Finite Group Databasebeta

← #13125974

Subgroups — #13125974

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
1#11719182C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3C13×#431C211yesmaximal, characteristic, complemented
4#11718508C214yesmaximal, complemented
5#11718398C214yesmaximal, complemented
6#11718355C211yesmaximal, characteristic, complemented
7#11718355C211yesmaximal, characteristic, complemented
8#11718343C211yesmaximal, characteristic, complemented
9#11718341C211yesmaximal, characteristic, complemented
10C2×#6127—21no—
11C2×C42×C13C2211yescharacteristic
12#88184—21no—
13#88184C2212yes—
14#88180C2212yes—
15#88178—21no—
16#88178—21no—
17#88129—21no—
18#88128C2211yescharacteristic
19C4×D52—21no—
20C4×D52C2212yes—
21#88124C2212yes—
22#88123C2211yescharacteristic
23#88123C2211yescharacteristic
24#88123C2211yescharacteristic
25C4×Dic26—21no—
26C4×Dic26—21no—
27C13×C4⋊C8C2212yes—
28C13×C22⋊C8C2212yes—
29C4×C8×C13C2211yescharacteristic
30C4×C8×C13C2211yescharacteristic
31#88061C2214yes—
32#88061C2214yes—
33#88058C2214yes—
34#88057C2214yes—
35C22×C4×C13D411yescharacteristic
36C22×C4×C13D411yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—22no—
39#6127—44no—
40C2×D52—21no—
41C2×D52—21no—
42C2×D52C2312yes—
43C2×C4×D13—22no—
44C2×Dic26—21no—
45C2×Dic26—21no—
46C2×Dic26—21no—
47C2×C8×C13C2312yes—
48C2×C8×C13C2312yes—
49C42×C13D411yescharacteristic
50C42×C13D411yescharacteristic
51C42×C13C2311yescharacteristic
52C42×C13C2311yescharacteristic
53C22⋊Dic13—22no—
54#6103—22no—
55#6103—22no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C4⋊Dic13—21no—
59C4⋊Dic13C2312yes—
60C4⋊Dic13C2312yes—
61C4⋊Dic13C2312yes—
62#6101—22no—
63#6101—22no—
64C4×Dic13—22no—
65#3228—131nomaximal, Sylow
66C23×C13C2×D411yescharacteristic
67C22×D13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2×D411yescharacteristic
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2411yescharacteristic
77C22⋊D13—44no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81D52—24no—
82D52—42no—
83D52—42no—
84C4×D13—44no—
85Dic26—42no—
86Dic26—42no—
87Dic26—42no—
88C8×C13—22no—
89C8×C13—22no—
90#533—131no—
91#532—131no—
92#500—131no—
93#498—131no—
94#486—131no—
95#486—131no—
96#482—134no—
97#478—134no—
98#431D1311yescharacteristic, complemented
99C22×C13—21no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13C22×D411yescharacteristic
103C2×D13—42no—
104C2×D13—42no—
105C2×D13—42no—
106C4×C13—21no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13#13512yes—
110C4×C13AGL(1,ℤ/8)12yes—
111C4×C132−1+412yes—
112Dic13—42no—
113Dic13—42no—
114Dic13—42no—
115C2×#41—261no—
116C4⋊Q8—131no—
117C4⋊Q8—131no—
118C4⋊Q8—131no—
119#127—131no—
120#125—132no—
121#124—261no—
122C22⋊Q8—261no—
123C22⋊Q8—261no—
124#121—132no—
125#121—261no—
126C4×Q8—261no—
127C4×Q8—261no—
128C4×D4—132no—
129C4×D4—261no—
130#117—132no—
131C2×C42C2×D1311yescharacteristic
132#107—134no—
133#106—134no—
134C4⋊C8C2×D1312yes—
135#102—134no—
136#102—134no—
137C22⋊C8C2×D1312yes—
138C4×C8C2×D1311yescharacteristic
139C4×C8C2×D1311yescharacteristic
140C2×C13—41no—
141C2×C13#53611yescharacteristic
142C2×C13C2×#13511yescharacteristic
143C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
144D13—82no—
145#41—524no—
146C2×Q8—261no—
147C2×Q8—261no—
148C2×Q8—261no—
149C2×D4—132no—
150C2×D4—262no—
151C2×D4—261no—
152C2×D4—261no—
153C22×C4—262no—
154C22×C4D5211yescharacteristic
155C22×C4D5211yescharacteristic
156C22×C4C22×D1311yescharacteristic
157C2×C8C22×D1312yes—
158C2×C8C22×D1312yes—
159C4⋊C4—132no—
160C4⋊C4—132no—
161C4⋊C4—132no—
162C4⋊C4—261no—
163C4⋊C4—262no—
164C4⋊C4—262no—
165C4⋊C4—261no—
166C4⋊C4—261no—
167C22⋊C4—262no—
168C22⋊C4—262no—
169C22⋊C4—262no—
170C42—262no—
171C42D5211yescharacteristic
172C42D5211yescharacteristic
173C42C22×D1311yescharacteristic
174C42C22×D1311yescharacteristic
175C13#322811yescharacteristic, complemented, Sylow
176C23—262no—
177C23C2×D5211yescharacteristic
178Q8—522no—
179Q8—522no—
180Q8—522no—
181D4—264no—
182D4—524no—
183D4—522no—
184D4—522no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—524no—
192C2×C4C2×D5211yescharacteristic
193C2×C4C2×D5211yescharacteristic
194C2×C4C2×D5211yescharacteristic
195C2×C4C2×D5211yescharacteristic
196C2×C4C2×D5211yescharacteristic
197C2×C4C23×D1311yescharacteristic
198C8—22no—
199C8—22no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—522no—
204C22—522no—
205C22—522no—
206C22C22×D5211yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—522no—
211C4—522no—
212C4—522no—
213C4#8815812yes—
214C4#8816212yes—
215C4#8825712yes—
216C2—41no—
217C2—1042no—
218C2#1171923111yescharacteristic
219C2C2×#8815811yescharacteristic
220C2C2×#8816211yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#431C2
socleC22×C13C22×D4
prime radical#11719182C2
hypercenter#431D13
hypocenterC13#3228
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #11719175C2semidirect
3. C13×#431C2semidirect
4. #11718508C2semidirect
5. #11718398C2semidirect
6. #11718355C2semidirect
7. #11718355C2semidirect
8. #11718343C2semidirect
9. #11718341C2semidirect
98. #431D13semidirect
175. C13#3228semidirect

Maximal subgroups

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

subgroupindex
#117191822
#117191752
C13×#4312
#117185082
#117183982
#117183552
#117183432
#117183412
#322813