Finite Group Databasebeta

← #31796170

Subgroups — #31796170

Order 17536.

284 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 70 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#22578422C211yesmaximal, characteristic, complemented
2C4×C4⋊#10587739C211yesmaximal, characteristic, complemented
3#22578255C214yesmaximal, complemented
4#22577954C211yesmaximal, characteristic
5C2×C4⋊#10587739—21no—
6C2×C4×#10587739—21no—
7C4⋊#11764047—21no—
8#17984145C2212yes—
9C4×#11764047—21no—
10(C2×#10587739)⋊C4C2212yes—
11C2×#14555511—21no—
12#17984085C411yescharacteristic, complemented
13#17984077—21no—
14#17984063—21no—
15#17984063C2212yes—
16#17984050—21no—
17#17984050C412yescomplemented
18C42×D137C2211yescharacteristic
19C4⋊Q8×C137C411yescharacteristic, complemented
20C22×#10587739—22no—
21C2×#11764047—22no—
22C4⋊#10587739—24no—
23C4×#10587739—42no—
24#14555511—42no—
25#14555511—42no—
26C2×D548—22no—
27C2×D548—21no—
28C2×D548—21no—
29C2×D548C2×C412yes—
30C2×C4×D137—22no—
31C2×C4×D137D411yescharacteristic
32C2×C4×D137D411yescharacteristic
33C2×C4×D137C2311yescharacteristic
34#14555487—22no—
35#14555487—22no—
36C4×Dic137C2×C411yescharacteristic
37C4×Dic137D411yescharacteristic
38C4×Dic137D411yescharacteristic
39C2×Q8×C137—21no—
40C4⋊C4×C137—21no—
41C4⋊C4×C137C2×C412yes—
42C42×C137C2×C411yescharacteristic
43C2×#10587739—24no—
44C2×#10587739—42no—
45C2×#10587739—42no—
46#11764047—42no—
47C22×D137—22no—
48C22×D137C2×D411yescharacteristic
49D548—42no—
50D548—42no—
51D548—42no—
52D548—42no—
53D548—42no—
54C2×Dic137C22⋊C411yescharacteristic
55C2×Dic137C22⋊C411yescharacteristic
56C2×Dic137C2×D411yescharacteristic
57C4×D137—22no—
58C4×D137—41no—
59C4×D137—44no—
60C4×D137D812yes—
61C4×D137SD1612yes—
62Q8×C137—42no—
63C2×C4×C137—22no—
64C2×C4×C137C22⋊C411yescharacteristic
65C2×C4×C137C22⋊C411yescharacteristic
66C2×C4×C137C22×C411yescharacteristic
67C22×C137C2×C22⋊C411yescharacteristic
68C2×D137—21no—
69C2×D137—21no—
70C2×D137—42no—
71C2×D137—42no—
72C2×D137—42no—
73C2×D137C2×D811yescharacteristic
74C2×D137C2×SD1611yescharacteristic
75#10587739—44no—
76C4×C137—21no—
77C4×C137—42no—
78C4×C137#10212yes—
79C4×C137#10412yes—
80Dic137—21no—
81Dic137—21no—
82Dic137#10212yes—
83C2×C137#41011yescharacteristic
84C2×C137C2×#10211yescharacteristic
85C2×C137C2×#10411yescharacteristic
86D137—21no—
87D137—21no—
88D137—82no—
89C137#150211yescharacteristic, complemented, Sylow
90#1502—1371nomaximal, Sylow
91#532—1371no—
92#431—1371no—
93C4×C4⋊C4—1371no—
94#327—1374no—
95C2×#41—2741no—
96C4⋊Q8#1058773911yescharacteristic, complemented
97#127—1371no—
98#124—2741no—
99#121—2741no—
100#121—1372no—
101C4×D4—2741no—
102C4×D4—1372no—
103C2×C4⋊C4—2741no—
104C2×C42—2741no—
105C2×C42—1371no—
106C4⋊C8—2741no—
107C22⋊C8—1372no—
108C4×C8—2741no—
109#95—1372no—
110#41—5482no—
111#41—5482no—
112C2×Q8—21no—
113C2×D4—2742no—
114C2×D4—2741no—
115C2×D4—2741no—
116C2×D4—1372no—
117C22×C4—2742no—
118C22×C4—2742no—
119C22×C4—1371no—
120C22×C4—1371no—
121C22×C4—1371no—
122C2×C8—2742no—
123C4⋊C4—21no—
124C4⋊C4—2744no—
125C4⋊C4C2×#1058773912yes—
126C22⋊C4—2742no—
127C22⋊C4—2742no—
128C42—5482no—
129C42—1371no—
130C42—1371no—
131C42—1371no—
132C42C2×#1058773911yescharacteristic
133C23—2742no—
134C23—1371no—
135Q8—42no—
136D4—5482no—
137D4—5482no—
138D4—5482no—
139D4—5482no—
140D4—5482no—
141C2×C4—22no—
142C2×C4—2742no—
143C2×C4—2744no—
144C2×C4—5481no—
145C2×C4—5484no—
146C2×C4—5482no—
147C2×C4—5482no—
148C2×C4—1371no—
149C2×C4—1371no—
150C2×C4—1371no—
151C2×C4—1372no—
152C2×C4—1372no—
153C2×C4C22⋊#1058773911yescharacteristic
154C2×C4C22⋊#1058773911yescharacteristic
155C2×C4C22×#1058773911yescharacteristic
156C8—5482no—
157C22—2741no—
158C22—2741no—
159C22—5482no—
160C22—5482no—
161C22—5482no—
162C22—1371no—
163C22—1371no—
164C22C2×C22⋊#1058773911yescharacteristic
165C4—21no—
166C4—42no—
167C4—2741no—
168C4—2741no—
169C4—5484no—
170C4—1372no—
171C4#1798415012yes—
172C4#1798415312yes—
173C2—2741no—
174C2—2741no—
175C2—10962no—
176C2#2257838411yescharacteristic
177C2C2×#1798415011yescharacteristic
178C2C2×#1798415311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10587739
commutatorC2×C4×C137C22×C4
FrattiniC2×C4C22×#10587739
FittingC4⋊Q8×C137C4
socleC22×C137C2×C22⋊C4
prime radical#22577954C2
cosocleC2×C4×D137C23
hypercenterC4⋊Q8#10587739
hypocenterC137#1502
LCSG ▷ C2×C4×C137 ▷ C22×C137 ▷ C137
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #22578422C2semidirect
2. C4×C4⋊#10587739C2semidirect
3. #22578255C2semidirect
12. #17984085C4semidirect
17. #17984050C4semidirect
19. C4⋊Q8×C137C4semidirect
89. C137#1502semidirect
96. C4⋊Q8#10587739semidirect

Maximal subgroups

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

subgroupindex
#225784222
C4×C4⋊#105877392
#225782552
#225779542
#1502137