Finite Group Databasebeta

← #28406866

Subgroups — #28406866

Order 14464.

250 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 52 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#20299585C212yesmaximal, complemented
2#20299509C212yesmaximal, complemented
3#20299506C212yesmaximal, complemented
4#20299146C211yesmaximal, characteristic
5C2×#14268656—22no—
6#16813683C2214yes—
7#16813682—22no—
8C2×#14268646C411yescharacteristic
9C2×#14268646C2211yescharacteristic
10#16813622C2211yescharacteristic
11#16813609C411yescharacteristic
12#16813609C2211yescharacteristic
13#16813593—22no—
14D4×Dic113—22no—
15C42×D113C411yescharacteristic
16#127×C113C411yescharacteristic
17#14268656—24no—
18#14268656—42no—
19C2×#11744753—42no—
20#14268646—41no—
21#14268646—41no—
22#14268646—41no—
23#14268646—41no—
24C2×Dic226C2×C411yescharacteristic
25C2×Dic226C2311yescharacteristic
26C2×C22⋊D113—21no—
27C2×C22⋊D113D412yes—
28C22×Dic113—21no—
29C22×Dic113D412yes—
30C2×C4×D113—21no—
31C2×C4×D113C2×C411yescharacteristic
32C4⋊Dic113—22no—
33C22⋊Dic113—22no—
34C22⋊Dic113—22no—
35C4×Dic113—21no—
36C4×Dic113C2×C411yescharacteristic
37C2×D4×C113—22no—
38C2×D4×C113C2×C411yescharacteristic
39C2×D4×C113C2×C411yescharacteristic
40C42×C113C2×C411yescharacteristic
41C23×C113—21no—
42C23×C113C22⋊C412yes—
43C22×D113C22⋊C411yescharacteristic
44D4×C113—41no—
45D4×C113—41no—
46D4×C113—44no—
47C2×C4×C113—21no—
48C2×C4×C113C22×C411yescharacteristic
49C22⋊D113—42no—
50C22⋊D113—42no—
51C2×Dic113—22no—
52C2×Dic113—22no—
53C2×Dic113—21no—
54C2×Dic113—21no—
55C2×Dic113—41no—
56C2×Dic113—41no—
57C2×Dic113C22⋊C411yescharacteristic
58C2×Dic113C2×D412yes—
59C4×D113—21no—
60C4×D113—21no—
61C4×D113—42no—
62Dic226—41no—
63Dic226—41no—
64#11744753—44no—
65C22×C113—22no—
66C22×C113—42no—
67C22×C113—42no—
68C22×C113—41no—
69C22×C113C2×C22⋊C411yescharacteristic
70C2×D113—21no—
71C2×D113—41no—
72C4×C113—22no—
73C4×C113—21no—
74Dic113—22no—
75Dic113—41no—
76Dic113—41no—
77Dic113#9911yescharacteristic
78Dic113#9911yescharacteristic
79C2×C113—21no—
80C2×C113—42no—
81C2×C113—81no—
82C2×C113C2×#9911yescharacteristic
83D113—41no—
84#2132—1131nomaximal, Sylow
85C113#213211yescharacteristic, complemented, Sylow
86#532—1131no—
87#413—1132no—
88#356—1132no—
89#355—1132no—
90C2×#41—1131no—
91C2×#41—1131no—
92C2×M16—2262no—
93C4⋊Q8—1131no—
94#127#9067311yescharacteristic
95#124—1131no—
96#124—1131no—
97#121—2262no—
98C4×D4—2262no—
99C2×C42—1131no—
100#101—1134no—
101#100—2262no—
102#41—4521no—
103#41—4521no—
104#41—4521no—
105#41—4521no—
106C2×Q8—1131no—
107C2×Q8—1131no—
108C2×D4—22no—
109C2×D4—1132no—
110C2×D4—2261no—
111C2×D4C2×#9067311yescharacteristic
112C2×D4C2×#9067311yescharacteristic
113C22×C4—1132no—
114C22×C4—1131no—
115C22×C4—2261no—
116C22×C4—2261no—
117M16—4522no—
118M16—2264no—
119C2×C8—4522no—
120C4⋊C4—2262no—
121C22⋊C4—2262no—
122C22⋊C4—2262no—
123C42—1131no—
124C42—2261no—
125C42C2×#9067311yescharacteristic
126C23—21no—
127C23—1131no—
128C23C22⋊#9067312yes—
129Q8—4521no—
130Q8—4521no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—4522no—
135D4—4522no—
136C2×C4—21no—
137C2×C4—1131no—
138C2×C4—1132no—
139C2×C4—4522no—
140C2×C4—4521no—
141C2×C4—4521no—
142C2×C4—2261no—
143C2×C4—2261no—
144C2×C4—2262no—
145C2×C4—2262no—
146C2×C4—2261no—
147C2×C4—2261no—
148C2×C4C22×#9067311yescharacteristic
149C8—4524no—
150C22—22no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22—4521no—
155C22—2261no—
156C22C2×C22⋊#9067311yescharacteristic
157C4—22no—
158C4—21no—
159C4—1131no—
160C4—1131no—
161C4—4521no—
162C4—4521no—
163C4—2262no—
164C2—21no—
165C2—42no—
166C2—81no—
167C2—4521no—
168C2D113⋊#9911yescharacteristic
subgroupG/H
centerC2D113⋊#99
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#127×C113C4
socleC2×C113C2×#99
prime radical#20299146C2
cosocleC2×Dic226C23
hypercenter#127#90673
hypocenterC113#2132
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20299585C2semidirect
2. #20299509C2semidirect
3. #20299506C2semidirect
85. C113#2132semidirect

Maximal subgroups

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

subgroupindex
#202995852
#202995092
#202995062
#202991462
#2132113