Finite Group Databasebeta

← #28389740

Subgroups — #28389740

Order 14464.

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

normal subgroups only

This group has 228 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#20298950C211yesmaximal, characteristic, complemented
3#20298894C211yesmaximal, characteristic, complemented
4#20298889C211yesmaximal, characteristic
5#20298328C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic
7#332×C113C211yesmaximal, characteristic, complemented
8C2×Q8×D113—21no—
9#16813622C2211yescharacteristic
10#16813621—21no—
11#16813600—22no—
12#16813598—21no—
13C4×Dic226C2211yescharacteristic
14C4×D452C2211yescharacteristic
15#16813584—21no—
16#16813556—21no—
17#16813554—21no—
18#16813547—21no—
19#16813545—22no—
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—
33C2×#11744751—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113D411yescharacteristic
37C4⋊Dic113D411yescharacteristic
38#14268626—22no—
39#14268626—21no—
40#14268624—22no—
41#14268624—21no—
42C4×Dic113—21no—
43C2×Q8×C113—21no—
44C2×C8×C113—21no—
45C2×C8×C113—21no—
46C4⋊C4×C113—21no—
47C4⋊C4×C113D412yes—
48C42×C113C2311yescharacteristic
49C22×D113—21no—
50Q8×C113—41no—
51Q8×C113—41no—
52C2×C4×C113—22no—
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×Dic113—21no—
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—41no—
60D452—21no—
61D452Q1612yes—
62C4×D113—44no—
63C4×D113—41no—
64C4×D113—41no—
65Dic226—21no—
66Dic226—44no—
67Dic226—42no—
68Dic226SD1612yes—
69C8×C113—41no—
70C8×C113—41no—
71#11744751—41no—
72C22×C113#12011yescharacteristic
73C2×D113—22no—
74C2×D113—41no—
75C2×D113—41no—
76C4×C113—21no—
77C4×C113—42no—
78C4×C113C2×SD1611yescharacteristic
79C4×C113C2×Q1611yescharacteristic
80C4×C113AGL(1,ℤ/8)11yescharacteristic
81C4×C113#13711yescharacteristic
82Dic113—22no—
83Dic113—41no—
84Dic113—41no—
85Dic113—81no—
86C2×C113#45011yescharacteristic
87C2×C113#45111yescharacteristic
88C2×C113#45411yescharacteristic
89D113—42no—
90#1637—1131nomaximal, Sylow
91C113#163711yescharacteristic, complemented, Sylow
92D4×Q8—1131no—
93#487—1131no—
94#477—1131no—
95#476—1131no—
96#332D11311yescharacteristic, complemented
97Q8⋊C8—1131no—
98D4⋊C8—1131no—
99C22×Q8—2261no—
100C4⋊Q8—1131no—
101C4⋊Q8—2261no—
102C4⋊Q8C2×D11311yescharacteristic
103C22⋊Q8—2261no—
104C22⋊Q8—2262no—
105C4×Q8—1131no—
106C4×D4—1131no—
107C4×D4—2261no—
108#107—2261no—
109#106—2261no—
110C4⋊C8C2×D11311yescharacteristic
111C4⋊C8C2×D11311yescharacteristic
112#103—2261no—
113#103—2262no—
114#102—2261no—
115C4×C8—1131no—
116C2×Q8—21no—
117C2×Q8—1131no—
118C2×Q8—4522no—
119C2×Q8—4522no—
120C2×Q8—2262no—
121C2×Q8—2261no—
122C2×D4—1131no—
123C22×C4—2262no—
124C22×C4—2261no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—2261no—
128C4⋊C4—21no—
129C4⋊C4—1131no—
130C4⋊C4—1131no—
131C4⋊C4—2262no—
132C4⋊C4—2261no—
133C4⋊C4—2261no—
134C4⋊C4—2261no—
135C4⋊C4D45212yes—
136C22⋊C4—2262no—
137C22⋊C4—2261no—
138C42—2261no—
139C42C22×D11311yescharacteristic
140C23—2261no—
141Q8—41no—
142Q8—41no—
143Q8—1132no—
144Q8—4522no—
145Q8—4524no—
146Q8—2261no—
147D4—1132no—
148D4—2261no—
149C2×C4—22no—
150C2×C4—4524no—
151C2×C4—4521no—
152C2×C4—4521no—
153C2×C4—4521no—
154C2×C4—2261no—
155C2×C4—2261no—
156C2×C4—2261no—
157C2×C4D4×D11311yescharacteristic
158C2×C4D4×D11311yescharacteristic
159C2×C4C2×D45211yescharacteristic
160C8—41no—
161C8—41no—
162C8—4521no—
163C22—4521no—
164C22—4521no—
165C22—2262no—
166C22#1681359211yescharacteristic
167C4—21no—
168C4—42no—
169C4—9041no—
170C4—4521no—
171C4—4521no—
172C4—2262no—
173C4SD16×D11311yescharacteristic
174C4Q16×D11311yescharacteristic
175C4#1681364611yescharacteristic
176C4#1681365111yescharacteristic
177C2—4522no—
178C2#2029875011yescharacteristic
179C2#2029875511yescharacteristic
180C2#2029877311yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#332×C113C2
socleC22×C113#120
prime radicalC2×D452D4
hypercenter#332D113
hypocenterC113#1637
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. #20298950C2semidirect
3. #20298894C2semidirect
5. #20298328C2semidirect
7. #332×C113C2semidirect
91. C113#1637semidirect
96. #332D113semidirect

Maximal subgroups

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

subgroupindex
#202992632
#202989502
#202988942
#202988892
#202983282
#202983252
#332×C1132
#1637113