Finite Group Databasebeta

← #28391022

Subgroups — #28391022

Order 14464.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#20299109C211yesmaximal, characteristic
2C2×#16813550C212yesmaximal, complemented
3#20298562C211yesmaximal, characteristic, complemented
4#20298358C212yesmaximal, complemented
5C2×#117×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2211yescharacteristic
7C2×#14268631C2212yes—
8#16813605—21no—
9#16813601C412yescomplemented
10#16813596C412yescomplemented
11#16813591—21no—
12C4×C22⋊D113—22no—
13#16813581C2211yescharacteristic
14#16813550—24no—
15C22⋊#11744751—22no—
16C23×C4×C113C2211yescharacteristic
17#117×C113—24no—
18C2×C4⋊C4×C113—21no—
19C2×C22⋊C4×C113—21no—
20C2×C42×C113C2212yes—
21#14268647—22no—
22#14268647—22no—
23C2×Dic226C2×C411yescharacteristic
24C2×D452C2×C411yescharacteristic
25C2×C22⋊D113—22no—
26C2×C22⋊D113—21no—
27C2×C4×D113—21no—
28#14268631—22no—
29#14268631—22no—
30C2×#11744751—22no—
31C4⋊Dic113C2×C412yes—
32#14268626—22no—
33C22⋊Dic113—22no—
34C22⋊Dic113—21no—
35#14268624—22no—
36C4×Dic113—21no—
37C24×C113D411yescharacteristic
38C22×C4×C113—22no—
39C22×C4×C113—22no—
40C22×C4×C113—22no—
41C22×C4×C113C2×C412yes—
42C22×C4×C113D412yes—
43C22×C4×C113D411yescharacteristic
44C22×C4×C113C2311yescharacteristic
45C4⋊C4×C113—24no—
46C22⋊C4×C113—24no—
47C42×C113—22no—
48C42×C113D414yescomplemented
49C23×C113—21no—
50C23×C113—21no—
51C23×C113—42no—
52C23×C113C22⋊C412yes—
53C23×C113C2×D411yescharacteristic
54C22×D113—21no—
55C2×C4×C113—21no—
56C2×C4×C113—21no—
57C2×C4×C113—24no—
58C2×C4×C113—24no—
59C2×C4×C113—24no—
60C2×C4×C113—44no—
61C2×C4×C113C22⋊C412yes—
62C2×C4×C113C22×C411yescharacteristic
63C2×C4×C113C2×D412yes—
64C2×C4×C113C2×D411yescharacteristic
65C2×C4×C113#4112yes—
66C22⋊D113—44no—
67C22⋊D113—41no—
68C22⋊D113—41no—
69C2×Dic113—22no—
70C2×Dic113—21no—
71D452—22no—
72C4×D113—42no—
73Dic226—22no—
74#11744751—42no—
75C22×C113—22no—
76C22×C113—22no—
77C22×C113—22no—
78C22×C113—22no—
79C22×C113—42no—
80C22×C113—42no—
81C22×C113C2×C22⋊C411yescharacteristic
82C22×C113#12011yescharacteristic
83C22×C113#12311yescharacteristic
84C2×D113—41no—
85C2×D113—42no—
86C4×C113—22no—
87C4×C113—44no—
88C4×C113C4×D412yes—
89C4×C113#12112yes—
90Dic113—41no—
91Dic113—42no—
92C2×C113—21no—
93C2×C113—21no—
94C2×C113—42no—
95C2×C113#38611yescharacteristic
96C2×C113#42112yes—
97D113—81no—
98#1897—1131nomaximal, Sylow
99C113#189711yescharacteristic, complemented, Sylow
100#525—1131no—
101C2×#117D11311yescharacteristic, complemented
102C2×#104—1132no—
103#407—1131no—
104#339—1132no—
105C2×#41—1131no—
106C23×C4C2×D11311yescharacteristic
107C2×M16—1132no—
108#123—2261no—
109C22⋊Q8—1132no—
110#121—1132no—
111#120—2261no—
112C4×D4—2262no—
113#117—24no—
114#117—1131no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D11312yes—
118#104—2264no—
119C22⋊C8—2262no—
120C24C22⋊D11311yescharacteristic
121#41—2262no—
122#41—2262no—
123C2×Q8—1131no—
124C2×D4—1131no—
125C2×D4—2262no—
126C2×D4—2261no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—2261no—
131C22×C4C4×D11312yes—
132C22×C4D45212yes—
133C22×C4C22⋊D11311yescharacteristic
134C22×C4C22×D11311yescharacteristic
135M16—2262no—
136M16—2262no—
137C2×C8—2262no—
138C4⋊C4—24no—
139C4⋊C4—1132no—
140C4⋊C4—2262no—
141C22⋊C4—24no—
142C22⋊C4—2262no—
143C22⋊C4—2261no—
144C22⋊C4—2262no—
145C42—22no—
146C42—2261no—
147C42C22⋊D11314yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—2261no—
152C23#1426862412yes—
153C23C2×C22⋊D11311yescharacteristic
154Q8—2262no—
155D4—4524no—
156D4—4521no—
157D4—4521no—
158D4—2262no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—4522no—
166C2×C4—2262no—
167C2×C4—2261no—
168C2×C4#1426862412yes—
169C2×C4C2×C4×D11311yescharacteristic
170C2×C4C2×C22⋊D11312yes—
171C2×C4C2×D45211yescharacteristic
172C2×C4#1426864712yes—
173C8—4522no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—4522no—
181C22—4521no—
182C22C2×#1426862411yescharacteristic
183C22#1681359111yescharacteristic
184C22#1681360511yescharacteristic
185C4—22no—
186C4—44no—
187C4—4522no—
188C4—4521no—
189C4C4×C22⋊D11312yes—
190C4#1681359612yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—9041no—
195C2#2029847711yescharacteristic
196C2#2029861612yes—
subgroupG/H
centerC2×C4C2×D452
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#117×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299109C2
cosocleC22×C4×C113C23
hypercenterC2×#117D113
hypocenterC113#1897
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#16813550C2semidirect
3. #20298562C2semidirect
4. #20298358C2semidirect
5. C2×#117×C113C2semidirect
9. #16813601C4semidirect
10. #16813596C4semidirect
48. C42×C113D4semidirect
99. C113#1897semidirect
101. C2×#117D113semidirect
147. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
C2×#168135502
#202985622
#202983582
C2×#117×C1132
#1897113