Finite Group Databasebeta

← #16787411

Subgroups — #16787411

Order 3328.

320 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 90 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#13131195C211yesmaximal, characteristic, complemented
2D13⋊(C4⋊C16)C211yesmaximal, characteristic, complemented
3#13129803C212yesmaximal, complemented
4D4⋊#6092C212yesmaximal, complemented
5#13123814C211yesmaximal, characteristic
6#11719262C411yescharacteristic
7C2×D13⋊C16—21no—
8C13×#436C411yescharacteristic
9#11718788—21no—
10#11718783—21no—
11D4×#1055C2211yescharacteristic
12#11718496C411yescharacteristic
13#11718491C2211yescharacteristic
14#11718386—21no—
15#11718381—21no—
16C4×C8×D13C2211yescharacteristic
17#11718340C411yescharacteristic
18#11718260—21no—
19#11718260—21no—
20#11718259—21no—
21C4⋊#6092C2212yes—
22C4×#6092C2212yes—
23C2×C13×M16—21no—
24C4×D4×C13C2×C411yescharacteristic
25#88192C811yescharacteristic
26#88190C811yescharacteristic
27C4×C22⋊D13—21no—
28#88180—21no—
29C22×#1055—21no—
30C2×C8×D13D411yescharacteristic
31C2×C8×D13D411yescharacteristic
32#88151C811yescharacteristic
33#88144C811yescharacteristic
34#88137—21no—
35#88133—21no—
36C42×D13C2×C411yescharacteristic
37C4×Dic26C2×C411yescharacteristic
38C2×#6092—22no—
39C2×#6092—22no—
40D13⋊C16—42no—
41C13×C4⋊C8C2×C411yescharacteristic
42C13×C22⋊C8—21no—
43C4×C8×C13C2×C411yescharacteristic
44C22⋊#1055—21no—
45#88060—21no—
46#88055—21no—
47#88055—21no—
48#88054—21no—
49#88054—21no—
50C8×Dic13—21no—
51C8×Dic13D411yescharacteristic
52C8×Dic13D411yescharacteristic
53C4⋊#1055C2×C411yescharacteristic
54C4×#1055C2311yescharacteristic
55#11622—131nomaximal, Sylow
56C2×D4×C13C2×C811yescharacteristic
57C22×C4×C13—21no—
58C2×C22⋊D13—21no—
59C2×C4×D13C22⋊C411yescharacteristic
60C2×C4×D13C2×C811yescharacteristic
61C2×C4×D13M1611yescharacteristic
62C2×Dic26C2×C811yescharacteristic
63C13×M16—42no—
64C2×C8×C13—21no—
65C2×C8×C13C22⋊C411yescharacteristic
66C2×C8×C13C22⋊C411yescharacteristic
67C13×C4⋊C4C2×C811yescharacteristic
68C13×C22⋊C4—21no—
69C42×C13C22×C411yescharacteristic
70C22⋊Dic13—21no—
71C22⋊Dic13—21no—
72C22⋊Dic13—21no—
73#6103—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13C2×C811yescharacteristic
77#6101—21no—
78#6101—21no—
79C4×Dic13—21no—
80C4×Dic13C22⋊C411yescharacteristic
81C4×Dic13C2×C811yescharacteristic
82C4×Dic13M1611yescharacteristic
83C2×#1055—21no—
84C2×#1055—41no—
85C2×#1055—41no—
86C2×#1055C2×D411yescharacteristic
87C2×#1055C2×D411yescharacteristic
88C8×D13—21no—
89C8×D13—21no—
90C8×D13—41no—
91#6092—42no—
92#6092—42no—
93#2966—131no—
94#2162—131no—
95C2×C4⋊C16—131no—
96Q8⋊C16—132no—
97D4⋊C16—132no—
98C23×C13—21no—
99C22×D13C22⋊C811yescharacteristic
100D4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13C22×C811yescharacteristic
106C2×C4×C13C2×M1611yescharacteristic
107C22⋊D13—42no—
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13C22⋊C811yescharacteristic
111C2×Dic13C22⋊C811yescharacteristic
112C2×Dic13C22⋊C811yescharacteristic
113C4×D13—22no—
114C4×D13—21no—
115C4×D13—21no—
116C4×D13—22no—
117Dic26—22no—
118C8×C13—21no—
119C8×C13—21no—
120C8×C13—41no—
121#1055—21no—
122#1055—41no—
123#1055AGL(1,ℤ/8)11yescharacteristic
124#1055#13711yescharacteristic
125#529—131no—
126C22×C16—261no—
127#446—131no—
128C8×Q8—131no—
129#436#26111yescharacteristic
130#435—261no—
131C8×D4—131no—
132C8×D4—261no—
133#433—261no—
134#432—131no—
135#405—261no—
136C2×C4×C8—131no—
137C4⋊C16—132no—
138C4⋊C16—261no—
139C4⋊C16—261no—
140C22⋊C16—261no—
141C4×C16—132no—
142C22×C13—41no—
143C22×C13—41no—
144C22×C13—41no—
145C22×C13C2×C22⋊C811yescharacteristic
146C2×D13—21no—
147C2×D13—21no—
148C2×D13#35012yes—
149C4×C13—21no—
150C4×C13—41no—
151C4×C13#41711yescharacteristic
152C4×C13#42111yescharacteristic
153C4×C13#50412yes—
154Dic13—21no—
155Dic13—21no—
156Dic13—21no—
157Dic13—41no—
158Dic13—41no—
159C2×M16—21no—
160C22×C8—131no—
161C22×C8—131no—
162C22×C8—261no—
163#126—261no—
164#125—131no—
165#124—131no—
166#123—261no—
167C22⋊Q8—131no—
168#121—131no—
169C4×Q8—131no—
170C4×D4—261no—
171C4×D4C2×#26111yescharacteristic
172#117—261no—
173C2×C42—131no—
174C2×C16—262no—
175C2×C16—262no—
176C2×C16—522no—
177C4⋊C8—131no—
178C4⋊C8—261no—
179C4⋊C8—261no—
180C4⋊C8C2×#26111yescharacteristic
181C22⋊C8—21no—
182C22⋊C8—261no—
183C22⋊C8—261no—
184#97—261no—
185#97—261no—
186C4×C8—131no—
187C4×C8—131no—
188C4×C8—131no—
189C4×C8—261no—
190C4×C8C2×#26111yescharacteristic
191C2×C13—81no—
192C2×C13#147711yescharacteristic
193C2×C13#211311yescharacteristic
194C2×C13C2×#35011yescharacteristic
195D13—22no—
196C2×Q8—131no—
197C2×D4—261no—
198C2×D4D13⋊C811yescharacteristic
199C22×C4—21no—
200C22×C4—131no—
201C22×C4—131no—
202C22×C4—131no—
203M16—42no—
204C2×C8—21no—
205C2×C8—131no—
206C2×C8—131no—
207C2×C8—261no—
208C2×C8—261no—
209C2×C8—261no—
210C2×C8—521no—
211C2×C8—521no—
212C2×C8—521no—
213C2×C8C22⋊#26111yescharacteristic
214C2×C8C22⋊#26111yescharacteristic
215C4⋊C4—131no—
216C4⋊C4—261no—
217C4⋊C4—261no—
218C4⋊C4—261no—
219C4⋊C4—261no—
220C4⋊C4D13⋊C811yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—261no—
223C22⋊C4—261no—
224C22⋊C4—261no—
225C22⋊C4—261no—
226C42—131no—
227C42—131no—
228C42—131no—
229C42—261no—
230C42C22×#26111yescharacteristic
231C16—522no—
232C16—522no—
233C13#1162211yescharacteristic, complemented, Sylow
234C23—21no—
235C23—131no—
236Q8—262no—
237D4—22no—
238D4—522no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—131no—
243C2×C4—131no—
244C2×C4—131no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—261no—
250C2×C4—261no—
251C2×C4C2×D13⋊C811yescharacteristic
252C2×C4D13⋊M1611yescharacteristic
253C2×C4C2×C22⋊#26111yescharacteristic
254C8—21no—
255C8—21no—
256C8—41no—
257C8—131no—
258C8—131no—
259C8—261no—
260C8—521no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—132no—
265C22—261no—
266C22—261no—
267C22D13⋊(C22⋊C8)11yescharacteristic
268C4—21no—
269C4—41no—
270C4—261no—
271C4—261no—
272C4—261no—
273C4—521no—
274C4—521no—
275C4#1171909612yes—
276C4#1171914011yescharacteristic
277C4#1171916411yescharacteristic
278C2—81no—
279C2—262no—
280C2#1313013211yescharacteristic
281C2#1313106711yescharacteristic
282C2D13⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC42C22×#261
FittingC13×#436C4
socleC22×C13C2×C22⋊C8
prime radical#88192C8
cosocleC4×#1055C23
hypercenter#436#261
hypocenterC13#11622
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #13131195C2semidirect
2. D13⋊(C4⋊C16)C2semidirect
3. #13129803C2semidirect
4. D4⋊#6092C2semidirect
233. C13#11622semidirect

Maximal subgroups

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

subgroupindex
#131311952
D13⋊(C4⋊C16)2
#131298032
D4⋊#60922
#131238142
#1162213