Finite Group Databasebeta

← #13125679

Subgroups — #13125679

Order 1664.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#11719332C212yesmaximal, complemented
2C13×#470C211yesmaximal, characteristic, complemented
3#11718848C212yesmaximal, complemented
4#11718796C211yesmaximal, characteristic, complemented
5#11718787C211yesmaximal, characteristic, complemented
6#11718710C212yesmaximal, complemented
7#11718527C212yesmaximal, complemented
8#11718476C212yesmaximal, complemented
9#11718472C212yesmaximal, complemented
10C2×#6131C2212yes—
11C22×C4×D13C2211yescharacteristic
12C2×C13×Q16C2211yescharacteristic, complemented
13C2×C13×M16C2211yescharacteristic
14C13×C22⋊Q8C2212yes—
15#88200C2212yes—
16C2×#6106C2212yescomplemented
17#88184C2212yes—
18C2×#6099C2211yescharacteristic
19C2×D104C2211yescharacteristic, complemented
20#88149C2212yes—
21#88148—22no—
22#88147—22no—
23#88146C2212yes—
24#88136—22no—
25#88135—22no—
26C13×#106C2211yescharacteristic, complemented
27C13×#103C2212yescomplemented
28#88075C2212yescomplemented
29#88061C2212yescomplemented
30#88060C2212yes—
31#88060C2212yes—
32#88057C2211yescharacteristic, complemented
33#88049C2212yescomplemented
34#88047C2212yescomplemented
35C23×D13D411yescharacteristic
36C2×Q8×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—22no—
39C22×Dic13D411yescharacteristic
40#6131—42no—
41#6131—42no—
42C2×D52—22no—
43C2×D52—22no—
44C2×D52C2312yes—
45C2×C4×D13—22no—
46C2×C4×D13—41no—
47C2×C4×D13—41no—
48C2×C4×D13D412yes—
49C2×C4×D13C2312yes—
50C13×Q16—41no—
51C13×M16—41no—
52C2×C8×C13C2311yescharacteristic
53C2×C8×C13C2311yescharacteristic
54C13×C4⋊C4—22no—
55C13×C4⋊C4C2312yes—
56C13×C22⋊C4—22no—
57#6106—42no—
58#6103—22no—
59#6103—22no—
60#6103—22no—
61#6103—22no—
62C4⋊Dic13C2312yes—
63#6101—22no—
64C4×Dic13—22no—
65#6099—41no—
66C2×#1055C2312yes—
67D104—41no—
68#3197—131nomaximal, Sylow
69C23×C13C2×D411yescharacteristic
70C22×D13—22no—
71C22×D13—41no—
72C22×D13—42no—
73C22×D13C2×D412yes—
74Q8×C13—22no—
75Q8×C13—22no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2411yescharacteristic
82C22⋊D13—44no—
83C2×Dic13—22no—
84C2×Dic13—41no—
85C2×Dic13C2×D412yes—
86D52—22no—
87D52—22no—
88D52—44no—
89D52—44no—
90C4×D13—22no—
91C4×D13—22no—
92C4×D13—42no—
93C4×D13—44no—
94C8×C13—21no—
95C8×C13—21no—
96#1055—22no—
97#525—132no—
98#485—132no—
99#482—132no—
100#470D1311yescharacteristic, complemented
101#469—131no—
102#468—132no—
103#452—132no—
104#449—132no—
105#407—131no—
106C22×C13—21no—
107C22×C13—22no—
108C22×C13C22×D411yescharacteristic
109C2×D13—22no—
110C2×D13—22no—
111C2×D13—22no—
112C2×D13—44no—
113C2×D13—42no—
114C2×D13—42no—
115C2×D13—42no—
116C4×C13—21no—
117C4×C13—42no—
118C4×C13—42no—
119C4×C13H(5,𝔽2)11yescharacteristic
120C4×C13H(5,𝔽2)11yescharacteristic
121Dic13—22no—
122Dic13—42no—
123C2×#41—132no—
124C23×C4—131no—
125C2×Q16C2×D1311yescharacteristic, complemented
126C2×SD16—132no—
127C2×D8—131no—
128C2×M16—131no—
129C2×M16C2×D1311yescharacteristic
130#123—262no—
131C22⋊Q8—132no—
132C22⋊Q8C2×D1312yes—
133#121—132no—
134#121—132no—
135#120—262no—
136C4×D4—262no—
137C4×D4—262no—
138#117—132no—
139#107—132no—
140#106—131no—
141#106C2×D1311yescharacteristic, complemented
142#103—132no—
143#103C2×D1312yescomplemented
144#102—132no—
145#102—132no—
146C22⋊C8—132no—
147C22⋊C8—132no—
148C2×C13—41no—
149C2×C13#53411yescharacteristic
150C2×C13#57512yes—
151D13—42no—
152D13—82no—
153C24—131no—
154#41—522no—
155#41—522no—
156C2×Q8C22×D1312yes—
157C2×D4—132no—
158C2×D4—262no—
159C2×D4—262no—
160C2×D4—262no—
161C22×C4—131no—
162C22×C4—132no—
163C22×C4—132no—
164C22×C4—262no—
165C22×C4—521no—
166C22×C4—521no—
167C22×C4C22×D1311yescharacteristic
168Q16—41no—
169SD16—522no—
170D8—521no—
171M16—41no—
172M16—521no—
173C2×C8—132no—
174C2×C8C22×D1311yescharacteristic
175C2×C8C22×D1311yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—132no—
178C4⋊C4—262no—
179C4⋊C4C22×D1312yes—
180C22⋊C4—22no—
181C22⋊C4—262no—
182C22⋊C4—262no—
183C22⋊C4—262no—
184C22⋊C4—262no—
185C42—262no—
186C13#319711yescharacteristic, complemented, Sylow
187C23—132no—
188C23—262no—
189C23—521no—
190C23—522no—
191C23D4×D1311yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—262no—
195D4—262no—
196D4—524no—
197D4—524no—
198D4—524no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—132no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—522no—
208C2×C4—524no—
209C2×C4—521no—
210C2×C4D4×D1311yescharacteristic
211C2×C4C23×D1311yescharacteristic
212C8—21no—
213C8—21no—
214C8—262no—
215C22—22no—
216C22—21no—
217C22—262no—
218C22—262no—
219C22—262no—
220C22—524no—
221C22—522no—
222C22—522no—
223C22—522no—
224C22C2×D4×D1311yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—262no—
229C4—522no—
230C4#8825111yescharacteristic
231C4#8825611yescharacteristic
232C2—41no—
233C2—522no—
234C2—1042no—
235C2#1171931011yescharacteristic
236C2#1171948212yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#470C2
socleC22×C13C22×D4
hypercenter#470D13
hypocenterC13#3197
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #11719332C2semidirect
2. C13×#470C2semidirect
3. #11718848C2semidirect
4. #11718796C2semidirect
5. #11718787C2semidirect
6. #11718710C2semidirect
7. #11718527C2semidirect
8. #11718476C2semidirect
9. #11718472C2semidirect
12. C2×C13×Q16C22semidirect
16. C2×#6106C22semidirect
19. C2×D104C22semidirect
26. C13×#106C22semidirect
27. C13×#103C22semidirect
28. #88075C22semidirect
29. #88061C22semidirect
32. #88057C22semidirect
33. #88049C22semidirect
34. #88047C22semidirect
100. #470D13semidirect
125. C2×Q16C2×D13semidirect
141. #106C2×D13semidirect
143. #103C2×D13semidirect
186. C13#3197semidirect

Maximal subgroups

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

subgroupindex
#117193322
C13×#4702
#117188482
#117187962
#117187872
#117187102
#117185272
#117184762
#117184722
#319713