Finite Group Databasebeta

← C2×#13123088 #16069326

Subgroups — C2×#13123088 #16069326

Order 3328.

3550 conjugacy classes of subgroups; only the 627 normal subgroups are shown.

normal subgroups only

This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 627 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
1#13123088C2116yesmaximal, direct product factor
2C2×#11718334C216yesmaximal, complemented
3C2×#11718608C213yesmaximal, complemented
4C2×#11718892C212yesmaximal, complemented
5C2×#11718616C213yesmaximal
6C2×C13×#393C211yesmaximal, characteristic, complemented
7C25×D13C2211yescharacteristic
8C23×Q8×C13C2211yescharacteristic, complemented
9C23×Dic26C2213yescomplemented
10C22×C13×C22⋊C4C2213yes—
11C22×C22⋊Dic13C2213yes—
12C22×#6103C2216yes—
13C22×#6103C2216yes—
14C13×#393C2218yescomplemented
15C2×C13×#95C2213yescomplemented
16#11718892C22116yescomplemented
17C2×#88071C2216yescomplemented
18C2×#88071C2213yescomplemented
19#11718616C22124yes—
20#11718608C22124yescomplemented
21#11718334C22148yescomplemented
22C25×C13C2311yescharacteristic
23C24×D13—46no—
24C24×D13—46no—
25C24×D13Q818yescomplemented
26C24×D13C2312yes—
27C24×D13C2314yes—
28C22×Q8×C13—46no—
29C22×Q8×C13C2314yescomplemented
30C23×C4×C13C2313yes—
31C23×C4×C13C2313yes—
32C23×Dic13C2316yes—
33C22×Dic26—46no—
34C22×Dic26—412no—
35C22×Dic26C23112yescomplemented
36C2×C13×C22⋊C4—46no—
37C2×C13×C22⋊C4C23112yes—
38C2×C22⋊Dic13—46no—
39C2×C22⋊Dic13C23112yes—
40C2×#6103—412no—
41C2×#6103—412no—
42C2×#6103C23124yes—
43C2×#6103C23124yes—
44C13×#95C23112yescomplemented
45#88071C23112yescomplemented
46#88071C23124yescomplemented
47C2×#2840—131nomaximal, Sylow
48C24×C13—26no—
49C24×C13—26no—
50C24×C13C2×Q814yes—
51C24×C13C2412yes—
52C24×C13C2411yescharacteristic
53C23×D13—212no—
54C23×D13—212no—
55C23×D13—448no—
56C23×D13—412no—
57C23×D13—412no—
58C23×D13—416no—
59C23×D13—448no—
60C23×D13C2×Q818yes—
61C23×D13C2×Q8116yescomplemented
62C23×D13C2414yes—
63C2×Q8×C13—412no—
64C2×Q8×C13—416no—
65C22×C4×C13—212no—
66C22×C4×C13—212no—
67C22×C4×C13—26no—
68C22×C4×C13—26no—
69C22×C4×C13C2416yes—
70C22×C4×C13C2416yes—
71C22×Dic13—212no—
72C22×Dic13—212no—
73C22×Dic13—212no—
74C22×Dic13C24112yes—
75C2×Dic26—412no—
76C2×Dic26—424no—
77C2×Dic26—448no—
78C13×C22⋊C4—412no—
79C22⋊Dic13—412no—
80#6103—424no—
81#6103—424no—
82#2840—1316no—
83C2×#393—136no—
84C2×#393—132no—
85C2×#393—133no—
86C2×#393D1311yescharacteristic, complemented
87C2×#379—133no—
88C23×C13—224no—
89C23×C13—26no—
90C23×C13—26no—
91C23×C13—44no—
92C23×C13—412no—
93C23×C13C22×Q814yes—
94C23×C13C22×Q812yes—
95C23×C13H(5,𝔽2)16yes—
96C23×C13H(5,𝔽2)16yes—
97C23×C13C2511yescharacteristic
98C22×D13—248no—
99C22×D13—212no—
100C22×D13—212no—
101C22×D13—448no—
102C22×D13—4128no—
103C22×D13—448no—
104C22×D13—416no—
105C22×D13—48no—
106C22×D13—424no—
107C22×D13C22×Q818yes—
108Q8×C13—416no—
109C2×C4×C13—212no—
110C2×C4×C13—212no—
111C2×C4×C13—26no—
112C2×C4×C13—26no—
113C2×C4×C13—412no—
114C2×C4×C13—412no—
115C2×Dic13—212no—
116C2×Dic13—212no—
117C2×Dic13—212no—
118C2×Dic13—424no—
119Dic26—448no—
120C26—131no—
121C23×Q8—133no—
122C23×Q8C2×D1311yescharacteristic, complemented
123C22×C22⋊C4—133no—
124C22×C22⋊C4—136no—
125C22×C22⋊C4—136no—
126C22×C22⋊C4C2×D1313yes—
127#393—1316no—
128#393—1324no—
129#393—1348no—
130#393C2×D1318yescomplemented
131#379—1324no—
132C2×#95—133no—
133C2×#95—136no—
134C2×#95C2×D1313yescomplemented
135C22×C13—212no—
136C22×C13—416no—
137C22×C13—46no—
138C22×C13—42no—
139C22×C13#543112yes—
140C22×C13H(3,𝔽4)14yes—
141C22×C13H(3,𝔽4)112yes—
142C22×C13C23×Q811yescharacteristic
143C22×C13C2×H(5,𝔽2)13yes—
144C22×C13C2×H(5,𝔽2)13yes—
145C2×D13—224no—
146C2×D13—464no—
147C2×D13—432no—
148C2×D13—412no—
149C2×D13—44no—
150C4×C13—46no—
151C4×C13—46no—
152Dic13—412no—
153C25—132no—
154C25—138no—
155C25—134no—
156C25—526no—
157C25—526no—
158C25C22×D1311yescharacteristic
159C22×Q8—46no—
160C22×Q8—1312no—
161C22×Q8—526no—
162C22×Q8—5212no—
163C22×Q8C22×D1314yescomplemented
164C23×C4—136no—
165C23×C4C22×D1313yes—
166C23×C4C22×D1313yes—
167C2×C22⋊C4—46no—
168C2×C22⋊C4—1312no—
169C2×C22⋊C4—1324no—
170C2×C22⋊C4—1324no—
171C2×C22⋊C4—5212no—
172C2×C22⋊C4—5212no—
173C2×C22⋊C4—526no—
174C2×C22⋊C4C22×D13112yes—
175#95—1324no—
176#95—1312no—
177#95C22×D13112yescomplemented
178C2×C13—44no—
179C2×C13#284018yescomplemented
180C2×C13C2×#54313yes—
181C2×C13C2×H(3,𝔽4)13yes—
182C2×C13C2×H(3,𝔽4)11yescharacteristic
183D13—48no—
184C24—26no—
185C24—26no—
186C24—138no—
187C24—134no—
188C24—1316no—
189C24—2612no—
190C24—2612no—
191C24—5248no—
192C24—5212no—
193C24—5212no—
194C24—5216no—
195C24—5248no—
196C24Q8×D1314yes—
197C24C23×D1312yes—
198C24C23×D1311yescharacteristic
199C2×Q8—412no—
200C2×Q8—416no—
201C2×Q8—5212no—
202C2×Q8—5224no—
203C2×Q8—5248no—
204C22×C4—26no—
205C22×C4—26no—
206C22×C4—212no—
207C22×C4—212no—
208C22×C4—1312no—
209C22×C4—2612no—
210C22×C4—2612no—
211C22×C4—2612no—
212C22×C4C23×D1316yes—
213C22×C4C23×D1316yes—
214C22⋊C4—412no—
215C22⋊C4—5224no—
216C22⋊C4—5224no—
217C22⋊C4—5212no—
218C13C2×#284011yescharacteristic, complemented, Sylow
219C23—224no—
220C23—26no—
221C23—26no—
222C23—44no—
223C23—412no—
224C23—138no—
225C23—2648no—
226C23—2612no—
227C23—2612no—
228C23—5248no—
229C23—52128no—
230C23—5248no—
231C23—5216no—
232C23—528no—
233C23—5224no—
234C23#8825116yes—
235C23C2×Q8×D1314yes—
236C23C2×Q8×D1312yes—
237C23#8825616yes—
238C23C24×D1311yescharacteristic
239Q8—416no—
240Q8—5248no—
241C2×C4—26no—
242C2×C4—26no—
243C2×C4—212no—
244C2×C4—212no—
245C2×C4—412no—
246C2×C4—412no—
247C2×C4—2612no—
248C2×C4—2612no—
249C2×C4—2612no—
250C2×C4—5224no—
251C22—212no—
252C22—416no—
253C22—46no—
254C22—42no—
255C22—2624no—
256C22—5264no—
257C22—5232no—
258C22—5212no—
259C22—524no—
260C22#1171929914yes—
261C22#11719339112yes—
262C22#11719388112yes—
263C22C2×#8825113yes—
264C22C22×Q8×D1311yescharacteristic
265C22C2×#8825613yes—
266C4—46no—
267C4—46no—
268C4—5212no—
269C2—44no—
270C2—528no—
271C2#1312308818yesdirect product factor
272C2C2×#1171933913yes—
273C2C2×#1171938813yes—
274C2C2×#1171929911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#393C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#393D13
hypocenterC13C2×#2840
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. #13123088C2direct (N × H)
2. C2×#11718334C2semidirect
3. C2×#11718608C2semidirect
4. C2×#11718892C2semidirect
6. C2×C13×#393C2semidirect
8. C23×Q8×C13C22semidirect
9. C23×Dic26C22semidirect
14. C13×#393C22semidirect
15. C2×C13×#95C22semidirect
16. #11718892C22semidirect
17. C2×#88071C22semidirect
18. C2×#88071C22semidirect
20. #11718608C22semidirect
21. #11718334C22semidirect
25. C24×D13Q8semidirect
29. C22×Q8×C13C23semidirect
35. C22×Dic26C23semidirect
44. C13×#95C23semidirect
45. #88071C23semidirect
46. #88071C23semidirect
61. C23×D13C2×Q8semidirect
86. C2×#393D13semidirect
122. C23×Q8C2×D13semidirect
130. #393C2×D13semidirect
134. C2×#95C2×D13semidirect
163. C22×Q8C22×D13semidirect
177. #95C22×D13semidirect
179. C2×C13#2840semidirect
218. C13C2×#2840semidirect
271. C2#13123088direct (N × H)

Maximal subgroups

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

subgroupindex
#131230882
C2×#117183342
C2×#117186082
C2×#117188922
C2×#117186162
C2×C13×#3932
C2×#284013