Finite Group Databasebeta

← C2×#22578260 #31796237

Subgroups — C2×#22578260 #31796237

Order 17536.

232 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C2×#17984143C211yesmaximal, characteristic
2C2×#17984143C211yesmaximal, characteristic
3#22578260C214yesmaximal, direct product factor
4C2×#17984079C211yesmaximal, characteristic
5C22×#11764047—21no—
6C22×#11764047—21no—
7#17984143—21no—
8#17984143—21no—
9#17984143C2212yes—
10#17984143C2212yes—
11#17984079—21no—
12#17984079—21no—
13#17984079C412yes—
14#17984079C2212yes—
15C2×C4⋊Dic137—21no—
16C2×C4⋊Dic137C411yescharacteristic
17C2×#14555489—21no—
18C2×C4×Dic137C2211yescharacteristic
19C2×C4⋊C4×C137C411yescharacteristic
20C2×#11764047—24no—
21C2×#11764047—24no—
22C2×#11764047—22no—
23C2×#11764047—22no—
24C22×Dic137—21no—
25C22×Dic137D411yescharacteristic
26C22×Dic137D411yescharacteristic
27C4⋊Dic137—22no—
28C4⋊Dic137—22no—
29C4⋊Dic137—21no—
30C4⋊Dic137C2×C412yes—
31#14555489—22no—
32#14555489—22no—
33C4×Dic137C2×C411yescharacteristic
34C4×Dic137D411yescharacteristic
35C4×Dic137D411yescharacteristic
36C4×Dic137C2311yescharacteristic
37C22×C4×C137—21no—
38C22×C4×C137C2×C411yescharacteristic
39C4⋊C4×C137—21no—
40C4⋊C4×C137C2×C412yes—
41#11764047—24no—
42#11764047—24no—
43C2×Dic137—22no—
44C2×Dic137—22no—
45C2×Dic137—22no—
46C2×Dic137—42no—
47C2×Dic137C22⋊C411yescharacteristic
48C2×Dic137C22⋊C411yescharacteristic
49C2×Dic137C2×D411yescharacteristic
50C2×Dic137C2×D411yescharacteristic
51C23×C137C22⋊C411yescharacteristic
52C2×C4×C137—22no—
53C2×C4×C137—22no—
54C2×C4×C137—42no—
55C2×C4×C137C22⋊C411yescharacteristic
56C2×C4×C137C22×C411yescharacteristic
57C22×C137#10112yes—
58C22×C137#10412yes—
59C22×C137#10412yes—
60C22×C137C2×C22⋊C411yescharacteristic
61C4×C137—21no—
62C4×C137—21no—
63C4×C137—42no—
64Dic137—21no—
65Dic137—21no—
66Dic137—21no—
67Dic137—21no—
68Dic137—42no—
69C2×C137#33014yescomplemented
70C2×C137C2×#10111yescharacteristic
71C2×C137C2×#10411yescharacteristic
72C2×C137C2×#10411yescharacteristic
73C137C2×#33011yescharacteristic, complemented, Sylow
74C2×#330—1371nomaximal, Sylow
75C2×#125—1371no—
76C2×#97—1371no—
77C2×#97—1371no—
78#330—1374no—
79C22×C8—2741no—
80C22×C8—2741no—
81#125—2741no—
82#125—2741no—
83#125—1372no—
84#125—1372no—
85C2×C4⋊C4—2741no—
86C2×C4⋊C4—2741no—
87C2×C4⋊C4—1371no—
88C2×C4⋊C4#1058773911yescharacteristic
89C2×C42—1371no—
90#97—2741no—
91#97—2741no—
92#97—1372no—
93#97—1372no—
94C22×C4—21no—
95C22×C4—2741no—
96C22×C4—1371no—
97C22×C4—1371no—
98C22×C4C2×#1058773911yescharacteristic
99C2×C8—2744no—
100C2×C8—2744no—
101C2×C8—2742no—
102C2×C8—2742no—
103C4⋊C4—21no—
104C4⋊C4—2742no—
105C4⋊C4—2742no—
106C4⋊C4—2742no—
107C4⋊C4—2742no—
108C4⋊C4—2741no—
109C4⋊C4—1372no—
110C4⋊C4C2×#1058773912yes—
111C42—1371no—
112C42—1371no—
113C42—1371no—
114C42—1371no—
115C23C22⋊#1058773911yescharacteristic
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—2742no—
120C2×C4—2742no—
121C2×C4—2742no—
122C2×C4—5482no—
123C2×C4—1371no—
124C2×C4—1371no—
125C2×C4—1371no—
126C2×C4—1371no—
127C2×C4C22⋊#1058773911yescharacteristic
128C2×C4C22×#1058773911yescharacteristic
129C8—2744no—
130C8—2744no—
131C22#1798414912yes—
132C22#1798415212yes—
133C22#1798415312yes—
134C22C2×C22⋊#1058773911yescharacteristic
135C4—21no—
136C4—21no—
137C4—42no—
138C4—2741no—
139C4—2741no—
140C4—2741no—
141C4—2741no—
142C4—5482no—
143C2#2257826014yesdirect product factor
144C2C2×#1798414911yescharacteristic
145C2C2×#1798415211yescharacteristic
146C2C2×#1798415311yescharacteristic
subgroupG/H
centerC23C22⋊#10587739
commutatorC2×C4×C137C22×C4
FrattiniC2×C4C22×#10587739
FittingC2×C4⋊C4×C137C4
socle, prime radicalC23×C137C22⋊C4
cosocleC4×Dic137C23
hypercenterC2×C4⋊C4#10587739
hypocenterC137C2×#330
LCSG ▷ C2×C4×C137 ▷ C22×C137 ▷ C137
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22578260C2direct (N × H)
69. C2×C137#330semidirect
73. C137C2×#330semidirect
143. C2#22578260direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179841432
#225782602
C2×#179840792
C2×#330137