Finite Group Databasebeta

← #13075646

Subgroups — #13075646

Order 1408.

456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4⋊Q8C211yesmaximal, characteristic
2C2×#66997C211yesmaximal, characteristic
3#10622843C211yesmaximal, characteristic
4#10622842C212yesmaximal
5#10622597C212yesmaximal
6#10622592C212yesmaximal
7#10622591C212yesmaximal
8#10622585C212yesmaximal
9#10622546C212yesmaximal
10C22×Q8×C11C2211yescharacteristic
11C22×Q8×C11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C11×C4⋊Q8—24no—
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C4⋊C4C2212yes—
16C2×C42×C11C2211yescharacteristic
17#66997—24no—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2211yescharacteristic
25C2×C4×Dic11C2211yescharacteristic
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C2×Q8×C11—22no—
34C2×Q8×C11—41no—
35C2×Q8×C11—41no—
36C2×Q8×C11—41no—
37C2×Q8×C11—41no—
38C2×Q8×C11D414yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48C2×Dic22—22no—
49C2×Dic22—41no—
50C2×Dic22—41no—
51C11×C4⋊C4—24no—
52C11×C4⋊C4—24no—
53C42×C11—22no—
54C4⋊Dic11—41no—
55Dic11⋊C4—24no—
56Dic11⋊C4—24no—
57Dic11⋊C4—42no—
58Dic11⋊C4—42no—
59Dic11⋊C4Q818yescomplemented
60C4×Dic11—22no—
61C4×Dic11—41no—
62#2734—111nomaximal, Sylow
63C23×C11C2411yescharacteristic
64Q8×C11—44no—
65Q8×C11—44no—
66C2×C4×C11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2×D412yes—
79C2×C4×C11C2×D412yes—
80C2×C4×C11C2×Q814yes—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—24no—
90C2×Dic11C2×Q814yes—
91C2×Dic11C2×Q814yes—
92Dic22—44no—
93C2×C4⋊Q8—111no—
94C2×C4⋊Q8D1111yescharacteristic
95#398—112no—
96#395—112no—
97#395—112no—
98#391—111no—
99#389—112no—
100#387—112no—
101#387—112no—
102C22×C11C22×D411yescharacteristic
103C22×C11C22×Q812yes—
104C22×C11H(5,𝔽2)11yescharacteristic
105C22×C11H(5,𝔽2)11yescharacteristic
106C22×C112−1+412yes—
107C4×C11—22no—
108C4×C11—22no—
109C4×C11—22no—
110C4×C11—24no—
111C4×C11—42no—
112Dic11—24no—
113Dic11—24no—
114Dic11—42no—
115Dic11—42no—
116C22×Q8—111no—
117C22×Q8C2×D1111yescharacteristic
118C22×Q8C2×D1111yescharacteristic
119C4⋊Q8—24no—
120C4⋊Q8—224no—
121C2×C4⋊C4—112no—
122C2×C4⋊C4—112no—
123C2×C4⋊C4—112no—
124C2×C4⋊C4—112no—
125C2×C4⋊C4—111no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4C2×D1112yes—
128C2×C4⋊C4C2×D1112yes—
129C2×C42—111no—
130C2×C42—111no—
131C2×C42C2×D1111yescharacteristic
132#95—112no—
133#95—112no—
134#95—112no—
135#95—112no—
136#95—112no—
137#95—112no—
138#95—112no—
139C2×C11#53411yescharacteristic
140C2×C11#54412yes—
141C2×C11D4×Q812yes—
142C2×C11Q8211yescharacteristic
143C2×C11#56311yescharacteristic
144C2×Q8—22no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—222no—
150C2×Q8—441no—
151C2×Q8—441no—
152C2×Q8C22⋊D1114yes—
153C22×C4—112no—
154C22×C4—112no—
155C22×C4—112no—
156C22×C4—112no—
157C22×C4C22×D1112yes—
158C22×C4C22×D1112yes—
159C22×C4C22×D1111yescharacteristic
160C22×C4C22×D1111yescharacteristic
161C22×C4C22×D1111yescharacteristic
162C4⋊C4—24no—
163C4⋊C4—24no—
164C4⋊C4—118no—
165C4⋊C4—224no—
166C4⋊C4—224no—
167C4⋊C4—442no—
168C4⋊C4—442no—
169C4⋊C4—441no—
170C42—22no—
171C42—222no—
172C42—441no—
173C11#273411yescharacteristic, complemented, Sylow
174C23C23×D1111yescharacteristic
175Q8—44no—
176Q8—44no—
177Q8—444no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—114no—
190C2×C4—114no—
191C2×C4—222no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—224no—
199C2×C4—222no—
200C2×C4Q8×D1114yes—
201C2×C4C2×C22⋊D1112yes—
202C2×C4C2×C22⋊D1112yes—
203C2×C4C2×C22⋊D1112yes—
204C22#6703711yescharacteristic
205C22#6703711yescharacteristic
206C22C2×Q8×D1112yes—
207C22#6704012yes—
208C22C22×C22⋊D1111yescharacteristic
209C4—22no—
210C4—22no—
211C4—22no—
212C4—24no—
213C4—42no—
214C4—224no—
215C4—224no—
216C4—442no—
217C4—442no—
218C2#1062325311yescharacteristic
219C2#1062326012yes—
220C2#1062326611yescharacteristic
221C2#1062333511yescharacteristic
222C2Q8×C22⋊D1112yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC2×C11×C4⋊Q8C2
hypercenterC2×C4⋊Q8D11
hypocenterC11#2734
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
59. Dic11⋊C4Q8semidirect
173. C11#2734semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C4⋊Q82
C2×#669972
#106228432
#106228422
#106225972
#106225922
#106225912
#106225852
#106225462
#273411