Finite Group Databasebeta

← #28406582

Subgroups — #28406582

Order 14464.

344 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 68 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#20299666C211yesmaximal, characteristic, complemented
2#20299590C212yesmaximal
3D113⋊#101C211yesmaximal, characteristic, complemented
4#20299469C212yesmaximal, complemented
5#124×D113C211yesmaximal, characteristic
6D113⋊M16C2212yes—
7Q8×#90673—24no—
8#16813701—22no—
9#16813701C2212yes—
10#16813684—24no—
11#16813683—22no—
12C2×Q8×D113C2211yescharacteristic
13C2×D4×D113C2211yescharacteristic
14#16813611C411yescharacteristic, complemented
15#16813610C411yescharacteristic, complemented
16#16813609C411yescharacteristic, complemented
17#16813608—22no—
18C22⋊C4×D113—22no—
19C42×D113C2211yescharacteristic
20#124×C113C411yescharacteristic, complemented
21#14268657—22no—
22#14268656—22no—
23#14268655—22no—
24C4⋊#90673—24no—
25C4⋊#90673D414yes—
26C22⋊#90673—22no—
27C4×#90673—24no—
28C4×#90673—22no—
29C23×D113—21no—
30C2×Dic226C2×C411yescharacteristic
31C2×Dic226D412yes—
32Q8×D113—22no—
33Q8×D113—22no—
34C2×D452C2×C411yescharacteristic
35C2×C22⋊D113—21no—
36D4×D113—22no—
37D4×D113—22no—
38C2×C4×D113—21no—
39C2×C4×D113D412yes—
40C2×C4×D113C2311yescharacteristic
41C22⋊Dic113—22no—
42#14268624—22no—
43#14268624—22no—
44C4×Dic113—21no—
45C4×Dic113C2×C411yescharacteristic
46C2×Q8×C113C2×C411yescharacteristic
47C2×D4×C113C2×C411yescharacteristic
48C22⋊C4×C113—22no—
49C42×C113C2×C411yescharacteristic
50C23×C113—21no—
51C22×D113—21no—
52C22×D113—44no—
53C22×D113—41no—
54C22×D113—41no—
55C22×D113C2×D411yescharacteristic
56C2×#90673—24no—
57Q8×C113—22no—
58D4×C113—22no—
59C2×C4×C113—21no—
60C2×C4×C113C22⋊C412yes—
61C2×C4×C113C22×C411yescharacteristic
62C22⋊D113—42no—
63C2×Dic113—21no—
64C2×Dic113C22⋊C412yes—
65C2×Dic113C2×D411yescharacteristic
66D452—22no—
67C4×D113—22no—
68C4×D113—22no—
69C4×D113—42no—
70C4×D113C2×D412yes—
71C4×D113#4112yes—
72Dic226—22no—
73Dic226—24no—
74#11744753—42no—
75C22×C113—42no—
76C22×C113—41no—
77C22×C113C2×C22⋊C411yescharacteristic
78C2×D113—22no—
79C2×D113—42no—
80C2×D113—41no—
81C2×D113—82no—
82C2×D113—82no—
83C2×D113#12011yescharacteristic
84C2×D113#12311yescharacteristic
85#90673—44no—
86C4×C113—22no—
87C4×C113—41no—
88C4×C113C4×D412yes—
89Dic113—22no—
90Dic113—41no—
91Dic113#12112yes—
92C2×C113—21no—
93C2×C113—81no—
94C2×C113#38611yescharacteristic
95D113—21no—
96D113—81no—
97D113#45412yes—
98#1888—1131nomaximal, Sylow
99C113#188811yescharacteristic, complemented, Sylow
100C2×#124—1131no—
101#519—1131no—
102#418—1132no—
103C2×#101—1131no—
104#339—1132no—
105C22×Q8—1131no—
106C22×D4—1131no—
107C2×M16—1132no—
108#124—1131no—
109#124—1131no—
110#124—1131no—
111#124—2262no—
112#124#9067311yescharacteristic, complemented
113C4×Q8—2264no—
114#117—1132no—
115#117—2262no—
116C2×C22⋊C4—2262no—
117C2×C42—1131no—
118#102—2264no—
119#101—2262no—
120C24—2261no—
121C2×Q8—1132no—
122C2×Q8—1131no—
123C2×Q8—2262no—
124C2×Q8—2262no—
125C2×Q8C2×#9067311yescharacteristic
126C2×D4—1131no—
127C2×D4—2262no—
128C2×D4—2262no—
129C2×D4—2261no—
130C2×D4C2×#9067311yescharacteristic
131C22×C4—1131no—
132C22×C4—1132no—
133C22×C4—2261no—
134M16—2262no—
135M16—2262no—
136C2×C8—2262no—
137C4⋊C4—1134no—
138C4⋊C4—2264no—
139C22⋊C4—22no—
140C22⋊C4—2262no—
141C22⋊C4—2262no—
142C22⋊C4—2262no—
143C22⋊C4—2262no—
144C42—1131no—
145C42—2261no—
146C42—2262no—
147C42—2264no—
148C42C2×#9067311yescharacteristic
149C23—21no—
150C23—1131no—
151C23—4521no—
152C23—4521no—
153C23—4524no—
154C23—2261no—
155Q8—22no—
156Q8—2264no—
157Q8—2262no—
158D4—22no—
159D4—4522no—
160D4—2262no—
161C2×C4—21no—
162C2×C4—1131no—
163C2×C4—1132no—
164C2×C4—1132no—
165C2×C4—1132no—
166C2×C4—4522no—
167C2×C4—2262no—
168C2×C4—2262no—
169C2×C4—2264no—
170C2×C4—2261no—
171C2×C4C22⋊#9067312yes—
172C2×C4C22×#9067311yescharacteristic
173C8—4522no—
174C22—42no—
175C22—41no—
176C22—1131no—
177C22—1131no—
178C22—9042no—
179C22—9042no—
180C22—4522no—
181C22—4521no—
182C22—2262no—
183C22C2×C22⋊#9067311yescharacteristic
184C4—22no—
185C4—41no—
186C4—1132no—
187C4—4521no—
188C4—4524no—
189C4—2262no—
190C4D4×#9067312yes—
191C2—21no—
192C2—81no—
193C2—1132no—
194C2—9041no—
195C2—2261no—
196C2#2029954611yescharacteristic
subgroupG/H
centerC2#20299546
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#124×C113C4
socleC2×C113#386
prime radicalC2×D4×D113C22
cosocleC2×C4×D113C23
hypercenter#124#90673
hypocenterC113#1888
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20299666C2semidirect
3. D113⋊#101C2semidirect
4. #20299469C2semidirect
14. #16813611C4semidirect
15. #16813610C4semidirect
16. #16813609C4semidirect
20. #124×C113C4semidirect
99. C113#1888semidirect
112. #124#90673semidirect

Maximal subgroups

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

subgroupindex
#202996662
#202995902
D113⋊#1012
#202994692
#124×D1132
#1888113