Finite Group Databasebeta

← #28402015

Subgroups — #28402015

Order 14464.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299203C211yesmaximal, characteristic
2#20298905C212yesmaximal, complemented
3#20298895C212yesmaximal, complemented
4#20298846C212yesmaximal, complemented
5#20298829C212yesmaximal, complemented
6#20298800C212yesmaximal, complemented
7#20298798C212yesmaximal, complemented
8#20298625C211yesmaximal, characteristic, complemented
9#541×C113C211yesmaximal, characteristic, complemented
10C2×#14268634C2212yes—
11C2×#14268634C2212yes—
12C2×#14268631C2211yescharacteristic
13C22×#11744751C2211yescharacteristic
14#16813619C2211yescharacteristic
15#16813614C2211yescharacteristic
16#16813607—22no—
17#16813596C2212yes—
18#16813595—22no—
19C4×D452C2212yes—
20#16813555C2212yes—
21#16813553C2212yes—
22C4⋊#11744751C2212yes—
23C4⋊#11744751C2212yes—
24#16813546C2212yes—
25#16813546C2212yes—
26#16813542C2212yes—
27#16813542C2212yes—
28C4⋊Q8×C113C2211yescharacteristic
29#126×C113—22no—
30#125×C113—22no—
31#125×C113C2211yescharacteristic
32C22⋊Q8×C113C2212yes—
33C4×Q8×C113C2212yes—
34#117×C113C2211yescharacteristic
35C2×D452—22no—
36C2×D452C2312yes—
37C2×C22⋊D113—22no—
38C2×C4×D113—22no—
39#14268634—42no—
40#14268634—42no—
41#14268631—41no—
42C2×#11744751—41no—
43C2×#11744751C2312yes—
44C2×#11744751C2312yes—
45C4⋊Dic113C2312yes—
46#14268626—22no—
47#14268624—22no—
48#14268624—22no—
49C2×Q8×C113C2312yes—
50C22×C4×C113C2311yescharacteristic
51C4⋊C4×C113—22no—
52C4⋊C4×C113—22no—
53C4⋊C4×C113—22no—
54C4⋊C4×C113—22no—
55C4⋊C4×C113D412yes—
56C4⋊C4×C113C2312yes—
57C22⋊C4×C113—22no—
58C22⋊C4×C113D412yes—
59C42×C113—22no—
60C42×C113C2311yescharacteristic
61C42×C113C2311yescharacteristic
62C23×C113C2×D411yescharacteristic
63C22×D113—22no—
64Q8×C113—22no—
65Q8×C113—22no—
66C2×C4×C113—21no—
67C2×C4×C113—21no—
68C2×C4×C113—22no—
69C2×C4×C113—22no—
70C2×C4×C113C2×D412yes—
71C2×C4×C113C2×D412yes—
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2411yescharacteristic
74C22⋊D113—82no—
75C2×Dic113—22no—
76D452—22no—
77D452—22no—
78D452—82no—
79C4×D113—82no—
80#11744751—22no—
81#11744751—22no—
82C22×C113—21no—
83C22×C113—22no—
84C22×C113C22×D411yescharacteristic
85C2×D113—42no—
86C2×D113—42no—
87C2×D113—42no—
88C4×C113—21no—
89C4×C113—22no—
90C4×C113—22no—
91C4×C113—42no—
92C4×C113—42no—
93C4×C113H(5,𝔽2)11yescharacteristic
94C4×C1132−1+411yescharacteristic
95Dic113—42no—
96C2×C113—41no—
97C2×C113#53711yescharacteristic
98C2×C113#57712yes—
99D113—82no—
100#3260—1131nomaximal, Sylow
101C113#326011yescharacteristic, complemented, Sylow
102#541D11311yescharacteristic, complemented
103#540—1131no—
104#479—1132no—
105#478—1132no—
106#468—1132no—
107#465—1132no—
108#461—1132no—
109#460—1132no—
110#424—1131no—
111C2×SD16—1132no—
112C2×SD16—1132no—
113C2×M16—1131no—
114C22×C8—1131no—
115C4⋊Q8C2×D11311yescharacteristic
116#127—1131no—
117#126—22no—
118#125—22no—
119#125—1131no—
120#125C2×D11311yescharacteristic
121#123—2262no—
122C22⋊Q8C2×D11312yes—
123#121—1132no—
124#121—2262no—
125C4×Q8C2×D11312yes—
126C4×D4—1132no—
127#117C2×D11311yescharacteristic
128#107—1132no—
129#106—1132no—
130C4⋊C8—1132no—
131C4⋊C8—1132no—
132#103—1132no—
133#103—1132no—
134#102—1132no—
135#102—1132no—
136C2×Q8C22×D11312yes—
137C2×D4—1132no—
138C2×D4—2262no—
139C2×D4—2262no—
140C22×C4—2262no—
141C22×C4C22×D11311yescharacteristic
142SD16—4522no—
143SD16—4522no—
144M16—4521no—
145C2×C8—1132no—
146C2×C8—1132no—
147C2×C8—4521no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—1132no—
153C4⋊C4—2262no—
154C4⋊C4C22⋊D11312yes—
155C4⋊C4C22×D11312yes—
156C22⋊C4—22no—
157C22⋊C4—2262no—
158C22⋊C4—2262no—
159C22⋊C4C22⋊D11312yes—
160C42—22no—
161C42C22×D11311yescharacteristic
162C42C22×D11311yescharacteristic
163C23—2262no—
164C23C2×C22⋊D11311yescharacteristic
165Q8—22no—
166Q8—22no—
167D4—9042no—
168D4—9042no—
169D4—2262no—
170D4—2262no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—9042no—
176C2×C4—2262no—
177C2×C4C2×C22⋊D11312yes—
178C2×C4C2×C22⋊D11312yes—
179C2×C4C2×C22⋊D11311yescharacteristic
180C2×C4C23×D11311yescharacteristic
181C8—2262no—
182C8—2262no—
183C22—22no—
184C22—21no—
185C22—4522no—
186C22—4522no—
187C22—4522no—
188C22C22×C22⋊D11311yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—42no—
193C4—42no—
194C4—4522no—
195C4#1681366811yescharacteristic
196C4#1681366911yescharacteristic
197C2—41no—
198C2—9042no—
199C2#2029917611yescharacteristic
200C2#2029940612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#541×C113C2
socleC22×C113C22×D4
prime radical#20299203C2
hypercenter#541D113
hypocenterC113#3260
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #20298905C2semidirect
3. #20298895C2semidirect
4. #20298846C2semidirect
5. #20298829C2semidirect
6. #20298800C2semidirect
7. #20298798C2semidirect
8. #20298625C2semidirect
9. #541×C113C2semidirect
101. C113#3260semidirect
102. #541D113semidirect

Maximal subgroups

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

subgroupindex
#202992032
#202989052
#202988952
#202988462
#202988292
#202988002
#202987982
#202986252
#541×C1132
#3260113