Finite Group Databasebeta

← #13115715

Subgroups — #13115715

Order 1664.

340 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 105 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×#6095C211yesmaximal, characteristic
2C2×C13×#107C211yesmaximal, characteristic, complemented
3C2×#88055C211yesmaximal, characteristic, complemented
4#11718649C211yesmaximal, characteristic
5#11718635C211yesmaximal, characteristic, complemented
6C2×#88050C211yesmaximal, characteristic, complemented
7C2×#88049C211yesmaximal, characteristic
8C22×D52C2211yescharacteristic
9C22×Dic26C2211yescharacteristic
10C22×C8×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×#6103—22no—
14C2×C4×Dic13C2211yescharacteristic
15C22×#1055C2211yescharacteristic
16C2×#6095—22no—
17C2×#6095—22no—
18C2×#6095C414yescomplemented
19C13×#107—22no—
20#88071—22no—
21#88055—22no—
22#88050—22no—
23#88049—22no—
24C23×D13—21no—
25C22×C4×C13—21no—
26C22×C4×C13—21no—
27C22×C4×C13C2311yescharacteristic
28C22×Dic13—21no—
29C22×Dic13D412yes—
30C2×D52—21no—
31C2×D52—21no—
32C2×D52—21no—
33C2×D52—21no—
34C2×D52—21no—
35C2×D52C2×C412yes—
36C2×Dic26—21no—
37C2×Dic26—21no—
38C2×Dic26—21no—
39C2×Dic26—21no—
40C2×Dic26—21no—
41C2×Dic26C2×C412yes—
42C2×C8×C13C2×C412yes—
43C2×C8×C13D412yes—
44C2×C8×C13D412yes—
45C13×C4⋊C4—21no—
46C13×C4⋊C4—21no—
47C13×C4⋊C4—21no—
48C13×C4⋊C4—21no—
49#6103—44no—
50C4×Dic13—21no—
51C4×Dic13—21no—
52C2×#1055—21no—
53C2×#1055—21no—
54C2×#1055D412yes—
55#6095—28no—
56#1973—131nomaximal, Sylow
57C23×C13C2×D411yescharacteristic
58C22×D13—22no—
59C22×D13—41no—
60C22×D13—41no—
61C22×D13—42no—
62C22×D13—42no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13—42no—
66C2×C4×C13—42no—
67C2×C4×C13C22×C411yescharacteristic
68C2×C4×C13C2×D411yescharacteristic
69C2×C4×C13C2×D411yescharacteristic
70C2×C4×C13C2×D411yescharacteristic
71C2×C4×C13#4111yescharacteristic
72C2×C4×C13#4111yescharacteristic
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—41no—
78C2×Dic13—41no—
79D52—22no—
80D52—22no—
81D52—41no—
82D52—41no—
83Dic26—22no—
84Dic26—22no—
85Dic26—41no—
86Dic26—41no—
87C8×C13C22⋊C414yescomplemented
88#1055—22no—
89C22×SD16—131no—
90C2×#107D1311yescharacteristic, complemented
91C2×#103—131no—
92C2×#102—131no—
93C2×#97—131no—
94#391—131no—
95#390—131no—
96C22×C13C4×D411yescharacteristic
97C22×C13#12111yescharacteristic
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—81no—
107C4×C13—81no—
108C4×C13C2×C22⋊C411yescharacteristic
109C4×C13C4×D411yescharacteristic
110C4×C13#12111yescharacteristic
111C4×C13#12411yescharacteristic
112Dic13—42no—
113Dic13—42no—
114C22×Q8—131no—
115C22×D4—131no—
116C2×SD16—134no—
117C2×SD16—262no—
118C2×SD16—262no—
119C22×C8—131no—
120C22×C8C2×D1311yescharacteristic
121C2×C4⋊C4C2×D1311yescharacteristic
122C2×C4⋊C4C2×D1311yescharacteristic
123C2×C22⋊C4—262no—
124C2×C42—131no—
125#107—22no—
126#103—262no—
127#102—262no—
128#97—262no—
129#95—262no—
130C2×C13#39011yescharacteristic
131C2×C13#44012yes—
132C2×C13#46812yes—
133C2×C13#49611yescharacteristic
134C2×C13#49711yescharacteristic
135D13—82no—
136C24—261no—
137C2×Q8—132no—
138C2×Q8—261no—
139C2×Q8—261no—
140C2×Q8—261no—
141C2×Q8—261no—
142C2×Q8—261no—
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
154SD16—268no—
155C2×C8—132no—
156C2×C8—261no—
157C2×C8—261no—
158C2×C8C4×D1312yes—
159C2×C8D5212yes—
160C2×C8C22⋊D1312yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C22⋊C4—524no—
166C42—261no—
167C42—261no—
168C13#197311yescharacteristic, complemented, Sylow
169C23—262no—
170C23—521no—
171C23—522no—
172C23—522no—
173C23—521no—
174C23D4×D1311yescharacteristic
175Q8—262no—
176Q8—262no—
177Q8—521no—
178Q8—521no—
179D4—262no—
180D4—262no—
181D4—521no—
182D4—521no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—521no—
192C2×C4—521no—
193C2×C4C2×C4×D1311yescharacteristic
194C2×C4C2×D5211yescharacteristic
195C2×C4D4×D1311yescharacteristic
196C2×C4#613111yescharacteristic
197C2×C4#613111yescharacteristic
198C2×C4C2×C22⋊D1311yescharacteristic
199C8—262no—
200C8#610314yescomplemented
201C22—524no—
202C22—522no—
203C22—1042no—
204C22—1041no—
205C22—1041no—
206C22#8814711yescharacteristic
207C22#8814911yescharacteristic
208C22#8816512yes—
209C22#8817212yes—
210C22#8819411yescharacteristic
211C4—81no—
212C4—81no—
213C4—522no—
214C4—522no—
215C4#8814711yescharacteristic
216C4#8814911yescharacteristic
217C4C2×#610311yescharacteristic
218C4#8820111yescharacteristic
219C2—1042no—
220C2#1171854712yes—
221C2#1171855012yes—
222C2#1171864911yescharacteristic
223C2#1171881511yescharacteristic
224C2#1171885111yescharacteristic
subgroupG/H
centerC23D4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC2×C13×#107C2
socleC23×C13C2×D4
prime radicalC22×D52C22
cosocleC22×C4×C13C23
hypercenterC2×#107D13
hypocenterC13#1973
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C13×#107C2semidirect
3. C2×#88055C2semidirect
5. #11718635C2semidirect
6. C2×#88050C2semidirect
18. C2×#6095C4semidirect
87. C8×C13C22⋊C4semidirect
90. C2×#107D13semidirect
168. C13#1973semidirect
200. C8#6103semidirect

Maximal subgroups

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

subgroupindex
C22×#60952
C2×C13×#1072
C2×#880552
#117186492
#117186352
C2×#880502
C2×#880492
#197313