Finite Group Databasebeta

← #13115649

Subgroups — #13115649

Order 1664.

344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#88201C211yesmaximal, characteristic
2C2×C13×#103C211yesmaximal, characteristic, complemented
3C2×#88075C211yesmaximal, characteristic, complemented
4C2×#88061C211yesmaximal, characteristic
5C2×#88055C211yesmaximal, characteristic, complemented
6#11718637C211yesmaximal, characteristic, complemented
7C2×#88049C211yesmaximal, characteristic
8C22×Q8×C13C2211yescharacteristic
9C22×D52C2211yescharacteristic
10C22×C8×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12#88201—22no—
13#88201C414yescomplemented
14C2×#6103—22no—
15C2×C4⋊Dic13C2211yescharacteristic
16C2×#6101—22no—
17C2×C4×Dic13C2211yescharacteristic
18C22×#1055C2211yescharacteristic
19C13×#103—22no—
20#88075—22no—
21#88061—22no—
22#88055—22no—
23#88049—22no—
24C23×D13—21no—
25C2×Q8×C13—21no—
26C2×Q8×C13—21no—
27C2×Q8×C13—21no—
28C2×Q8×C13—21no—
29C2×Q8×C13—21no—
30C2×Q8×C13C2×C412yes—
31C22×C4×C13—21no—
32C22×C4×C13—21no—
33C22×C4×C13C2311yescharacteristic
34C22×Dic13—21no—
35C22×Dic13D412yes—
36C2×D52—21no—
37C2×D52—21no—
38C2×D52—21no—
39C2×D52—21no—
40C2×D52—21no—
41C2×D52C2×C412yes—
42C2×C8×C13—21no—
43C2×C8×C13—21no—
44C2×C8×C13D412yes—
45C13×C4⋊C4—21no—
46C13×C4⋊C4—21no—
47#6103—28no—
48C4⋊Dic13—21no—
49C4⋊Dic13—21no—
50#6101—44no—
51C4×Dic13C2×C412yes—
52C4×Dic13D412yes—
53C2×#1055—21no—
54C2×#1055—21no—
55C2×#1055D412yes—
56#1959—131nomaximal, Sylow
57C23×C13C2×D411yescharacteristic
58C22×D13—22no—
59C22×D13—41no—
60C22×D13—41no—
61C22×D13—42no—
62C22×D13—42no—
63Q8×C13—22no—
64Q8×C13—22no—
65Q8×C13—41no—
66Q8×C13—41no—
67C2×C4×C13—22no—
68C2×C4×C13—41no—
69C2×C4×C13—41no—
70C2×C4×C13—41no—
71C2×C4×C13—42no—
72C2×C4×C13C22×C411yescharacteristic
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13#4111yescharacteristic
77C2×C4×C13#4111yescharacteristic
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—41no—
81C2×Dic13—42no—
82C2×Dic13C22⋊C414yes—
83D52—22no—
84D52—22no—
85D52—41no—
86D52—41no—
87C8×C13—22no—
88#1055—22no—
89C2×#124—131no—
90C2×#103—131no—
91C2×#103D1311yescharacteristic, complemented
92C2×#102—131no—
93C2×#102—131no—
94C2×#97—131no—
95#384—131no—
96C22×C13C2×C22⋊C411yescharacteristic
97C22×C13#12411yescharacteristic
98C22×C13#12711yescharacteristic
99C22×C13AGL(1,ℤ/8)12yes—
100C22×C13#13712yes—
101C2×D13—42no—
102C2×D13—44no—
103C2×D13—82no—
104C2×D13—81no—
105C2×D13—81no—
106C4×C13—42no—
107C4×C13—81no—
108C4×C13C4×D411yescharacteristic
109C4×C13C4×D411yescharacteristic
110C4×C13#12111yescharacteristic
111C4×C13#12111yescharacteristic
112Dic13—24no—
113Dic13—81no—
114C22×Q8C2×D1311yescharacteristic
115C22×D4—131no—
116C22×C8—131no—
117C22×C8C2×D1311yescharacteristic
118#124—134no—
119#124—262no—
120C2×C4⋊C4—131no—
121C2×C4⋊C4—262no—
122C2×C4⋊C4C2×D1311yescharacteristic
123C2×C22⋊C4—262no—
124C2×C42—131no—
125#103—22no—
126#103—262no—
127#102—262no—
128#102—262no—
129#97—262no—
130C2×C13#39011yescharacteristic
131C2×C13#41712yes—
132C2×C13#48912yes—
133C2×C13#49611yescharacteristic
134C2×C13#49711yescharacteristic
135D13—82no—
136C24—261no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C4×D1312yes—
143C2×D4—132no—
144C2×D4—261no—
145C2×D4—261no—
146C2×D4—261no—
147C2×D4—261no—
148C2×D4—261no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—132no—
152C22×C4—261no—
153C22×C4C22×D1311yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—132no—
157C2×C8—261no—
158C2×C8—261no—
159C2×C8C22⋊D1312yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—261no—
163C4⋊C4—261no—
164C4⋊C4—524no—
165C22⋊C4—268no—
166C42—132no—
167C42—132no—
168C13#195911yescharacteristic, complemented, Sylow
169C23—262no—
170C23—521no—
171C23—522no—
172C23—522no—
173C23—521no—
174C23D4×D1311yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179D4—262no—
180D4—262no—
181D4—521no—
182D4—521no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—41no—
188C2×C4—134no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—522no—
192C2×C4—521no—
193C2×C4C2×C4×D1311yescharacteristic
194C2×C4#612711yescharacteristic
195C2×C4D4×D1311yescharacteristic
196C2×C4D4×D1311yescharacteristic
197C2×C4#612911yescharacteristic
198C2×C4C2×C22⋊D1311yescharacteristic
199C8—22no—
200C8—262no—
201C22—524no—
202C22—522no—
203C22—1042no—
204C22—1041no—
205C22—1041no—
206C22C22⋊C4×D1311yescharacteristic
207C22#8813911yescharacteristic
208C22#8816812yes—
209C22#8817212yes—
210C22#8819411yescharacteristic
211C4—42no—
212C4—81no—
213C4—264no—
214C4—1041no—
215C4#8813511yescharacteristic
216C4#8813811yescharacteristic
217C4C4×C22⋊D1311yescharacteristic
218C4#8819311yescharacteristic
219C2—1042no—
220C2#1171845612yes—
221C2#1171846412yes—
222C2#1171861811yescharacteristic
223C2#1171883711yescharacteristic
224C2#1171885111yescharacteristic
subgroupG/H
centerC23D4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC2×C13×#103C2
socleC23×C13C2×D4
prime radicalC22×D52C22
cosocleC22×C4×C13C23
hypercenterC2×#103D13
hypocenterC13#1959
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×C13×#103C2semidirect
3. C2×#88075C2semidirect
5. C2×#88055C2semidirect
6. #11718637C2semidirect
13. #88201C4semidirect
91. C2×#103D13semidirect
168. C13#1959semidirect

Maximal subgroups

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

subgroupindex
C2×#882012
C2×C13×#1032
C2×#880752
C2×#880612
C2×#880552
#117186372
C2×#880492
#195913