Finite Group Databasebeta

← #16787573

Subgroups — #16787573

Order 3328.

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

normal subgroups only

This group has 378 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
1C4×D13⋊C16C211yesmaximal, characteristic, complemented
2#13130394C211yesmaximal, characteristic, complemented
3#13129790C214yesmaximal, complemented
4#13125413C211yesmaximal, characteristic
5#11719421—21no—
6C2×D13⋊C16—21no—
7#11719052—21no—
8C13×#493C411yescharacteristic
9#11718818—21no—
10#11718818C412yes—
11D8×Dic13—21no—
12D8×Dic13C2212yes—
13#11718731—21no—
14C4×C8×D13C2211yescharacteristic
15#11718343C411yescharacteristic
16#11718257C2212yes—
17#11718254—21no—
18#11718254C2212yes—
19C4×#6092—21no—
20C2×#6129—41no—
21C2×#6118—41no—
22C2×C13×D8—21no—
23C2×C13×D8C2×C412yes—
24C13×#127—21no—
25#88192—22no—
26#88192—41no—
27#88190—41no—
28D4×Dic13—22no—
29D4×Dic13—41no—
30C2×C8×D13C2×C411yescharacteristic
31C2×C8×D13D411yescharacteristic
32C42×D13D411yescharacteristic
33#88123—21no—
34C4⋊#1057—22no—
35C4⋊#1057—41no—
36C2×#6092—22no—
37D13⋊C16—24no—
38C4×C8×C13C2×C411yescharacteristic
39#88072—22no—
40#88072—22no—
41#88058—21no—
42#88058C2×C412yes—
43C8×Dic13D411yescharacteristic
44C8×Dic13C2311yescharacteristic
45C4×#1055D411yescharacteristic
46#11671—131nomaximal, Sylow
47C2×D4×C13—22no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×C22⋊D13—42no—
51C22×Dic13—42no—
52#6129—82no—
53#6129—82no—
54C2×C4×D13C22⋊C411yescharacteristic
55C2×C4×D13D811yescharacteristic
56C2×C4×D13SD1611yescharacteristic
57C2×Dic26—41no—
58C2×#1057—42no—
59#6118—82no—
60C13×D8—24no—
61C13×D8—42no—
62C2×C8×C13C22⋊C411yescharacteristic
63C2×C8×C13C22×C411yescharacteristic
64C42×C13C22⋊C411yescharacteristic
65C22⋊Dic13—42no—
66C22⋊Dic13—42no—
67C4⋊Dic13—22no—
68C4⋊Dic13—41no—
69C4×Dic13D811yescharacteristic
70C4×Dic13SD1611yescharacteristic
71C4×Dic13C2×D411yescharacteristic
72C2×#1055C22⋊C411yescharacteristic
73C2×#1055C2×D411yescharacteristic
74C8×D13—22no—
75C8×D13—22no—
76#6092—24no—
77#3169—131no—
78C2×C4×C16—131no—
79#1567—131no—
80#1331—134no—
81C23×C13—42no—
82C22×D13#10211yescharacteristic
83D4×C13—42no—
84D4×C13—42no—
85D4×C13—82no—
86D4×C13—82no—
87C2×C4×C13#10211yescharacteristic
88C2×C4×C13#10211yescharacteristic
89C2×C4×C13C2×C22⋊C411yescharacteristic
90C22⋊D13—84no—
91C2×Dic13—42no—
92C2×Dic13—82no—
93C2×Dic13—82no—
94C2×Dic13#10211yescharacteristic
95C2×Dic13C2×D811yescharacteristic
96C2×Dic13C2×SD1611yescharacteristic
97C4×D13—22no—
98C4×D13—21no—
99C4×D13—21no—
100C4×D13D1612yes—
101C4×D13SD3212yes—
102Dic26—82no—
103#1057—82no—
104C8×C13#10412yes—
105C8×C13#13112yes—
106#1055—21no—
107#1055—21no—
108#532—261no—
109C22×C16—261no—
110#500—131no—
111#493#26111yescharacteristic
112#486—261no—
113#466—132no—
114#466—261no—
115C4×D8—132no—
116C4×D8—261no—
117#423—261no—
118C2×C4×C8—131no—
119C4×C16—132no—
120C4×C16—261no—
121#335—132no—
122#335—261no—
123C22×C13—82no—
124C22×C13—82no—
125C22×C13—82no—
126C22×C13C2×#10211yescharacteristic
127C2×D13—21no—
128C2×D13—21no—
129C2×D13#35712yes—
130C4×C13#35712yes—
131C4×C13#35912yes—
132C4×C13#40811yescharacteristic
133C4×C13C2×#10411yescharacteristic
134Dic13—21no—
135Dic13—21no—
136Dic13—82no—
137Dic13C2×D1611yescharacteristic
138Dic13C2×SD3211yescharacteristic
139C2×#41—521no—
140C2×D8—21no—
141C2×D8C2×#26112yes—
142C2×M16—521no—
143C22×C8—131no—
144C22×C8—131no—
145C4⋊Q8—261no—
146#127—21no—
147#124—521no—
148#121—262no—
149#121—521no—
150C4×D4—262no—
151C4×D4—521no—
152C2×C42—131no—
153C2×C16—262no—
154C2×C16—264no—
155#107—132no—
156#107—261no—
157C4⋊C8—262no—
158C4⋊C8—521no—
159#102—262no—
160#102—262no—
161C4×C8—131no—
162C4×C8—131no—
163C4×C8—131no—
164C4×C8C2×#26111yescharacteristic
165C2×C13—162no—
166C2×C13#149211yescharacteristic
167C2×C13C2×#35711yescharacteristic
168C2×C13C2×#35911yescharacteristic
169D13—22no—
170#41—1042no—
171#41—1042no—
172C2×Q8—521no—
173C2×D4—22no—
174C2×D4—41no—
175C2×D4—41no—
176C2×D4—522no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—522no—
181D8—24no—
182D8—42no—
183M16—1042no—
184C2×C8—131no—
185C2×C8—131no—
186C2×C8—262no—
187C2×C8—262no—
188C2×C8—522no—
189C2×C8C22⋊#26111yescharacteristic
190C2×C8C22×#26111yescharacteristic
191C4⋊C4—262no—
192C4⋊C4—521no—
193C22⋊C4—522no—
194C22⋊C4—522no—
195C42—131no—
196C42—131no—
197C42—131no—
198C42C22⋊#26111yescharacteristic
199C16—264no—
200C13#1167111yescharacteristic, complemented, Sylow
201C23—42no—
202C23—131no—
203Q8—1042no—
204D4—42no—
205D4—42no—
206D4—82no—
207D4—82no—
208D4—1044no—
209C2×C4—131no—
210C2×C4—132no—
211C2×C4—132no—
212C2×C4—131no—
213C2×C4—131no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—261no—
217C2×C4—522no—
218C2×C4—1042no—
219C2×C4—1042no—
220C2×C4#8811511yescharacteristic
221C2×C4#8811511yescharacteristic
222C2×C4C2×C22⋊#26111yescharacteristic
223C8—261no—
224C8—261no—
225C8—1042no—
226C8#8811612yes—
227C8#8823812yes—
228C22—82no—
229C22—82no—
230C22—82no—
231C22—132no—
232C22—261no—
233C22—261no—
234C22C2×#8811511yescharacteristic
235C4—131no—
236C4—131no—
237C4—261no—
238C4—261no—
239C4—1042no—
240C4#1171827612yes—
241C4#1171827712yes—
242C4C2×#8811611yescharacteristic
243C4#1171914711yescharacteristic
244C2—162no—
245C2—262no—
246C2#1313018211yescharacteristic
247C2C2×#1171827611yescharacteristic
248C2C2×#1171827711yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#493C4
socleC22×C13C2×#102
prime radical#13125413C2
cosocleC8×Dic13C23
hypercenter#493#261
hypocenterC13#11671
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. C4×D13⋊C16C2semidirect
2. #13130394C2semidirect
3. #13129790C2semidirect
200. C13#11671semidirect

Maximal subgroups

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

subgroupindex
C4×D13⋊C162
#131303942
#131297902
#131254132
#1167113