Finite Group Databasebeta

← #13073069

Subgroups — #13073069

Order 1408.

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

normal subgroups only

This group has 484 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×#66979C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic
3C4×C11×C22⋊C4C211yesmaximal, characteristic
4#10622566C214yesmaximal
5#10622549C211yesmaximal, characteristic, complemented
6#10622548C211yesmaximal, characteristic, complemented
7#10622542C211yesmaximal, characteristic, complemented
8#10622542C211yesmaximal, characteristic, complemented
9#10622266C214yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×C22⋊C4C2212yes—
13C2×C42×C11C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2212yes—
17#66979—24no—
18C2×C4⋊Dic11C2214yes—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22#66977—24no—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2212yes—
25C11×#95C2212yes—
26C11⋊#95C2214yes—
27C11⋊#95C2214yes—
28C11⋊#95C2214yes—
29C24×C11C2311yescharacteristic
30C22×C4×C11—22no—
31C22×C4×C11—22no—
32C22×C4×C11D414yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C2×Dic22—22no—
42C2×Dic22—22no—
43C2×Dic22—22no—
44C11×C22⋊C4—24no—
45C42×C11—22no—
46C42×C11—22no—
47C22⋊Dic11—24no—
48C22⋊Dic11—24no—
49C4⋊Dic11—22no—
50C4⋊Dic11—22no—
51C4⋊Dic11—22no—
52C4⋊Dic11—28no—
53Dic11⋊C4—24no—
54C4×Dic11—24no—
55#2499—111nomaximal, Sylow
56C23×C11—22no—
57C23×C11—21no—
58C23×C11—21no—
59C23×C11—22no—
60C23×C11C2×D412yes—
61C23×C11C2411yescharacteristic
62C2×C4×C11—22no—
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11—22no—
66C2×C4×C11—28no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×D412yes—
72C2×C4×C11#4114yes—
73C2×C4×C11#4112yes—
74C2×C4×C11#4112yes—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—24no—
80C2×Dic11—24no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—24no—
84Dic22—44no—
85C2×C22⋊Q8—111no—
86C2×#117—111no—
87#397—114no—
88#391—111no—
89#391—111no—
90#387—114no—
91#384—111no—
92#382—111no—
93C4×C22⋊C4D1111yescharacteristic
94C22×C11—22no—
95C22×C11—22no—
96C22×C11—22no—
97C22×C11—42no—
98C22×C11—42no—
99C22×C11C22×D411yescharacteristic
100C22×C11C2×#4112yes—
101C22×C11C2×#4111yescharacteristic
102C22×C11C2×#4111yescharacteristic
103C22×C112−1+412yes—
104C4×C11—22no—
105C4×C11—24no—
106C4×C11—42no—
107C4×C11#12314yes—
108Dic11—42no—
109Dic11—42no—
110Dic11—42no—
111Dic11—42no—
112C22×Q8—111no—
113C23×C4C2×D1111yescharacteristic
114C22⋊Q8—224no—
115#117—224no—
116C2×C4⋊C4—111no—
117C2×C4⋊C4—111no—
118C2×C4⋊C4—111no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—114no—
121C2×C22⋊C4—112no—
122C2×C22⋊C4—112no—
123C2×C22⋊C4C2×D1112yes—
124C2×C42—112no—
125C2×C42C2×D1111yescharacteristic
126C2×C42C2×D1111yescharacteristic
127#95—114no—
128#95—114no—
129#95—114no—
130#95C2×D1112yes—
131C2×C11—42no—
132C2×C11C2×#12311yescharacteristic
133C2×C11#53211yescharacteristic
134C2×C11#53611yescharacteristic
135C2×C11#55212yes—
136C2×C11#55612yes—
137C24C22×D1111yescharacteristic
138C2×Q8—222no—
139C2×Q8—222no—
140C2×Q8—222no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—112no—
144C22×C4—112no—
145C22×C4—112no—
146C22×C4—112no—
147C22×C4D4414yes—
148C22×C4C22×D1112yes—
149C22×C4C22×D1111yescharacteristic
150C22×C4C22×D1112yes—
151C22×C4C22×D1111yescharacteristic
152C4⋊C4—222no—
153C4⋊C4—222no—
154C4⋊C4—224no—
155C4⋊C4—222no—
156C4⋊C4—228no—
157C22⋊C4—24no—
158C22⋊C4—224no—
159C22⋊C4—224no—
160C42—22no—
161C42—22no—
162C42—224no—
163C11#249911yescharacteristic, complemented, Sylow
164C23—22no—
165C23—21no—
166C23—21no—
167C23—22no—
168C23C2×D4412yes—
169C23C23×D1111yescharacteristic
170Q8—444no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—28no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—224no—
184C2×C4—224no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—224no—
188C2×C4C2×D4412yes—
189C2×C4C2×D4412yes—
190C2×C4#433914yes—
191C2×C4#434112yes—
192C2×C4#434112yes—
193C22—22no—
194C22—22no—
195C22—22no—
196C22—42no—
197C22—42no—
198C22C22×D4411yescharacteristic
199C22C2×#433912yes—
200C22C2×#434111yescharacteristic
201C22C2×#434111yescharacteristic
202C22#6704312yes—
203C4—22no—
204C4—24no—
205C4—42no—
206C4—442no—
207C4—442no—
208C4—442no—
209C4—442no—
210C4#6693914yes—
211C2—42no—
212C2#1062300811yescharacteristic
213C2C2×#6693911yescharacteristic
214C2#1062305711yescharacteristic
215C2#1062307212yes—
216C2#1062307312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C22⋊C4C2
prime radicalC24×C11C23
hypercenterC4×C22⋊C4D11
hypocenterC11#2499
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. #10622549C2semidirect
6. #10622548C2semidirect
7. #10622542C2semidirect
8. #10622542C2semidirect
9. #10622266C2semidirect
163. C11#2499semidirect

Maximal subgroups

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

subgroupindex
C2×#669792
C2×#669772
C4×C11×C22⋊C42
#106225662
#106225492
#106225482
#106225422
#106222662
#249911