Finite Group Databasebeta

← #15777184

Subgroups — #15777184

Order 3328.

232 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 71 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#13117091C211yesmaximal, characteristic
2Q8×#6090C211yesmaximal, characteristic, complemented
3#13114206C211yesmaximal, characteristic, complemented
4#13112909C211yesmaximal, characteristic, complemented
5#13112884C211yesmaximal, characteristic, complemented
6#13112882C211yesmaximal, characteristic
7C13×#1668C211yesmaximal, characteristic
8C13×#493C2211yescharacteristic
9C13×#460—21no—
10C8×Q8×C13C2211yescharacteristic
11C2×#88067—21no—
12C2×#88067—21no—
13#11718681—21no—
14#11718360C2211yescharacteristic
15C13×#335C2211yescharacteristic
16C13×#331—21no—
17#11718074—21no—
18C4⋊#6090—21no—
19C4⋊#6090C2211yescharacteristic
20C4×#6090—21no—
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×SD16—41no—
24C2×C13×D8—21no—
25C2×C13×D8—21no—
26C13×#127—21no—
27C4×Q8×C13D411yescharacteristic
28C2×Dic52—21no—
29C2×Dic52—21no—
30#88123—21no—
31C13×C4⋊C8—21no—
32C13×C4⋊C8—21no—
33C13×C4⋊C8D411yescharacteristic
34C13×#102—41no—
35C4×C8×C13—21no—
36C4×C8×C13C2311yescharacteristic
37#88075—41no—
38#88067—42no—
39#88067—42no—
40C2×#6090—21no—
41C2×#6090D411yescharacteristic
42C2×#6090D411yescharacteristic
43#88048—41no—
44C4⋊#1055—21no—
45#12441—131nomaximal, Sylow
46C2×Q8×C13D811yescharacteristic
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×Dic26—41no—
51C13×SD16—82no—
52C13×D8—41no—
53C13×D8—41no—
54C13×D8—81no—
55C2×C8×C13—21no—
56C2×C8×C13—41no—
57C2×C8×C13C2×D411yescharacteristic
58C2×C8×C13#4111yescharacteristic
59C13×C4⋊C4—21no—
60C13×C4⋊C4D811yescharacteristic
61C42×C13—21no—
62C42×C13C2×D411yescharacteristic
63C4⋊Dic13—41no—
64C4⋊Dic13—41no—
65C2×#1055—41no—
66Dic52—41no—
67Dic52—41no—
68Dic52—81no—
69#6090—21no—
70#6090—41no—
71#6090SD1612yescomplemented
72#2248—131no—
73Q8×C16—131no—
74#1670—131no—
75#1668D1311yescharacteristic
76#1372—131no—
77#1362—131no—
78#1361—131no—
79C23×C13—81no—
80Q8×C13—21no—
81Q8×C13SD3212yescomplemented
82D4×C13—81no—
83D4×C13—81no—
84D4×C13—81no—
85D4×C13—81no—
86D4×C13—161no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13#12111yescharacteristic
90C2×C4×C13C2×D811yescharacteristic
91C2×C4×C13#13511yescharacteristic
92C2×Dic13—81no—
93Dic26—81no—
94Dic26—81no—
95C8×C13—21no—
96C8×C13—41no—
97C8×C13—81no—
98C8×C13C2×SD1611yescharacteristic
99C8×C13AGL(1,ℤ/8)11yescharacteristic
100#1055—81no—
101C2×SD32—261no—
102C2×SD32—261no—
103#494—131no—
104#493C2×D1311yescharacteristic
105#475—261no—
106#460—21no—
107C8×Q8C2×D1311yescharacteristic
108C4⋊C16—131no—
109C4⋊C16—261no—
110C4×C16—131no—
111C4×C16—261no—
112#335—131no—
113#335C2×D1311yescharacteristic
114#332—261no—
115#331—21no—
116C22×C13—161no—
117C22×C13—161no—
118C22×C13—161no—
119C22×C13#46611yescharacteristic
120C4×C13—22no—
121C4×C13—21no—
122C4×C13—41no—
123C4×C13#46011yescharacteristic
124C4×C13#47211yescharacteristic
125C4×C13C2×SD3211yescharacteristic
126C4×C13#50811yescharacteristic
127Dic13—161no—
128C2×Q16—261no—
129C2×Q16—261no—
130C2×SD16—41no—
131C2×D8—21no—
132C2×D8—21no—
133C4⋊Q8—261no—
134#127—21no—
135C4×Q8C22⋊D1311yescharacteristic
136SD32—522no—
137SD32—522no—
138C2×C16—131no—
139C2×C16—131no—
140C2×C16—261no—
141#106—521no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—261no—
145C4⋊C8C22⋊D1311yescharacteristic
146#103—521no—
147#102—41no—
148C4×C8—21no—
149C4×C8C22×D1311yescharacteristic
150C2×C13—321no—
151C2×C13#166811yescharacteristic
152C2×C13#221711yescharacteristic
153C2×C13#222311yescharacteristic
154C2×Q8—521no—
155C2×Q8#610411yescharacteristic
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159Q16—521no—
160Q16—521no—
161Q16—1041no—
162SD16—82no—
163D8—41no—
164D8—41no—
165D8—81no—
166C2×C8—21no—
167C2×C8—41no—
168C2×C8—521no—
169C2×C8D4×D1311yescharacteristic
170C2×C8#612911yescharacteristic
171C4⋊C4—21no—
172C4⋊C4—521no—
173C4⋊C4—521no—
174C4⋊C4#610411yescharacteristic
175C42—21no—
176C42C2×C22⋊D1311yescharacteristic
177C16—132no—
178C16—261no—
179C16—521no—
180C13#1244111yescharacteristic, complemented, Sylow
181C23—81no—
182Q8—21no—
183Q8—1041no—
184Q8—1041no—
185Q8#8806712yescomplemented
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—1041no—
194C2×C4C2×#610411yescharacteristic
195C2×C4#8819311yescharacteristic
196C2×C4#8820411yescharacteristic
197C8—21no—
198C8—41no—
199C8—81no—
200C8—1041no—
201C8SD16×D1311yescharacteristic
202C8#8816811yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1171869911yescharacteristic
207C4—22no—
208C4—21no—
209C4—41no—
210C4—2081no—
211C4C2×#8806711yescharacteristic
212C4#1171882411yescharacteristic
213C4#1171885511yescharacteristic
214C4#1171886011yescharacteristic
215C2—321no—
216C2#1311419411yescharacteristic
217C2#1311693011yescharacteristic
218C2#1311696411yescharacteristic
subgroupG/H
centerC22#11718699
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1668C2
socleC22×C13#466
prime radicalC13×#493C22
hypercenter#1668D13
hypocenterC13#12441
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1668

Complements

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

NH ≅ G/Ntype
2. Q8×#6090C2semidirect
3. #13114206C2semidirect
4. #13112909C2semidirect
5. #13112884C2semidirect
71. #6090SD16semidirect
81. Q8×C13SD32semidirect
180. C13#12441semidirect
185. Q8#88067semidirect

Maximal subgroups

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

subgroupindex
#131170912
Q8×#60902
#131142062
#131129092
#131128842
#131128822
C13×#16682
#1244113