Finite Group Databasebeta

← #13073613

Subgroups — #13073613

Order 1408.

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

normal subgroups only

This group has 604 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×#67000C211yesmaximal, characteristic
2C2×#66997C211yesmaximal, characteristic, complemented
3C2×#66946C211yesmaximal, characteristic
4C2×#66928C211yesmaximal, characteristic
5C11×#391C211yesmaximal, characteristic, complemented
6#10622587C211yesmaximal, characteristic, complemented
7C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
8#10622288C214yesmaximal, complemented
9#10622280C214yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C22×C4×D11C2212yes—
13C22×Dic22C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C42×C11C2211yescharacteristic
16#67000—24no—
17#66997—24no—
18C2×(C2×D11)⋊C4C2214yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2214yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2211yescharacteristic
25C2×C4×Dic11C2211yescharacteristic
26#66946—24no—
27#66928—24no—
28C11×#95C2214yes—
29C11⋊#95C2214yes—
30C11⋊#95C2212yes—
31C23×D11C2312yes—
32C2×Q8×C11—22no—
33C2×Q8×C11—22no—
34C2×Q8×C11—22no—
35C22×C4×C11C2312yes—
36C22×C4×C11C2312yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2311yescharacteristic
42C22×Dic11C2311yescharacteristic
43C2×D44—22no—
44C2×D44—22no—
45C2×D44D414yes—
46C2×C4×D11—24no—
47C2×C4×D11—28no—
48C2×Dic22—22no—
49C2×Dic22—22no—
50C2×Dic22—22no—
51C11×C4⋊C4—22no—
52C42×C11—22no—
53(C2×D11)⋊C4—24no—
54(C2×D11)⋊C4—28no—
55(C2×D11)⋊C4—28no—
56Dic11⋊C4—24no—
57Dic11⋊C4—24no—
58Dic11⋊C4—24no—
59C4×Dic11—22no—
60C4×Dic11D414yes—
61#2547—111nomaximal, Sylow
62C23×C11C2411yescharacteristic
63C22×D11—22no—
64C22×D11—24no—
65C22×D11—22no—
66C22×D11—24no—
67C22×D11C2×D414yes—
68Q8×C11—44no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—24no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2×D412yes—
79C2×C4×C11#4112yes—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11C2×D412yes—
88C2×Dic11C2×D412yes—
89C2×Dic11#4114yes—
90D44—28no—
91C4×D11—48no—
92Dic22—44no—
93C2×C4⋊Q8—111no—
94C2×#124—111no—
95C2×#124—111no—
96C2×C4×D4—111no—
97#397—114no—
98#391—111no—
99#391D1111yescharacteristic, complemented
100#380—114no—
101C4×C4⋊C4—111no—
102C22×C11C22×D411yescharacteristic
103C22×C11C22×D411yescharacteristic
104C22×C11C2×#4111yescharacteristic
105C22×C11C2×#4112yes—
106C22×C112−1+412yes—
107C2×D11—24no—
108C2×D11—28no—
109C2×D11—42no—
110C2×D11—42no—
111C2×D11—44no—
112C4×C11—42no—
113C4×C11—42no—
114C4×C11—42no—
115C4×C11#12114yes—
116Dic11—22no—
117Dic11—42no—
118Dic11—42no—
119Dic11#12414yescomplemented
120C22×Q8—111no—
121C22×Q8C2×D1111yescharacteristic
122C22×D4—111no—
123C23×C4—112no—
124C4⋊Q8—224no—
125#124—224no—
126#124—224no—
127C4×D4—224no—
128C2×C4⋊C4—112no—
129C2×C4⋊C4—112no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4C2×D1111yescharacteristic
132C2×C22⋊C4—112no—
133C2×C22⋊C4—114no—
134C2×C22⋊C4—114no—
135C2×C42—111no—
136C2×C42—111no—
137C2×C42C2×D1111yescharacteristic
138#95—112no—
139#95—114no—
140#95C2×D1114yes—
141C2×C11C2×#12111yescharacteristic
142C2×C11C2×#12411yescharacteristic
143C2×C11#53611yescharacteristic
144C2×C11#54712yes—
145C2×C11#55612yes—
146D11—44no—
147C24—112no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—222no—
152C2×Q8—222no—
153C2×Q8—222no—
154C2×D4—114no—
155C2×D4—222no—
156C2×D4—222no—
157C22×C4—111no—
158C22×C4—111no—
159C22×C4—112no—
160C22×C4—112no—
161C22×C4—224no—
162C22×C4—228no—
163C22×C4C22×D1112yes—
164C22×C4C22×D1112yes—
165C22×C4C22×D1112yes—
166C22×C4C22×D1111yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—224no—
169C4⋊C4—224no—
170C4⋊C4—224no—
171C22⋊C4—224no—
172C22⋊C4—228no—
173C22⋊C4—228no—
174C42—22no—
175C42—114no—
176C42—222no—
177C11#254711yescharacteristic, complemented, Sylow
178C23—114no—
179C23—222no—
180C23—222no—
181C23—224no—
182C23—224no—
183C23C23×D1111yescharacteristic
184Q8—44no—
185Q8—444no—
186D4—228no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—112no—
196C2×C4—114no—
197C2×C4—112no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—448no—
206C2×C4#433912yes—
207C2×C4D4×D1112yes—
208C2×C4D4×D1112yes—
209C22—224no—
210C22—228no—
211C22—442no—
212C22—444no—
213C22—442no—
214C22C2×#433911yescharacteristic
215C22C2×D4×D1111yescharacteristic
216C22C2×D4×D1111yescharacteristic
217C22#6704012yes—
218C22#41×D1112yes—
219C4—42no—
220C4—42no—
221C4—42no—
222C4—114no—
223C4—222no—
224C4—442no—
225C4—442no—
226C4#6693714yes—
227C2—444no—
228C2C2×#6693711yescharacteristic
229C2#1062309912yes—
230C2#1062316212yes—
231C2D11×#12411yescharacteristic
232C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC22×D44C22
hypercenter#391D11
hypocenterC11#2547
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#66997C2semidirect
5. C11×#391C2semidirect
6. #10622587C2semidirect
7. C4×Dic11⋊C4C2semidirect
8. #10622288C2semidirect
9. #10622280C2semidirect
99. #391D11semidirect
119. Dic11#124semidirect
177. C11#2547semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669972
C2×#669462
C2×#669282
C11×#3912
#106225872
C4×Dic11⋊C42
#106222882
#106222802
#254711