Finite Group Databasebeta

← #13074437

Subgroups — #13074437

Order 1408.

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

normal subgroups only

This group has 488 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×#117C211yesmaximal, characteristic
2C2×#66922C211yesmaximal, characteristic, complemented
3#10622825C212yesmaximal
4#10622599C212yesmaximal, complemented
5#10622592C212yesmaximal, complemented
6#10622562C212yesmaximal
7#10622560C212yesmaximal
8#10622549C211yesmaximal, characteristic, complemented
9#10622541C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×Dic22C2212yes—
12C11×#117—24no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C42×C11C2211yescharacteristic
18C2×C42×C11C2211yescharacteristic
19C2×C22⋊Dic11C2214yes—
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2212yes—
22C2×C4⋊Dic11C2212yes—
23C2×Dic11⋊C4C2214yes—
24#66922—24no—
25C11⋊#95C2214yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2214yes—
29C24×C11C2311yescharacteristic
30C22×C4×C11—22no—
31C22×C4×C11—22no—
32C22×C4×C11Q814yescomplemented
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×Dic11C2314yes—
40C22×Dic11C2314yes—
41C2×Dic22—24no—
42C2×Dic22—44no—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—22no—
45C11×C22⋊C4—22no—
46C11×C22⋊C4—22no—
47C42×C11—22no—
48C42×C11D414yes—
49C22⋊Dic11—44no—
50C4⋊Dic11—24no—
51C4⋊Dic11—24no—
52C4⋊Dic11—24no—
53Dic11⋊C4—44no—
54#2628—111nomaximal, Sylow
55C23×C11—21no—
56C23×C11—21no—
57C23×C11—22no—
58C23×C11—22no—
59C23×C11C2×Q812yes—
60C23×C11C2411yescharacteristic
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—28no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×D412yes—
72C2×C4×C11C2×D412yes—
73C2×C4×C11C2×Q812yes—
74C2×C4×C11C2×Q812yes—
75C2×C4×C11#4112yes—
76C2×Dic11—24no—
77C2×Dic11—24no—
78C2×Dic11—24no—
79C2×Dic11—24no—
80C2×Dic11—24no—
81C2×Dic11—24no—
82Dic22—48no—
83C2×C4⋊Q8—111no—
84C2×#117D1111yescharacteristic
85#400—112no—
86#399—112no—
87#395—112no—
88#393—112no—
89#389—112no—
90#382—111no—
91#380—112no—
92C22×C11—22no—
93C22×C11—24no—
94C22×C11—41no—
95C22×C11—41no—
96C22×C11—42no—
97C22×C11C22×D411yescharacteristic
98C22×C11C22×Q811yescharacteristic
99C22×C11C2×#4111yescharacteristic
100C22×C11H(5,𝔽2)12yes—
101C22×C112−1+412yes—
102C4×C11—22no—
103C4×C11—22no—
104C4×C11—22no—
105C4×C11—41no—
106C4×C11—41no—
107C4×C11C22⋊Q814yes—
108Dic11—44no—
109Dic11—44no—
110C22×Q8—112no—
111C23×C4C2×D1111yescharacteristic
112C4⋊Q8—224no—
113#117—24no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—114no—
118C2×C4⋊C4C2×D1111yescharacteristic
119C2×C4⋊C4C2×D1111yescharacteristic
120C2×C22⋊C4—114no—
121C2×C22⋊C4C2×D1111yescharacteristic
122C2×C22⋊C4C2×D1111yescharacteristic
123C2×C42C2×D1111yescharacteristic
124C2×C42C2×D1111yescharacteristic
125#95—114no—
126#95—112no—
127#95—112no—
128#95—114no—
129C2×C11—42no—
130C2×C11C2×C22⋊Q811yescharacteristic
131C2×C11#53511yescharacteristic
132C2×C11#53611yescharacteristic
133C2×C11#54212yes—
134C2×C11#54412yes—
135C24C22×D1111yescharacteristic
136C2×Q8—224no—
137C2×Q8—444no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—114no—
141C22×C4—114no—
142C22×C4Dic2214yescomplemented
143C22×C4C22×D1111yescharacteristic
144C22×C4C22×D1111yescharacteristic
145C22×C4C22×D1111yescharacteristic
146C22×C4C22×D1111yescharacteristic
147C22×C4C22×D1111yescharacteristic
148C22×C4C22×D1111yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—224no—
152C4⋊C4—224no—
153C4⋊C4—224no—
154C4⋊C4—444no—
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—444no—
158C42—22no—
159C42C22⋊D1114yes—
160C11#262811yescharacteristic, complemented, Sylow
161C23—21no—
162C23—22no—
163C23—22no—
164C23—21no—
165C23C2×Dic2212yes—
166C23C23×D1111yescharacteristic
167Q8—448no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—224no—
178C2×C4—224no—
179C2×C4—224no—
180C2×C4—224no—
181C2×C4—224no—
182C2×C4—224no—
183C2×C4C2×Dic2212yes—
184C2×C4C2×Dic2212yes—
185C2×C4#433912yes—
186C2×C4C2×C22⋊D1112yes—
187C2×C4C2×C22⋊D1112yes—
188C2×C4C2×C22⋊D1112yes—
189C22—24no—
190C22—22no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22C22×Dic2211yescharacteristic
195C22C2×#433911yescharacteristic
196C22#6704212yes—
197C22#6704312yes—
198C22C22×C22⋊D1111yescharacteristic
199C4—22no—
200C4—22no—
201C4—22no—
202C4—41no—
203C4—41no—
204C4—444no—
205C4—444no—
206C4#6697714yes—
207C2—42no—
208C2#1062305012yes—
209C2#1062306512yes—
210C2C2×#6697711yescharacteristic
211C2#1062335611yescharacteristic
212C2#1062336111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#117C2
prime radicalC24×C11C23
hypercenterC2×#117D11
hypocenterC11#2628
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#66922C2semidirect
4. #10622599C2semidirect
5. #10622592C2semidirect
8. #10622549C2semidirect
9. #10622541C2semidirect
32. C22×C4×C11Q8semidirect
142. C22×C4Dic22semidirect
160. C11#2628semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1172
C2×#669222
#106228252
#106225992
#106225922
#106225622
#106225602
#106225492
#106225412
#262811