Finite Group Databasebeta

← #28406580

Subgroups — #28406580

Order 14464.

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

normal subgroups only

This group has 324 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
2#20299591C212yesmaximal
3D113⋊#101C211yesmaximal, characteristic
4#20299469C212yesmaximal
5C4⋊Q8×D113C211yesmaximal, characteristic
6D113⋊M16C2212yes—
7Q8×#90673—24no—
8#16813701—22no—
9#16813701C2212yes—
10#16813685—24no—
11#16813683—22no—
12C2×Q8×D113C2211yescharacteristic
13C2×Q8×D113C2211yescharacteristic
14#16813622C411yescharacteristic, complemented
15#16813621—22no—
16#16813620C411yescharacteristic, complemented
17#16813620C411yescharacteristic, complemented
18C4⋊C4×D113—22no—
19C42×D113C2211yescharacteristic
20C4⋊Q8×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—
29C2×Dic226—21no—
30C2×Dic226C2×C411yescharacteristic
31C2×Dic226C2×C411yescharacteristic
32C2×Dic226D412yes—
33Q8×D113—22no—
34Q8×D113—22no—
35Q8×D113—22no—
36Q8×D113—22no—
37C2×C4×D113—21no—
38C2×C4×D113—21no—
39C2×C4×D113D412yes—
40C2×C4×D113C2311yescharacteristic
41C4⋊Dic113—22no—
42#14268626—22no—
43#14268626—22no—
44C4×Dic113—21no—
45C4×Dic113C2×C411yescharacteristic
46C2×Q8×C113C2×C411yescharacteristic
47C2×Q8×C113C2×C411yescharacteristic
48C4⋊C4×C113—22no—
49C42×C113C2×C411yescharacteristic
50C22×D113C2×D411yescharacteristic
51C2×#90673—24no—
52Q8×C113—22no—
53Q8×C113—22no—
54C2×C4×C113—21no—
55C2×C4×C113—21no—
56C2×C4×C113C22⋊C412yes—
57C2×C4×C113C22×C411yescharacteristic
58C2×Dic113—21no—
59C2×Dic113—21no—
60C2×Dic113C22⋊C412yes—
61C2×Dic113C2×D411yescharacteristic
62C4×D113—24no—
63C4×D113—22no—
64C4×D113—22no—
65C4×D113—41no—
66C4×D113—41no—
67C4×D113C2×D412yes—
68C4×D113#4112yes—
69Dic226—22no—
70Dic226—24no—
71Dic226—22no—
72Dic226—42no—
73#11744753—42no—
74C22×C113C2×C22⋊C411yescharacteristic
75C2×D113—22no—
76C2×D113#12011yescharacteristic
77C2×D113#12311yescharacteristic
78#90673—44no—
79C4×C113—22no—
80C4×C113—22no—
81C4×C113—41no—
82C4×C113C4×D412yes—
83Dic113—22no—
84Dic113—22no—
85Dic113—41no—
86Dic113#12112yes—
87C2×C113—21no—
88C2×C113#38611yescharacteristic
89D113—21no—
90D113#45612yes—
91#1886—1131nomaximal, Sylow
92C113#188611yescharacteristic, complemented, Sylow
93C2×C4⋊Q8—1131no—
94#519—1131no—
95#419—1132no—
96C2×#101—1131no—
97#339—1132no—
98C22×Q8—1131no—
99C22×Q8—1131no—
100C2×M16—1132no—
101C4⋊Q8—1131no—
102C4⋊Q8—1131no—
103C4⋊Q8—1131no—
104C4⋊Q8—2262no—
105C4⋊Q8#9067311yescharacteristic, complemented
106C4×Q8—2264no—
107#117—1132no—
108#117—2262no—
109C2×C4⋊C4—2262no—
110C2×C42—1131no—
111#103—2264no—
112#101—2262no—
113C2×Q8—1132no—
114C2×Q8—1131no—
115C2×Q8—1131no—
116C2×Q8—2261no—
117C2×Q8—2262no—
118C2×Q8—2262no—
119C2×Q8—2262no—
120C2×Q8—2262no—
121C2×Q8C2×#9067311yescharacteristic
122C2×Q8C2×#9067311yescharacteristic
123C22×C4—1131no—
124C22×C4—1132no—
125C22×C4—2261no—
126C22×C4—2261no—
127M16—2262no—
128M16—2262no—
129C2×C8—2262no—
130C4⋊C4—22no—
131C4⋊C4—1134no—
132C4⋊C4—2262no—
133C4⋊C4—2262no—
134C4⋊C4—2264no—
135C4⋊C4—2262no—
136C22⋊C4—2262no—
137C42—1131no—
138C42—2261no—
139C42—2262no—
140C42—2264no—
141C42C2×#9067311yescharacteristic
142C23—1131no—
143Q8—22no—
144Q8—22no—
145Q8—4522no—
146Q8—2264no—
147Q8—2262no—
148Q8—2262no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—1131no—
152C2×C4—1132no—
153C2×C4—1132no—
154C2×C4—1132no—
155C2×C4—4521no—
156C2×C4—4521no—
157C2×C4—2262no—
158C2×C4—2262no—
159C2×C4—2264no—
160C2×C4—2264no—
161C2×C4—2261no—
162C2×C4—2261no—
163C2×C4C22⋊#9067312yes—
164C2×C4C22×#9067311yescharacteristic
165C8—4522no—
166C22—1131no—
167C22—1131no—
168C22—2262no—
169C22C2×C22⋊#9067311yescharacteristic
170C4—22no—
171C4—22no—
172C4—41no—
173C4—1132no—
174C4—4524no—
175C4—4521no—
176C4—2262no—
177C4—2262no—
178C4D4×#9067312yes—
179C2—21no—
180C2—1132no—
181C2—2261no—
182C2#2029954611yescharacteristic
subgroupG/H
centerC2#20299546
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4⋊Q8×C113C4
socleC2×C113#386
prime radicalC22×D113C2×D4
cosocleC2×C4×D113C23
hypercenterC4⋊Q8#90673
hypocenterC113#1886
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
14. #16813622C4semidirect
16. #16813620C4semidirect
17. #16813620C4semidirect
20. C4⋊Q8×C113C4semidirect
92. C113#1886semidirect
105. C4⋊Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202996662
#202995912
D113⋊#1012
#202994692
C4⋊Q8×D1132
#1886113