Finite Group Databasebeta

← C2×#21460949 #30608329

Subgroups — C2×#21460949 #30608329

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#21460949C214yesmaximal, direct product factor
4C2×#16840156C211yesmaximal, characteristic
5C2×#14519838—21no—
6C2×#14519836—21no—
7#16840671—21no—
8#16840671C2212yes—
9#16840669—21no—
10#16840669C2212yes—
11C22×Dic244—21no—
12C22×#11758190—21no—
13C2×#14519777C411yescharacteristic, complemented
14C2×#14519765C2211yescharacteristic
15#16840156—21no—
16#16840156—21no—
17#16840156C412yescomplemented
18#16840156C2212yes—
19C2×#97×C61C411yescharacteristic, complemented
20C2×#11758217—41no—
21C2×C22⋊#6923—41no—
22#14519838—22no—
23#14519838—41no—
24#14519836—22no—
25#14519836—41no—
26C22×Dic122—21no—
27C22×Dic122D411yescharacteristic
28C22×D244D411yescharacteristic
29C2×Dic244—22no—
30C2×Dic244—22no—
31C2×Dic244—42no—
32C2×Dic244—42no—
33C2×#11758190—22no—
34C2×#11758190—22no—
35C2×#11758190—42no—
36C2×#11758190—42no—
37#14519777—21no—
38#14519777—41no—
39#14519777C2×C412yescomplemented
40#14519765—41no—
41#14519765C2×C411yescharacteristic
42#14519765D411yescharacteristic
43#14519765D411yescharacteristic
44#14519765C2311yescharacteristic
45C2×C4⋊Dic61—41no—
46C2×#11758198—41no—
47C22×C8×C61—21no—
48C2×C42×C61C2×C411yescharacteristic
49#97×C61—21no—
50#97×C61C2×C412yescomplemented
51C23×D61—21no—
52C22×#6923—81no—
53C22×C4×C61—21no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×Dic61—21no—
56C22×Dic61—41no—
57C2×D244—21no—
58C2×D244—41no—
59C2×D244—41no—
60C2×D244C22⋊C411yescharacteristic
61C2×D244C2×D411yescharacteristic
62C2×Dic122—22no—
63C2×Dic122—21no—
64C2×Dic122—41no—
65C2×Dic122—41no—
66C2×Dic122—41no—
67C2×Dic122—41no—
68C2×Dic122—41no—
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—
78C2×C8×C61—22no—
79C2×C8×C61—22no—
80C2×C8×C61—22no—
81C42×C61—21no—
82C42×C61C22⋊C411yescharacteristic
83C42×C61C22×C411yescharacteristic
84#11758198—41no—
85#11758198—41no—
86#11758198—41no—
87#11758198—41no—
88C4⋊Dic61—42no—
89C4⋊Dic61—42no—
90Dic244—44no—
91Dic244—44no—
92#11758190—44no—
93#11758190—44no—
94C23×C61#9911yescharacteristic
95C22×D61—21no—
96C22×D61—21no—
97C22×D61—41no—
98C22×D61—41no—
99C22×D61—82no—
100C2×#6923—82no—
101C2×#6923—162no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—42no—
107C2×C4×C61#9911yescharacteristic
108C2×C4×C61C2×C22⋊C411yescharacteristic
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—42no—
114C2×Dic61—81no—
115C2×Dic61—81no—
116D244—41no—
117D244—41no—
118D244—81no—
119Dic122—41no—
120Dic122—41no—
121Dic122—42no—
122Dic122—42no—
123Dic122—81no—
124Dic122—81no—
125Dic122—81no—
126#92420—82no—
127C8×C61—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—
144Dic61—41no—
145Dic61—41no—
146Dic61—82no—
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—611no—
160C2×#124—611no—
161#497—612no—
162#497—612no—
163#497—1221no—
164#497—1221no—
165C2×#101—1221no—
166C2×#99—1221no—
167C2×#97#692311yescharacteristic, complemented
168#355—612no—
169#355—1221no—
170#354—612no—
171#354—1221no—
172C61C2×#140711yescharacteristic, complemented, Sylow
173C22×Q8—611no—
174C22×Q8—1221no—
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—21no—
186C4⋊Q8—612no—
187C4⋊Q8—1221no—
188C4⋊Q8—2441no—
189#124—611no—
190#124—611no—
191#124—611no—
192#124—611no—
193#124—2441no—
194C2×C4⋊C4—2441no—
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—21no—
203#97C2×#692312yescomplemented
204C24—1221no—
205C2×Q8—611no—
206C2×Q8—611no—
207C2×Q8—1221no—
208C2×Q8—1222no—
209C2×Q8—2441no—
210C2×Q8—2441no—
211C2×Q8—2441no—
212C2×Q8—2441no—
213C2×Q8—2441no—
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—1221no—
223C22×C4—4881no—
224C22×C4—2441no—
225C22×C4C22⋊#692311yescharacteristic
226Q16—2444no—
227Q16—2444no—
228SD16—2444no—
229SD16—2444no—
230M16—4881no—
231M16—2442no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—4881no—
236C4⋊C4—2442no—
237C4⋊C4—2442no—
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#1451983611yescharacteristic
253Q8—4881no—
254Q8—4881no—
255Q8—4881no—
256Q8—2442no—
257Q8—2442no—
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—1221no—
269C2×C4—1221no—
270C2×C4—9762no—
271C2×C4—4882no—
272C2×C4—4881no—
273C2×C4—4881no—
274C2×C4—2442no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4#1451983611yescharacteristic
278C2×C4C2×C22⋊#692311yescharacteristic
279C8—24no—
280C8—4882no—
281C22—22no—
282C22—9761no—
283C22—4881no—
284C22—4881no—
285C22—4882no—
286C22—2441no—
287C22—2441no—
288C22#1684066711yescharacteristic
289C22#1684066711yescharacteristic
290C22C2×#1451983611yescharacteristic
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—9762no—
296C4—4882no—
297C4—2441no—
298C4—2441no—
299C2—21no—
300C2—21no—
301C2—4881no—
302C2—4881no—
303C2#2146094912yesdirect product factor
304C2C2×#1684066711yescharacteristic
subgroupG/H
centerC22#16840667
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×#97×C61C4
socleC22×C61#353
prime radicalC22×D244D4
cosocle#14519765C23
hypercenterC2×#97#6923
hypocenterC61C2×#1407
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
3. #21460949C2direct (N × H)
13. C2×#14519777C4semidirect
17. #16840156C4semidirect
19. C2×#97×C61C4semidirect
39. #14519777C2×C4semidirect
50. #97×C61C2×C4semidirect
153. C2×C61#1407semidirect
167. C2×#97#6923semidirect
172. C61C2×#1407semidirect
203. #97C2×#6923semidirect
303. C2#21460949direct (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
#214609492
C2×#168401562
C2×#140761