Finite Group Databasebeta

← #13125122

Subgroups — #13125122

Order 1664.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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×#540C211yesmaximal, characteristic
2#11719221C211yesmaximal, characteristic, complemented
3#11718736C212yesmaximal, complemented
4#11718724C212yesmaximal, complemented
5#11718701C212yesmaximal, complemented
6#11718696C212yesmaximal, complemented
7#11718679C212yesmaximal, complemented
8C4×#6105C212yesmaximal, complemented
9#11718661C211yesmaximal, characteristic, complemented
10C22×Dic26C2211yescharacteristic
11C13×#127C2211yescharacteristic
12C13×#125C2211yescharacteristic
13C13×#123—22no—
14C13×#121—22no—
15C13×#121C2212yes—
16C4×D4×C13C2212yes—
17C13×#117C2211yescharacteristic
18C2×#6105C2212yes—
19C2×#6105C2212yes—
20#88180C2211yescharacteristic
21#88141—22no—
22#88131—22no—
23C4×Dic26C2212yes—
24C4×Dic26C2212yes—
25#88072C2212yes—
26#88072C2212yes—
27C22⋊#1055C2212yes—
28#88050C2212yes—
29#88050C2212yes—
30#88048C2212yes—
31#88047C2212yes—
32C4⋊#1055C2212yes—
33#88043C2211yescharacteristic
34C4×#1055C2211yescharacteristic
35C2×D4×C13—22no—
36C2×D4×C13—22no—
37C2×D4×C13C2312yes—
38C22×C4×C13—22no—
39C22×C4×C13C2311yescharacteristic
40C22×Dic13—21no—
41C2×Dic26—21no—
42C2×Dic26—24no—
43C2×Dic26C2312yes—
44C13×C4⋊C4—22no—
45C13×C4⋊C4D412yes—
46C13×C4⋊C4C2312yes—
47C13×C22⋊C4—22no—
48C13×C22⋊C4—22no—
49C13×C22⋊C4D412yes—
50C42×C13C2311yescharacteristic
51C42×C13C2311yescharacteristic
52C22⋊Dic13—21no—
53#6105—24no—
54#6105—24no—
55C4⋊Dic13C2312yes—
56#6101—22no—
57#6101—22no—
58C4×Dic13—22no—
59C4×Dic13—22no—
60C4×Dic13—21no—
61C2×#1055C2312yes—
62C2×#1055C2312yes—
63#3126—131nomaximal, Sylow
64C23×C13—22no—
65C23×C13C2×D411yescharacteristic
66D4×C13—22no—
67D4×C13—22no—
68D4×C13—82no—
69D4×C13—82no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—82no—
73C2×C4×C13C2×D412yes—
74C2×C4×C13C2×D412yes—
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2411yescharacteristic
77C2×Dic13—24no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80Dic26—24no—
81Dic26—22no—
82Dic26#4114yes—
83#1055—22no—
84#1055—22no—
85#540D1311yescharacteristic
86#519—131no—
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×C13—42no—
97C22×C13—42no—
98C22×C13—42no—
99C22×C13C22×D411yescharacteristic
100C4×C13—21no—
101C4×C13—22no—
102C4×C13—22no—
103C4×C13—42no—
104C4×C13C2×#4112yes—
105Dic13—24no—
106Dic13—42no—
107C22×Q8—131no—
108C2×SD16—132no—
109C2×SD16—132no—
110#127C2×D1311yescharacteristic
111#125C2×D1311yescharacteristic
112#123—22no—
113#121—22no—
114#121C2×D1312yes—
115C4×Q8—132no—
116C4×Q8—132no—
117C4×Q8—262no—
118C4×D4C2×D1312yes—
119#117—131no—
120#117—262no—
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—82no—
134C2×C13#52511yescharacteristic
135C2×C13#57712yes—
136C2×Q8—132no—
137C2×Q8—264no—
138C2×Q8—261no—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4C22×D1312yes—
142C22×C4—22no—
143C22×C4—261no—
144C22×C4C22×D1311yescharacteristic
145SD16—264no—
146SD16—264no—
147C2×C8—132no—
148C2×C8—132no—
149C4⋊C4—22no—
150C4⋊C4—132no—
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4C22⋊D1312yes—
154C4⋊C4C22×D1312yes—
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—261no—
158C22⋊C4C22⋊D1312yes—
159C42—261no—
160C42—262no—
161C42—262no—
162C42C22×D1311yescharacteristic
163C42C22×D1311yescharacteristic
164C13#312611yescharacteristic, complemented, Sylow
165C23—22no—
166C23C2×C22⋊D1311yescharacteristic
167Q8—134no—
168Q8—264no—
169Q8—262no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—264no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4C2×C22⋊D1312yes—
181C2×C4C2×C22⋊D1312yes—
182C2×C4C2×C22⋊D1311yescharacteristic
183C2×C4C23×D1311yescharacteristic
184C8—262no—
185C8—262no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D1311yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—264no—
197C4—522no—
198C4#41×D1312yes—
199C2—41no—
200C2—82no—
201C2#1171953311yescharacteristic
202C2#1171954112yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#540C2
socleC22×C13C22×D4
hypercenter#540D13
hypocenterC13#3126
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
2. #11719221C2semidirect
3. #11718736C2semidirect
4. #11718724C2semidirect
5. #11718701C2semidirect
6. #11718696C2semidirect
7. #11718679C2semidirect
8. C4×#6105C2semidirect
9. #11718661C2semidirect
164. C13#3126semidirect

Maximal subgroups

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

subgroupindex
C13×#5402
#117192212
#117187362
#117187242
#117187012
#117186962
#117186792
C4×#61052
#117186612
#312613