Finite Group Databasebeta

← C2×#21460951 #30608346

Subgroups — C2×#21460951 #30608346

Order 15616.

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

normal subgroups only

This group has 526 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, complemented
2#21460951C214yesmaximal, direct product factor
3C2×#16840139C211yesmaximal, characteristic
4C2×#14519836—22no—
5#16840667—22no—
6#16840667C2214yescomplemented
7C22×D488—22no—
8C2×#14519774C411yescharacteristic, complemented
9C2×#14519774C2211yescharacteristic
10#16840139—22no—
11#16840139C412yescomplemented
12#16840139C2212yes—
13C2×C4×C8×C61C411yescharacteristic, complemented
14C2×C22⋊#6923—42no—
15#14519836—24no—
16#14519836—42no—
17C22×D244—21no—
18C22×D244—41no—
19C22×D244—41no—
20C22×D244D412yes—
21C2×D488—24no—
22C2×D488—24no—
23C2×D488—44no—
24C2×D488—44no—
25#14519774—21no—
26#14519774—41no—
27#14519774—41no—
28#14519774C2×C411yescharacteristic
29#14519774C2×C412yescomplemented
30#14519774D412yes—
31#14519774C2311yescharacteristic
32C22×C8×C61—21no—
33C2×C42×C61C2×C411yescharacteristic
34C4×C8×C61—21no—
35C4×C8×C61C2×C412yescomplemented
36C23×D61—22no—
37C23×D61—41no—
38C22×#6923—82no—
39C22×C4×C61—21no—
40C22×C4×C61C22⋊C411yescharacteristic
41C2×D244—22no—
42C2×D244—22no—
43C2×D244—42no—
44C2×D244—42no—
45C2×D244—42no—
46C2×D244—42no—
47C2×D244—41no—
48C2×D244—42no—
49C2×D244—41no—
50C2×D244—42no—
51C2×D244—42no—
52C2×D244—41no—
53C2×D244—84no—
54C2×D244—84no—
55C2×D244C22⋊C412yes—
56C2×D244C2×D412yes—
57C22⋊#6923—44no—
58C22⋊#6923—82no—
59C2×C8×C61—22no—
60C2×C8×C61—22no—
61C2×C8×C61—22no—
62C42×C61—21no—
63C42×C61C22⋊C411yescharacteristic
64C42×C61C22×C411yescharacteristic
65D488—48no—
66D488—48no—
67C23×C61#9911yescharacteristic
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—42no—
71C22×D61—42no—
72C22×D61—42no—
73C22×D61—84no—
74C22×D61—84no—
75C22×D61—81no—
76C22×D61—81no—
77C2×#6923—84no—
78C2×#6923—164no—
79C2×C4×C61—24no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61#9911yescharacteristic
85C2×C4×C61C2×C22⋊C411yescharacteristic
86D244—42no—
87D244—42no—
88D244—44no—
89D244—82no—
90D244—82no—
91D244—82no—
92D244—84no—
93D244—82no—
94D244—84no—
95D244—84no—
96C8×C61—24no—
97C2×#1408—611nomaximal, Sylow
98C22×C61—22no—
99C22×C61#35311yescharacteristic
100C22×C61#35311yescharacteristic
101C22×C61C2×#9911yescharacteristic
102C2×D61—42no—
103C2×D61—42no—
104C2×D61—84no—
105C2×D61—82no—
106C2×D61—82no—
107C2×D61—84no—
108C2×D61—82no—
109C2×D61—162no—
110C2×D61—162no—
111C2×D61—162no—
112#6923—164no—
113C4×C61—22no—
114C4×C61—22no—
115C4×C61—21no—
116C4×C61—21no—
117C2×#493—611no—
118C2×#353—612no—
119#1408—614no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61#140812yescomplemented
123C2×C61C2×#35311yescharacteristic
124D61—82no—
125D61—82no—
126D61—162no—
127C22×D8—1222no—
128C2×#127—611no—
129C2×#127—611no—
130#493—612no—
131#493—612no—
132#493—1222no—
133C2×#99—1222no—
134C2×C4×C8#692311yescharacteristic, complemented
135#353—614no—
136#353—1222no—
137C61C2×#140811yescharacteristic, complemented, Sylow
138C22×D4—612no—
139C22×D4—1221no—
140C22×D4—2441no—
141C22×D4—2441no—
142C2×D8—1224no—
143C2×D8—1224no—
144C2×D8—2444no—
145C2×D8—2444no—
146C22×C8—21no—
147#127—612no—
148#127—611no—
149#127—611no—
150#127—612no—
151#127—1221no—
152#127—2441no—
153#127—2441no—
154C2×C22⋊C4—2442no—
155C2×C42C2×#692311yescharacteristic
156#99—1224no—
157#99—2442no—
158C4×C8—21no—
159C4×C8C2×#692312yescomplemented
160C24—1222no—
161C24—2441no—
162C2×D4—612no—
163C2×D4—612no—
164C2×D4—1222no—
165C2×D4—1222no—
166C2×D4—4884no—
167C2×D4—4884no—
168C2×D4—2442no—
169C2×D4—2441no—
170C2×D4—2441no—
171C2×D4—2442no—
172C2×D4—2442no—
173C2×D4—2442no—
174C2×D4—2442no—
175C2×D4—2442no—
176C2×D4—2442no—
177C2×D4—2441no—
178C22×C4—21no—
179C22×C4—4882no—
180C22×C4C22⋊#692311yescharacteristic
181D8—2448no—
182D8—2448no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—22no—
186C22⋊C4—4882no—
187C22⋊C4—2444no—
188C42—21no—
189C42C22⋊#692311yescharacteristic
190C42C22×#692311yescharacteristic
191C23—1222no—
192C23—1222no—
193C23—4884no—
194C23—4884no—
195C23—4881no—
196C23—4881no—
197C23—2442no—
198C23—2442no—
199C23—2442no—
200C23#1451983611yescharacteristic
201D4—4884no—
202D4—4884no—
203D4—4884no—
204D4—4882no—
205D4—4882no—
206D4—4882no—
207D4—4882no—
208D4—2444no—
209D4—2442no—
210D4—2442no—
211C2×C4—24no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—9764no—
217C2×C4—4884no—
218C2×C4#1451983611yescharacteristic
219C2×C4C2×C22⋊#692311yescharacteristic
220C8—24no—
221C22—22no—
222C22—9762no—
223C22—9762no—
224C22—9762no—
225C22—4884no—
226C22—4882no—
227C22—4882no—
228C22—4882no—
229C22—4884no—
230C22—2442no—
231C22—2442no—
232C22#1684066711yescharacteristic
233C22#1684066711yescharacteristic
234C22C2×#1451983611yescharacteristic
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—9764no—
240C2—21no—
241C2—21no—
242C2—9762no—
243C2—4882no—
244C2—4882no—
245C2#2146095112yesdirect product factor
246C2C2×#1684066711yescharacteristic
subgroupG/H
centerC22#16840667
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×C4×C8×C61C4
socleC22×C61#353
prime radicalC2×#16840139C2
cosocle#14519774C23
hypercenterC2×C4×C8#6923
hypocenterC61C2×#1408
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
1. C2×#16840667C2semidirect
2. #21460951C2direct (N × H)
6. #16840667C22semidirect
8. C2×#14519774C4semidirect
11. #16840139C4semidirect
13. C2×C4×C8×C61C4semidirect
29. #14519774C2×C4semidirect
35. C4×C8×C61C2×C4semidirect
122. C2×C61#1408semidirect
134. C2×C4×C8#6923semidirect
137. C61C2×#1408semidirect
159. C4×C8C2×#6923semidirect
245. C2#21460951direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406672
#214609512
C2×#168401392
C2×#140861