Finite Group Databasebeta

← #31796171

Subgroups — #31796171

Order 17536.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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#22578421C211yesmaximal, characteristic
2C4×C4⋊#10587739C211yesmaximal, characteristic
3#22578257C212yesmaximal
4#22578256C212yesmaximal
5#22577957C211yesmaximal, characteristic
6C2×C4⋊#10587739—21no—
7C2×C4×#10587739—21no—
8#17984155—21no—
9#17984145C2212yes—
10C4×#11764047—21no—
11(C2×#10587739)⋊C4C2212yes—
12#17984087C411yescharacteristic, complemented
13#17984086C411yescharacteristic, complemented
14#17984078—21no—
15#17984068C2211yescharacteristic
16#17984066—21no—
17#17984064C2211yescharacteristic
18C4×Dic274—21no—
19C4×Dic274C411yescharacteristic, complemented
20#17984045—21no—
21C42×D137C2211yescharacteristic
22C4×Q8×C137C411yescharacteristic, complemented
23C22×#10587739—22no—
24C2×#11764047—22no—
25C4⋊#10587739—24no—
26C4×#10587739—42no—
27C2×Dic274—21no—
28C2×Dic274C2×C411yescharacteristic
29C2×C4×D137D411yescharacteristic
30C2×C4×D137D411yescharacteristic
31C2×C4×D137C2311yescharacteristic
32C4⋊Dic137—21no—
33C4⋊Dic137C2×C411yescharacteristic
34#14555489—21no—
35#14555489—21no—
36#14555489—21no—
37#14555489—21no—
38#14555489—21no—
39#14555487—21no—
40#14555487—21no—
41C4×Dic137—21no—
42C4×Dic137C2×C411yescharacteristic
43C4×Dic137D411yescharacteristic
44C4×Dic137D411yescharacteristic
45C2×Q8×C137C2×C411yescharacteristic
46C4⋊C4×C137—21no—
47C4⋊C4×C137C2×C411yescharacteristic
48C42×C137—21no—
49C42×C137C2×C411yescharacteristic
50C2×#10587739—24no—
51C2×#10587739—42no—
52C2×#10587739—42no—
53#11764047—42no—
54C22×D137C2×D411yescharacteristic
55Dic274—42no—
56Dic274—41no—
57C2×Dic137—21no—
58C2×Dic137—21no—
59C2×Dic137C22⋊C411yescharacteristic
60C2×Dic137C22⋊C411yescharacteristic
61C2×Dic137C2×D411yescharacteristic
62C4×D137—22no—
63C4×D137—41no—
64C4×D137SD1612yes—
65C4×D137Q1612yes—
66Q8×C137—41no—
67C2×C4×C137—21no—
68C2×C4×C137—21no—
69C2×C4×C137C22⋊C411yescharacteristic
70C2×C4×C137C22⋊C411yescharacteristic
71C2×C4×C137C22×C411yescharacteristic
72C22×C137C2×C22⋊C411yescharacteristic
73C2×D137—21no—
74C2×D137—21no—
75C2×D137C2×SD1611yescharacteristic
76C2×D137C2×Q1611yescharacteristic
77#10587739—44no—
78C4×C137—21no—
79C4×C137—21no—
80C4×C137—41no—
81C4×C137—41no—
82C4×C137#10312yes—
83Dic137—21no—
84Dic137—41no—
85Dic137—41no—
86Dic137#10312yes—
87Dic137#10412yes—
88C2×C137#41011yescharacteristic
89C2×C137C2×#10311yescharacteristic
90C2×C137C2×#10411yescharacteristic
91D137—21no—
92D137—21no—
93C137#150311yescharacteristic, complemented, Sylow
94#1503—1371nomaximal, Sylow
95#533—1371no—
96#431—1371no—
97C4×C4⋊C4—1371no—
98#328—1372no—
99#328—1372no—
100C4⋊Q8—1371no—
101C4⋊Q8—1371no—
102#125—2741no—
103C22⋊Q8—2741no—
104C22⋊Q8—1371no—
105C22⋊Q8—1371no—
106C4×Q8—2741no—
107C4×Q8—1371no—
108C4×Q8#1058773911yescharacteristic, complemented
109#117—2741no—
110C2×C4⋊C4—2741no—
111C2×C42—2741no—
112C2×C42—1371no—
113C4⋊C8—2741no—
114C22⋊C8—1372no—
115C4×C8—2741no—
116#95—1372no—
117C2×Q8—2741no—
118C2×Q8—1371no—
119C2×Q8C2×#1058773911yescharacteristic
120C22×C4—2742no—
121C22×C4—1371no—
122C22×C4—1371no—
123C22×C4—1371no—
124C2×C8—2742no—
125C4⋊C4—21no—
126C4⋊C4—2741no—
127C4⋊C4—2741no—
128C4⋊C4—2741no—
129C4⋊C4—2741no—
130C4⋊C4—2741no—
131C4⋊C4—2744no—
132C4⋊C4—2741no—
133C4⋊C4—1371no—
134C4⋊C4C2×#1058773911yescharacteristic
135C22⋊C4—2741no—
136C22⋊C4—2741no—
137C42—21no—
138C42—2741no—
139C42—5482no—
140C42—1371no—
141C42—1371no—
142C42—1371no—
143C42C2×#1058773911yescharacteristic
144C23—1371no—
145Q8—41no—
146Q8—5481no—
147Q8—5482no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—2742no—
151C2×C4—2744no—
152C2×C4—2741no—
153C2×C4—2741no—
154C2×C4—5481no—
155C2×C4—5482no—
156C2×C4—5482no—
157C2×C4—1371no—
158C2×C4—1371no—
159C2×C4—1371no—
160C2×C4—1372no—
161C2×C4—1372no—
162C2×C4C22⋊#1058773911yescharacteristic
163C2×C4C22⋊#1058773911yescharacteristic
164C2×C4C22×#1058773911yescharacteristic
165C8—5482no—
166C22—2741no—
167C22—2741no—
168C22—1371no—
169C22—1371no—
170C22C2×C22⋊#1058773911yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—2741no—
176C4—5484no—
177C4—5481no—
178C4—5481no—
179C4—1372no—
180C4—1372no—
181C4#1798415112yes—
182C2—2741no—
183C2—2741no—
184C2#2257838211yescharacteristic
185C2C2×#1798415111yescharacteristic
186C2D137⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10587739
commutatorC2×C4×C137C22×C4
FrattiniC2×C4C22×#10587739
FittingC4×Q8×C137C4
socleC22×C137C2×C22⋊C4
prime radicalC22×D137C2×D4
cosocleC2×C4×D137C23
hypercenterC4×Q8#10587739
hypocenterC137#1503
LCSG ▷ C2×C4×C137 ▷ C22×C137 ▷ C137
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #17984087C4semidirect
13. #17984086C4semidirect
19. C4×Dic274C4semidirect
22. C4×Q8×C137C4semidirect
93. C137#1503semidirect
108. C4×Q8#10587739semidirect

Maximal subgroups

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

subgroupindex
#225784212
C4×C4⋊#105877392
#225782572
#225782562
#225779572
#1503137