Finite Group Databasebeta

← C4×#17984146 #31796533

Subgroups — C4×#17984146 #31796533

Order 17536.

412 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 96 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×#17984146C212yesmaximal
2C4×C22⋊#10587739C212yesmaximal, complemented
3#22578281C212yesmaximal, complemented
4C2×C4×C22⋊D137C211yesmaximal, characteristic
5C2×C22⋊#10587739C2214yes—
6C2×C4×#10587739—22no—
7#17984146C418yesdirect product factor
8(C2×#10587739)⋊C4—22no—
9C22×C22⋊D137C2211yescharacteristic
10C22×C4×D137C2211yescharacteristic
11C4×C22⋊D137—22no—
12C4×C22⋊D137—22no—
13C2×#14555489C411yescharacteristic, complemented
14C2×C22⋊Dic137C411yescharacteristic, complemented
15C2×#14555487C2211yescharacteristic
16C2×C4×Dic137C411yescharacteristic, complemented
17C23×C4×C137C411yescharacteristic, complemented
18C22×#10587739—24no—
19C22⋊#10587739—24no—
20C22⋊#10587739C2×C418yescomplemented
21C4×#10587739—44no—
22C23×D137C2311yescharacteristic
23C2×C22⋊D137—22no—
24C2×C22⋊D137—22no—
25C2×C22⋊D137C2×C414yes—
26C22×Dic137C2×C411yescharacteristic
27C22×Dic137C2×C411yescharacteristic
28C22×Dic137C2×C411yescharacteristic
29C2×C4×D137—42no—
30C2×C4×D137D412yes—
31C2×C4×D137D412yes—
32#14555489—22no—
33C22⋊Dic137—22no—
34#14555487—22no—
35C4×Dic137—21no—
36C4×Dic137—21no—
37C24×C137C2×C411yescharacteristic
38C22×C4×C137—21no—
39C22×C4×C137—21no—
40C22×C4×C137—42no—
41C22×C4×C137C2×C411yescharacteristic
42C22×C4×C137C2×C411yescharacteristic
43C2×#10587739—28no—
44C2×#10587739—44no—
45C2×#10587739—44no—
46C22×D137—41no—
47C22×D137—41no—
48C22×D137C22×C412yes—
49C22×D137C2×D412yes—
50C22×D137#4112yes—
51C22⋊D137—28no—
52C2×Dic137—21no—
53C2×Dic137—21no—
54C2×Dic137—21no—
55C2×Dic137—41no—
56C2×Dic137—41no—
57C2×Dic137C4212yescomplemented
58C2×Dic137C22⋊C412yes—
59C4×D137—24no—
60C4×D137—42no—
61C23×C137—21no—
62C23×C137—21no—
63C23×C137—41no—
64C23×C137—41no—
65C23×C137C4212yescomplemented
66C23×C137C22×C411yescharacteristic
67C2×C4×C137—22no—
68C2×C4×C137—21no—
69C2×C4×C137—42no—
70C2×C4×C137—42no—
71C2×C4×C137—41no—
72C2×C4×C137C22⋊C411yescharacteristic
73C2×C4×C137C22⋊C411yescharacteristic
74C22×C137—21no—
75C22×C137—21no—
76C22×C137—22no—
77C22×C137—42no—
78C22×C137—42no—
79C22×C137—41no—
80C22×C137—41no—
81C22×C137C2×C4211yescharacteristic
82C22×C137C2×C22⋊C411yescharacteristic
83C22×C137#11711yescharacteristic
84C2×D137—22no—
85C2×D137—22no—
86C2×D137—42no—
87C2×D137—42no—
88C2×D137C4×D414yes—
89#10587739—48no—
90C4×C137—21no—
91C4×C137—41no—
92C4×C137#9912yescomplemented
93Dic137—22no—
94Dic137—22no—
95Dic137—41no—
96C2×C137—21no—
97C2×C137—21no—
98C2×C137—42no—
99C2×C137C4×C22⋊C411yescharacteristic
100C2×C137C2×#9911yescharacteristic
101C2×C137#41011yescharacteristic
102D137—24no—
103C137C4×#9911yescharacteristic, complemented, Sylow
104C4×#99—1371nomaximal, Sylow
105C2×C4×D4—1371no—
106C2×#99—1372no—
107C4×C22⋊C4—1372no—
108#342—1372no—
109C22×D4—1371no—
110C23×C4—1371no—
111C23×C4#1058773911yescharacteristic, complemented
112C4×D4—2742no—
113C4×D4—2742no—
114C2×C4⋊C4—1371no—
115C2×C22⋊C4—1371no—
116C2×C22⋊C4—1371no—
117C2×C22⋊C4—1374no—
118C2×C42—2742no—
119C2×C42—1371no—
120#99—1378no—
121#95—2742no—
122C24—1371no—
123C24C2×#1058773911yescharacteristic
124C2×D4—2742no—
125C2×D4—2742no—
126C2×D4—1374no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—42no—
130C22×C4—2744no—
131C22×C4—5482no—
132C22×C4—1371no—
133C22×C4—1372no—
134C22×C4—1371no—
135C22×C4—1371no—
136C22×C4—1372no—
137C22×C4C2×#1058773911yescharacteristic
138C22×C4C2×#1058773911yescharacteristic
139C4⋊C4—2742no—
140C22⋊C4—2742no—
141C22⋊C4—2744no—
142C22⋊C4—2742no—
143C22⋊C4—1378no—
144C42—2741no—
145C42—2741no—
146C42—5484no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—5481no—
152C23—5481no—
153C23—1372no—
154C23—1372no—
155C23—1372no—
156C23C4×#1058773912yescomplemented
157C23C22×#1058773911yescharacteristic
158D4—2748no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—41no—
164C2×C4—2741no—
165C2×C4—2741no—
166C2×C4—2744no—
167C2×C4—2748no—
168C2×C4—2741no—
169C2×C4—5482no—
170C2×C4—5481no—
171C2×C4—5484no—
172C2×C4—5484no—
173C2×C4—5481no—
174C2×C4—1372no—
175C2×C4—1372no—
176C2×C4C22⋊#1058773911yescharacteristic
177C2×C4C22⋊#1058773911yescharacteristic
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—2742no—
186C22—2742no—
187C22—5482no—
188C22—5482no—
189C22—1374no—
190C22C2×C4×#1058773911yescharacteristic
191C22C2×C22⋊#1058773911yescharacteristic
192C22#1798416711yescharacteristic
193C4—21no—
194C4—41no—
195C4—2742no—
196C4—2742no—
197C4—5488no—
198C4—5481no—
199C4#1798414612yesdirect product factor
200C2—21no—
201C2—21no—
202C2—42no—
203C2—2744no—
204C2C4×C22⋊#1058773911yescharacteristic
205C2C2×#1798414611yescharacteristic
206C2#2257838211yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10587739
commutatorC22×C137C2×C42
FrattiniC23C22×#10587739
FittingC23×C4×C137C4
socleC22×C137C2×C22⋊C4
prime radicalC22×C22⋊D137C22
cosocleC23×D137C23
hypercenterC23×C4#10587739
hypocenterC137C4×#99
LCSG ▷ C22×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#10587739C2semidirect
3. #22578281C2semidirect
7. #17984146C4direct (N × H)
13. C2×#14555489C4semidirect
14. C2×C22⋊Dic137C4semidirect
16. C2×C4×Dic137C4semidirect
17. C23×C4×C137C4semidirect
20. C22⋊#10587739C2×C4semidirect
57. C2×Dic137C42semidirect
65. C23×C137C42semidirect
92. C4×C137#99semidirect
103. C137C4×#99semidirect
111. C23×C4#10587739semidirect
156. C23C4×#10587739semidirect
199. C4#17984146direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179841462
C4×C22⋊#105877392
#225782812
C2×C4×C22⋊D1372
C4×#99137