Finite Group Databasebeta

← #31795651

Subgroups — #31795651

Order 17536.

228 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 54 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#22577262C211yesmaximal, characteristic
4C2×#14555518C412yescomplemented
5C2×C4⋊#10587739—21no—
6C2×C22⋊#10587739—21no—
7#17984145—21no—
8C22⋊#11764047—21no—
9(C2×#10587739)⋊C4C412yescomplemented
10C22×C4×D137C2211yescharacteristic
11C2×#14555489—21no—
12C2×#14555487—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—42no—
25C2×C4×D137C2×C411yescharacteristic
26C2×C4×D137C2×C411yescharacteristic
27C2×C4×D137D411yescharacteristic
28C2×C4×D137Q811yescharacteristic
29#14555489—42no—
30#14555487—41no—
31#14555487—41no—
32C22×C4×C137—21no—
33C22×C4×C137C2×C411yescharacteristic
34C2×#10587739—42no—
35C2×#10587739—42no—
36C2×#10587739—42no—
37#11764047—42no—
38C22×D137—41no—
39C22×D137—41no—
40C22×D137C22⋊C411yescharacteristic
41C22×D137C4⋊C411yescharacteristic
42C22×D137D811yescharacteristic
43C22×D137SD1611yescharacteristic
44C22×D137SD1611yescharacteristic
45C22×D137Q1611yescharacteristic
46C2×Dic137—22no—
47C2×Dic137—41no—
48C2×Dic137—41no—
49C2×Dic137—41no—
50C2×Dic137C22⋊C411yescharacteristic
51C2×Dic137C4⋊C411yescharacteristic
52C4×D137—22no—
53C4×D137—22no—
54C4×D137—41no—
55C4×D137—41no—
56C23×C137C22⋊C411yescharacteristic
57C2×C4×C137—41no—
58C2×C4×C137—41no—
59C2×C4×C137—41no—
60C2×C4×C137—41no—
61C2×C4×C137C4211yescharacteristic
62C2×C4×C137C4⋊C411yescharacteristic
63C22×C137—21no—
64C22×C137—21no—
65C22×C137#9511yescharacteristic
66C22×C137#10211yescharacteristic
67C22×C137#10311yescharacteristic
68C2×D137—21no—
69C2×D137—21no—
70C2×D137—21no—
71C2×D137—21no—
72C2×D137—41no—
73C2×D137—41no—
74C2×D137—41no—
75C2×D137—41no—
76C2×D137#10211yescharacteristic
77C2×D137#10311yescharacteristic
78C2×D137#10611yescharacteristic
79C2×D137#10711yescharacteristic
80#10587739—82no—
81C4×C137—21no—
82C4×C137—21no—
83C4×C137—81no—
84Dic137—21no—
85Dic137—81no—
86Dic137#9912yes—
87C2×C137—21no—
88C2×C137—21no—
89C2×C137H(3,ℤ/4)11yescharacteristic
90C2×C137#34011yescharacteristic
91C2×C137#34211yescharacteristic
92D137—21no—
93D137—21no—
94D137—21no—
95D137—21no—
96C137#128911yescharacteristic, complemented, Sylow
97#1289—1371nomaximal, Sylow
98C2×C22⋊C8—1371no—
99#380—1371no—
100#380—1371no—
101C23×C4—1371no—
102C22×C8—1372no—
103C2×C4⋊C4—2741no—
104C2×C4⋊C4—2741no—
105C2×C22⋊C4—2741no—
106C2×C22⋊C4—2741no—
107C22⋊C8—2741no—
108C22⋊C8—2741no—
109#95—1372no—
110#95—1371no—
111#95#1058773911yescharacteristic, complemented
112C24—1371no—
113C22×C4—21no—
114C22×C4—2742no—
115C22×C4—2741no—
116C22×C4—5482no—
117C22×C4—1371no—
118C22×C4—1371no—
119C22×C4—1371no—
120C22×C4—1371no—
121C22×C4—1371no—
122C22×C4C2×#1058773911yescharacteristic
123C2×C8—2742no—
124C2×C8—5482no—
125C4⋊C4—5482no—
126C4⋊C4—5482no—
127C22⋊C4—5481no—
128C22⋊C4—5481no—
129C22⋊C4—5481no—
130C22⋊C4—5481no—
131C23—5481no—
132C23—5481no—
133C23—1371no—
134C23—1371no—
135C23—1371no—
136C23—1371no—
137C23—1371no—
138C23—1371no—
139C23C22⋊#1058773911yescharacteristic
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—2742no—
145C2×C4—2742no—
146C2×C4—2742no—
147C2×C4—5481no—
148C2×C4—5481no—
149C2×C4—5481no—
150C2×C4—5481no—
151C2×C4—5482no—
152C2×C4—5482no—
153C2×C4—5482no—
154C2×C4—5481no—
155C2×C4—1371no—
156C2×C4—1371no—
157C2×C4C4×#1058773911yescharacteristic
158C2×C4C4⋊#1058773911yescharacteristic
159C8—5482no—
160C22—21no—
161C22—21no—
162C22—2741no—
163C22—2741no—
164C22—2741no—
165C22—2741no—
166C22—5481no—
167C22—5481no—
168C22—5481no—
169C22—5481no—
170C22—1371no—
171C22—1371no—
172C22—1371no—
173C22—1371no—
174C22(C2×#10587739)⋊C411yescharacteristic
175C22#1798415011yescharacteristic
176C22#1798415111yescharacteristic
177C4—21no—
178C4—21no—
179C4—81no—
180C4—2741no—
181C4—10961no—
182C4—10962no—
183C4—1372no—
184C2—21no—
185C2—21no—
186C2—2741no—
187C2—2741no—
188C2—2741no—
189C2—2741no—
190C2#2257827011yescharacteristic
191C2#2257827611yescharacteristic
192C2#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#1289
LCSG ▷ C2×C4×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×#14555518C4semidirect
9. (C2×#10587739)⋊C4C4semidirect
13. #17983995C4semidirect
14. #95×C137C4semidirect
96. C137#1289semidirect
111. #95#10587739semidirect

Maximal subgroups

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

subgroupindex
#225783712
#225783452
#225772622
#1289137