Finite Group Databasebeta

← #13076964

Subgroups — #13076964

Order 1408.

644 conjugacy classes of subgroups; only the 201 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 201 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×C22⋊Q8C211yesmaximal, characteristic
2C2×#66997C211yesmaximal, characteristic, complemented
3C2×#66977C211yesmaximal, characteristic
4C22×C4×Dic11C211yesmaximal, characteristic
5#10622843C211yesmaximal, characteristic, complemented
6#10622589C211yesmaximal, characteristic, complemented
7#10622587C211yesmaximal, characteristic, complemented
8#10622585C214yesmaximal, complemented
9#10622555C214yesmaximal
10C22×Q8×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C23×Dic11C2212yes—
13C22×Dic22C2211yescharacteristic
14C11×C22⋊Q8—24no—
15C2×C11×C4⋊C4C2212yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C22⋊Dic11C2212yes—
19#66997—24no—
20C2×C4⋊Dic11C2211yescharacteristic
21#66977—24no—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2214yes—
24C2×Dic11⋊C4C2214yes—
25C2×C4×Dic11—24no—
26C2×C4×Dic11C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28C2×C4×Dic11C2211yescharacteristic
29C11⋊#95C2214yes—
30C11⋊#95C2214yes—
31C24×C11C2311yescharacteristic
32C2×Q8×C11—22no—
33C2×Q8×C11—22no—
34C2×Q8×C11—22no—
35C22×C4×C11—22no—
36C22×C4×C11—22no—
37C22×C4×C11D414yes—
38C22×C4×C11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×Dic11—24no—
43C22×Dic11—24no—
44C22×Dic11Q818yescomplemented
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48C22×Dic11C2312yes—
49C2×Dic22—22no—
50C2×Dic22—22no—
51C2×Dic22—22no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—24no—
54C11×C22⋊C4—24no—
55C22⋊Dic11—24no—
56C4⋊Dic11—22no—
57Dic11⋊C4—28no—
58Dic11⋊C4—28no—
59Dic11⋊C4—24no—
60C4×Dic11—24no—
61C4×Dic11—22no—
62C4×Dic11D414yes—
63#2857—111nomaximal, Sylow
64C23×C11—21no—
65C23×C11—22no—
66C23×C11—21no—
67C23×C11C2×D412yes—
68C23×C11C2×Q814yes—
69C23×C11C2411yescharacteristic
70Q8×C11—44no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—28no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—24no—
78C2×C4×C11—22no—
79C2×C4×C11C2×D412yes—
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2×D412yes—
82C2×C4×C11#4112yes—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—216no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—24no—
90C2×Dic11—22no—
91C2×Dic11C2×D414yes—
92C2×Dic11C2×Q814yes—
93C2×Dic11C2×Q814yes—
94C2×Dic11#4114yes—
95Dic22—44no—
96C2×C4⋊Q8—111no—
97C2×C22⋊Q8—111no—
98C2×C22⋊Q8D1111yescharacteristic
99C22×C42—111no—
100#391—111no—
101#391—111no—
102#389—114no—
103#384—111no—
104#380—114no—
105C22×C11—22no—
106C22×C11—24no—
107C22×C11—22no—
108C22×C11—24no—
109C22×C11C4⋊Q814yescomplemented
110C22×C11C22×D411yescharacteristic
111C22×C11C22×D411yescharacteristic
112C22×C11C22×Q812yes—
113C22×C11C2×#4111yescharacteristic
114C22×C11C2×#4112yes—
115C4×C11—22no—
116C4×C11—42no—
117C4×C11—42no—
118C4×C11#12114yes—
119Dic11—24no—
120Dic11—42no—
121Dic11—42no—
122Dic11C22⋊Q818yescomplemented
123C22×Q8—111no—
124C22×Q8C2×D1111yescharacteristic
125C23×C4—112no—
126C23×C4C2×D1111yescharacteristic
127C4⋊Q8—224no—
128C22⋊Q8—24no—
129C22⋊Q8—224no—
130C2×C4⋊C4—111no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4—114no—
133C2×C4⋊C4—114no—
134C2×C4⋊C4C2×D1111yescharacteristic
135C2×C4⋊C4C2×D1112yes—
136C2×C22⋊C4—112no—
137C2×C22⋊C4C2×D1112yes—
138C2×C42—111no—
139C2×C42—112no—
140C2×C42—111no—
141C2×C42—224no—
142#95—114no—
143#95—114no—
144C2×C11—24no—
145C2×C11C2×#12111yescharacteristic
146C2×C11C2×C22⋊Q812yes—
147C2×C11C2×C4⋊Q811yescharacteristic
148C2×C11#53211yescharacteristic
149C2×C11#53312yes—
150C24C22×D1111yescharacteristic
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—22no—
154C2×Q8—222no—
155C2×Q8—222no—
156C2×Q8—222no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—112no—
160C22×C4—118no—
161C22×C4—112no—
162C22×C4—112no—
163C22×C4—112no—
164C22×C4—224no—
165C22×C4—224no—
166C22×C4C22⋊D1114yes—
167C22×C4C22×D1112yes—
168C22×C4C22×D1112yes—
169C22×C4C22×D1111yescharacteristic
170C22×C4C22×D1111yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—24no—
173C4⋊C4—228no—
174C4⋊C4—228no—
175C4⋊C4—224no—
176C4⋊C4—222no—
177C22⋊C4—24no—
178C22⋊C4—224no—
179C42—114no—
180C42—224no—
181C42—222no—
182C11#285711yescharacteristic, complemented, Sylow
183C23—21no—
184C23—21no—
185C23—22no—
186C23Q8×D1114yes—
187C23C2×C22⋊D1112yes—
188C23C23×D1111yescharacteristic
189Q8—44no—
190Q8—444no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—28no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—114no—
200C2×C4—114no—
201C2×C4—114no—
202C2×C4—114no—
203C2×C4—2216no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—224no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4D4×D1112yes—
212C2×C4#434112yes—
213C2×C4C2×C22⋊D1112yes—
214C2×C4C2×C22⋊D1112yes—
215C22—22no—
216C22—22no—
217C22—24no—
218C22—24no—
219C22#6699714yescomplemented
220C22C2×D4×D1111yescharacteristic
221C22C2×#434111yescharacteristic
222C22C2×Q8×D1112yes—
223C22#41×D1112yes—
224C22C22×C22⋊D1111yescharacteristic
225C4—22no—
226C4—42no—
227C4—42no—
228C4—118no—
229C4—224no—
230C4—442no—
231C4—442no—
232C4#6699214yes—
233C2—24no—
234C2#1062315312yes—
235C2D11×C22⋊Q812yes—
236C2C2×#6699211yescharacteristic
237C2C2×#6699711yescharacteristic
238C2#1062336311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC24×C11C23
hypercenterC2×C22⋊Q8D11
hypocenterC11#2857
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#66997C2semidirect
5. #10622843C2semidirect
6. #10622589C2semidirect
7. #10622587C2semidirect
8. #10622585C2semidirect
44. C22×Dic11Q8semidirect
109. C22×C11C4⋊Q8semidirect
122. Dic11C22⋊Q8semidirect
182. C11#2857semidirect
219. C22#66997semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669972
C2×#669772
C22×C4×Dic112
#106228432
#106225892
#106225872
#106225852
#106225552
#285711