Finite Group Databasebeta

← #16788922

Subgroups — #16788922

Order 3328.

240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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#13130468C211yesmaximal, characteristic, complemented
2#13130417C211yesmaximal, characteristic, complemented
3#13129870C211yesmaximal, characteristic, complemented
4#13129791C211yesmaximal, characteristic, complemented
5#13129791C211yesmaximal, characteristic, complemented
6#1057⋊C16C211yesmaximal, characteristic, complemented
7#13116682C211yesmaximal, characteristic
8#11719076—21no—
9#11719073—21no—
10C2×D208C411yescharacteristic
11#11718533C2211yescharacteristic
12#11718533C2211yescharacteristic
13#11718257C2211yescharacteristic
14#11718254C2211yescharacteristic
15#11718254C2211yescharacteristic
16C8×#1057C2211yescharacteristic
17#11718243—21no—
18#11718243—21no—
19C13×#366C411yescharacteristic
20C16×Dic13C2211yescharacteristic
21#11718083C411yescharacteristic
22#11718083C411yescharacteristic
23C2×#6118—41no—
24C2×D13⋊C8—41no—
25C2×D104C2×C411yescharacteristic
26C2×D104C2×C411yescharacteristic
27#88147—21no—
28#88147—21no—
29#88111—41no—
30#88111—41no—
31C4⋊#1057—21no—
32C4⋊#1057—21no—
33C4×#1057D411yescharacteristic
34C4×#1057D411yescharacteristic
35C2×#6092—21no—
36C2×C13×C16C2×C411yescharacteristic
37C13×#107C2×C411yescharacteristic
38C13×#107C2×C411yescharacteristic
39C8×Dic13C2311yescharacteristic
40C2×#6090C2×C411yescharacteristic
41#88049—21no—
42#88049—21no—
43D208—22no—
44#12073—131nomaximal, Sylow
45C2×D52—21no—
46C2×D52—21no—
47C2×C4×D13—41no—
48C2×C4×D13—41no—
49C2×#1057—21no—
50C2×#1057—41no—
51C2×#1057—41no—
52C2×#1057D811yescharacteristic
53C2×#1057D811yescharacteristic
54#6118—82no—
55D13⋊C8—82no—
56C2×C8×C13C22×C411yescharacteristic
57C13×C4⋊C4—21no—
58C13×C4⋊C4—21no—
59#6103—41no—
60#6103—41no—
61C4×Dic13C2×D411yescharacteristic
62C2×#1055#4111yescharacteristic
63D104—21no—
64D104—21no—
65D104—21no—
66D104M1612yescomplemented
67#6092—41no—
68C13×C16—21no—
69#6090—21no—
70C4×D16—131no—
71#1589—131no—
72C8×D8—131no—
73#1372—131no—
74#1331—131no—
75#1331—131no—
76#1312—131no—
77C22×D13—41no—
78C22×D13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—41no—
81C2×C4×C13C4×D411yescharacteristic
82C2×Dic13C2×D811yescharacteristic
83C2×Dic13#13511yescharacteristic
84D52—22no—
85D52—41no—
86D52—41no—
87D52—41no—
88C4×D13—81no—
89C4×D13—81no—
90C4×D13—81no—
91C4×D13—81no—
92#1057—22no—
93#1057—21no—
94#1057—21no—
95#1057—81no—
96#1057—81no—
97C8×C13C2×M1611yescharacteristic
98C8×C13#13111yescharacteristic
99#1055—21no—
100C2×D16—131no—
101C4×D8—131no—
102C4×D8—131no—
103#436—261no—
104C8×D4—261no—
105#366#26111yescharacteristic
106#357—131no—
107#357—131no—
108C4×C16—131no—
109C4×C16—131no—
110#335—131no—
111#335—131no—
112D4⋊C8—261no—
113D4⋊C8—261no—
114C82—131no—
115C22×C13C4×D811yescharacteristic
116C2×D13—42no—
117C2×D13—81no—
118C2×D13—81no—
119C2×D13—81no—
120C2×D13—81no—
121C2×D13—81no—
122C4×C13—81no—
123C4×C13—81no—
124C4×C13#43511yescharacteristic
125C4×C13#44411yescharacteristic
126Dic13—21no—
127Dic13#50911yescharacteristic
128Dic13#50911yescharacteristic
129C2×D8—131no—
130C2×D8—131no—
131C2×M16—521no—
132C22×C8—521no—
133C4×D4—261no—
134C4×D4—261no—
135D16—262no—
136C2×C16—131no—
137C2×C16—261no—
138C2×C16C2×#26111yescharacteristic
139#107C2×#26111yescharacteristic
140#107C2×#26111yescharacteristic
141C4⋊C8—261no—
142C4⋊C8—261no—
143#102—261no—
144#102—261no—
145C22⋊C8—521no—
146C22⋊C8—521no—
147C4×C8—131no—
148C4×C8—131no—
149C4×C8—131no—
150C2×C13#158111yescharacteristic
151C2×C13#217711yescharacteristic
152C2×C13#217811yescharacteristic
153D13—82no—
154D13—161no—
155C2×D4—261no—
156C2×D4—261no—
157C22×C4—521no—
158C22×C4—521no—
159D8—132no—
160D8—261no—
161D8—261no—
162D8—261no—
163M16—1042no—
164C2×C8—131no—
165C2×C8—131no—
166C2×C8—131no—
167C2×C8—261no—
168C2×C8—521no—
169C2×C8—521no—
170C2×C8—1042no—
171C2×C8C22×#26111yescharacteristic
172C4⋊C4—21no—
173C4⋊C4—21no—
174C22⋊C4—521no—
175C22⋊C4—521no—
176C42—131no—
177C16—21no—
178C16—261no—
179C16—521no—
180C13#1207311yescharacteristic, complemented, Sylow
181C23—521no—
182C23—521no—
183D4—262no—
184D4—521no—
185D4—521no—
186D4—521no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—131no—
190C2×C4—131no—
191C2×C4—1041no—
192C2×C4—1041no—
193C2×C4—1041no—
194C2×C4—1041no—
195C2×C4D4×#26111yescharacteristic
196C8—261no—
197C8—261no—
198C8—262no—
199C8—261no—
200C8—1041no—
201C8—1041no—
202C8D13⋊M1611yescharacteristic
203C8#8824011yescharacteristic
204C22—522no—
205C22—1041no—
206C22—1041no—
207C22—1041no—
208C22—1041no—
209C22—1041no—
210C22D8×#26111yescharacteristic
211C4—81no—
212C4—81no—
213C4—131no—
214C4—131no—
215C4—261no—
216C4#1171907511yescharacteristic
217C4#1171911211yescharacteristic
218C2—1042no—
219C2—2081no—
220C2#1313043611yescharacteristic
221C2#1313123411yescharacteristic
222C2#1313123711yescharacteristic
subgroupG/H
centerC22D8×#261
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#366C4
socleC22×C13C4×D8
prime radicalC2×D208C4
cosocleC8×Dic13C23
hypercenter#366#261
hypocenterC13#12073
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
1. #13130468C2semidirect
2. #13130417C2semidirect
3. #13129870C2semidirect
4. #13129791C2semidirect
5. #13129791C2semidirect
6. #1057⋊C16C2semidirect
66. D104M16semidirect
180. C13#12073semidirect

Maximal subgroups

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

subgroupindex
#131304682
#131304172
#131298702
#131297912
#1057⋊C162
#131166822
#1207313