Finite Group Databasebeta

← #13076646

Subgroups — #13076646

Order 1408.

528 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 133 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×#66983C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic, complemented
3C11×#381C211yesmaximal, characteristic, complemented
4#10622574C214yesmaximal, complemented
5#10622290C212yesmaximal, complemented
6#10622286C212yesmaximal, complemented
7#10622285C212yesmaximal, complemented
8#10622274C212yesmaximal, complemented
9C23×C4×C11C2211yescharacteristic
10C22×C22⋊D11C2212yes—
11C22×D44C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C2×C11×C22⋊C4C2212yes—
14C2×C22⋊Dic11C2212yes—
15#66983—24no—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2214yes—
18C2×(C2×D11)⋊C4C2214yes—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2211yescharacteristic
21C2×C4⋊Dic11C2214yes—
22#66977—24no—
23C2×Dic11⋊C4C2212yes—
24C11×#95C2212yes—
25C11×#95C2212yes—
26C11⋊#95C2214yes—
27C24×C11C2311yescharacteristic
28C23×D11C2312yes—
29C22×C4×C11—42no—
30C22×C4×C11D414yes—
31C22×C4×C11C2314yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C2×C22⋊D11—24no—
35C2×C22⋊D11—44no—
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C2×D44—22no—
40C2×D44—42no—
41C2×Dic22—22no—
42C2×Dic22—42no—
43C11×C22⋊C4—42no—
44C22⋊Dic11—24no—
45(C2×D11)⋊C4—24no—
46(C2×D11)⋊C4—44no—
47(C2×D11)⋊C4—44no—
48C4⋊Dic11—22no—
49C4⋊Dic11—22no—
50C4⋊Dic11—44no—
51Dic11⋊C4—24no—
52#2816—111nomaximal, Sylow
53C23×C11—22no—
54C23×C11—22no—
55C23×C11—22no—
56C23×C11C2×D412yes—
57C23×C11C2411yescharacteristic
58C22×D11—22no—
59C22×D11—24no—
60C22×D11—24no—
61C22×D11—24no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—24no—
65C2×C4×C11—24no—
66C2×C4×C11—24no—
67C2×C4×C11—44no—
68C2×C4×C11C2×D412yes—
69C2×C4×C11C2×D412yes—
70C22⋊D11—48no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—24no—
76C2×Dic11—22no—
77C2×Dic11—24no—
78D44—44no—
79Dic22—44no—
80C2×C22⋊Q8—111no—
81C2×#121—111no—
82#399—112no—
83#398—112no—
84#394—114no—
85#394—112no—
86#393—112no—
87#381D1111yescharacteristic, complemented
88C22×C11—22no—
89C22×C11—22no—
90C22×C11—22no—
91C22×C11—44no—
92C22×C11C22×D411yescharacteristic
93C22×C11H(5,𝔽2)12yes—
94C22×C11H(5,𝔽2)12yes—
95C22×C112−1+412yes—
96C2×D11—42no—
97C2×D11—42no—
98C2×D11—42no—
99C2×D11—48no—
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—44no—
103Dic11—42no—
104Dic11—42no—
105Dic11—42no—
106C22×Q8—111no—
107C22×D4—112no—
108C22×D4—111no—
109C23×C4C2×D1111yescharacteristic
110C22⋊Q8—224no—
111#121—224no—
112C2×C4⋊C4—111no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4—111no—
115C2×C4⋊C4—114no—
116C2×C22⋊C4—112no—
117C2×C22⋊C4—112no—
118C2×C22⋊C4—114no—
119C2×C22⋊C4—114no—
120C2×C22⋊C4C2×D1112yes—
121#95—114no—
122#95C2×D1112yes—
123#95C2×D1112yes—
124C2×C11—42no—
125C2×C11#53411yescharacteristic
126C2×C11#53511yescharacteristic
127C2×C11#53611yescharacteristic
128C2×C11#56214yes—
129D11—82no—
130C24—112no—
131C24C22×D1111yescharacteristic
132C2×Q8—222no—
133C2×Q8—442no—
134C2×D4—224no—
135C2×D4—222no—
136C2×D4—442no—
137C2×D4—444no—
138C22×C4—42no—
139C22×C4—112no—
140C22×C4—112no—
141C22×C4—112no—
142C22×C4D4414yes—
143C22×C4C22×D1114yes—
144C22×C4C22×D1111yescharacteristic
145C22×C4C22×D1111yescharacteristic
146C4⋊C4—222no—
147C4⋊C4—224no—
148C4⋊C4—222no—
149C4⋊C4—444no—
150C22⋊C4—42no—
151C22⋊C4—224no—
152C22⋊C4—224no—
153C22⋊C4—444no—
154C22⋊C4—444no—
155C11#281611yescharacteristic, complemented, Sylow
156C23—22no—
157C23—22no—
158C23—22no—
159C23—222no—
160C23—224no—
161C23—224no—
162C23—224no—
163C23C2×D4412yes—
164C23C23×D1111yescharacteristic
165Q8—444no—
166D4—444no—
167D4—448no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—44no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4—224no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—224no—
181C2×C4C2×D4412yes—
182C2×C4C2×D4412yes—
183C22—22no—
184C22—22no—
185C22—22no—
186C22—44no—
187C22—442no—
188C22—442no—
189C22—442no—
190C22—448no—
191C22C22×D4411yescharacteristic
192C22#6703712yes—
193C22#6704212yes—
194C22#6704312yes—
195C4—22no—
196C4—22no—
197C4—44no—
198C4—442no—
199C4—442no—
200C4—442no—
201C2—42no—
202C2—882no—
203C2#1062302411yescharacteristic
204C2#1062305611yescharacteristic
205C2#1062305711yescharacteristic
206C2#1062319814yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radicalC2×#66983C2
hypercenter#381D11
hypocenterC11#2816
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#66977C2semidirect
3. C11×#381C2semidirect
4. #10622574C2semidirect
5. #10622290C2semidirect
6. #10622286C2semidirect
7. #10622285C2semidirect
8. #10622274C2semidirect
87. #381D11semidirect
155. C11#2816semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C2×#669772
C11×#3812
#106225742
#106222902
#106222862
#106222852
#106222742
#281611