Finite Group Databasebeta

← #13130141

Subgroups — #13130141

Order 1664.

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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#11719301C211yesmaximal, characteristic
2#11719125C211yesmaximal, characteristic, complemented
3C2×C4⋊#1057C211yesmaximal, characteristic, complemented
4D4⋊#1057C212yesmaximal, complemented
5#11718243C212yesmaximal, complemented
6C2×#6129—21no—
7C22×#1057—21no—
8C13×#121C411yescharacteristic
9#88194C411yescharacteristic
10#88193—21no—
11D4×Dic13C2211yescharacteristic
12#88184C411yescharacteristic
13C2×C4×Dic13C2211yescharacteristic
14#88147C2211yescharacteristic
15#88142C411yescharacteristic
16#88139—21no—
17#88135—21no—
18C22⋊#1057—21no—
19#88112—21no—
20C4⋊#1057—21no—
21C4⋊#1057C2212yes—
22C4×#1057C2212yes—
23C2×D4×C13—21no—
24C2×D4×C13C2×C411yescharacteristic
25C22×C4×C13C2×C411yescharacteristic
26C2×C22⋊D13—21no—
27C2×C22⋊D13—21no—
28C2×C22⋊D13—21no—
29C22×Dic13—21no—
30C22×Dic13D411yescharacteristic
31C22×Dic13D411yescharacteristic
32#6129—42no—
33#6129—42no—
34C2×D52C2×C411yescharacteristic
35C2×C4×D13—21no—
36C2×Dic26—21no—
37C2×#1057—22no—
38C2×#1057—22no—
39C2×#1057—42no—
40C13×C4⋊C4C2×C411yescharacteristic
41C13×C22⋊C4—21no—
42C22⋊Dic13—21no—
43#6103—21no—
44#6103—21no—
45C4⋊Dic13C2×C411yescharacteristic
46#6101—21no—
47C4×Dic13C2×C411yescharacteristic
48C4×Dic13D411yescharacteristic
49C4×Dic13D411yescharacteristic
50C4×Dic13C2311yescharacteristic
51#1480—131nomaximal, Sylow
52C23×C13—21no—
53C23×C13C22⋊C411yescharacteristic
54C22×D13—21no—
55D4×C13—22no—
56D4×C13—42no—
57C2×C4×C13—22no—
58C2×C4×C13—21no—
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22×C411yescharacteristic
61C22⋊D13—42no—
62C22⋊D13—42no—
63C22⋊D13—42no—
64C2×Dic13—21no—
65C2×Dic13—41no—
66C2×Dic13—41no—
67C2×Dic13—41no—
68C2×Dic13C22⋊C411yescharacteristic
69C2×Dic13C22⋊C411yescharacteristic
70C2×Dic13D812yes—
71C2×Dic13SD1612yes—
72C2×Dic13C2×D411yescharacteristic
73C2×Dic13C2×D411yescharacteristic
74D52—22no—
75C4×D13—41no—
76C4×D13—41no—
77Dic26—42no—
78#1057—42no—
79#1057—42no—
80#532—131no—
81#431—131no—
82C2×C4⋊C8—131no—
83D4⋊C8—132no—
84D4⋊C8—132no—
85C22×C13—21no—
86C22×C13—21no—
87C22×C13—41no—
88C22×C13—41no—
89C22×C13—41no—
90C22×C13#10212yes—
91C22×C13C2×C22⋊C411yescharacteristic
92C2×D13—41no—
93C2×D13—41no—
94C2×D13—41no—
95C4×C13—21no—
96C4×C13—41no—
97C4×C13#13112yes—
98Dic13—21no—
99Dic13—21no—
100Dic13—41no—
101Dic13#10212yes—
102Dic13C2×D811yescharacteristic
103Dic13C2×SD1611yescharacteristic
104C2×#41—261no—
105C22×C8—261no—
106C4⋊Q8—131no—
107#127—131no—
108#124—261no—
109#121—131no—
110#121—261no—
111#121#26111yescharacteristic
112C4×D4—131no—
113C4×D4—131no—
114C4×D4—261no—
115C2×C42—131no—
116C4⋊C8—132no—
117C4⋊C8—261no—
118C4⋊C8—261no—
119C22⋊C8—261no—
120C4×C8—132no—
121C2×C13—22no—
122C2×C13—81no—
123C2×C13#40811yescharacteristic
124C2×C13C2×#10211yescharacteristic
125C2×C13#42111yescharacteristic
126D13—81no—
127#41—522no—
128#41—522no—
129C2×Q8—261no—
130C2×D4—21no—
131C2×D4—131no—
132C2×D4—261no—
133C2×D4—261no—
134C2×D4—261no—
135C2×D4C2×#26111yescharacteristic
136C22×C4—131no—
137C22×C4—131no—
138C22×C4—261no—
139C22×C4—261no—
140C22×C4C2×#26111yescharacteristic
141C2×C8—262no—
142C2×C8—262no—
143C2×C8—522no—
144C4⋊C4—131no—
145C4⋊C4—261no—
146C4⋊C4C2×#26111yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—261no—
149C22⋊C4—261no—
150C22⋊C4—261no—
151C42—131no—
152C42—131no—
153C42—131no—
154C42—131no—
155C13#148011yescharacteristic, complemented, Sylow
156C23—21no—
157C23—261no—
158C23C22⋊#26111yescharacteristic
159Q8—522no—
160D4—22no—
161D4—42no—
162D4—262no—
163D4—522no—
164D4—522no—
165D4—522no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—132no—
169C2×C4—132no—
170C2×C4—131no—
171C2×C4—131no—
172C2×C4—131no—
173C2×C4—131no—
174C2×C4—261no—
175C2×C4—521no—
176C2×C4—521no—
177C2×C4—521no—
178C2×C4—521no—
179C2×C4—521no—
180C2×C4C22⋊#26111yescharacteristic
181C2×C4C22×#26111yescharacteristic
182C8—522no—
183C8—522no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—521no—
190C22—521no—
191C22—521no—
192C22#8811512yes—
193C22C2×C22⋊#26111yescharacteristic
194C4—21no—
195C4—41no—
196C4—132no—
197C4—131no—
198C4—131no—
199C4—261no—
200C4—261no—
201C4—521no—
202C4#8823812yes—
203C2—22no—
204C2—81no—
205C2—1041no—
206C2C2×#8811511yescharacteristic
207C2#1171914611yescharacteristic
208C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#121C4
socleC22×C13C2×C22⋊C4
prime radical#11719301C2
cosocleC4×Dic13C23
hypercenter#121#261
hypocenterC13#1480
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11719125C2semidirect
3. C2×C4⋊#1057C2semidirect
4. D4⋊#1057C2semidirect
5. #11718243C2semidirect
155. C13#1480semidirect

Maximal subgroups

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

subgroupindex
#117193012
#117191252
C2×C4⋊#10572
D4⋊#10572
#117182432
#148013