Finite Group Databasebeta

← #16788240

Subgroups — #16788240

Order 3328.

358 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 74 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#13131199C211yesmaximal, characteristic, complemented
2#13130758C211yesmaximal, characteristic, complemented
3#13129823C214yesmaximal, complemented
4#13125416C211yesmaximal, characteristic
5#11719430—21no—
6#11719060—21no—
7C13×#500C411yescharacteristic, complemented
8#11718749—21no—
9#11718544—21no—
10#11718544C2212yes—
11#11718533—21no—
12#11718533C412yescomplemented
13#11718356C411yescharacteristic, complemented
14C4×C8×D13C2211yescharacteristic
15#11718265—21no—
16#11718265C2212yes—
17#11718260—21no—
18#11718259C2212yes—
19#11718231—21no—
20C2×#6131—41no—
21C2×C4⋊#261—22no—
22C13×C4⋊Q8—21no—
23#88201—41no—
24C2×D104—21no—
25C2×D104C2×C412yes—
26C2×C8×D13D411yescharacteristic
27C2×C8×D13C2311yescharacteristic
28#88149—22no—
29#88149—41no—
30#88147—22no—
31#88147—41no—
32#88128—21no—
33C42×D13D411yescharacteristic
34(C2×#261)⋊C4—41no—
35(C2×#261)⋊C4—41no—
36C2×#6092—22no—
37C13×#107—21no—
38C13×#107C2×C412yes—
39C4×C8×C13C2×C411yescharacteristic
40C8×Dic13C2×C411yescharacteristic
41C8×Dic13D411yescharacteristic
42#88049—22no—
43#88049—22no—
44C4×#1055D411yescharacteristic
45#11858—131nomaximal, Sylow
46C22×#261—42no—
47C2×Q8×C13—41no—
48#6131—84no—
49C2×D52—22no—
50C2×D52—42no—
51C2×D52—41no—
52C2×D52—41no—
53C2×C4×D13—42no—
54C2×C4×D13D811yescharacteristic
55C2×C4×D13D811yescharacteristic
56C2×C4×D13C2×D411yescharacteristic
57C4⋊#261—42no—
58C4⋊#261—42no—
59C2×C8×C13C22⋊C411yescharacteristic
60C2×C8×C13C22×C411yescharacteristic
61C13×C4⋊C4—22no—
62C13×C4⋊C4—41no—
63C42×C13C22⋊C411yescharacteristic
64#6103—42no—
65#6103—42no—
66C4×Dic13C22⋊C411yescharacteristic
67C4×Dic13SD1611yescharacteristic
68C4×Dic13SD1611yescharacteristic
69C2×#1055C22⋊C411yescharacteristic
70C2×#1055C2×D411yescharacteristic
71D104—42no—
72D104—42no—
73C8×D13—41no—
74C8×D13—41no—
75#6092—42no—
76#3169—131no—
77#2163—131no—
78#1835—131no—
79#1347—134no—
80C22×D13—42no—
81C22×D13C2×D811yescharacteristic
82C2×#261—82no—
83C2×#261—82no—
84C2×#261—82no—
85Q8×C13—82no—
86C2×C4×C13—42no—
87C2×C4×C13#10211yescharacteristic
88C2×C4×C13#10211yescharacteristic
89C2×C4×C13C2×C22⋊C411yescharacteristic
90C2×Dic13#10211yescharacteristic
91C2×Dic13#10211yescharacteristic
92C2×Dic13C2×SD1611yescharacteristic
93D52—42no—
94D52—42no—
95D52—82no—
96D52—82no—
97D52—84no—
98C4×D13—22no—
99C4×D13—21no—
100C4×D13—21no—
101C4×D13—41no—
102C4×D13—84no—
103C8×C13—21no—
104C8×C13—21no—
105#1055—21no—
106#1055—21no—
107#532—261no—
108#500#26111yescharacteristic, complemented
109#493—131no—
110#486—261no—
111#466—132no—
112#466—261no—
113C4×D8—132no—
114C4×D8—261no—
115C2×C4×C8—131no—
116#382—261no—
117C4⋊C16—261no—
118C22⋊C16—132no—
119#346—261no—
120#340—132no—
121#340—261no—
122C22×C13C2×#10211yescharacteristic
123C2×D13—21no—
124C2×D13—21no—
125C2×D13—82no—
126C2×D13—82no—
127C2×D13—82no—
128C2×D13#50912yes—
129#261—162no—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—82no—
133C4×C13#41011yescharacteristic
134C4×C13#42111yescharacteristic
135Dic13—21no—
136Dic13—21no—
137Dic13—21no—
138C2×#41—521no—
139C2×D8—132no—
140C2×D8—261no—
141C22×C8—131no—
142C22×C8—131no—
143C4⋊Q8—21no—
144#127—261no—
145#124—521no—
146#121—262no—
147#121—521no—
148C4×D4—262no—
149C4×D4—521no—
150C2×C4⋊C4—262no—
151C2×C42—131no—
152C2×C16—262no—
153#107—21no—
154#107C2×#26112yes—
155#102—262no—
156#102—262no—
157C4×C8—131no—
158C4×C8—131no—
159C4×C8—131no—
160C4×C8C2×#26111yescharacteristic
161#95—521no—
162#95—521no—
163C2×C13#151711yescharacteristic
164C2×C13#214011yescharacteristic
165C2×C13#214511yescharacteristic
166D13—22no—
167D13—162no—
168#41—1044no—
169C2×Q8—41no—
170C2×D4—262no—
171C2×D4—522no—
172C2×D4—521no—
173C2×D4—521no—
174C22×C4—131no—
175C22×C4—131no—
176C22×C4—131no—
177C22×C4—522no—
178C22×C4—522no—
179D8—522no—
180D8—522no—
181C2×C8—131no—
182C2×C8—131no—
183C2×C8—521no—
184C2×C8—521no—
185C2×C8C22⋊#26111yescharacteristic
186C2×C8C22×#26111yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—522no—
190C4⋊C4—522no—
191C22⋊C4—522no—
192C22⋊C4—522no—
193C42—131no—
194C42—131no—
195C42—131no—
196C42C22⋊#26111yescharacteristic
197C16—522no—
198C13#1185811yescharacteristic, complemented, Sylow
199C23—131no—
200C23—522no—
201Q8—82no—
202D4—522no—
203D4—522no—
204D4—1042no—
205D4—1042no—
206D4—1044no—
207C2×C4—42no—
208C2×C4—131no—
209C2×C4—131no—
210C2×C4—131no—
211C2×C4—262no—
212C2×C4—261no—
213C2×C4—261no—
214C2×C4—521no—
215C2×C4—1044no—
216C2×C4—1042no—
217C2×C4—1042no—
218C2×C4—1042no—
219C2×C4#8811511yescharacteristic
220C2×C4#8811511yescharacteristic
221C2×C4C2×C22⋊#26111yescharacteristic
222C8—21no—
223C8—21no—
224C8—261no—
225C8—261no—
226C22—132no—
227C22—261no—
228C22—261no—
229C22—1042no—
230C22—1042no—
231C22—1042no—
232C22C2×#8811511yescharacteristic
233C4—21no—
234C4—21no—
235C4—82no—
236C4—261no—
237C4—261no—
238C4—261no—
239C4—2082no—
240C4#1171915511yescharacteristic
241C4#1171915611yescharacteristic
242C2—262no—
243C2—2082no—
244C2#1313026711yescharacteristic
245C2#1313114511yescharacteristic
246C2#1313115811yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#500C4
socleC22×C13C2×#102
prime radical#13125416C2
cosocleC2×C8×D13C23
hypercenter#500#261
hypocenterC13#11858
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #13131199C2semidirect
2. #13130758C2semidirect
3. #13129823C2semidirect
7. C13×#500C4semidirect
12. #11718533C4semidirect
13. #11718356C4semidirect
108. #500#261semidirect
198. C13#11858semidirect

Maximal subgroups

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

subgroupindex
#131311992
#131307582
#131298232
#131254162
#1185813