Finite Group Databasebeta

← #28406579

Subgroups — #28406579

Order 14464.

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

normal subgroups only

This group has 360 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#20299665C211yesmaximal, characteristic
2#20299591C212yesmaximal, complemented
3D113⋊#100C211yesmaximal, characteristic
4#20299469C212yesmaximal, complemented
5#124×D113C211yesmaximal, characteristic
6D113⋊M16C2212yes—
7D4×#90673—24no—
8#16813701C2212yes—
9C2×C22⋊#90673—22no—
10#16813685—24no—
11#16813682—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
21C22×#90673—24no—
22#14268657—22no—
23#14268656—22no—
24#14268655—22no—
25C4⋊#90673D414yes—
26C22⋊#90673—24no—
27C22⋊#90673—22no—
28C4×#90673—22no—
29C23×D113D412yes—
30C2×Dic226—21no—
31C2×Dic226C2×C411yescharacteristic, complemented
32Q8×D113—22no—
33Q8×D113—22no—
34C2×D452C2×C411yescharacteristic
35C2×C22⋊D113D412yes—
36D4×D113—22no—
37D4×D113—22no—
38C2×C4×D113—21no—
39C2×C4×D113—21no—
40C2×C4×D113C2311yescharacteristic
41C22⋊Dic113—22no—
42#14268624—22no—
43#14268624—22no—
44C4×Dic113—21no—
45C4×Dic113C2×C411yescharacteristic, complemented
46C2×Q8×C113C2×C411yescharacteristic, complemented
47C2×D4×C113C2×C411yescharacteristic
48C22⋊C4×C113—22no—
49C42×C113C2×C411yescharacteristic, complemented
50C23×C113C22⋊C412yes—
51C22×D113—22no—
52C22×D113—22no—
53C22×D113—44no—
54C22×D113C22⋊C412yes—
55C22×D113C2×D411yescharacteristic
56C2×#90673—24no—
57C2×#90673—84no—
58Q8×C113—22no—
59D4×C113—22no—
60C2×C4×C113—21no—
61C2×C4×C113—21no—
62C2×C4×C113C22×C411yescharacteristic
63C22⋊D113—24no—
64C2×Dic113—21no—
65C2×Dic113—21no—
66C2×Dic113C2×D411yescharacteristic
67D452—22no—
68C4×D113—42no—
69C4×D113—41no—
70C4×D113—41no—
71C4×D113C2×D412yes—
72C4×D113#4112yes—
73Dic226—22no—
74Dic226—42no—
75#11744753—42no—
76C22×C113—22no—
77C22×C113—42no—
78C22×C113C2×C22⋊C411yescharacteristic
79C2×D113—22no—
80C2×D113—22no—
81C2×D113—44no—
82C2×D113—42no—
83C2×D113—82no—
84C2×D113#12011yescharacteristic
85C2×D113#12311yescharacteristic
86#90673—44no—
87C4×C113—41no—
88C4×C113—41no—
89C4×C113C4×D412yes—
90Dic113—41no—
91Dic113—41no—
92Dic113#12112yes—
93C2×C113—21no—
94C2×C113—42no—
95C2×C113#38611yescharacteristic
96D113—21no—
97D113—42no—
98D113#45512yes—
99#1885—1131nomaximal, Sylow
100C113#188511yescharacteristic, complemented, Sylow
101C2×#124—1131no—
102#518—1131no—
103#419—1132no—
104C2×#100—1131no—
105#339—1132no—
106C22×Q8—1131no—
107C22×D4—1131no—
108C2×M16—1132no—
109#124—1131no—
110#124—1131no—
111#124—1131no—
112#124—2262no—
113#124#9067311yescharacteristic, complemented
114C4×D4—2264no—
115#117—1132no—
116C2×C22⋊C4—2262no—
117C2×C22⋊C4—2262no—
118C2×C42—1131no—
119#103—2264no—
120#100—2262no—
121C24—1132no—
122C2×Q8—1131no—
123C2×Q8—2261no—
124C2×Q8—2262no—
125C2×Q8—2262no—
126C2×Q8C2×#9067311yescharacteristic, complemented
127C2×D4—1132no—
128C2×D4—1131no—
129C2×D4—2262no—
130C2×D4—2262no—
131C2×D4C2×#9067311yescharacteristic
132C22×C4—1131no—
133C22×C4—2261no—
134C22×C4—2261no—
135C22×C4—2264no—
136M16—2262no—
137M16—2262no—
138C2×C8—2262no—
139C4⋊C4—1134no—
140C22⋊C4—22no—
141C22⋊C4—2262no—
142C22⋊C4—2262no—
143C22⋊C4—2262no—
144C22⋊C4—2264no—
145C22⋊C4—2262no—
146C42—1131no—
147C42—2261no—
148C42—2262no—
149C42C2×#9067311yescharacteristic, complemented
150C23—1131no—
151C23—1132no—
152C23—4524no—
153C23—2262no—
154C23—2262no—
155C23C22⋊#9067312yes—
156Q8—22no—
157Q8—4522no—
158Q8—2262no—
159D4—22no—
160D4—2264no—
161D4—2262no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—1131no—
165C2×C4—1132no—
166C2×C4—1132no—
167C2×C4—9044no—
168C2×C4—4521no—
169C2×C4—4521no—
170C2×C4—4522no—
171C2×C4—2264no—
172C2×C4—2261no—
173C2×C4—2261no—
174C2×C4C22×#9067311yescharacteristic
175C8—4522no—
176C22—22no—
177C22—42no—
178C22—1131no—
179C22—1131no—
180C22—9042no—
181C22—4522no—
182C22—4524no—
183C22—2262no—
184C22—2262no—
185C22C2×C22⋊#9067311yescharacteristic
186C4—41no—
187C4—41no—
188C4—1132no—
189C4—4521no—
190C4—4524no—
191C4—4521no—
192C4D4×#9067312yes—
193C2—21no—
194C2—42no—
195C2—1132no—
196C2—4522no—
197C2—2261no—
198C2#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#1885
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
2. #20299591C2semidirect
4. #20299469C2semidirect
14. #16813611C4semidirect
15. #16813610C4semidirect
16. #16813609C4semidirect
20. #124×C113C4semidirect
31. C2×Dic226C2×C4semidirect
45. C4×Dic113C2×C4semidirect
46. C2×Q8×C113C2×C4semidirect
49. C42×C113C2×C4semidirect
100. C113#1885semidirect
113. #124#90673semidirect
126. C2×Q8C2×#90673semidirect
149. C42C2×#90673semidirect

Maximal subgroups

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

subgroupindex
#202996652
#202995912
D113⋊#1002
#202994692
#124×D1132
#1885113