Finite Group Databasebeta

← #16777396

Subgroups — #16777396

Order 3328.

314 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 72 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
1D13⋊(C22⋊C16)C211yesmaximal, characteristic
2#13130713C211yesmaximal, characteristic
3#13114864C211yesmaximal, characteristic
4C22×C8×D13C2211yescharacteristic
5#11719136—21no—
6C2×#88102—21no—
7C2×D13⋊C16C412yescomplemented
8#11718648—21no—
9C2×#88047—21no—
10C22⋊#6092—21no—
11#11718265C412yescomplemented
12#11718259—21no—
13C13×#340C411yescharacteristic, complemented
14#11718143C411yescharacteristic, complemented
15C22×C4×D13D411yescharacteristic
16C2×C22⋊#261—41no—
17C2×C4⋊#261—22no—
18C22×C8×C13C2×C411yescharacteristic
19C2×C13×C4⋊C4—21no—
20C2×#6103—41no—
21C2×C4⋊Dic13—21no—
22C22×#1055D411yescharacteristic
23C2×C8×D13—42no—
24C2×C8×D13C2×C411yescharacteristic
25C2×C8×D13C2×C411yescharacteristic
26C2×C8×D13D411yescharacteristic
27C2×C8×D13Q811yescharacteristic
28(C2×#261)⋊C4—41no—
29C2×#6092—22no—
30#88102—42no—
31D13⋊C16—42no—
32#88071—41no—
33#88047—42no—
34#7230—131nomaximal, Sylow
35C23×D13D811yescharacteristic
36C22×#261—42no—
37C22×C4×C13—41no—
38C22×C4×C13C22⋊C411yescharacteristic
39C22×Dic13—41no—
40C22×Dic13SD1611yescharacteristic
41C2×C4×D13—41no—
42C2×C4×D13—41no—
43C2×C4×D13C22⋊C411yescharacteristic
44C2×C4×D13C4⋊C411yescharacteristic
45C2×C4×D13SD1611yescharacteristic
46C2×C4×D13Q1611yescharacteristic
47C22⋊#261—81no—
48C22⋊#261—81no—
49C4⋊#261—42no—
50C4⋊#261—42no—
51C2×C8×C13—41no—
52C2×C8×C13C4211yescharacteristic
53C2×C8×C13C4⋊C411yescharacteristic
54C13×C4⋊C4—41no—
55C13×C4⋊C4—41no—
56#6103—81no—
57#6103—81no—
58C4⋊Dic13—41no—
59C4⋊Dic13—41no—
60C2×#1055—22no—
61C2×#1055C22⋊C411yescharacteristic
62C2×#1055C4⋊C411yescharacteristic
63C8×D13—22no—
64C8×D13—22no—
65C8×D13—41no—
66C8×D13—41no—
67#6092—42no—
68C2×C22⋊C16—131no—
69#1808—131no—
70#1808—131no—
71C23×C13#10211yescharacteristic
72C22×D13—41no—
73C22×D13—41no—
74C22×D13#10211yescharacteristic
75C22×D13#10711yescharacteristic
76C22×D13D1611yescharacteristic
77C22×D13SD3211yescharacteristic
78C22×D13SD3211yescharacteristic
79C22×D13Q3211yescharacteristic
80C2×#261—82no—
81C2×#261—82no—
82C2×#261—82no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—81no—
86C2×C4×C13—81no—
87C2×C4×C13—81no—
88C2×C4×C13#9511yescharacteristic
89C2×C4×C13#10311yescharacteristic
90C2×Dic13—41no—
91C2×Dic13—81no—
92C2×Dic13—81no—
93C2×Dic13—81no—
94C2×Dic13#10311yescharacteristic
95C2×Dic13#10611yescharacteristic
96C4×D13—21no—
97C4×D13—21no—
98C4×D13—21no—
99C4×D13—21no—
100C4×D13—41no—
101C4×D13—41no—
102C8×C13—21no—
103C8×C13—21no—
104#1055—21no—
105#1055#9912yes—
106C23×C8—131no—
107C22×C16—132no—
108C2×#107—261no—
109C2×#107—261no—
110#380—261no—
111#380—261no—
112C22⋊C16—261no—
113C22⋊C16—261no—
114#340—132no—
115#340—131no—
116#340#26111yescharacteristic, complemented
117C22×C13—21no—
118C22×C13—21no—
119C22×C13#34011yescharacteristic
120C22×C13#35711yescharacteristic
121C22×C13#35811yescharacteristic
122C2×D13—21no—
123C2×D13—21no—
124C2×D13—21no—
125C2×D13—21no—
126C2×D13—41no—
127C2×D13—41no—
128C2×D13—41no—
129C2×D13—41no—
130C2×D13#35711yescharacteristic
131C2×D13#35811yescharacteristic
132C2×D13#36611yescharacteristic
133C2×D13#36711yescharacteristic
134#261—162no—
135C4×C13—21no—
136C4×C13—161no—
137C4×C13H(3,ℤ/4)11yescharacteristic
138C4×C13#34211yescharacteristic
139Dic13—21no—
140Dic13—21no—
141Dic13—161no—
142C23×C4—131no—
143C22×C8—131no—
144C22×C8—131no—
145C22×C8—131no—
146C22×C8—131no—
147C22×C8—131no—
148C22×C8—522no—
149C22×C8C2×#26111yescharacteristic
150C2×C4⋊C4—21no—
151C2×C4⋊C4—262no—
152C2×C4⋊C4—261no—
153C2×C22⋊C4—521no—
154C2×C22⋊C4—521no—
155C2×C16—262no—
156C2×C16—522no—
157#107—522no—
158#107—522no—
159#95—521no—
160#95—521no—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13#128911yescharacteristic
164C2×C13#138011yescharacteristic
165C2×C13#138411yescharacteristic
166D13—21no—
167D13—21no—
168D13—21no—
169D13—21no—
170C24—131no—
171C22×C4—41no—
172C22×C4—131no—
173C22×C4—131no—
174C22×C4—131no—
175C22×C4—131no—
176C22×C4—131no—
177C22×C4—521no—
178C22×C4—521no—
179C22×C4—522no—
180C22×C4—521no—
181C22×C4C22⋊#26111yescharacteristic
182C2×C8—41no—
183C2×C8—131no—
184C2×C8—131no—
185C2×C8—262no—
186C2×C8—262no—
187C2×C8—262no—
188C2×C8—521no—
189C2×C8—521no—
190C2×C8C4×#26111yescharacteristic
191C2×C8C4⋊#26111yescharacteristic
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—521no—
195C4⋊C4—521no—
196C4⋊C4—522no—
197C4⋊C4—522no—
198C22⋊C4—1041no—
199C22⋊C4—1041no—
200C22⋊C4—1041no—
201C22⋊C4—1041no—
202C16—522no—
203C13#723011yescharacteristic, complemented, Sylow
204C23—131no—
205C23—131no—
206C23—131no—
207C23—131no—
208C23—131no—
209C23—131no—
210C23—521no—
211C23—521no—
212C23#8811511yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—81no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—131no—
219C2×C4—131no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—521no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4—1041no—
228C2×C4—1041no—
229C2×C4—1042no—
230C2×C4—1042no—
231C2×C4—1042no—
232C2×C4—1041no—
233C2×C4(C2×#261)⋊C411yescharacteristic
234C2×C4#8811711yescharacteristic
235C8—21no—
236C8—21no—
237C8—132no—
238C8—261no—
239C22—21no—
240C22—21no—
241C22—131no—
242C22—131no—
243C22—131no—
244C22—131no—
245C22—261no—
246C22—261no—
247C22—261no—
248C22—261no—
249C22—521no—
250C22—521no—
251C22—521no—
252C22—521no—
253C22#1171824611yescharacteristic
254C22#1171827611yescharacteristic
255C22#1171828011yescharacteristic
256C4—21no—
257C4—161no—
258C4—261no—
259C4—261no—
260C4—2081no—
261C4—2082no—
262C4#1171823511yescharacteristic
263C4#1171823811yescharacteristic
264C2—21no—
265C2—21no—
266C2—261no—
267C2—261no—
268C2—261no—
269C2—261no—
270C2#1312969811yescharacteristic
271C2#1312989311yescharacteristic
272C2#1312990311yescharacteristic
subgroupG/H
centerC22#11718246
commutatorC2×C8×C13C42
FrattiniC22×C8C2×#261
FittingC13×#340C4
socleC22×C13#340
prime radicalC23×D13D8
cosocleC22×C8×D13C22
hypercenter#340#261
hypocenterC13#7230
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
7. C2×D13⋊C16C4semidirect
11. #11718265C4semidirect
13. C13×#340C4semidirect
14. #11718143C4semidirect
116. #340#261semidirect
203. C13#7230semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C22⋊C16)2
#131307132
#131148642
#723013