Finite Group Databasebeta

← #13073100

Subgroups — #13073100

Order 1408.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×#66999C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic
3C11×#391C211yesmaximal, characteristic, complemented
4#10622843C211yesmaximal, characteristic, complemented
5#10622590C211yesmaximal, characteristic, complemented
6C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#10622549C211yesmaximal, characteristic, complemented
8#10622277C214yesmaximal
9#10622271C214yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×C4×D11C2212yes—
12C22×C4×D11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15#66999—24no—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23C4⋊C4×D11—24no—
24C11×#95C2214yes—
25C11⋊#95C2212yes—
26C11⋊#95C2214yes—
27C11⋊#95C2214yes—
28C11⋊#95C2214yes—
29C23×D11C2311yescharacteristic
30C2×Q8×C11—22no—
31C2×Q8×C11—22no—
32C2×Q8×C11—22no—
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2311yescharacteristic
41C2×C4×D11—24no—
42C2×C4×D11—28no—
43C2×C4×D11—22no—
44C2×C4×D11—22no—
45C2×C4×D11D414yes—
46C11×C4⋊C4—22no—
47C42×C11—22no—
48(C2×D11)⋊C4—24no—
49(C2×D11)⋊C4—24no—
50C4⋊Dic11—22no—
51C4⋊Dic11—22no—
52Dic11⋊C4—24no—
53Dic11⋊C4—24no—
54C4×Dic11—22no—
55#2503—111nomaximal, Sylow
56C23×C11C2411yescharacteristic
57C22×D11—21no—
58C22×D11—21no—
59C22×D11—22no—
60C22×D11C2×D412yes—
61C22×D11#4114yes—
62Q8×C11—44no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—24no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11C2×D412yes—
72C2×C4×C11#4112yes—
73C2×C4×C11#4112yes—
74C2×Dic11—21no—
75C2×Dic11—21no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—24no—
81C2×Dic11—24no—
82C2×Dic11—22no—
83C2×Dic11C2×D412yes—
84C4×D11—28no—
85C4×D11—48no—
86C2×C22⋊Q8—111no—
87C22×C4⋊C4—111no—
88#400—114no—
89#391—111no—
90#391D1111yescharacteristic, complemented
91#382—111no—
92#382—111no—
93#381—114no—
94C4×C22⋊C4—111no—
95C22×C11C22×D411yescharacteristic
96C22×C11C2×#4111yescharacteristic
97C22×C11C2×#4111yescharacteristic
98C22×C11C2×#4112yes—
99C22×C112−1+412yes—
100C2×D11—22no—
101C2×D11—22no—
102C2×D11—24no—
103C2×D11—24no—
104C2×D11#12414yes—
105C4×C11—42no—
106C4×C11—42no—
107C4×C11—42no—
108C4×C11#12314yes—
109Dic11—22no—
110Dic11—42no—
111Dic11—42no—
112Dic11—42no—
113C22×Q8C2×D1111yescharacteristic
114C23×C4—111no—
115C23×C4—112no—
116C22⋊Q8—224no—
117C2×C4⋊C4—111no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—111no—
120C2×C4⋊C4—112no—
121C2×C4⋊C4—224no—
122C2×C4⋊C4C2×D1111yescharacteristic
123C2×C22⋊C4—112no—
124C2×C22⋊C4—112no—
125C2×C42—111no—
126C2×C42C2×D1111yescharacteristic
127#95—112no—
128#95—114no—
129#95—114no—
130#95—114no—
131#95C2×D1114yes—
132C2×C11C2×#12311yescharacteristic
133C2×C11C2×#12411yescharacteristic
134C2×C11#53611yescharacteristic
135C2×C11#55212yes—
136C2×C11#55212yes—
137D11—24no—
138C24—111no—
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—22no—
142C22×C4—111no—
143C22×C4—114no—
144C22×C4—112no—
145C22×C4—112no—
146C22×C4—112no—
147C22×C4—224no—
148C22×C4—228no—
149C22×C4—222no—
150C22×C4—222no—
151C22×C4C22×D1112yes—
152C22×C4C22×D1112yes—
153C22×C4C22×D1112yes—
154C22×C4C22×D1111yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—224no—
157C4⋊C4—224no—
158C4⋊C4—222no—
159C4⋊C4—222no—
160C22⋊C4—224no—
161C22⋊C4—224no—
162C42—22no—
163C42—222no—
164C11#250311yescharacteristic, complemented, Sylow
165C23—112no—
166C23—114no—
167C23—221no—
168C23—221no—
169C23—222no—
170C23C23×D1111yescharacteristic
171Q8—44no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—112no—
181C2×C4—221no—
182C2×C4—221no—
183C2×C4—228no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—224no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—224no—
191C2×C4—448no—
192C2×C4#433912yes—
193C2×C4D4×D1112yes—
194C2×C4#434112yes—
195C22—114no—
196C22—222no—
197C22—222no—
198C22—224no—
199C22—224no—
200C22C2×#433911yescharacteristic
201C22C2×D4×D1111yescharacteristic
202C22C2×#434111yescharacteristic
203C22#6704012yes—
204C22#41×D1112yes—
205C4—42no—
206C4—42no—
207C4—42no—
208C4—222no—
209C4—442no—
210C4—442no—
211C4—442no—
212C4#6693614yes—
213C2—224no—
214C2C2×#6693611yescharacteristic
215C2#1062311212yes—
216C2#1062317012yes—
217C2D11×#12411yescharacteristic
218C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC23×D11C23
hypercenter#391D11
hypocenterC11#2503
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. C11×#391C2semidirect
4. #10622843C2semidirect
5. #10622590C2semidirect
7. #10622549C2semidirect
9. #10622271C2semidirect
90. #391D11semidirect
164. C11#2503semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×C4⋊C4×D112
C11×#3912
#106228432
#106225902
C4×(C2×D11)⋊C42
#106225492
#106222772
#106222712
#250311