Finite Group Databasebeta

← C2×#21460960 #30608387

Subgroups — C2×#21460960 #30608387

Order 15616.

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×#16840667C212yesmaximal
2#21460960C214yesmaximal, direct product factor
3C2×#16840127C211yesmaximal, characteristic
4C2×#14519836—22no—
5#16840667—22no—
6#16840667C2214yes—
7C2×#14519774C2211yescharacteristic
8C2×#14519769C411yescharacteristic, complemented
9#16840127—22no—
10#16840127C412yescomplemented
11#16840127C2212yes—
12C2×#14519699—22no—
13C2×#97×C61C411yescharacteristic, complemented
14C2×C22⋊#6923—42no—
15#14519836—24no—
16#14519836—42no—
17C22×D244—41no—
18C22×D244D412yes—
19#14519774—41no—
20#14519774C2×C411yescharacteristic
21#14519774D412yes—
22#14519774C2311yescharacteristic
23#14519769—21no—
24#14519769—41no—
25#14519769C2×C412yescomplemented
26C2×C4⋊Dic61—21no—
27C2×#11758196—41no—
28#14519699—24no—
29#14519699—24no—
30C22×C8×C61—21no—
31C2×C42×C61C2×C411yescharacteristic
32#97×C61—21no—
33#97×C61C2×C412yescomplemented
34C23×D61—22no—
35C22×#6923—82no—
36C22×C4×C61—21no—
37C22×C4×C61C22⋊C411yescharacteristic
38C22×Dic61—41no—
39C2×D244—22no—
40C2×D244—42no—
41C2×D244—42no—
42C2×D244—41no—
43C2×D244—42no—
44C2×D244—41no—
45C2×D244—84no—
46C2×D244C22⋊C412yes—
47C2×D244C2×D412yes—
48C22⋊#6923—44no—
49C22⋊#6923—82no—
50C2×C8×C61—22no—
51C2×C8×C61—41no—
52C2×C8×C61—41no—
53C42×C61—21no—
54C42×C61C22⋊C411yescharacteristic
55C42×C61C22×C411yescharacteristic
56C4⋊Dic61—22no—
57C4⋊Dic61—41no—
58#11758196—42no—
59#11758196—42no—
60C23×C61#9911yescharacteristic
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—42no—
64C22×D61—42no—
65C22×D61—84no—
66C2×#6923—84no—
67C2×#6923—164no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—42no—
73C2×C4×C61#9911yescharacteristic
74C2×C4×C61C2×C22⋊C411yescharacteristic
75C2×Dic61—42no—
76C2×Dic61—82no—
77D244—42no—
78D244—42no—
79D244—82no—
80D244—82no—
81D244—84no—
82D244—82no—
83C8×C61—42no—
84C2×#1412—611nomaximal, Sylow
85C22×C61—22no—
86C22×C61#35411yescharacteristic
87C22×C61#35411yescharacteristic
88C22×C61C2×#9911yescharacteristic
89C2×D61—42no—
90C2×D61—42no—
91C2×D61—84no—
92C2×D61—82no—
93C2×D61—82no—
94C2×D61—162no—
95#6923—164no—
96C4×C61—21no—
97C4×C61—21no—
98C4×C61—41no—
99C4×C61—41no—
100Dic61—82no—
101C2×#490—611no—
102C2×#353—612no—
103#1412—614no—
104C2×C61—21no—
105C2×C61—21no—
106C2×C61#141212yescomplemented
107C2×C61C2×#35411yescharacteristic
108D61—82no—
109D61—82no—
110C2×#127—611no—
111C2×#125—611no—
112#490—612no—
113#490—612no—
114#490—1222no—
115C2×#102—1222no—
116C2×#99—1222no—
117C2×#97#692311yescharacteristic, complemented
118#353—614no—
119#353—1222no—
120C61C2×#141211yescharacteristic, complemented, Sylow
121C22×D4—612no—
122C22×D4—2441no—
123C22×C8—21no—
124#127—612no—
125#127—611no—
126#127—611no—
127#127—2441no—
128#125—612no—
129#125—1221no—
130#125—2441no—
131C2×C4⋊C4—1221no—
132C2×C4⋊C4—2441no—
133C2×C22⋊C4—2442no—
134C2×C42C2×#692311yescharacteristic
135#102—1224no—
136#102—1224no—
137#99—1224no—
138#99—2442no—
139#97—21no—
140#97C2×#692312yescomplemented
141C24—1222no—
142C2×D4—612no—
143C2×D4—612no—
144C2×D4—1222no—
145C2×D4—4884no—
146C2×D4—2442no—
147C2×D4—2441no—
148C2×D4—2441no—
149C2×D4—2442no—
150C2×D4—2442no—
151C22×C4—21no—
152C22×C4—4882no—
153C22×C4—2441no—
154C22×C4C22⋊#692311yescharacteristic
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—41no—
158C4⋊C4—1222no—
159C4⋊C4—2442no—
160C4⋊C4—2442no—
161C4⋊C4—2441no—
162C22⋊C4—4882no—
163C22⋊C4—2444no—
164C42—21no—
165C42C22⋊#692311yescharacteristic
166C42C22×#692311yescharacteristic
167C23—1222no—
168C23—1222no—
169C23—4884no—
170C23—2442no—
171C23—2442no—
172C23#1451983611yescharacteristic
173D4—4882no—
174D4—4884no—
175D4—4882no—
176D4—4882no—
177D4—2442no—
178D4—2442no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—9764no—
185C2×C4—4884no—
186C2×C4—4882no—
187C2×C4—2442no—
188C2×C4#1451983611yescharacteristic
189C2×C4C2×C22⋊#692311yescharacteristic
190C8—42no—
191C22—22no—
192C22—9762no—
193C22—4882no—
194C22—4882no—
195C22—4884no—
196C22—2442no—
197C22—2442no—
198C22#1684066911yescharacteristic
199C22#1684066911yescharacteristic
200C22C2×#1451983611yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—9764no—
206C4—4882no—
207C2—21no—
208C2—21no—
209C2—4882no—
210C2—4882no—
211C2#2146096012yesdirect product factor
212C2C2×#1684066911yescharacteristic
subgroupG/H
centerC22#16840669
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×#97×C61C4
socleC22×C61#354
prime radicalC2×#14519774C22
cosocle#14519774C23
hypercenterC2×#97#6923
hypocenterC61C2×#1412
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #21460960C2direct (N × H)
8. C2×#14519769C4semidirect
10. #16840127C4semidirect
13. C2×#97×C61C4semidirect
25. #14519769C2×C4semidirect
33. #97×C61C2×C4semidirect
106. C2×C61#1412semidirect
117. C2×#97#6923semidirect
120. C61C2×#1412semidirect
140. #97C2×#6923semidirect
211. C2#21460960direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406672
#214609602
C2×#168401272
C2×#141261