Finite Group Databasebeta

← C2×#22625071 #34014356

Subgroups — C2×#22625071 #34014356

Order 18688.

390 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 64 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×#17989492C212yesmaximal
2#22625071C214yesmaximal, direct product factor
3C2×#17988953C211yesmaximal, characteristic
4C2×#14556650—22no—
5#17989492—22no—
6#17989492C2214yes—
7C2×#14556588C2211yescharacteristic
8#17988953—22no—
9#17988953C412yescomplemented
10#17988953C2212yes—
11C2×#14556511—22no—
12C2×#14556502C411yescharacteristic, complemented
13C2×#125×C73C411yescharacteristic, complemented
14C2×C22⋊#64408—42no—
15#14556650—24no—
16#14556650—42no—
17C22×D292—41no—
18C22×D292D412yes—
19C22×#10596831—21no—
20#14556588—41no—
21#14556588C2×C411yescharacteristic
22#14556588D412yes—
23#14556588C2311yescharacteristic
24#14556511—24no—
25#14556511—24no—
26#14556502—21no—
27#14556502C2×C412yescomplemented
28#125×C73—21no—
29#125×C73—41no—
30#125×C73C2×C412yescomplemented
31C2×C4⋊C4×C73—21no—
32C2×C4⋊C4×C73—41no—
33C2×C42×C73C2×C411yescharacteristic
34C22×#64408—82no—
35C22⋊#64408—44no—
36C22⋊#64408—82no—
37C23×D73—22no—
38C2×D292—22no—
39C2×D292—42no—
40C2×D292—42no—
41C2×D292—41no—
42C2×D292—42no—
43C2×D292—41no—
44C2×D292—84no—
45C2×D292C22⋊C412yes—
46C2×D292C2×D412yes—
47C2×#10596831—22no—
48C2×#10596831—41no—
49C2×#10596831—41no—
50C22×C4×C73—21no—
51C22×C4×C73—41no—
52C22×C4×C73C22⋊C411yescharacteristic
53C4⋊C4×C73—22no—
54C4⋊C4×C73—42no—
55C4⋊C4×C73—42no—
56C4⋊C4×C73—41no—
57C42×C73—21no—
58C42×C73C22⋊C411yescharacteristic
59C42×C73C22×C411yescharacteristic
60C23×C73#9911yescharacteristic
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—42no—
64C22×D73—42no—
65C22×D73—84no—
66C2×#64408—84no—
67C2×#64408—164no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—42no—
73C2×C4×C73—42no—
74C2×C4×C73—82no—
75C2×C4×C73#9911yescharacteristic
76C2×C4×C73C2×C22⋊C411yescharacteristic
77D292—42no—
78D292—42no—
79D292—82no—
80D292—82no—
81D292—84no—
82D292—82no—
83#10596831—42no—
84C22×C73—22no—
85C22×C73#35411yescharacteristic
86C22×C73#35411yescharacteristic
87C22×C73C2×#9911yescharacteristic
88C2×D73—42no—
89C2×D73—42no—
90C2×D73—84no—
91C2×D73—82no—
92C2×D73—82no—
93C2×D73—162no—
94#64408—164no—
95C4×C73—21no—
96C4×C73—21no—
97C4×C73—41no—
98C4×C73—41no—
99C4×C73—82no—
100C2×#1412—731nomaximal, Sylow
101C2×C73—21no—
102C2×C73—21no—
103C2×C73#141212yescomplemented
104C2×C73C2×#35411yescharacteristic
105D73—82no—
106D73—82no—
107C2×#490—731no—
108C2×#353—732no—
109#1412—734no—
110C73C2×#141211yescharacteristic, complemented, Sylow
111C2×#127—731no—
112C2×#125#6440811yescharacteristic, complemented
113#490—732no—
114#490—732no—
115#490—1462no—
116C2×#102—1462no—
117C2×#99—1462no—
118C2×#97—731no—
119#353—734no—
120#353—1462no—
121C22×D4—2921no—
122C22×D4—732no—
123C22×C8—1461no—
124#127—2921no—
125#127—732no—
126#127—731no—
127#127—731no—
128#125—21no—
129#125—41no—
130#125C2×#6440812yescomplemented
131C2×C4⋊C4—21no—
132C2×C4⋊C4—41no—
133C2×C22⋊C4—2922no—
134C2×C42C2×#6440811yescharacteristic
135#102—1464no—
136#102—1464no—
137#99—2922no—
138#99—1464no—
139#97—732no—
140#97—1461no—
141C24—1462no—
142C2×D4—2922no—
143C2×D4—2922no—
144C2×D4—2922no—
145C2×D4—2921no—
146C2×D4—2921no—
147C2×D4—5844no—
148C2×D4—732no—
149C2×D4—732no—
150C2×D4—1462no—
151C22×C4—21no—
152C22×C4—41no—
153C22×C4—5842no—
154C22×C4C22⋊#6440811yescharacteristic
155C2×C8—2921no—
156C2×C8—2921no—
157C2×C8—1462no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—41no—
162C22⋊C4—2924no—
163C22⋊C4—5842no—
164C42—21no—
165C42C22⋊#6440811yescharacteristic
166C42C22×#6440811yescharacteristic
167C23—2922no—
168C23—2922no—
169C23—5844no—
170C23—1462no—
171C23—1462no—
172C23#1455664911yescharacteristic
173D4—2922no—
174D4—2922no—
175D4—5842no—
176D4—5844no—
177D4—5842no—
178D4—5842no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—5844no—
187C2×C4—11684no—
188C2×C4#1455664911yescharacteristic
189C2×C4C2×C22⋊#6440811yescharacteristic
190C8—2922no—
191C22—22no—
192C22—2922no—
193C22—2922no—
194C22—5842no—
195C22—5842no—
196C22—5844no—
197C22—11682no—
198C22#1798949311yescharacteristic
199C22#1798949311yescharacteristic
200C22C2×#1455664911yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—82no—
206C4—11684no—
207C2—21no—
208C2—21no—
209C2—5842no—
210C2—5842no—
211C2#2262507112yesdirect product factor
212C2C2×#1798949311yescharacteristic
subgroupG/H
centerC22#17989493
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
FittingC2×#125×C73C4
socleC22×C73#354
prime radicalC2×#14556588C22
cosocle#14556588C23
hypercenterC2×#125#64408
hypocenterC73C2×#1412
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #22625071C2direct (N × H)
9. #17988953C4semidirect
12. C2×#14556502C4semidirect
13. C2×#125×C73C4semidirect
27. #14556502C2×C4semidirect
30. #125×C73C2×C4semidirect
103. C2×C73#1412semidirect
110. C73C2×#1412semidirect
112. C2×#125#64408semidirect
130. #125C2×#64408semidirect
211. C2#22625071direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179894922
#226250712
C2×#179889532
C2×#141273