Finite Group Databasebeta

← C2×#21460953 #30608349

Subgroups — C2×#21460953 #30608349

Order 15616.

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

normal subgroups only

This group has 474 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#21460953C214yesmaximal, direct product factor
3C2×#16840135C211yesmaximal, characteristic
4C2×#14519836—22no—
5#16840667—22no—
6#16840667C2214yes—
7C22×#11758190—22no—
8C2×#14519777C411yescharacteristic, complemented
9C2×#14519774C2211yescharacteristic
10#16840135—22no—
11#16840135C412yescomplemented
12#16840135C2212yes—
13C2×C4×C8×C61C411yescharacteristic, complemented
14C2×C22⋊#6923—42no—
15#14519836—24no—
16#14519836—42no—
17C22×Dic122—21no—
18C22×D244—41no—
19C22×D244D412yes—
20C2×#11758190—24no—
21C2×#11758190—24no—
22C2×#11758190—44no—
23C2×#11758190—44no—
24#14519777—21no—
25#14519777—41no—
26#14519777C2×C412yescomplemented
27#14519774—41no—
28#14519774C2×C411yescharacteristic
29#14519774D412yes—
30#14519774C2311yescharacteristic
31C2×C4⋊Dic61—41no—
32C22×C8×C61—21no—
33C2×C42×C61C2×C411yescharacteristic
34C4×C8×C61—21no—
35C4×C8×C61C2×C412yescomplemented
36C23×D61—22no—
37C22×#6923—82no—
38C22×C4×C61—21no—
39C22×C4×C61C22⋊C411yescharacteristic
40C22×Dic61—41no—
41C2×D244—22no—
42C2×D244—42no—
43C2×D244—42no—
44C2×D244—41no—
45C2×D244—42no—
46C2×D244—41no—
47C2×D244—84no—
48C2×D244C22⋊C412yes—
49C2×D244C2×D412yes—
50C2×Dic122—22no—
51C2×Dic122—42no—
52C2×Dic122—42no—
53C2×Dic122—41no—
54C22⋊#6923—44no—
55C22⋊#6923—82no—
56C2×C8×C61—22no—
57C2×C8×C61—22no—
58C2×C8×C61—22no—
59C42×C61—21no—
60C42×C61C22⋊C411yescharacteristic
61C42×C61C22×C411yescharacteristic
62C4⋊Dic61—42no—
63C4⋊Dic61—42no—
64#11758190—48no—
65#11758190—48no—
66C23×C61#9911yescharacteristic
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—42no—
70C22×D61—42no—
71C22×D61—84no—
72C2×#6923—84no—
73C2×#6923—164no—
74C2×C4×C61—24no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61#9911yescharacteristic
80C2×C4×C61C2×C22⋊C411yescharacteristic
81C2×Dic61—42no—
82C2×Dic61—81no—
83C2×Dic61—81no—
84D244—42no—
85D244—42no—
86D244—82no—
87D244—82no—
88D244—84no—
89D244—82no—
90Dic122—44no—
91Dic122—82no—
92C8×C61—24no—
93C2×#1409—611nomaximal, Sylow
94C22×C61—22no—
95C22×C61#35311yescharacteristic
96C22×C61#35311yescharacteristic
97C22×C61C2×#9911yescharacteristic
98C2×D61—42no—
99C2×D61—42no—
100C2×D61—84no—
101C2×D61—82no—
102C2×D61—82no—
103C2×D61—162no—
104#6923—164no—
105C4×C61—22no—
106C4×C61—22no—
107C4×C61—21no—
108C4×C61—21no—
109Dic61—82no—
110C2×#492—611no—
111C2×#353—612no—
112#1409—614no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#140912yescomplemented
116C2×C61C2×#35311yescharacteristic
117D61—82no—
118D61—82no—
119C22×SD16—1222no—
120C2×C4⋊Q8—611no—
121C2×#127—611no—
122#492—612no—
123#492—612no—
124#492—1222no—
125C2×#99—1222no—
126C2×C4×C8#692311yescharacteristic, complemented
127#353—614no—
128#353—1222no—
129C61C2×#140911yescharacteristic, complemented, Sylow
130C22×Q8—1221no—
131C22×D4—612no—
132C22×D4—2441no—
133C2×SD16—1224no—
134C2×SD16—1224no—
135C2×SD16—2444no—
136C2×SD16—2444no—
137C22×C8—21no—
138C4⋊Q8—612no—
139C4⋊Q8—1221no—
140C4⋊Q8—2441no—
141#127—612no—
142#127—611no—
143#127—611no—
144#127—2441no—
145C2×C4⋊C4—2441no—
146C2×C22⋊C4—2442no—
147C2×C42C2×#692311yescharacteristic
148#99—1224no—
149#99—2442no—
150C4×C8—21no—
151C4×C8C2×#692312yescomplemented
152C24—1222no—
153C2×Q8—1222no—
154C2×Q8—2442no—
155C2×Q8—2442no—
156C2×Q8—2441no—
157C2×D4—612no—
158C2×D4—612no—
159C2×D4—1222no—
160C2×D4—4884no—
161C2×D4—2442no—
162C2×D4—2441no—
163C2×D4—2441no—
164C2×D4—2442no—
165C2×D4—2442no—
166C22×C4—21no—
167C22×C4—4882no—
168C22×C4—2441no—
169C22×C4C22⋊#692311yescharacteristic
170SD16—2448no—
171SD16—2448no—
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—22no—
175C4⋊C4—2442no—
176C4⋊C4—2442no—
177C22⋊C4—4882no—
178C22⋊C4—2444no—
179C42—21no—
180C42C22⋊#692311yescharacteristic
181C42C22×#692311yescharacteristic
182C23—1222no—
183C23—1222no—
184C23—4884no—
185C23—2442no—
186C23—2442no—
187C23#1451983611yescharacteristic
188Q8—4882no—
189Q8—2444no—
190D4—4884no—
191D4—4882no—
192D4—4882no—
193D4—4882no—
194D4—2442no—
195D4—2442no—
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—9764no—
202C2×C4—4884no—
203C2×C4—4881no—
204C2×C4—4881no—
205C2×C4—2442no—
206C2×C4#1451983611yescharacteristic
207C2×C4C2×C22⋊#692311yescharacteristic
208C8—24no—
209C22—22no—
210C22—9762no—
211C22—4882no—
212C22—4882no—
213C22—4884no—
214C22—2442no—
215C22—2442no—
216C22#1684066711yescharacteristic
217C22#1684066711yescharacteristic
218C22C2×#1451983611yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—9764no—
224C4—4882no—
225C2—21no—
226C2—21no—
227C2—4882no—
228C2—4882no—
229C2#2146095312yesdirect product factor
230C2C2×#1684066711yescharacteristic
subgroupG/H
centerC22#16840667
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×C4×C8×C61C4
socleC22×C61#353
prime radicalC2×#14519774C22
cosocle#14519774C23
hypercenterC2×C4×C8#6923
hypocenterC61C2×#1409
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #21460953C2direct (N × H)
8. C2×#14519777C4semidirect
11. #16840135C4semidirect
13. C2×C4×C8×C61C4semidirect
26. #14519777C2×C4semidirect
35. C4×C8×C61C2×C4semidirect
115. C2×C61#1409semidirect
126. C2×C4×C8#6923semidirect
129. C61C2×#1409semidirect
151. C4×C8C2×#6923semidirect
229. C2#21460953direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406672
#214609532
C2×#168401352
C2×#140961