Finite Group Databasebeta

← #13072890

Subgroups — #13072890

Order 1408.

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

normal subgroups only

This group has 672 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
1C22×C11×C22⋊C4C211yesmaximal, characteristic
2C2×#66979C211yesmaximal, characteristic, complemented
3#10622860C212yesmaximal
4#10622824C211yesmaximal, characteristic, complemented
5#10622823C212yesmaximal, complemented
6#10622566C212yesmaximal, complemented
7#10622562C212yesmaximal, complemented
8#10622557C214yesmaximal, complemented
9C25×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C2×C11×C22⋊C4—24no—
13C2×C11×C22⋊C4C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2214yes—
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2214yes—
19#66979—24no—
20C2×C4⋊Dic11C2211yescharacteristic, complemented
21C2×C4⋊Dic11C2211yescharacteristic, complemented
22C2×Dic11⋊C4C2214yescomplemented
23C2×C4×Dic11C2212yescomplemented
24C11⋊#95C2212yescomplemented
25C11⋊#95C2214yescomplemented
26C11⋊#95C2212yescomplemented
27C24×C11—22no—
28C24×C11—24no—
29C24×C11—24no—
30C24×C11—42no—
31C24×C11C2312yes—
32C24×C11C2311yescharacteristic
33C22×C4×C11—24no—
34C22×C4×C11—22no—
35C22×C4×C11—42no—
36C22×C4×C11D414yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×Dic11C2314yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C11×C22⋊C4—24no—
44C11×C22⋊C4—24no—
45C22⋊Dic11—24no—
46C22⋊Dic11—28no—
47C22⋊Dic11—24no—
48C22⋊Dic11—44no—
49C4⋊Dic11—22no—
50C4⋊Dic11—22no—
51Dic11⋊C4—44no—
52C4×Dic11—24no—
53#2482—111nomaximal, Sylow
54C23×C11—22no—
55C23×C11—22no—
56C23×C11—28no—
57C23×C11—22no—
58C23×C11—22no—
59C23×C11—24no—
60C23×C11—24no—
61C23×C11—416no—
62C23×C11—44no—
63C23×C11—44no—
64C23×C11C2×D412yes—
65C23×C11#4114yes—
66C23×C11#4114yes—
67C23×C11C2411yescharacteristic
68C2×C4×C11—28no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—24no—
73C2×C4×C11—44no—
74C2×C4×C11C2×D412yes—
75C2×C4×C11C2×D412yes—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—24no—
79C2×Dic11—24no—
80C2×Dic11—24no—
81C2×Dic11—24no—
82C2×Dic11—24no—
83C2×#117—111no—
84C22×C22⋊C4D1111yescharacteristic
85#399—112no—
86#397—112no—
87#388—114no—
88#385—112no—
89#381—111no—
90#379—112no—
91C22×C11—22no—
92C22×C11—22no—
93C22×C11—28no—
94C22×C11—24no—
95C22×C11—28no—
96C22×C11—416no—
97C22×C11—42no—
98C22×C11—42no—
99C22×C11—44no—
100C22×C11#12314yes—
101C22×C11C22×D411yescharacteristic
102C22×C11C2×#4112yes—
103C22×C11C2×#4112yes—
104C22×C11H(5,𝔽2)12yes—
105C4×C11—22no—
106C4×C11—22no—
107C4×C11—42no—
108Dic11—42no—
109Dic11—42no—
110Dic11—44no—
111C25C2×D1111yescharacteristic
112C23×C4C2×D1111yescharacteristic
113C23×C4C2×D1111yescharacteristic
114#117—224no—
115C2×C4⋊C4—111no—
116C2×C4⋊C4—111no—
117C2×C4⋊C4—114no—
118C2×C22⋊C4—24no—
119C2×C22⋊C4—112no—
120C2×C22⋊C4—112no—
121C2×C22⋊C4—114no—
122C2×C22⋊C4—114no—
123C2×C22⋊C4C2×D1112yes—
124C2×C22⋊C4C2×D1112yes—
125C2×C42—112no—
126#95—112no—
127#95—112no—
128#95—114no—
129C2×C11—24no—
130C2×C11—44no—
131C2×C11C2×#12311yescharacteristic
132C2×C11#52511yescharacteristic
133C2×C11#53511yescharacteristic
134C2×C11#55114yes—
135C24—24no—
136C24—22no—
137C24—24no—
138C24—42no—
139C24C22×D1112yes—
140C24C22×D1111yescharacteristic
141C22×C4—24no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4—114no—
145C22×C4—112no—
146C22×C4—112no—
147C22×C4C22⋊D1114yes—
148C22×C4C22×D1112yes—
149C22×C4C22×D1111yescharacteristic
150C22×C4C22×D1111yescharacteristic
151C4⋊C4—222no—
152C4⋊C4—222no—
153C4⋊C4—444no—
154C22⋊C4—24no—
155C22⋊C4—24no—
156C22⋊C4—228no—
157C22⋊C4—224no—
158C22⋊C4—224no—
159C22⋊C4—444no—
160C42—224no—
161C11#248211yescharacteristic, complemented, Sylow
162C23—22no—
163C23—22no—
164C23—28no—
165C23—22no—
166C23—24no—
167C23—24no—
168C23—22no—
169C23—416no—
170C23—44no—
171C23—44no—
172C23#433914yes—
173C23#434114yes—
174C23C2×C22⋊D1112yes—
175C23C23×D1111yescharacteristic
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—44no—
182C2×C4—224no—
183C2×C4—224no—
184C2×C4—224no—
185C2×C4—224no—
186C2×C4—224no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4C2×C22⋊D1112yes—
190C2×C4C2×C22⋊D1112yes—
191C22—28no—
192C22—22no—
193C22—22no—
194C22—28no—
195C22—24no—
196C22—416no—
197C22—44no—
198C22—42no—
199C22—42no—
200C22#6698814yes—
201C22C2×#433912yes—
202C22C2×#434112yes—
203C22#6703712yes—
204C22C22×C22⋊D1111yescharacteristic
205C4—22no—
206C4—22no—
207C4—42no—
208C4—444no—
209C4—442no—
210C4—442no—
211C2—24no—
212C2—44no—
213C2#1062302614yes—
214C2#1062332211yescharacteristic
215C2C2×#6698811yescharacteristic
216C2#1062333611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC22×C11×C22⋊C4C2
prime radicalC25×C11C22
hypercenterC22×C22⋊C4D11
hypocenterC11#2482
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#66979C2semidirect
4. #10622824C2semidirect
5. #10622823C2semidirect
6. #10622566C2semidirect
7. #10622562C2semidirect
8. #10622557C2semidirect
20. C2×C4⋊Dic11C22semidirect
21. C2×C4⋊Dic11C22semidirect
22. C2×Dic11⋊C4C22semidirect
23. C2×C4×Dic11C22semidirect
24. C11⋊#95C22semidirect
25. C11⋊#95C22semidirect
26. C11⋊#95C22semidirect
161. C11#2482semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊C42
C2×#669792
#106228602
#106228242
#106228232
#106225662
#106225622
#106225572
#248211