Finite Group Databasebeta

← C2×#21460946 #30608324

Subgroups — C2×#21460946 #30608324

Order 15616.

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

normal subgroups only

This group has 468 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, complemented
2C2×#16840669C211yesmaximal, characteristic, complemented
3#21460946C214yesmaximal, direct product factor
4C2×#16840149C211yesmaximal, characteristic
5C2×#14519838—21no—
6C2×#14519836—21no—
7#16840671—21no—
8#16840671C2212yescomplemented
9#16840669—21no—
10#16840669C2212yescomplemented
11C22×#11758200—21no—
12C22×#11758199—21no—
13C2×#14519765C2211yescharacteristic
14#16840149—21no—
15#16840149—21no—
16#16840149C412yescomplemented
17#16840149C2212yes—
18C2×#14519688C411yescharacteristic, complemented
19C2×#127×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
28C2×#11758200—22no—
29C2×#11758200—22no—
30C2×#11758200—42no—
31C2×#11758200—42no—
32C2×#11758199—22no—
33C2×#11758199—22no—
34C2×#11758199—42no—
35C2×#11758199—42no—
36C22×#92418—21no—
37#14519765—41no—
38#14519765C2×C411yescharacteristic
39#14519765D411yescharacteristic
40#14519765D411yescharacteristic
41#14519765C2311yescharacteristic
42C2×#11758198—41no—
43#14519688—21no—
44#14519688C2×C412yescomplemented
45C22×D4×C61—21no—
46C22×D4×C61—41no—
47#127×C61—21no—
48#127×C61—41no—
49#127×C61C2×C412yescomplemented
50C2×C42×C61C2×C411yescharacteristic
51C24×C61—41no—
52C23×D61—21no—
53C22×#6923—81no—
54C2×D4×C61—22no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61—42no—
60C2×D4×C61—42no—
61C2×D4×C61—41no—
62C2×D4×C61—84no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×Dic61—21no—
66C2×D244—21no—
67C2×D244—41no—
68C2×D244—41no—
69C2×D244C22⋊C411yescharacteristic
70C2×D244C2×D411yescharacteristic
71C2×Dic122—21no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×Dic122C22⋊C411yescharacteristic
75C2×Dic122C2×D411yescharacteristic
76C22⋊#6923—42no—
77C22⋊#6923—81no—
78#11758217—42no—
79#11758217—81no—
80C2×#92420—81no—
81C42×C61—21no—
82C42×C61C22⋊C411yescharacteristic
83C42×C61C22×C411yescharacteristic
84#11758200—44no—
85#11758200—44no—
86#11758199—44no—
87#11758199—44no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—41no—
92C2×#92418—22no—
93C2×#92418—22no—
94C2×#92418—22no—
95C23×C61—42no—
96C23×C61—84no—
97C23×C61—81no—
98C23×C61—81no—
99C23×C61#9911yescharacteristic
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—41no—
103C22×D61—41no—
104C22×D61—82no—
105C2×#6923—82no—
106C2×#6923—162no—
107D4×C61—42no—
108D4×C61—42no—
109D4×C61—81no—
110D4×C61—81no—
111D4×C61—84no—
112D4×C61—84no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—42no—
118C2×C4×C61#9911yescharacteristic
119C2×C4×C61C2×C22⋊C411yescharacteristic
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124D244—41no—
125D244—41no—
126D244—81no—
127Dic122—41no—
128Dic122—41no—
129Dic122—81no—
130#92420—82no—
131#92418—24no—
132C2×#1406—611nomaximal, Sylow
133C22×C61—22no—
134C22×C61—84no—
135C22×C61—82no—
136C22×C61—162no—
137C22×C61—162no—
138C22×C61#35311yescharacteristic
139C22×C61#35311yescharacteristic
140C22×C61C2×#9911yescharacteristic
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—82no—
144C2×D61—81no—
145C2×D61—81no—
146C2×D61—161no—
147#6923—162no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—41no—
151C4×C61—41no—
152Dic61—41no—
153Dic61—41no—
154C2×#496—611no—
155C2×#355—611no—
156C2×#354—611no—
157#1406—614no—
158C2×C61—21no—
159C2×C61—21no—
160C2×C61—162no—
161C2×C61#140612yescomplemented
162C2×C61C2×#35311yescharacteristic
163D61—81no—
164D61—81no—
165C22×SD16—1221no—
166C22×D8—1221no—
167C2×#127#692311yescharacteristic, complemented
168C2×#124—611no—
169#496—612no—
170#496—612no—
171#496—1221no—
172#496—1221no—
173C2×#101—1221no—
174C2×#99—1221no—
175C2×#97—611no—
176#355—612no—
177#355—1221no—
178#354—612no—
179#354—1221no—
180C61C2×#140611yescharacteristic, complemented, Sylow
181C22×Q8—611no—
182C22×D4—21no—
183C22×D4—41no—
184C22×D4—611no—
185C2×SD16—1222no—
186C2×SD16—1222no—
187C2×SD16—2442no—
188C2×SD16—2442no—
189C2×D8—1222no—
190C2×D8—1222no—
191C2×D8—2442no—
192C2×D8—2442no—
193C2×M16—2441no—
194C22×C8—1221no—
195#127—21no—
196#127—41no—
197#127C2×#692312yescomplemented
198#124—611no—
199#124—611no—
200#124—611no—
201#124—611no—
202#124—2441no—
203C2×C22⋊C4—2441no—
204C2×C22⋊C4—2441no—
205C2×C42C2×#692311yescharacteristic
206#101—1222no—
207#101—2441no—
208#99—1222no—
209#99—2441no—
210#97—612no—
211#97—1221no—
212C24—41no—
213C24—1221no—
214C2×Q8—611no—
215C2×Q8—611no—
216C2×Q8—1221no—
217C2×Q8—2441no—
218C2×Q8—2441no—
219C2×D4—22no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—41no—
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—41no—
227C2×D4—84no—
228C2×D4—611no—
229C2×D4—611no—
230C2×D4—1221no—
231C2×D4—2441no—
232C2×D4—2441no—
233C22×C4—21no—
234C22×C4—1221no—
235C22×C4—4881no—
236C22×C4C22⋊#692311yescharacteristic
237SD16—2444no—
238SD16—2444no—
239D8—2444no—
240D8—2444no—
241M16—4881no—
242M16—2442no—
243C2×C8—1222no—
244C2×C8—1222no—
245C2×C8—1222no—
246C2×C8—4881no—
247C22⋊C4—4881no—
248C22⋊C4—2441no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C22⋊C4—2441no—
252C22⋊C4—2442no—
253C42—21no—
254C42C22⋊#692311yescharacteristic
255C42C22×#692311yescharacteristic
256C23—42no—
257C23—84no—
258C23—81no—
259C23—81no—
260C23—1221no—
261C23—1221no—
262C23—4882no—
263C23—2441no—
264C23—2441no—
265C23#1451983511yescharacteristic
266Q8—4881no—
267Q8—2441no—
268Q8—2441no—
269D4—42no—
270D4—42no—
271D4—81no—
272D4—81no—
273D4—84no—
274D4—84no—
275D4—4881no—
276D4—2441no—
277D4—2441no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—9762no—
286C2×C4—4882no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4#1451983511yescharacteristic
290C2×C4C2×C22⋊#692311yescharacteristic
291C8—1224no—
292C8—4882no—
293C22—22no—
294C22—84no—
295C22—82no—
296C22—162no—
297C22—162no—
298C22—9761no—
299C22—4881no—
300C22—4881no—
301C22—4882no—
302C22—2441no—
303C22—2441no—
304C22#1684066611yescharacteristic
305C22#1684066611yescharacteristic
306C22C2×#1451983511yescharacteristic
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—9762no—
312C4—2441no—
313C4—2441no—
314C2—21no—
315C2—21no—
316C2—162no—
317C2—4881no—
318C2—4881no—
319C2#2146094612yesdirect product factor
320C2C2×#1684066611yescharacteristic
subgroupG/H
centerC22#16840666
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×#127×C61C4
socleC22×C61#353
prime radicalC2×#16840149C2
cosocle#14519765C23
hypercenterC2×#127#6923
hypocenterC61C2×#1406
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×#16840671C2semidirect
2. C2×#16840669C2semidirect
3. #21460946C2direct (N × H)
8. #16840671C22semidirect
10. #16840669C22semidirect
16. #16840149C4semidirect
18. C2×#14519688C4semidirect
19. C2×#127×C61C4semidirect
44. #14519688C2×C4semidirect
49. #127×C61C2×C4semidirect
161. C2×C61#1406semidirect
167. C2×#127#6923semidirect
180. C61C2×#1406semidirect
197. #127C2×#6923semidirect
319. C2#21460946direct (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
#214609462
C2×#168401492
C2×#140661