Finite Group Databasebeta

← #31795663

Subgroups — #31795663

Order 17536.

276 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 60 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#22578371C211yesmaximal, characteristic
2#22578345C211yesmaximal, characteristic
3#95×D137C211yesmaximal, characteristic
4C2×#14555518—21no—
5C2×C4⋊#10587739C412yescomplemented
6C2×C22⋊#10587739—21no—
7#17984145C412yescomplemented
8C22⋊#11764047—21no—
9(C2×#10587739)⋊C4—21no—
10C22×C4×D137—21no—
11C22×C4×D137C2211yescharacteristic
12#17983995—21no—
13#17983995C411yescharacteristic, complemented
14#95×C137C411yescharacteristic, complemented
15C22×#10587739—22no—
16#14555518—42no—
17C2×#11764047—22no—
18C4⋊#10587739—42no—
19C22⋊#10587739—41no—
20C22⋊#10587739—41no—
21C23×D137D411yescharacteristic
22C22×Dic137—21no—
23C22×Dic137D411yescharacteristic
24C2×C4×D137—24no—
25C2×C4×D137—42no—
26C2×C4×D137—42no—
27C2×C4×D137—41no—
28C2×C4×D137—41no—
29C2×C4×D137C2×C411yescharacteristic
30C2×C4×D137C2×C411yescharacteristic
31C2×C4×D137D411yescharacteristic
32C2×C4×D137Q811yescharacteristic
33C22×C4×C137—21no—
34C22×C4×C137C2×C411yescharacteristic
35C2×#10587739—42no—
36C2×#10587739—42no—
37C2×#10587739—42no—
38#11764047—42no—
39C22×D137—22no—
40C22×D137—22no—
41C22×D137C22⋊C411yescharacteristic
42C22×D137C4⋊C411yescharacteristic
43C22×D137D811yescharacteristic
44C22×D137SD1611yescharacteristic
45C22×D137SD1611yescharacteristic
46C22×D137Q1611yescharacteristic
47C2×Dic137—22no—
48C2×Dic137—41no—
49C2×Dic137—41no—
50C2×Dic137—41no—
51C2×Dic137C22⋊C411yescharacteristic
52C2×Dic137C4⋊C411yescharacteristic
53C4×D137—22no—
54C4×D137—22no—
55C4×D137—41no—
56C4×D137—41no—
57C4×D137—44no—
58C4×D137—44no—
59C23×C137C22⋊C411yescharacteristic
60C2×C4×C137—22no—
61C2×C4×C137—41no—
62C2×C4×C137—41no—
63C2×C4×C137—41no—
64C2×C4×C137C4211yescharacteristic
65C2×C4×C137C4⋊C411yescharacteristic
66C22×C137—21no—
67C22×C137—21no—
68C22×C137#9511yescharacteristic
69C22×C137#10211yescharacteristic
70C22×C137#10311yescharacteristic
71C2×D137—21no—
72C2×D137—21no—
73C2×D137—22no—
74C2×D137—22no—
75C2×D137—22no—
76C2×D137—22no—
77C2×D137#9912yes—
78C2×D137#10211yescharacteristic
79C2×D137#10311yescharacteristic
80C2×D137#10412yes—
81C2×D137#10611yescharacteristic
82C2×D137#10711yescharacteristic
83#10587739—82no—
84C4×C137—21no—
85C4×C137—21no—
86C4×C137—42no—
87Dic137—21no—
88Dic137—21no—
89Dic137—42no—
90C2×C137—21no—
91C2×C137—21no—
92C2×C137#33911yescharacteristic
93C2×C137#34011yescharacteristic
94C2×C137#34211yescharacteristic
95D137—21no—
96D137—21no—
97D137#32712yes—
98D137#32812yes—
99C137#129411yescharacteristic, complemented, Sylow
100#1294—1371nomaximal, Sylow
101C2×C22⋊C8—1371no—
102#380—1371no—
103C2×#95—1371no—
104C23×C4—2741no—
105C23×C4—1371no—
106C22×C8—2741no—
107C2×C4⋊C4—1372no—
108C2×C22⋊C4—2741no—
109C22⋊C8—2741no—
110C22⋊C8—1372no—
111#95—2741no—
112#95—2741no—
113#95—1371no—
114#95#1058773911yescharacteristic, complemented
115C24—1371no—
116C22×C4—21no—
117C22×C4—2744no—
118C22×C4—2741no—
119C22×C4—2742no—
120C22×C4—5482no—
121C22×C4—5482no—
122C22×C4—5481no—
123C22×C4—5481no—
124C22×C4—1371no—
125C22×C4—1371no—
126C22×C4—1371no—
127C22×C4—1371no—
128C22×C4—1371no—
129C22×C4C2×#1058773911yescharacteristic
130C2×C8—2742no—
131C2×C8—5482no—
132C4⋊C4—5482no—
133C22⋊C4—5481no—
134C22⋊C4—5481no—
135C23—2742no—
136C23—2742no—
137C23—1371no—
138C23—1371no—
139C23—1371no—
140C23—1371no—
141C23—1371no—
142C23—1371no—
143C23C22⋊#1058773911yescharacteristic
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—2742no—
149C2×C4—2742no—
150C2×C4—2742no—
151C2×C4—5481no—
152C2×C4—5481no—
153C2×C4—5484no—
154C2×C4—5484no—
155C2×C4—5481no—
156C2×C4—5481no—
157C2×C4—5481no—
158C2×C4—5482no—
159C2×C4—5482no—
160C2×C4—5482no—
161C2×C4—1371no—
162C2×C4—1371no—
163C2×C4C4×#1058773911yescharacteristic
164C2×C4C4⋊#1058773911yescharacteristic
165C8—5482no—
166C22—21no—
167C22—21no—
168C22—2742no—
169C22—2742no—
170C22—2742no—
171C22—2742no—
172C22—2741no—
173C22—2741no—
174C22—1371no—
175C22—1371no—
176C22—1372no—
177C22—1371no—
178C22—1371no—
179C22—1372no—
180C22(C2×#10587739)⋊C411yescharacteristic
181C22#1798415011yescharacteristic
182C22#1798415111yescharacteristic
183C4—21no—
184C4—21no—
185C4—42no—
186C4—2741no—
187C4—2741no—
188C4—5482no—
189C4—10962no—
190C2—21no—
191C2—21no—
192C2—2741no—
193C2—2741no—
194C2—1372no—
195C2—1372no—
196C2#2257827411yescharacteristic
197C2#2257827611yescharacteristic
198C2#2257828011yescharacteristic
subgroupG/H
centerC22(C2×#10587739)⋊C4
commutatorC2×C4×C137C42
FrattiniC22×C4C2×#10587739
Fitting#95×C137C4
socleC22×C137#95
prime radicalC23×D137D4
cosocleC22×C4×D137C22
hypercenter#95#10587739
hypocenterC137#1294
LCSG ▷ C2×C4×C137 ▷ C22×C137 ▷ C137
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊#10587739C4semidirect
7. #17984145C4semidirect
13. #17983995C4semidirect
14. #95×C137C4semidirect
99. C137#1294semidirect
114. #95#10587739semidirect

Maximal subgroups

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

subgroupindex
#225783712
#225783452
#95×D1372
#1294137