Finite Group Databasebeta

← C2×SD16×#10587739 #31797537

Subgroups — C2×SD16×#10587739 #31797537

Order 17536.

552 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 178 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×Q8×#10587739C211yesmaximal, characteristic, complemented
2C2×D4×#10587739C211yesmaximal, characteristic
3SD16×#10587739C218yesmaximal, direct product factor
4C2×#17984156C211yesmaximal, characteristic, complemented
5C2×#17984151C211yesmaximal, characteristic, complemented
6C2×#17984150C211yesmaximal, characteristic
7C2×C8×#10587739C211yesmaximal, characteristic, complemented
8C2×SD16×D137C211yesmaximal, characteristic
9C23×#10587739—21no—
10C2×#14555518C2211yescharacteristic
11Q8×#10587739—22no—
12Q8×#10587739C2214yescomplemented
13D4×#10587739—22no—
14D4×#10587739C2214yes—
15C2×C4⋊#10587739—21no—
16C2×C4⋊#10587739C2211yescharacteristic
17C2×C4⋊#10587739C2211yescharacteristic
18C2×C22⋊#10587739—21no—
19C2×C4×#10587739—21no—
20C2×C4×#10587739C2211yescharacteristic
21#17984156C2214yescomplemented
22#17984151C2214yescomplemented
23#17984150C2214yes—
24C8×#10587739C2214yescomplemented
25C2×Q8×D137C2211yescharacteristic
26C2×D4×D137C2211yescharacteristic
27C2×#14555499C411yescharacteristic, complemented
28C2×#14555498C411yescharacteristic, complemented
29C2×#14555497C411yescharacteristic, complemented
30SD16×D137C414yescomplemented
31SD16×D137C2214yes—
32C2×C8×D137C2211yescharacteristic
33C2×SD16×C137C411yescharacteristic, complemented
34C22×#10587739—24no—
35C22×#10587739—21no—
36C22×#10587739—21no—
37C22×#10587739—44no—
38C22×#10587739D411yescharacteristic
39C22×#10587739D411yescharacteristic
40#14555518—21no—
41#14555518C2312yes—
42C2×#11764047—21no—
43C4⋊#10587739—24no—
44C4⋊#10587739—21no—
45C4⋊#10587739—21no—
46C4⋊#10587739C2312yes—
47C4⋊#10587739C2312yes—
48C22⋊#10587739—24no—
49C4×#10587739—24no—
50C4×#10587739D412yes—
51C4×#10587739C2312yes—
52C23×D137—21no—
53C2×Dic274—21no—
54C2×Dic274C2×C411yescharacteristic, complemented
55Q8×D137—21no—
56Q8×D137—21no—
57Q8×D137C2×C412yescomplemented
58Q8×D137C2312yes—
59C2×D548C2×C411yescharacteristic
60C2×C22⋊D137—21no—
61D4×D137—21no—
62D4×D137—21no—
63D4×D137C2×C412yes—
64D4×D137C2312yes—
65C2×C4×D137—21no—
66C2×C4×D137C2311yescharacteristic
67#14555499C2×C414yescomplemented
68#14555498C2×C414yescomplemented
69#14555497C2×C414yescomplemented
70C2×#11764040C2×C411yescharacteristic, complemented
71C8×D137C2×C412yescomplemented
72C8×D137C2312yes—
73C2×Q8×C137C2×C411yescharacteristic, complemented
74C2×D4×C137C2×C411yescharacteristic
75SD16×C137C2×C414yescomplemented
76C2×C8×C137C2×C411yescharacteristic, complemented
77C2×#10587739—22no—
78C2×#10587739—22no—
79C2×#10587739—22no—
80C2×#10587739—42no—
81C2×#10587739—42no—
82C2×#10587739—48no—
83C2×#10587739SD1614yesdirect product factor
84C2×#10587739C2×D412yes—
85C2×#10587739C2×D412yes—
86#11764047—22no—
87C22×D137—21no—
88C22×D137—22no—
89C22×D137—22no—
90C22×D137—42no—
91C22×D137—42no—
92C22×D137C2×D411yescharacteristic
93Dic274—21no—
94Dic274—22no—
95Dic274—22no—
96Dic274C22×C412yescomplemented
97D548—21no—
98D548C22×C412yes—
99C22⋊D137—22no—
100C22⋊D137—22no—
101C2×Dic137—21no—
102C2×Dic137#4111yescharacteristic
103C4×D137—22no—
104C4×D137—22no—
105C4×D137C22×C411yescharacteristic
106C4×D137C2×D411yescharacteristic
107C4×D137#4111yescharacteristic
108C4×D137C2411yescharacteristic
109#11764040C22×C412yescomplemented
110C23×C137—21no—
111Q8×C137—21no—
112Q8×C137C22×C412yescomplemented
113D4×C137—21no—
114D4×C137C22×C412yes—
115C2×C4×C137—21no—
116C2×C4×C137C22×C411yescharacteristic
117C8×C137C22×C412yescomplemented
118C22×C137—22no—
119C22×C137—42no—
120C22×C137C4×D411yescharacteristic
121C2×D137—22no—
122C2×D137—42no—
123C2×D137—42no—
124C2×D137—42no—
125C2×D137—44no—
126C2×D137C4×D411yescharacteristic
127C2×D137C2×SD1612yes—
128C2×D137#13512yes—
129C2×D137C22×D411yescharacteristic
130#10587739—22no—
131#10587739—42no—
132#10587739—42no—
133#10587739C2×SD1614yesdirect product factor
134C4×C137—22no—
135C4×C137C4×D411yescharacteristic
136C4×C137C23×C411yescharacteristic
137Dic137—22no—
138Dic137C4×D411yescharacteristic
139Dic137C2×#4111yescharacteristic
140C2×C137—42no—
141C2×C137C4×SD1612yescomplemented
142C2×C137C2×C4×D411yescharacteristic
143D137—42no—
144D137C4×SD1612yescomplemented
145D137C22×SD1611yescharacteristic
146D137C2×#13511yescharacteristic
147C137C2×C4×SD1611yescharacteristic, complemented, Sylow
148C2×C4×SD16—1371nomaximal, Sylow
149C22×SD16—1371no—
150C2×C4×Q8—1371no—
151C2×C4×D4—1371no—
152C4×SD16—1378no—
153C2×#106—1371no—
154C2×#103—1371no—
155C2×#102—1371no—
156C2×C4×C8—1371no—
157C22×Q8—1371no—
158C22×D4—1371no—
159C23×C4—2741no—
160C2×SD16—1371no—
161C2×SD16—1371no—
162C2×SD16—1374no—
163C2×SD16—1374no—
164C2×SD16—1371no—
165C2×SD16#1058773911yescharacteristic, direct product factor
166C22×C8—1371no—
167C22×C8—1371no—
168C4×Q8—2742no—
169C4×Q8—1374no—
170C4×D4—2742no—
171C4×D4—1374no—
172C2×C4⋊C4—2741no—
173C2×C4⋊C4—1371no—
174C2×C4⋊C4—1371no—
175C2×C22⋊C4—2741no—
176C2×C42—2741no—
177C2×C42—1371no—
178#106—1374no—
179#103—1374no—
180#102—1374no—
181C4×C8—1374no—
182C24—2741no—
183C2×Q8—2741no—
184C2×Q8—2741no—
185C2×Q8—2741no—
186C2×Q8—1372no—
187C2×Q8—1372no—
188C2×Q8—1371no—
189C2×Q8C2×#1058773911yescharacteristic, complemented
190C2×D4—2741no—
191C2×D4—2741no—
192C2×D4—2741no—
193C2×D4—1372no—
194C2×D4—1372no—
195C2×D4—1371no—
196C2×D4C2×#1058773911yescharacteristic
197C22×C4—2741no—
198C22×C4—2741no—
199C22×C4—2741no—
200C22×C4—2744no—
201C22×C4—5484no—
202C22×C4—1371no—
203C22×C4—1371no—
204C22×C4—1371no—
205SD16—1374no—
206SD16—1374no—
207SD16—1374no—
208SD16C2×#1058773914yesdirect product factor
209C2×C8—2741no—
210C2×C8—2741no—
211C2×C8—1372no—
212C2×C8—1371no—
213C2×C8—1372no—
214C2×C8—1372no—
215C2×C8C2×#1058773911yescharacteristic, complemented
216C4⋊C4—2744no—
217C4⋊C4—2741no—
218C4⋊C4—2741no—
219C4⋊C4—1372no—
220C4⋊C4—1372no—
221C22⋊C4—2744no—
222C42—2744no—
223C42—1372no—
224C42—1372no—
225C23—21no—
226C23—2742no—
227C23—2742no—
228C23—2741no—
229C23—5482no—
230C23—5482no—
231C23—1371no—
232Q8—21no—
233Q8—2742no—
234Q8—2742no—
235Q8—2741no—
236Q8—1372no—
237Q8C22×#1058773912yescomplemented
238D4—21no—
239D4—2742no—
240D4—2742no—
241D4—2741no—
242D4—1372no—
243D4C22×#1058773912yes—
244C2×C4—21no—
245C2×C4—2742no—
246C2×C4—2742no—
247C2×C4—2742no—
248C2×C4—2741no—
249C2×C4—2742no—
250C2×C4—2742no—
251C2×C4—5482no—
252C2×C4—5482no—
253C2×C4—5488no—
254C2×C4—1372no—
255C2×C4—1372no—
256C2×C4—1374no—
257C2×C4—1371no—
258C2×C4—1371no—
259C2×C4—1371no—
260C2×C4—1371no—
261C2×C4—1371no—
262C2×C4C22×#1058773911yescharacteristic
263C8—2742no—
264C8—1372no—
265C8C22×#1058773912yescomplemented
266C22—22no—
267C22—42no—
268C22—2742no—
269C22—5482no—
270C22—5482no—
271C22—5484no—
272C22—5482no—
273C22—1372no—
274C22—1372no—
275C22—1371no—
276C22—1371no—
277C22D4×#1058773911yescharacteristic
278C4—22no—
279C4—2742no—
280C4—2742no—
281C4—5482no—
282C4—5482no—
283C4—1374no—
284C4—1371no—
285C4—1371no—
286C4D4×#1058773911yescharacteristic
287C4C23×#1058773911yescharacteristic
288C2—42no—
289C2—5482no—
290C2—1371no—
291C2—1371no—
292C2—1372no—
293C2SD16×#1058773912yesdirect product factor
294C2C2×D4×#1058773911yescharacteristic
subgroupG/H
centerC22D4×#10587739
commutatorC4×C137C23×C4
FrattiniC4C23×#10587739
FittingC2×SD16×C137C4
socleC22×C137C4×D4
prime radicalC2×D4×D137C22
cosocleC4×D137C24
hypercenterC2×SD16#10587739
hypocenterC137C2×C4×SD16
LCSG ▷ C4×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#10587739C2semidirect
3. SD16×#10587739C2direct (N × H)
4. C2×#17984156C2semidirect
5. C2×#17984151C2semidirect
7. C2×C8×#10587739C2semidirect
12. Q8×#10587739C22semidirect
21. #17984156C22semidirect
22. #17984151C22semidirect
24. C8×#10587739C22semidirect
27. C2×#14555499C4semidirect
28. C2×#14555498C4semidirect
29. C2×#14555497C4semidirect
30. SD16×D137C4semidirect
33. C2×SD16×C137C4semidirect
54. C2×Dic274C2×C4semidirect
57. Q8×D137C2×C4semidirect
67. #14555499C2×C4semidirect
68. #14555498C2×C4semidirect
69. #14555497C2×C4semidirect
70. C2×#11764040C2×C4semidirect
71. C8×D137C2×C4semidirect
73. C2×Q8×C137C2×C4semidirect
75. SD16×C137C2×C4semidirect
76. C2×C8×C137C2×C4semidirect
83. C2×#10587739SD16direct (N × H)
96. Dic274C22×C4semidirect
109. #11764040C22×C4semidirect
112. Q8×C137C22×C4semidirect
117. C8×C137C22×C4semidirect
133. #10587739C2×SD16direct (N × H)
141. C2×C137C4×SD16semidirect
144. D137C4×SD16semidirect
147. C137C2×C4×SD16semidirect
165. C2×SD16#10587739direct (N × H)
189. C2×Q8C2×#10587739semidirect
208. SD16C2×#10587739direct (N × H)
215. C2×C8C2×#10587739semidirect
237. Q8C22×#10587739semidirect
265. C8C22×#10587739semidirect
293. C2SD16×#10587739direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×#105877392
C2×D4×#105877392
SD16×#105877392
C2×#179841562
C2×#179841512
C2×#179841502
C2×C8×#105877392
C2×SD16×D1372
C2×C4×SD16137