Finite Group Databasebeta

← C3×#3318 #85182

Subgroups — C3×#3318 #85182

Order 384.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#553C211yesmaximal, characteristic, complemented
2C3×D42C211yesmaximal, characteristic, complemented
3C3×#490C211yesmaximal, characteristic, complemented
4C3×#482C211yesmaximal, characteristic, complemented
5C3×#481C211yesmaximal, characteristic, complemented
6C3×#478C211yesmaximal, characteristic, complemented
7C3×#469C211yesmaximal, characteristic, complemented
8C3×#466C211yesmaximal, characteristic, complemented
9C3×#459C211yesmaximal, characteristic, complemented
10C3×#447C211yesmaximal, characteristic, complemented
11C3×#447C211yesmaximal, characteristic, complemented
12C3×#442C211yesmaximal, characteristic, complemented
13C3×#435C211yesmaximal, characteristic, complemented
14C3×#418C211yesmaximal, characteristic, complemented
15C2×C3×#102C211yesmaximal, characteristic, complemented
16#3318C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D4—21no—
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C2×C3×D8C2211yescharacteristic
21C2×C3×D8C2211yescharacteristic, complemented
22C2×C3×D8C2211yescharacteristic, complemented
23C2×C3×M16C2211yescharacteristic, complemented
24C22×C3×C8C2211yescharacteristic, complemented
25C3×#127C2211yescharacteristic
26C3×#126—21no—
27C3×#125C2211yescharacteristic, complemented
28C3×#123—21no—
29C3×#121—21no—
30C3×#121—21no—
31C3×#121C2211yescharacteristic
32C3×#121C2211yescharacteristic
33C3×#121C2211yescharacteristic, complemented
34C3×#121C2211yescharacteristic, complemented
35C3×#120—21no—
36C3×#120—21no—
37C3×C4×D4—21no—
38C3×C4×D4C2211yescharacteristic
39C3×C4×D4C2211yescharacteristic
40C3×C4×D4C2211yescharacteristic, complemented
41C3×#117C2211yescharacteristic, complemented
42C2×C3×C4⋊C4C2211yescharacteristic, complemented
43C3×#107C2211yescharacteristic, complemented
44C3×#106C2211yescharacteristic, complemented
45C3×#106C2211yescharacteristic, complemented
46C3×C4⋊C8C2211yescharacteristic, complemented
47C3×#102C2211yescharacteristic
48C3×#102C2211yescharacteristic
49C3×#102C2211yescharacteristic
50C3×#102C2211yescharacteristic, complemented
51C3×#102C2211yescharacteristic, complemented
52C3×#102C2211yescharacteristic, complemented
53C3×#102C2211yescharacteristic, complemented
54C3×#102C2211yescharacteristic, complemented
55C3×#102C2211yescharacteristic, complemented
56C3×#102C2211yescharacteristic, complemented
57C3×C22⋊C8C2211yescharacteristic, complemented
58C3×C22⋊C8C2211yescharacteristic, complemented
59C3×#97C2211yescharacteristic, complemented
60#553C2×C311yescharacteristic, complemented
61D42C2×C311yescharacteristic, complemented
62#490C2×C311yescharacteristic, complemented
63#482C2×C311yescharacteristic, complemented
64#481C2×C311yescharacteristic, complemented
65#478C2×C311yescharacteristic, complemented
66#469C2×C311yescharacteristic, complemented
67#466C2×C311yescharacteristic, complemented
68#459C2×C311yescharacteristic, complemented
69#447C2×C311yescharacteristic, complemented
70#447C2×C311yescharacteristic, complemented
71#442C2×C311yescharacteristic, complemented
72#435C2×C311yescharacteristic, complemented
73#418C2×C311yescharacteristic, complemented
74C2×#102C2×C311yescharacteristic, complemented
75C24×C3—21no—
76C24×C3—21no—
77C2×C3×D4—22no—
78C2×C3×D4—22no—
79C2×C3×D4—21no—
80C2×C3×D4—21no—
81C2×C3×D4—21no—
82C2×C3×D4—21no—
83C2×C3×D4—21no—
84C2×C3×D4—21no—
85C2×C3×D4—21no—
86C2×C3×D4—21no—
87C2×C3×D4—41no—
88C2×C3×D4—41no—
89C2×C3×D4—44no—
90C2×C3×D4D411yescharacteristic
91C2×C3×D4C2311yescharacteristic
92C2×C3×D4C2311yescharacteristic
93C2×C3×D4C2311yescharacteristic
94C2×C3×D4C2311yescharacteristic
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4C2311yescharacteristic
99C22×C3×C4C2311yescharacteristic
100C3×D8—22no—
101C3×D8—41no—
102C3×D8—41no—
103C3×M16—41no—
104C2×C3×C8—41no—
105C2×C3×C8C2311yescharacteristic
106C2×C3×C8C2311yescharacteristic
107C2×C3×C8C2311yescharacteristic
108C2×C3×C8C2311yescharacteristic
109C3×C4⋊C4—21no—
110C3×C4⋊C4—21no—
111C3×C4⋊C4—21no—
112C3×C4⋊C4D411yescharacteristic
113C3×C4⋊C4C2311yescharacteristic
114C3×C4⋊C4C2311yescharacteristic
115C3×C4⋊C4C2311yescharacteristic
116C3×C4⋊C4C2311yescharacteristic
117C3×C22⋊C4—21no—
118C3×C22⋊C4—21no—
119C3×C22⋊C4—21no—
120C3×C22⋊C4—21no—
121C3×C22⋊C4—21no—
122C3×C22⋊C4—21no—
123C3×C22⋊C4—21no—
124C3×C22⋊C4D411yescharacteristic
125C3×C22⋊C4D411yescharacteristic
126C3×C42—21no—
127C3×C42C2311yescharacteristic
128C22×D4—21no—
129C22×D4C22×C311yescharacteristic
130C22×D4C22×C311yescharacteristic
131C2×D8C22×C311yescharacteristic
132C2×D8C22×C311yescharacteristic, complemented
133C2×D8C22×C311yescharacteristic, complemented
134C2×M16C22×C311yescharacteristic, complemented
135C22×C8C22×C311yescharacteristic, complemented
136#127C22×C311yescharacteristic
137#126—21no—
138#125C22×C311yescharacteristic, complemented
139#123—21no—
140#121—21no—
141#121—21no—
142#121C22×C311yescharacteristic
143#121C22×C311yescharacteristic
144#121C22×C311yescharacteristic, complemented
145#121C22×C311yescharacteristic, complemented
146#120—21no—
147#120—21no—
148C4×D4—21no—
149C4×D4C22×C311yescharacteristic
150C4×D4C22×C311yescharacteristic
151C4×D4C22×C311yescharacteristic, complemented
152#117C22×C311yescharacteristic, complemented
153C2×C4⋊C4C22×C311yescharacteristic, complemented
154#107C22×C311yescharacteristic, complemented
155#106C22×C311yescharacteristic, complemented
156#106C22×C311yescharacteristic, complemented
157C4⋊C8C22×C311yescharacteristic, complemented
158#102C22×C311yescharacteristic
159#102C22×C311yescharacteristic
160#102C22×C311yescharacteristic
161#102C22×C311yescharacteristic, complemented
162#102C22×C311yescharacteristic, complemented
163#102C22×C311yescharacteristic, complemented
164#102C22×C311yescharacteristic, complemented
165#102C22×C311yescharacteristic, complemented
166#102C22×C311yescharacteristic, complemented
167#102C22×C311yescharacteristic, complemented
168C22⋊C8C22×C311yescharacteristic, complemented
169C22⋊C8C22×C311yescharacteristic, complemented
170#97C22×C311yescharacteristic, complemented
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—42no—
176C23×C3—42no—
177C23×C3—42no—
178C23×C3—42no—
179C23×C3—81no—
180C23×C3—81no—
181C23×C3C2×D411yescharacteristic
182C23×C3C2×D411yescharacteristic
183C3×D4—22no—
184C3×D4—21no—
185C3×D4—21no—
186C3×D4—21no—
187C3×D4—21no—
188C3×D4—21no—
189C3×D4—21no—
190C3×D4—21no—
191C3×D4—42no—
192C3×D4—42no—
193C3×D4—42no—
194C3×D4—42no—
195C3×D4—42no—
196C3×D4—42no—
197C3×D4—81no—
198C3×D4—81no—
199C3×D4#4112yes—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—42no—
209C2×C3×C4—81no—
210C2×C3×C4—81no—
211C2×C3×C4C2×D411yescharacteristic
212C2×C3×C4C2×D411yescharacteristic
213C2×C3×C4C2×D411yescharacteristic
214C2×C3×C4C2×D411yescharacteristic
215C2×C3×C4C2411yescharacteristic
216C3×C8—21no—
217C3×C8—21no—
218C3×C8—21no—
219C3×C8—21no—
220C24—21no—
221C24—21no—
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—44no—
235C2×D4C3×D411yescharacteristic
236C2×D4C23×C311yescharacteristic
237C2×D4C23×C311yescharacteristic
238C2×D4C23×C311yescharacteristic
239C2×D4C23×C311yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4C23×C311yescharacteristic
244C22×C4C23×C311yescharacteristic
245D8—22no—
246D8—41no—
247D8—41no—
248M16—41no—
249C2×C8—41no—
250C2×C8C23×C311yescharacteristic
251C2×C8C23×C311yescharacteristic
252C2×C8C23×C311yescharacteristic
253C2×C8C23×C311yescharacteristic
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4C3×D411yescharacteristic
258C4⋊C4C23×C311yescharacteristic
259C4⋊C4C23×C311yescharacteristic
260C4⋊C4C23×C311yescharacteristic
261C4⋊C4C23×C311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4C3×D411yescharacteristic
270C22⋊C4C3×D411yescharacteristic
271C42—21no—
272C42C23×C311yescharacteristic
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—22no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—41no—
290C22×C3—84no—
291C22×C3—84no—
292C22×C3AGL(1,ℤ/8)12yes—
293C22×C3C22×D411yescharacteristic
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—41no—
302C3×C4C2×#4111yescharacteristic
303C3×C4H(5,𝔽2)11yescharacteristic
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—42no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—81no—
314C23C2×C3×D411yescharacteristic
315C23C2×C3×D411yescharacteristic
316D4—22no—
317D4—21no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—81no—
331D4—81no—
332D4C3×#4112yes—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4C2×C3×D411yescharacteristic
345C2×C4C2×C3×D411yescharacteristic
346C2×C4C2×C3×D411yescharacteristic
347C2×C4C2×C3×D411yescharacteristic
348C2×C4C24×C311yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C2×C3—22no—
354C2×C3—41no—
355C2×C3—42no—
356C2×C3—81no—
357C2×C3—81no—
358C2×C3—81no—
359C2×C3#54611yescharacteristic
360C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
361C2×C3#57611yescharacteristic
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—84no—
380C22—84no—
381C22C3×AGL(1,ℤ/8)12yes—
382C22C22×C3×D411yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4C2×C3×#4111yescharacteristic
392C4C3×H(5,𝔽2)11yescharacteristic
393C3#331811yescharacteristic, direct product factor, Sylow
394C2—22no—
395C2—41no—
396C2—42no—
397C2—81no—
398C2—81no—
399C2—81no—
400C2C3×#54611yescharacteristic
401C2C2×C3×AGL(1,ℤ/8)11yescharacteristic
402C2C3×#57611yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#553C2semidirect
2. C3×D42C2semidirect
3. C3×#490C2semidirect
4. C3×#482C2semidirect
5. C3×#481C2semidirect
6. C3×#478C2semidirect
7. C3×#469C2semidirect
8. C3×#466C2semidirect
9. C3×#459C2semidirect
10. C3×#447C2semidirect
11. C3×#447C2semidirect
12. C3×#442C2semidirect
13. C3×#435C2semidirect
14. C3×#418C2semidirect
15. C2×C3×#102C2semidirect
16. #3318C3direct (N × H)
21. C2×C3×D8C22semidirect
22. C2×C3×D8C22semidirect
23. C2×C3×M16C22semidirect
24. C22×C3×C8C22semidirect
27. C3×#125C22semidirect
33. C3×#121C22semidirect
34. C3×#121C22semidirect
40. C3×C4×D4C22semidirect
41. C3×#117C22semidirect
42. C2×C3×C4⋊C4C22semidirect
43. C3×#107C22semidirect
44. C3×#106C22semidirect
45. C3×#106C22semidirect
46. C3×C4⋊C8C22semidirect
50. C3×#102C22semidirect
51. C3×#102C22semidirect
52. C3×#102C22semidirect
53. C3×#102C22semidirect
54. C3×#102C22semidirect
55. C3×#102C22semidirect
56. C3×#102C22semidirect
57. C3×C22⋊C8C22semidirect
58. C3×C22⋊C8C22semidirect
59. C3×#97C22semidirect
60. #553C2×C3semidirect
61. D42C2×C3semidirect
62. #490C2×C3semidirect
63. #482C2×C3semidirect
64. #481C2×C3semidirect
65. #478C2×C3semidirect
66. #469C2×C3semidirect
67. #466C2×C3semidirect
68. #459C2×C3semidirect
69. #447C2×C3semidirect
70. #447C2×C3semidirect
71. #442C2×C3semidirect
72. #435C2×C3semidirect
73. #418C2×C3semidirect
74. C2×#102C2×C3semidirect
132. C2×D8C22×C3semidirect
133. C2×D8C22×C3semidirect
134. C2×M16C22×C3semidirect
135. C22×C8C22×C3semidirect
138. #125C22×C3semidirect
144. #121C22×C3semidirect
145. #121C22×C3semidirect
151. C4×D4C22×C3semidirect
152. #117C22×C3semidirect
153. C2×C4⋊C4C22×C3semidirect
154. #107C22×C3semidirect
155. #106C22×C3semidirect
156. #106C22×C3semidirect
157. C4⋊C8C22×C3semidirect
161. #102C22×C3semidirect
162. #102C22×C3semidirect
163. #102C22×C3semidirect
164. #102C22×C3semidirect
165. #102C22×C3semidirect
166. #102C22×C3semidirect
167. #102C22×C3semidirect
168. C22⋊C8C22×C3semidirect
169. C22⋊C8C22×C3semidirect
170. #97C22×C3semidirect
393. C3#3318direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5532
C3×D422
C3×#4902
C3×#4822
C3×#4812
C3×#4782
C3×#4692
C3×#4662
C3×#4592
C3×#4472
C3×#4422
C3×#4352
C3×#4182
C2×C3×#1022
#33183