Finite Group Databasebeta

← #13125484

Subgroups — #13125484

Order 1664.

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

normal subgroups only

This group has 386 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#11719267C212yesmaximal, complemented
2C13×#442C211yesmaximal, characteristic, complemented
3#11718820C211yesmaximal, characteristic, complemented
4#11718812C211yesmaximal, characteristic, complemented
5C4×#6104C212yesmaximal, complemented
6#11718526C211yesmaximal, characteristic, complemented
7#11718519C211yesmaximal, characteristic, complemented
8#11718436C212yesmaximal, complemented
9#11718425C212yesmaximal, complemented
10#11718372C211yesmaximal, characteristic, complemented
11#11718369C211yesmaximal, characteristic, complemented
12C2×C13×D8C2211yescharacteristic
13C4×D4×C13C2212yes—
14#88194C2212yes—
15#88192C2212yes—
16C2×#6104C2212yes—
17#88184—22no—
18#88183—22no—
19C2×D104C2211yescharacteristic
20C2×#6094C2211yescharacteristic
21C2×C8×D13C2211yescharacteristic
22#88149C2212yes—
23#88144C2212yes—
24#88138—22no—
25#88137—22no—
26C4×D52C2212yes—
27#88126C2211yescharacteristic
28C13×#106C2211yescharacteristic
29C13×#102C2212yes—
30C13×#97C2211yescharacteristic
31#88072C2212yes—
32#88061C2212yes—
33#88057C2211yescharacteristic
34#88055C2211yescharacteristic
35C8×Dic13C2211yescharacteristic
36#88049C2212yes—
37#88047C2212yes—
38C4×#1055C2211yescharacteristic
39C2×D4×C13C2312yes—
40C22×C4×C13—22no—
41C2×C22⋊D13—22no—
42C2×C22⋊D13—22no—
43C2×C22⋊D13—22no—
44C2×D52—22no—
45C2×D52C2312yes—
46C2×C4×D13—22no—
47C2×C4×D13C2311yescharacteristic
48C13×D8—22no—
49C2×C8×C13C2311yescharacteristic
50C2×C8×C13C2311yescharacteristic
51C13×C4⋊C4C2312yes—
52C13×C22⋊C4—22no—
53C42×C13C2311yescharacteristic
54C22⋊Dic13—22no—
55#6104—24no—
56#6103—22no—
57#6103—22no—
58#6103D412yes—
59C4⋊Dic13—22no—
60C4⋊Dic13C2312yes—
61#6101—22no—
62#6101D412yes—
63C4×Dic13C2311yescharacteristic
64C2×#1055C2311yescharacteristic
65C2×#1055C2311yescharacteristic
66D104—22no—
67#6094—22no—
68C8×D13—22no—
69#3176—131nomaximal, Sylow
70C23×C13—22no—
71C22×D13—22no—
72C22×D13C2×D411yescharacteristic
73D4×C13—22no—
74D4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—82no—
77C2×C4×C13C2×D412yes—
78C2×C4×C13C2411yescharacteristic
79C22⋊D13—82no—
80C22⋊D13—82no—
81C22⋊D13—82no—
82C2×Dic13—22no—
83C2×Dic13C2×D412yes—
84C2×Dic13C2×D411yescharacteristic
85D52—22no—
86D52—22no—
87D52—82no—
88C4×D13—21no—
89C4×D13—21no—
90C4×D13—82no—
91C8×C13—21no—
92C8×C13#4112yes—
93#1055—21no—
94#1055#4112yes—
95#540—132no—
96#499—131no—
97#493—131no—
98#490—132no—
99#469—131no—
100#469—131no—
101#466—132no—
102#442—131no—
103#442D1311yescharacteristic, complemented
104C4×D8—132no—
105#405—131no—
106C22×C13—42no—
107C22×C13—42no—
108C22×C13—42no—
109C22×C13C22×D411yescharacteristic
110C2×D13—21no—
111C2×D13—22no—
112C2×D13—42no—
113C2×D13—42no—
114C2×D13—42no—
115C4×C13—22no—
116C4×C13—42no—
117C4×C13C2×#4111yescharacteristic
118C4×C13C2×#4111yescharacteristic
119Dic13—21no—
120Dic13—22no—
121Dic13—42no—
122C2×D8—132no—
123C2×D8—131no—
124C2×D8C2×D1311yescharacteristic
125C2×M16—131no—
126C22×C8—131no—
127#127—132no—
128#125—132no—
129#123—262no—
130#123—262no—
131#121—132no—
132#121—132no—
133#121—262no—
134#121—262no—
135C4×D4—132no—
136C4×D4C2×D1312yes—
137#117—131no—
138#107—132no—
139#106—131no—
140#106C2×D1311yescharacteristic
141#102—132no—
142#102—132no—
143#102—132no—
144#102C2×D1312yes—
145#97—131no—
146#97C2×D1311yescharacteristic
147C4×C8—131no—
148C4×C8—131no—
149C2×C13—82no—
150C2×C13#53211yescharacteristic
151C2×C13#57612yes—
152D13—41no—
153D13—82no—
154C2×D4—132no—
155C2×D4—262no—
156C2×D4—262no—
157C2×D4—262no—
158C2×D4—262no—
159C2×D4C22×D1312yes—
160C22×C4—22no—
161C22×C4—131no—
162C22×C4—262no—
163D8—22no—
164D8—264no—
165D8—262no—
166M16—262no—
167C2×C8—131no—
168C2×C8—131no—
169C2×C8—262no—
170C2×C8C22×D1311yescharacteristic
171C2×C8C22×D1311yescharacteristic
172C4⋊C4—132no—
173C4⋊C4—132no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4C22×D1312yes—
177C22⋊C4—22no—
178C22⋊C4—132no—
179C22⋊C4—262no—
180C22⋊C4—262no—
181C22⋊C4—262no—
182C42—131no—
183C42C22×D1311yescharacteristic
184C13#317611yescharacteristic, complemented, Sylow
185C23—22no—
186C23—131no—
187C23—262no—
188D4—22no—
189D4—22no—
190D4—262no—
191D4—262no—
192D4—1042no—
193D4—1042no—
194D4—1042no—
195D4—1042no—
196C2×C4—22no—
197C2×C4—82no—
198C2×C4—132no—
199C2×C4—131no—
200C2×C4—261no—
201C2×C4—261no—
202C2×C4—262no—
203C2×C4—1042no—
204C2×C4D4×D1312yes—
205C2×C4C23×D1311yescharacteristic
206C8—21no—
207C8—132no—
208C8—261no—
209C8#612712yes—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—262no—
214C22—261no—
215C22—522no—
216C22—522no—
217C22—522no—
218C22C2×D4×D1311yescharacteristic
219C4—22no—
220C4—42no—
221C4—262no—
222C4—261no—
223C4—522no—
224C4C2×#612711yescharacteristic
225C4#41×D1311yescharacteristic
226C2—82no—
227C2—521no—
228C2—1042no—
229C2#1171925311yescharacteristic
230C2#1171947912yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#442C2
socleC22×C13C22×D4
hypercenter#442D13
hypocenterC13#3176
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #11719267C2semidirect
2. C13×#442C2semidirect
3. #11718820C2semidirect
4. #11718812C2semidirect
5. C4×#6104C2semidirect
6. #11718526C2semidirect
7. #11718519C2semidirect
8. #11718436C2semidirect
9. #11718425C2semidirect
10. #11718372C2semidirect
11. #11718369C2semidirect
103. #442D13semidirect
184. C13#3176semidirect

Maximal subgroups

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

subgroupindex
#117192672
C13×#4422
#117188202
#117188122
C4×#61042
#117185262
#117185192
#117184362
#117184252
#117183722
#117183692
#317613