Finite Group Databasebeta

← #28401976

Subgroups — #28401976

Order 14464.

354 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 109 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#20299134C212yesmaximal, complemented
2#20298903C212yesmaximal, complemented
3#20298897C212yesmaximal, complemented
4#20298851C211yesmaximal, characteristic
5#20298846C212yesmaximal, complemented
6#20298822C212yesmaximal, complemented
7#20298816C212yesmaximal, complemented
8#20298621C211yesmaximal, characteristic, complemented
9#470×C113C211yesmaximal, characteristic, complemented
10C2×#14268634C2212yes—
11C2×D904C2211yescharacteristic
12C2×#14268631C2211yescharacteristic
13#16813617—22no—
14#16813613C2212yes—
15#16813611C2212yes—
16#16813606—22no—
17#16813596C2212yes—
18Q8×Dic113C2212yes—
19#16813584C2212yes—
20#16813582—22no—
21#16813580—22no—
22C2×C4×Dic113C2211yescharacteristic
23#16813555C2212yes—
24#16813554C2211yescharacteristic
25#16813551C2212yes—
26#16813551C2212yes—
27#16813546C2212yes—
28#16813544C2212yes—
29#16813542C2212yes—
30C2×Q16×C113C2211yescharacteristic
31C2×M16×C113C2211yescharacteristic
32C22⋊Q8×C113C2212yes—
33#106×C113C2211yescharacteristic
34#103×C113C2212yes—
35C2×D452C2312yes—
36C2×C22⋊D113—22no—
37C22×Dic113D412yes—
38C2×C4×D113—22no—
39#14268634—42no—
40D904—41no—
41#14268631—41no—
42C2×#11744751C2312yes—
43C4⋊Dic113—22no—
44C4⋊Dic113—22no—
45C4⋊Dic113C2312yes—
46#14268626—22no—
47#14268624—22no—
48#14268624—22no—
49#14268624—22no—
50#14268624—22no—
51C4×Dic113—22no—
52C4×Dic113D411yescharacteristic
53C4×Dic113D411yescharacteristic
54C4×Dic113C2312yes—
55C2×Q8×C113C2312yes—
56C22×C4×C113C2311yescharacteristic
57Q16×C113—41no—
58M16×C113—41no—
59C2×C8×C113C2311yescharacteristic
60C2×C8×C113C2311yescharacteristic
61C4⋊C4×C113—22no—
62C4⋊C4×C113C2312yes—
63C22⋊C4×C113—22no—
64C23×C113C2×D411yescharacteristic
65C22×D113—22no—
66Q8×C113—22no—
67Q8×C113—22no—
68C2×C4×C113—21no—
69C2×C4×C113—21no—
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2411yescharacteristic
74C22⋊D113—44no—
75C2×Dic113—22no—
76C2×Dic113—42no—
77C2×Dic113C2×D412yes—
78C2×Dic113C2×D412yes—
79D452—22no—
80D452—22no—
81C4×D113—44no—
82C8×C113—21no—
83C8×C113—21no—
84#11744751—22no—
85C22×C113—21no—
86C22×C113—22no—
87C22×C113C22×D411yescharacteristic
88C2×D113—42no—
89C2×D113—42no—
90C2×D113—42no—
91C4×C113—21no—
92C4×C113—42no—
93C4×C113—42no—
94C4×C113H(5,𝔽2)11yescharacteristic
95C4×C1132−1+411yescharacteristic
96Dic113—22no—
97Dic113—22no—
98Dic113—42no—
99C2×C113—41no—
100C2×C113#53711yescharacteristic
101C2×C113#57512yes—
102D113—82no—
103#3256—1131nomaximal, Sylow
104C113#325611yescharacteristic, complemented, Sylow
105#529—1132no—
106#479—1132no—
107#478—1132no—
108#470D11311yescharacteristic, complemented
109#469—1131no—
110#468—1132no—
111#464—1132no—
112#463—1132no—
113#423—1131no—
114C2×Q16C2×D11311yescharacteristic
115C2×SD16—1132no—
116C2×D8—1131no—
117C2×M16—1131no—
118C2×M16C2×D11311yescharacteristic
119#126—2262no—
120#125—1132no—
121#124—1132no—
122#123—2262no—
123C22⋊Q8C2×D11312yes—
124#121—1132no—
125C4×Q8—1132no—
126C4×D4—1132no—
127C4×D4—2262no—
128#117—2262no—
129C2×C42—1131no—
130#107—1132no—
131#106—1131no—
132#106C2×D11311yescharacteristic
133C4⋊C8—1132no—
134C4⋊C8—1132no—
135#103—1132no—
136#103C2×D11312yes—
137#102—1132no—
138#102—1132no—
139C2×Q8C22×D11312yes—
140C2×D4—1132no—
141C2×D4—2262no—
142C22×C4—1132no—
143C22×C4—2262no—
144C22×C4C22×D11311yescharacteristic
145Q16—41no—
146SD16—4522no—
147D8—4521no—
148M16—41no—
149M16—4521no—
150C2×C8—1132no—
151C2×C8C22×D11311yescharacteristic
152C2×C8C22×D11311yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—1132no—
155C4⋊C4—2262no—
156C4⋊C4—2262no—
157C4⋊C4—2262no—
158C4⋊C4C22×D11312yes—
159C22⋊C4—22no—
160C22⋊C4—2262no—
161C22⋊C4—2262no—
162C22⋊C4—2262no—
163C22⋊C4—2262no—
164C42—1131no—
165C42—1131no—
166C42—1132no—
167C42—2262no—
168C23—2262no—
169C23D4×D11311yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—4524no—
173D4—2262no—
174D4—2262no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—1132no—
180C2×C4—1132no—
181C2×C4—4524no—
182C2×C4—4522no—
183C2×C4—2262no—
184C2×C4D4×D11311yescharacteristic
185C2×C4C23×D11311yescharacteristic
186C8—21no—
187C8—21no—
188C8—2262no—
189C22—22no—
190C22—21no—
191C22—4522no—
192C22—4522no—
193C22—4522no—
194C22C2×D4×D11311yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—4522no—
199C4—2262no—
200C4—2262no—
201C4#1681366711yescharacteristic
202C4#1681366911yescharacteristic
203C2—41no—
204C2—9042no—
205C2#2029917511yescharacteristic
206C2#2029939712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#470×C113C2
socleC22×C113C22×D4
prime radical#20298851C2
hypercenter#470D113
hypocenterC113#3256
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #20299134C2semidirect
2. #20298903C2semidirect
3. #20298897C2semidirect
5. #20298846C2semidirect
6. #20298822C2semidirect
7. #20298816C2semidirect
8. #20298621C2semidirect
9. #470×C113C2semidirect
104. C113#3256semidirect
108. #470D113semidirect

Maximal subgroups

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

subgroupindex
#202991342
#202989032
#202988972
#202988512
#202988462
#202988222
#202988162
#202986212
#470×C1132
#3256113