Finite Group Databasebeta

← C2×#21462217 #30624287

Subgroups — C2×#21462217 #30624287

Order 15616.

798 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 192 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×D8×#6923C212yesmaximal, complemented
2#21462217C218yesmaximal, direct product factor
3C2×#16840689C211yesmaximal, characteristic, complemented
4C2×#16840674C212yesmaximal, complemented
5C2×#16840649C211yesmaximal, characteristic, complemented
6C2×D16×D61C211yesmaximal, characteristic
7C2×D4×#6923—22no—
8C2×D61⋊C16C2211yescharacteristic
9D8×#6923—24no—
10D8×#6923C2218yescomplemented
11C2×#14519846C2212yes—
12C2×#14519839—22no—
13C2×C8×#6923C2211yescharacteristic
14#16840689C2214yescomplemented
15#16840674C2218yescomplemented
16#16840649C2214yescomplemented
17C2×D8×D61C2212yes—
18C2×D976C411yescharacteristic, complemented
19C2×#14519718C412yescomplemented
20D16×D61C414yescomplemented
21D16×D61C2214yes—
22C2×C16×D61C2211yescharacteristic
23C2×D16×C61C411yescharacteristic, complemented
24C23×#6923—42no—
25C2×D61⋊C8D411yescharacteristic
26D4×#6923—28no—
27D4×#6923—44no—
28C2×C4⋊#6923—22no—
29C2×C22⋊#6923—42no—
30C2×C4×#6923D411yescharacteristic
31D61⋊C16—21no—
32D61⋊C16C2312yes—
33C2×#11758187—21no—
34#14519846—22no—
35#14519846C2314yes—
36#14519839—28no—
37C8×#6923D412yes—
38C8×#6923C2312yes—
39C2×D4×D61—22no—
40C2×D488C2×C412yescomplemented
41C2×#11758199—22no—
42D8×D61—22no—
43D8×D61—22no—
44D8×D61C2×C414yescomplemented
45D8×D61C2314yes—
46C2×C8×D61C2311yescharacteristic
47D976C2×C414yescomplemented
48#14519718C2×C418yescomplemented
49C2×#11758185C2×C411yescharacteristic, complemented
50C16×D61C2×C412yescomplemented
51C16×D61C2312yes—
52C2×D8×C61C2×C412yescomplemented
53D16×C61C2×C414yescomplemented
54C2×C16×C61C2×C411yescharacteristic, complemented
55C23×D61—42no—
56C22×#6923—42no—
57C22×#6923—48no—
58C22×#6923—88no—
59C22×#6923D812yes—
60C2×D4×C61—22no—
61C2×C22⋊D61—42no—
62D4×D61—24no—
63D4×D61—24no—
64D4×D61—42no—
65D4×D61—42no—
66C2×D244—22no—
67C2×C4×D61C2×D411yescharacteristic
68C22⋊#6923—48no—
69C2×#92420—21no—
70C4⋊#6923—24no—
71C4⋊#6923—42no—
72C4×#6923D812yes—
73C4×#6923C2×D412yes—
74D61⋊C8—21no—
75D61⋊C8C2×D412yes—
76D8×C61—22no—
77D8×C61C22×C414yescomplemented
78C2×C8×C61C22×C411yescharacteristic
79#11758199—24no—
80#11758199—24no—
81C2×#92418#4111yescharacteristic
82D488—22no—
83D488C22×C414yescomplemented
84C8×D61C22×C411yescharacteristic
85C8×D61C2×D411yescharacteristic
86C8×D61#4111yescharacteristic
87C8×D61C2411yescharacteristic
88#11758187—22no—
89C16×C61C22×C412yescomplemented
90#11758185C22×C412yescomplemented
91C23×C61—42no—
92C22×D61—42no—
93C22×D61—44no—
94C22×D61—44no—
95C22×D61—84no—
96C22×D61—84no—
97C22×D61C2×D811yescharacteristic
98C2×#6923—24no—
99C2×#6923—44no—
100C2×#6923—816no—
101C2×#6923—84no—
102C2×#6923C2×D814yes—
103D4×C61—24no—
104D4×C61—42no—
105C2×C4×C61C4×D411yescharacteristic
106C22⋊D61—44no—
107C22⋊D61—44no—
108C2×Dic61#13511yescharacteristic
109D244—24no—
110D244—42no—
111C4×D61C4×D411yescharacteristic
112C4×D61C2×D811yescharacteristic
113C4×D61#13511yescharacteristic
114C4×D61C22×D411yescharacteristic
115#92420—22no—
116C8×C61C4×D411yescharacteristic
117C8×C61C23×C411yescharacteristic
118#92418C4×D411yescharacteristic
119#92418C2×#4111yescharacteristic
120C2×#2177—611nomaximal, Sylow
121C22×C61—44no—
122C22×C61—84no—
123C22×C61C4×D811yescharacteristic
124C2×D61—44no—
125C2×D61—84no—
126C2×D61—84no—
127C2×D61—84no—
128C2×D61—88no—
129C2×D61C4×D811yescharacteristic
130C2×D61#50914yes—
131C2×D61C22×D811yescharacteristic
132#6923—24no—
133#6923—84no—
134C4×C61C4×D811yescharacteristic
135C4×C61C2×C4×D411yescharacteristic
136Dic61C4×D811yescharacteristic
137Dic61C2×#13511yescharacteristic
138C22×D16—611no—
139C2×C4×D8—612no—
140#2177—618no—
141C2×#367—611no—
142C2×#357—612no—
143C2×#346—611no—
144C2×C61—84no—
145C2×C61#217712yescomplemented
146C2×C61C2×C4×D811yescharacteristic
147D61—84no—
148D61#217712yescomplemented
149D61C2×#50912yes—
150C22×D8—612no—
151C2×C4×D4—1222no—
152C2×D16—612no—
153C2×D16—614no—
154C2×D16—614no—
155C2×D16—611no—
156C2×D16#692311yescharacteristic, complemented
157C22×C16—611no—
158C22×C16—611no—
159C4×D8—618no—
160C4×D8—1224no—
161C2×#107—612no—
162C2×#102—1222no—
163C2×C4×C8—611no—
164#367—614no—
165#357—618no—
166#346—614no—
167C61C2×#217711yescharacteristic, complemented, Sylow
168C22×D4—1222no—
169C23×C4—2442no—
170C2×D8—614no—
171C2×D8—614no—
172C2×D8—612no—
173C2×D8—1222no—
174C2×D8—1222no—
175C2×D8—1222no—
176C2×D8C2×#692312yescomplemented
177C22×C8—611no—
178C22×C8—611no—
179C4×D4—1228no—
180C4×D4—2444no—
181C2×C4⋊C4—1222no—
182C2×C22⋊C4—2442no—
183C2×C42—611no—
184D16—618no—
185D16—614no—
186D16C2×#692314yescomplemented
187C2×C16—611no—
188C2×C16—612no—
189C2×C16—612no—
190C2×C16—612no—
191C2×C16—1221no—
192C2×C16—1221no—
193C2×C16C2×#692311yescharacteristic, complemented
194#107—614no—
195#107—1222no—
196#102—1228no—
197C4×C8—612no—
198C4×C8—612no—
199C24—2442no—
200C2×D4—22no—
201C2×D4—1224no—
202C2×D4—1224no—
203C2×D4—1222no—
204C2×D4—2442no—
205C2×D4—2442no—
206C2×D4—2442no—
207C22×C4—611no—
208C22×C4—612no—
209C22×C4—4888no—
210C22×C4—2448no—
211C22×C4—2442no—
212D8—22no—
213D8—614no—
214D8—1224no—
215D8—1224no—
216D8—1222no—
217D8C22×#692314yescomplemented
218C2×C8—611no—
219C2×C8—611no—
220C2×C8—611no—
221C2×C8—611no—
222C2×C8—611no—
223C2×C8—612no—
224C2×C8—1221no—
225C2×C8—1221no—
226C2×C8C22×#692311yescharacteristic
227C4⋊C4—1224no—
228C4⋊C4—2442no—
229C22⋊C4—2448no—
230C42—612no—
231C42—612no—
232C16—612no—
233C16—1222no—
234C16C22×#692312yescomplemented
235C23—42no—
236C23—611no—
237C23—4884no—
238C23—4884no—
239C23—2444no—
240C23—2444no—
241C23—2442no—
242D4—24no—
243D4—42no—
244D4—1224no—
245D4—2444no—
246D4—2444no—
247D4—2442no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—611no—
252C2×C4—611no—
253C2×C4—614no—
254C2×C4—1224no—
255C2×C4—48816no—
256C2×C4—4884no—
257C2×C4—2444no—
258C2×C4D4×#692311yescharacteristic
259C8—611no—
260C8—611no—
261C8—1222no—
262C8D4×#692311yescharacteristic
263C8C23×#692311yescharacteristic
264C22—44no—
265C22—84no—
266C22—611no—
267C22—611no—
268C22—614no—
269C22—4884no—
270C22—4884no—
271C22—4888no—
272C22—4884no—
273C22—2444no—
274C22D8×#692311yescharacteristic
275C4—611no—
276C4—611no—
277C4—1224no—
278C4—4884no—
279C4D8×#692311yescharacteristic
280C4C2×D4×#692311yescharacteristic
281C2—84no—
282C2—612no—
283C2—612no—
284C2—4884no—
285C2#2146221712yesdirect product factor
286C2C2×D8×#692311yescharacteristic
subgroupG/H
centerC22D8×#6923
commutatorC8×C61C23×C4
FrattiniC8C23×#6923
FittingC2×D16×C61C4
socleC22×C61C4×D8
prime radicalC2×D16×D61C2
cosocleC8×D61C24
hypercenterC2×D16#6923
hypocenterC61C2×#2177
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×D8×#6923C2semidirect
2. #21462217C2direct (N × H)
3. C2×#16840689C2semidirect
4. C2×#16840674C2semidirect
5. C2×#16840649C2semidirect
10. D8×#6923C22semidirect
14. #16840689C22semidirect
15. #16840674C22semidirect
16. #16840649C22semidirect
18. C2×D976C4semidirect
19. C2×#14519718C4semidirect
20. D16×D61C4semidirect
23. C2×D16×C61C4semidirect
40. C2×D488C2×C4semidirect
44. D8×D61C2×C4semidirect
47. D976C2×C4semidirect
48. #14519718C2×C4semidirect
49. C2×#11758185C2×C4semidirect
50. C16×D61C2×C4semidirect
52. C2×D8×C61C2×C4semidirect
53. D16×C61C2×C4semidirect
54. C2×C16×C61C2×C4semidirect
77. D8×C61C22×C4semidirect
83. D488C22×C4semidirect
89. C16×C61C22×C4semidirect
90. #11758185C22×C4semidirect
145. C2×C61#2177semidirect
148. D61#2177semidirect
156. C2×D16#6923semidirect
167. C61C2×#2177semidirect
176. C2×D8C2×#6923semidirect
186. D16C2×#6923semidirect
193. C2×C16C2×#6923semidirect
217. D8C22×#6923semidirect
234. C16C22×#6923semidirect
285. C2#21462217direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D8×#69232
#214622172
C2×#168406892
C2×#168406742
C2×#168406492
C2×D16×D612
C2×#217761