Finite Group Databasebeta

← C4×#10587551 #14544528

Subgroups — C4×#10587551 #14544528

Order 2176.

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×#10587551C212yesmaximal
2C4×C22⋊#595C212yesmaximal, complemented
3#11763687C212yesmaximal, complemented
4C2×C4×C22⋊D17C211yesmaximal, characteristic
5C23×C4×C17C411yescharacteristic, complemented
6C22×C22⋊D17C2211yescharacteristic
7C22×C4×D17C2211yescharacteristic
8C2×C22⋊#595C2214yes—
9C2×C4×#595—22no—
10C2×C22⋊Dic17C411yescharacteristic, complemented
11C4×C22⋊D17—22no—
12C4×C22⋊D17—22no—
13C2×#63227C2211yescharacteristic
14C2×#63225C411yescharacteristic, complemented
15C2×C4×Dic17C411yescharacteristic, complemented
16#10587551C418yesdirect product factor
17(C2×#595)⋊C4—22no—
18C24×C17C2×C411yescharacteristic
19C23×D17C2311yescharacteristic
20C22×#595—24no—
21C22×C4×C17—21no—
22C22×C4×C17—21no—
23C22×C4×C17—42no—
24C22×C4×C17C2×C411yescharacteristic
25C22×C4×C17C2×C411yescharacteristic
26C2×C22⋊D17—22no—
27C2×C22⋊D17—22no—
28C2×C22⋊D17C2×C414yes—
29C22×Dic17C2×C411yescharacteristic
30C22×Dic17C2×C411yescharacteristic
31C22×Dic17C2×C411yescharacteristic
32C2×C4×D17—42no—
33C2×C4×D17D412yes—
34C2×C4×D17D412yes—
35C22⋊#595—24no—
36C22⋊#595C2×C418yescomplemented
37C4×#595—44no—
38C22⋊Dic17—22no—
39#63227—22no—
40#63225—22no—
41C4×Dic17—21no—
42C4×Dic17—21no—
43C23×C17—21no—
44C23×C17—21no—
45C23×C17—41no—
46C23×C17—41no—
47C23×C17C4212yescomplemented
48C23×C17C22×C411yescharacteristic
49C22×D17—41no—
50C22×D17—41no—
51C22×D17C22×C412yes—
52C22×D17C2×D412yes—
53C22×D17#4112yes—
54C2×#595—28no—
55C2×#595—44no—
56C2×#595—44no—
57C2×C4×C17—22no—
58C2×C4×C17—21no—
59C2×C4×C17—42no—
60C2×C4×C17—42no—
61C2×C4×C17—41no—
62C2×C4×C17C22⋊C411yescharacteristic
63C2×C4×C17C22⋊C411yescharacteristic
64C22⋊D17—28no—
65C2×Dic17—21no—
66C2×Dic17—21no—
67C2×Dic17—21no—
68C2×Dic17—41no—
69C2×Dic17—41no—
70C2×Dic17C4212yescomplemented
71C2×Dic17C22⋊C412yes—
72C4×D17—24no—
73C4×D17—42no—
74C4×#99—171nomaximal, Sylow
75C22×C17—21no—
76C22×C17—21no—
77C22×C17—22no—
78C22×C17—42no—
79C22×C17—42no—
80C22×C17—41no—
81C22×C17—41no—
82C22×C17C2×C4211yescharacteristic
83C22×C17C2×C22⋊C411yescharacteristic
84C22×C17#11711yescharacteristic
85C2×D17—22no—
86C2×D17—22no—
87C2×D17—42no—
88C2×D17—42no—
89C2×D17C4×D414yes—
90#595—48no—
91C4×C17—21no—
92C4×C17—41no—
93C4×C17#9912yescomplemented
94Dic17—22no—
95Dic17—22no—
96Dic17—41no—
97C2×C4×D4—171no—
98C2×#99—172no—
99C4×C22⋊C4—172no—
100#342—172no—
101C2×C17—21no—
102C2×C17—21no—
103C2×C17—42no—
104C2×C17C4×C22⋊C411yescharacteristic
105C2×C17C2×#9911yescharacteristic
106C2×C17#41011yescharacteristic
107D17—24no—
108C22×D4—171no—
109C23×C4—171no—
110C23×C4#59511yescharacteristic, complemented
111C4×D4—342no—
112C4×D4—342no—
113C2×C4⋊C4—171no—
114C2×C22⋊C4—174no—
115C2×C22⋊C4—171no—
116C2×C22⋊C4—171no—
117C2×C42—171no—
118C2×C42—342no—
119#99—178no—
120#95—342no—
121C17C4×#9911yescharacteristic, complemented, Sylow
122C24—171no—
123C24C2×#59511yescharacteristic
124C2×D4—174no—
125C2×D4—342no—
126C2×D4—342no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—42no—
130C22×C4—171no—
131C22×C4—171no—
132C22×C4—172no—
133C22×C4—172no—
134C22×C4—171no—
135C22×C4—344no—
136C22×C4—682no—
137C22×C4C2×#59511yescharacteristic
138C22×C4C2×#59511yescharacteristic
139C4⋊C4—342no—
140C22⋊C4—178no—
141C22⋊C4—342no—
142C22⋊C4—342no—
143C22⋊C4—344no—
144C42—341no—
145C42—341no—
146C42—684no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—172no—
152C23—172no—
153C23—172no—
154C23—681no—
155C23—681no—
156C23C4×#59512yescomplemented
157C23C22×#59511yescharacteristic
158D4—348no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—41no—
164C2×C4—172no—
165C2×C4—172no—
166C2×C4—341no—
167C2×C4—341no—
168C2×C4—344no—
169C2×C4—348no—
170C2×C4—341no—
171C2×C4—682no—
172C2×C4—681no—
173C2×C4—684no—
174C2×C4—684no—
175C2×C4—681no—
176C2×C4C22⋊#59511yescharacteristic
177C2×C4C22⋊#59511yescharacteristic
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—174no—
186C22—342no—
187C22—342no—
188C22—682no—
189C22—682no—
190C22C2×C4×#59511yescharacteristic
191C22#1058767711yescharacteristic
192C22C2×C22⋊#59511yescharacteristic
193C4—21no—
194C4—41no—
195C4—342no—
196C4—342no—
197C4—688no—
198C4—681no—
199C4#1058755112yesdirect product factor
200C2—21no—
201C2—21no—
202C2—42no—
203C2—344no—
204C2C4×C22⋊#59511yescharacteristic
205C2C2×#1058755111yescharacteristic
206C2#1176378811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#595
commutatorC22×C17C2×C42
FrattiniC23C22×#595
FittingC23×C4×C17C4
socleC22×C17C2×C22⋊C4
prime radicalC22×C22⋊D17C22
cosocleC23×D17C23
hypercenterC23×C4#595
hypocenterC17C4×#99
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#595C2semidirect
3. #11763687C2semidirect
5. C23×C4×C17C4semidirect
10. C2×C22⋊Dic17C4semidirect
14. C2×#63225C4semidirect
15. C2×C4×Dic17C4semidirect
16. #10587551C4direct (N × H)
36. C22⋊#595C2×C4semidirect
47. C23×C17C42semidirect
70. C2×Dic17C42semidirect
93. C4×C17#99semidirect
110. C23×C4#595semidirect
121. C17C4×#99semidirect
156. C23C4×#595semidirect
199. C4#10587551direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#105875512
C4×C22⋊#5952
#117636872
C2×C4×C22⋊D172
C4×#9917