Finite Group Databasebeta

← #13127824

Subgroups — #13127824

Order 1664.

360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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#11719273C212yesmaximal, complemented
2C4×C13×Q16C211yesmaximal, characteristic, complemented
3#11718852C211yesmaximal, characteristic
4#11718842C211yesmaximal, characteristic, complemented
5#11718689C212yesmaximal, complemented
6#11718534C211yesmaximal, characteristic, complemented
7#11718533C211yesmaximal, characteristic
8#11718479C212yesmaximal, complemented
9#11718459C212yesmaximal, complemented
10#11718357C211yesmaximal, characteristic
11C8×Dic26C211yesmaximal, characteristic, complemented
12C2×C13×Q16C2211yescharacteristic
13C4×Q8×C13C2212yes—
14#88201C2212yes—
15#88198C2212yes—
16C2×#6107C2212yes—
17C2×#6106C2212yes—
18C2×Dic52C2211yescharacteristic
19C2×D104C2211yescharacteristic
20C2×#6095C2212yes—
21#88152—22no—
22#88150—22no—
23#88147C2212yes—
24#88141C2212yes—
25#88130—22no—
26#88129C2212yes—
27#88126—22no—
28C4×Dic26C2211yescharacteristic
29C13×#107C2211yescharacteristic
30C13×#103C2212yes—
31C4×C8×C13C2211yescharacteristic
32#88054C2211yescharacteristic
33#88054C2211yescharacteristic
34C8×Dic13C2211yescharacteristic
35C8×Dic13C2211yescharacteristic
36#88050C2212yes—
37#88049C2212yes—
38C4⋊#1055C2211yescharacteristic
39C2×Q8×C13C2312yes—
40C2×D52C2312yes—
41C2×C4×D13—22no—
42C2×Dic26D411yescharacteristic
43C2×Dic26C2312yes—
44C13×Q16—22no—
45C2×C8×C13C2311yescharacteristic
46C2×C8×C13C2311yescharacteristic
47C13×C4⋊C4—22no—
48C13×C4⋊C4C2312yes—
49C42×C13—22no—
50C42×C13C2311yescharacteristic
51#6107—42no—
52#6106—42no—
53#6103—22no—
54#6103—22no—
55#6103—22no—
56#6103—22no—
57#6103—22no—
58C4⋊Dic13D411yescharacteristic
59#6101—22no—
60#6101—22no—
61#6101—22no—
62#6101D411yescharacteristic
63#6101D411yescharacteristic
64C4×Dic13—22no—
65C4×Dic13C2311yescharacteristic
66C4×Dic13C2311yescharacteristic
67C2×#1055C2311yescharacteristic
68C2×#1055C2311yescharacteristic
69Dic52—22no—
70D104—22no—
71#6095—42no—
72#3393—131nomaximal, Sylow
73C22×D13—22no—
74Q8×C13—22no—
75Q8×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2411yescharacteristic
81C2×Dic13—22no—
82C2×Dic13C2×D411yescharacteristic
83C2×Dic13C2×D411yescharacteristic
84C2×Dic13C2×D411yescharacteristic
85C2×Dic13C2×D411yescharacteristic
86D52—22no—
87D52—22no—
88C4×D13—44no—
89Dic26—22no—
90Dic26—22no—
91Dic26—22no—
92C8×C13—21no—
93C8×C13#4112yes—
94#1055—21no—
95#1055—21no—
96#556—132no—
97#495—131no—
98#495—131no—
99#494—131no—
100#464—132no—
101#464—132no—
102#461—132no—
103C8×Q8—131no—
104C4×Q16—131no—
105C4×Q16D1311yescharacteristic, complemented
106C4×D8—131no—
107C22×C13C22×D411yescharacteristic
108C2×D13—42no—
109C2×D13—42no—
110C2×D13—42no—
111C4×C13—21no—
112C4×C13—21no—
113C4×C13—42no—
114C4×C13—42no—
115C4×C13C2×#4111yescharacteristic
116C4×C13H(5,𝔽2)11yescharacteristic
117Dic13—21no—
118Dic13—21no—
119Dic13—21no—
120Dic13—42no—
121Dic13#13512yes—
122C2×Q16—132no—
123C2×Q16—131no—
124C2×Q16C2×D1311yescharacteristic
125C2×SD16—132no—
126C2×SD16—132no—
127C2×D8—131no—
128C4⋊Q8—132no—
129#126—262no—
130#126—262no—
131#124—132no—
132#124—132no—
133C22⋊Q8—262no—
134C4×Q8—131no—
135C4×Q8—132no—
136C4×Q8C2×D1312yes—
137C4×D4—132no—
138#117—262no—
139#107C2×D1311yescharacteristic
140C4⋊C8—131no—
141C4⋊C8—131no—
142C4⋊C8—131no—
143#103—132no—
144#103C2×D1312yes—
145#102—132no—
146C4×C8—131no—
147C4×C8—131no—
148C4×C8C2×D1311yescharacteristic
149C2×C13#55011yescharacteristic
150C2×C13C2×#13511yescharacteristic
151C2×C13#57811yescharacteristic
152D13—82no—
153C2×Q8—131no—
154C2×Q8—132no—
155C2×Q8C22×D1312yes—
156C2×D4—132no—
157C22×C4—262no—
158Q16—22no—
159Q16—262no—
160Q16—522no—
161SD16—522no—
162SD16—522no—
163D8—262no—
164C2×C8—131no—
165C2×C8—131no—
166C2×C8C22×D1311yescharacteristic
167C2×C8C22×D1311yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—131no—
170C4⋊C4—131no—
171C4⋊C4—131no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4C22×D1312yes—
176C22⋊C4—262no—
177C22⋊C4—262no—
178C22⋊C4—262no—
179C22⋊C4—262no—
180C22⋊C4—262no—
181C42—22no—
182C42—131no—
183C42—131no—
184C42—262no—
185C42C22×D1311yescharacteristic
186C13#339311yescharacteristic, complemented, Sylow
187C23—262no—
188Q8—22no—
189Q8—22no—
190Q8—262no—
191Q8—262no—
192Q8—262no—
193D4—262no—
194D4—262no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—131no—
198C2×C4—131no—
199C2×C4—131no—
200C2×C4—131no—
201C2×C4—262no—
202C2×C4—524no—
203C2×C4D4×D1311yescharacteristic
204C2×C4D4×D1311yescharacteristic
205C2×C4C23×D1311yescharacteristic
206C8—21no—
207C8—261no—
208C8—261no—
209C8#612712yes—
210C22—522no—
211C22—522no—
212C22—522no—
213C22C2×D4×D1311yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—42no—
218C4—132no—
219C4—261no—
220C4—261no—
221C4—261no—
222C4—522no—
223C4C2×#612711yescharacteristic
224C4#8825611yescharacteristic
225C2—1042no—
226C2#1171925811yescharacteristic
227C2#1171947111yescharacteristic
228C2D13×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×Q16C2
socleC22×C13C22×D4
prime radicalC2×D104C22
hypercenterC4×Q16D13
hypocenterC13#3393
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #11719273C2semidirect
2. C4×C13×Q16C2semidirect
4. #11718842C2semidirect
5. #11718689C2semidirect
6. #11718534C2semidirect
8. #11718479C2semidirect
9. #11718459C2semidirect
11. C8×Dic26C2semidirect
105. C4×Q16D13semidirect
186. C13#3393semidirect

Maximal subgroups

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

subgroupindex
#117192732
C4×C13×Q162
#117188522
#117188422
#117186892
#117185342
#117185332
#117184792
#117184592
#117183572
C8×Dic262
#339313