Finite Group Databasebeta

← #15777133

Subgroups — #15777133

Order 3328.

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

normal subgroups only

This group has 252 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, complemented
2D4×#6090C211yesmaximal, characteristic, complemented
3#13114201C211yesmaximal, characteristic, complemented
4#13112909C211yesmaximal, characteristic, complemented
5#13112884C211yesmaximal, characteristic, complemented
6#13112882C211yesmaximal, characteristic, complemented
7C13×#1667C211yesmaximal, characteristic
8C13×#493C2211yescharacteristic
9C13×#459—21no—
10C8×D4×C13C2211yescharacteristic
11C2×#88067—21no—
12C2×#88067—21no—
13C22×#6090—21no—
14#11718668—21no—
15#11718360C2211yescharacteristic
16C13×#335C2211yescharacteristic
17C13×#331—21no—
18C22⋊#6090—21no—
19#11718074—21no—
20C4⋊#6090C2211yescharacteristic
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×D8—21no—
24C2×C13×D8—21no—
25C2×C13×D8—41no—
26C22×C8×C13—21no—
27C13×#127—21no—
28C4×D4×C13D411yescharacteristic
29C2×Dic52—21no—
30C2×Dic52—21no—
31#88123—21no—
32C13×C4⋊C8—21no—
33C13×C4⋊C8D411yescharacteristic
34C13×#102—41no—
35C13×C22⋊C8—21no—
36C4×C8×C13C2311yescharacteristic
37#88072—41no—
38#88067—42no—
39#88067—42no—
40C2×#6090—21no—
41C2×#6090—42no—
42C2×#6090D411yescharacteristic
43C2×#6090D411yescharacteristic
44#88047—41no—
45C4⋊#1055—21no—
46#12432—131nomaximal, Sylow
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13D811yescharacteristic
51C22×C4×C13—21no—
52C2×Dic26—41no—
53C13×D8—41no—
54C13×D8—41no—
55C13×D8—81no—
56C13×D8—82no—
57C2×C8×C13—21no—
58C2×C8×C13—41no—
59C2×C8×C13—41no—
60C2×C8×C13—41no—
61C2×C8×C13C2×D411yescharacteristic
62C2×C8×C13#4111yescharacteristic
63C13×C4⋊C4D811yescharacteristic
64C13×C22⋊C4—21no—
65C42×C13C2×D411yescharacteristic
66C4⋊Dic13—41no—
67C4⋊Dic13—41no—
68C2×#1055—41no—
69Dic52—41no—
70Dic52—41no—
71Dic52—81no—
72#6090—21no—
73#6090—41no—
74#6090D812yescomplemented
75#2248—131no—
76D4×C16—131no—
77#1669—131no—
78#1667D1311yescharacteristic
79#1372—131no—
80#1362—131no—
81#1361—131no—
82C23×C13—21no—
83C23×C13—81no—
84D4×C13—21no—
85D4×C13—81no—
86D4×C13—81no—
87D4×C13—81no—
88D4×C13—81no—
89D4×C13—161no—
90D4×C13SD3212yescomplemented
91C2×C4×C13—21no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13#12111yescharacteristic
95C2×C4×C13C2×D811yescharacteristic
96C2×C4×C13#13511yescharacteristic
97C2×Dic13—81no—
98Dic26—81no—
99Dic26—81no—
100C8×C13—21no—
101C8×C13—41no—
102C8×C13—81no—
103C8×C13C2×D811yescharacteristic
104C8×C13AGL(1,ℤ/8)11yescharacteristic
105#1055—81no—
106C2×SD32—261no—
107C2×SD32—261no—
108C22×C16—261no—
109#494—131no—
110#493C2×D1311yescharacteristic
111#474—261no—
112#459—21no—
113C8×D4C2×D1311yescharacteristic
114C4⋊C16—131no—
115C22⋊C16—261no—
116C4×C16—131no—
117#335—131no—
118#335C2×D1311yescharacteristic
119#332—261no—
120#331—21no—
121C22×C13—22no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—161no—
125C22×C13—161no—
126C22×C13—161no—
127C22×C13#46611yescharacteristic
128C4×C13—21no—
129C4×C13—41no—
130C4×C13#45911yescharacteristic
131C4×C13#47211yescharacteristic
132C4×C13C2×SD3211yescharacteristic
133C4×C13#50811yescharacteristic
134Dic13—161no—
135C2×Q16—261no—
136C2×Q16—261no—
137C2×D8—21no—
138C2×D8—21no—
139C2×D8—41no—
140C22×C8—21no—
141C4⋊Q8—261no—
142#127—21no—
143C4×D4C22⋊D1311yescharacteristic
144SD32—522no—
145SD32—522no—
146C2×C16—131no—
147C2×C16—131no—
148C2×C16—261no—
149C2×C16—522no—
150#107—521no—
151C4⋊C8—21no—
152C4⋊C8—261no—
153C4⋊C8C22⋊D1311yescharacteristic
154#102—41no—
155#102—521no—
156C22⋊C8—21no—
157C4×C8C22×D1311yescharacteristic
158C2×C13—42no—
159C2×C13—321no—
160C2×C13#166711yescharacteristic
161C2×C13#221711yescharacteristic
162C2×C13#222311yescharacteristic
163C2×Q8—521no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4#610411yescharacteristic
168C22×C4—21no—
169Q16—521no—
170Q16—521no—
171Q16—1041no—
172D8—41no—
173D8—41no—
174D8—81no—
175D8—82no—
176C2×C8—21no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—521no—
181C2×C8D4×D1311yescharacteristic
182C2×C8#612911yescharacteristic
183C4⋊C4—521no—
184C4⋊C4—521no—
185C4⋊C4#610411yescharacteristic
186C22⋊C4—21no—
187C42C2×C22⋊D1311yescharacteristic
188C16—132no—
189C16—261no—
190C16—521no—
191C13#1243211yescharacteristic, complemented, Sylow
192C23—21no—
193C23—81no—
194Q8—1041no—
195Q8—1041no—
196D4—21no—
197D4—81no—
198D4—81no—
199D4—81no—
200D4—81no—
201D4—161no—
202D4#8806712yescomplemented
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—1041no—
207C2×C4C2×#610411yescharacteristic
208C2×C4#8819311yescharacteristic
209C2×C4#8820411yescharacteristic
210C8—21no—
211C8—41no—
212C8—81no—
213C8—1041no—
214C8D8×D1311yescharacteristic
215C8#8816511yescharacteristic
216C22—22no—
217C22—41no—
218C22—41no—
219C22—161no—
220C22—161no—
221C22—161no—
222C22#1171869911yescharacteristic
223C4—21no—
224C4—41no—
225C4—2081no—
226C4C2×#8806711yescharacteristic
227C4#1171881111yescharacteristic
228C4#1171885511yescharacteristic
229C4#1171886011yescharacteristic
230C2—42no—
231C2—321no—
232C2#1311418911yescharacteristic
233C2#1311693011yescharacteristic
234C2#1311696411yescharacteristic
subgroupG/H
centerC22#11718699
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
Fitting, prime radicalC13×#1667C2
socleC22×C13#466
hypercenter#1667D13
hypocenterC13#12432
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. #13117091C2semidirect
2. D4×#6090C2semidirect
3. #13114201C2semidirect
4. #13112909C2semidirect
5. #13112884C2semidirect
6. #13112882C2semidirect
74. #6090D8semidirect
90. D4×C13SD32semidirect
191. C13#12432semidirect
202. D4#88067semidirect

Maximal subgroups

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

subgroupindex
#131170912
D4×#60902
#131142012
#131129092
#131128842
#131128822
C13×#16672
#1243213