Finite Group Databasebeta

← C2×#20299637 #28407325

Subgroups — C2×#20299637 #28407325

Order 14464.

544 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 170 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×#90673C211yesmaximal, characteristic, complemented
2C2×D4×#90673C211yesmaximal, characteristic
3#20299637C218yesmaximal, direct product factor
4C2×#16813691C211yesmaximal, characteristic, complemented
5C2×#16813685C211yesmaximal, characteristic, complemented
6C2×#16813684C211yesmaximal, characteristic
7C2×#16813676C211yesmaximal, characteristic, complemented
8C2×SD16×D113C211yesmaximal, characteristic
9C23×#90673—21no—
10C2×#14268655C2211yescharacteristic
11Q8×#90673—22no—
12Q8×#90673C2214yescomplemented
13D4×#90673—22no—
14D4×#90673C2214yes—
15C2×C4⋊#90673—21no—
16C2×C4⋊#90673C2211yescharacteristic
17C2×C4⋊#90673C2211yescharacteristic
18C2×C22⋊#90673—21no—
19C2×C4×#90673—21no—
20C2×C4×#90673C2211yescharacteristic
21#16813691C2214yescomplemented
22#16813685C2214yescomplemented
23#16813684C2214yes—
24#16813676C2214yescomplemented
25C2×Q8×D113C2211yescharacteristic
26C2×D4×D113C2211yescharacteristic
27C2×#14268636C411yescharacteristic, complemented
28C2×#14268635C411yescharacteristic, complemented
29C2×#14268634C411yescharacteristic, complemented
30SD16×D113C414yescomplemented
31SD16×D113C2214yes—
32C2×C8×D113C2211yescharacteristic
33C2×SD16×C113C411yescharacteristic, complemented
34C22×#90673—21no—
35C22×#90673—21no—
36C22×#90673—24no—
37C22×#90673—44no—
38C22×#90673D411yescharacteristic
39C22×#90673D411yescharacteristic
40#14268655—21no—
41#14268655C2312yes—
42C2×#11744753—21no—
43C4⋊#90673—24no—
44C4⋊#90673—21no—
45C4⋊#90673—21no—
46C4⋊#90673C2312yes—
47C4⋊#90673C2312yes—
48C22⋊#90673—24no—
49C4×#90673—24no—
50C4×#90673D412yes—
51C4×#90673C2312yes—
52C23×D113—21no—
53C2×Dic226—21no—
54C2×Dic226C2×C411yescharacteristic, complemented
55Q8×D113—21no—
56Q8×D113—21no—
57Q8×D113C2×C412yescomplemented
58Q8×D113C2312yes—
59C2×D452C2×C411yescharacteristic
60C2×C22⋊D113—21no—
61D4×D113—21no—
62D4×D113—21no—
63D4×D113C2×C412yes—
64D4×D113C2312yes—
65C2×C4×D113—21no—
66C2×C4×D113C2311yescharacteristic
67#14268636C2×C414yescomplemented
68#14268635C2×C414yescomplemented
69#14268634C2×C414yescomplemented
70C2×#11744751C2×C411yescharacteristic, complemented
71C8×D113C2×C412yescomplemented
72C8×D113C2312yes—
73C2×Q8×C113C2×C411yescharacteristic, complemented
74C2×D4×C113C2×C411yescharacteristic
75SD16×C113C2×C414yescomplemented
76C2×C8×C113C2×C411yescharacteristic, complemented
77C23×C113—21no—
78C22×D113—21no—
79C22×D113—22no—
80C22×D113—22no—
81C22×D113—42no—
82C22×D113—42no—
83C22×D113C2×D411yescharacteristic
84C2×#90673—22no—
85C2×#90673—22no—
86C2×#90673—22no—
87C2×#90673—22no—
88C2×#90673—48no—
89C2×#90673—42no—
90C2×#90673—42no—
91C2×#90673C2×D412yes—
92C2×#90673C2×D412yes—
93Q8×C113—21no—
94Q8×C113C22×C412yescomplemented
95D4×C113—21no—
96D4×C113C22×C412yes—
97C2×C4×C113—21no—
98C2×C4×C113C22×C411yescharacteristic
99C22⋊D113—22no—
100C22⋊D113—22no—
101C2×Dic113—21no—
102C2×Dic113#4111yescharacteristic
103D452—21no—
104D452C22×C412yes—
105C4×D113—22no—
106C4×D113—22no—
107C4×D113C22×C411yescharacteristic
108C4×D113C2×D411yescharacteristic
109C4×D113#4111yescharacteristic
110C4×D113C2411yescharacteristic
111Dic226—21no—
112Dic226—22no—
113Dic226—22no—
114Dic226C22×C412yescomplemented
115#11744753—22no—
116C8×C113C22×C412yescomplemented
117#11744751C22×C412yescomplemented
118C22×C113—22no—
119C22×C113—42no—
120C22×C113C4×D411yescharacteristic
121C2×D113—22no—
122C2×D113—42no—
123C2×D113—42no—
124C2×D113—42no—
125C2×D113—44no—
126C2×D113C4×D411yescharacteristic
127C2×D113AGL(1,ℤ/8)12yes—
128C2×D113#13712yes—
129C2×D113C22×D411yescharacteristic
130#90673—22no—
131#90673—22no—
132#90673—42no—
133#90673—42no—
134C4×C113—22no—
135C4×C113C4×D411yescharacteristic
136C4×C113C23×C411yescharacteristic
137Dic113—22no—
138Dic113C4×D411yescharacteristic
139Dic113C2×#4111yescharacteristic
140C2×C113—42no—
141C2×C113#44012yescomplemented
142C2×C113C2×C4×D411yescharacteristic
143D113—42no—
144D113#44012yescomplemented
145D113C2×AGL(1,ℤ/8)11yescharacteristic
146D113C2×#13711yescharacteristic
147C2×#440—1131nomaximal, Sylow
148C113C2×#44011yescharacteristic, complemented, Sylow
149C22×SD16—1131no—
150C2×C4×Q8—1131no—
151C2×C4×D4—1131no—
152#440—1138no—
153C2×#107—1131no—
154C2×#103—1131no—
155C2×#102—1131no—
156C2×#97—1131no—
157C22×Q8—1131no—
158C22×D4—1131no—
159C23×C4—2261no—
160C2×SD16—1131no—
161C2×SD16—1131no—
162C2×SD16—1134no—
163C2×SD16—1134no—
164C2×SD16—1131no—
165C2×SD16#9067311yescharacteristic, complemented
166C22×C8—1131no—
167C22×C8—1131no—
168C4×Q8—1134no—
169C4×Q8—2262no—
170C4×D4—1134no—
171C4×D4—2262no—
172C2×C4⋊C4—1131no—
173C2×C4⋊C4—1131no—
174C2×C4⋊C4—2261no—
175C2×C22⋊C4—2261no—
176C2×C42—1131no—
177C2×C42—2261no—
178#107—1134no—
179#103—1134no—
180#102—1134no—
181#97—1134no—
182C24—2261no—
183C2×Q8—1132no—
184C2×Q8—1132no—
185C2×Q8—1131no—
186C2×Q8—2261no—
187C2×Q8—2261no—
188C2×Q8—2261no—
189C2×Q8C2×#9067311yescharacteristic, complemented
190C2×D4—1132no—
191C2×D4—1132no—
192C2×D4—1131no—
193C2×D4—2261no—
194C2×D4—2261no—
195C2×D4—2261no—
196C2×D4C2×#9067311yescharacteristic
197C22×C4—1131no—
198C22×C4—1131no—
199C22×C4—1131no—
200C22×C4—4524no—
201C22×C4—2261no—
202C22×C4—2264no—
203C22×C4—2261no—
204C22×C4—2261no—
205SD16—1134no—
206SD16—1134no—
207SD16—1134no—
208SD16C2×#9067314yescomplemented
209C2×C8—1131no—
210C2×C8—1132no—
211C2×C8—1132no—
212C2×C8—1132no—
213C2×C8—2261no—
214C2×C8—2261no—
215C2×C8C2×#9067311yescharacteristic, complemented
216C4⋊C4—1132no—
217C4⋊C4—1132no—
218C4⋊C4—2261no—
219C4⋊C4—2261no—
220C4⋊C4—2264no—
221C22⋊C4—2264no—
222C42—1132no—
223C42—1132no—
224C42—2264no—
225C23—21no—
226C23—1131no—
227C23—4522no—
228C23—4522no—
229C23—2262no—
230C23—2262no—
231C23—2261no—
232Q8—21no—
233Q8—1132no—
234Q8—2262no—
235Q8—2262no—
236Q8—2261no—
237Q8C22×#9067312yescomplemented
238D4—21no—
239D4—1132no—
240D4—2262no—
241D4—2262no—
242D4—2261no—
243D4C22×#9067312yes—
244C2×C4—21no—
245C2×C4—1131no—
246C2×C4—1131no—
247C2×C4—1131no—
248C2×C4—1131no—
249C2×C4—1131no—
250C2×C4—1132no—
251C2×C4—1132no—
252C2×C4—4522no—
253C2×C4—4522no—
254C2×C4—4528no—
255C2×C4—2262no—
256C2×C4—2262no—
257C2×C4—2262no—
258C2×C4—2262no—
259C2×C4—2262no—
260C2×C4—2262no—
261C2×C4—2261no—
262C2×C4C22×#9067311yescharacteristic
263C8—1132no—
264C8—2262no—
265C8C22×#9067312yescomplemented
266C22—22no—
267C22—42no—
268C22—1132no—
269C22—1132no—
270C22—1131no—
271C22—1131no—
272C22—4522no—
273C22—4522no—
274C22—4524no—
275C22—4522no—
276C22—2262no—
277C22D4×#9067311yescharacteristic
278C4—22no—
279C4—1131no—
280C4—1131no—
281C4—4522no—
282C4—4522no—
283C4—2262no—
284C4—2262no—
285C4—2262no—
286C4D4×#9067311yescharacteristic
287C4C23×#9067311yescharacteristic
288C2—42no—
289C2—1131no—
290C2—1131no—
291C2—1132no—
292C2—4522no—
293C2#2029963712yesdirect product factor
294C2C2×D4×#9067311yescharacteristic
subgroupG/H
centerC22D4×#90673
commutatorC4×C113C23×C4
FrattiniC4C23×#90673
FittingC2×SD16×C113C4
socleC22×C113C4×D4
prime radicalC2×D4×D113C22
cosocleC4×D113C24
hypercenterC2×SD16#90673
hypocenterC113C2×#440
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#90673C2semidirect
3. #20299637C2direct (N × H)
4. C2×#16813691C2semidirect
5. C2×#16813685C2semidirect
7. C2×#16813676C2semidirect
12. Q8×#90673C22semidirect
21. #16813691C22semidirect
22. #16813685C22semidirect
24. #16813676C22semidirect
27. C2×#14268636C4semidirect
28. C2×#14268635C4semidirect
29. C2×#14268634C4semidirect
30. SD16×D113C4semidirect
33. C2×SD16×C113C4semidirect
54. C2×Dic226C2×C4semidirect
57. Q8×D113C2×C4semidirect
67. #14268636C2×C4semidirect
68. #14268635C2×C4semidirect
69. #14268634C2×C4semidirect
70. C2×#11744751C2×C4semidirect
71. C8×D113C2×C4semidirect
73. C2×Q8×C113C2×C4semidirect
75. SD16×C113C2×C4semidirect
76. C2×C8×C113C2×C4semidirect
94. Q8×C113C22×C4semidirect
114. Dic226C22×C4semidirect
116. C8×C113C22×C4semidirect
117. #11744751C22×C4semidirect
141. C2×C113#440semidirect
144. D113#440semidirect
148. C113C2×#440semidirect
165. C2×SD16#90673semidirect
189. C2×Q8C2×#90673semidirect
208. SD16C2×#90673semidirect
215. C2×C8C2×#90673semidirect
237. Q8C22×#90673semidirect
265. C8C22×#90673semidirect
293. C2#20299637direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×#906732
C2×D4×#906732
#202996372
C2×#168136912
C2×#168136852
C2×#168136842
C2×#168136762
C2×SD16×D1132
C2×#440113