Finite Group Databasebeta

← #13127443

Subgroups — #13127443

Order 1664.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#11719263C212yesmaximal, complemented
2C4×C13×D8C211yesmaximal, characteristic, complemented
3#11718820C212yesmaximal, complemented
4#11718670C212yesmaximal, complemented
5#11718542C212yesmaximal, complemented
6#11718445C212yesmaximal, complemented
7#11718435C212yesmaximal, complemented
8#11718349C211yesmaximal, characteristic, complemented
9#11718344C211yesmaximal, characteristic, complemented
10C2×C13×D8C2211yescharacteristic
11C4×D4×C13C2212yes—
12#88192C2212yes—
13#88192C2212yes—
14#88183—22no—
15C4×C22⋊D13—22no—
16C2×#6094C2212yes—
17#88146C2212yes—
18C4⋊C4×D13C2212yes—
19#88138—22no—
20#88133—22no—
21C4×D52C2211yescharacteristic
22#88124C2212yes—
23C13×#107C2211yescharacteristic
24C13×#102C2212yes—
25C4×C8×C13C2211yescharacteristic
26#88072C2212yes—
27#88072C2212yes—
28#88060C2212yes—
29#88058C2211yescharacteristic
30#88058C2211yescharacteristic
31#88057C2212yes—
32#88048C2212yes—
33#88047C2212yes—
34C4⋊#1055C2211yescharacteristic
35C2×D4×C13C2312yes—
36C22×C4×C13—22no—
37C2×C22⋊D13—22no—
38C2×C22⋊D13—22no—
39C2×D52D411yescharacteristic
40C2×C4×D13—22no—
41C2×C4×D13C2312yes—
42C13×D8—22no—
43C2×C8×C13C2311yescharacteristic
44C2×C8×C13C2311yescharacteristic
45C13×C4⋊C4C2312yes—
46C13×C22⋊C4—22no—
47C42×C13C2311yescharacteristic
48C22⋊Dic13—22no—
49C22⋊Dic13—22no—
50#6103—22no—
51#6103D412yes—
52C4⋊Dic13D411yescharacteristic
53C4⋊Dic13C2312yes—
54C4⋊Dic13C2312yes—
55#6101—22no—
56#6101—22no—
57#6101—22no—
58C4×Dic13—22no—
59C2×#1055C2312yes—
60#6094—24no—
61#3355—131nomaximal, Sylow
62C23×C13—22no—
63C22×D13C2×D412yes—
64D4×C13—22no—
65D4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—82no—
68C2×C4×C13C2×D411yescharacteristic
69C2×C4×C13C2×D411yescharacteristic
70C2×C4×C13C2411yescharacteristic
71C22⋊D13—44no—
72C22⋊D13—82no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13C2×D412yes—
76D52—41no—
77C4×D13—22no—
78C4×D13—22no—
79C4×D13—82no—
80C8×C13—21no—
81C8×C13#4112yes—
82#1055—22no—
83#553—132no—
84#499—131no—
85#482—132no—
86#480—132no—
87#478—132no—
88#469—132no—
89C4×D8D1311yescharacteristic, complemented
90#436—131no—
91#428—132no—
92C22×C13—42no—
93C22×C13—42no—
94C22×C13—42no—
95C22×C13C22×D411yescharacteristic
96C2×D13—22no—
97C2×D13—22no—
98C2×D13—22no—
99C4×C13—21no—
100C4×C13—21no—
101C4×C13—42no—
102C4×C13C2×#4111yescharacteristic
103C4×C132−1+411yescharacteristic
104Dic13—22no—
105Dic13—42no—
106Dic13—42no—
107C2×D8C2×D1311yescharacteristic
108C2×M16—132no—
109#126—262no—
110#125—132no—
111#123—262no—
112#121—132no—
113#121—132no—
114#121—262no—
115C4×D4—131no—
116C4×D4—262no—
117C4×D4C2×D1312yes—
118#117—132no—
119C2×C4⋊C4—132no—
120#107—131no—
121#107—131no—
122#107—132no—
123#107C2×D1311yescharacteristic
124#106—132no—
125#106—132no—
126C4⋊C8—131no—
127#102—132no—
128#102—132no—
129#102C2×D1312yes—
130C22⋊C8—132no—
131C4×C8C2×D1311yescharacteristic
132C2×C13—82no—
133C2×C13#54711yescharacteristic
134C2×C13#57511yescharacteristic
135C2×C13#57611yescharacteristic
136D13—42no—
137C2×D4—131no—
138C2×D4—262no—
139C2×D4—262no—
140C2×D4C22×D1312yes—
141C22×C4—22no—
142C22×C4—132no—
143C22×C4—262no—
144D8—22no—
145M16—264no—
146C2×C8—132no—
147C2×C8C22×D1311yescharacteristic
148C2×C8C22×D1311yescharacteristic
149C4⋊C4—131no—
150C4⋊C4—132no—
151C4⋊C4—132no—
152C4⋊C4—262no—
153C4⋊C4—262no—
154C4⋊C4—262no—
155C4⋊C4C22×D1312yes—
156C22⋊C4—22no—
157C22⋊C4—132no—
158C22⋊C4—262no—
159C22⋊C4—262no—
160C22⋊C4—262no—
161C42—262no—
162C42C22×D1311yescharacteristic
163C13#335511yescharacteristic, complemented, Sylow
164C23—22no—
165C23—132no—
166D4—22no—
167D4—22no—
168D4—521no—
169D4—524no—
170D4—1042no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—132no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—1042no—
179C2×C4D4×D1311yescharacteristic
180C2×C4D4×D1311yescharacteristic
181C2×C4C23×D1311yescharacteristic
182C8—21no—
183C8—262no—
184C8#612712yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—262no—
189C22—262no—
190C22—262no—
191C22C2×D4×D1311yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—262no—
196C4—522no—
197C4—522no—
198C4C2×#612711yescharacteristic
199C4#8825711yescharacteristic
200C2—82no—
201C2—522no—
202C2#1171925611yescharacteristic
203C2#1171946211yescharacteristic
204C2#1171947311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×D8C2
socleC22×C13C22×D4
hypercenterC4×D8D13
hypocenterC13#3355
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #11719263C2semidirect
2. C4×C13×D8C2semidirect
3. #11718820C2semidirect
4. #11718670C2semidirect
5. #11718542C2semidirect
6. #11718445C2semidirect
7. #11718435C2semidirect
8. #11718349C2semidirect
9. #11718344C2semidirect
89. C4×D8D13semidirect
163. C13#3355semidirect

Maximal subgroups

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

subgroupindex
#117192632
C4×C13×D82
#117188202
#117186702
#117185422
#117184452
#117184352
#117183492
#117183442
#335513