Finite Group Databasebeta

← #72241988

Subgroups — #72241988

Order 5616.

580 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 84 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#72241981C212yesmaximal, complemented
2C3×#64603⋊C3C212yesmaximal, complemented
3C2×(C3⋊(D13⋊C3))⋊D3C211yesmaximal, characteristic, complemented
4C13⋊C3×#624C211yesmaximal, characteristic, complemented
5C2×C3⋊D3×D13⋊C3C211yesmaximal, characteristic, complemented
6#14273068C311yesmaximal, characteristic, complemented
7D3×C4⋊(D13⋊C3)—32nomaximal
8C2×C3⋊(C3⋊(D13⋊C3))C2211yescharacteristic, complemented
9C2×C3⋊D3×C13⋊C3C2211yescharacteristic
10C2×C3×C3⋊(D13⋊C3)C2212yescomplemented
11C2×C32×D13⋊C3C2211yescharacteristic, complemented
12(C3⋊(D13⋊C3))⋊D3—22no—
13C3⋊D3×D13⋊C3—22no—
14C3×Dic3×C13⋊C3C2212yescomplemented
15C2×(C3⋊D3)⋊D13C2×C311yescharacteristic, complemented
16C2×C3⋊D3×D13C2×C311yescharacteristic, complemented
17C2×D3×D13⋊C3—32no—
18C2×D3×D13⋊C3—32no—
19C2×D3×D13⋊C3—61no—
20#11745533C2×C312yescomplemented
21C13×#624C2×C311yescharacteristic, complemented
22C3×#64603C2×C312yescomplemented
23C4⋊(C3⋊(D13⋊C3))—32no—
24C4×D3×C13⋊C3—32no—
25C3×C4⋊(D13⋊C3)—32no—
26#64603⋊C3—22no—
27#64603⋊C3—32no—
28#64603⋊C3D312yescomplemented
29C2×C32×C13⋊C3C2311yescharacteristic
30C3⋊(C3⋊(D13⋊C3))—21no—
31C3⋊D3×C13⋊C3D412yescomplemented
32C3×C3⋊(D13⋊C3)—22no—
33C32×D13⋊C3—21no—
34D3×D52—32no—
35C2×C4⋊(D13⋊C3)—91no—
36C2×C3⋊D39C22×C311yescharacteristic, complemented
37C2×C13×C3⋊D3C22×C311yescharacteristic
38C2×C3×D39C22×C312yescomplemented
39C2×C32×D13C22×C311yescharacteristic, complemented
40(C3⋊D3)⋊D13—22no—
41C3⋊D3×D13—22no—
42C2×C3⋊(D13⋊C3)—22no—
43C2×C3⋊(D13⋊C3)—32no—
44C2×C3⋊(D13⋊C3)—61no—
45C2×C3⋊(D13⋊C3)C2×D312yescomplemented
46C2×D3×C13⋊C3—32no—
47C2×D3×C13⋊C3—61no—
48C2×C3×D13⋊C3—22no—
49C2×C3×D13⋊C3—21no—
50C2×C3×D13⋊C3—32no—
51C2×C3×D13⋊C3—41no—
52C2×C3×D13⋊C3C2×D312yescomplemented
53D3×D13⋊C3—64no—
54D3×D13⋊C3—62no—
55D3×D13⋊C3—62no—
56D3×D13⋊C3—64no—
57C3×Dic3×C13C22×C312yescomplemented
58C3×C4×C13⋊C3—32no—
59Dic3×C13⋊C3—22no—
60Dic3×C13⋊C3C2×D312yescomplemented
61C3×#3811—131nomaximal, Hall
62C32×C13⋊C3C2×D411yescharacteristic, complemented, Hall
63C2×D3×D13—32no—
64C2×D3×D13—32no—
65C2×D3×D13—61no—
66C22×D13⋊C3—91no—
67C22×D13⋊C3—91no—
68D156—32no—
69C4×D3×C13—32no—
70C3×D52—32no—
71C2×C4×C13⋊C3—91no—
72#64603—32no—
73#64603C3×D312yescomplemented
74C4⋊(D13⋊C3)—32no—
75C4⋊(D13⋊C3)—62no—
76C4⋊(D13⋊C3)—92no—
77C2×C32×C13C23×C311yescharacteristic
78C3⋊D39—21no—
79C13×C3⋊D3C3×D412yescomplemented
80C3×D39—22no—
81C32×D13—21no—
82C2×C3×C13⋊C3—22no—
83C2×C3×C13⋊C3—21no—
84C2×C3×C13⋊C3—41no—
85C2×C3×C13⋊C3C22×D312yes—
86C3⋊(D13⋊C3)—22no—
87C3⋊(D13⋊C3)—42no—
88C3⋊(D13⋊C3)—61no—
89C3⋊(D13⋊C3)—61no—
90C3⋊(D13⋊C3)—62no—
91D3×C13⋊C3—34no—
92D3×C13⋊C3—62no—
93C3×D13⋊C3—21no—
94C3×D13⋊C3—21no—
95C3×D13⋊C3—22no—
96C3×D13⋊C3—42no—
97C3×D13⋊C3—41no—
98C3×D13⋊C3—41no—
99C3×D13⋊C3—62no—
100C22×C3×C3⋊D3—131no—
101C2×C3×D32—131no—
102C32×#67—132no—
103C3×#626—132no—
104C3×#624—261no—
105C2×D52—91noHall
106C2×D39—32no—
107C2×D39—61no—
108C2×D39C2×C3×D312yescomplemented
109C2×D3×C13—32no—
110C2×D3×C13—61no—
111C2×C3×D13—21no—
112C2×C3×D13—32no—
113C2×C3×D13C2×C3×D312yescomplemented
114C22×C13⋊C3—91no—
115D3×D13—64no—
116D3×D13—64no—
117D3×D13—62no—
118D3×D13—62no—
119C2×D13⋊C3—22no—
120C2×D13⋊C3—32no—
121C2×D13⋊C3—41no—
122C2×D13⋊C3—62no—
123C2×D13⋊C3—91no—
124C2×D13⋊C3—182no—
125C2×D13⋊C3—182no—
126C2×D13⋊C3D3211yescharacteristic, complemented
127C3×C4×C13—32no—
128Dic3×C13C2×C3×D312yescomplemented
129C4×C13⋊C3—32no—
130C4×C13⋊C3—62no—
131C3×D3×D4—392no—
132#3811—131no—
133C32×C13C2×C3×D411yescharacteristic, complemented
134C3×C13⋊C3—22no—
135C3×C13⋊C3—21no—
136C3×C13⋊C3—41no—
137C3×C13⋊C3D3×D412yescomplemented
138C22×C33—131no—
139C2×C3×C3⋊D3—131no—
140C2×C3×C3⋊D3—262no—
141C2×C3×C3⋊D3—261no—
142C2×C32×D3—132no—
143C3×D32—262no—
144C32×Dic3—262no—
145C22×D13—91no—
146C22×D13—91no—
147C2×C4×C13—91no—
148D52—32no—
149D52—92no—
150C2×C3×C13—21no—
151C2×C3×C13C22×C3×D312yes—
152D39—22no—
153D39—61no—
154D39—61no—
155D39—62no—
156C3×D13—21no—
157C3×D13—21no—
158C3×D13—22no—
159C3×D13—62no—
160D3×C13—34no—
161D3×C13—62no—
162C2×C13⋊C3—22no—
163C2×C13⋊C3—41no—
164C2×C13⋊C3—92no—
165C2×C13⋊C3C2×D3211yescharacteristic
166D13⋊C3—21no—
167D13⋊C3—42no—
168D13⋊C3—41no—
169D13⋊C3—41no—
170D13⋊C3—62no—
171D13⋊C3—122no—
172D13⋊C3—181no—
173C22×C3⋊D3—131no—
174C22×C3×D3—392no—
175C22×C3×D3—392no—
176C22×C3×D3—781no—
177C2×D32—131no—
178C32×D4—392no—
179C3×#67—132no—
180C3×#67—132no—
181C3×#67—262no—
182C3×#67—392no—
183C3×D12—392no—
184C3×C4×D3—782no—
185#626—132no—
186#624D13⋊C311yescharacteristic, complemented
187C2×C33—261no—
188C2×C33—261no—
189C3×C3⋊D3—261no—
190C3×C3⋊D3—262no—
191C32×D3—262no—
192C22×C13—91no—
193C2×D13—32no—
194C2×D13—91no—
195C2×D13—182no—
196C2×D13—182no—
197C2×D13C3×D3211yescharacteristic, complemented
198C4×C13—32no—
199C2×C3×D4—1171no—
200D3×D4—392no—
201C3×C13—21no—
202C3×C13C3×D3×D412yescomplemented
203C13⋊C3—22no—
204C13⋊C3—41no—
205C13⋊C3#381111yescharacteristic, complemented
206C22×C32—132no—
207C22×C32—131no—
208C22×C32—261no—
209C22×C32—262no—
210C22×C32—392no—
211C22×C32—521no—
212C2×C3⋊D3—131no—
213C2×C3⋊D3—262no—
214C2×C3⋊D3C2×D13⋊C311yescharacteristic
215C2×C3×D3—132no—
216C2×C3×D3—132no—
217C2×C3×D3—262no—
218C2×C3×D3—392no—
219C2×C3×D3—782no—
220C2×C3×D3—781no—
221C2×C3×D3—784no—
222C2×C3×D3—784no—
223C2×C3×D3—782no—
224C2×C3×D3—782no—
225C2×C3×D3—1561no—
226D32—262no—
227C32×C4—782no—
228C3×Dic3—262no—
229C3×Dic3—522no—
230C3×Dic3C2×D13⋊C312yescomplemented
231C33—261noSylow
232C2×C13—92no—
233C2×C13C2×C3×D3211yescharacteristic
234D13—21no—
235D13—62no—
236D13—181no—
237C23×C3—1171no—
238C23×C3—1171no—
239C22×D3—392no—
240C22×D3—392no—
241C22×D3—781no—
242C3×D4—392no—
243C3×D4—392no—
244C3×D4—782no—
245C3×D4—1172no—
246C2×C3×C4—2341no—
247#67—132no—
248#67—392no—
249D12—392no—
250C4×D3—32no—
251C2×C32—261no—
252C2×C32—262no—
253C2×C32—261no—
254C2×C32—261no—
255C2×C32—262no—
256C2×C32—521no—
257C2×C32—522no—
258C2×C32—521no—
259C2×C32—521no—
260C2×C32—522no—
261C2×C32—782no—
262C2×C32—1041no—
263C2×C32C22×D13⋊C311yescharacteristic
264C3⋊D3—261no—
265C3⋊D3C4⋊(D13⋊C3)12yescomplemented
266C3×D3—262no—
267C3×D3—262no—
268C3×D3—522no—
269C3×D3—784no—
270C3×D3—782no—
271C3×D3—781no—
272C3×D3—781no—
273C3×D3—1562no—
274C2×D4—1171noSylow
275C13C3×#381111yescharacteristic, complemented, Sylow
276C22×C3—131no—
277C22×C3—132no—
278C22×C3—261no—
279C22×C3—262no—
280C22×C3—392no—
281C22×C3—392no—
282C22×C3—521no—
283C22×C3—782no—
284C22×C3—1171no—
285C22×C3—2341no—
286C22×C3—2342no—
287C22×C3—2342no—
288C2×D3—32no—
289C2×D3—61no—
290C2×D3—132no—
291C2×D3—392no—
292C2×D3—781no—
293C2×D3—784no—
294C2×D3—784no—
295C2×D3—782no—
296C2×D3—782no—
297C3×C4—32no—
298C3×C4—782no—
299C3×C4—1562no—
300Dic3D3×D13⋊C312yescomplemented
301C32—262no—
302C32—521no—
303C32—522no—
304C32—1041no—
305C32C2×C4⋊(D13⋊C3)11yescharacteristic, complemented
306C23—1171no—
307C23—1171no—
308D4—392no—
309D4—1172no—
310C2×C4—91no—
311C2×C3—21no—
312C2×C3—261no—
313C2×C3—261no—
314C2×C3—261no—
315C2×C3—262no—
316C2×C3—261no—
317C2×C3—522no—
318C2×C3—521no—
319C2×C3—521no—
320C2×C3—522no—
321C2×C3—782no—
322C2×C3—782no—
323C2×C3—1041no—
324C2×C3—1562no—
325C2×C3—2342no—
326C2×C3—2341no—
327C2×C3C2×D3×D13⋊C312yes—
328D3—34no—
329D3—62no—
330D3—262no—
331D3—781no—
332D3—781no—
333D3—782no—
334C22—91no—
335C22—131no—
336C22—392no—
337C22—1171no—
338C22—2342no—
339C22—2342no—
340C4—32no—
341C3—21no—
342C3—261no—
343C3—522no—
344C3—1041no—
345C3D3×C4⋊(D13⋊C3)12yescomplemented
346C2—92no—
347C2—261no—
348C2—782no—
349C2—2341no—
350C2D32×D13⋊C311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D32×D13⋊C3
commutator, Fitting, socle, cosocleC2×C32×C13C23×C3
hypocenterC32×C13C2×C3×D4
LCSG ▷ C2×C32×C13 ▷ C32×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #72241981C2semidirect
2. C3×#64603⋊C3C2semidirect
3. C2×(C3⋊(D13⋊C3))⋊D3C2semidirect
4. C13⋊C3×#624C2semidirect
5. C2×C3⋊D3×D13⋊C3C2semidirect
6. #14273068C3semidirect
8. C2×C3⋊(C3⋊(D13⋊C3))C22semidirect
10. C2×C3×C3⋊(D13⋊C3)C22semidirect
11. C2×C32×D13⋊C3C22semidirect
14. C3×Dic3×C13⋊C3C22semidirect
15. C2×(C3⋊D3)⋊D13C2×C3semidirect
16. C2×C3⋊D3×D13C2×C3semidirect
20. #11745533C2×C3semidirect
21. C13×#624C2×C3semidirect
22. C3×#64603C2×C3semidirect
28. #64603⋊C3D3semidirect
31. C3⋊D3×C13⋊C3D4semidirect
36. C2×C3⋊D39C22×C3semidirect
38. C2×C3×D39C22×C3semidirect
39. C2×C32×D13C22×C3semidirect
45. C2×C3⋊(D13⋊C3)C2×D3semidirect
52. C2×C3×D13⋊C3C2×D3semidirect
57. C3×Dic3×C13C22×C3semidirect
60. Dic3×C13⋊C3C2×D3semidirect
62. C32×C13⋊C3C2×D4semidirect
73. #64603C3×D3semidirect
79. C13×C3⋊D3C3×D4semidirect
108. C2×D39C2×C3×D3semidirect
113. C2×C3×D13C2×C3×D3semidirect
126. C2×D13⋊C3D32semidirect
128. Dic3×C13C2×C3×D3semidirect
133. C32×C13C2×C3×D4semidirect
137. C3×C13⋊C3D3×D4semidirect
186. #624D13⋊C3semidirect
197. C2×D13C3×D32semidirect
202. C3×C13C3×D3×D4semidirect
205. C13⋊C3#3811semidirect
230. C3×Dic3C2×D13⋊C3semidirect
265. C3⋊D3C4⋊(D13⋊C3)semidirect
275. C13C3×#3811semidirect
300. Dic3D3×D13⋊C3semidirect
305. C32C2×C4⋊(D13⋊C3)semidirect
345. C3D3×C4⋊(D13⋊C3)semidirect

Maximal subgroups

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

subgroupindex
#722419812
C3×#64603⋊C32
C2×(C3⋊(D13⋊C3))⋊D32
C13⋊C3×#6242
C2×C3⋊D3×D13⋊C32
#142730683
D3×C4⋊(D13⋊C3)3
C3×#381113