Finite Group Databasebeta

← #31796239

Subgroups — #31796239

Order 17536.

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

normal subgroups only

This group has 234 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
1C4×#14555520C211yesmaximal, characteristic, complemented
2#22578362C211yesmaximal, characteristic, complemented
3#22578260C212yesmaximal, complemented
4#22578258C212yesmaximal, complemented
5#22577935C211yesmaximal, characteristic
6C2×#14555520—21no—
7C2×#14555518—21no—
8#17984143—21no—
9#17984143C2212yes—
10#17984143C2212yes—
11C4×#11764047—21no—
12#17984081—21no—
13#17984079C2211yescharacteristic
14#17984075C2211yescharacteristic
15#17984070—21no—
16#17984068C411yescharacteristic
17#17984059C411yescharacteristic
18C4×Dic274C411yescharacteristic
19C4×C22⋊D137—21no—
20#17984047—21no—
21C42×D137C2211yescharacteristic
22C4×D4×C137C411yescharacteristic
23#14555520—24no—
24#14555518—24no—
25C2×#11764047—22no—
26C2×#11764047—22no—
27C2×Dic274C2×C411yescharacteristic
28C2×C22⋊D137—21no—
29C2×C4×D137C2×C411yescharacteristic
30C2×C4×D137D411yescharacteristic
31C2×C4×D137D411yescharacteristic
32C4⋊Dic137—21no—
33C4⋊Dic137—21no—
34C4⋊Dic137C2×C411yescharacteristic
35#14555489—21no—
36#14555489—21no—
37C22⋊Dic137—21no—
38C22⋊Dic137—21no—
39C22⋊Dic137—21no—
40#14555487—21no—
41C4×Dic137—21no—
42C4×Dic137D411yescharacteristic
43C4×Dic137D411yescharacteristic
44C4×Dic137C2311yescharacteristic
45C2×D4×C137C2×C411yescharacteristic
46C22×C4×C137—21no—
47C4⋊C4×C137C2×C411yescharacteristic
48C22⋊C4×C137—21no—
49C42×C137C2×C411yescharacteristic
50#11764047—24no—
51#11764047—24no—
52C22×D137C22⋊C411yescharacteristic
53Dic274—41no—
54C22⋊D137—42no—
55C2×Dic137—21no—
56C2×Dic137—21no—
57C2×Dic137C22⋊C411yescharacteristic
58C2×Dic137C2×D411yescharacteristic
59C2×Dic137C2×D411yescharacteristic
60C4×D137—22no—
61C4×D137—22no—
62C4×D137—41no—
63C23×C137—21no—
64D4×C137—41no—
65C2×C4×C137—21no—
66C2×C4×C137—42no—
67C2×C4×C137C22⋊C411yescharacteristic
68C2×C4×C137C22⋊C411yescharacteristic
69C2×C4×C137C22×C411yescharacteristic
70C22×C137—41no—
71C22×C137—41no—
72C22×C137—41no—
73C22×C137C2×C22⋊C411yescharacteristic
74C2×D137—21no—
75C2×D137—21no—
76C2×D137#10412yes—
77C4×C137—21no—
78C4×C137—21no—
79C4×C137—41no—
80C4×C137#10412yes—
81Dic137—21no—
82Dic137—21no—
83Dic137—21no—
84Dic137—41no—
85Dic137—41no—
86C2×C137—81no—
87C2×C137#41311yescharacteristic
88C2×C137C2×#10411yescharacteristic
89C2×C137C2×#10411yescharacteristic
90D137—22no—
91C137#152411yescharacteristic, complemented, Sylow
92#1524—1371nomaximal, Sylow
93#529—1371no—
94C4×M16—1371no—
95C2×#97—1371no—
96#330—1372no—
97#329—1372no—
98C2×M16—2741no—
99C22×C8—2741no—
100#126—2741no—
101#125—1371no—
102#124—1371no—
103#123—2741no—
104C22⋊Q8—1371no—
105#121—1371no—
106C4×Q8—1371no—
107C4×D4—2741no—
108C4×D4#1058773911yescharacteristic
109#117—2741no—
110C2×C42—1371no—
111#97—2741no—
112#97—1372no—
113#97—1372no—
114C4×C8—2741no—
115C2×Q8—1371no—
116C2×D4—2741no—
117C2×D4C2×#1058773911yescharacteristic
118C22×C4—21no—
119C22×C4—1371no—
120C22×C4—1371no—
121C22×C4—1371no—
122M16—2744no—
123C2×C8—2744no—
124C2×C8—2742no—
125C2×C8—2742no—
126C4⋊C4—2741no—
127C4⋊C4—2741no—
128C4⋊C4—2741no—
129C4⋊C4—2741no—
130C4⋊C4—1371no—
131C4⋊C4C2×#1058773911yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—2741no—
134C22⋊C4—2741no—
135C22⋊C4—2741no—
136C22⋊C4—2741no—
137C42—2741no—
138C42—1371no—
139C42—1371no—
140C42—1371no—
141C42C2×#1058773911yescharacteristic
142C23—21no—
143C23—1371no—
144Q8—5481no—
145D4—41no—
146D4—5482no—
147C2×C4—21no—
148C2×C4—42no—
149C2×C4—2742no—
150C2×C4—2742no—
151C2×C4—2741no—
152C2×C4—2741no—
153C2×C4—5481no—
154C2×C4—1371no—
155C2×C4—1371no—
156C2×C4—1371no—
157C2×C4C22⋊#1058773911yescharacteristic
158C2×C4C22⋊#1058773911yescharacteristic
159C2×C4C22×#1058773911yescharacteristic
160C8—2744no—
161C8—2744no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22—2741no—
166C22—2741no—
167C22—1372no—
168C22C2×C22⋊#1058773911yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—2741no—
173C4—2741no—
174C4—2741no—
175C4—5481no—
176C4—5481no—
177C4#1798415212yes—
178C2—81no—
179C2—2742no—
180C2#2257838911yescharacteristic
181C2C2×#1798415211yescharacteristic
182C2D137⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10587739
commutatorC2×C4×C137C22×C4
FrattiniC2×C4C22×#10587739
FittingC4×D4×C137C4
socleC22×C137C2×C22⋊C4
prime radical#17984059C4
cosocleC4×Dic137C23
hypercenterC4×D4#10587739
hypocenterC137#1524
LCSG ▷ C2×C4×C137 ▷ C22×C137 ▷ C137
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#14555520C2semidirect
2. #22578362C2semidirect
3. #22578260C2semidirect
4. #22578258C2semidirect
91. C137#1524semidirect

Maximal subgroups

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

subgroupindex
C4×#145555202
#225783622
#225782602
#225782582
#225779352
#1524137