Finite Group Databasebeta

← #16788905

Subgroups — #16788905

Order 3328.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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
2D8×#1057C211yesmaximal, characteristic, complemented
3#13129867C211yesmaximal, characteristic, complemented
4#13129791C211yesmaximal, characteristic, complemented
5#13129790C211yesmaximal, characteristic, complemented
6#1057⋊C16C211yesmaximal, characteristic, complemented
7#13116680C211yesmaximal, characteristic
8D4×#1057—21no—
9#11719076—21no—
10D8×Dic13C2211yescharacteristic
11C2×#88066C411yescharacteristic
12#11718533C2211yescharacteristic
13D4⋊#1057—21no—
14#11718257C2211yescharacteristic
15#11718254C2211yescharacteristic
16#11718254C2211yescharacteristic
17C8×#1057C2211yescharacteristic
18#11718243—21no—
19C13×#357C411yescharacteristic
20#11718101C411yescharacteristic
21C16×Dic13C2211yescharacteristic
22#11718081C411yescharacteristic
23C22×#1057—41no—
24C2×#6118—41no—
25C2×C13×D8C2×C411yescharacteristic
26D4×Dic13—21no—
27C2×D104C2×C411yescharacteristic
28#88147—21no—
29C22⋊#1057—41no—
30#88111—41no—
31C4⋊#1057—21no—
32C4⋊#1057—21no—
33C4×#1057D411yescharacteristic
34C4×#1057D411yescharacteristic
35C2×#6092—21no—
36C2×C13×C16C2×C411yescharacteristic
37C13×#107C2×C411yescharacteristic
38#88072—21no—
39#88066—22no—
40#88058C2×C411yescharacteristic
41C8×Dic13C2311yescharacteristic
42C2×#6090C2×C411yescharacteristic
43#88049—21no—
44#12069—131nomaximal, Sylow
45C2×D4×C13—21no—
46C22×Dic13—41no—
47C2×D52—21no—
48C2×C4×D13—41no—
49C2×#1057—21no—
50C2×#1057—41no—
51C2×#1057—41no—
52C2×#1057—82no—
53C2×#1057D811yescharacteristic
54C2×#1057D811yescharacteristic
55#6118—82no—
56C13×D8—21no—
57C13×D8M1612yescomplemented
58C2×C8×C13C22×C411yescharacteristic
59C13×C4⋊C4—21no—
60C22⋊Dic13—41no—
61#6103—41no—
62C4⋊Dic13—21no—
63C4×Dic13C2×D411yescharacteristic
64C2×#1055#4111yescharacteristic
65D104—21no—
66D104—21no—
67#6092—41no—
68C13×C16—21no—
69#6090—21no—
70C4×D16—131no—
71#1589—131no—
72C8×D8—131no—
73#1371—131no—
74#1331—131no—
75#1331—131no—
76#1312—131no—
77C23×C13—41no—
78C22×D13—41no—
79D4×C13—22no—
80D4×C13—41no—
81C2×C4×C13—41no—
82C2×C4×C13C4×D411yescharacteristic
83C2×Dic13—41no—
84C2×Dic13—81no—
85C2×Dic13—81no—
86C2×Dic13C2×D811yescharacteristic
87C2×Dic13#13511yescharacteristic
88D52—41no—
89D52—41no—
90C4×D13—81no—
91C4×D13—81no—
92#1057—21no—
93#1057—41no—
94#1057—81no—
95#1057—81no—
96#1057D1612yescomplemented
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—131no—
106#357—131no—
107#357#26111yescharacteristic
108C4×C16—131no—
109C4×C16—131no—
110#335—131no—
111#335—131no—
112D4⋊C8—261no—
113D4⋊C8—261no—
114C82—131no—
115C22×C13—42no—
116C22×C13—81no—
117C22×C13—81no—
118C22×C13C4×D811yescharacteristic
119C2×D13—81no—
120C2×D13—81no—
121C2×D13—81no—
122C4×C13—81no—
123C4×C13#43511yescharacteristic
124C4×C13#44411yescharacteristic
125Dic13—21no—
126Dic13—81no—
127Dic13C2×D1611yescharacteristic
128Dic13#50811yescharacteristic
129C2×D8—131no—
130C2×D8C2×#26111yescharacteristic
131C2×M16—521no—
132C22×C8—521no—
133C4×D4—261no—
134C4×D4—261no—
135D16—262no—
136C2×C16—131no—
137C2×C16—261no—
138C2×C16C2×#26111yescharacteristic
139#107—131no—
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—82no—
151C2×C13#158111yescharacteristic
152C2×C13C4×D1611yescharacteristic
153C2×C13#217911yescharacteristic
154D13—161no—
155C2×D4—21no—
156C2×D4—261no—
157C22×C4—521no—
158C22×C4—521no—
159D8—21no—
160D8—261no—
161D8—261no—
162D8#611812yescomplemented
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—261no—
174C22⋊C4—521no—
175C22⋊C4—521no—
176C42—131no—
177C16—21no—
178C16—261no—
179C16—521no—
180C13#1206911yescharacteristic, complemented, Sylow
181C23—41no—
182C23—521no—
183D4—22no—
184D4—41no—
185D4—521no—
186D4—521no—
187C2×C4—41no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—521no—
191C2×C4—1041no—
192C2×C4—1041no—
193C2×C4—1041no—
194C2×C4—1041no—
195C2×C4D4×#26111yescharacteristic
196C8—132no—
197C8—261no—
198C8—261no—
199C8—521no—
200C8—1041no—
201C8—1041no—
202C8C2×#611811yescharacteristic
203C8#8823811yescharacteristic
204C22—42no—
205C22—81no—
206C22—81no—
207C22—1041no—
208C22—1041no—
209C22—1041no—
210C22D8×#26111yescharacteristic
211C4—81no—
212C4—131no—
213C4—131no—
214C4—261no—
215C4—1041no—
216C4#1171906411yescharacteristic
217C4#1171910811yescharacteristic
218C2—82no—
219C2—2081no—
220C2#1313043511yescharacteristic
221C2D16×#26111yescharacteristic
222C2#1313123811yescharacteristic
subgroupG/H
centerC22D8×#261
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#357C4
socleC22×C13C4×D8
prime radicalC2×#88066C4
cosocleC8×Dic13C23
hypercenter#357#261
hypocenterC13#12069
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. #13130468C2semidirect
2. D8×#1057C2semidirect
3. #13129867C2semidirect
4. #13129791C2semidirect
5. #13129790C2semidirect
6. #1057⋊C16C2semidirect
57. C13×D8M16semidirect
96. #1057D16semidirect
162. D8#6118semidirect
180. C13#12069semidirect

Maximal subgroups

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

subgroupindex
#131304682
D8×#10572
#131298672
#131297912
#131297902
#1057⋊C162
#131166802
#1206913