no—
160C22×C4—112no—
161C22×C4—112no—
162C22×C4—224no—
163C22×C4—228no—
164C22×C4C22×D1112yes—
165C22×C4C22×D1112yes—
166C22×C4C22×D1111yescharacteristic
167C4⋊C4—224no—
168C4⋊C4—224no—
169C4⋊C4—224no—
170C4⋊C4—222no—
171C22⋊C4—28no—
172C22⋊C4—224no—
173C22⋊C4—228no—
174C42—22no—
175C42—114no—
176C42—222no—
177C11#254711yescharacteristic, complemented, Sylow
178C23—22no—
179C23—22no—
180C23—24no—
181C23—24no—
182C23C2×C22⋊D1114yes—
183C23C23×D1111yescharacteristic
184Q8—44no—
185Q8—444no—
186D4—28no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—112no—
194C2×C4—114no—
195C2×C4—112no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—224no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—448no—
206C2×C4D4×D1112yes—
207C2×C4#434112yes—
208C2×C4C2×C22⋊D1112yes—
209C22—24no—
210C22—28no—
211C22—44no—
212C22—42no—
213C22—42no—
214C22C2×D4×D1111yescharacteristic
215C22C2×#434111yescharacteristic
216C22#41×D1112yes—
217C22#6704312yes—
218C22C22×C22⋊D1111yescharacteristic
219C4—42no—
220C4—42no—
221C4—114no—
222C4—222no—
223C4—442no—
224C4—442no—
225C4—442no—
226C4#6699214yes—
227C2—44no—
228C2#1062320212yes—
229C2D11×#12411yescharacteristic
230C2#1062320611yescharacteristic
231C2C2×#6699211yescharacteristic
232C2#1062335512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
prime radicalC22×D4×C11C22
hypercenterC2×#124D11
hypocenterC11#2547
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×#66997C2semidirect
5. #10622843C2semidirect
6. #10622565C2semidirect
7. #10622555C2semidirect
8. C4×Dic11⋊C4C2semidirect
9. #10622542C2semidirect
119. Dic11#124semidirect
177. C11#2547semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#669972
C2×#669892
C2×D4×Dic112
#106228432
#106225652
#106225552
C4×Dic11⋊C42
#106225422
#254711