Finite Group Databasebeta

← #13127237

Subgroups — #13127237

Order 1664.

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

normal subgroups only

This group has 366 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#11719400C212yesmaximal, complemented
2C13×#499C211yesmaximal, characteristic, complemented
3#11718727C212yesmaximal, complemented
4#11718544C211yesmaximal, characteristic, complemented
5#11718544C211yesmaximal, characteristic, complemented
6#11718541C211yesmaximal, characteristic, complemented
7D13×#107C211yesmaximal, characteristic, complemented
8#11718527C212yesmaximal, complemented
9#11718524C212yesmaximal, complemented
10C4×D104C211yesmaximal, characteristic, complemented
11C8×D52C211yesmaximal, characteristic, complemented
12C13×#125C2212yes—
13C2×D104C2211yescharacteristic
14C2×C8×D13C2211yescharacteristic
15C2×C8×D13C2211yescharacteristic
16#88152—22no—
17#88149—22no—
18#88149C2212yes—
19#88149C2212yes—
20#88148—22no—
21#88147—22no—
22#88146C2212yes—
23C4⋊C4×D13C2212yes—
24C4×D52C2211yescharacteristic
25C4×D52C2212yes—
26C13×#107C2211yescharacteristic
27C13×#107C2211yescharacteristic
28C13×#106C2212yes—
29C4×C8×C13C2211yescharacteristic
30#88061C2212yes—
31#88060C2211yescharacteristic
32#88060C2211yescharacteristic
33#88058C2211yescharacteristic
34#88049C2212yes—
35#88049C2212yes—
36#88048C2212yes—
37#88047C2212yes—
38C4⋊#1055C2211yescharacteristic
39C2×D52—22no—
40C2×D52—22no—
41C2×D52D411yescharacteristic
42C2×D52C2312yes—
43C2×C4×D13—22no—
44C2×C4×D13—22no—
45C2×C4×D13C2311yescharacteristic
46C2×C4×D13C2311yescharacteristic
47C2×C8×C13C2311yescharacteristic
48C2×C8×C13C2311yescharacteristic
49C13×C4⋊C4—22no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4C2312yes—
52C13×C4⋊C4C2312yes—
53C42×C13C2311yescharacteristic
54#6103—22no—
55#6103—22no—
56#6103—22no—
57#6103—22no—
58#6103D411yescharacteristic
59#6103D411yescharacteristic
60C4⋊Dic13D411yescharacteristic
61C4⋊Dic13C2312yes—
62#6101—22no—
63C4×Dic13—22no—
64C2×#1055C2311yescharacteristic
65C2×#1055C2311yescharacteristic
66D104—22no—
67C8×D13—22no—
68C8×D13—22no—
69#3339—131nomaximal, Sylow
70C22×D13—22no—
71C22×D13C2×D411yescharacteristic
72C22×D13C2×D411yescharacteristic
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2411yescharacteristic
78C2×Dic13—22no—
79C2×Dic13C2×D411yescharacteristic
80C2×Dic13C2×D411yescharacteristic
81D52—22no—
82D52—22no—
83D52—22no—
84D52—44no—
85D52—82no—
86C4×D13—21no—
87C4×D13—21no—
88C4×D13—21no—
89C4×D13—21no—
90C4×D13—82no—
91C4×D13—82no—
92C8×C13—21no—
93C8×C13#4112yes—
94#1055—21no—
95#1055—21no—
96#553—132no—
97#499D1311yescharacteristic, complemented
98#482—132no—
99#481—132no—
100#478—132no—
101#466—131no—
102#466—131no—
103C4×D8—131no—
104C8×D4—131no—
105#427—131no—
106C2×#107—131no—
107C22×C13C22×D411yescharacteristic
108C2×D13—21no—
109C2×D13—21no—
110C2×D13—21no—
111C2×D13—21no—
112C2×D13—21no—
113C2×D13—42no—
114C2×D13—42no—
115C2×D13—42no—
116C2×D13#13512yes—
117C4×C13—21no—
118C4×C13—21no—
119C4×C13—42no—
120C4×C13—42no—
121C4×C13C2×#4111yescharacteristic
122C4×C132−1+411yescharacteristic
123Dic13—21no—
124Dic13—21no—
125Dic13—42no—
126C2×D8—131no—
127C22×C8—131no—
128C22×C8—131no—
129#126—262no—
130#125C2×D1312yes—
131#123—262no—
132#121—132no—
133#121—132no—
134#121—262no—
135C4×D4—131no—
136C4×D4—132no—
137C4×D4—262no—
138#117—132no—
139C2×C4⋊C4—132no—
140#107—131no—
141#107—132no—
142#107C2×D1311yescharacteristic
143#107C2×D1311yescharacteristic
144#106—132no—
145#106C2×D1312yes—
146C4⋊C8—131no—
147#102—132no—
148#102—132no—
149#102—132no—
150C22⋊C8—131no—
151C22⋊C8—131no—
152C4×C8C2×D1311yescharacteristic
153C2×C13#54711yescharacteristic
154C2×C13C2×#13511yescharacteristic
155C2×C13#57611yescharacteristic
156D13—22no—
157D13—41no—
158D13—82no—
159C2×D4—131no—
160C2×D4—132no—
161C2×D4—262no—
162C2×D4—262no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—262no—
166C22×C4—262no—
167D8—262no—
168C2×C8—131no—
169C2×C8—131no—
170C2×C8—262no—
171C2×C8—262no—
172C2×C8C22×D1311yescharacteristic
173C2×C8C22×D1311yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—131no—
177C4⋊C4—132no—
178C4⋊C4—262no—
179C4⋊C4C22×D1312yes—
180C4⋊C4C22×D1312yes—
181C22⋊C4—131no—
182C22⋊C4—131no—
183C22⋊C4—262no—
184C22⋊C4—262no—
185C22⋊C4—262no—
186C22⋊C4—262no—
187C42—262no—
188C42C22×D1311yescharacteristic
189C13#333911yescharacteristic, complemented, Sylow
190C23—131no—
191C23—131no—
192C23—262no—
193D4—262no—
194D4—262no—
195D4—262no—
196D4—524no—
197D4—1042no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—131no—
201C2×C4—131no—
202C2×C4—261no—
203C2×C4—261no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—262no—
207C2×C4—1042no—
208C2×C4—1042no—
209C2×C4D4×D1311yescharacteristic
210C2×C4D4×D1311yescharacteristic
211C2×C4C23×D1311yescharacteristic
212C8—21no—
213C8—261no—
214C8—261no—
215C8#613112yes—
216C22—132no—
217C22—261no—
218C22—261no—
219C22—261no—
220C22—261no—
221C22—261no—
222C22—522no—
223C22—522no—
224C22—522no—
225C22C2×D4×D1311yescharacteristic
226C4—21no—
227C4—21no—
228C4—42no—
229C4—42no—
230C4—261no—
231C4—261no—
232C4—522no—
233C4C2×#613111yescharacteristic
234C4#8825411yescharacteristic
235C2—262no—
236C2—521no—
237C2—1042no—
238C2#1171943111yescharacteristic
239C2D13×#13511yescharacteristic
240C2#1171947411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#499C2
socleC22×C13C22×D4
hypercenter#499D13
hypocenterC13#3339
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #11719400C2semidirect
2. C13×#499C2semidirect
3. #11718727C2semidirect
4. #11718544C2semidirect
5. #11718544C2semidirect
6. #11718541C2semidirect
7. D13×#107C2semidirect
8. #11718527C2semidirect
9. #11718524C2semidirect
10. C4×D104C2semidirect
11. C8×D52C2semidirect
97. #499D13semidirect
189. C13#3339semidirect

Maximal subgroups

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

subgroupindex
#117194002
C13×#4992
#117187272
#117185442
#117185412
D13×#1072
#117185272
#117185242
C4×D1042
C8×D522
#333913