Finite Group Databasebeta

← #28400860

Subgroups — #28400860

Order 14464.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#20299075C211yesmaximal, characteristic, complemented
2#20298919C212yesmaximal, complemented
3#20298902C212yesmaximal, complemented
4#20298795C212yesmaximal, complemented
5#20298736C212yesmaximal, complemented
6#20298698C212yesmaximal, complemented
7C4×#14268635C212yesmaximal, complemented
8#20298659C211yesmaximal, characteristic, complemented
9#540×C113C211yesmaximal, characteristic
10C22×Dic226C2211yescharacteristic
11C2×#14268635C2212yes—
12C2×#14268635C2212yes—
13C4×Dic226C2212yes—
14C4×Dic226C2212yes—
15#16813587—22no—
16#16813581C2211yescharacteristic
17#16813578—22no—
18#16813555C2212yes—
19#16813553C2212yes—
20C4⋊#11744751C2212yes—
21#16813545C2212yes—
22#16813545C2212yes—
23#16813543C2212yes—
24#16813543C2212yes—
25C22⋊#11744751C2212yes—
26#16813533C2211yescharacteristic
27C4×#11744751C2211yescharacteristic
28#127×C113C2211yescharacteristic
29#125×C113C2211yescharacteristic
30#123×C113—22no—
31#121×C113—22no—
32#121×C113C2212yes—
33C4×D4×C113C2212yes—
34#117×C113C2211yescharacteristic
35C2×Dic226—21no—
36C2×Dic226—24no—
37C2×Dic226C2312yes—
38C22×Dic113—21no—
39#14268635—24no—
40#14268635—24no—
41C2×#11744751C2312yes—
42C2×#11744751C2312yes—
43C4⋊Dic113C2312yes—
44#14268626—22no—
45#14268626—22no—
46C22⋊Dic113—21no—
47C4×Dic113—22no—
48C4×Dic113—22no—
49C4×Dic113—21no—
50C2×D4×C113—22no—
51C2×D4×C113—22no—
52C2×D4×C113C2312yes—
53C22×C4×C113—22no—
54C22×C4×C113C2311yescharacteristic
55C4⋊C4×C113—22no—
56C4⋊C4×C113D412yes—
57C4⋊C4×C113C2312yes—
58C22⋊C4×C113—22no—
59C22⋊C4×C113—22no—
60C22⋊C4×C113D412yes—
61C42×C113C2311yescharacteristic
62C42×C113C2311yescharacteristic
63C23×C113—22no—
64C23×C113C2×D411yescharacteristic
65D4×C113—22no—
66D4×C113—22no—
67D4×C113—82no—
68D4×C113—82no—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—82no—
72C2×C4×C113C2×D412yes—
73C2×C4×C113C2×D412yes—
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2411yescharacteristic
76C2×Dic113—24no—
77C2×Dic113—22no—
78C2×Dic113—22no—
79Dic226—24no—
80Dic226—22no—
81Dic226#4114yes—
82#11744751—22no—
83#11744751—22no—
84C22×C113—21no—
85C22×C113—22no—
86C22×C113—42no—
87C22×C113—42no—
88C22×C113—42no—
89C22×C113C22×D411yescharacteristic
90C4×C113—21no—
91C4×C113—22no—
92C4×C113—22no—
93C4×C113—42no—
94C4×C113C2×#4112yes—
95Dic113—24no—
96Dic113—42no—
97C2×C113—41no—
98C2×C113—82no—
99C2×C113#52511yescharacteristic
100C2×C113#57712yes—
101#3126—1131nomaximal, Sylow
102C113#312611yescharacteristic, complemented, Sylow
103#540D11311yescharacteristic
104#519—1131no—
105#482—1132no—
106#479—1132no—
107#460—1132no—
108#448—1132no—
109#440—1132no—
110C4×SD16—1132no—
111#433—1131no—
112C22×Q8—1131no—
113C2×SD16—1132no—
114C2×SD16—1132no—
115#127C2×D11311yescharacteristic
116#125C2×D11311yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D11312yes—
120C4×Q8—1132no—
121C4×Q8—1132no—
122C4×Q8—2262no—
123C4×D4C2×D11312yes—
124#117—1131no—
125#117—2262no—
126#117C2×D11311yescharacteristic
127#107—1132no—
128#106—1132no—
129C4⋊C8—1132no—
130#103—1132no—
131#103—1132no—
132#102—1132no—
133#102—1132no—
134C22⋊C8—1132no—
135#97—1131no—
136C4×C8—1131no—
137C2×Q8—1132no—
138C2×Q8—2264no—
139C2×Q8—2261no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D11312yes—
143C22×C4—22no—
144C22×C4—2261no—
145C22×C4C22×D11311yescharacteristic
146SD16—2264no—
147SD16—2264no—
148C2×C8—1132no—
149C2×C8—1132no—
150C4⋊C4—22no—
151C4⋊C4—1132no—
152C4⋊C4—2262no—
153C4⋊C4—2262no—
154C4⋊C4C22⋊D11312yes—
155C4⋊C4C22×D11312yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—2261no—
159C22⋊C4C22⋊D11312yes—
160C42—2261no—
161C42—2262no—
162C42—2262no—
163C42C22×D11311yescharacteristic
164C42C22×D11311yescharacteristic
165C23—22no—
166C23C2×C22⋊D11311yescharacteristic
167Q8—1134no—
168Q8—2264no—
169Q8—2262no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—2262no—
178C2×C4—2264no—
179C2×C4—2262no—
180C2×C4C2×C22⋊D11312yes—
181C2×C4C2×C22⋊D11312yes—
182C2×C4C2×C22⋊D11311yescharacteristic
183C2×C4C23×D11311yescharacteristic
184C8—2262no—
185C8—2262no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D11311yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—4522no—
197C4—2264no—
198C4#41×D11312yes—
199C2—41no—
200C2—82no—
201C2#2029910511yescharacteristic
202C2#2029940912yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radical#540×C113C2
socleC22×C113C22×D4
hypercenter#540D113
hypocenterC113#3126
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20299075C2semidirect
2. #20298919C2semidirect
3. #20298902C2semidirect
4. #20298795C2semidirect
5. #20298736C2semidirect
6. #20298698C2semidirect
7. C4×#14268635C2semidirect
8. #20298659C2semidirect
102. C113#3126semidirect

Maximal subgroups

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

subgroupindex
#202990752
#202989192
#202989022
#202987952
#202987362
#202986982
C4×#142686352
#202986592
#540×C1132
#3126113