Finite Group Databasebeta

← #15772142

Subgroups — #15772142

Order 3328.

454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×#11718495C211yesmaximal, characteristic
2D13×C22⋊C16C212yesmaximal, complemented
3#13112776C211yesmaximal, characteristic, complemented
4#13112759C212yesmaximal, complemented
5C13×#1322C211yesmaximal, characteristic, complemented
6C22×C8×D13C411yescharacteristic
7C22×C8×D13C2211yescharacteristic
8C2×C4×D52C411yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×#88060C411yescharacteristic
11C2×#88060C2211yescharacteristic
12C2×C4×#1055C411yescharacteristic
13C2×C16×D13—22no—
14#11718495—22no—
15#11718495—22no—
16C13×C22⋊C16C2212yes—
17C22⋊#6090C2212yes—
18#11718099—22no—
19C22×D52C811yescharacteristic
20C22×C4×D13C2×C411yescharacteristic
21C22×C4×D13C2×C411yescharacteristic
22C22×C8×C13C2×C411yescharacteristic
23C22×C8×C13C2311yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×#6103C811yescharacteristic
26C2×#6103C811yescharacteristic
27C2×C4⋊Dic13C811yescharacteristic
28C22×#1055C2×C411yescharacteristic
29C22×#1055C2×C411yescharacteristic
30C2×C8×D13—21no—
31C2×C8×D13—21no—
32C2×C8×D13—42no—
33C2×C8×D13—42no—
34C2×C8×D13D412yes—
35C2×C8×D13D412yes—
36C4×D52—22no—
37C4×D52—22no—
38C2×C13×C16—22no—
39C13×C4⋊C8—22no—
40#88060—22no—
41#88060—22no—
42C2×#6090—22no—
43C4×#1055—21no—
44C4×#1055—21no—
45C16×D13—44no—
46#11465—131nomaximal, Sylow
47C23×D13C2×C811yescharacteristic
48C23×D13C2×C811yescharacteristic
49C22×C4×C13C2×C811yescharacteristic
50C22×C4×C13C2×C811yescharacteristic
51C22×C4×C13C22×C411yescharacteristic
52C22×Dic13C2×C811yescharacteristic
53C22×Dic13C2×C811yescharacteristic
54C2×D52—22no—
55C2×D52—22no—
56C2×D52C1614yescomplemented
57C2×C4×D13—21no—
58C2×C4×D13—21no—
59C2×C4×D13—41no—
60C2×C4×D13—41no—
61C2×C4×D13—41no—
62C2×C4×D13—41no—
63C2×C4×D13C22⋊C412yes—
64C2×C4×D13M1612yes—
65C2×C8×C13—21no—
66C2×C8×C13—41no—
67C2×C8×C13—41no—
68C2×C8×C13C2×D412yes—
69C42×C13—21no—
70C42×C13—21no—
71#6103—22no—
72#6103—22no—
73C4⋊Dic13—22no—
74C2×#1055—22no—
75C2×#1055—21no—
76C2×#1055—41no—
77C2×#1055C22⋊C411yescharacteristic
78C2×#1055C22⋊C411yescharacteristic
79C8×D13—24no—
80C8×D13—42no—
81C8×D13—42no—
82C8×D13—42no—
83C13×C16—42no—
84#6090—42no—
85C2×C8×D4—131no—
86C2×C22⋊C16—132no—
87#1322—131no—
88#1322D1311yescharacteristic, complemented
89#1314—132no—
90C23×C13C22×C811yescharacteristic
91C22×D13—21no—
92C22×D13—21no—
93C22×D13—41no—
94C22×D13—41no—
95C22×D13—41no—
96C22×D13—41no—
97C22×D13C22⋊C812yes—
98C22×D13C2×C1612yes—
99C22×D13C2×C1612yescomplemented
100C22×D13M3212yes—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13C2×C1612yescomplemented
108C2×C4×C13C2×C22⋊C411yescharacteristic
109C2×C4×C13C2×M1611yescharacteristic
110C2×Dic13—21no—
111C2×Dic13—41no—
112C2×Dic13—41no—
113C2×Dic13C22⋊C812yes—
114D52—28no—
115C4×D13—22no—
116C4×D13—22no—
117C4×D13—42no—
118C4×D13—42no—
119C4×D13—41no—
120C4×D13—41no—
121C8×C13—22no—
122C8×C13—41no—
123#1055—21no—
124#1055—41no—
125#1055#9912yes—
126C23×C8—131no—
127C23×C8—131no—
128C2×C4×D4—131no—
129C22×C16—262no—
130C8×D4—262no—
131C8×D4—262no—
132C2×C4⋊C8C2×D1311yescharacteristic
133C2×C22⋊C8—131no—
134C2×C22⋊C8—131no—
135C2×C4×C8—131no—
136C22⋊C16—132no—
137C22⋊C16—262no—
138C22⋊C16C2×D1312yes—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13C2×C22⋊C811yescharacteristic
142C22×C13C22×C1611yescharacteristic
143C22×C13C2×M3211yescharacteristic
144C2×D13—22no—
145C2×D13—22no—
146C2×D13—22no—
147C2×D13—42no—
148C2×D13—42no—
149C2×D13—42no—
150C2×D13—41no—
151C2×D13—41no—
152C2×D13—42no—
153C2×D13C22⋊C1614yes—
154C4×C13—22no—
155C4×C13—21no—
156C4×C13—41no—
157C4×C13C2×#9911yescharacteristic
158C4×C13#41311yescharacteristic
159Dic13—22no—
160Dic13—41no—
161C22×D4—131no—
162C23×C4—131no—
163C23×C4—131no—
164C22×C8—131no—
165C22×C8—132no—
166C22×C8—132no—
167C22×C8—131no—
168C22×C8—261no—
169C22×C8—261no—
170C22×C8—522no—
171C22×C8—522no—
172C22×C8C4×D1311yescharacteristic
173C22×C8C22×D1311yescharacteristic
174C4×D4—262no—
175C4×D4—262no—
176C2×C4⋊C4—131no—
177C2×C22⋊C4—131no—
178C2×C22⋊C4—131no—
179C2×C42C4×D1311yescharacteristic
180C2×C16—22no—
181C2×C16—262no—
182C2×C16—524no—
183C4⋊C8—22no—
184C22⋊C8—262no—
185C22⋊C8—262no—
186C4×C8—261no—
187C4×C8—261no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13#145911yescharacteristic
191C2×C13C2×C22⋊C1611yescharacteristic
192C2×C13#211511yescharacteristic
193D13—24no—
194D13—42no—
195C24—131no—
196C24—131no—
197C2×D4—134no—
198C2×D4—262no—
199C2×D4—262no—
200C22×C4—131no—
201C22×C4—132no—
202C22×C4—132no—
203C22×C4—131no—
204C22×C4—261no—
205C22×C4—261no—
206C22×C4—521no—
207C22×C4—521no—
208C22×C4—521no—
209C22×C4—521no—
210C22×C4C8×D1311yescharacteristic
211C22×C4C8×D1311yescharacteristic
212C22×C4C2×C4×D1311yescharacteristic
213C2×C8—21no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—131no—
217C2×C8—131no—
218C2×C8—264no—
219C2×C8—262no—
220C2×C8—261no—
221C2×C8—522no—
222C2×C8—522no—
223C2×C8—522no—
224C2×C8—521no—
225C2×C8D4×D1312yes—
226C4⋊C4—262no—
227C22⋊C4—262no—
228C22⋊C4—262no—
229C42—21no—
230C42—21no—
231C16—42no—
232C16—522no—
233C13#1146511yescharacteristic, complemented, Sylow
234C23—132no—
235C23—132no—
236C23—132no—
237C23—132no—
238C23—261no—
239C23—261no—
240C23—521no—
241C23—521no—
242C23—521no—
243C23—521no—
244C23C2×C8×D1311yescharacteristic
245D4—268no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—132no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—261no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4C16×D1312yescomplemented
263C2×C4C22⋊C4×D1311yescharacteristic
264C2×C4M16×D1311yescharacteristic
265C8—22no—
266C8—41no—
267C8—132no—
268C8—261no—
269C8—521no—
270C22—21no—
271C22—21no—
272C22—134no—
273C22—262no—
274C22—262no—
275C22—262no—
276C22—522no—
277C22—522no—
278C22—522no—
279C22—522no—
280C22—521no—
281C22—521no—
282C22D13×C22⋊C811yescharacteristic
283C22C2×C16×D1311yescharacteristic
284C22D13×M3211yescharacteristic
285C4—22no—
286C4—21no—
287C4—41no—
288C4—262no—
289C4—521no—
290C4D13×#9911yescharacteristic
291C4#1171841211yescharacteristic
292C2—21no—
293C2—21no—
294C2—264no—
295C2—522no—
296C2#1311315311yescharacteristic
297C2D13×C22⋊C1611yescharacteristic
298C2#1311645511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC22×C13C22×C16
FrattiniC22×C8C22×D13
FittingC13×#1322C2
socleC22×C13C2×C22⋊C8
prime radicalC22×D52C8
cosocleC22×C8×C13C23
hypercenter#1322D13
hypocenterC13#11465
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. D13×C22⋊C16C2semidirect
3. #13112776C2semidirect
4. #13112759C2semidirect
5. C13×#1322C2semidirect
56. C2×D52C16semidirect
88. #1322D13semidirect
99. C22×D13C2×C16semidirect
107. C2×C4×C13C2×C16semidirect
233. C13#11465semidirect
262. C2×C4C16×D13semidirect

Maximal subgroups

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

subgroupindex
C2×#117184952
D13×C22⋊C162
#131127762
#131127592
C13×#13222
#1146513