Finite Group Databasebeta

← #28406674

Subgroups — #28406674

Order 14464.

248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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×C4⋊#11744753C212yesmaximal
2C2×C4⋊#11744753C211yesmaximal, characteristic
3C2×#16813677C211yesmaximal, characteristic
4#20299464C212yesmaximal
5#20298449C211yesmaximal, characteristic
6C22×#11744753C2212yes—
7C22×#11744753C2211yescharacteristic
8C22×#11744753C2211yescharacteristic
9C4⋊#11744753—24no—
10C4⋊#11744753—22no—
11#16813677—22no—
12C2×#14268626C412yes—
13C2×C4×Dic113C2212yes—
14C2×C4×Dic113C2211yescharacteristic
15#16813529C411yescharacteristic
16#95×C113C411yescharacteristic
17C2×#11744753—21no—
18C2×#11744753—21no—
19C2×#11744753—21no—
20C2×#11744753—21no—
21C2×#11744753—22no—
22C2×#11744753—22no—
23C2×#11744753—22no—
24C2×#11744753D412yes—
25C2×#11744753Q812yes—
26C22×Dic113C2×C412yes—
27C22×Dic113C2×C411yescharacteristic
28C22×Dic113C2311yescharacteristic
29#14268626—24no—
30C4×Dic113—22no—
31C4×Dic113—22no—
32C4×Dic113D412yes—
33C4×Dic113Q812yes—
34C22×C4×C113C2×C411yescharacteristic
35C22×C4×C113C2×C412yes—
36C23×C113C22×C411yescharacteristic
37C2×C4×C113—22no—
38C2×C4×C113—22no—
39C2×C4×C113—22no—
40C2×C4×C113C4⋊C412yes—
41C2×C4×C113M1614yes—
42C2×Dic113—22no—
43C2×Dic113—22no—
44C2×Dic113—22no—
45C2×Dic113—22no—
46C2×Dic113C4⋊C412yes—
47C2×Dic113C2×D411yescharacteristic
48C2×Dic113C2×D411yescharacteristic
49C2×Dic113C2×Q811yescharacteristic
50C2×Dic113C2×Q811yescharacteristic
51C2×Dic113#4111yescharacteristic
52C2×Dic113#4111yescharacteristic
53#11744753—22no—
54#11744753—22no—
55#11744753—42no—
56C22×C113C2×C4⋊C411yescharacteristic
57C22×C113C4×D411yescharacteristic
58C22×C113C4×Q811yescharacteristic
59C22×C113C2×M1612yes—
60C22×C113#13112yes—
61C4×C113—22no—
62C4×C113—24no—
63Dic113—22no—
64Dic113—42no—
65Dic113#12111yescharacteristic
66Dic113C22⋊Q811yescharacteristic
67Dic113#12511yescharacteristic
68Dic113C4⋊Q811yescharacteristic
69C2×C113#38911yescharacteristic
70C2×C113#42311yescharacteristic
71C2×C113#42411yescharacteristic
72C2×C113#43512yes—
73C2×C113#44612yes—
74#1940—1131nomaximal, Sylow
75C113#194011yescharacteristic, complemented, Sylow
76C2×C4⋊C8—1131no—
77C2×C4⋊C8—1132no—
78C2×#97—1131no—
79C4×C4⋊C4—1131no—
80#336—1132no—
81C22×C8—1131no—
82C22×C8—1131no—
83C22×C8—1132no—
84C2×C4⋊C4—1132no—
85C2×C42—1131no—
86C2×C42—1132no—
87C4⋊C8—2262no—
88C4⋊C8—2264no—
89#97—2262no—
90#95—1131no—
91#95#9067311yescharacteristic
92C22×C4—1131no—
93C22×C4—1131no—
94C22×C4—1132no—
95C22×C4C2×#9067311yescharacteristic
96C22×C4C2×#9067312yes—
97C2×C8—1132no—
98C2×C8—1132no—
99C2×C8—2262no—
100C2×C8—2262no—
101C2×C8—2262no—
102C2×C8—2261no—
103C2×C8—2261no—
104C2×C8—2261no—
105C2×C8—2261no—
106C4⋊C4—2264no—
107C42—1132no—
108C42—1132no—
109C42—2262no—
110C42—2262no—
111C23C22×#9067311yescharacteristic
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—1131no—
116C2×C4—1131no—
117C2×C4—1131no—
118C2×C4—1131no—
119C2×C4—1131no—
120C2×C4—1131no—
121C2×C4—1132no—
122C2×C4—2262no—
123C2×C4—2262no—
124C2×C4—2262no—
125C2×C4—2262no—
126C2×C4C4⋊#9067312yes—
127C2×C4#1426865714yes—
128C8—4522no—
129C8—2262no—
130C8—2262no—
131C22C2×C4⋊#9067311yescharacteristic
132C22D4×#9067311yescharacteristic
133C22Q8×#9067311yescharacteristic
134C22C2×#1426865712yes—
135C22#1681370912yes—
136C4—22no—
137C4—24no—
138C4—1131no—
139C4—1131no—
140C4—1131no—
141C4—1131no—
142C4—4522no—
143C4—2262no—
144C2#2029954911yescharacteristic
145C2#2029960211yescharacteristic
146C2#2029960411yescharacteristic
147C2#2029962712yes—
148C2#2029964812yes—
subgroupG/H
center, FrattiniC23C22×#90673
commutator, socle, prime radicalC23×C113C22×C4
Fitting#95×C113C4
cosocleC22×Dic113C23
hypercenter#95#90673
hypocenterC113#1940
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
75. C113#1940semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#117447532
C2×#168136772
#202994642
#202984492
#1940113