Finite Group Databasebeta

← C3×#2418 #84282

Subgroups — C3×#2418 #84282

Order 384.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#123C211yesmaximal, characteristic, complemented
2C2×C3×#120C211yesmaximal, characteristic
3C2×C3×C4×D4C211yesmaximal, characteristic, complemented
4C22×C3×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#399C211yesmaximal, characteristic, complemented
6C3×#397C211yesmaximal, characteristic, complemented
7C3×#394C211yesmaximal, characteristic, complemented
8C3×#394C211yesmaximal, characteristic, complemented
9C3×#388C211yesmaximal, characteristic, complemented
10C3×#388C211yesmaximal, characteristic, complemented
11C3×#386C211yesmaximal, characteristic, complemented
12C3×#386C211yesmaximal, characteristic, complemented
13C3×#385C211yesmaximal, characteristic, complemented
14C3×#380C211yesmaximal, characteristic, complemented
15C3×#379C211yesmaximal, characteristic, complemented
16#2418C311yesmaximal, characteristic, direct product factor, Sylow
17C25×C3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C22×C3×D4C2211yescharacteristic
21C23×C3×C4C2211yescharacteristic
22C23×C3×C4C2211yescharacteristic
23C23×C3×C4C2211yescharacteristic, complemented
24C3×#123—24no—
25C3×#120—24no—
26C3×C4×D4—24no—
27C2×C3×C4⋊C4C2211yescharacteristic, complemented
28C2×C3×C4⋊C4C2211yescharacteristic, complemented
29C2×C3×C4⋊C4C2211yescharacteristic, complemented
30C2×C3×C4⋊C4C2211yescharacteristic, complemented
31C2×C3×C4⋊C4C2211yescharacteristic, complemented
32C2×C3×C22⋊C4—24no—
33C2×C3×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊C4C2211yescharacteristic
35C2×C3×C22⋊C4C2211yescharacteristic
36C2×C3×C22⋊C4C2211yescharacteristic
37C2×C3×C22⋊C4C2211yescharacteristic
38C2×C3×C22⋊C4C2211yescharacteristic
39C2×C3×C22⋊C4C2211yescharacteristic
40C2×C3×C22⋊C4C2211yescharacteristic
41C2×C3×C22⋊C4C2211yescharacteristic
42C2×C3×C22⋊C4C2211yescharacteristic
43C2×C3×C22⋊C4C2211yescharacteristic
44C2×C3×C22⋊C4C2211yescharacteristic
45C2×C3×C22⋊C4C2211yescharacteristic
46C2×C3×C22⋊C4C2211yescharacteristic, complemented
47C2×C3×C22⋊C4C2211yescharacteristic, complemented
48C2×C3×C22⋊C4C2211yescharacteristic, complemented
49C2×C3×C42C2211yescharacteristic, complemented
50C3×#95C2211yescharacteristic, complemented
51C3×#95C2211yescharacteristic, complemented
52C3×#95C2211yescharacteristic, complemented
53C3×#95C2211yescharacteristic, complemented
54C3×#95C2211yescharacteristic, complemented
55C3×#95C2211yescharacteristic, complemented
56C2×#123C2×C311yescharacteristic, complemented
57C2×#120C2×C311yescharacteristic
58C2×C4×D4C2×C311yescharacteristic, complemented
59C22×C22⋊C4C2×C311yescharacteristic, complemented
60#399C2×C311yescharacteristic, complemented
61#397C2×C311yescharacteristic, complemented
62#394C2×C311yescharacteristic, complemented
63#394C2×C311yescharacteristic, complemented
64#388C2×C311yescharacteristic, complemented
65#388C2×C311yescharacteristic, complemented
66#386C2×C311yescharacteristic, complemented
67#386C2×C311yescharacteristic, complemented
68#385C2×C311yescharacteristic, complemented
69#380C2×C311yescharacteristic, complemented
70#379C2×C311yescharacteristic, complemented
71C24×C3—22no—
72C24×C3—22no—
73C24×C3—22no—
74C24×C3—22no—
75C24×C3—22no—
76C24×C3—41no—
77C24×C3—41no—
78C24×C3C2311yescharacteristic
79C24×C3C2311yescharacteristic
80C24×C3C2311yescharacteristic
81C24×C3C2311yescharacteristic
82C2×C3×D4—22no—
83C2×C3×D4—22no—
84C2×C3×D4—22no—
85C2×C3×D4—22no—
86C2×C3×D4—22no—
87C2×C3×D4—22no—
88C2×C3×D4—41no—
89C2×C3×D4—41no—
90C2×C3×D4D414yes—
91C22×C3×C4—22no—
92C22×C3×C4—22no—
93C22×C3×C4—22no—
94C22×C3×C4—22no—
95C22×C3×C4—22no—
96C22×C3×C4—22no—
97C22×C3×C4—41no—
98C22×C3×C4—41no—
99C22×C3×C4—41no—
100C22×C3×C4C2311yescharacteristic
101C22×C3×C4C2311yescharacteristic
102C22×C3×C4C2311yescharacteristic
103C22×C3×C4C2311yescharacteristic
104C22×C3×C4C2311yescharacteristic
105C22×C3×C4C2311yescharacteristic
106C22×C3×C4C2311yescharacteristic
107C22×C3×C4C2311yescharacteristic
108C22×C3×C4C2311yescharacteristic
109C22×C3×C4C2311yescharacteristic
110C22×C3×C4C2311yescharacteristic
111C3×C4⋊C4—22no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—41no—
115C3×C4⋊C4—41no—
116C3×C22⋊C4—22no—
117C3×C22⋊C4—22no—
118C3×C22⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C22⋊C4—22no—
121C3×C22⋊C4—22no—
122C3×C22⋊C4—22no—
123C3×C22⋊C4—22no—
124C3×C22⋊C4—22no—
125C3×C22⋊C4—22no—
126C3×C22⋊C4—22no—
127C3×C22⋊C4—22no—
128C3×C22⋊C4—41no—
129C3×C22⋊C4—41no—
130C3×C22⋊C4—41no—
131C3×C22⋊C4D414yescomplemented
132C3×C42—22no—
133C25C22×C311yescharacteristic
134C22×D4C22×C311yescharacteristic
135C22×D4C22×C311yescharacteristic
136C22×D4C22×C311yescharacteristic
137C23×C4C22×C311yescharacteristic
138C23×C4C22×C311yescharacteristic
139C23×C4C22×C311yescharacteristic, complemented
140#123—24no—
141#120—24no—
142C4×D4—24no—
143C2×C4⋊C4C22×C311yescharacteristic, complemented
144C2×C4⋊C4C22×C311yescharacteristic, complemented
145C2×C4⋊C4C22×C311yescharacteristic, complemented
146C2×C4⋊C4C22×C311yescharacteristic, complemented
147C2×C4⋊C4C22×C311yescharacteristic, complemented
148C2×C22⋊C4—24no—
149C2×C22⋊C4C22×C311yescharacteristic
150C2×C22⋊C4C22×C311yescharacteristic
151C2×C22⋊C4C22×C311yescharacteristic
152C2×C22⋊C4C22×C311yescharacteristic
153C2×C22⋊C4C22×C311yescharacteristic
154C2×C22⋊C4C22×C311yescharacteristic
155C2×C22⋊C4C22×C311yescharacteristic
156C2×C22⋊C4C22×C311yescharacteristic
157C2×C22⋊C4C22×C311yescharacteristic
158C2×C22⋊C4C22×C311yescharacteristic
159C2×C22⋊C4C22×C311yescharacteristic
160C2×C22⋊C4C22×C311yescharacteristic
161C2×C22⋊C4C22×C311yescharacteristic
162C2×C22⋊C4C22×C311yescharacteristic, complemented
163C2×C22⋊C4C22×C311yescharacteristic, complemented
164C2×C22⋊C4C22×C311yescharacteristic, complemented
165C2×C42C22×C311yescharacteristic, complemented
166#95C22×C311yescharacteristic, complemented
167#95C22×C311yescharacteristic, complemented
168#95C22×C311yescharacteristic, complemented
169#95C22×C311yescharacteristic, complemented
170#95C22×C311yescharacteristic, complemented
171#95C22×C311yescharacteristic, complemented
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—28no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—44no—
196C23×C3—44no—
197C23×C3—44no—
198C23×C3—44no—
199C23×C3—44no—
200C23×C3—44no—
201C23×C3C2×D412yes—
202C23×C3C2×D412yes—
203C23×C3C2×D412yes—
204C23×C3#4112yes—
205C23×C3#4112yes—
206C23×C3#4112yes—
207C23×C3C2411yescharacteristic
208C3×D4—28no—
209C3×D4—44no—
210C3×D4—44no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—44no—
242C2×C3×C4—44no—
243C2×C3×C4—44no—
244C2×C3×C4C2×D412yes—
245C2×C3×C4C2×D412yes—
246C2×C3×C4C2×D412yes—
247C24—22no—
248C24—22no—
249C24—22no—
250C24—22no—
251C24—22no—
252C24—41no—
253C24—41no—
254C24C23×C311yescharacteristic
255C24C23×C311yescharacteristic
256C24C23×C311yescharacteristic
257C24C23×C311yescharacteristic
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4C3×D414yes—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4C23×C311yescharacteristic
277C22×C4C23×C311yescharacteristic
278C22×C4C23×C311yescharacteristic
279C22×C4C23×C311yescharacteristic
280C22×C4C23×C311yescharacteristic
281C22×C4C23×C311yescharacteristic
282C22×C4C23×C311yescharacteristic
283C22×C4C23×C311yescharacteristic
284C22×C4C23×C311yescharacteristic
285C22×C4C23×C311yescharacteristic
286C22×C4C23×C311yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4C3×D414yescomplemented
308C42—22no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—416no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3#12314yescomplemented
338C22×C3C22×D411yescharacteristic
339C22×C3C22×D411yescharacteristic
340C22×C3C2×#4111yescharacteristic
341C22×C3C2×#4111yescharacteristic
342C22×C3C2×#4111yescharacteristic
343C22×C3H(5,𝔽2)11yescharacteristic
344C22×C3H(5,𝔽2)11yescharacteristic
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—22no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—28no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—44no—
380C23—44no—
381C23—44no—
382C23—44no—
383C23—44no—
384C23—44no—
385C23C2×C3×D412yes—
386C23C2×C3×D412yes—
387C23C2×C3×D412yes—
388C23C3×#4112yes—
389C23C3×#4112yes—
390C23C3×#4112yes—
391C23C24×C311yescharacteristic
392D4—28no—
393D4—44no—
394D4—44no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4C2×C3×D412yes—
429C2×C4C2×C3×D412yes—
430C2×C4C2×C3×D412yes—
431C2×C3—24no—
432C2×C3—42no—
433C2×C3—42no—
434C2×C3—42no—
435C2×C3C2×#12311yescharacteristic
436C2×C3#52511yescharacteristic
437C2×C3#53811yescharacteristic
438C2×C3D4211yescharacteristic
439C2×C3#54611yescharacteristic
440C2×C3#54611yescharacteristic
441C2×C3#55111yescharacteristic
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—416no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22C3×#12314yescomplemented
471C22C22×C3×D411yescharacteristic
472C22C22×C3×D411yescharacteristic
473C22C2×C3×#4111yescharacteristic
474C22C2×C3×#4111yescharacteristic
475C22C2×C3×#4111yescharacteristic
476C22C3×H(5,𝔽2)11yescharacteristic
477C22C3×H(5,𝔽2)11yescharacteristic
478C4—22no—
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—41no—
489C3#241811yescharacteristic, direct product factor, Sylow
490C2—24no—
491C2—42no—
492C2—42no—
493C2—42no—
494C2C2×C3×#12311yescharacteristic
495C2C3×#52511yescharacteristic
496C2C3×#53811yescharacteristic
497C2C3×D4211yescharacteristic
498C2C3×#54611yescharacteristic
499C2C3×#54611yescharacteristic
500C2C3×#55111yescharacteristic
subgroupG/H
center, socleC23×C3C24
commutator, Frattini, cosocleC23C24×C3
prime radicalC2×C3×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#123C2semidirect
3. C2×C3×C4×D4C2semidirect
4. C22×C3×C22⋊C4C2semidirect
5. C3×#399C2semidirect
6. C3×#397C2semidirect
7. C3×#394C2semidirect
8. C3×#394C2semidirect
9. C3×#388C2semidirect
10. C3×#388C2semidirect
11. C3×#386C2semidirect
12. C3×#386C2semidirect
13. C3×#385C2semidirect
14. C3×#380C2semidirect
15. C3×#379C2semidirect
16. #2418C3direct (N × H)
23. C23×C3×C4C22semidirect
27. C2×C3×C4⋊C4C22semidirect
28. C2×C3×C4⋊C4C22semidirect
29. C2×C3×C4⋊C4C22semidirect
30. C2×C3×C4⋊C4C22semidirect
31. C2×C3×C4⋊C4C22semidirect
46. C2×C3×C22⋊C4C22semidirect
47. C2×C3×C22⋊C4C22semidirect
48. C2×C3×C22⋊C4C22semidirect
49. C2×C3×C42C22semidirect
50. C3×#95C22semidirect
51. C3×#95C22semidirect
52. C3×#95C22semidirect
53. C3×#95C22semidirect
54. C3×#95C22semidirect
55. C3×#95C22semidirect
56. C2×#123C2×C3semidirect
58. C2×C4×D4C2×C3semidirect
59. C22×C22⋊C4C2×C3semidirect
60. #399C2×C3semidirect
61. #397C2×C3semidirect
62. #394C2×C3semidirect
63. #394C2×C3semidirect
64. #388C2×C3semidirect
65. #388C2×C3semidirect
66. #386C2×C3semidirect
67. #386C2×C3semidirect
68. #385C2×C3semidirect
69. #380C2×C3semidirect
70. #379C2×C3semidirect
131. C3×C22⋊C4D4semidirect
139. C23×C4C22×C3semidirect
143. C2×C4⋊C4C22×C3semidirect
144. C2×C4⋊C4C22×C3semidirect
145. C2×C4⋊C4C22×C3semidirect
146. C2×C4⋊C4C22×C3semidirect
147. C2×C4⋊C4C22×C3semidirect
162. C2×C22⋊C4C22×C3semidirect
163. C2×C22⋊C4C22×C3semidirect
164. C2×C22⋊C4C22×C3semidirect
165. C2×C42C22×C3semidirect
166. #95C22×C3semidirect
167. #95C22×C3semidirect
168. #95C22×C3semidirect
169. #95C22×C3semidirect
170. #95C22×C3semidirect
171. #95C22×C3semidirect
307. C22⋊C4C3×D4semidirect
337. C22×C3#123semidirect
470. C22C3×#123semidirect
489. C3#2418direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1232
C2×C3×#1202
C2×C3×C4×D42
C22×C3×C22⋊C42
C3×#3992
C3×#3972
C3×#3942
C3×#3882
C3×#3862
C3×#3852
C3×#3802
C3×#3792
#24183