Finite Group Databasebeta

← #13126030

Subgroups — #13126030

Order 1664.

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

normal subgroups only

This group has 366 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×#532C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3#11718741C212yesmaximal, complemented
4#11718732C212yesmaximal, complemented
5#11718696C214yesmaximal, complemented
6#11718669C212yesmaximal, complemented
7#11718668C212yesmaximal, complemented
8#11718587C211yesmaximal, characteristic, complemented
9C2×C13×#41—21no—
10C13×C4⋊Q8C2211yescharacteristic
11C13×#127C2211yescharacteristic
12C13×#124—21no—
13C13×#121—21no—
14C13×#121C2212yes—
15C4×D4×C13—21no—
16C4×D4×C13C2212yes—
17C2×C42×C13C2211yescharacteristic
18#88180C2212yes—
19#88178—21no—
20#88178—21no—
21#88124C2212yes—
22#88123C2211yescharacteristic
23#88123C2211yescharacteristic
24C4×Dic26—21no—
25C4×Dic26—21no—
26#88072C2214yes—
27#88072C2214yes—
28C22⋊#1055C2212yes—
29#88048C2214yes—
30#88047C2214yes—
31C4⋊#1055C2212yes—
32#88043C2212yes—
33C13×#41—44no—
34C2×Q8×C13—21no—
35C2×D4×C13—22no—
36C2×D4×C13—21no—
37C2×D4×C13—21no—
38C2×D4×C13C2312yes—
39C22×C4×C13—22no—
40C22×C4×C13D411yescharacteristic
41C22×C4×C13D411yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C2×Dic26—21no—
44C2×Dic26—21no—
45C13×C4⋊C4—21no—
46C13×C4⋊C4C2312yes—
47C13×C22⋊C4—22no—
48C13×C22⋊C4—22no—
49C42×C13D411yescharacteristic
50C42×C13D411yescharacteristic
51C42×C13C2311yescharacteristic
52C42×C13C2311yescharacteristic
53C22⋊Dic13—22no—
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56C4⋊Dic13C2312yes—
57C4⋊Dic13C2312yes—
58#6101—22no—
59#6101—22no—
60C4×Dic13—22no—
61C2×#1055C2314yes—
62#3235—131nomaximal, Sylow
63C23×C13—22no—
64C23×C13C2×D411yescharacteristic
65Q8×C13—42no—
66D4×C13—24no—
67D4×C13—42no—
68D4×C13—42no—
69D4×C13—44no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—41no—
74C2×C4×C13—44no—
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2411yescharacteristic
81C2×Dic13—22no—
82C2×Dic13—22no—
83Dic26—42no—
84Dic26—42no—
85#1055—24no—
86#533—131no—
87#532D1311yescharacteristic
88#501—132no—
89#490—132no—
90#482—134no—
91#476—132no—
92#474—132no—
93#432—131no—
94C22×C13—21no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13—42no—
98C22×C13—42no—
99C22×C13—42no—
100C22×C13C22×D411yescharacteristic
101C4×C13—21no—
102C4×C13—21no—
103C4×C13—21no—
104C4×C13—21no—
105C4×C13—42no—
106C4×C13AGL(1,ℤ/8)12yes—
107C4×C132−1+412yes—
108Dic13—42no—
109Dic13—42no—
110C2×#41—21no—
111C4⋊Q8—131no—
112C4⋊Q8—131no—
113C4⋊Q8C2×D1311yescharacteristic
114#127C2×D1311yescharacteristic
115#125—132no—
116#124—21no—
117C22⋊Q8—261no—
118C22⋊Q8—261no—
119#121—21no—
120#121C2×D1312yes—
121C4×Q8—261no—
122C4×Q8—261no—
123C4×D4—21no—
124C4×D4C2×D1312yes—
125#117—132no—
126C2×C42C2×D1311yescharacteristic
127#107—134no—
128#106—134no—
129C4⋊C8—132no—
130#102—134no—
131#102—134no—
132C22⋊C8—132no—
133#97—132no—
134C2×C13—41no—
135C2×C13—82no—
136C2×C13#53611yescharacteristic
137C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C13#57511yescharacteristic
139#41—44no—
140C2×Q8—21no—
141C2×Q8—261no—
142C2×Q8—261no—
143C2×D4—22no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4C22×D1312yes—
147C22×C4—22no—
148C22×C4C22⋊D1311yescharacteristic
149C22×C4C22⋊D1311yescharacteristic
150C22×C4C22×D1311yescharacteristic
151C2×C8—134no—
152C4⋊C4—21no—
153C4⋊C4—132no—
154C4⋊C4—132no—
155C4⋊C4—262no—
156C4⋊C4—262no—
157C4⋊C4—261no—
158C4⋊C4—261no—
159C4⋊C4C22×D1312yes—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—262no—
163C42—262no—
164C42C22⋊D1311yescharacteristic
165C42C22⋊D1311yescharacteristic
166C42C22×D1311yescharacteristic
167C42C22×D1311yescharacteristic
168C13#323511yescharacteristic, complemented, Sylow
169C23—22no—
170C23C2×C22⋊D1311yescharacteristic
171Q8—42no—
172Q8—522no—
173Q8—522no—
174D4—24no—
175D4—42no—
176D4—42no—
177D4—44no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—44no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4C2×C22⋊D1311yescharacteristic
186C2×C4C2×C22⋊D1311yescharacteristic
187C2×C4C2×C22⋊D1311yescharacteristic
188C2×C4C2×C22⋊D1311yescharacteristic
189C2×C4C2×C22⋊D1311yescharacteristic
190C2×C4C23×D1311yescharacteristic
191C8—264no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—42no—
196C22—42no—
197C22—42no—
198C22C22×C22⋊D1311yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—42no—
204C4—522no—
205C4—522no—
206C4#8818612yes—
207C4#8825712yes—
208C2—41no—
209C2—82no—
210C2C2×#8818611yescharacteristic
211C2#1171952711yescharacteristic
212C2#1171953011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#532C2
socleC22×C13C22×D4
hypercenter#532D13
hypocenterC13#3235
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
2. #11719175C2semidirect
3. #11718741C2semidirect
4. #11718732C2semidirect
5. #11718696C2semidirect
6. #11718669C2semidirect
7. #11718668C2semidirect
8. #11718587C2semidirect
168. C13#3235semidirect

Maximal subgroups

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

subgroupindex
C13×#5322
#117191752
#117187412
#117187322
#117186962
#117186692
#117186682
#117185872
#323513