Finite Group Databasebeta

← #28389845

Subgroups — #28389845

Order 14464.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#20299322C211yesmaximal, characteristic
2#20298994C211yesmaximal, characteristic, complemented
3#20298879C211yesmaximal, characteristic
4#20298809C211yesmaximal, characteristic, complemented
5#20298328C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic
7#332×C113C211yesmaximal, characteristic, complemented
8C2×Dic452—21no—
9#16813622C2211yescharacteristic
10#16813617—22no—
11#16813611—21no—
12#16813602—21no—
13Q8×Dic113—21no—
14C4×Dic226C2211yescharacteristic
15C4×D452C2211yescharacteristic
16#16813580—21no—
17#16813556—21no—
18#16813553—22no—
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—
29Dic452—42no—
30C2×#11744751—21no—
31C4⋊Dic113—22no—
32C4⋊Dic113—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113D411yescharacteristic
35C4⋊Dic113D411yescharacteristic
36#14268626—21no—
37#14268624—22no—
38#14268624—22no—
39#14268624—21no—
40C4×Dic113—22no—
41C4×Dic113—21no—
42C2×Q8×C113—21no—
43C2×C8×C113—21no—
44C2×C8×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113D412yes—
47C42×C113C2311yescharacteristic
48C22×D113—21no—
49Q8×C113—41no—
50Q8×C113—41no—
51C2×C4×C113—22no—
52C2×C4×C113C2×D411yescharacteristic
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113C2×D411yescharacteristic
55C2×Dic113—21no—
56C2×Dic113—21no—
57C2×Dic113—21no—
58C2×Dic113—41no—
59D452—21no—
60D452—21no—
61C4×D113—41no—
62C4×D113—41no—
63Dic226—21no—
64Dic226—21no—
65Dic226—41no—
66Dic226—41no—
67C8×C113—41no—
68C8×C113—41no—
69#11744751—22no—
70C22×C113#12011yescharacteristic
71C2×D113—41no—
72C2×D113—41no—
73C2×D113—41no—
74C4×C113—21no—
75C4×C113—42no—
76C4×C113#13511yescharacteristic
77C4×C113#13511yescharacteristic
78C4×C113AGL(1,ℤ/8)11yescharacteristic
79C4×C113#13711yescharacteristic
80Dic113—41no—
81Dic113—41no—
82Dic113—41no—
83Dic113—81no—
84C2×C113#44911yescharacteristic
85C2×C113#45211yescharacteristic
86C2×C113#45611yescharacteristic
87D113—81no—
88#1652—1131nomaximal, Sylow
89C113#165211yescharacteristic, complemented, Sylow
90#556—1131no—
91#498—1131no—
92#474—1131no—
93#462—1131no—
94#332D11311yescharacteristic, complemented
95Q8⋊C8—1131no—
96D4⋊C8—1131no—
97C2×Q16—2261no—
98C4⋊Q8—1131no—
99C4⋊Q8C2×D11311yescharacteristic
100#126—2262no—
101#124—2261no—
102C22⋊Q8—2261no—
103C4×Q8—1131no—
104C4×Q8—2261no—
105C4×D4—1131no—
106#117—2261no—
107#107—2261no—
108#106—2262no—
109C4⋊C8C2×D11311yescharacteristic
110C4⋊C8C2×D11311yescharacteristic
111#103—2261no—
112#102—2261no—
113C4×C8—1131no—
114C2×Q8—21no—
115C2×Q8—1131no—
116C2×Q8—2261no—
117C2×D4—1131no—
118C22×C4—2261no—
119Q16—4522no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—2261no—
123C4⋊C4—21no—
124C4⋊C4—1131no—
125C4⋊C4—1131no—
126C4⋊C4—2262no—
127C4⋊C4—2261no—
128C4⋊C4—2261no—
129C4⋊C4—2261no—
130C4⋊C4D45212yes—
131C22⋊C4—2262no—
132C22⋊C4—2262no—
133C22⋊C4—2261no—
134C42—2262no—
135C42—2261no—
136C42C22×D11311yescharacteristic
137C23—2261no—
138Q8—41no—
139Q8—41no—
140Q8—4521no—
141Q8—4521no—
142Q8—2261no—
143Q8—2261no—
144D4—2261no—
145D4—2261no—
146C2×C4—22no—
147C2×C4—4521no—
148C2×C4—4521no—
149C2×C4—4521no—
150C2×C4—2261no—
151C2×C4—2261no—
152C2×C4—2261no—
153C2×C4D4×D11311yescharacteristic
154C2×C4D4×D11311yescharacteristic
155C2×C4C2×D45211yescharacteristic
156C8—41no—
157C8—41no—
158C8—2262no—
159C22—4521no—
160C22—4521no—
161C22—4521no—
162C22#1681359211yescharacteristic
163C4—21no—
164C4—42no—
165C4—9041no—
166C4—4521no—
167C4—4521no—
168C4—4521no—
169C4#1681364111yescharacteristic
170C4#1681364511yescharacteristic
171C4#1681364911yescharacteristic
172C4#1681365111yescharacteristic
173C2—9041no—
174C2#2029874611yescharacteristic
175C2#2029876111yescharacteristic
176C2#2029878311yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#332×C113C2
socleC22×C113#120
prime radicalC2×D452D4
hypercenter#332D113
hypocenterC113#1652
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. #20298994C2semidirect
4. #20298809C2semidirect
5. #20298328C2semidirect
7. #332×C113C2semidirect
89. C113#1652semidirect
94. #332D113semidirect

Maximal subgroups

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

subgroupindex
#202993222
#202989942
#202988792
#202988092
#202983282
#202983252
#332×C1132
#1652113