Finite Group Databasebeta

← #28406751

Subgroups — #28406751

Order 14464.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#14268657C211yesmaximal, characteristic
2C4×C4⋊#90673C211yesmaximal, characteristic
3#20299468C212yesmaximal
4#20299468C212yesmaximal
5#20299154C211yesmaximal, characteristic
6C2×#14268657C2212yes—
7C2×C4⋊#90673—21no—
8C2×C4×#90673C2212yes—
9#16813677—21no—
10C4×#11744753—21no—
11(C2×#90673)⋊C4—21no—
12#16813621C411yescharacteristic, complemented
13#16813621C411yescharacteristic, complemented
14#16813614C411yescharacteristic, complemented
15#16813600—21no—
16#16813600—21no—
17#16813587—21no—
18#16813587—21no—
19#16813580C2211yescharacteristic
20#16813580C2211yescharacteristic
21C42×D113C2211yescharacteristic
22#125×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24#14268657—22no—
25#14268657Q814yescomplemented
26C2×#11744753—22no—
27C4⋊#90673—24no—
28C4×#90673—24no—
29C2×Dic226—21no—
30C2×Dic226—21no—
31C2×C4×D113D411yescharacteristic
32C2×C4×D113D411yescharacteristic
33C2×C4×D113C2311yescharacteristic
34C4⋊Dic113C2×C411yescharacteristic
35C4⋊Dic113C2×C411yescharacteristic
36#14268626—21no—
37#14268626—21no—
38#14268626—21no—
39#14268626—21no—
40#14268624—21no—
41#14268624—21no—
42C4×Dic113—21no—
43C4×Dic113—21no—
44C4×Dic113C2×C411yescharacteristic
45C4×Dic113D411yescharacteristic
46C4×Dic113D411yescharacteristic
47C4⋊C4×C113—21no—
48C4⋊C4×C113—21no—
49C4⋊C4×C113C2×C411yescharacteristic
50C4⋊C4×C113C2×C411yescharacteristic
51C42×C113C2×C411yescharacteristic
52C22×D113C2×D411yescharacteristic
53C2×#90673—24no—
54C2×#90673—42no—
55C2×#90673—42no—
56C2×C4×C113—21no—
57C2×C4×C113—21no—
58C2×C4×C113C22⋊C411yescharacteristic
59C2×C4×C113C22⋊C411yescharacteristic
60C2×C4×C113C22×C411yescharacteristic
61C2×Dic113—21no—
62C2×Dic113—21no—
63C2×Dic113C22⋊C411yescharacteristic
64C2×Dic113C22⋊C411yescharacteristic
65C2×Dic113C2×D411yescharacteristic
66C4×D113—22no—
67C4×D113—41no—
68C4×D113C2×Q812yes—
69C4×D113#4112yes—
70Dic226—42no—
71Dic226—42no—
72#11744753—24no—
73C22×C113C2×C22⋊C411yescharacteristic
74C2×D113—21no—
75C2×D113—21no—
76C2×D113#12411yescharacteristic
77C2×D113C4⋊Q811yescharacteristic
78#90673—44no—
79C4×C113—21no—
80C4×C113—21no—
81C4×C113—41no—
82C4×C113—41no—
83C4×C113C4×Q812yes—
84Dic113—21no—
85Dic113—41no—
86Dic113—41no—
87Dic113#10412yes—
88Dic113C22⋊Q812yes—
89C2×C113#39111yescharacteristic
90C2×C113C2×#10411yescharacteristic
91C2×C113#42111yescharacteristic
92D113—21no—
93D113—21no—
94#1986—1131nomaximal, Sylow
95C113#198611yescharacteristic, complemented, Sylow
96#533—1131no—
97C4×M16—1131no—
98C4×C4⋊C4—1131no—
99#339—1132no—
100#339—1132no—
101C2×M16—1132no—
102C4⋊Q8—1131no—
103C4⋊Q8—1131no—
104#125—1131no—
105#125#9067311yescharacteristic, complemented
106C22⋊Q8—2261no—
107C22⋊Q8—2261no—
108C4×Q8—2261no—
109C4×Q8—2261no—
110#117—1131no—
111#117—1131no—
112C2×C4⋊C4—2261no—
113C2×C42—1131no—
114C2×C42—1132no—
115#97—2261no—
116C4×C8—2261no—
117#95—2261no—
118C2×Q8—2261no—
119C2×Q8—2261no—
120C22×C4—1131no—
121C22×C4—1131no—
122C22×C4—1131no—
123C22×C4—2262no—
124M16—1134no—
125M16—2262no—
126C2×C8—2262no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—1131no—
130C4⋊C4—1131no—
131C4⋊C4—2261no—
132C4⋊C4—2261no—
133C4⋊C4—2264no—
134C4⋊C4—2261no—
135C4⋊C4—2261no—
136C4⋊C4C2×#9067311yescharacteristic
137C4⋊C4C2×#9067311yescharacteristic
138C22⋊C4—2261no—
139C22⋊C4—2261no—
140C42—1131no—
141C42—1131no—
142C42—1131no—
143C42—2261no—
144C42—2261no—
145C42—2264no—
146C42C2×#9067311yescharacteristic
147C23—1131no—
148Q8—4522no—
149Q8—4522no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—1131no—
153C2×C4—1131no—
154C2×C4—1132no—
155C2×C4—1132no—
156C2×C4—1131no—
157C2×C4—4521no—
158C2×C4—4522no—
159C2×C4—4522no—
160C2×C4—2262no—
161C2×C4—2264no—
162C2×C4—2261no—
163C2×C4—2261no—
164C2×C4C22⋊#9067311yescharacteristic
165C2×C4C22⋊#9067311yescharacteristic
166C2×C4C22×#9067311yescharacteristic
167C8—2264no—
168C22—1131no—
169C22—1131no—
170C22—2261no—
171C22—2261no—
172C22C2×C22⋊#9067311yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—1132no—
178C4—1132no—
179C4—4524no—
180C4—4521no—
181C4—4521no—
182C4—2261no—
183C4Q8×#9067312yes—
184C2—2261no—
185C2—2261no—
186C2(C2×#90673)⋊Q811yescharacteristic
187C2D113⋊#10411yescharacteristic
188C2#2029959511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#125×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×D113C2×D4
cosocleC2×C4×D113C23
hypercenter#125#90673
hypocenterC113#1986
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #16813621C4semidirect
13. #16813621C4semidirect
14. #16813614C4semidirect
22. #125×C113C4semidirect
25. #14268657Q8semidirect
95. C113#1986semidirect
105. #125#90673semidirect

Maximal subgroups

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

subgroupindex
C4×#142686572
C4×C4⋊#906732
#202994682
#202991542
#1986113