Finite Group Databasebeta

← #13113393

Subgroups — #13113393

Order 1664.

284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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#11719496C211yesmaximal, characteristic
2C2×C13×C22⋊C8C211yesmaximal, characteristic, complemented
3#11718872C211yesmaximal, characteristic, complemented
4#11718062C212yesmaximal, complemented
5#11718059C212yesmaximal, complemented
6C23×C4×C13C2211yescharacteristic
7C2×#6127C411yescharacteristic, complemented
8C22×C8×C13—21no—
9#88207—21no—
10C2×C22⋊Dic13—21no—
11#88184C411yescharacteristic, complemented
12#88184C2211yescharacteristic
13#88183—21no—
14C4×C22⋊D13—21no—
15C4×C22⋊D13—21no—
16#88180C411yescharacteristic, complemented
17#88178C411yescharacteristic, complemented
18#88178C2211yescharacteristic
19C13×C22⋊C8—21no—
20C13×C22⋊C8C2212yes—
21#88071—21no—
22#88071C2212yes—
23C24×C13D411yescharacteristic
24C22×C4×C13—42no—
25C22×C4×C13C2×C411yescharacteristic
26C22×C4×C13C2×C411yescharacteristic
27C22×C4×C13D411yescharacteristic
28C22×C4×C13D411yescharacteristic
29C22×C4×C13D411yescharacteristic
30C22×C4×C13C2311yescharacteristic
31C2×C22⋊D13—21no—
32C2×C22⋊D13—21no—
33C2×C22⋊D13—21no—
34C22×Dic13—22no—
35#6127—42no—
36C2×D52C2×C411yescharacteristic
37C2×C4×D13—21no—
38C2×Dic26C2×C411yescharacteristic
39C2×C8×C13—22no—
40C2×C8×C13—42no—
41C22⋊Dic13—21no—
42C22⋊Dic13—21no—
43C22⋊Dic13—21no—
44C22⋊Dic13—42no—
45#6103—21no—
46#6103—21no—
47C4⋊Dic13C2×C411yescharacteristic
48C4⋊Dic13C2×C411yescharacteristic
49#6101—21no—
50#6101—21no—
51C4×Dic13—21no—
52#1516—131nomaximal, Sylow
53C23×C13—22no—
54C23×C13—22no—
55C23×C13—41no—
56C23×C13C22⋊C411yescharacteristic
57C23×C13C22⋊C411yescharacteristic
58C23×C13C2×D411yescharacteristic
59C22×D13—21no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13C22⋊C411yescharacteristic
67C2×C4×C13C22⋊C411yescharacteristic
68C2×C4×C13C22×C411yescharacteristic
69C2×C4×C13C2×D411yescharacteristic
70C22⋊D13—42no—
71C22⋊D13—42no—
72C22⋊D13—42no—
73C2×Dic13—21no—
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—42no—
77C2×Dic13—42no—
78C2×Dic13—42no—
79D52—41no—
80C4×D13—42no—
81Dic26—41no—
82C8×C13—42no—
83#525—131no—
84C2×C22⋊C8D1311yescharacteristic, complemented
85#381—131no—
86#328—132no—
87#327—132no—
88C22×C13—21no—
89C22×C13—21no—
90C22×C13—21no—
91C22×C13—21no—
92C22×C13—21no—
93C22×C13—21no—
94C22×C13—21no—
95C22×C13—44no—
96C22×C13#9912yes—
97C22×C13C2×C22⋊C411yescharacteristic
98C22×C13#13512yes—
99C2×D13—41no—
100C2×D13—41no—
101C2×D13—41no—
102C4×C13—21no—
103C4×C13—21no—
104C4×C13—21no—
105C4×C13—21no—
106Dic13—41no—
107Dic13—41no—
108Dic13—41no—
109Dic13—82no—
110C2×#41—131no—
111C23×C4C2×D1311yescharacteristic
112C22×C8—21no—
113#123—261no—
114C22⋊Q8—131no—
115C22⋊Q8—131no—
116#121—131no—
117#121—131no—
118#120—261no—
119C4×D4—261no—
120C4×D4—261no—
121#117—131no—
122C2×C22⋊C4—261no—
123C22⋊C8—21no—
124C22⋊C8C2×D1312yes—
125#95—132no—
126#95—261no—
127C2×C13—22no—
128C2×C13—22no—
129C2×C13—41no—
130C2×C13C2×#9911yescharacteristic
131C2×C13#41611yescharacteristic
132C2×C13#42111yescharacteristic
133D13—81no—
134C24D5211yescharacteristic
135#41—522no—
136C2×Q8—131no—
137C2×D4—131no—
138C2×D4—261no—
139C2×D4—261no—
140C2×D4—261no—
141C22×C4—42no—
142C22×C4—261no—
143C22×C4—262no—
144C22×C4C4×D1311yescharacteristic
145C22×C4C4×D1311yescharacteristic
146C22×C4D5211yescharacteristic
147C22×C4C22⋊D1311yescharacteristic
148C22×C4C22⋊D1311yescharacteristic
149C22×C4C22×D1311yescharacteristic
150C2×C8—22no—
151C2×C8—42no—
152C4⋊C4—131no—
153C4⋊C4—131no—
154C4⋊C4—261no—
155C4⋊C4—261no—
156C22⋊C4—261no—
157C22⋊C4—261no—
158C22⋊C4—261no—
159C22⋊C4—261no—
160C22⋊C4—261no—
161C22⋊C4—522no—
162C42—261no—
163C13#151611yescharacteristic, complemented, Sylow
164C23—22no—
165C23—22no—
166C23—41no—
167C23—261no—
168C23#610311yescharacteristic
169C23#610311yescharacteristic
170C23C2×D5211yescharacteristic
171Q8—521no—
172D4—521no—
173D4—522no—
174D4—522no—
175D4—522no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—261no—
183C2×C4—261no—
184C2×C4—261no—
185C2×C4—522no—
186C2×C4—522no—
187C2×C4—522no—
188C2×C4—522no—
189C2×C4#610311yescharacteristic
190C2×C4#610311yescharacteristic
191C2×C4C2×C4×D1311yescharacteristic
192C2×C4C2×C22⋊D1311yescharacteristic
193C8—42no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—521no—
203C22—521no—
204C22—521no—
205C22#8804612yes—
206C22#8815812yes—
207C22C2×#610311yescharacteristic
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—521no—
213C4—521no—
214C4—521no—
215C4—1042no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—1041no—
220C2C2×#8804611yescharacteristic
221C2#1171877411yescharacteristic
222C2#1171880011yescharacteristic
subgroupG/H
centerC22C2×#6103
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC2×C13×C22⋊C8C2
socleC22×C13C2×C22⋊C4
prime radical#11719496C2
cosocleC22×C4×C13C23
hypercenterC2×C22⋊C8D13
hypocenterC13#1516
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C13×C22⋊C8C2semidirect
3. #11718872C2semidirect
4. #11718062C2semidirect
5. #11718059C2semidirect
7. C2×#6127C4semidirect
11. #88184C4semidirect
16. #88180C4semidirect
17. #88178C4semidirect
84. C2×C22⋊C8D13semidirect
163. C13#1516semidirect

Maximal subgroups

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

subgroupindex
#117194962
C2×C13×C22⋊C82
#117188722
#117180622
#117180592
#151613