Finite Group Databasebeta

← #28389726

Subgroups — #28389726

Order 14464.

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

normal subgroups only

This group has 234 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#20299251C211yesmaximal, characteristic
2#20298950C211yesmaximal, characteristic, complemented
3#20298889C211yesmaximal, characteristic, complemented
4#20298889C211yesmaximal, characteristic, complemented
5#20298325C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic, complemented
7#332×C113C211yesmaximal, characteristic, complemented
8C2×#14268648—21no—
9#16813622C2211yescharacteristic
10#16813607—22no—
11#16813598—21no—
12#16813597—21no—
13C4×D452C2211yescharacteristic
14C4×D452C2211yescharacteristic
15C4⋊C4×D113—21no—
16#16813554—21no—
17#16813554—21no—
18#16813545—22no—
19#16813544—21no—
20#16813544—21no—
21C4×#11744751C2211yescharacteristic
22C4⋊Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25#14268648—42no—
26#14268648—42no—
27C2×Dic226—21no—
28C2×D452—22no—
29C2×D452D411yescharacteristic
30C2×D452D411yescharacteristic
31C2×C4×D113—22no—
32C2×C4×D113—21no—
33C2×C4×D113—21no—
34C2×#11744751—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113D411yescharacteristic
38C4⋊Dic113D411yescharacteristic
39#14268626—22no—
40#14268624—22no—
41#14268624—21no—
42#14268624—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—
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—41no—
60D452—21no—
61D452—21no—
62D452—21no—
63D452—44no—
64D452SD1612yes—
65C4×D113—44no—
66C4×D113—41no—
67C4×D113—41no—
68C4×D113—41no—
69C4×D113—41no—
70Dic226—42no—
71C8×C113—41no—
72C8×C113—41no—
73#11744751—41no—
74C22×C113#12011yescharacteristic
75C2×D113—22no—
76C2×D113—41no—
77C2×D113—41no—
78C2×D113—41no—
79C2×D113—41no—
80C2×D113—41no—
81C4×C113—21no—
82C4×C113—42no—
83C4×C113C2×SD1611yescharacteristic
84C4×C113#13511yescharacteristic
85C4×C113AGL(1,ℤ/8)11yescharacteristic
86C4×C113#13711yescharacteristic
87Dic113—41no—
88Dic113—41no—
89Dic113—81no—
90C2×C113#45011yescharacteristic
91C2×C113#45211yescharacteristic
92C2×C113#45411yescharacteristic
93D113—42no—
94D113—81no—
95#1635—1131nomaximal, Sylow
96C113#163511yescharacteristic, complemented, Sylow
97#547—1131no—
98#487—1131no—
99#476—1131no—
100#476—1131no—
101#332D11311yescharacteristic, complemented
102D4⋊C8—1131no—
103D4⋊C8—1131no—
104C2×#41—2261no—
105C4⋊Q8—1131no—
106C4⋊Q8C2×D11311yescharacteristic
107#123—2262no—
108C22⋊Q8—2261no—
109#121—2261no—
110C4×D4—1131no—
111C4×D4—1131no—
112C2×C4⋊C4—2261no—
113#106—2261no—
114#106—2261no—
115C4⋊C8C2×D11311yescharacteristic
116C4⋊C8C2×D11311yescharacteristic
117#103—2262no—
118#102—2261no—
119#102—2261no—
120C4×C8—1131no—
121#41—4522no—
122#41—4522no—
123C2×Q8—21no—
124C2×Q8—2261no—
125C2×D4—1131no—
126C2×D4—1131no—
127C2×D4—2262no—
128C22×C4—2262no—
129C22×C4—2261no—
130C22×C4—2261no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—2261no—
134C4⋊C4—21no—
135C4⋊C4—1131no—
136C4⋊C4—1131no—
137C4⋊C4—2262no—
138C4⋊C4—2261no—
139C4⋊C4—2261no—
140C4⋊C4D45212yes—
141C22⋊C4—2262no—
142C22⋊C4—2261no—
143C22⋊C4—2261no—
144C42C22×D11311yescharacteristic
145C23—2261no—
146C23—2261no—
147Q8—41no—
148Q8—41no—
149Q8—4522no—
150D4—1132no—
151D4—4524no—
152D4—2261no—
153D4—2261no—
154D4—2261no—
155C2×C4—22no—
156C2×C4—4524no—
157C2×C4—4521no—
158C2×C4—4521no—
159C2×C4—4521no—
160C2×C4—4521no—
161C2×C4—4521no—
162C2×C4—2261no—
163C2×C4—2261no—
164C2×C4D4×D11311yescharacteristic
165C2×C4D4×D11311yescharacteristic
166C2×C4C2×D45211yescharacteristic
167C8—41no—
168C8—41no—
169C8—4521no—
170C22—4521no—
171C22—4521no—
172C22—4521no—
173C22—4521no—
174C22—4521no—
175C22—2262no—
176C22#1681359211yescharacteristic
177C4—21no—
178C4—42no—
179C4—9041no—
180C4—4521no—
181C4—4521no—
182C4SD16×D11311yescharacteristic
183C4#1681364311yescharacteristic
184C4#1681364611yescharacteristic
185C4#1681365411yescharacteristic
186C2—9041no—
187C2—4522no—
188C2#2029875011yescharacteristic
189C2#2029876311yescharacteristic
190C2#2029877311yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#332×C113C2
socleC22×C113#120
prime radical#20299251C2
hypercenter#332D113
hypocenterC113#1635
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. #20298889C2semidirect
4. #20298889C2semidirect
5. #20298325C2semidirect
6. #20298325C2semidirect
7. #332×C113C2semidirect
96. C113#1635semidirect
101. #332D113semidirect

Maximal subgroups

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

subgroupindex
#202992512
#202989502
#202988892
#202983252
#332×C1132
#1635113