Finite Group Databasebeta

← #15777343

Subgroups — #15777343

Order 3328.

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

normal subgroups only

This group has 234 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#13117060C211yesmaximal, characteristic, complemented
2#13114235C211yesmaximal, characteristic, complemented
3#13114191C211yesmaximal, characteristic
4#13112910C211yesmaximal, characteristic, complemented
5#13112893C211yesmaximal, characteristic, complemented
6#13112883C211yesmaximal, characteristic, complemented
7D4×C13×C16C211yesmaximal, characteristic, complemented
8C22×C13×C16—21no—
9C8×D4×C13C2211yescharacteristic
10#11718676—21no—
11#11718669—21no—
12#11718356C2211yescharacteristic
13#11718343C2211yescharacteristic
14C13×C4⋊C16C2211yescharacteristic
15C13×C22⋊C16—21no—
16C4×C13×C16C2211yescharacteristic
17#11718101—21no—
18#11718101—21no—
19#11718077—21no—
20#11718073—21no—
21#11718050C2211yescharacteristic
22#11718050C2211yescharacteristic
23C22×C8×C13—21no—
24C4×D4×C13D411yescharacteristic
25C2×#6104—41no—
26C2×D104—21no—
27C2×D104—21no—
28#88128—21no—
29#88123—21no—
30C2×C13×C16—21no—
31C2×C13×C16—42no—
32C2×C13×C16D411yescharacteristic
33C2×C13×C16D411yescharacteristic
34C13×C4⋊C8D411yescharacteristic
35C13×C22⋊C8—21no—
36C4×C8×C13C2311yescharacteristic
37#88072—41no—
38#88058—21no—
39#88058—21no—
40#88049—41no—
41#88048—41no—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44#12468—131nomaximal, Sylow
45C2×D4×C13D811yescharacteristic
46C22×C4×C13—21no—
47C2×D52—41no—
48C2×D52—41no—
49C2×D52—41no—
50C2×Dic26—41no—
51C2×C8×C13—21no—
52C2×C8×C13—41no—
53C2×C8×C13—41no—
54C2×C8×C13C2×D411yescharacteristic
55C2×C8×C13#4111yescharacteristic
56C13×C4⋊C4D811yescharacteristic
57C13×C22⋊C4—21no—
58C42×C13C2×D411yescharacteristic
59#6104—82no—
60C4⋊Dic13—41no—
61C4⋊Dic13—41no—
62C2×#1055—41no—
63C2×#1055—41no—
64D104—41no—
65D104—41no—
66D104—81no—
67C13×C16—21no—
68C13×C16—21no—
69C13×C16—41no—
70#2240—131no—
71D4×C16D1311yescharacteristic, complemented
72#1675—131no—
73#1667—131no—
74#1372—131no—
75#1365—131no—
76#1361—131no—
77C23×C13—21no—
78C22×D13—81no—
79D4×C13—21no—
80D4×C13SD3212yes—
81C2×C4×C13—21no—
82C2×C4×C13—41no—
83C2×C4×C13—41no—
84C2×C4×C13#12111yescharacteristic
85C2×C4×C13C2×D811yescharacteristic
86C2×C4×C13#13511yescharacteristic
87C2×Dic13—81no—
88D52—81no—
89D52—81no—
90D52—81no—
91D52—81no—
92D52—161no—
93Dic26—161no—
94C8×C13—21no—
95C8×C13—41no—
96C8×C13#13511yescharacteristic
97C8×C13AGL(1,ℤ/8)11yescharacteristic
98#1055—81no—
99#1055—81no—
100C22×C16—21no—
101#500—131no—
102#493—131no—
103#476—261no—
104#459—261no—
105C8×D4C2×D1311yescharacteristic
106C4⋊C16C2×D1311yescharacteristic
107#357—261no—
108#357—261no—
109C22⋊C16—21no—
110C4×C16C2×D1311yescharacteristic
111#335—131no—
112#335—131no—
113#333—261no—
114#331—261no—
115C22×C13—22no—
116C22×C13—41no—
117C22×C13—41no—
118C22×C13#46611yescharacteristic
119C2×D13—161no—
120C2×D13—161no—
121C2×D13—161no—
122C4×C13—21no—
123C4×C13—41no—
124C4×C13#46311yescharacteristic
125C4×C13#47111yescharacteristic
126C4×C13C2×SD3211yescharacteristic
127C4×C13#50811yescharacteristic
128Dic13—161no—
129C2×D8—261no—
130C2×D8—261no—
131C2×D8—521no—
132C22×C8—21no—
133C4⋊Q8—261no—
134#127—261no—
135C4×D4D5211yescharacteristic
136C2×C16—21no—
137C2×C16—42no—
138C2×C16C22⋊D1311yescharacteristic
139C2×C16C22⋊D1311yescharacteristic
140#107—261no—
141#107—261no—
142#106—521no—
143C4⋊C8—261no—
144C4⋊C8—261no—
145C4⋊C8D5211yescharacteristic
146#102—521no—
147#102—521no—
148C22⋊C8—21no—
149C4×C8C22×D1311yescharacteristic
150C2×C13—42no—
151C2×C13#168111yescharacteristic
152C2×C13#221711yescharacteristic
153C2×C13#222111yescharacteristic
154D13—321no—
155C2×Q8—521no—
156C2×D4—521no—
157C2×D4—521no—
158C2×D4—521no—
159C2×D4D10411yescharacteristic
160C22×C4—21no—
161D8—521no—
162D8—521no—
163D8—1041no—
164D8—1042no—
165C2×C8—21no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—521no—
169C2×C8—521no—
170C2×C8#612711yescharacteristic
171C2×C8C2×C22⋊D1311yescharacteristic
172C4⋊C4—521no—
173C4⋊C4—521no—
174C4⋊C4D10411yescharacteristic
175C22⋊C4—21no—
176C42C2×D5211yescharacteristic
177C16—21no—
178C16—21no—
179C16—41no—
180C13#1246811yescharacteristic, complemented, Sylow
181C23—21no—
182C23—1041no—
183Q8—2081no—
184D4—21no—
185D4—1041no—
186D4—1041no—
187D4—1041no—
188D4—1041no—
189D4—2081no—
190D4#8804012yes—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—1041no—
195C2×C4C2×D10411yescharacteristic
196C2×C4#8815811yescharacteristic
197C2×C4#8818411yescharacteristic
198C8—21no—
199C8—41no—
200C8—1041no—
201C8—1041no—
202C8#8818611yescharacteristic
203C8#8820411yescharacteristic
204C22—22no—
205C22—41no—
206C22—41no—
207C22—2081no—
208C22—2081no—
209C22—2081no—
210C22#1171877611yescharacteristic
211C4—21no—
212C4—41no—
213C4—2081no—
214C4C2×#8804011yescharacteristic
215C4#1171856511yescharacteristic
216C4#1171867711yescharacteristic
217C4#1171880211yescharacteristic
218C2—42no—
219C2—4161no—
220C2#1311427311yescharacteristic
221C2#1311693211yescharacteristic
222C2#1311695611yescharacteristic
subgroupG/H
centerC22#11718776
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingD4×C13×C16C2
socleC22×C13#466
prime radical#13114191C2
hypercenterD4×C16D13
hypocenterC13#12468
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #13117060C2semidirect
2. #13114235C2semidirect
4. #13112910C2semidirect
5. #13112893C2semidirect
6. #13112883C2semidirect
7. D4×C13×C16C2semidirect
71. D4×C16D13semidirect
180. C13#12468semidirect

Maximal subgroups

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

subgroupindex
#131170602
#131142352
#131141912
#131129102
#131128932
#131128832
D4×C13×C162
#1246813