Finite Group Databasebeta

← C2×#21460950 #30608344

Subgroups — C2×#21460950 #30608344

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#21460950C214yesmaximal, direct product factor
3C2×#16840138C211yesmaximal, characteristic
4C2×#14519836—22no—
5#16840667—22no—
6#16840667C2214yescomplemented
7C22×#11758199—22no—
8C2×#14519774C2211yescharacteristic
9#16840138—22no—
10#16840138C412yescomplemented
11#16840138C2212yes—
12C2×C4×#92418C411yescharacteristic, complemented
13C2×#127×C61C411yescharacteristic, complemented
14C2×C22⋊#6923—42no—
15#14519836—24no—
16#14519836—42no—
17C22×D244—41no—
18C22×D244D412yes—
19C2×#11758199—24no—
20C2×#11758199—24no—
21C2×#11758199—44no—
22C2×#11758199—44no—
23C22×#92418—21no—
24#14519774—41no—
25#14519774C2×C411yescharacteristic
26#14519774D412yes—
27#14519774C2311yescharacteristic
28C4×#92418—21no—
29C4×#92418C2×C412yescomplemented
30C22×D4×C61—21no—
31C22×D4×C61—41no—
32#127×C61—21no—
33#127×C61—41no—
34#127×C61C2×C412yescomplemented
35C2×C42×C61C2×C411yescharacteristic
36C24×C61—41no—
37C23×D61—22no—
38C22×#6923—82no—
39C2×D4×C61—22no—
40C2×D4×C61—42no—
41C2×D4×C61—42no—
42C2×D4×C61—42no—
43C2×D4×C61—42no—
44C2×D4×C61—41no—
45C2×D4×C61—84no—
46C22×C4×C61—21no—
47C22×C4×C61C22⋊C411yescharacteristic
48C2×D244—22no—
49C2×D244—42no—
50C2×D244—42no—
51C2×D244—41no—
52C2×D244—42no—
53C2×D244—41no—
54C2×D244—84no—
55C2×D244C22⋊C412yes—
56C2×D244C2×D412yes—
57C22⋊#6923—44no—
58C22⋊#6923—82no—
59C42×C61—21no—
60C42×C61C22⋊C411yescharacteristic
61C42×C61C22×C411yescharacteristic
62#11758199—48no—
63#11758199—48no—
64C2×#92418—22no—
65C2×#92418—22no—
66C2×#92418—22no—
67C23×C61—42no—
68C23×C61—84no—
69C23×C61—81no—
70C23×C61—81no—
71C23×C61#9911yescharacteristic
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—42no—
75C22×D61—42no—
76C22×D61—84no—
77C2×#6923—84no—
78C2×#6923—164no—
79D4×C61—44no—
80D4×C61—82no—
81D4×C61—84no—
82D4×C61—84no—
83C2×C4×C61—24no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61#9911yescharacteristic
89C2×C4×C61C2×C22⋊C411yescharacteristic
90D244—42no—
91D244—42no—
92D244—82no—
93D244—82no—
94D244—84no—
95D244—82no—
96#92418—24no—
97C2×#1408—611nomaximal, Sylow
98C22×C61—22no—
99C22×C61—84no—
100C22×C61—82no—
101C22×C61—162no—
102C22×C61—162no—
103C22×C61#35311yescharacteristic
104C22×C61#35311yescharacteristic
105C22×C61C2×#9911yescharacteristic
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—84no—
109C2×D61—82no—
110C2×D61—82no—
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—162no—
123C2×C61#140812yescomplemented
124C2×C61C2×#35311yescharacteristic
125D61—82no—
126D61—82no—
127C22×D8—1222no—
128C2×#127—611no—
129C2×#127#692311yescharacteristic, complemented
130#493—612no—
131#493—612no—
132#493—1222no—
133C2×#99—1222no—
134C2×C4×C8—611no—
135#353—614no—
136#353—1222no—
137C61C2×#140811yescharacteristic, complemented, Sylow
138C22×D4—21no—
139C22×D4—41no—
140C22×D4—612no—
141C22×D4—2441no—
142C2×D8—1224no—
143C2×D8—1224no—
144C2×D8—2444no—
145C2×D8—2444no—
146C22×C8—1221no—
147#127—21no—
148#127—41no—
149#127—612no—
150#127—611no—
151#127—611no—
152#127—2441no—
153#127C2×#692312yescomplemented
154C2×C22⋊C4—2442no—
155C2×C42C2×#692311yescharacteristic
156#99—1224no—
157#99—2442no—
158C4×C8—612no—
159C4×C8—1221no—
160C24—41no—
161C24—1222no—
162C2×D4—22no—
163C2×D4—42no—
164C2×D4—42no—
165C2×D4—42no—
166C2×D4—42no—
167C2×D4—41no—
168C2×D4—84no—
169C2×D4—612no—
170C2×D4—612no—
171C2×D4—1222no—
172C2×D4—4884no—
173C2×D4—2442no—
174C2×D4—2441no—
175C2×D4—2441no—
176C2×D4—2442no—
177C2×D4—2442no—
178C22×C4—21no—
179C22×C4—4882no—
180C22×C4C22⋊#692311yescharacteristic
181D8—2448no—
182D8—2448no—
183C2×C8—1222no—
184C2×C8—1222no—
185C2×C8—1222no—
186C22⋊C4—4882no—
187C22⋊C4—2444no—
188C42—21no—
189C42C22⋊#692311yescharacteristic
190C42C22×#692311yescharacteristic
191C23—42no—
192C23—84no—
193C23—81no—
194C23—81no—
195C23—1222no—
196C23—1222no—
197C23—4884no—
198C23—2442no—
199C23—2442no—
200C23#1451983511yescharacteristic
201D4—44no—
202D4—82no—
203D4—84no—
204D4—84no—
205D4—4884no—
206D4—4882no—
207D4—4882no—
208D4—4882no—
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#1451983511yescharacteristic
219C2×C4C2×C22⋊#692311yescharacteristic
220C8—1224no—
221C22—22no—
222C22—84no—
223C22—82no—
224C22—162no—
225C22—162no—
226C22—9762no—
227C22—4882no—
228C22—4882no—
229C22—4884no—
230C22—2442no—
231C22—2442no—
232C22#1684066611yescharacteristic
233C22#1684066611yescharacteristic
234C22C2×#1451983511yescharacteristic
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—9764no—
240C2—21no—
241C2—21no—
242C2—162no—
243C2—4882no—
244C2—4882no—
245C2#2146095012yesdirect product factor
246C2C2×#1684066611yescharacteristic
subgroupG/H
centerC22#16840666
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×#127×C61C4
socleC22×C61#353
prime radicalC2×#16840138C2
cosocle#14519774C23
hypercenterC2×#127#6923
hypocenterC61C2×#1408
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#16840667C2semidirect
2. #21460950C2direct (N × H)
6. #16840667C22semidirect
10. #16840138C4semidirect
12. C2×C4×#92418C4semidirect
13. C2×#127×C61C4semidirect
29. C4×#92418C2×C4semidirect
34. #127×C61C2×C4semidirect
123. C2×C61#1408semidirect
129. C2×#127#6923semidirect
137. C61C2×#1408semidirect
153. #127C2×#6923semidirect
245. C2#21460950direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406672
#214609502
C2×#168401382
C2×#140861