Finite Group Databasebeta

← #13073525

Subgroups — #13073525

Order 1408.

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

normal subgroups only

This group has 604 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×C4×D4×C11C211yesmaximal, characteristic
2C2×#66977C212yesmaximal, complemented
3C2×C4×Dic22C211yesmaximal, characteristic, complemented
4#10622835C212yesmaximal
5#10622825C212yesmaximal, complemented
6#10622593C212yesmaximal, complemented
7#10622557C214yesmaximal, complemented
8#10622549C211yesmaximal, characteristic, complemented
9C22×D4×C11C2211yescharacteristic
10C23×C4×C11C2212yes—
11C22×Dic22C2211yescharacteristic
12C4×D4×C11—24no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C42×C11C2211yescharacteristic
16C2×C22⋊Dic11C2214yes—
17C2×C22⋊Dic11C2214yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2212yes—
20#66977—28no—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2214yes—
23C2×C4×Dic11C2212yes—
24C4×Dic22—24no—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2214yes—
28C24×C11C2312yes—
29C2×D4×C11—24no—
30C2×D4×C11—22no—
31C22×C4×C11—24no—
32C22×C4×C11—24no—
33C22×C4×C11—24no—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×Dic11C2314yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C2×Dic22—22no—
42C2×Dic22—22no—
43C2×Dic22D414yescomplemented
44C11×C4⋊C4—22no—
45C11×C22⋊C4—24no—
46C42×C11D414yes—
47C22⋊Dic11—28no—
48C22⋊Dic11—28no—
49C4⋊Dic11—22no—
50C4⋊Dic11—24no—
51Dic11⋊C4—28no—
52Dic11⋊C4—24no—
53C4×Dic11—24no—
54#2536—111nomaximal, Sylow
55C23×C11—22no—
56C23×C11—22no—
57C23×C11—22no—
58C23×C11—22no—
59C23×C11—22no—
60C23×C11—22no—
61C23×C11#4114yes—
62C23×C11C2411yescharacteristic
63D4×C11—28no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—48no—
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×D412yes—
72C2×C4×C11C2×D412yes—
73C2×C4×C11C2×D412yes—
74C2×C4×C11#4112yes—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—24no—
79C2×Dic11—24no—
80C2×Dic11—24no—
81C2×Dic11—24no—
82C2×Dic11C2×D414yes—
83Dic22—28no—
84C2×C22⋊Q8—112no—
85C2×C4×Q8—111no—
86C2×C4×D4D1111yescharacteristic
87#398—112no—
88#394—112no—
89#388—114no—
90#382—111no—
91#380—112no—
92C22×C11—24no—
93C22×C11—24no—
94C22×C11—24no—
95C22×C11—42no—
96C22×C11—42no—
97C22×C11—42no—
98C22×C11—42no—
99C22×C11C22×D411yescharacteristic
100C22×C11C22×D411yescharacteristic
101C22×C11C2×#4112yes—
102C22×C11C2×#4111yescharacteristic
103C22×C112−1+412yes—
104C4×C11—22no—
105C4×C11—22no—
106C4×C11—42no—
107C4×C11#12114yes—
108Dic11—24no—
109Dic11—42no—
110Dic11—44no—
111C22×Q8—111no—
112C22×D4C2×D1111yescharacteristic
113C23×C4C2×D1112yes—
114C22⋊Q8—228no—
115C4×Q8—224no—
116C4×D4—24no—
117C2×C4⋊C4—111no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—114no—
121C2×C4⋊C4C2×D1111yescharacteristic
122C2×C22⋊C4—114no—
123C2×C22⋊C4—114no—
124C2×C22⋊C4C2×D1112yes—
125C2×C42—112no—
126C2×C42C2×D1111yescharacteristic
127#95—114no—
128#95—112no—
129#95—112no—
130C2×C11—44no—
131C2×C11C2×#12111yescharacteristic
132C2×C11#52511yescharacteristic
133C2×C11#53611yescharacteristic
134C2×C11#54812yes—
135C2×C11#55212yes—
136C24C22×D1112yes—
137C2×Q8—114no—
138C2×Q8—222no—
139C2×Q8—222no—
140C2×D4—24no—
141C2×D4—22no—
142C22×C4—24no—
143C22×C4—24no—
144C22×C4—24no—
145C22×C4—112no—
146C22×C4—114no—
147C22×C4—112no—
148C22×C4C22×D1112yes—
149C22×C4C22×D1111yescharacteristic
150C22×C4C22×D1111yescharacteristic
151C22×C4C22×D1111yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—228no—
154C4⋊C4—224no—
155C4⋊C4—224no—
156C4⋊C4—222no—
157C22⋊C4—24no—
158C22⋊C4—228no—
159C22⋊C4—228no—
160C42—224no—
161C42C22⋊D1114yes—
162C11#253611yescharacteristic, complemented, Sylow
163C23—22no—
164C23—22no—
165C23—22no—
166C23—22no—
167C23—22no—
168C23—22no—
169C23#433914yes—
170C23C23×D1111yescharacteristic
171Q8—228no—
172D4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—48no—
179C2×C4—114no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—224no—
183C2×C4—224no—
184C2×C4—224no—
185C2×C4—224no—
186C2×C4—222no—
187C2×C4D4×D1112yes—
188C2×C4#434112yes—
189C2×C4C2×C22⋊D1112yes—
190C2×C4C2×C22⋊D1112yes—
191C2×C4C2×C22⋊D1112yes—
192C22—24no—
193C22—24no—
194C22—24no—
195C22—42no—
196C22—42no—
197C22—42no—
198C22—42no—
199C22C2×#433912yes—
200C22C2×D4×D1111yescharacteristic
201C22C2×#434111yescharacteristic
202C22#6704312yes—
203C22C22×C22⋊D1111yescharacteristic
204C4—22no—
205C4—22no—
206C4—42no—
207C4—224no—
208C4—442no—
209C4—444no—
210C4#6699114yes—
211C2—44no—
212C2#1062307212yes—
213C2#1062308312yes—
214C2#1062332211yescharacteristic
215C2C2×#6699111yescharacteristic
216C2#1062335611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
prime radicalC22×D4×C11C22
hypercenterC2×C4×D4D11
hypocenterC11#2536
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#66977C2semidirect
3. C2×C4×Dic22C2semidirect
5. #10622825C2semidirect
6. #10622593C2semidirect
7. #10622557C2semidirect
8. #10622549C2semidirect
43. C2×Dic22D4semidirect
162. C11#2536semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
C2×#669772
C2×C4×Dic222
#106228352
#106228252
#106225932
#106225572
#106225492
#253611