Finite Group Databasebeta

← #13130707

Subgroups — #13130707

Order 1664.

292 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C4×Q8×D13C211yesmaximal, characteristic
2C2×#88117C212yesmaximal
3#11719060C211yesmaximal, characteristic
4D13⋊(C4⋊C8)C211yesmaximal, characteristic
5#11718246C212yesmaximal
6C2×Q8×D13C2211yescharacteristic
7C2×C4⋊#261C2212yes—
8C2×D13⋊C8C2212yes—
9C4×Q8×C13C411yescharacteristic, complemented
10Q8×Dic13C411yescharacteristic, complemented
11C4⋊C4×D13—21no—
12C4⋊C4×D13C2211yescharacteristic
13#88141—21no—
14#88141C411yescharacteristic, complemented
15C42×D13—21no—
16C42×D13C2211yescharacteristic
17C4×Dic26—21no—
18C4×Dic26C411yescharacteristic, complemented
19#88117—24no—
20(C2×#261)⋊C4—21no—
21(C2×#261)⋊C4—21no—
22#88112—21no—
23C4⋊#1057—21no—
24C22×#261—22no—
25C2×Q8×C13C2×C411yescharacteristic
26Q8×D13—21no—
27Q8×D13—21no—
28Q8×D13D412yes—
29Q8×D13Q812yes—
30C2×C4×D13—21no—
31C2×C4×D13—21no—
32C2×C4×D13D411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×C4×D13C2311yescharacteristic
35C2×Dic26—21no—
36C2×Dic26C2×C411yescharacteristic
37C2×#1057—22no—
38C4⋊#261—22no—
39C4⋊#261—22no—
40D13⋊C8—22no—
41D13⋊C8—22no—
42C13×C4⋊C4—21no—
43C13×C4⋊C4C2×C411yescharacteristic
44C42×C13—21no—
45C42×C13C2×C411yescharacteristic
46C4⋊Dic13—21no—
47C4⋊Dic13C2×C411yescharacteristic
48#6101—21no—
49#6101—21no—
50#6101—21no—
51C4×Dic13—21no—
52C4×Dic13—21no—
53C4×Dic13—21no—
54C4×Dic13C2×C411yescharacteristic
55C4×Dic13D411yescharacteristic
56C4×Dic13D411yescharacteristic
57#1805—131nomaximal, Sylow
58C22×D13C2×D411yescharacteristic
59C2×#261—42no—
60C2×#261—42no—
61C2×#261—42no—
62Q8×C13—21no—
63Q8×C13C4⋊C412yes—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13C22⋊C411yescharacteristic
67C2×C4×C13C22⋊C411yescharacteristic
68C2×C4×C13C22×C411yescharacteristic
69C2×Dic13—21no—
70C2×Dic13—21no—
71C2×Dic13C22⋊C411yescharacteristic
72C2×Dic13C22⋊C411yescharacteristic
73C2×Dic13C2×D411yescharacteristic
74C4×D13—22no—
75C4×D13—22no—
76C4×D13—22no—
77C4×D13—22no—
78C4×D13—42no—
79C4×D13C2×D411yescharacteristic
80C4×D13C2×Q811yescharacteristic
81C4×D13#4111yescharacteristic
82C4×D13#4111yescharacteristic
83Dic26—21no—
84Dic26—22no—
85Dic26—22no—
86Dic26C4⋊C412yes—
87#1057—42no—
88C2×C4×Q8—131no—
89C2×C4⋊C8—131no—
90C2×#103—132no—
91#382—131no—
92#340—132no—
93C22×C13C2×C22⋊C411yescharacteristic
94C2×D13#12111yescharacteristic
95C2×D13C22⋊Q811yescharacteristic
96C2×D13#13512yes—
97C2×D13#13712yes—
98#261—82no—
99C4×C13—22no—
100C4×C13—21no—
101C4×C13—21no—
102C4×C13—41no—
103C4×C13C2×C4⋊C411yescharacteristic
104C4×C13#11711yescharacteristic
105Dic13—22no—
106Dic13—21no—
107Dic13—21no—
108Dic13—41no—
109Dic13#12111yescharacteristic
110Dic13C22⋊Q811yescharacteristic
111C22×Q8—131no—
112C22×C8—132no—
113C4×Q8—131no—
114C4×Q8—131no—
115C4×Q8—131no—
116C4×Q8—261no—
117C4×Q8—261no—
118C4×Q8#26111yescharacteristic, complemented
119C2×C4⋊C4—131no—
120C2×C4⋊C4—132no—
121C2×C4⋊C4—261no—
122C2×C42—131no—
123C2×C42—261no—
124C4⋊C8—261no—
125C4⋊C8—261no—
126#103—264no—
127#95—261no—
128#95—261no—
129C2×C13#38011yescharacteristic
130C2×C13#41611yescharacteristic
131C2×C13#41911yescharacteristic
132D13#46412yes—
133D13#47912yes—
134C2×Q8—132no—
135C2×Q8—132no—
136C2×Q8—131no—
137C2×Q8—261no—
138C2×Q8—261no—
139C2×Q8—261no—
140C2×Q8C2×#26111yescharacteristic
141C22×C4—131no—
142C22×C4—131no—
143C22×C4—131no—
144C22×C4—261no—
145C22×C4—261no—
146C22×C4—262no—
147C2×C8—262no—
148C2×C8—262no—
149C2×C8—262no—
150C4⋊C4—21no—
151C4⋊C4—131no—
152C4⋊C4—261no—
153C4⋊C4—261no—
154C4⋊C4—261no—
155C4⋊C4—262no—
156C4⋊C4—262no—
157C4⋊C4—261no—
158C4⋊C4C2×#26111yescharacteristic
159C42—21no—
160C42—131no—
161C42—131no—
162C42—131no—
163C42—261no—
164C42—261no—
165C42—261no—
166C42C2×#26111yescharacteristic
167C13#180511yescharacteristic, complemented, Sylow
168C23—131no—
169Q8—21no—
170Q8—132no—
171Q8—262no—
172Q8—262no—
173Q8—261no—
174Q8C4⋊#26112yes—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—131no—
178C2×C4—131no—
179C2×C4—131no—
180C2×C4—131no—
181C2×C4—131no—
182C2×C4—131no—
183C2×C4—131no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4—261no—
189C2×C4—261no—
190C2×C4—522no—
191C2×C4—522no—
192C2×C4—522no—
193C2×C4—522no—
194C2×C4C22⋊#26111yescharacteristic
195C2×C4C22⋊#26111yescharacteristic
196C2×C4C22×#26111yescharacteristic
197C8—522no—
198C22—131no—
199C22—131no—
200C22—132no—
201C22—132no—
202C22C2×C22⋊#26111yescharacteristic
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—131no—
208C4—131no—
209C4—262no—
210C4—261no—
211C4—261no—
212C4—521no—
213C4—1042no—
214C4C2×C4⋊#26111yescharacteristic
215C4#8823711yescharacteristic
216C2—132no—
217C2—132no—
218C2#1171913611yescharacteristic
219C2#1171915311yescharacteristic
220C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×Q8×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C2×D4
cosocleC2×C4×D13C23
hypercenterC4×Q8#261
hypocenterC13#1805
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
9. C4×Q8×C13C4semidirect
10. Q8×Dic13C4semidirect
14. #88141C4semidirect
18. C4×Dic26C4semidirect
118. C4×Q8#261semidirect
167. C13#1805semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D132
C2×#881172
#117190602
D13⋊(C4⋊C8)2
#117182462
#180513