Finite Group Databasebeta

← #15777333

Subgroups — #15777333

Order 3328.

240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C16×D52C211yesmaximal, characteristic, complemented
2#13114222C211yesmaximal, characteristic, complemented
3#13114188C211yesmaximal, characteristic
4#13112908C211yesmaximal, characteristic, complemented
5#13112891C211yesmaximal, characteristic, complemented
6#13112882C211yesmaximal, characteristic, complemented
7C13×#2240C211yesmaximal, characteristic, complemented
8C13×#500C2211yescharacteristic
9C13×#493C2211yescharacteristic
10#11718744—21no—
11#11718733—21no—
12C2×C16×D13—21no—
13C8×D52C2211yescharacteristic
14C13×#357—21no—
15C13×#357—21no—
16C4×C13×C16C2211yescharacteristic
17#11718139—21no—
18#11718136—21no—
19#11718099—21no—
20C4⋊#6090C2211yescharacteristic
21#11718050C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×D8—21no—
24C2×C13×D8—21no—
25C13×C4⋊Q8—21no—
26C13×#127—21no—
27C2×#6106—41no—
28C2×#6104—41no—
29C2×C8×D13—21no—
30C4×D52D411yescharacteristic
31C2×C13×C16D411yescharacteristic
32C2×C13×C16D411yescharacteristic
33C13×#107—21no—
34C13×#107—21no—
35C4×C8×C13C2311yescharacteristic
36#88075—41no—
37#88072—41no—
38#88060—21no—
39C2×#6090—21no—
40C4⋊#1055—21no—
41C4⋊#1055—21no—
42C4⋊#1055D411yescharacteristic
43C16×D13—42no—
44#12467—131nomaximal, Sylow
45C2×Q8×C13—41no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D52D811yescharacteristic
50C2×C4×D13—21no—
51C13×D8—41no—
52C13×D8—41no—
53C13×D8—81no—
54C2×C8×C13C2×D411yescharacteristic
55C2×C8×C13#4111yescharacteristic
56C13×C4⋊C4—41no—
57C13×C4⋊C4—41no—
58C42×C13C2×D411yescharacteristic
59#6106—82no—
60#6104—82no—
61#6103—21no—
62C4⋊Dic13D811yescharacteristic
63C2×#1055—21no—
64C2×#1055—41no—
65C2×#1055—41no—
66C8×D13—41no—
67C8×D13—41no—
68C13×C16—21no—
69C13×C16—21no—
70#6090—41no—
71#2240D1311yescharacteristic, complemented
72D4×C16—131no—
73#1673—131no—
74#1667—131no—
75#1371—131no—
76#1364—131no—
77#1361—131no—
78C23×C13—81no—
79C22×D13—21no—
80Q8×C13—81no—
81Q8×C13—81no—
82D4×C13—81no—
83D4×C13—81no—
84D4×C13—81no—
85D4×C13—81no—
86D4×C13—161no—
87C2×C4×C13—81no—
88C2×C4×C13#12111yescharacteristic
89C2×C4×C13C2×D811yescharacteristic
90C2×C4×C13#13511yescharacteristic
91C2×Dic13—21no—
92D52—21no—
93D52D1612yes—
94C4×D13—41no—
95C4×D13—41no—
96C8×C13—21no—
97C8×C13#13511yescharacteristic
98C8×C13AGL(1,ℤ/8)11yescharacteristic
99#1055—41no—
100#1055—81no—
101#1055—81no—
102C22×C16—261no—
103#500C2×D1311yescharacteristic
104#493C2×D1311yescharacteristic
105#461—261no—
106#459—261no—
107C8×D4—131no—
108C4⋊C16—131no—
109#357—21no—
110#357—21no—
111C22⋊C16—261no—
112C4×C16C2×D1311yescharacteristic
113#335—131no—
114#335—131no—
115#332—261no—
116#331—261no—
117C22×C13—161no—
118C22×C13—161no—
119C22×C13—161no—
120C22×C13#46611yescharacteristic
121C2×D13—22no—
122C2×D13—41no—
123C2×D13—41no—
124C4×C13—21no—
125C4×C13—161no—
126C4×C13#46311yescharacteristic
127C4×C13#47111yescharacteristic
128C4×C13C2×D1611yescharacteristic
129C4×C13#50811yescharacteristic
130Dic13—41no—
131C2×SD16—521no—
132C2×D8—21no—
133C2×D8—21no—
134C2×D8—521no—
135C22×C8—261no—
136C4⋊Q8—21no—
137#127—21no—
138C4×D4—131no—
139C2×C16—261no—
140C2×C16—522no—
141C2×C16C22⋊D1311yescharacteristic
142C2×C16C22⋊D1311yescharacteristic
143#107—21no—
144#107—21no—
145C4⋊C8—131no—
146C4⋊C8—261no—
147C4⋊C8—261no—
148#103—521no—
149#102—521no—
150C22⋊C8—261no—
151C4×C8C22×D1311yescharacteristic
152C2×C13—321no—
153C2×C13#168111yescharacteristic
154C2×C13#221511yescharacteristic
155C2×C13#222311yescharacteristic
156D13—42no—
157C2×Q8—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—131no—
162C22×C4—261no—
163SD16—1042no—
164D8—41no—
165D8—41no—
166D8—81no—
167D8—1042no—
168C2×C8—261no—
169C2×C8—521no—
170C2×C8—521no—
171C2×C8—521no—
172C2×C8—521no—
173C2×C8#612911yescharacteristic
174C2×C8C2×C22⋊D1311yescharacteristic
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—131no—
178C22⋊C4—261no—
179C42D4×D1311yescharacteristic
180C16—21no—
181C16—21no—
182C16—521no—
183C13#1246711yescharacteristic, complemented, Sylow
184C23—81no—
185C23—261no—
186Q8—81no—
187Q8—81no—
188D4—81no—
189D4—81no—
190D4—81no—
191D4—81no—
192D4—132no—
193D4—161no—
194D4—261no—
195C2×C4—81no—
196C2×C4—261no—
197C2×C4—521no—
198C2×C4—521no—
199C2×C4D8×D1311yescharacteristic
200C2×C4#8816611yescharacteristic
201C2×C4#8819211yescharacteristic
202C8—21no—
203C8—521no—
204C8—1041no—
205C8—1041no—
206C8#8820311yescharacteristic
207C8#8820411yescharacteristic
208C22—161no—
209C22—161no—
210C22—161no—
211C22—262no—
212C22—521no—
213C22—521no—
214C22#1171881811yescharacteristic
215C4—21no—
216C4—161no—
217C4—521no—
218C4D13×D1611yescharacteristic
219C4#1171857311yescharacteristic
220C4#1171871811yescharacteristic
221C4#1171883811yescharacteristic
222C2—321no—
223C2—522no—
224C2#1311427011yescharacteristic
225C2#1311691911yescharacteristic
226C2#1311696311yescharacteristic
subgroupG/H
centerC22#11718818
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2240C2
socleC22×C13#466
prime radical#13114188C2
hypercenter#2240D13
hypocenterC13#12467
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. C16×D52C2semidirect
2. #13114222C2semidirect
4. #13112908C2semidirect
5. #13112891C2semidirect
6. #13112882C2semidirect
7. C13×#2240C2semidirect
71. #2240D13semidirect
183. C13#12467semidirect

Maximal subgroups

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

subgroupindex
C16×D522
#131142222
#131141882
#131129082
#131128912
#131128822
C13×#22402
#1246713