Finite Group Databasebeta

← #13125968

Subgroups — #13125968

Order 1664.

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

normal subgroups only

This group has 370 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×#532C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3#11718740C211yesmaximal, characteristic, complemented
4#11718739C211yesmaximal, characteristic, complemented
5#11718731C211yesmaximal, characteristic, complemented
6#11718731C211yesmaximal, characteristic, complemented
7#11718696C214yesmaximal, complemented
8#11718670C214yesmaximal, complemented
9#11718586C211yesmaximal, characteristic, complemented
10C2×C13×#41—21no—
11C13×C4⋊Q8C2211yescharacteristic
12C13×#127C2211yescharacteristic
13C13×#124—21no—
14C13×#121—21no—
15C13×#121C2212yes—
16C4×D4×C13—21no—
17C4×D4×C13C2212yes—
18C2×C42×C13C2211yescharacteristic
19#88180C2212yes—
20#88178—21no—
21#88178—21no—
22#88124C2212yes—
23#88123C2211yescharacteristic
24#88123C2211yescharacteristic
25C4×Dic26—21no—
26C4×Dic26—21no—
27#88072C2214yes—
28#88072C2214yes—
29C22⋊#1055C2212yes—
30#88048C2214yes—
31#88047C2214yes—
32C4⋊#1055C2212yes—
33C4×#1055C2211yescharacteristic
34C4×#1055C2211yescharacteristic
35C13×#41—44no—
36C2×Q8×C13—21no—
37C2×D4×C13—22no—
38C2×D4×C13—21no—
39C2×D4×C13—21no—
40C2×D4×C13C2312yes—
41C22×C4×C13—22no—
42C22×C4×C13D411yescharacteristic
43C22×C4×C13D411yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C2×Dic26—21no—
46C2×Dic26—21no—
47C13×C4⋊C4—21no—
48C13×C4⋊C4C2312yes—
49C13×C22⋊C4—22no—
50C13×C22⋊C4—22no—
51C42×C13D411yescharacteristic
52C42×C13D411yescharacteristic
53C42×C13C2311yescharacteristic
54C42×C13C2311yescharacteristic
55C22⋊Dic13—22no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C4⋊Dic13C2312yes—
59C4⋊Dic13C2312yes—
60#6101—22no—
61#6101—22no—
62C4×Dic13—22no—
63C2×#1055C2312yes—
64C2×#1055C2312yes—
65#3228—131nomaximal, Sylow
66C23×C13—22no—
67C23×C13C2×D411yescharacteristic
68Q8×C13—42no—
69D4×C13—24no—
70D4×C13—44no—
71D4×C13—42no—
72D4×C13—42no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—44no—
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2411yescharacteristic
84C2×Dic13—22no—
85C2×Dic13—22no—
86Dic26—42no—
87Dic26—42no—
88#1055—22no—
89#1055—22no—
90#533—131no—
91#532D1311yescharacteristic
92#500—131no—
93#498—131no—
94#486—131no—
95#486—131no—
96#482—134no—
97#478—134no—
98#431—131no—
99C22×C13—21no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13C22×D411yescharacteristic
106C4×C13—21no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—42no—
110C4×C13#13512yes—
111C4×C13AGL(1,ℤ/8)12yes—
112C4×C132−1+412yes—
113Dic13—42no—
114Dic13—42no—
115C2×#41—21no—
116C4⋊Q8—131no—
117C4⋊Q8—131no—
118C4⋊Q8C2×D1311yescharacteristic
119#127C2×D1311yescharacteristic
120#125—132no—
121#124—21no—
122C22⋊Q8—261no—
123C22⋊Q8—261no—
124#121—21no—
125#121C2×D1312yes—
126C4×Q8—261no—
127C4×Q8—261no—
128C4×D4—21no—
129C4×D4C2×D1312yes—
130#117—132no—
131C2×C42C2×D1311yescharacteristic
132#107—134no—
133#106—134no—
134C4⋊C8—132no—
135#102—134no—
136#102—134no—
137C22⋊C8—132no—
138C4×C8—131no—
139C4×C8—131no—
140C2×C13—41no—
141C2×C13—82no—
142C2×C13#53611yescharacteristic
143C2×C13C2×#13511yescharacteristic
144C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
145#41—44no—
146C2×Q8—21no—
147C2×Q8—261no—
148C2×Q8—261no—
149C2×D4—22no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4C22×D1312yes—
153C22×C4—22no—
154C22×C4C22⋊D1311yescharacteristic
155C22×C4C22⋊D1311yescharacteristic
156C22×C4C22×D1311yescharacteristic
157C2×C8—132no—
158C2×C8—132no—
159C4⋊C4—21no—
160C4⋊C4—132no—
161C4⋊C4—132no—
162C4⋊C4—262no—
163C4⋊C4—262no—
164C4⋊C4—261no—
165C4⋊C4—261no—
166C4⋊C4C22×D1312yes—
167C22⋊C4—22no—
168C22⋊C4—22no—
169C22⋊C4—262no—
170C42—262no—
171C42C22⋊D1311yescharacteristic
172C42C22⋊D1311yescharacteristic
173C42C22×D1311yescharacteristic
174C42C22×D1311yescharacteristic
175C13#322811yescharacteristic, complemented, Sylow
176C23—22no—
177C23C2×C22⋊D1311yescharacteristic
178Q8—42no—
179Q8—522no—
180Q8—522no—
181D4—24no—
182D4—44no—
183D4—42no—
184D4—42no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—44no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4C2×C22⋊D1311yescharacteristic
193C2×C4C2×C22⋊D1311yescharacteristic
194C2×C4C2×C22⋊D1311yescharacteristic
195C2×C4C2×C22⋊D1311yescharacteristic
196C2×C4C2×C22⋊D1311yescharacteristic
197C2×C4C23×D1311yescharacteristic
198C8—262no—
199C8—262no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22C22×C22⋊D1311yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—42no—
211C4—522no—
212C4—522no—
213C4#8818612yes—
214C4#8820412yes—
215C4#8825712yes—
216C2—41no—
217C2—82no—
218C2C2×#8818611yescharacteristic
219C2C2×#8820411yescharacteristic
220C2#1171953011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#532C2
socleC22×C13C22×D4
hypercenter#532D13
hypocenterC13#3228
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. #11718740C2semidirect
4. #11718739C2semidirect
5. #11718731C2semidirect
6. #11718731C2semidirect
7. #11718696C2semidirect
8. #11718670C2semidirect
9. #11718586C2semidirect
175. C13#3228semidirect

Maximal subgroups

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

subgroupindex
C13×#5322
#117191752
#117187402
#117187392
#117187312
#117186962
#117186702
#117185862
#322813