Finite Group Databasebeta

← #28389824

Subgroups — #28389824

Order 14464.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299263C211yesmaximal, characteristic
2#20299001C211yesmaximal, characteristic, complemented
3#20298879C211yesmaximal, characteristic
4#20298809C211yesmaximal, characteristic, complemented
5#20298328C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic
7#332×C113C211yesmaximal, characteristic, complemented
8C2×Q8×D113—21no—
9C2×Dic452—21no—
10#16813622C2211yescharacteristic
11#16813621—21no—
12#16813600—22no—
13#16813598—21no—
14C4×Dic226C2211yescharacteristic
15C4×D452C2211yescharacteristic
16#16813584—21no—
17#16813556—21no—
18#16813555—22no—
19#16813547—21no—
20#16813544—21no—
21C4×#11744751C2211yescharacteristic
22C4⋊Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25C2×Dic226—22no—
26C2×Dic226—21no—
27C2×Dic226D411yescharacteristic
28Q8×D113—42no—
29Q8×D113—42no—
30C2×D452D411yescharacteristic
31C2×C4×D113—22no—
32C2×C4×D113—21no—
33Dic452—42no—
34C2×#11744751—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113D411yescharacteristic
38C4⋊Dic113D411yescharacteristic
39#14268626—22no—
40#14268626—21no—
41#14268624—22no—
42#14268624—21no—
43C4×Dic113—21no—
44C2×Q8×C113—21no—
45C2×C8×C113—21no—
46C2×C8×C113—21no—
47C4⋊C4×C113—21no—
48C4⋊C4×C113D412yes—
49C42×C113C2311yescharacteristic
50C22×D113—21no—
51Q8×C113—41no—
52Q8×C113—41no—
53C2×C4×C113—22no—
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×C4×C113C2×D411yescharacteristic
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—21no—
60C2×Dic113—41no—
61D452—21no—
62D452Q1612yescomplemented
63C4×D113—44no—
64C4×D113—41no—
65C4×D113—41no—
66Dic226—21no—
67Dic226—44no—
68Dic226—41no—
69Dic226—41no—
70Dic226D812yes—
71C8×C113—41no—
72C8×C113—41no—
73#11744751—22no—
74C22×C113#12011yescharacteristic
75C2×D113—22no—
76C2×D113—41no—
77C2×D113—41no—
78C4×C113—21no—
79C4×C113—42no—
80C4×C113C2×D811yescharacteristic
81C4×C113C2×Q1611yescharacteristic
82C4×C113AGL(1,ℤ/8)11yescharacteristic
83C4×C113#13711yescharacteristic
84Dic113—22no—
85Dic113—41no—
86Dic113—41no—
87Dic113—81no—
88C2×C113#44711yescharacteristic
89C2×C113#45111yescharacteristic
90C2×C113#45611yescharacteristic
91D113—42no—
92#1649—1131nomaximal, Sylow
93C113#164911yescharacteristic, complemented, Sylow
94D4×Q8—1131no—
95#500—1131no—
96#474—1131no—
97#462—1131no—
98#332D11311yescharacteristic, complemented
99Q8⋊C8—1131no—
100D4⋊C8—1131no—
101C22×Q8—2261no—
102C2×Q16—2261no—
103C4⋊Q8—1131no—
104C4⋊Q8—2261no—
105C4⋊Q8C2×D11311yescharacteristic
106C22⋊Q8—2261no—
107C22⋊Q8—2262no—
108C4×Q8—1131no—
109C4×D4—1131no—
110C4×D4—2261no—
111#107—2261no—
112#107—2262no—
113C4⋊C8C2×D11311yescharacteristic
114C4⋊C8C2×D11311yescharacteristic
115#103—2261no—
116#102—2261no—
117C4×C8—1131no—
118C2×Q8—21no—
119C2×Q8—1131no—
120C2×Q8—4522no—
121C2×Q8—4522no—
122C2×Q8—2262no—
123C2×Q8—2261no—
124C2×D4—1131no—
125C22×C4—2262no—
126C22×C4—2261no—
127Q16—4522no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—2261no—
131C4⋊C4—21no—
132C4⋊C4—1131no—
133C4⋊C4—1131no—
134C4⋊C4—2262no—
135C4⋊C4—2261no—
136C4⋊C4—2261no—
137C4⋊C4—2261no—
138C4⋊C4D45212yes—
139C22⋊C4—2262no—
140C22⋊C4—2261no—
141C42—2261no—
142C42C22×D11311yescharacteristic
143C23—2261no—
144Q8—41no—
145Q8—41no—
146Q8—1132no—
147Q8—4524no—
148Q8—4521no—
149Q8—4521no—
150Q8—2261no—
151D4—1132no—
152D4—2261no—
153C2×C4—22no—
154C2×C4—4524no—
155C2×C4—4521no—
156C2×C4—4521no—
157C2×C4—4521no—
158C2×C4—2261no—
159C2×C4—2261no—
160C2×C4—2261no—
161C2×C4D4×D11311yescharacteristic
162C2×C4D4×D11311yescharacteristic
163C2×C4C2×D45211yescharacteristic
164C8—41no—
165C8—41no—
166C8—2262no—
167C22—4521no—
168C22—4521no—
169C22—2262no—
170C22#1681359211yescharacteristic
171C4—21no—
172C4—42no—
173C4—9041no—
174C4—4521no—
175C4—4521no—
176C4—2262no—
177C4D8×D11311yescharacteristic
178C4Q16×D11311yescharacteristic
179C4#1681364911yescharacteristic
180C4#1681365111yescharacteristic
181C2—4522no—
182C2#2029873311yescharacteristic
183C2#2029875511yescharacteristic
184C2#2029878311yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#332×C113C2
socleC22×C113#120
prime radicalC2×D452D4
hypercenter#332D113
hypocenterC113#1649
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #20299001C2semidirect
4. #20298809C2semidirect
5. #20298328C2semidirect
7. #332×C113C2semidirect
62. D452Q16semidirect
93. C113#1649semidirect
98. #332D113semidirect

Maximal subgroups

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

subgroupindex
#202992632
#202990012
#202988792
#202988092
#202983282
#202983252
#332×C1132
#1649113