Finite Group Databasebeta

← #28392256

Subgroups — #28392256

Order 14464.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299147C211yesmaximal, characteristic
2#20298581C212yesmaximal, complemented
3#20298396C212yesmaximal, complemented
4#20298395C211yesmaximal, characteristic, complemented
5#355×C113C211yesmaximal, characteristic, complemented
6C2×#14268648C2211yescharacteristic
7C2×#14268646C411yescharacteristic
8M16×D113—22no—
9#16813620C2211yescharacteristic
10#16813618C411yescharacteristic
11#16813610C411yescharacteristic
12#16813595—22no—
13#16813582—22no—
14C42×D113C411yescharacteristic
15#16813541C2212yes—
16#16813538—22no—
17#124×C113C2211yescharacteristic
18#101×C113C2212yes—
19#14268648—41no—
20#14268648—41no—
21#14268646—41no—
22#14268646—41no—
23C2×Dic226C2×C411yescharacteristic
24C2×D452C2×C411yescharacteristic
25C2×D452D412yes—
26C2×C22⋊D113—22no—
27C2×C22⋊D113—21no—
28C22×Dic113—21no—
29C2×C4×D113—21no—
30C2×C4×D113C2×C411yescharacteristic
31C2×C4×D113D412yes—
32#14268631—22no—
33#14268630—42no—
34C8×D113—42no—
35#14268626—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×D113C22⋊C412yes—
46C22×D113C22⋊C411yescharacteristic
47Q8×C113—41no—
48D4×C113—41no—
49C2×C4×C113—21no—
50C2×C4×C113C22×C411yescharacteristic
51C2×C4×C113C2×D412yes—
52C22⋊D113—44no—
53C22⋊D113—42no—
54C2×Dic113—21no—
55C2×Dic113—21no—
56C2×Dic113—41no—
57C2×Dic113—41no—
58C2×Dic113C22⋊C411yescharacteristic
59D452—41no—
60D452—42no—
61C4×D113—22no—
62C4×D113—22no—
63C4×D113—21no—
64C4×D113—21no—
65C4×D113—42no—
66Dic226—41no—
67C8×C113—42no—
68#11744751—42no—
69C22×C113—42no—
70C22×C113—41no—
71C22×C113C2×C22⋊C411yescharacteristic
72C2×D113—21no—
73C2×D113—22no—
74C2×D113—41no—
75C2×D113—42no—
76C4×C113—22no—
77C4×C113—21no—
78C4×C113—41no—
79Dic113—22no—
80Dic113—41no—
81Dic113#9911yescharacteristic
82Dic113#9911yescharacteristic
83C2×C113—21no—
84C2×C113—81no—
85C2×C113C2×#9911yescharacteristic
86D113—41no—
87D113—42no—
88#2132—1131nomaximal, Sylow
89C113#213211yescharacteristic, complemented, Sylow
90#532—1131no—
91#413—1132no—
92#356—1132no—
93#355—1131no—
94#355D11311yescharacteristic, complemented
95C2×#41—1131no—
96C2×#41—1131no—
97C2×M16—2262no—
98C4⋊Q8—1131no—
99#127—1131no—
100#124—1131no—
101#124C2×D11311yescharacteristic
102#121—2262no—
103C4×D4—2262no—
104C2×C42—1131no—
105#101—1132no—
106#101C2×D11312yes—
107#100—2262no—
108#41—4521no—
109#41—4521no—
110#41—4521no—
111#41—4521no—
112C2×Q8—1131no—
113C2×Q8C22×D11311yescharacteristic
114C2×D4—1131no—
115C2×D4—1132no—
116C2×D4—2262no—
117C2×D4—2261no—
118C2×D4C4×D11311yescharacteristic
119C22×C4—1131no—
120C22×C4—1132no—
121C22×C4—2261no—
122C22×C4—2261no—
123M16—22no—
124M16—4522no—
125M16—2262no—
126C2×C8—4522no—
127C4⋊C4—2262no—
128C22⋊C4—22no—
129C22⋊C4—2262no—
130C42—1131no—
131C42—2261no—
132C42C4×D11311yescharacteristic
133C23—21no—
134C23—1132no—
135C23—1131no—
136Q8—41no—
137Q8—4521no—
138D4—41no—
139D4—4522no—
140D4—4521no—
141D4—4522no—
142D4—4524no—
143C2×C4—21no—
144C2×C4—1131no—
145C2×C4—4522no—
146C2×C4—4521no—
147C2×C4—4521no—
148C2×C4—2262no—
149C2×C4—2262no—
150C2×C4—2261no—
151C2×C4—2261no—
152C2×C4—2261no—
153C2×C4—2261no—
154C2×C4C2×C4×D11311yescharacteristic
155C2×C4D4×D11312yes—
156C8—42no—
157C8—4522no—
158C22—42no—
159C22—41no—
160C22—4521no—
161C22—4522no—
162C22—2261no—
163C22—2262no—
164C22C22⋊C4×D11311yescharacteristic
165C4—22no—
166C4—21no—
167C4—41no—
168C4—1131no—
169C4—1131no—
170C4—4521no—
171C4—2262no—
172C2—21no—
173C2—81no—
174C2—4521no—
175C2—4522no—
176C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC2×C4×C113C22×C4
FrattiniC2×Q8C22×D113
Fitting#355×C113C2
socleC2×C113C2×#99
prime radical#20299147C2
cosocleC2×Q8×C113C23
hypercenter#355D113
hypocenterC113#2132
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. #20298581C2semidirect
3. #20298396C2semidirect
4. #20298395C2semidirect
5. #355×C113C2semidirect
89. C113#2132semidirect
94. #355D113semidirect

Maximal subgroups

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

subgroupindex
#202991472
#202985812
#202983962
#202983952
#355×C1132
#2132113