Finite Group Databasebeta

← #28389709

Subgroups — #28389709

Order 14464.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299309C211yesmaximal, characteristic
2#20298977C211yesmaximal, characteristic, complemented
3#20298894C211yesmaximal, characteristic, complemented
4#20298889C211yesmaximal, characteristic
5#20298328C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic
7#333×C113C211yesmaximal, characteristic, complemented
8C2×#14268637—22no—
9#16813622C2211yescharacteristic
10#16813613—21no—
11#16813602—21no—
12#16813598—22no—
13C4×Dic226C2211yescharacteristic
14C4×D452C2211yescharacteristic
15#16813584—21no—
16C4⋊C4×D113—21no—
17#16813556—21no—
18#16813554—21no—
19#16813547—21no—
20#16813544—21no—
21C4×#11744751C2211yescharacteristic
22C4⋊Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25C2×Dic226—21no—
26C2×Dic226D411yescharacteristic
27C2×D452D411yescharacteristic
28C2×C4×D113—21no—
29C2×C4×D113—22no—
30#14268637—44no—
31C2×#11744751—21no—
32C4⋊Dic113—22no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113D411yescharacteristic
36C4⋊Dic113D411yescharacteristic
37#14268626—22no—
38#14268626—21no—
39#14268624—22no—
40#14268624—21no—
41C4×Dic113—21no—
42C2×Q8×C113D412yes—
43C2×C8×C113—21no—
44C2×C8×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113—21no—
47C42×C113C2311yescharacteristic
48C22×D113—21no—
49Q8×C113—42no—
50C2×C4×C113—22no—
51C2×C4×C113C2×D411yescharacteristic
52C2×C4×C113C2×D411yescharacteristic
53C2×C4×C113C2×D411yescharacteristic
54C2×Dic113—21no—
55C2×Dic113—21no—
56C2×Dic113—21no—
57C2×Dic113—41no—
58D452—21no—
59D452Q1612yescomplemented
60C4×D113—41no—
61C4×D113—41no—
62C4×D113—82no—
63Dic226—21no—
64Dic226—21no—
65Dic226—42no—
66C8×C113—41no—
67C8×C113—41no—
68#11744751—22no—
69C22×C113#12011yescharacteristic
70C2×D113—22no—
71C2×D113—41no—
72C2×D113—41no—
73C4×C113—21no—
74C4×C113—42no—
75C4×C113C2×Q1611yescharacteristic
76C4×C113#13511yescharacteristic
77C4×C113#13711yescharacteristic
78C4×C113#13711yescharacteristic
79Dic113—41no—
80Dic113—41no—
81Dic113—41no—
82Dic113—81no—
83C2×C113#45111yescharacteristic
84C2×C113#45211yescharacteristic
85C2×C113#45311yescharacteristic
86D113—42no—
87#1632—1131nomaximal, Sylow
88C113#163211yescharacteristic, complemented, Sylow
89#554—1131no—
90#494—1131no—
91#477—1131no—
92#476—1131no—
93#333D11311yescharacteristic, complemented
94Q8⋊C8—1131no—
95D4⋊C8—1131no—
96C2×Q16—2262no—
97C4⋊Q8—1131no—
98C4⋊Q8C2×D11311yescharacteristic
99#125—2261no—
100C22⋊Q8—2261no—
101C22⋊Q8—2262no—
102C4×Q8—1131no—
103C4×D4—1131no—
104C4×D4—2261no—
105C2×C4⋊C4—2261no—
106#107—2261no—
107#106—2261no—
108C4⋊C8C2×D11311yescharacteristic
109C4⋊C8C2×D11311yescharacteristic
110#103—2261no—
111#102—2261no—
112C4×C8—1131no—
113C2×Q8—1131no—
114C2×Q8—2261no—
115C2×Q8D45212yes—
116C2×D4—1131no—
117C22×C4—2262no—
118C22×C4—2261no—
119Q16—4524no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—2261no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—1131no—
126C4⋊C4—1131no—
127C4⋊C4—2262no—
128C4⋊C4—2262no—
129C4⋊C4—2261no—
130C4⋊C4—2261no—
131C4⋊C4—2261no—
132C22⋊C4—2262no—
133C22⋊C4—2261no—
134C42—2261no—
135C42C22×D11311yescharacteristic
136C23—2261no—
137Q8—42no—
138Q8—4522no—
139Q8—2261no—
140Q8—2261no—
141D4—1132no—
142D4—2261no—
143C2×C4—22no—
144C2×C4—9042no—
145C2×C4—4521no—
146C2×C4—4521no—
147C2×C4—4521no—
148C2×C4—2261no—
149C2×C4—2261no—
150C2×C4—2261no—
151C2×C4D4×D11311yescharacteristic
152C2×C4D4×D11311yescharacteristic
153C2×C4C2×D45211yescharacteristic
154C8—41no—
155C8—41no—
156C8—2262no—
157C22—4521no—
158C22—4521no—
159C22—2262no—
160C22#1681359211yescharacteristic
161C4—21no—
162C4—42no—
163C4—9041no—
164C4—4521no—
165C4—4521no—
166C4—4521no—
167C4Q16×D11311yescharacteristic
168C4#1681364311yescharacteristic
169C4#1681365111yescharacteristic
170C4#1681365411yescharacteristic
171C2—4522no—
172C2#2029875511yescharacteristic
173C2#2029876311yescharacteristic
174C2#2029876811yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#333×C113C2
socleC22×C113#120
prime radicalC2×D452D4
hypercenter#333D113
hypocenterC113#1632
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #20298977C2semidirect
3. #20298894C2semidirect
5. #20298328C2semidirect
7. #333×C113C2semidirect
59. D452Q16semidirect
88. C113#1632semidirect
93. #333D113semidirect

Maximal subgroups

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

subgroupindex
#202993092
#202989772
#202988942
#202988892
#202983282
#202983252
#333×C1132
#1632113