Finite Group Databasebeta

← #13074555

Subgroups — #13074555

Order 1408.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#66941C211yesmaximal, characteristic, complemented
3C11×#391C211yesmaximal, characteristic, complemented
4#10622843C211yesmaximal, characteristic, complemented
5#10622601C211yesmaximal, characteristic
6#10622552C211yesmaximal, characteristic
7#10622545C211yesmaximal, characteristic, complemented
8#10622288C214yesmaximal, complemented
9#10622286C214yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C22×Dic22C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15#67000—24no—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2214yes—
19C2×(C2×D11)⋊C4C2214yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23C2×C4×Dic11C2211yescharacteristic
24#66941—24no—
25C11×#95C2214yes—
26C11⋊#95C2212yes—
27C11⋊#95C2214yes—
28C11⋊#95C2212yes—
29C23×D11C2312yes—
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×Dic11C2311yescharacteristic
40C22×Dic11C2311yescharacteristic
41C2×D44—22no—
42C2×D44—22no—
43C2×D44—22no—
44C2×Dic22—24no—
45C2×Dic22—44no—
46C11×C4⋊C4—22no—
47C42×C11—22no—
48(C2×D11)⋊C4—24no—
49(C2×D11)⋊C4—24no—
50(C2×D11)⋊C4—44no—
51(C2×D11)⋊C4—44no—
52C4⋊Dic11—22no—
53Dic11⋊C4—24no—
54C4×Dic11—22no—
55C4×Dic11D414yes—
56#2640—111nomaximal, Sylow
57C23×C11C2411yescharacteristic
58C22×D11—22no—
59C22×D11—22no—
60C22×D11—22no—
61C22×D11—24no—
62C22×D11—24no—
63Q8×C11—44no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—24no—
71C2×C4×C11—22no—
72C2×C4×C11C2×D412yes—
73C2×C4×C11#4112yes—
74C2×C4×C11#4112yes—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—24no—
81C2×Dic11—22no—
82C2×Dic11C2×D412yes—
83C2×Dic11C2×D412yes—
84D44—44no—
85Dic22—48no—
86C2×C4⋊Q8—111no—
87C2×#124—111no—
88#397—114no—
89#393—114no—
90#391—111no—
91#391D1111yescharacteristic, complemented
92#390—111no—
93#390—111no—
94#376—111no—
95C22×C11C22×D411yescharacteristic
96C22×C11C2×#4111yescharacteristic
97C22×C11C2×#4111yescharacteristic
98C22×C11H(5,𝔽2)12yes—
99C22×C112−1+412yes—
100C2×D11—42no—
101C2×D11—42no—
102C2×D11—42no—
103C2×D11—44no—
104C2×D11—44no—
105C4×C11—42no—
106C4×C11—42no—
107C4×C11—42no—
108C4×C11#12414yes—
109Dic11—22no—
110Dic11—22no—
111Dic11—42no—
112Dic11—42no—
113C22×Q8—112no—
114C22×Q8C2×D1111yescharacteristic
115C22×D4—111no—
116C4⋊Q8—224no—
117#124—224no—
118C2×C4⋊C4—111no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4C2×D1111yescharacteristic
121C2×C22⋊C4—112no—
122C2×C22⋊C4—112no—
123C2×C22⋊C4—114no—
124C2×C22⋊C4—114no—
125C2×C42—111no—
126C2×C42—111no—
127C2×C42C2×D1111yescharacteristic
128#95—112no—
129#95—112no—
130#95—114no—
131#95C2×D1114yes—
132C2×C11C2×#12411yescharacteristic
133C2×C11#53511yescharacteristic
134C2×C11#53611yescharacteristic
135C2×C11#54212yes—
136C2×C11#54212yes—
137D11—82no—
138C24—112no—
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—224no—
143C2×Q8—444no—
144C2×D4—222no—
145C2×D4—222no—
146C2×D4—222no—
147C22×C4—111no—
148C22×C4—111no—
149C22×C4—112no—
150C22×C4—112no—
151C22×C4C22×D1112yes—
152C22×C4C22×D1112yes—
153C22×C4C22×D1112yes—
154C22×C4C22×D1111yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—224no—
157C4⋊C4—222no—
158C22⋊C4—224no—
159C22⋊C4—224no—
160C22⋊C4—444no—
161C22⋊C4—444no—
162C42—22no—
163C42—114no—
164C42—222no—
165C11#264011yescharacteristic, complemented, Sylow
166C23—222no—
167C23—222no—
168C23—222no—
169C23—224no—
170C23—224no—
171C23C23×D1111yescharacteristic
172Q8—44no—
173Q8—448no—
174D4—444no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—112no—
184C2×C4—112no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—224no—
192C2×C4#433912yes—
193C2×C4D4×D1112yes—
194C2×C4#434112yes—
195C22—442no—
196C22—442no—
197C22—444no—
198C22—444no—
199C22—442no—
200C22C2×#433911yescharacteristic
201C22C2×D4×D1111yescharacteristic
202C22C2×#434111yescharacteristic
203C22#6704012yes—
204C22#6704212yes—
205C4—42no—
206C4—42no—
207C4—42no—
208C4—222no—
209C4—222no—
210C4—442no—
211C4—442no—
212C4#6693814yes—
213C2—882no—
214C2C2×#6693811yescharacteristic
215C2#1062311312yes—
216C2#1062317412yes—
217C2#1062320511yescharacteristic
218C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC22×D44C22
hypercenter#391D11
hypocenterC11#2640
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#66941C2semidirect
3. C11×#391C2semidirect
4. #10622843C2semidirect
7. #10622545C2semidirect
8. #10622288C2semidirect
9. #10622286C2semidirect
91. #391D11semidirect
165. C11#2640semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669412
C11×#3912
#106228432
#106226012
#106225522
#106225452
#106222882
#106222862
#264011