Finite Group Databasebeta

← C2×#22558380 #30776176

Subgroups — C2×#22558380 #30776176

Order 17152.

390 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16863189C212yesmaximal
2#22558380C214yesmaximal, direct product factor
3C2×#490×C67C211yesmaximal, characteristic
4C2×#14523958—22no—
5#16863189—22no—
6#16863189C2214yes—
7C2×#127×C67C2211yescharacteristic
8C2×#125×C67C411yescharacteristic, complemented
9#490×C67—22no—
10#490×C67C412yescomplemented
11#490×C67C2212yes—
12C2×#102×C67—22no—
13C2×#97×C67C411yescharacteristic, complemented
14C2×C22⋊Dic67—42no—
15#14523958—24no—
16#14523958—42no—
17C22×D4×C67—41no—
18C22×D4×C67D412yes—
19C22×C8×C67—21no—
20#127×C67—41no—
21#127×C67C2×C411yescharacteristic
22#127×C67D412yes—
23#127×C67C2311yescharacteristic
24#125×C67—21no—
25#125×C67—41no—
26#125×C67C2×C412yescomplemented
27C2×C4⋊C4×C67—21no—
28C2×C4⋊C4×C67—41no—
29C2×C42×C67C2×C411yescharacteristic
30#102×C67—24no—
31#102×C67—24no—
32#97×C67—21no—
33#97×C67C2×C412yescomplemented
34C22×Dic67—82no—
35C22⋊Dic67—44no—
36C22⋊Dic67—82no—
37C24×C67—22no—
38C2×D4×C67—22no—
39C2×D4×C67—42no—
40C2×D4×C67—42no—
41C2×D4×C67—41no—
42C2×D4×C67—42no—
43C2×D4×C67—41no—
44C2×D4×C67—84no—
45C2×D4×C67C22⋊C412yes—
46C2×D4×C67C2×D412yes—
47C22×C4×C67—21no—
48C22×C4×C67—41no—
49C22×C4×C67C22⋊C411yescharacteristic
50C2×C8×C67—22no—
51C2×C8×C67—41no—
52C2×C8×C67—41no—
53C4⋊C4×C67—22no—
54C4⋊C4×C67—42no—
55C4⋊C4×C67—42no—
56C4⋊C4×C67—41no—
57C42×C67—21no—
58C42×C67C22⋊C411yescharacteristic
59C42×C67C22×C411yescharacteristic
60C23×C67—22no—
61C23×C67—22no—
62C23×C67—42no—
63C23×C67—42no—
64C23×C67—84no—
65C23×C67#9911yescharacteristic
66D4×C67—42no—
67D4×C67—42no—
68D4×C67—82no—
69D4×C67—82no—
70D4×C67—84no—
71D4×C67—82no—
72C2×C4×C67—21no—
73C2×C4×C67—21no—
74C2×C4×C67—21no—
75C2×C4×C67—21no—
76C2×C4×C67—42no—
77C2×C4×C67—42no—
78C2×C4×C67—82no—
79C2×C4×C67#9911yescharacteristic
80C2×C4×C67C2×C22⋊C411yescharacteristic
81C2×Dic67—84no—
82C2×Dic67—164no—
83C8×C67—42no—
84C22×C67—22no—
85C22×C67—42no—
86C22×C67—42no—
87C22×C67—82no—
88C22×C67—82no—
89C22×C67—84no—
90C22×C67—162no—
91C22×C67#35411yescharacteristic
92C22×C67#35411yescharacteristic
93C22×C67C2×#9911yescharacteristic
94C4×C67—21no—
95C4×C67—21no—
96C4×C67—41no—
97C4×C67—41no—
98C4×C67—82no—
99Dic67—164no—
100C2×#1412—671nomaximal, Sylow
101C2×C67—21no—
102C2×C67—21no—
103C2×C67—82no—
104C2×C67—82no—
105C2×C67#141212yescomplemented
106C2×C67C2×#35411yescharacteristic
107C2×#490D6711yescharacteristic
108C2×#353—672no—
109#1412—674no—
110C67C2×#141211yescharacteristic, complemented, Sylow
111C2×#127C2×D6711yescharacteristic
112C2×#125Dic6711yescharacteristic, complemented
113#490—22no—
114#490Dic6712yescomplemented
115#490C2×D6712yes—
116C2×#102—22no—
117C2×#99—1342no—
118C2×#97Dic6711yescharacteristic, complemented
119#353—674no—
120#353—1342no—
121C22×D4—41no—
122C22×D4C22⋊D6712yes—
123C22×C8—21no—
124#127—41no—
125#127C2×Dic6711yescharacteristic
126#127C22⋊D6712yes—
127#127C22×D6711yescharacteristic
128#125—21no—
129#125—41no—
130#125C2×Dic6712yescomplemented
131C2×C4⋊C4—21no—
132C2×C4⋊C4—41no—
133C2×C22⋊C4—2682no—
134C2×C42C2×Dic6711yescharacteristic
135#102—24no—
136#102—24no—
137#99—2682no—
138#99—1344no—
139#97—21no—
140#97C2×Dic6712yescomplemented
141C24—22no—
142C2×D4—22no—
143C2×D4—42no—
144C2×D4—42no—
145C2×D4—41no—
146C2×D4—42no—
147C2×D4—41no—
148C2×D4—84no—
149C2×D4C22⋊Dic6712yes—
150C2×D4C2×C22⋊D6712yes—
151C22×C4—21no—
152C22×C4—41no—
153C22×C4—5362no—
154C22×C4C22⋊Dic6711yescharacteristic
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—41no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—41no—
162C22⋊C4—2684no—
163C22⋊C4—5362no—
164C42—21no—
165C42C22⋊Dic6711yescharacteristic
166C42C22×Dic6711yescharacteristic
167C23—22no—
168C23—22no—
169C23—42no—
170C23—42no—
171C23—84no—
172C23#1452395811yescharacteristic
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178D4—82no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—5364no—
187C2×C4—10724no—
188C2×C4#1452395811yescharacteristic
189C2×C4C2×C22⋊Dic6711yescharacteristic
190C8—42no—
191C22—22no—
192C22—42no—
193C22—42no—
194C22—82no—
195C22—82no—
196C22—84no—
197C22—162no—
198C22#1686319111yescharacteristic
199C22#1686319111yescharacteristic
200C22C2×#1452395811yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—82no—
206C4—10724no—
207C2—21no—
208C2—21no—
209C2—82no—
210C2—82no—
211C2#2255838012yesdirect product factor
212C2C2×#1686319111yescharacteristic
subgroupG/H
centerC22#16863191
commutatorC42×C67C22×C4
Frattini#127C22×D67
FittingC2×#490×C67C2
socleC22×C67#354
prime radicalC2×#127×C67C22
cosocle#127×C67C23
hypercenterC2×#490D67
hypocenterC67C2×#1412
LCSG ▷ C42×C67 ▷ C2×C4×C67 ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#127 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
2. #22558380C2direct (N × H)
8. C2×#125×C67C4semidirect
10. #490×C67C4semidirect
13. C2×#97×C67C4semidirect
26. #125×C67C2×C4semidirect
33. #97×C67C2×C4semidirect
105. C2×C67#1412semidirect
110. C67C2×#1412semidirect
112. C2×#125Dic67semidirect
114. #490Dic67semidirect
118. C2×#97Dic67semidirect
130. #125C2×Dic67semidirect
140. #97C2×Dic67semidirect
211. C2#22558380direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168631892
#225583802
C2×#490×C672
C2×#141267