Finite Group Databasebeta

← #16784479

Subgroups — #16784479

Order 3328.

298 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 96 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#13130951C212yesmaximal
2#13130394C211yesmaximal, characteristic
3C8×#6118C211yesmaximal, characteristic
4#13129728C212yesmaximal
5D13×#335C211yesmaximal, characteristic
6C2×#88103—22no—
7#11719052C2212yes—
8#11719051C2211yescharacteristic
9C4×#6118C2211yescharacteristic
10D13×C4⋊C8C2212yes—
11C4×C8×D13C2211yescharacteristic
12#11718268—22no—
13#11718254—21no—
14#11718254—21no—
15#1057⋊C8—21no—
16C8×#1057—21no—
17C13×#335C411yescharacteristic
18#11718071C412yes—
19#11718050C411yescharacteristic
20C2×#6118—22no—
21C2×#6118D411yescharacteristic
22C2×#6118D411yescharacteristic
23C2×C8×D13—22no—
24C2×C8×D13Q811yescharacteristic
25C2×C8×D13Q811yescharacteristic
26C42×D13C2311yescharacteristic
27#88111Q812yes—
28#88110—21no—
29C4⋊#1057—22no—
30C4⋊#1057—21no—
31C4⋊#1057—22no—
32C4×#1057—21no—
33C4×#1057—21no—
34#88103—44no—
35C13×C4⋊C8C2×C412yes—
36C4×C8×C13C2×C411yescharacteristic
37#88054—22no—
38C8×Dic13D411yescharacteristic
39C8×Dic13D411yescharacteristic
40C4⋊#1055C2×C412yes—
41C4×#1055C2×C411yescharacteristic
42#9624—131nomaximal, Sylow
43C2×C4×D13C2×D411yescharacteristic
44C2×C4×D13C2×Q811yescharacteristic
45C2×C4×D13C2×Q811yescharacteristic
46C2×#1057—21no—
47C2×#1057—21no—
48C2×#1057—22no—
49C2×#1057—42no—
50#6118—21no—
51#6118—21no—
52#6118—42no—
53#6118—42no—
54#6118D812yes—
55#6118Q1612yes—
56C2×C8×C13—22no—
57C2×C8×C13C4⋊C411yescharacteristic
58C2×C8×C13C4⋊C411yescharacteristic
59C42×C13C22×C411yescharacteristic
60C4×Dic13C2×D411yescharacteristic
61C4×Dic13#4111yescharacteristic
62C4×Dic13#4111yescharacteristic
63C2×#1055—22no—
64C2×#1055C4⋊C411yescharacteristic
65C2×#1055C4⋊C411yescharacteristic
66C8×D13—22no—
67C8×D13—41no—
68C8×D13—42no—
69C8×D13—42no—
70#1950—132no—
71#1567—131no—
72C2×#335—131no—
73C8×M16—131no—
74#1301—132no—
75C22×D13C4⋊Q811yescharacteristic
76C2×C4×C13C2×C4⋊C411yescharacteristic
77C2×C4×C13C4×D411yescharacteristic
78C2×C4×C13C4×Q811yescharacteristic
79C2×Dic13#12111yescharacteristic
80C2×Dic13C22⋊Q811yescharacteristic
81C2×Dic13#12511yescharacteristic
82C4×D13—21no—
83C4×D13—21no—
84C4×D13—41no—
85C4×D13C2×D811yescharacteristic
86C4×D13C2×Q1611yescharacteristic
87C4×D13#13511yescharacteristic
88C4×D13#13511yescharacteristic
89#1057—22no—
90#1057—22no—
91#1057—42no—
92#1057—82no—
93C8×C13—21no—
94C8×C13—42no—
95C8×C13#10812yescomplemented
96#1055—21no—
97#1055—21no—
98#1055—42no—
99#431—131no—
100C2×#108—262no—
101#423—132no—
102C2×C4⋊C8—132no—
103C4×M16—131no—
104C2×C4×C8—131no—
105#341—262no—
106#335—132no—
107#335—131no—
108#335—261no—
109#335—261no—
110#335#26111yescharacteristic
111#322—261no—
112C82—261no—
113C22×C13#38911yescharacteristic
114C2×D13—21no—
115C2×D13—21no—
116C2×D13#49911yescharacteristic
117C2×D13#50011yescharacteristic
118C4×C13—21no—
119C4×C13C2×#10811yescharacteristic
120C4×C13#43011yescharacteristic
121C4×C13C4×D811yescharacteristic
122C4×C13C4×Q1611yescharacteristic
123Dic13—21no—
124Dic13—21no—
125Dic13#46611yescharacteristic
126Dic13#46711yescharacteristic
127C2×M16—131no—
128C2×M16—131no—
129C2×M16—262no—
130C22×C8—131no—
131C22×C8—131no—
132C22×C8—262no—
133C2×C42—131no—
134#108—524no—
135C4⋊C8—132no—
136C4⋊C8—262no—
137C4⋊C8—261no—
138C4⋊C8—262no—
139C4⋊C8—262no—
140C4⋊C8C2×#26112yes—
141C22⋊C8—132no—
142#97—261no—
143C4×C8—131no—
144C4×C8—131no—
145C4×C8—131no—
146C4×C8—261no—
147C4×C8—261no—
148C4×C8C2×#26111yescharacteristic
149C2×C13#194211yescharacteristic
150C2×C13#195011yescharacteristic
151C2×C13#195311yescharacteristic
152D13—21no—
153D13—21no—
154C22×C4—131no—
155C22×C4—131no—
156C22×C4—131no—
157M16—132no—
158M16—132no—
159M16—261no—
160M16—261no—
161M16—522no—
162M16—522no—
163C2×C8—22no—
164C2×C8—131no—
165C2×C8—131no—
166C2×C8—261no—
167C2×C8—261no—
168C2×C8—262no—
169C2×C8—262no—
170C2×C8—262no—
171C2×C8—521no—
172C2×C8—522no—
173C2×C8—522no—
174C2×C8—522no—
175C2×C8C4⋊#26111yescharacteristic
176C2×C8C4⋊#26111yescharacteristic
177C42—131no—
178C42—131no—
179C42—131no—
180C42C22×#26111yescharacteristic
181C13#962411yescharacteristic, complemented, Sylow
182C23—131no—
183C2×C4—131no—
184C2×C4—131no—
185C2×C4—131no—
186C2×C4—131no—
187C2×C4—131no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—261no—
191C2×C4—261no—
192C2×C4—521no—
193C2×C4C2×C4⋊#26111yescharacteristic
194C2×C4D4×#26111yescharacteristic
195C2×C4Q8×#26111yescharacteristic
196C8—21no—
197C8—42no—
198C8—262no—
199C8—262no—
200C8—261no—
201C8—261no—
202C8—522no—
203C8—522no—
204C8—1042no—
205C8#8810312yescomplemented
206C22—131no—
207C22—131no—
208C22—261no—
209C22—261no—
210C22#1171908311yescharacteristic
211C4—21no—
212C4—131no—
213C4—131no—
214C4—261no—
215C4—261no—
216C4C2×#8810311yescharacteristic
217C4#1171910011yescharacteristic
218C4D8×#26111yescharacteristic
219C4Q16×#26111yescharacteristic
220C2—261no—
221C2—261no—
222C2#1313094011yescharacteristic
223C2#1313095111yescharacteristic
224C2#1313095611yescharacteristic
subgroupG/H
centerC22#11719083
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#335C4
socleC22×C13#389
prime radicalC22×D13C4⋊Q8
cosocleC42×D13C23
hypercenter#335#261
hypocenterC13#9624
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #335

Complements

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

NH ≅ G/Ntype
95. C8×C13#108semidirect
181. C13#9624semidirect
205. C8#88103semidirect

Maximal subgroups

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

subgroupindex
#131309512
#131303942
C8×#61182
#131297282
D13×#3352
#962413