Finite Group Databasebeta

← #355×D113 #28392250

Subgroups — #355×D113 #28392250

Order 14464.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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
1#124×D113C211yesmaximal, characteristic
2#101×D113C212yesmaximal, complemented
3#20298395C211yesmaximal, characteristic, complemented
4#20298394C212yesmaximal, complemented
5#355×C113C211yesmaximal, characteristic, complemented
6C2×Q8×D113C2211yescharacteristic
7C2×D4×D113C411yescharacteristic
8M16×D113—22no—
9#16813611C2211yescharacteristic
10#16813610C411yescharacteristic
11#16813609C411yescharacteristic
12#16813608—22no—
13C22⋊C4×D113—22no—
14C42×D113C411yescharacteristic
15#16813541C2212yescomplemented
16#16813540—22no—
17#124×C113C2211yescharacteristic
18#101×C113C2212yescomplemented
19C23×D113—21no—
20C2×Dic226C2×C411yescharacteristic
21C2×Dic226D412yes—
22Q8×D113—41no—
23Q8×D113—41no—
24C2×D452C2×C411yescharacteristic
25C2×C22⋊D113—21no—
26D4×D113—41no—
27D4×D113—41no—
28C2×C4×D113—21no—
29C2×C4×D113C2×C411yescharacteristic
30C2×C4×D113D412yes—
31#14268631—22no—
32#14268630—42no—
33C8×D113—42no—
34C22⋊Dic113—22no—
35#14268624—22no—
36#14268624—22no—
37C4×Dic113—21no—
38C4×Dic113C2×C411yescharacteristic
39C2×Q8×C113C2311yescharacteristic
40C2×D4×C113C2×C411yescharacteristic
41M16×C113—22no—
42C22⋊C4×C113—22no—
43C42×C113C2×C411yescharacteristic
44C23×C113—21no—
45C22×D113—21no—
46C22×D113—44no—
47C22×D113—41no—
48C22×D113—41no—
49C22×D113C22⋊C411yescharacteristic
50Q8×C113—41no—
51D4×C113—41no—
52C2×C4×C113—21no—
53C2×C4×C113C22×C411yescharacteristic
54C2×C4×C113C2×D412yes—
55C22⋊D113—42no—
56C2×Dic113—21no—
57C2×Dic113C22⋊C411yescharacteristic
58C2×Dic113C22⋊C412yes—
59D452—41no—
60C4×D113—22no—
61C4×D113—22no—
62C4×D113—21no—
63C4×D113—21no—
64C4×D113—42no—
65Dic226—41no—
66Dic226—42no—
67C8×C113—42no—
68#11744751—42no—
69C22×C113—42no—
70C22×C113—41no—
71C22×C113C2×C22⋊C411yescharacteristic
72C2×D113—22no—
73C2×D113—42no—
74C2×D113—41no—
75C2×D113—82no—
76C2×D113—82no—
77C2×D113#9911yescharacteristic
78C2×D113#9911yescharacteristic
79C4×C113—22no—
80C4×C113—21no—
81C4×C113—41no—
82Dic113—22no—
83Dic113—21no—
84Dic113—41no—
85C2×C113—21no—
86C2×C113—81no—
87C2×C113C2×#9911yescharacteristic
88D113—21no—
89D113—81no—
90D113#35512yesdirect product factor
91C2×#355—1131nomaximal, Sylow
92C113C2×#35511yescharacteristic, complemented, Sylow
93C2×#124—1131no—
94C2×#101—1132no—
95#355—1131no—
96#355—1132no—
97#355D11311yescharacteristic, direct product factor
98C22×Q8—1131no—
99C22×D4—1131no—
100C2×M16—2262no—
101#124—1131no—
102#124—1131no—
103#124—1131no—
104#124—2262no—
105#124C2×D11311yescharacteristic
106C2×C22⋊C4—2262no—
107C2×C42—1131no—
108#101—1132no—
109#101—2262no—
110#101C2×D11312yescomplemented
111C24—2261no—
112C2×Q8—1131no—
113C2×Q8—1132no—
114C2×Q8—4521no—
115C2×Q8—4521no—
116C2×Q8C22×D11311yescharacteristic
117C2×D4—1131no—
118C2×D4—4521no—
119C2×D4—4521no—
120C2×D4—2261no—
121C2×D4C4×D11311yescharacteristic
122C22×C4—1131no—
123C22×C4—1132no—
124C22×C4—2261no—
125M16—22no—
126M16—4522no—
127M16—2262no—
128C2×C8—4522no—
129C22⋊C4—22no—
130C22⋊C4—2262no—
131C22⋊C4—2262no—
132C22⋊C4—2262no—
133C42—1131no—
134C42—2261no—
135C42C4×D11311yescharacteristic
136C23—21no—
137C23—1131no—
138C23—4521no—
139C23—4521no—
140C23—4524no—
141C23—2261no—
142Q8—41no—
143Q8—4522no—
144Q8—4521no—
145D4—41no—
146D4—4521no—
147D4—4522no—
148C2×C4—21no—
149C2×C4—1131no—
150C2×C4—1132no—
151C2×C4—4522no—
152C2×C4—2262no—
153C2×C4—2262no—
154C2×C4—2261no—
155C2×C4—2261no—
156C2×C4—2261no—
157C2×C4C2×C4×D11311yescharacteristic
158C2×C4D4×D11312yes—
159C8—42no—
160C8—4522no—
161C22—42no—
162C22—41no—
163C22—1131no—
164C22—1131no—
165C22—9042no—
166C22—9042no—
167C22—4522no—
168C22—4521no—
169C22—2262no—
170C22C22⋊C4×D11311yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—4521no—
175C4—2261no—
176C4—2262no—
177C2—21no—
178C2—81no—
179C2—1132no—
180C2—9041no—
181C2—2261no—
182C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC2×C4×C113C22×C4
FrattiniC2×Q8C22×D113
Fitting#355×C113C2
socleC2×C113C2×#99
prime radicalC2×D4×D113C4
cosocleC2×Q8×C113C23
hypercenter#355D113
hypocenterC113C2×#355
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D113C2semidirect
3. #20298395C2semidirect
4. #20298394C2semidirect
5. #355×C113C2semidirect
15. #16813541C22semidirect
18. #101×C113C22semidirect
90. D113#355direct (N × H)
92. C113C2×#355semidirect
97. #355D113direct (N × H)
110. #101C2×D113semidirect

Maximal subgroups

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

subgroupindex
#124×D1132
#101×D1132
#202983952
#202983942
#355×C1132
C2×#355113