Finite Group Databasebeta

← C2×#21460948 #30608327

Subgroups — C2×#21460948 #30608327

Order 15616.

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

normal subgroups only

This group has 416 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#21460948C214yesmaximal, direct product factor
4C2×#16840154C211yesmaximal, characteristic
5C2×#14519838—21no—
6C2×#14519836—21no—
7#16840671—21no—
8#16840671C2212yes—
9#16840669—21no—
10#16840669C2212yes—
11C22×#11758202—21no—
12C22×#11758201—21no—
13C2×#14519765C2211yescharacteristic
14#16840154—21no—
15#16840154—21no—
16#16840154C412yescomplemented
17#16840154C2212yes—
18C2×#14519688C411yescharacteristic, complemented
19C2×C4⋊Q8×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×#11758202—22no—
29C2×#11758202—22no—
30C2×#11758202—42no—
31C2×#11758202—42no—
32C2×#11758201—22no—
33C2×#11758201—22no—
34C2×#11758201—42no—
35C2×#11758201—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×Q8×C61—21no—
46C4⋊Q8×C61—21no—
47C4⋊Q8×C61—41no—
48C4⋊Q8×C61C2×C412yescomplemented
49C2×C4⋊C4×C61—41no—
50C2×C42×C61C2×C411yescharacteristic
51C23×D61—21no—
52C22×#6923—81no—
53C2×Q8×C61—22no—
54C2×Q8×C61—41no—
55C2×Q8×C61—41no—
56C2×Q8×C61—41no—
57C2×Q8×C61—41no—
58C2×Q8×C61—41no—
59C22×C4×C61—21no—
60C22×C4×C61—41no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×Dic61—21no—
63C2×D244—21no—
64C2×D244—41no—
65C2×D244—41no—
66C2×D244C22⋊C411yescharacteristic
67C2×D244C2×D411yescharacteristic
68C2×Dic122—21no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122C22⋊C411yescharacteristic
72C2×Dic122C2×D411yescharacteristic
73C22⋊#6923—42no—
74C22⋊#6923—81no—
75#11758217—42no—
76#11758217—81no—
77C2×#92420—81no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61—42no—
80C42×C61—21no—
81C42×C61C22⋊C411yescharacteristic
82C42×C61C22×C411yescharacteristic
83#11758202—44no—
84#11758202—44no—
85#11758201—44no—
86#11758201—44no—
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91C2×#92418—22no—
92C2×#92418—22no—
93C2×#92418—22no—
94C23×C61#9911yescharacteristic
95C22×D61—21no—
96C22×D61—21no—
97C22×D61—41no—
98C22×D61—41no—
99C22×D61—82no—
100C2×#6923—82no—
101C2×#6923—162no—
102Q8×C61—42no—
103Q8×C61—42no—
104Q8×C61—81no—
105Q8×C61—81no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—42no—
111C2×C4×C61—42no—
112C2×C4×C61—81no—
113C2×C4×C61—81no—
114C2×C4×C61#9911yescharacteristic
115C2×C4×C61C2×C22⋊C411yescharacteristic
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120D244—41no—
121D244—41no—
122D244—81no—
123Dic122—41no—
124Dic122—41no—
125Dic122—81no—
126#92420—82no—
127#92418—24no—
128C2×#1407—611nomaximal, Sylow
129C22×C61—22no—
130C22×C61#35311yescharacteristic
131C22×C61#35311yescharacteristic
132C22×C61C2×#9911yescharacteristic
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—82no—
136C2×D61—81no—
137C2×D61—81no—
138C2×D61—161no—
139#6923—162no—
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—82no—
145Dic61—41no—
146Dic61—41no—
147C2×#497—611no—
148C2×#355—611no—
149C2×#354—611no—
150#1407—614no—
151C2×C61—21no—
152C2×C61—21no—
153C2×C61#140712yescomplemented
154C2×C61C2×#35311yescharacteristic
155D61—81no—
156D61—81no—
157C22×Q16—1221no—
158C22×SD16—1221no—
159C2×C4⋊Q8#692311yescharacteristic, complemented
160C2×#124—611no—
161#497—612no—
162#497—612no—
163#497—1221no—
164#497—1221no—
165C2×#101—1221no—
166C2×#99—1221no—
167C2×#97—611no—
168#355—612no—
169#355—1221no—
170#354—612no—
171#354—1221no—
172C61C2×#140711yescharacteristic, complemented, Sylow
173C22×Q8—21no—
174C22×Q8—611no—
175C22×D4—611no—
176C2×Q16—1222no—
177C2×Q16—1222no—
178C2×Q16—2442no—
179C2×Q16—2442no—
180C2×SD16—1222no—
181C2×SD16—1222no—
182C2×SD16—2442no—
183C2×SD16—2442no—
184C2×M16—2441no—
185C22×C8—1221no—
186C4⋊Q8—21no—
187C4⋊Q8—41no—
188C4⋊Q8C2×#692312yescomplemented
189#124—611no—
190#124—611no—
191#124—611no—
192#124—611no—
193#124—2441no—
194C2×C4⋊C4—41no—
195C2×C22⋊C4—2441no—
196C2×C22⋊C4—2441no—
197C2×C42C2×#692311yescharacteristic
198#101—1222no—
199#101—2441no—
200#99—1222no—
201#99—2441no—
202#97—612no—
203#97—1221no—
204C24—1221no—
205C2×Q8—22no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—611no—
212C2×Q8—611no—
213C2×Q8—1221no—
214C2×Q8—2441no—
215C2×Q8—2441no—
216C2×D4—611no—
217C2×D4—611no—
218C2×D4—1221no—
219C2×D4—2441no—
220C2×D4—2441no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4—1221no—
224C22×C4—4881no—
225C22×C4C22⋊#692311yescharacteristic
226Q16—2444no—
227Q16—2444no—
228SD16—2444no—
229SD16—2444no—
230M16—4881no—
231M16—2442no—
232C2×C8—1222no—
233C2×C8—1222no—
234C2×C8—1222no—
235C2×C8—4881no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C22⋊C4—4881no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C22⋊C4—2441no—
243C22⋊C4—2442no—
244C42—21no—
245C42C22⋊#692311yescharacteristic
246C42C22×#692311yescharacteristic
247C23—1221no—
248C23—1221no—
249C23—4882no—
250C23—2441no—
251C23—2441no—
252C23#1451983511yescharacteristic
253Q8—42no—
254Q8—42no—
255Q8—81no—
256Q8—81no—
257Q8—4881no—
258Q8—2441no—
259Q8—2441no—
260D4—4881no—
261D4—2441no—
262D4—2441no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—9762no—
274C2×C4—4882no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4#1451983511yescharacteristic
278C2×C4C2×C22⋊#692311yescharacteristic
279C8—1224no—
280C8—4882no—
281C22—22no—
282C22—9761no—
283C22—4881no—
284C22—4881no—
285C22—4882no—
286C22—2441no—
287C22—2441no—
288C22#1684066611yescharacteristic
289C22#1684066611yescharacteristic
290C22C2×#1451983511yescharacteristic
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—82no—
296C4—9762no—
297C4—2441no—
298C4—2441no—
299C2—21no—
300C2—21no—
301C2—4881no—
302C2—4881no—
303C2#2146094812yesdirect product factor
304C2C2×#1684066611yescharacteristic
subgroupG/H
centerC22#16840666
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61#353
prime radicalC22×D244D4
cosocle#14519765C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61C2×#1407
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
3. #21460948C2direct (N × H)
16. #16840154C4semidirect
18. C2×#14519688C4semidirect
19. C2×C4⋊Q8×C61C4semidirect
44. #14519688C2×C4semidirect
48. C4⋊Q8×C61C2×C4semidirect
153. C2×C61#1407semidirect
159. C2×C4⋊Q8#6923semidirect
172. C61C2×#1407semidirect
188. C4⋊Q8C2×#6923semidirect
303. C2#21460948direct (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
#214609482
C2×#168401542
C2×#140761