Finite Group Databasebeta

← #13125127

Subgroups — #13125127

Order 1664.

382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C13×#519C211yesmaximal, characteristic, complemented
2#11719240C211yesmaximal, characteristic
3#11718888C212yesmaximal, complemented
4#11718688C212yesmaximal, complemented
5#11718687C212yesmaximal, complemented
6C4×#6106C212yesmaximal, complemented
7#11718683C212yesmaximal, complemented
8#11718664C212yesmaximal, complemented
9#11718661C211yesmaximal, characteristic, complemented
10C22×Q8×C13C2211yescharacteristic
11C4×Q8×C13—22no—
12C4×Q8×C13C2212yes—
13C4×Q8×C13C2212yes—
14C13×#117—22no—
15C13×#117C2211yescharacteristic
16C13×#117C2211yescharacteristic
17C2×#6106C2212yes—
18C2×#6106C2212yes—
19#88184C2212yes—
20#88148—22no—
21#88138—22no—
22#88128C2211yescharacteristic
23C4×D52C2212yes—
24#88124C2211yescharacteristic
25#88075C2212yes—
26#88075C2212yes—
27C22⋊#1055C2212yes—
28#88049C2212yes—
29#88049C2212yes—
30#88048C2212yes—
31#88047C2212yes—
32C4⋊#1055C2212yes—
33#88043C2211yescharacteristic
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—24no—
36C2×Q8×C13—21no—
37C2×Q8×C13C2312yes—
38C22×C4×C13—21no—
39C22×C4×C13C2311yescharacteristic
40C2×C22⋊D13—22no—
41C2×D52—22no—
42C2×D52C2312yes—
43C2×C4×D13—22no—
44C13×C4⋊C4—22no—
45C13×C4⋊C4—22no—
46C13×C4⋊C4D412yes—
47C13×C4⋊C4C2312yes—
48C13×C22⋊C4—21no—
49C13×C22⋊C4D412yes—
50C42×C13—22no—
51C42×C13—22no—
52C42×C13—21no—
53C42×C13C2311yescharacteristic
54C42×C13C2311yescharacteristic
55#6106—24no—
56#6106—24no—
57#6103—22no—
58#6103—22no—
59C4⋊Dic13C2312yes—
60#6101—22no—
61C2×#1055C2312yes—
62C2×#1055C2312yes—
63#3126—131nomaximal, Sylow
64C23×C13C2×D411yescharacteristic
65C22×D13—22no—
66Q8×C13—24no—
67Q8×C13—22no—
68Q8×C13#4114yes—
69C2×C4×C13—24no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D412yes—
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D412yes—
76C2×C4×C13C2411yescharacteristic
77C22⋊D13—82no—
78C2×Dic13—22no—
79D52—22no—
80D52—22no—
81D52—82no—
82C4×D13—82no—
83#1055—22no—
84#1055—22no—
85#540—131no—
86#519D1311yescharacteristic, complemented
87#482—132no—
88#479—132no—
89#460—132no—
90#448—132no—
91#440—132no—
92C4×SD16—132no—
93#433—131no—
94C22×C13—21no—
95C22×C13—22no—
96C22×C13C22×D411yescharacteristic
97C2×D13—42no—
98C2×D13—42no—
99C2×D13—42no—
100C4×C13—24no—
101C4×C13—21no—
102C4×C13—22no—
103C4×C13—22no—
104C4×C13—42no—
105C4×C13C2×#4112yes—
106Dic13—42no—
107C22×Q8C2×D1311yescharacteristic
108C2×SD16—132no—
109C2×SD16—132no—
110#127—131no—
111#125—131no—
112#123—262no—
113#121—132no—
114#121—262no—
115C4×Q8—22no—
116C4×Q8C2×D1312yes—
117C4×Q8C2×D1312yes—
118C4×D4—132no—
119#117—22no—
120#117C2×D1311yescharacteristic
121#117C2×D1311yescharacteristic
122#107—132no—
123#106—132no—
124C4⋊C8—132no—
125#103—132no—
126#103—132no—
127#102—132no—
128#102—132no—
129C22⋊C8—132no—
130#97—131no—
131C4×C8—131no—
132C2×C13—41no—
133C2×C13#52511yescharacteristic
134C2×C13#57712yes—
135D13—82no—
136C2×Q8—24no—
137C2×Q8—21no—
138C2×Q8C22×D1312yes—
139C2×D4—132no—
140C2×D4—262no—
141C2×D4—262no—
142C22×C4—21no—
143C22×C4—262no—
144C22×C4C22×D1311yescharacteristic
145SD16—264no—
146SD16—264no—
147C2×C8—132no—
148C2×C8—132no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—132no—
152C4⋊C4—262no—
153C4⋊C4C22⋊D1312yes—
154C4⋊C4C22×D1312yes—
155C22⋊C4—21no—
156C22⋊C4—262no—
157C22⋊C4—262no—
158C22⋊C4C22⋊D1312yes—
159C42—22no—
160C42—22no—
161C42—21no—
162C42C22×D1311yescharacteristic
163C42C22×D1311yescharacteristic
164C13#312611yescharacteristic, complemented, Sylow
165C23—262no—
166C23C2×C22⋊D1311yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#612714yes—
170D4—262no—
171D4—262no—
172D4—1042no—
173D4—1042no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—262no—
179C2×C4—1042no—
180C2×C4C2×C22⋊D1312yes—
181C2×C4C2×C22⋊D1312yes—
182C2×C4C2×C22⋊D1311yescharacteristic
183C2×C4C23×D1311yescharacteristic
184C8—262no—
185C8—262no—
186C22—21no—
187C22—22no—
188C22—522no—
189C22—522no—
190C22—522no—
191C22C22×C22⋊D1311yescharacteristic
192C4—24no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—522no—
198C4C2×#612712yes—
199C2—41no—
200C2—1042no—
201C2#1171949611yescharacteristic
202C2#1171954212yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#519C2
socleC22×C13C22×D4
prime radical#11719240C2
hypercenter#519D13
hypocenterC13#3126
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C13×#519C2semidirect
3. #11718888C2semidirect
4. #11718688C2semidirect
5. #11718687C2semidirect
6. C4×#6106C2semidirect
7. #11718683C2semidirect
8. #11718664C2semidirect
9. #11718661C2semidirect
86. #519D13semidirect
164. C13#3126semidirect

Maximal subgroups

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

subgroupindex
C13×#5192
#117192402
#117188882
#117186882
#117186872
C4×#61062
#117186832
#117186642
#117186612
#312613