Finite Group Databasebeta

← #28392245

Subgroups — #28392245

Order 14464.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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#20299162C211yesmaximal, characteristic
2#20298572C211yesmaximal, characteristic, complemented
3#20298390C214yesmaximal, complemented
4#410×C113C211yesmaximal, characteristic, complemented
5C22×D452C411yescharacteristic, complemented
6#16813618C2212yes—
7#16813611C412yescomplemented
8#16813596—21no—
9#16813596—21no—
10#16813590—21no—
11#16813590—21no—
12#16813581—21no—
13#16813581C411yescharacteristic, complemented
14#16813537—21no—
15#16813537C2212yescomplemented
16C2×#41×C113C2211yescharacteristic
17#117×C113—21no—
18#99×C113—21no—
19#99×C113C2212yescomplemented
20C23×D113—21no—
21C2×D452—21no—
22C2×D452—41no—
23C2×D452—41no—
24C2×D452C2×C412yes—
25C2×C22⋊D113—22no—
26C2×C22⋊D113—22no—
27C4⋊Dic113—21no—
28C4⋊Dic113—41no—
29C22⋊Dic113—21no—
30C22⋊Dic113—22no—
31#14268624—22no—
32#14268624—22no—
33C4×Dic113—41no—
34C4×Dic113C2×C412yes—
35#41×C113—41no—
36#41×C113—41no—
37C2×Q8×C113C2×C411yescharacteristic
38C2×D4×C113D411yescharacteristic
39C2×D4×C113D411yescharacteristic
40C2×D4×C113C2311yescharacteristic
41C22×C4×C113C2×C411yescharacteristic
42C22×C4×C113D411yescharacteristic
43C22×C4×C113D411yescharacteristic
44C4⋊C4×C113—41no—
45C22⋊C4×C113—22no—
46C42×C113—41no—
47C23×C113C22⋊C411yescharacteristic
48C23×C113C2×D411yescharacteristic
49C23×C113C2×D411yescharacteristic
50C22×D113—22no—
51C22×D113—42no—
52C22×D113—82no—
53Q8×C113—41no—
54D4×C113—41no—
55D4×C113—41no—
56D4×C113—41no—
57C2×C4×C113—21no—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—21no—
61C2×C4×C113—21no—
62C2×C4×C113—21no—
63C2×C4×C113—42no—
64C2×C4×C113C22⋊C411yescharacteristic
65C2×C4×C113C22⋊C411yescharacteristic
66C2×C4×C113C22⋊C411yescharacteristic
67C2×C4×C113C22×C411yescharacteristic
68C22⋊D113—82no—
69C22⋊D113—82no—
70C2×Dic113—22no—
71C2×Dic113—42no—
72D452—42no—
73D452—41no—
74D452—41no—
75C22×C113—21no—
76C22×C113—21no—
77C22×C113—21no—
78C22×C113—41no—
79C22×C113—41no—
80C22×C113—41no—
81C22×C113C2×C22⋊C411yescharacteristic
82C2×D113—42no—
83C2×D113—42no—
84C2×D113—42no—
85C2×D113—84no—
86C4×C113—21no—
87C4×C113—21no—
88C4×C113—21no—
89C4×C113—82no—
90C4×C113#9911yescharacteristic
91C4×C113#9911yescharacteristic
92Dic113—42no—
93Dic113—82no—
94C2×C113—21no—
95C2×C113—41no—
96C2×C113—41no—
97C2×C113—41no—
98C2×C113C2×#9911yescharacteristic
99D113—82no—
100#2128—1131nomaximal, Sylow
101C113#212811yescharacteristic, complemented, Sylow
102#535—1131no—
103#410—1131no—
104#410D11311yescharacteristic, complemented
105#353—1134no—
106C2×#41C2×D11311yescharacteristic
107C22×D4—1131no—
108#127—1132no—
109#124—1132no—
110#121—2261no—
111#121—2261no—
112#120—2261no—
113#120—2261no—
114#117—21no—
115#117—1131no—
116#117—2261no—
117#99—21no—
118#99—1132no—
119#99—2261no—
120#99C2×D11312yescomplemented
121C24—2261no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D11311yescharacteristic
125C2×D4—1132no—
126C2×D4—4521no—
127C2×D4—4521no—
128C2×D4—2262no—
129C2×D4—2262no—
130C2×D4—2261no—
131C2×D4D45211yescharacteristic
132C2×D4C22⋊D11311yescharacteristic
133C2×D4C22×D11311yescharacteristic
134C22×C4C4×D11311yescharacteristic
135C22×C4D45211yescharacteristic
136C22×C4C22⋊D11311yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—4521no—
139C4⋊C4—2261no—
140C22⋊C4—22no—
141C22⋊C4—2262no—
142C22⋊C4—2261no—
143C22⋊C4—2262no—
144C22⋊C4—2262no—
145C42—41no—
146C42—1132no—
147C42—4521no—
148C23—9042no—
149C23—4522no—
150C23—2262no—
151C23#1426862411yescharacteristic
152C23C2×C22⋊D11311yescharacteristic
153C23C2×D45211yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—9042no—
159D4—9042no—
160D4—4522no—
161D4—4521no—
162D4—4521no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—4522no—
171C2×C4—2262no—
172C2×C4#1426862411yescharacteristic
173C2×C4#1426862411yescharacteristic
174C2×C4#1426862411yescharacteristic
175C2×C4C2×C4×D11311yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—9044no—
183C22—4522no—
184C22—4522no—
185C22—4522no—
186C22C2×#1426862411yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—9042no—
192C4—4522no—
193C4#1681353611yescharacteristic
194C4#1681353611yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—9042no—
200C2C2×#1681353611yescharacteristic
subgroupG/H
centerC2C2×#16813536
commutatorC2×C4×C113C22×C4
FrattiniC2×D4C22×D113
Fitting#410×C113C2
socleC2×C113C2×#99
prime radical#20299162C2
cosocleC2×D4×C113C23
hypercenter#410D113
hypocenterC113#2128
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #20298572C2semidirect
3. #20298390C2semidirect
4. #410×C113C2semidirect
5. C22×D452C4semidirect
7. #16813611C4semidirect
13. #16813581C4semidirect
15. #16813537C22semidirect
19. #99×C113C22semidirect
101. C113#2128semidirect
104. #410D113semidirect
120. #99C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991622
#202985722
#202983902
#410×C1132
#2128113