Finite Group Databasebeta

← #13130949

Subgroups — #13130949

Order 1664.

240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C2×#88102C211yesmaximal, characteristic
2C2×#88101C211yesmaximal, characteristic
3#11719060C211yesmaximal, characteristic
4C4×C4⋊#261C211yesmaximal, characteristic
5D13×C4⋊C8C211yesmaximal, characteristic
6#11718265C211yesmaximal, characteristic
7#11718265C211yesmaximal, characteristic
8C2×C4⋊#261C2211yescharacteristic
9C2×C4⋊#261C2211yescharacteristic
10C2×C4⋊#261C2211yescharacteristic
11C2×C4⋊#261C2211yescharacteristic
12C2×C4×#261—21no—
13C2×C8×D13C2211yescharacteristic
14C2×C8×D13C2211yescharacteristic
15C42×D13C2211yescharacteristic
16(C2×#261)⋊C4—21no—
17(C2×#261)⋊C4—21no—
18(C2×#261)⋊C4—21no—
19#88102—22no—
20#88101—22no—
21C13×C4⋊C8C411yescharacteristic, complemented
22#88054C411yescharacteristic, complemented
23#88054C411yescharacteristic, complemented
24C4⋊#1055C411yescharacteristic, complemented
25C22×#261—21no—
26C22×#261—21no—
27C22×#261—21no—
28C22×#261—21no—
29C2×C4×D13D411yescharacteristic
30C2×C4×D13D411yescharacteristic
31C2×C4×D13C2311yescharacteristic
32C4⋊#261—21no—
33C4⋊#261—21no—
34C4⋊#261—21no—
35C4⋊#261—21no—
36C4⋊#261—21no—
37C4⋊#261—21no—
38C4⋊#261D412yes—
39C4⋊#261Q812yes—
40C4×#261—42no—
41C2×C8×C13C2×C411yescharacteristic
42C2×C8×C13C2×C411yescharacteristic
43C42×C13C2×C411yescharacteristic
44C4×Dic13C2×C411yescharacteristic
45C4×Dic13Q811yescharacteristic
46C4×Dic13Q811yescharacteristic
47C2×#1055C2×C411yescharacteristic
48C2×#1055C2×C411yescharacteristic
49C8×D13—21no—
50C8×D13—21no—
51C8×D13—21no—
52C8×D13—21no—
53#1949—131nomaximal, Sylow
54C22×D13C2×D411yescharacteristic
55C2×#261—22no—
56C2×#261—22no—
57C2×#261—41no—
58C2×#261—41no—
59C2×#261—41no—
60C2×#261—41no—
61C2×#261—41no—
62C2×#261—41no—
63C2×#261—41no—
64C2×#261—41no—
65C2×#261—41no—
66C2×#261—41no—
67C2×C4×C13C4⋊C411yescharacteristic
68C2×C4×C13C4⋊C411yescharacteristic
69C2×C4×C13C22×C411yescharacteristic
70C2×Dic13C4⋊C411yescharacteristic
71C2×Dic13C4⋊C411yescharacteristic
72C2×Dic13C2×Q811yescharacteristic
73C4×D13—21no—
74C4×D13—21no—
75C4×D13—21no—
76C4×D13—21no—
77C4×D13C2×D411yescharacteristic
78C4×D13C2×Q811yescharacteristic
79C4×D13#4111yescharacteristic
80C4×D13#4111yescharacteristic
81C8×C13—21no—
82C8×C13—21no—
83#1055—21no—
84#1055—21no—
85C2×#107—131no—
86C2×#106—131no—
87C2×C4⋊C8—131no—
88#382—131no—
89C4×C4⋊C4—131no—
90#340—131no—
91#340—131no—
92C22×C13C2×C4⋊C411yescharacteristic
93C2×D13#12111yescharacteristic
94C2×D13C22⋊Q811yescharacteristic
95C2×D13#13511yescharacteristic
96C2×D13#13511yescharacteristic
97C2×D13AGL(1,ℤ/8)11yescharacteristic
98C2×D13#13711yescharacteristic
99#261—42no—
100#261—42no—
101#261—81no—
102#261—81no—
103C4×C13—21no—
104C4×C13—21no—
105C4×C13C4×D411yescharacteristic
106C4×C13C4×Q811yescharacteristic
107Dic13—21no—
108Dic13—21no—
109Dic13#12511yescharacteristic
110Dic13C4⋊Q811yescharacteristic
111C22×C8—131no—
112C22×C8—131no—
113C2×C4⋊C4—131no—
114C2×C4⋊C4—131no—
115C2×C4⋊C4—131no—
116C2×C4⋊C4—131no—
117C2×C42—131no—
118C2×C42—261no—
119#107—262no—
120#106—262no—
121C4⋊C8—131no—
122C4⋊C8—131no—
123C4⋊C8—131no—
124C4⋊C8#26111yescharacteristic, complemented
125#95—261no—
126#95—261no—
127#95—261no—
128C2×C13#38911yescharacteristic
129C2×C13#42711yescharacteristic
130C2×C13#42811yescharacteristic
131D13#46311yescharacteristic
132D13#46411yescharacteristic
133D13#47811yescharacteristic
134D13#47911yescharacteristic
135C22×C4—131no—
136C22×C4—131no—
137C22×C4—131no—
138C22×C4—261no—
139C22×C4—261no—
140C22×C4—261no—
141C22×C4—261no—
142C2×C8—131no—
143C2×C8—131no—
144C2×C8—261no—
145C2×C8—261no—
146C2×C8—261no—
147C2×C8—261no—
148C2×C8C2×#26111yescharacteristic
149C2×C8C2×#26111yescharacteristic
150C4⋊C4—132no—
151C4⋊C4—132no—
152C4⋊C4—261no—
153C4⋊C4—261no—
154C4⋊C4—261no—
155C4⋊C4—261no—
156C4⋊C4—261no—
157C4⋊C4—261no—
158C42—131no—
159C42—131no—
160C42—131no—
161C42—522no—
162C42C2×#26111yescharacteristic
163C13#194911yescharacteristic, complemented, Sylow
164C23—131no—
165C2×C4—131no—
166C2×C4—131no—
167C2×C4—131no—
168C2×C4—131no—
169C2×C4—131no—
170C2×C4—131no—
171C2×C4—131no—
172C2×C4—261no—
173C2×C4—261no—
174C2×C4—261no—
175C2×C4—261no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—521no—
179C2×C4—521no—
180C2×C4—521no—
181C2×C4—521no—
182C2×C4—521no—
183C2×C4—521no—
184C2×C4—521no—
185C2×C4—521no—
186C2×C4—521no—
187C2×C4—521no—
188C2×C4C4⋊#26111yescharacteristic
189C2×C4C4⋊#26111yescharacteristic
190C2×C4C22×#26111yescharacteristic
191C8—21no—
192C8—21no—
193C8—261no—
194C8—261no—
195C22—131no—
196C22—131no—
197C22—131no—
198C22—131no—
199C22—131no—
200C22—131no—
201C22C2×C4⋊#26111yescharacteristic
202C4—21no—
203C4—21no—
204C4—131no—
205C4—131no—
206C4—261no—
207C4—261no—
208C4—522no—
209C4—522no—
210C4—1041no—
211C4—1041no—
212C4D4×#26111yescharacteristic
213C4Q8×#26111yescharacteristic
214C2—131no—
215C2—131no—
216C2—131no—
217C2—131no—
218C2#1171908311yescharacteristic
219C2#1171909211yescharacteristic
220C2#1171909811yescharacteristic
subgroupG/H
centerC22C2×C4⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊C8C4
socleC22×C13C2×C4⋊C4
prime radicalC22×D13C2×D4
cosocleC2×C4×D13C23
hypercenterC4⋊C8#261
hypocenterC13#1949
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
21. C13×C4⋊C8C4semidirect
22. #88054C4semidirect
23. #88054C4semidirect
24. C4⋊#1055C4semidirect
124. C4⋊C8#261semidirect
163. C13#1949semidirect

Maximal subgroups

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

subgroupindex
C2×#881022
C2×#881012
#117190602
C4×C4⋊#2612
D13×C4⋊C82
#117182652
#194913