Finite Group Databasebeta

← C2×#21460964 #30608412

Subgroups — C2×#21460964 #30608412

Order 15616.

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

normal subgroups only

This group has 340 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×#16840671C211yesmaximal, characteristic
2C2×#16840669C211yesmaximal, characteristic
3#21460964C214yesmaximal, direct product factor
4C2×#16840119C211yesmaximal, characteristic
5C2×#14519838—21no—
6C2×#14519836—21no—
7#16840671—21no—
8#16840671C2212yes—
9#16840669—21no—
10#16840669C2212yes—
11C2×#14519765C2211yescharacteristic
12#16840119—21no—
13#16840119—21no—
14#16840119C412yescomplemented
15#16840119C2212yes—
16C2×#14519700—21no—
17C2×#14519697—21no—
18C2×C4×#92418C411yescharacteristic, complemented
19C2×#125×C61C411yescharacteristic, complemented
20C2×#11758217—41no—
21C2×C22⋊#6923—41no—
22#14519838—22no—
23#14519838—41no—
24#14519836—22no—
25#14519836—41no—
26C22×Dic122D411yescharacteristic
27C22×D244D411yescharacteristic
28C22×#92418—21no—
29#14519765—41no—
30#14519765C2×C411yescharacteristic
31#14519765D411yescharacteristic
32#14519765D411yescharacteristic
33#14519765C2311yescharacteristic
34C2×#11758198—41no—
35#14519700—22no—
36#14519700—22no—
37#14519697—22no—
38#14519697—22no—
39C4×#92418—21no—
40C4×#92418C2×C412yescomplemented
41#125×C61—21no—
42#125×C61—41no—
43#125×C61C2×C412yescomplemented
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—41no—
46C2×C42×C61C2×C411yescharacteristic
47C23×D61—21no—
48C22×#6923—81no—
49C22×C4×C61—21no—
50C22×C4×C61—41no—
51C22×C4×C61C22⋊C411yescharacteristic
52C22×Dic61—21no—
53C2×D244—21no—
54C2×D244—41no—
55C2×D244—41no—
56C2×D244C22⋊C411yescharacteristic
57C2×D244C2×D411yescharacteristic
58C2×Dic122—21no—
59C2×Dic122—41no—
60C2×Dic122—41no—
61C2×Dic122C22⋊C411yescharacteristic
62C2×Dic122C2×D411yescharacteristic
63C22⋊#6923—42no—
64C22⋊#6923—81no—
65#11758217—42no—
66#11758217—81no—
67C2×#92420—81no—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—41no—
72C42×C61—21no—
73C42×C61C22⋊C411yescharacteristic
74C42×C61C22×C411yescharacteristic
75#11758198—41no—
76#11758198—41no—
77#11758198—41no—
78#11758198—41no—
79C2×#92418—22no—
80C2×#92418—41no—
81C2×#92418—41no—
82C23×C61#9911yescharacteristic
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—41no—
86C22×D61—41no—
87C22×D61—82no—
88C2×#6923—82no—
89C2×#6923—162no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—82no—
97C2×C4×C61#9911yescharacteristic
98C2×C4×C61C2×C22⋊C411yescharacteristic
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103D244—41no—
104D244—41no—
105D244—81no—
106Dic122—41no—
107Dic122—41no—
108Dic122—81no—
109#92420—82no—
110#92418—42no—
111C2×#1414—611nomaximal, Sylow
112C22×C61—22no—
113C22×C61#35411yescharacteristic
114C22×C61#35411yescharacteristic
115C22×C61C2×#9911yescharacteristic
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—82no—
119C2×D61—81no—
120C2×D61—81no—
121C2×D61—161no—
122#6923—162no—
123C4×C61—21no—
124C4×C61—21no—
125C4×C61—41no—
126C4×C61—41no—
127C4×C61—82no—
128Dic61—41no—
129Dic61—41no—
130C2×#488—611no—
131C2×#355—611no—
132C2×#354—611no—
133#1414—614no—
134C2×C61—21no—
135C2×C61—21no—
136C2×C61#141412yescomplemented
137C2×C61C2×#35411yescharacteristic
138D61—81no—
139D61—81no—
140C2×#125#692311yescharacteristic, complemented
141C2×#124—611no—
142#488—612no—
143#488—612no—
144#488—1221no—
145#488—1221no—
146C2×#103—1221no—
147C2×#102—1221no—
148C2×#101—1221no—
149C2×#99—1221no—
150C2×C4×C8—611no—
151#355—612no—
152#355—1221no—
153#354—612no—
154#354—1221no—
155C61C2×#141411yescharacteristic, complemented, Sylow
156C22×Q8—611no—
157C22×D4—611no—
158C2×M16—2441no—
159C22×C8—1221no—
160#125—21no—
161#125—41no—
162#125C2×#692312yescomplemented
163#124—611no—
164#124—611no—
165#124—611no—
166#124—611no—
167#124—2441no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—41no—
170C2×C22⋊C4—2441no—
171C2×C22⋊C4—2441no—
172C2×C42C2×#692311yescharacteristic
173#103—1222no—
174#103—1222no—
175#102—1222no—
176#102—1222no—
177#101—1222no—
178#101—2441no—
179#99—1222no—
180#99—2441no—
181C4×C8—612no—
182C4×C8—1221no—
183C24—1221no—
184C2×Q8—611no—
185C2×Q8—611no—
186C2×Q8—1221no—
187C2×Q8—2441no—
188C2×Q8—2441no—
189C2×D4—611no—
190C2×D4—611no—
191C2×D4—1221no—
192C2×D4—2441no—
193C2×D4—2441no—
194C22×C4—21no—
195C22×C4—41no—
196C22×C4—1221no—
197C22×C4—4881no—
198C22×C4C22⋊#692311yescharacteristic
199M16—4881no—
200M16—2442no—
201C2×C8—1222no—
202C2×C8—4881no—
203C2×C8—2441no—
204C2×C8—2441no—
205C4⋊C4—22no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C22⋊C4—4881no—
210C22⋊C4—2441no—
211C22⋊C4—2441no—
212C22⋊C4—2441no—
213C22⋊C4—2441no—
214C22⋊C4—2442no—
215C42—21no—
216C42C22⋊#692311yescharacteristic
217C42C22×#692311yescharacteristic
218C23—1221no—
219C23—1221no—
220C23—4882no—
221C23—2441no—
222C23—2441no—
223C23#1451983511yescharacteristic
224Q8—4881no—
225Q8—2441no—
226Q8—2441no—
227D4—4881no—
228D4—2441no—
229D4—2441no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—82no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—9762no—
240C2×C4—4882no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4#1451983511yescharacteristic
244C2×C4C2×C22⋊#692311yescharacteristic
245C8—4882no—
246C8—2442no—
247C22—22no—
248C22—9761no—
249C22—4881no—
250C22—4881no—
251C22—4882no—
252C22—2441no—
253C22—2441no—
254C22#1684066811yescharacteristic
255C22#1684066811yescharacteristic
256C22C2×#1451983511yescharacteristic
257C4—21no—
258C4—21no—
259C4—41no—
260C4—41no—
261C4—82no—
262C4—9762no—
263C4—2441no—
264C4—2441no—
265C2—21no—
266C2—21no—
267C2—4881no—
268C2—4881no—
269C2#2146096412yesdirect product factor
270C2C2×#1684066811yescharacteristic
subgroupG/H
centerC22#16840668
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×#125×C61C4
socleC22×C61#354
prime radicalC22×D244D4
cosocle#14519765C23
hypercenterC2×#125#6923
hypocenterC61C2×#1414
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #21460964C2direct (N × H)
14. #16840119C4semidirect
18. C2×C4×#92418C4semidirect
19. C2×#125×C61C4semidirect
40. C4×#92418C2×C4semidirect
43. #125×C61C2×C4semidirect
136. C2×C61#1414semidirect
140. C2×#125#6923semidirect
155. C61C2×#1414semidirect
162. #125C2×#6923semidirect
269. C2#21460964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406712
C2×#168406692
#214609642
C2×#168401192
C2×#141461