Finite Group Databasebeta

← #15777346

Subgroups — #15777346

Order 3328.

234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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#13117061C211yesmaximal, characteristic, complemented
2#13116655C211yesmaximal, characteristic, complemented
3#13114232C211yesmaximal, characteristic, complemented
4#13114192C211yesmaximal, characteristic
5#13112909C211yesmaximal, characteristic, complemented
6#13112883C211yesmaximal, characteristic, complemented
7C13×#1365C211yesmaximal, characteristic, complemented
8C13×#500C2211yescharacteristic
9#11718745—21no—
10C2×C16×D13—21no—
11#11718504—21no—
12#11718356C2211yescharacteristic
13C8×D52C2211yescharacteristic
14C13×C4⋊C16C2211yescharacteristic
15C13×#335C2211yescharacteristic
16#11718138—21no—
17#11718099—21no—
18#11718083—21no—
19#11718083—21no—
20#11718077—21no—
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C13×C4⋊Q8—21no—
24C2×D104—21no—
25C2×D104—21no—
26C2×D104—41no—
27C2×C8×D13—21no—
28#88128—21no—
29C4×D52D411yescharacteristic
30C2×C13×C16—21no—
31C13×#107—21no—
32C13×#107—21no—
33C13×C4⋊C8—21no—
34C4×C8×C13C2311yescharacteristic
35#88061—41no—
36#88060—21no—
37C2×#6090D411yescharacteristic
38C2×#6090D411yescharacteristic
39#88049—41no—
40#88048—41no—
41C4⋊#1055—21no—
42C4⋊#1055D411yescharacteristic
43C16×D13—42no—
44#12468—131nomaximal, Sylow
45C2×Q8×C13—41no—
46C2×D52—41no—
47C2×D52—41no—
48C2×D52—41no—
49C2×D52D811yescharacteristic
50C2×C4×D13—21no—
51C2×C8×C13—41no—
52C2×C8×C13C2×D411yescharacteristic
53C2×C8×C13#4111yescharacteristic
54C13×C4⋊C4—41no—
55C13×C4⋊C4—41no—
56C42×C13C2×D411yescharacteristic
57#6103—21no—
58C4⋊Dic13D811yescharacteristic
59C2×#1055—21no—
60C2×#1055—41no—
61D104—41no—
62D104—41no—
63D104—81no—
64D104—82no—
65C8×D13—41no—
66C8×D13—41no—
67C13×C16—41no—
68#6090—21no—
69#6090—21no—
70#2240—131no—
71D4×C16—131no—
72#1675—131no—
73#1667—131no—
74#1372—131no—
75#1365D1311yescharacteristic, complemented
76#1361—131no—
77C22×D13—21no—
78C22×D13—81no—
79Q8×C13—161no—
80C2×C4×C13—81no—
81C2×C4×C13#12111yescharacteristic
82C2×C4×C13C2×D811yescharacteristic
83C2×C4×C13#13511yescharacteristic
84C2×Dic13—21no—
85D52—21no—
86D52—81no—
87D52—81no—
88D52—81no—
89D52—81no—
90D52—161no—
91D52SD3212yes—
92C4×D13—41no—
93C4×D13—41no—
94C8×C13—21no—
95C8×C13—81no—
96C8×C13#13511yescharacteristic
97C8×C13AGL(1,ℤ/8)11yescharacteristic
98#1055—41no—
99#1055—81no—
100C22×C16—261no—
101#500C2×D1311yescharacteristic
102#493—131no—
103#476—261no—
104#459—261no—
105C8×D4—131no—
106C4⋊C16C2×D1311yescharacteristic
107#357—261no—
108#357—261no—
109C22⋊C16—261no—
110C4×C16—131no—
111#335—131no—
112#335C2×D1311yescharacteristic
113#333—261no—
114#331—261no—
115C22×C13#46611yescharacteristic
116C2×D13—22no—
117C2×D13—41no—
118C2×D13—41no—
119C2×D13—161no—
120C2×D13—161no—
121C2×D13—161no—
122C4×C13—21no—
123C4×C13—161no—
124C4×C13#46311yescharacteristic
125C4×C13#47111yescharacteristic
126C4×C13C2×SD3211yescharacteristic
127C4×C13#50811yescharacteristic
128Dic13—41no—
129C2×D8—261no—
130C2×D8—261no—
131C2×D8—521no—
132C22×C8—261no—
133C4⋊Q8—21no—
134#127—261no—
135C4×D4—131no—
136C2×C16—21no—
137C2×C16—131no—
138C2×C16—131no—
139C2×C16—522no—
140#107—21no—
141#107—21no—
142#106—521no—
143C4⋊C8—21no—
144C4⋊C8—131no—
145C4⋊C8—261no—
146#102—521no—
147#102—521no—
148C22⋊C8—261no—
149C4×C8C22×D1311yescharacteristic
150C2×C13#168111yescharacteristic
151C2×C13#221711yescharacteristic
152C2×C13#222111yescharacteristic
153D13—42no—
154D13—321no—
155C2×Q8—41no—
156C2×D4—131no—
157C2×D4—521no—
158C2×D4—521no—
159C2×D4—521no—
160C22×C4—261no—
161D8—521no—
162D8—521no—
163D8—1041no—
164D8—1042no—
165C2×C8—41no—
166C2×C8—261no—
167C2×C8—521no—
168C2×C8—521no—
169C2×C8—521no—
170C2×C8#612711yescharacteristic
171C2×C8D4×D1311yescharacteristic
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—131no—
175C22⋊C4—261no—
176C42D4×D1311yescharacteristic
177C16—41no—
178C16—261no—
179C16—261no—
180C13#1246811yescharacteristic, complemented, Sylow
181C23—261no—
182C23—1041no—
183Q8—161no—
184D4—132no—
185D4—261no—
186D4—1041no—
187D4—1041no—
188D4—1041no—
189D4—1041no—
190D4—2081no—
191C2×C4—81no—
192C2×C4—261no—
193C2×C4—521no—
194C2×C4—521no—
195C2×C4#8813811yescharacteristic
196C2×C4D8×D1311yescharacteristic
197C2×C4#8817011yescharacteristic
198C8—21no—
199C8—81no—
200C8—521no—
201C8—1041no—
202C8#8816811yescharacteristic
203C8#8817311yescharacteristic
204C22—262no—
205C22—521no—
206C22—521no—
207C22—2081no—
208C22—2081no—
209C22—2081no—
210C22#1171843611yescharacteristic
211C4—21no—
212C4—161no—
213C4—521no—
214C4#1171841511yescharacteristic
215C4#1171848011yescharacteristic
216C4D13×SD3211yescharacteristic
217C4#1171858011yescharacteristic
218C2—522no—
219C2—4161no—
220C2#1311427611yescharacteristic
221C2#1311693511yescharacteristic
222C2#1311695511yescharacteristic
subgroupG/H
centerC22#11718436
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1365C2
socleC22×C13#466
prime radical#13114192C2
hypercenter#1365D13
hypocenterC13#12468
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
1. #13117061C2semidirect
2. #13116655C2semidirect
3. #13114232C2semidirect
5. #13112909C2semidirect
6. #13112883C2semidirect
7. C13×#1365C2semidirect
75. #1365D13semidirect
180. C13#12468semidirect

Maximal subgroups

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

subgroupindex
#131170612
#131166552
#131142322
#131141922
#131129092
#131128832
C13×#13652
#1246813