Finite Group Databasebeta

← #28337625

Subgroups — #28337625

Order 13696.

466 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 69 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#20293253C211yesmaximal, characteristic, complemented
2#20292483C212yesmaximal
3#20292394C211yesmaximal, characteristic, complemented
4#20292393C212yesmaximal, complemented
5#379×C107C211yesmaximal, characteristic
6#16812088—22no—
7#16812086—24no—
8C2×C22⋊Dic107—24no—
9C2×C22⋊Dic107C2212yes—
10C2×C22⋊Dic107C2212yes—
11C25×C107C2211yescharacteristic
12C2×C22⋊C4×C107—22no—
13C2×C22⋊C4×C107C2211yescharacteristic
14C2×C22⋊C4×C107C2211yescharacteristic
15C2×Dic214—22no—
16C22×Dic107—22no—
17C22×Dic107D414yes—
18C4⋊Dic107—22no—
19Dic107⋊C4—24no—
20C22⋊Dic107—22no—
21C22⋊Dic107—22no—
22C22⋊Dic107—22no—
23C22⋊Dic107—22no—
24C22⋊Dic107—48no—
25C24×C107—22no—
26C24×C107—21no—
27C24×C107—22no—
28C24×C107—21no—
29C24×C107—44no—
30C24×C107Q812yescomplemented
31C24×C107C2311yescharacteristic
32C22×C4×C107—21no—
33C22×C4×C107D412yes—
34C22⋊C4×C107—22no—
35C22⋊C4×C107—22no—
36C22⋊C4×C107—44no—
37C23×C107—24no—
38C23×C107—28no—
39C23×C107—24no—
40C23×C107—22no—
41C23×C107—44no—
42C23×C107—42no—
43C23×C107—44no—
44C23×C107—42no—
45C23×C107—48no—
46C23×C107—44no—
47C23×C107—41no—
48C23×C107—42no—
49C23×C107—41no—
50C23×C107C2×D412yes—
51C23×C107C2×D411yescharacteristic
52C23×C107C2×Q811yescharacteristic
53C23×C107#4112yes—
54C23×C107#4111yescharacteristic
55C2×C4×C107—22no—
56C2×C4×C107—42no—
57C2×C4×C107—42no—
58C2×C4×C107—41no—
59C2×Dic107—24no—
60C2×Dic107—44no—
61C2×Dic107—44no—
62C2×Dic107—42no—
63Dic214—82no—
64C22×C107—24no—
65C22×C107—22no—
66C22×C107—24no—
67C22×C107—28no—
68C22×C107—41no—
69C22×C107—42no—
70C22×C107—41no—
71C22×C107—48no—
72C22×C107—44no—
73C22×C107—44no—
74C22×C107—42no—
75C22×C107—42no—
76C22×C107—44no—
77C22×C107#12011yescharacteristic
78C22×C107C22⋊Q812yes—
79C22×C107C22⋊Q811yescharacteristic
80C22×C107#12412yes—
81C22×C107#12411yescharacteristic
82C4×C107—42no—
83C4×C107—81no—
84Dic107—44no—
85Dic107—82no—
86C2×C107—22no—
87C2×C107—21no—
88C2×C107—22no—
89C2×C107—21no—
90C2×C107—44no—
91C2×C107#39311yescharacteristic
92C2×C107B(4,𝔽2)12yes—
93#2029—1071nomaximal, Sylow
94C107#202911yescharacteristic, complemented, Sylow
95#543—1071no—
96#379—1072no—
97#379D10711yescharacteristic
98#342—1072no—
99#342—1071no—
100C25C2×D10711yescharacteristic
101C22⋊Q8—2144no—
102C22⋊Q8—2142no—
103C2×C22⋊C4—22no—
104C2×C22⋊C4—1072no—
105C2×C22⋊C4—1072no—
106C2×C22⋊C4—2144no—
107C2×C22⋊C4C2×D10711yescharacteristic
108C2×C22⋊C4C2×D10711yescharacteristic
109C24—22no—
110C24—21no—
111C24—22no—
112C24—21no—
113C24—44no—
114C24Dic21412yescomplemented
115C24C22×D10711yescharacteristic
116C2×Q8—2142no—
117C22×C4—21no—
118C22×C4—1074no—
119C22×C4—2142no—
120C22×C4C22⋊D10712yes—
121C4⋊C4—2144no—
122C4⋊C4—2142no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—44no—
126C22⋊C4—4288no—
127C22⋊C4—2142no—
128C22⋊C4—2142no—
129C22⋊C4—2142no—
130C22⋊C4—2142no—
131C23—24no—
132C23—28no—
133C23—24no—
134C23—22no—
135C23—44no—
136C23—42no—
137C23—42no—
138C23—44no—
139C23—48no—
140C23—44no—
141C23—41no—
142C23—42no—
143C23—41no—
144C23D4×D10712yes—
145C23C2×C22⋊D10711yescharacteristic
146C23C2×Dic21411yescharacteristic
147C23#1313381712yes—
148C23#1313381811yescharacteristic
149Q8—8562no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—4284no—
155C2×C4—4282no—
156C2×C4—4284no—
157C2×C4—2144no—
158C22—22no—
159C22—24no—
160C22—28no—
161C22—24no—
162C22—41no—
163C22—42no—
164C22—41no—
165C22—44no—
166C22—48no—
167C22—44no—
168C22—42no—
169C22—42no—
170C22—44no—
171C22#1681207711yescharacteristic
172C22#1681208612yes—
173C22#1681208811yescharacteristic
174C22#1681209512yes—
175C22#1681209611yescharacteristic
176C4—42no—
177C4—81no—
178C4—8562no—
179C4—4284no—
180C2—21no—
181C2—22no—
182C2—22no—
183C2—21no—
184C2—44no—
185C2#2029253911yescharacteristic
186C2#2029281312yes—
subgroupG/H
centerC22#16812077
commutator, cosocleC24×C107C23
FrattiniC24C22×D107
Fitting#379×C107C2
socleC22×C107#120
prime radicalC25×C107C22
hypercenter#379D107
hypocenterC107#2029
LCSG ▷ C24×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #20293253C2semidirect
3. #20292394C2semidirect
4. #20292393C2semidirect
30. C24×C107Q8semidirect
94. C107#2029semidirect
114. C24Dic214semidirect

Maximal subgroups

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

subgroupindex
#202932532
#202924832
#202923942
#202923932
#379×C1072
#2029107