Finite Group Databasebeta

← C2×SD16×#595 #14545532

Subgroups — C2×SD16×#595 #14545532

Order 2176.

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×#595C211yesmaximal, characteristic, complemented
2C2×D4×#595C211yesmaximal, characteristic
3SD16×#595C218yesmaximal, direct product factor
4C2×#10587533C211yesmaximal, characteristic, complemented
5C2×#10587549C211yesmaximal, characteristic, complemented
6C2×#10587547C211yesmaximal, characteristic
7C2×C8×#595C211yesmaximal, characteristic, complemented
8C2×SD16×D17C211yesmaximal, characteristic
9C23×#595—21no—
10C2×Q8×D17C2211yescharacteristic
11C2×D4×D17C2211yescharacteristic
12C2×C22⋊#595—21no—
13Q8×#595—22no—
14Q8×#595C2214yescomplemented
15D4×#595—22no—
16D4×#595C2214yes—
17C2×C4⋊#595—21no—
18C2×C4⋊#595C2211yescharacteristic
19C2×C4⋊#595C2211yescharacteristic
20C2×C4×#595—21no—
21C2×C4×#595C2211yescharacteristic
22C2×#63242C2211yescharacteristic
23C2×SD16×C17C411yescharacteristic, complemented
24C2×#63230C411yescharacteristic, complemented
25C2×#63229C411yescharacteristic, complemented
26SD16×D17C414yescomplemented
27SD16×D17C2214yes—
28C2×#63219C411yescharacteristic, complemented
29C2×C8×D17C2211yescharacteristic
30#10587549C2214yescomplemented
31#10587547C2214yes—
32#10587533C2214yescomplemented
33C8×#595C2214yescomplemented
34C23×D17—21no—
35C22×#595—21no—
36C22×#595—21no—
37C22×#595—24no—
38C22×#595—44no—
39C22×#595D411yescharacteristic
40C22×#595D411yescharacteristic
41C2×Q8×C17C2×C411yescharacteristic, complemented
42C2×D4×C17C2×C411yescharacteristic
43C2×C22⋊D17—21no—
44Q8×D17—21no—
45Q8×D17—21no—
46Q8×D17C2×C412yescomplemented
47Q8×D17C2312yes—
48D4×D17—21no—
49D4×D17—21no—
50D4×D17C2×C412yes—
51D4×D17C2312yes—
52C2×D68C2×C411yescharacteristic
53C2×C4×D17—21no—
54C2×C4×D17C2311yescharacteristic
55C2×Dic34—21no—
56C2×Dic34C2×C411yescharacteristic, complemented
57C22⋊#595—24no—
58C2×#3624—21no—
59C4⋊#595—24no—
60C4⋊#595—21no—
61C4⋊#595—21no—
62C4⋊#595C2312yes—
63C4⋊#595C2312yes—
64C4×#595—24no—
65C4×#595D412yes—
66C4×#595C2312yes—
67#63242—21no—
68#63242C2312yes—
69SD16×C17C2×C414yescomplemented
70C2×C8×C17C2×C411yescharacteristic, complemented
71#63230C2×C414yescomplemented
72#63229C2×C414yescomplemented
73C2×#3622C2×C411yescharacteristic, complemented
74#63219C2×C414yescomplemented
75C8×D17C2×C412yescomplemented
76C8×D17C2312yes—
77C23×C17—21no—
78C22×D17—21no—
79C22×D17—22no—
80C22×D17—22no—
81C22×D17—42no—
82C22×D17—42no—
83C22×D17C2×D411yescharacteristic
84C2×#595—22no—
85C2×#595—22no—
86C2×#595—22no—
87C2×#595—42no—
88C2×#595—42no—
89C2×#595—48no—
90C2×#595SD1614yesdirect product factor
91C2×#595C2×D412yes—
92C2×#595C2×D412yes—
93Q8×C17—21no—
94Q8×C17C22×C412yescomplemented
95D4×C17—21no—
96D4×C17C22×C412yes—
97C2×C4×C17—21no—
98C2×C4×C17C22×C411yescharacteristic
99C22⋊D17—22no—
100C22⋊D17—22no—
101C2×Dic17—21no—
102C2×Dic17#4111yescharacteristic
103D68—21no—
104D68C22×C412yes—
105C4×D17—22no—
106C4×D17—22no—
107C4×D17C22×C411yescharacteristic
108C4×D17C2×D411yescharacteristic
109C4×D17#4111yescharacteristic
110C4×D17C2411yescharacteristic
111Dic34—21no—
112Dic34—22no—
113Dic34—22no—
114Dic34C22×C412yescomplemented
115#3624—22no—
116C8×C17C22×C412yescomplemented
117#3622C22×C412yescomplemented
118C2×C4×SD16—171nomaximal, Sylow
119C22×C17—22no—
120C22×C17—42no—
121C22×C17C4×D411yescharacteristic
122C2×D17—22no—
123C2×D17—42no—
124C2×D17—42no—
125C2×D17—42no—
126C2×D17—44no—
127C2×D17C4×D411yescharacteristic
128C2×D17C2×SD1612yes—
129C2×D17#13512yes—
130C2×D17C22×D411yescharacteristic
131#595—22no—
132#595—42no—
133#595—42no—
134#595C2×SD1614yesdirect product factor
135C4×C17—22no—
136C4×C17C4×D411yescharacteristic
137C4×C17C23×C411yescharacteristic
138Dic17—22no—
139Dic17C4×D411yescharacteristic
140Dic17C2×#4111yescharacteristic
141C22×SD16—171no—
142C2×C4×Q8—171no—
143C2×C4×D4—171no—
144C4×SD16—178no—
145C2×#106—171no—
146C2×#103—171no—
147C2×#102—171no—
148C2×C4×C8—171no—
149C2×C17—42no—
150C2×C17C4×SD1612yescomplemented
151C2×C17C2×C4×D411yescharacteristic
152D17—42no—
153D17C4×SD1612yescomplemented
154D17C22×SD1611yescharacteristic
155D17C2×#13511yescharacteristic
156C22×Q8—171no—
157C22×D4—171no—
158C23×C4—341no—
159C2×SD16—171no—
160C2×SD16—171no—
161C2×SD16—174no—
162C2×SD16—174no—
163C2×SD16—171no—
164C2×SD16#59511yescharacteristic, direct product factor
165C22×C8—171no—
166C22×C8—171no—
167C4×Q8—174no—
168C4×Q8—342no—
169C4×D4—174no—
170C4×D4—342no—
171C2×C4⋊C4—171no—
172C2×C4⋊C4—171no—
173C2×C4⋊C4—341no—
174C2×C22⋊C4—341no—
175C2×C42—171no—
176C2×C42—341no—
177#106—174no—
178#103—174no—
179#102—174no—
180C4×C8—174no—
181C17C2×C4×SD1611yescharacteristic, complemented, Sylow
182C24—341no—
183C2×Q8—172no—
184C2×Q8—172no—
185C2×Q8—171no—
186C2×Q8—341no—
187C2×Q8—341no—
188C2×Q8—341no—
189C2×Q8C2×#59511yescharacteristic, complemented
190C2×D4—172no—
191C2×D4—172no—
192C2×D4—171no—
193C2×D4—341no—
194C2×D4—341no—
195C2×D4—341no—
196C2×D4C2×#59511yescharacteristic
197C22×C4—171no—
198C22×C4—171no—
199C22×C4—171no—
200C22×C4—341no—
201C22×C4—344no—
202C22×C4—341no—
203C22×C4—341no—
204C22×C4—684no—
205SD16—174no—
206SD16—174no—
207SD16—174no—
208SD16C2×#59514yesdirect product factor
209C2×C8—171no—
210C2×C8—172no—
211C2×C8—172no—
212C2×C8—172no—
213C2×C8—341no—
214C2×C8—341no—
215C2×C8C2×#59511yescharacteristic, complemented
216C4⋊C4—172no—
217C4⋊C4—172no—
218C4⋊C4—341no—
219C4⋊C4—341no—
220C4⋊C4—344no—
221C22⋊C4—344no—
222C42—172no—
223C42—172no—
224C42—344no—
225C23—21no—
226C23—171no—
227C23—342no—
228C23—342no—
229C23—341no—
230C23—682no—
231C23—682no—
232Q8—21no—
233Q8—172no—
234Q8—342no—
235Q8—342no—
236Q8—341no—
237Q8C22×#59512yescomplemented
238D4—21no—
239D4—172no—
240D4—342no—
241D4—342no—
242D4—341no—
243D4C22×#59512yes—
244C2×C4—21no—
245C2×C4—172no—
246C2×C4—174no—
247C2×C4—171no—
248C2×C4—171no—
249C2×C4—171no—
250C2×C4—171no—
251C2×C4—171no—
252C2×C4—172no—
253C2×C4—342no—
254C2×C4—342no—
255C2×C4—342no—
256C2×C4—341no—
257C2×C4—342no—
258C2×C4—342no—
259C2×C4—688no—
260C2×C4—682no—
261C2×C4—682no—
262C2×C4C22×#59511yescharacteristic
263C8—172no—
264C8—342no—
265C8C22×#59512yescomplemented
266C22—22no—
267C22—42no—
268C22—172no—
269C22—172no—
270C22—171no—
271C22—171no—
272C22—342no—
273C22—682no—
274C22—682no—
275C22—684no—
276C22—682no—
277C22D4×#59511yescharacteristic
278C4—22no—
279C4—174no—
280C4—171no—
281C4—171no—
282C4—342no—
283C4—342no—
284C4—682no—
285C4—682no—
286C4D4×#59511yescharacteristic
287C4C23×#59511yescharacteristic
288C2—42no—
289C2—171no—
290C2—171no—
291C2—172no—
292C2—682no—
293C2SD16×#59512yesdirect product factor
294C2C2×D4×#59511yescharacteristic
subgroupG/H
centerC22D4×#595
commutatorC4×C17C23×C4
FrattiniC4C23×#595
FittingC2×SD16×C17C4
socleC22×C17C4×D4
prime radicalC2×D4×D17C22
cosocleC4×D17C24
hypercenterC2×SD16#595
hypocenterC17C2×C4×SD16
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#595C2semidirect
3. SD16×#595C2direct (N × H)
4. C2×#10587533C2semidirect
5. C2×#10587549C2semidirect
7. C2×C8×#595C2semidirect
14. Q8×#595C22semidirect
23. C2×SD16×C17C4semidirect
24. C2×#63230C4semidirect
25. C2×#63229C4semidirect
26. SD16×D17C4semidirect
28. C2×#63219C4semidirect
30. #10587549C22semidirect
32. #10587533C22semidirect
33. C8×#595C22semidirect
41. C2×Q8×C17C2×C4semidirect
46. Q8×D17C2×C4semidirect
56. C2×Dic34C2×C4semidirect
69. SD16×C17C2×C4semidirect
70. C2×C8×C17C2×C4semidirect
71. #63230C2×C4semidirect
72. #63229C2×C4semidirect
73. C2×#3622C2×C4semidirect
74. #63219C2×C4semidirect
75. C8×D17C2×C4semidirect
90. C2×#595SD16direct (N × H)
94. Q8×C17C22×C4semidirect
114. Dic34C22×C4semidirect
116. C8×C17C22×C4semidirect
117. #3622C22×C4semidirect
134. #595C2×SD16direct (N × H)
150. C2×C17C4×SD16semidirect
153. D17C4×SD16semidirect
164. C2×SD16#595direct (N × H)
181. C17C2×C4×SD16semidirect
189. C2×Q8C2×#595semidirect
208. SD16C2×#595direct (N × H)
215. C2×C8C2×#595semidirect
237. Q8C22×#595semidirect
265. C8C22×#595semidirect
293. C2SD16×#595direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×#5952
C2×D4×#5952
SD16×#5952
C2×#105875332
C2×#105875492
C2×#105875472
C2×C8×#5952
C2×SD16×D172
C2×C4×SD1617