Finite Group Databasebeta

← #16788913

Subgroups — #16788913

Order 3328.

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

normal subgroups only

This group has 224 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
2Q16×#1057C211yesmaximal, characteristic, complemented
3#13129869C211yesmaximal, characteristic, complemented
4#13129792C211yesmaximal, characteristic, complemented
5#13129791C211yesmaximal, characteristic
6#1057⋊C16C211yesmaximal, characteristic, complemented
7#13116685C211yesmaximal, characteristic
8Q8×#1057—21no—
9#11719076—21no—
10Q16×Dic13C2211yescharacteristic
11C2×#88068C411yescharacteristic
12#11718533C2211yescharacteristic
13Q8⋊#1057—21no—
14#11718257C2211yescharacteristic
15#11718254C2211yescharacteristic
16#11718254C2211yescharacteristic
17C8×#1057C2211yescharacteristic
18#11718243—21no—
19C13×#358C411yescharacteristic
20#11718101C411yescharacteristic
21C16×Dic13C2211yescharacteristic
22#11718082C411yescharacteristic
23C2×#6118—41no—
24C2×C13×Q16C2×C411yescharacteristic
25Q8×Dic13—21no—
26C2×D104C2×C411yescharacteristic
27#88147—21no—
28#88111—41no—
29C4⋊#1057—21no—
30C4⋊#1057—21no—
31C4⋊#1057—41no—
32C4×#1057—41no—
33C4×#1057D411yescharacteristic
34C4×#1057D411yescharacteristic
35C2×#6092—21no—
36C2×C13×C16C2×C411yescharacteristic
37C13×#107C2×C411yescharacteristic
38#88075—21no—
39#88068—22no—
40#88058C2×C411yescharacteristic
41C8×Dic13C2311yescharacteristic
42C2×#6090C2×C411yescharacteristic
43#88049—21no—
44#12071—131nomaximal, Sylow
45C2×Q8×C13—21no—
46C2×D52—21no—
47C2×C4×D13—41no—
48C2×#1057—21no—
49C2×#1057—41no—
50C2×#1057—41no—
51C2×#1057D811yescharacteristic
52C2×#1057D811yescharacteristic
53#6118—82no—
54C13×Q16—21no—
55C13×Q16M1612yescomplemented
56C2×C8×C13C22×C411yescharacteristic
57C13×C4⋊C4—21no—
58#6103—41no—
59C4⋊Dic13—21no—
60C4⋊Dic13—41no—
61C4×Dic13—41no—
62C4×Dic13C2×D411yescharacteristic
63C2×#1055#4111yescharacteristic
64D104—21no—
65D104—21no—
66#6092—41no—
67C13×C16—21no—
68#6090—21no—
69C4×SD32—131no—
70#1589—131no—
71C8×Q16—131no—
72#1372—131no—
73#1332—131no—
74#1331—131no—
75#1312—131no—
76C22×D13—41no—
77Q8×C13—22no—
78Q8×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—41no—
81C2×C4×C13C4×D411yescharacteristic
82C2×Dic13—41no—
83C2×Dic13C2×D811yescharacteristic
84C2×Dic13#13511yescharacteristic
85D52—41no—
86D52—41no—
87C4×D13—81no—
88C4×D13—81no—
89#1057—21no—
90#1057—41no—
91#1057—81no—
92#1057—81no—
93#1057SD3212yescomplemented
94C8×C13C2×M1611yescharacteristic
95C8×C13#13111yescharacteristic
96#1055—21no—
97C2×SD32—131no—
98C8×Q8—261no—
99C4×Q16—131no—
100C4×D8—131no—
101#436—261no—
102#367—131no—
103#358#26111yescharacteristic
104#357—131no—
105C4×C16—131no—
106C4×C16—131no—
107#335—131no—
108#335—131no—
109Q8⋊C8—261no—
110D4⋊C8—261no—
111C82—131no—
112C22×C13C4×D811yescharacteristic
113C2×D13—81no—
114C2×D13—81no—
115C2×D13—81no—
116C4×C13—42no—
117C4×C13—81no—
118C4×C13#43511yescharacteristic
119C4×C13#44411yescharacteristic
120Dic13—21no—
121Dic13—81no—
122Dic13C2×SD3211yescharacteristic
123Dic13#50811yescharacteristic
124C2×Q16C2×#26111yescharacteristic
125C2×D8—131no—
126C2×M16—521no—
127C4×Q8—261no—
128C4×D4—261no—
129SD32—262no—
130C2×C16—131no—
131C2×C16—261no—
132C2×C16C2×#26111yescharacteristic
133#107—131no—
134#107C2×#26111yescharacteristic
135C4⋊C8—261no—
136C4⋊C8—261no—
137C4⋊C8—521no—
138#103—261no—
139#102—261no—
140C22⋊C8—521no—
141C4×C8—131no—
142C4×C8—131no—
143C4×C8—131no—
144C4×C8—521no—
145C2×C13#158111yescharacteristic
146C2×C13C4×SD3211yescharacteristic
147C2×C13#217911yescharacteristic
148D13—161no—
149C2×Q8—21no—
150C2×D4—261no—
151C22×C4—521no—
152Q16—21no—
153Q16#611812yescomplemented
154D8—261no—
155D8—261no—
156M16—1042no—
157C2×C8—131no—
158C2×C8—131no—
159C2×C8—131no—
160C2×C8—261no—
161C2×C8—521no—
162C2×C8—521no—
163C2×C8C22×#26111yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—261no—
166C4⋊C4—521no—
167C22⋊C4—521no—
168C42—131no—
169C42—521no—
170C16—21no—
171C16—261no—
172C16—521no—
173C13#1207111yescharacteristic, complemented, Sylow
174C23—521no—
175Q8—22no—
176Q8—41no—
177D4—521no—
178D4—521no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—131no—
182C2×C4—131no—
183C2×C4—521no—
184C2×C4—1041no—
185C2×C4—1041no—
186C2×C4D4×#26111yescharacteristic
187C8—132no—
188C8—261no—
189C8—261no—
190C8—521no—
191C8—1041no—
192C8—1041no—
193C8C2×#611811yescharacteristic
194C8#8823811yescharacteristic
195C22—1041no—
196C22—1041no—
197C22—1041no—
198C22D8×#26111yescharacteristic
199C4—42no—
200C4—81no—
201C4—131no—
202C4—131no—
203C4—261no—
204C4—1041no—
205C4#1171906411yescharacteristic
206C4#1171910811yescharacteristic
207C2—2081no—
208C2#1313043511yescharacteristic
209C2SD32×#26111yescharacteristic
210C2#1313123911yescharacteristic
subgroupG/H
centerC22D8×#261
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#358C4
socleC22×C13C4×D8
prime radicalC2×D104C2×C4
cosocleC8×Dic13C23
hypercenter#358#261
hypocenterC13#12071
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
2. Q16×#1057C2semidirect
3. #13129869C2semidirect
4. #13129792C2semidirect
6. #1057⋊C16C2semidirect
55. C13×Q16M16semidirect
93. #1057SD32semidirect
153. Q16#6118semidirect
173. C13#12071semidirect

Maximal subgroups

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

subgroupindex
#131304682
Q16×#10572
#131298692
#131297922
#131297912
#1057⋊C162
#131166852
#1207113