Finite Group Databasebeta

← #13115778

Subgroups — #13115778

Order 1664.

260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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#11719222C211yesmaximal, characteristic
2M16×Dic13C211yesmaximal, characteristic
3C4×#6101C211yesmaximal, characteristic
4C13×#339C211yesmaximal, characteristic
5#11718147C211yesmaximal, characteristic
6#11718124C211yesmaximal, characteristic
7#11718115C211yesmaximal, characteristic
8C2×C13×M16C2211yescharacteristic
9C13×#117C2211yescharacteristic
10C2×C42×C13C2211yescharacteristic
11#88180C2211yescharacteristic
12C2×#6101—21no—
13C2×C4×Dic13C2211yescharacteristic
14C2×C4×Dic13C2211yescharacteristic
15C2×#6099C2211yescharacteristic
16#88144C411yescharacteristic, complemented
17#88144C411yescharacteristic, complemented
18#88142C411yescharacteristic, complemented
19#88142C411yescharacteristic, complemented
20#88132—21no—
21#88132—21no—
22C4×Dic26—21no—
23C4×Dic26—21no—
24#88071—21no—
25#88055—21no—
26C8×Dic13—21no—
27C22×C4×C13—21no—
28C22×C4×C13C2311yescharacteristic
29C22×Dic13—21no—
30C22×Dic13D411yescharacteristic
31C22×Dic13D411yescharacteristic
32C2×Dic26—21no—
33C2×Dic26—21no—
34C13×M16—21no—
35C13×M16Q812yescomplemented
36C2×C8×C13—21no—
37C13×C4⋊C4C2×C411yescharacteristic
38C13×C4⋊C4C2×C411yescharacteristic
39C13×C22⋊C4—21no—
40C42×C13—21no—
41C42×C13—21no—
42C42×C13—21no—
43C22⋊Dic13—21no—
44C4⋊Dic13—21no—
45C4⋊Dic13—21no—
46C4⋊Dic13C2×C411yescharacteristic
47C4⋊Dic13C2×C411yescharacteristic
48#6101—24no—
49#6101—21no—
50#6101—21no—
51#6101—21no—
52#6101—21no—
53C4×Dic13—21no—
54C4×Dic13—21no—
55C4×Dic13—21no—
56C4×Dic13C2×C411yescharacteristic
57C4×Dic13C2×C411yescharacteristic
58C4×Dic13D411yescharacteristic
59C4×Dic13D411yescharacteristic
60#6099—21no—
61#6099Q812yescomplemented
62C2×#1055—21no—
63#1986—131nomaximal, Sylow
64C23×C13C2×D411yescharacteristic
65C2×C4×C13—22no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—41no—
69C2×C4×C13—41no—
70C2×C4×C13C22×C411yescharacteristic
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2×Q811yescharacteristic
73C2×C4×C13C2×Q811yescharacteristic
74C2×C4×C13#4111yescharacteristic
75C2×C4×C13#4111yescharacteristic
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13—41no—
81C2×Dic13—41no—
82C2×Dic13—41no—
83C2×Dic13C22⋊C411yescharacteristic
84C2×Dic13C22⋊C411yescharacteristic
85C2×Dic13C22⋊C411yescharacteristic
86C2×Dic13C22⋊C411yescharacteristic
87Dic26—42no—
88Dic26—42no—
89C8×C13—22no—
90#1055—22no—
91#533—131no—
92C4×M16—131no—
93C4×C4⋊C4—131no—
94#339—131no—
95#339—131no—
96#339—131no—
97#339D1311yescharacteristic
98C22×C13—21no—
99C22×C13—21no—
100C22×C13C2×C22⋊C411yescharacteristic
101C22×C13#12411yescharacteristic
102C22×C13C4⋊Q811yescharacteristic
103C4×C13—42no—
104C4×C13—41no—
105C4×C13—41no—
106C4×C13C4×Q811yescharacteristic
107C4×C13C4×Q811yescharacteristic
108C4×C13C22⋊Q811yescharacteristic
109C4×C13C22⋊Q811yescharacteristic
110Dic13—21no—
111Dic13—21no—
112Dic13—21no—
113Dic13—42no—
114Dic13—41no—
115Dic13—41no—
116Dic13#10412yes—
117C2×M16—131no—
118C2×M16C2×D1311yescharacteristic
119C4⋊Q8—131no—
120C4⋊Q8—131no—
121#125—131no—
122#125—131no—
123C22⋊Q8—261no—
124C22⋊Q8—261no—
125C4×Q8—261no—
126C4×Q8—261no—
127#117—131no—
128#117C2×D1311yescharacteristic
129C2×C4⋊C4—261no—
130C2×C42—131no—
131C2×C42—131no—
132C2×C42C2×D1311yescharacteristic
133#97—261no—
134C4×C8—261no—
135#95—261no—
136C2×C13—21no—
137C2×C13—21no—
138C2×C13#39111yescharacteristic
139C2×C13C2×#10411yescharacteristic
140C2×C13#42111yescharacteristic
141C2×Q8—261no—
142C2×Q8—261no—
143C22×C4—21no—
144C22×C4—131no—
145C22×C4—131no—
146C22×C4—261no—
147C22×C4C22×D1311yescharacteristic
148M16—21no—
149M16—132no—
150M16—261no—
151M16Dic2612yescomplemented
152C2×C8—21no—
153C2×C8—261no—
154C4⋊C4—131no—
155C4⋊C4—131no—
156C4⋊C4—261no—
157C4⋊C4—261no—
158C4⋊C4—261no—
159C4⋊C4—261no—
160C4⋊C4—261no—
161C4⋊C4—261no—
162C4⋊C4—264no—
163C4⋊C4C4×D1311yescharacteristic
164C4⋊C4C4×D1311yescharacteristic
165C22⋊C4—21no—
166C22⋊C4—261no—
167C42—21no—
168C42—21no—
169C42—21no—
170C42—131no—
171C42—131no—
172C42—131no—
173C42—131no—
174C42—261no—
175C42—261no—
176C42—261no—
177C13#198611yescharacteristic, complemented, Sylow
178C23D4×D1311yescharacteristic
179Q8—522no—
180Q8—522no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—131no—
187C2×C4—131no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—521no—
195C2×C4—521no—
196C2×C4—521no—
197C2×C4C2×Dic2611yescharacteristic
198C2×C4C2×C4×D1311yescharacteristic
199C2×C4#612711yescharacteristic
200C2×C4D4×D1311yescharacteristic
201C2×C4#612911yescharacteristic
202C2×C4Q8×D1311yescharacteristic
203C8—22no—
204C8—262no—
205C22—21no—
206C22—21no—
207C22C22⋊C4×D1311yescharacteristic
208C22#8813911yescharacteristic
209C22#8814211yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—132no—
214C4—261no—
215C4—261no—
216C4—261no—
217C4—522no—
218C4—521no—
219C4—521no—
220C4C4×Dic2611yescharacteristic
221C4#8813211yescharacteristic
222C4#8814111yescharacteristic
223C4#8815011yescharacteristic
224C2—21no—
225C2—21no—
226C2#1171830711yescharacteristic
227C2D13×#10411yescharacteristic
228C2#1171848211yescharacteristic
subgroupG/H
centerC2×C4D4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#339C2
socleC22×C13C2×C22⋊C4
prime radicalC23×C13C2×D4
cosocleC22×C4×C13C23
hypercenter#339D13
hypocenterC13#1986
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
16. #88144C4semidirect
17. #88144C4semidirect
18. #88142C4semidirect
19. #88142C4semidirect
35. C13×M16Q8semidirect
61. #6099Q8semidirect
151. M16Dic26semidirect
177. C13#1986semidirect

Maximal subgroups

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

subgroupindex
#117192222
M16×Dic132
C4×#61012
C13×#3392
#117181472
#117181242
#117181152
#198613