Finite Group Databasebeta

← #28389803

Subgroups — #28389803

Order 14464.

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

normal subgroups only

This group has 212 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#20299314C211yesmaximal, characteristic
2#20298948C211yesmaximal, characteristic, complemented
3#20298879C211yesmaximal, characteristic, complemented
4#20298804C211yesmaximal, characteristic, complemented
5#20298325C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic, complemented
7#333×C113C211yesmaximal, characteristic, complemented
8C2×#14268636—21no—
9#16813622C2211yescharacteristic
10#16813611—22no—
11#16813597—21no—
12#16813597—21no—
13C4×D452C2211yescharacteristic
14C4×D452C2211yescharacteristic
15#16813580—21no—
16#16813580—21no—
17#16813556—21no—
18#16813547—21no—
19#16813546—22no—
20#16813544—21no—
21C4×#11744751C2211yescharacteristic
22C4⋊Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25C2×Dic226—21no—
26C2×D452—22no—
27C2×D452D411yescharacteristic
28C2×D452D411yescharacteristic
29C2×C4×D113—21no—
30C2×C4×D113—21no—
31#14268636—42no—
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113D411yescharacteristic
36C4⋊Dic113D411yescharacteristic
37#14268624—22no—
38#14268624—22no—
39#14268624—21no—
40#14268624—21no—
41C4×Dic113—22no—
42C2×Q8×C113D412yes—
43C2×C8×C113—21no—
44C2×C8×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113—21no—
47C42×C113C2311yescharacteristic
48C22×D113—21no—
49C22×D113—21no—
50Q8×C113—42no—
51C2×C4×C113—22no—
52C2×C4×C113C2×D411yescharacteristic
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113C2×D411yescharacteristic
55C2×Dic113—21no—
56C2×Dic113—21no—
57C2×Dic113—41no—
58D452—21no—
59D452—21no—
60D452—21no—
61D452—21no—
62D452—82no—
63C4×D113—41no—
64C4×D113—41no—
65C4×D113—41no—
66C4×D113—41no—
67Dic226—41no—
68Dic226—41no—
69C8×C113—41no—
70C8×C113—41no—
71#11744751—41no—
72C22×C113#12011yescharacteristic
73C2×D113—41no—
74C2×D113—41no—
75C2×D113—41no—
76C2×D113—41no—
77C2×D113—41no—
78C2×D113—41no—
79C4×C113—21no—
80C4×C113—42no—
81C4×C113#13511yescharacteristic
82C4×C113#13511yescharacteristic
83C4×C113AGL(1,ℤ/8)11yescharacteristic
84C4×C113#13711yescharacteristic
85Dic113—41no—
86Dic113—41no—
87Dic113—81no—
88C2×C113#44911yescharacteristic
89C2×C113#45211yescharacteristic
90C2×C113#45511yescharacteristic
91D113—81no—
92D113—81no—
93#1646—1131nomaximal, Sylow
94C113#164611yescharacteristic, complemented, Sylow
95#555—1131no—
96#487—1131no—
97#474—1131no—
98#461—1131no—
99#333D11311yescharacteristic, complemented
100D4⋊C8—1131no—
101D4⋊C8—1131no—
102C2×SD16—2261no—
103C4⋊Q8—1131no—
104C4⋊Q8C2×D11311yescharacteristic
105#124—2262no—
106#121—2261no—
107#121—2261no—
108C4×D4—1131no—
109C4×D4—1131no—
110#117—2261no—
111#117—2261no—
112#107—2261no—
113C4⋊C8C2×D11311yescharacteristic
114C4⋊C8C2×D11311yescharacteristic
115#103—2261no—
116#103—2262no—
117#102—2261no—
118C4×C8—1131no—
119C2×Q8—2261no—
120C2×Q8D45212yes—
121C2×D4—1131no—
122C2×D4—1131no—
123C2×D4—2262no—
124C22×C4—2261no—
125C22×C4—2261no—
126SD16—4522no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—2261no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—1131no—
133C4⋊C4—1131no—
134C4⋊C4—2261no—
135C4⋊C4—2261no—
136C22⋊C4—2262no—
137C22⋊C4—2262no—
138C22⋊C4—2261no—
139C22⋊C4—2261no—
140C42—2262no—
141C42C22×D11311yescharacteristic
142C23—2261no—
143C23—2261no—
144Q8—42no—
145Q8—4521no—
146Q8—4521no—
147D4—9042no—
148D4—2261no—
149D4—2261no—
150D4—2261no—
151D4—2261no—
152C2×C4—22no—
153C2×C4—4521no—
154C2×C4—4521no—
155C2×C4—4521no—
156C2×C4—4521no—
157C2×C4—4521no—
158C2×C4—2261no—
159C2×C4—2261no—
160C2×C4D4×D11311yescharacteristic
161C2×C4D4×D11311yescharacteristic
162C2×C4C2×D45211yescharacteristic
163C8—41no—
164C8—41no—
165C8—4521no—
166C22—4521no—
167C22—4521no—
168C22—4521no—
169C22—4521no—
170C22—4521no—
171C22—4521no—
172C22#1681359211yescharacteristic
173C4—21no—
174C4—42no—
175C4—9041no—
176C4—4521no—
177C4—4521no—
178C4#1681364311yescharacteristic
179C4#1681364511yescharacteristic
180C4#1681364911yescharacteristic
181C4#1681365411yescharacteristic
182C2—9041no—
183C2—9041no—
184C2#2029874611yescharacteristic
185C2#2029876311yescharacteristic
186C2#2029877811yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#333×C113C2
socleC22×C113#120
prime radical#20299314C2
hypercenter#333D113
hypocenterC113#1646
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. #20298948C2semidirect
3. #20298879C2semidirect
4. #20298804C2semidirect
5. #20298325C2semidirect
6. #20298325C2semidirect
7. #333×C113C2semidirect
94. C113#1646semidirect
99. #333D113semidirect

Maximal subgroups

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

subgroupindex
#202993142
#202989482
#202988792
#202988042
#202983252
#333×C1132
#1646113