Finite Group Databasebeta

← C2×#20291113 #28328366

Subgroups — C2×#20291113 #28328366

Order 13568.

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×#6157C212yesmaximal, complemented
2#20291113C218yesmaximal, direct product factor
3C2×#16811550C211yesmaximal, characteristic, complemented
4C2×#16811535C212yesmaximal, complemented
5C2×#16811510C211yesmaximal, characteristic, complemented
6C2×D16×D53C211yesmaximal, characteristic
7C2×D4×#6157—22no—
8C2×D53⋊C16C2211yescharacteristic
9D8×#6157—24no—
10D8×#6157C2218yescomplemented
11C2×#13133286C2212yes—
12C2×#13133279—22no—
13C2×C8×#6157C2211yescharacteristic
14#16811550C2214yescomplemented
15#16811535C2218yescomplemented
16#16811510C2214yescomplemented
17C2×D8×D53C2212yes—
18C2×D848C411yescharacteristic, complemented
19C2×#13133158C412yescomplemented
20D16×D53C414yescomplemented
21D16×D53C2214yes—
22C2×C16×D53C2211yescharacteristic
23C2×D16×C53C411yescharacteristic, complemented
24C23×#6157—42no—
25C2×D53⋊C8D411yescharacteristic
26D4×#6157—28no—
27D4×#6157—44no—
28C2×C4⋊#6157—22no—
29C2×C22⋊#6157—42no—
30C2×C4×#6157D411yescharacteristic
31D53⋊C16—21no—
32D53⋊C16C2312yes—
33C2×#11719910—21no—
34#13133286—22no—
35#13133286C2314yes—
36#13133279—28no—
37C8×#6157D412yes—
38C8×#6157C2312yes—
39C2×D4×D53—22no—
40C2×D424C2×C412yescomplemented
41C2×#11719922—22no—
42D8×D53—22no—
43D8×D53—22no—
44D8×D53C2×C414yescomplemented
45D8×D53C2314yes—
46C2×C8×D53C2311yescharacteristic
47D848C2×C414yescomplemented
48#13133158C2×C418yescomplemented
49C2×#11719908C2×C411yescharacteristic, complemented
50C16×D53C2×C412yescomplemented
51C16×D53C2312yes—
52C2×D8×C53C2×C412yescomplemented
53D16×C53C2×C414yescomplemented
54C2×C16×C53C2×C411yescharacteristic, complemented
55C23×D53—42no—
56C22×#6157—42no—
57C22×#6157—48no—
58C22×#6157—88no—
59C22×#6157D812yes—
60C2×D4×C53—22no—
61C2×C22⋊D53—42no—
62D4×D53—24no—
63D4×D53—24no—
64D4×D53—42no—
65D4×D53—42no—
66C2×D212—22no—
67C2×C4×D53C2×D411yescharacteristic
68C22⋊#6157—48no—
69C2×#88324—21no—
70C4⋊#6157—24no—
71C4⋊#6157—42no—
72C4×#6157D812yes—
73C4×#6157C2×D412yes—
74D53⋊C8—21no—
75D53⋊C8C2×D412yes—
76D8×C53—22no—
77D8×C53C22×C414yescomplemented
78C2×C8×C53C22×C411yescharacteristic
79#11719922—24no—
80#11719922—24no—
81C2×#88322#4111yescharacteristic
82D424—22no—
83D424C22×C414yescomplemented
84C8×D53C22×C411yescharacteristic
85C8×D53C2×D411yescharacteristic
86C8×D53#4111yescharacteristic
87C8×D53C2411yescharacteristic
88#11719910—22no—
89C16×C53C22×C412yescomplemented
90#11719908C22×C412yescomplemented
91C23×C53—42no—
92C22×D53—42no—
93C22×D53—44no—
94C22×D53—44no—
95C22×D53—84no—
96C22×D53—84no—
97C22×D53C2×D811yescharacteristic
98C2×#6157—24no—
99C2×#6157—44no—
100C2×#6157—816no—
101C2×#6157—84no—
102C2×#6157C2×D814yes—
103D4×C53—24no—
104D4×C53—42no—
105C2×C4×C53C4×D411yescharacteristic
106C22⋊D53—44no—
107C22⋊D53—44no—
108C2×Dic53#13511yescharacteristic
109D212—24no—
110D212—42no—
111C4×D53C4×D411yescharacteristic
112C4×D53C2×D811yescharacteristic
113C4×D53#13511yescharacteristic
114C4×D53C22×D411yescharacteristic
115#88324—22no—
116C8×C53C4×D411yescharacteristic
117C8×C53C23×C411yescharacteristic
118#88322C4×D411yescharacteristic
119#88322C2×#4111yescharacteristic
120C2×#2177—531nomaximal, Sylow
121C22×C53—44no—
122C22×C53—84no—
123C22×C53C4×D811yescharacteristic
124C2×D53—44no—
125C2×D53—84no—
126C2×D53—84no—
127C2×D53—84no—
128C2×D53—88no—
129C2×D53C4×D811yescharacteristic
130C2×D53#50914yes—
131C2×D53C22×D811yescharacteristic
132#6157—24no—
133#6157—84no—
134C4×C53C4×D811yescharacteristic
135C4×C53C2×C4×D411yescharacteristic
136Dic53C4×D811yescharacteristic
137Dic53C2×#13511yescharacteristic
138C22×D16—531no—
139C2×C4×D8—532no—
140#2177—538no—
141C2×#367—531no—
142C2×#357—532no—
143C2×#346—531no—
144C2×C53—84no—
145C2×C53#217712yescomplemented
146C2×C53C2×C4×D811yescharacteristic
147D53—84no—
148D53#217712yescomplemented
149D53C2×#50912yes—
150C22×D8—532no—
151C2×C4×D4—1062no—
152C2×D16—532no—
153C2×D16—534no—
154C2×D16—534no—
155C2×D16—531no—
156C2×D16#615711yescharacteristic, complemented
157C22×C16—531no—
158C22×C16—531no—
159C4×D8—538no—
160C4×D8—1064no—
161C2×#107—532no—
162C2×#102—1062no—
163C2×C4×C8—531no—
164#367—534no—
165#357—538no—
166#346—534no—
167C53C2×#217711yescharacteristic, complemented, Sylow
168C22×D4—1062no—
169C23×C4—2122no—
170C2×D8—534no—
171C2×D8—534no—
172C2×D8—532no—
173C2×D8—1062no—
174C2×D8—1062no—
175C2×D8—1062no—
176C2×D8C2×#615712yescomplemented
177C22×C8—531no—
178C22×C8—531no—
179C4×D4—1068no—
180C4×D4—2124no—
181C2×C4⋊C4—1062no—
182C2×C22⋊C4—2122no—
183C2×C42—531no—
184D16—538no—
185D16—534no—
186D16C2×#615714yescomplemented
187C2×C16—531no—
188C2×C16—532no—
189C2×C16—532no—
190C2×C16—532no—
191C2×C16—1061no—
192C2×C16—1061no—
193C2×C16C2×#615711yescharacteristic, complemented
194#107—534no—
195#107—1062no—
196#102—1068no—
197C4×C8—532no—
198C4×C8—532no—
199C24—2122no—
200C2×D4—22no—
201C2×D4—1064no—
202C2×D4—1064no—
203C2×D4—1062no—
204C2×D4—2122no—
205C2×D4—2122no—
206C2×D4—2122no—
207C22×C4—531no—
208C22×C4—532no—
209C22×C4—4248no—
210C22×C4—2128no—
211C22×C4—2122no—
212D8—22no—
213D8—534no—
214D8—1064no—
215D8—1064no—
216D8—1062no—
217D8C22×#615714yescomplemented
218C2×C8—531no—
219C2×C8—531no—
220C2×C8—531no—
221C2×C8—531no—
222C2×C8—531no—
223C2×C8—532no—
224C2×C8—1061no—
225C2×C8—1061no—
226C2×C8C22×#615711yescharacteristic
227C4⋊C4—1064no—
228C4⋊C4—2122no—
229C22⋊C4—2128no—
230C42—532no—
231C42—532no—
232C16—532no—
233C16—1062no—
234C16C22×#615712yescomplemented
235C23—42no—
236C23—531no—
237C23—4244no—
238C23—4244no—
239C23—2124no—
240C23—2124no—
241C23—2122no—
242D4—24no—
243D4—42no—
244D4—1064no—
245D4—2124no—
246D4—2124no—
247D4—2122no—
248C2×C4—531no—
249C2×C4—531no—
250C2×C4—531no—
251C2×C4—531no—
252C2×C4—531no—
253C2×C4—534no—
254C2×C4—1064no—
255C2×C4—42416no—
256C2×C4—4244no—
257C2×C4—2124no—
258C2×C4D4×#615711yescharacteristic
259C8—531no—
260C8—531no—
261C8—1062no—
262C8D4×#615711yescharacteristic
263C8C23×#615711yescharacteristic
264C22—44no—
265C22—84no—
266C22—534no—
267C22—531no—
268C22—531no—
269C22—4244no—
270C22—4244no—
271C22—4248no—
272C22—4244no—
273C22—2124no—
274C22D8×#615711yescharacteristic
275C4—531no—
276C4—531no—
277C4—1064no—
278C4—4244no—
279C4D8×#615711yescharacteristic
280C4C2×D4×#615711yescharacteristic
281C2—84no—
282C2—532no—
283C2—532no—
284C2—4244no—
285C2#2029111312yesdirect product factor
286C2C2×D8×#615711yescharacteristic
subgroupG/H
centerC22D8×#6157
commutatorC8×C53C23×C4
FrattiniC8C23×#6157
FittingC2×D16×C53C4
socleC22×C53C4×D8
prime radicalC2×D16×D53C2
cosocleC8×D53C24
hypercenterC2×D16#6157
hypocenterC53C2×#2177
LCSG ▷ C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53
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×#6157C2semidirect
2. #20291113C2direct (N × H)
3. C2×#16811550C2semidirect
4. C2×#16811535C2semidirect
5. C2×#16811510C2semidirect
10. D8×#6157C22semidirect
14. #16811550C22semidirect
15. #16811535C22semidirect
16. #16811510C22semidirect
18. C2×D848C4semidirect
19. C2×#13133158C4semidirect
20. D16×D53C4semidirect
23. C2×D16×C53C4semidirect
40. C2×D424C2×C4semidirect
44. D8×D53C2×C4semidirect
47. D848C2×C4semidirect
48. #13133158C2×C4semidirect
49. C2×#11719908C2×C4semidirect
50. C16×D53C2×C4semidirect
52. C2×D8×C53C2×C4semidirect
53. D16×C53C2×C4semidirect
54. C2×C16×C53C2×C4semidirect
77. D8×C53C22×C4semidirect
83. D424C22×C4semidirect
89. C16×C53C22×C4semidirect
90. #11719908C22×C4semidirect
145. C2×C53#2177semidirect
148. D53#2177semidirect
156. C2×D16#6157semidirect
167. C53C2×#2177semidirect
176. C2×D8C2×#6157semidirect
186. D16C2×#6157semidirect
193. C2×C16C2×#6157semidirect
217. D8C22×#6157semidirect
234. C16C22×#6157semidirect
285. C2#20291113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D8×#61572
#202911132
C2×#168115502
C2×#168115352
C2×#168115102
C2×D16×D532
C2×#217753