Finite Group Databasebeta

← #28389718

Subgroups — #28389718

Order 14464.

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

normal subgroups only

This group has 218 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#20299313C211yesmaximal, characteristic
2#20298977C211yesmaximal, characteristic, complemented
3#20298885C211yesmaximal, characteristic, complemented
4#20298346C211yesmaximal, characteristic, complemented
5D4⋊#11744751C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic, complemented
7#476×C113C211yesmaximal, characteristic, complemented
8C2×#14268637—22no—
9#16813622C2211yescharacteristic
10#16813608—22no—
11#16813596—21no—
12#16813593—21no—
13C4×D452C2211yescharacteristic
14#16813581—21no—
15#16813580—21no—
16#16813553—21no—
17C4⋊#11744751C2211yescharacteristic
18#16813542—21no—
19C4×#11744751C2211yescharacteristic
20C4⋊Q8×C113C2211yescharacteristic
21C4×D4×C113C2211yescharacteristic
22#106×C113—21no—
23C4⋊C8×C113C2211yescharacteristic
24#102×C113—21no—
25C2×Dic226D412yes—
26C2×D452D411yescharacteristic
27C2×C22⋊D113—22no—
28C2×C4×D113—21no—
29#14268637—44no—
30C2×#11744751—21no—
31C2×#11744751—21no—
32C4⋊Dic113—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113D411yescharacteristic
35C22⋊Dic113—22no—
36#14268624—22no—
37#14268624—21no—
38C4×Dic113—22no—
39C2×Q8×C113—21no—
40C2×D4×C113D411yescharacteristic
41C22×C4×C113—21no—
42C2×C8×C113—21no—
43C4⋊C4×C113—21no—
44C4⋊C4×C113—21no—
45C4⋊C4×C113D411yescharacteristic
46C22⋊C4×C113—21no—
47C42×C113C2311yescharacteristic
48C23×C113—21no—
49C22×D113—21no—
50Q8×C113—42no—
51D4×C113—21no—
52D4×C113—21no—
53C2×C4×C113—21no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113C2×D411yescharacteristic
60C22⋊D113—82no—
61C2×Dic113—21no—
62C2×Dic113—22no—
63D452—21no—
64D452—21no—
65C4×D113—41no—
66C4×D113—41no—
67Dic226—42no—
68C8×C113—41no—
69#11744751—22no—
70#11744751—41no—
71C22×C113—41no—
72C22×C113—41no—
73C22×C113—41no—
74C22×C113#12011yescharacteristic
75C2×D113—41no—
76C2×D113—41no—
77C2×D113—41no—
78C4×C113—21no—
79C4×C113—41no—
80C4×C113—81no—
81C4×C113#13511yescharacteristic
82C4×C113#13511yescharacteristic
83C4×C113#13711yescharacteristic
84C4×C113#13711yescharacteristic
85Dic113—41no—
86Dic113—42no—
87C2×C113—81no—
88C2×C113#45211yescharacteristic
89C2×C113#45211yescharacteristic
90C2×C113#45311yescharacteristic
91D113—81no—
92#1634—1131nomaximal, Sylow
93C113#163411yescharacteristic, complemented, Sylow
94#555—1131no—
95#494—1131no—
96#476—1131no—
97#476D11311yescharacteristic, complemented
98#333—1131no—
99D4⋊C8—1131no—
100D4⋊C8—1131no—
101C2×Q16—2262no—
102C4⋊Q8—1131no—
103C4⋊Q8C2×D11311yescharacteristic
104#124—2262no—
105#121—2261no—
106#121—2261no—
107C4×D4—1131no—
108C4×D4C2×D11311yescharacteristic
109#117—2261no—
110#117—2261no—
111#106—21no—
112#106—2261no—
113C4⋊C8—1131no—
114C4⋊C8C2×D11311yescharacteristic
115#102—21no—
116#102—2261no—
117C4×C8—1131no—
118C2×Q8—21no—
119C2×Q8—1132no—
120C2×D4—1131no—
121C2×D4—2262no—
122C2×D4C22⋊D11311yescharacteristic
123C22×C4—21no—
124C22×C4—2261no—
125Q16—4524no—
126C2×C8—21no—
127C2×C8—2261no—
128C2×C8—2261no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—1131no—
132C4⋊C4—2261no—
133C4⋊C4—2261no—
134C4⋊C4C22⋊D11311yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—2262no—
137C22⋊C4—2262no—
138C22⋊C4—2261no—
139C42—2262no—
140C42C22×D11311yescharacteristic
141C23—21no—
142C23—2261no—
143Q8—42no—
144Q8—4522no—
145D4—21no—
146D4—21no—
147D4—9042no—
148D4—2261no—
149D4—2261no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—4521no—
155C2×C4—4521no—
156C2×C4—2261no—
157C2×C4—2262no—
158C2×C4D4×D11311yescharacteristic
159C2×C4D4×D11311yescharacteristic
160C2×C4C2×C22⋊D11311yescharacteristic
161C8—41no—
162C8—4521no—
163C8—2262no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—4521no—
168C22—4521no—
169C22—4521no—
170C22#1681359011yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—4521no—
175C4—4522no—
176C4#1681364211yescharacteristic
177C4#1681364311yescharacteristic
178C4#1681365111yescharacteristic
179C4#1681365311yescharacteristic
180C2—81no—
181C2—9041no—
182C2#2029875711yescharacteristic
183C2#2029875811yescharacteristic
184C2#2029876411yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#476×C113C2
socleC22×C113#120
prime radical#20299313C2
hypercenter#476D113
hypocenterC113#1634
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #20298977C2semidirect
3. #20298885C2semidirect
4. #20298346C2semidirect
5. D4⋊#11744751C2semidirect
6. #20298325C2semidirect
7. #476×C113C2semidirect
93. C113#1634semidirect
97. #476D113semidirect

Maximal subgroups

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

subgroupindex
#202993132
#202989772
#202988852
#202983462
D4⋊#117447512
#202983252
#476×C1132
#1634113