Finite Group Databasebeta

← #13130786

Subgroups — #13130786

Order 1664.

360 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C22×C4⋊#261C211yesmaximal, characteristic
2#11719136C211yesmaximal, characteristic
3C2×#88101C212yesmaximal, complemented
4D13×C22⋊C8C211yesmaximal, characteristic
5#11718265C212yesmaximal, complemented
6C23×#261—21no—
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C2×C4⋊#261—21no—
10C2×C4⋊#261—24no—
11C2×C4⋊#261C2211yescharacteristic
12C2×C4⋊#261C2211yescharacteristic
13C2×C4⋊#261C2212yes—
14C2×C8×D13C2212yes—
15(C2×#261)⋊C4—21no—
16#88101—24no—
17C13×C22⋊C8C411yescharacteristic, complemented
18C22⋊#1055C411yescharacteristic, complemented
19#88060C412yescomplemented
20C23×D13D411yescharacteristic
21C22×#261—24no—
22C22×#261—22no—
23C22×#261—21no—
24C22×#261—21no—
25C22×#261—42no—
26C22×#261—42no—
27C22×C4×C13C2×C411yescharacteristic
28C22×Dic13Q811yescharacteristic
29C2×C4×D13—22no—
30C2×C4×D13—22no—
31C2×C4×D13C2×C411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×C4×D13Q811yescharacteristic
34C2×C4×D13C2311yescharacteristic
35C22⋊#261—42no—
36C4⋊#261—24no—
37C4⋊#261—22no—
38C4⋊#261—22no—
39C4⋊#261—22no—
40C4⋊#261D414yes—
41C2×C8×C13C2×C412yescomplemented
42C2×#1055C2×C412yescomplemented
43C8×D13—22no—
44C8×D13—22no—
45#1853—131nomaximal, Sylow
46C23×C13C4⋊C411yescharacteristic
47C22×D13—21no—
48C22×D13—21no—
49C22×D13—21no—
50C22×D13—21no—
51C22×D13C4⋊C411yescharacteristic
52C22×D13SD1612yes—
53C22×D13SD1612yes—
54C22×D13C2×D411yescharacteristic
55C2×#261—24no—
56C2×#261—48no—
57C2×#261—42no—
58C2×#261—42no—
59C2×#261—41no—
60C2×#261—41no—
61C2×#261—41no—
62C2×#261—41no—
63C2×#261—41no—
64C2×#261—41no—
65C2×C4×C13—22no—
66C2×C4×C13C4⋊C411yescharacteristic
67C2×C4×C13C22×C411yescharacteristic
68C2×Dic13—22no—
69C2×Dic13C4⋊C411yescharacteristic
70C2×Dic13C2×Q811yescharacteristic
71C4×D13—21no—
72C4×D13—21no—
73C4×D13—22no—
74C4×D13—22no—
75C4×D13C2×D412yes—
76C4×D13#4112yes—
77C8×C13—22no—
78#1055—22no—
79C22×C4⋊C4—131no—
80C2×#106—132no—
81C2×C22⋊C8—131no—
82#380—131no—
83#340—132no—
84C22×C13—21no—
85C22×C13—21no—
86C22×C13#10612yescomplemented
87C22×C13C2×C4⋊C411yescharacteristic
88C2×D13—21no—
89C2×D13—21no—
90C2×D13—22no—
91C2×D13—22no—
92C2×D13—22no—
93C2×D13—22no—
94C2×D13#10612yescomplemented
95C2×D13#12011yescharacteristic
96C2×D13#12311yescharacteristic
97C2×D13C2×SD1611yescharacteristic
98C2×D13C2×SD1611yescharacteristic
99C2×D13AGL(1,ℤ/8)11yescharacteristic
100C2×D13#13711yescharacteristic
101#261—44no—
102#261—81no—
103#261—81no—
104C4×C13—21no—
105C4×C13C4×D412yes—
106Dic13—21no—
107Dic13C22⋊Q812yes—
108C23×C4—131no—
109C23×C4—261no—
110C22×C8—132no—
111C2×C4⋊C4—132no—
112C2×C4⋊C4—131no—
113C2×C4⋊C4—131no—
114C2×C4⋊C4—264no—
115C2×C4⋊C4—261no—
116C2×C22⋊C4—261no—
117#106—264no—
118C22⋊C8—131no—
119C22⋊C8—132no—
120C22⋊C8#26111yescharacteristic, complemented
121#95—261no—
122C2×C13—22no—
123C2×C13#38511yescharacteristic
124C2×C13C2×#10611yescharacteristic
125C2×C13#42811yescharacteristic
126D13—22no—
127D13#44811yescharacteristic
128D13#45011yescharacteristic
129D13#48111yescharacteristic
130D13#48311yescharacteristic
131C24—131no—
132C22×C4—131no—
133C22×C4—131no—
134C22×C4—131no—
135C22×C4—131no—
136C22×C4—131no—
137C22×C4—262no—
138C22×C4—262no—
139C22×C4—262no—
140C22×C4—264no—
141C22×C4—261no—
142C22×C4—261no—
143C22×C4—522no—
144C22×C4—522no—
145C22×C4C2×#26111yescharacteristic
146C2×C8—132no—
147C2×C8—262no—
148C2×C8—262no—
149C2×C8C2×#26112yescomplemented
150C4⋊C4—134no—
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4—262no—
154C4⋊C4—264no—
155C22⋊C4—522no—
156C13#185311yescharacteristic, complemented, Sylow
157C23—131no—
158C23—132no—
159C23—132no—
160C23—131no—
161C23—261no—
162C23—261no—
163C23—261no—
164C23—261no—
165C23C4⋊#26111yescharacteristic
166C2×C4—22no—
167C2×C4—131no—
168C2×C4—132no—
169C2×C4—132no—
170C2×C4—131no—
171C2×C4—262no—
172C2×C4—261no—
173C2×C4—261no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—264no—
177C2×C4—522no—
178C2×C4—522no—
179C2×C4—528no—
180C2×C4—521no—
181C2×C4—521no—
182C2×C4—521no—
183C2×C4—521no—
184C2×C4—521no—
185C2×C4—521no—
186C2×C4C4⋊#26111yescharacteristic
187C2×C4C22×#26111yescharacteristic
188C8—22no—
189C8—262no—
190C22—21no—
191C22—21no—
192C22—131no—
193C22—131no—
194C22—131no—
195C22—131no—
196C22—131no—
197C22—131no—
198C22—132no—
199C22—262no—
200C22—262no—
201C22—262no—
202C22—262no—
203C22—261no—
204C22—261no—
205C22#8810112yescomplemented
206C22C2×C4⋊#26111yescharacteristic
207C4—21no—
208C4—132no—
209C4—261no—
210C4—524no—
211C4—1041no—
212C4—1041no—
213C4D4×#26112yes—
214C2—22no—
215C2—131no—
216C2—131no—
217C2—131no—
218C2—131no—
219C2—262no—
220C2#1171907011yescharacteristic
221C2C2×#8810111yescharacteristic
222C2#1171909811yescharacteristic
subgroupG/H
centerC22C2×C4⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C22⋊C8C4
socleC22×C13C2×C4⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenterC22⋊C8#261
hypocenterC13#1853
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#88101C2semidirect
5. #11718265C2semidirect
17. C13×C22⋊C8C4semidirect
18. C22⋊#1055C4semidirect
19. #88060C4semidirect
41. C2×C8×C13C2×C4semidirect
42. C2×#1055C2×C4semidirect
86. C22×C13#106semidirect
94. C2×D13#106semidirect
120. C22⋊C8#261semidirect
149. C2×C8C2×#261semidirect
156. C13#1853semidirect
205. C22#88101semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#2612
#117191362
C2×#881012
D13×C22⋊C82
#117182652
#185313