Finite Group Databasebeta

← C2×#21460952 #30608347

Subgroups — C2×#21460952 #30608347

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#21460952C214yesmaximal, direct product factor
3C2×#16840136C211yesmaximal, characteristic
4C2×#14519836—22no—
5#16840667—22no—
6#16840667C2214yes—
7C22×#11758201—22no—
8C2×#14519774C2211yescharacteristic
9#16840136—22no—
10#16840136C412yescomplemented
11#16840136C2212yes—
12C2×C4×#92418C411yescharacteristic, complemented
13C2×C4⋊Q8×C61C411yescharacteristic, complemented
14C2×C22⋊#6923—42no—
15#14519836—24no—
16#14519836—42no—
17C22×D244—41no—
18C22×D244D412yes—
19C2×#11758201—24no—
20C2×#11758201—24no—
21C2×#11758201—44no—
22C2×#11758201—44no—
23C22×#92418—21no—
24#14519774—41no—
25#14519774C2×C411yescharacteristic
26#14519774D412yes—
27#14519774C2311yescharacteristic
28C4×#92418—21no—
29C4×#92418C2×C412yescomplemented
30C22×Q8×C61—21no—
31C4⋊Q8×C61—21no—
32C4⋊Q8×C61—41no—
33C4⋊Q8×C61C2×C412yescomplemented
34C2×C4⋊C4×C61—41no—
35C2×C42×C61C2×C411yescharacteristic
36C23×D61—22no—
37C22×#6923—82no—
38C2×Q8×C61—22no—
39C2×Q8×C61—42no—
40C2×Q8×C61—42no—
41C2×Q8×C61—41no—
42C22×C4×C61—21no—
43C22×C4×C61—41no—
44C22×C4×C61C22⋊C411yescharacteristic
45C2×D244—22no—
46C2×D244—42no—
47C2×D244—42no—
48C2×D244—41no—
49C2×D244—42no—
50C2×D244—41no—
51C2×D244—84no—
52C2×D244C22⋊C412yes—
53C2×D244C2×D412yes—
54C22⋊#6923—44no—
55C22⋊#6923—82no—
56C4⋊C4×C61—42no—
57C4⋊C4×C61—42no—
58C42×C61—21no—
59C42×C61C22⋊C411yescharacteristic
60C42×C61C22×C411yescharacteristic
61#11758201—48no—
62#11758201—48no—
63C2×#92418—22no—
64C2×#92418—22no—
65C2×#92418—22no—
66C23×C61#9911yescharacteristic
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—42no—
70C22×D61—42no—
71C22×D61—84no—
72C2×#6923—84no—
73C2×#6923—164no—
74Q8×C61—44no—
75Q8×C61—82no—
76C2×C4×C61—24no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—42no—
82C2×C4×C61—81no—
83C2×C4×C61—81no—
84C2×C4×C61#9911yescharacteristic
85C2×C4×C61C2×C22⋊C411yescharacteristic
86D244—42no—
87D244—42no—
88D244—82no—
89D244—82no—
90D244—84no—
91D244—82no—
92#92418—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—
109C4×C61—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#692311yescharacteristic, complemented
121C2×#127—611no—
122#492—612no—
123#492—612no—
124#492—1222no—
125C2×#99—1222no—
126C2×C4×C8—611no—
127#353—614no—
128#353—1222no—
129C61C2×#140911yescharacteristic, complemented, Sylow
130C22×Q8—21no—
131C22×D4—612no—
132C22×D4—2441no—
133C2×SD16—1224no—
134C2×SD16—1224no—
135C2×SD16—2444no—
136C2×SD16—2444no—
137C22×C8—1221no—
138C4⋊Q8—21no—
139C4⋊Q8—41no—
140C4⋊Q8C2×#692312yescomplemented
141#127—612no—
142#127—611no—
143#127—611no—
144#127—2441no—
145C2×C4⋊C4—41no—
146C2×C22⋊C4—2442no—
147C2×C42C2×#692311yescharacteristic
148#99—1224no—
149#99—2442no—
150C4×C8—612no—
151C4×C8—1221no—
152C24—1222no—
153C2×Q8—22no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8—41no—
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—41no—
168C22×C4—4882no—
169C22×C4C22⋊#692311yescharacteristic
170SD16—2448no—
171SD16—2448no—
172C2×C8—1222no—
173C2×C8—1222no—
174C2×C8—1222no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C22⋊C4—4882no—
178C22⋊C4—2444no—
179C42—21no—
180C42C22⋊#692311yescharacteristic
181C42C22×#692311yescharacteristic
182C23—1222no—
183C23—1222no—
184C23—4884no—
185C23—2442no—
186C23—2442no—
187C23#1451983511yescharacteristic
188Q8—44no—
189Q8—82no—
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—42no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—9764no—
205C2×C4—4884no—
206C2×C4#1451983511yescharacteristic
207C2×C4C2×C22⋊#692311yescharacteristic
208C8—1224no—
209C22—22no—
210C22—9762no—
211C22—4882no—
212C22—4882no—
213C22—4884no—
214C22—2442no—
215C22—2442no—
216C22#1684066611yescharacteristic
217C22#1684066611yescharacteristic
218C22C2×#1451983511yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—9764no—
225C2—21no—
226C2—21no—
227C2—4882no—
228C2—4882no—
229C2#2146095212yesdirect product factor
230C2C2×#1684066611yescharacteristic
subgroupG/H
centerC22#16840666
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61#353
prime radicalC2×#14519774C22
cosocle#14519774C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61C2×#1409
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #21460952C2direct (N × H)
10. #16840136C4semidirect
12. C2×C4×#92418C4semidirect
13. C2×C4⋊Q8×C61C4semidirect
29. C4×#92418C2×C4semidirect
33. C4⋊Q8×C61C2×C4semidirect
115. C2×C61#1409semidirect
120. C2×C4⋊Q8#6923semidirect
129. C61C2×#1409semidirect
140. C4⋊Q8C2×#6923semidirect
229. C2#21460952direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406672
#214609522
C2×#168401362
C2×#140961