Finite Group Databasebeta

← #15777136

Subgroups — #15777136

Order 3328.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#13117092C211yesmaximal, characteristic, complemented
2C16×D52C211yesmaximal, characteristic, complemented
3#13114202C211yesmaximal, characteristic, complemented
4#13114192C211yesmaximal, characteristic
5#13112884C211yesmaximal, characteristic, complemented
6#13112881C211yesmaximal, characteristic, complemented
7C13×#1372C211yesmaximal, characteristic, complemented
8C2×#88040—21no—
9C2×#88040—21no—
10C2×C16×D13—21no—
11#11718507—21no—
12#11718504—21no—
13#11718360C2211yescharacteristic
14#11718356C2211yescharacteristic
15C8×D52C2211yescharacteristic
16C4×C13×C16C2211yescharacteristic
17C13×#335C2211yescharacteristic
18C13×#335C2211yescharacteristic
19#11718099—21no—
20#11718078—21no—
21#11718077—21no—
22C4⋊#6090C2211yescharacteristic
23C2×Dic52—21no—
24C2×Dic52—21no—
25C2×D104—21no—
26C2×D104—21no—
27C2×D104—41no—
28C2×C8×D13—21no—
29#88128—21no—
30C4×D52D411yescharacteristic
31#88123—21no—
32C2×C13×C16D411yescharacteristic
33C2×C13×C16D411yescharacteristic
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C4×C8×C13C2311yescharacteristic
37#88061—41no—
38#88061—41no—
39#88060—21no—
40#88058—41no—
41C2×#6090—21no—
42C4⋊#1055D411yescharacteristic
43#88040—42no—
44#88040—42no—
45C16×D13—42no—
46#12432—131nomaximal, Sylow
47C2×D52—41no—
48C2×D52—41no—
49C2×D52—41no—
50C2×D52D811yescharacteristic
51C2×C4×D13—21no—
52C2×Dic26—41no—
53C2×C8×C13—41no—
54C2×C8×C13—41no—
55C2×C8×C13C2×D411yescharacteristic
56C2×C8×C13#4111yescharacteristic
57C42×C13C2×D411yescharacteristic
58#6103—21no—
59C4⋊Dic13—41no—
60C4⋊Dic13—41no—
61C4⋊Dic13D811yescharacteristic
62C2×#1055—21no—
63Dic52—41no—
64Dic52—41no—
65Dic52—81no—
66D104—41no—
67D104—41no—
68D104—81no—
69D104—82no—
70C8×D13—41no—
71C8×D13—41no—
72C13×C16—21no—
73C13×C16D812yescomplemented
74#6090—41no—
75#2248—131no—
76D4×C16—131no—
77#1669—131no—
78#1667—131no—
79#1372D1311yescharacteristic, complemented
80#1362—131no—
81#1361—131no—
82C22×D13—21no—
83C22×D13—81no—
84C2×C4×C13#12111yescharacteristic
85C2×C4×C13C2×D811yescharacteristic
86C2×C4×C13#13511yescharacteristic
87C2×Dic13—21no—
88C2×Dic13—81no—
89D52—21no—
90D52—81no—
91D52—81no—
92D52—81no—
93D52—81no—
94D52—161no—
95D52SD3212yescomplemented
96C4×D13—41no—
97C4×D13—41no—
98Dic26—81no—
99Dic26—81no—
100C8×C13—21no—
101C8×C13—81no—
102C8×C13—81no—
103C8×C13C2×D811yescharacteristic
104C8×C13AGL(1,ℤ/8)11yescharacteristic
105#1055—41no—
106C2×SD32—261no—
107C2×SD32—261no—
108C22×C16—261no—
109#494—131no—
110#493—131no—
111#474—261no—
112#459—261no—
113C8×D4—131no—
114C4⋊C16—131no—
115C22⋊C16—261no—
116C4×C16C2×D1311yescharacteristic
117#335C2×D1311yescharacteristic
118#335C2×D1311yescharacteristic
119#332—261no—
120#331—261no—
121C22×C13#46611yescharacteristic
122C2×D13—22no—
123C2×D13—41no—
124C2×D13—41no—
125C2×D13—161no—
126C2×D13—161no—
127C2×D13—161no—
128C4×C13—21no—
129C4×C13#45911yescharacteristic
130C4×C13#47211yescharacteristic
131C4×C13C2×SD3211yescharacteristic
132C4×C13#50811yescharacteristic
133Dic13—41no—
134Dic13—161no—
135C2×Q16—261no—
136C2×Q16—261no—
137C2×D8—261no—
138C2×D8—261no—
139C2×D8—521no—
140C22×C8—261no—
141C4⋊Q8—261no—
142#127—261no—
143C4×D4—131no—
144SD32—522no—
145SD32—522no—
146C2×C16—261no—
147C2×C16—522no—
148C2×C16D5211yescharacteristic
149C2×C16D5211yescharacteristic
150#107—521no—
151C4⋊C8—21no—
152C4⋊C8—21no—
153C4⋊C8—131no—
154#102—521no—
155#102—521no—
156C22⋊C8—261no—
157C4×C8C22×D1311yescharacteristic
158C2×C13#166711yescharacteristic
159C2×C13#221711yescharacteristic
160C2×C13#222311yescharacteristic
161D13—42no—
162D13—321no—
163C2×Q8—521no—
164C2×D4—131no—
165C2×D4—521no—
166C2×D4—521no—
167C2×D4—521no—
168C22×C4—261no—
169Q16—521no—
170Q16—521no—
171Q16—1041no—
172D8—521no—
173D8—521no—
174D8—1041no—
175D8—1042no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—261no—
179C2×C8—521no—
180C2×C8—521no—
181C2×C8C2×D5211yescharacteristic
182C2×C8#613111yescharacteristic
183C4⋊C4—131no—
184C4⋊C4—521no—
185C4⋊C4—521no—
186C22⋊C4—261no—
187C42D4×D1311yescharacteristic
188C16—21no—
189C16—521no—
190C16D10412yescomplemented
191C13#1243211yescharacteristic, complemented, Sylow
192C23—261no—
193C23—1041no—
194Q8—1041no—
195Q8—1041no—
196D4—132no—
197D4—261no—
198D4—1041no—
199D4—1041no—
200D4—1041no—
201D4—1041no—
202D4—2081no—
203C2×C4—261no—
204C2×C4—521no—
205C2×C4—521no—
206C2×C4—1041no—
207C2×C4#8814911yescharacteristic
208C2×C4D8×D1311yescharacteristic
209C2×C4#8817311yescharacteristic
210C8—21no—
211C8—81no—
212C8—81no—
213C8—521no—
214C8C2×D10411yescharacteristic
215C8#8816211yescharacteristic
216C22—262no—
217C22—521no—
218C22—521no—
219C22—2081no—
220C22—2081no—
221C22—2081no—
222C22#1171854411yescharacteristic
223C4—21no—
224C4—521no—
225C4—2081no—
226C4#1171850411yescharacteristic
227C4#1171855811yescharacteristic
228C4D13×SD3211yescharacteristic
229C4#1171857711yescharacteristic
230C2—522no—
231C2—4161no—
232C2#1311419211yescharacteristic
233C2#1311693311yescharacteristic
234C2#1311696711yescharacteristic
subgroupG/H
centerC22#11718544
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1372C2
socleC22×C13#466
prime radical#13114192C2
hypercenter#1372D13
hypocenterC13#12432
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1372

Complements

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

NH ≅ G/Ntype
1. #13117092C2semidirect
2. C16×D52C2semidirect
3. #13114202C2semidirect
5. #13112884C2semidirect
6. #13112881C2semidirect
7. C13×#1372C2semidirect
73. C13×C16D8semidirect
79. #1372D13semidirect
95. D52SD32semidirect
190. C16D104semidirect
191. C13#12432semidirect

Maximal subgroups

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

subgroupindex
#131170922
C16×D522
#131142022
#131141922
#131128842
#131128812
C13×#13722
#1243213