Finite Group Databasebeta

← C3×#3268 #85132

Subgroups — C3×#3268 #85132

Order 384.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C3×#135C211yesmaximal, characteristic, complemented
3C3×#550C211yesmaximal, characteristic, complemented
4C3×#546C211yesmaximal, characteristic, complemented
5C3×#496C211yesmaximal, characteristic, complemented
6C3×#468C211yesmaximal, characteristic, complemented
7C3×#466C211yesmaximal, characteristic, complemented
8C3×#464C211yesmaximal, characteristic, complemented
9C3×#459C211yesmaximal, characteristic, complemented
10C3×#452C211yesmaximal, characteristic, complemented
11C3×#449C211yesmaximal, characteristic, complemented
12C3×#449C211yesmaximal, characteristic, complemented
13C3×#447C211yesmaximal, characteristic, complemented
14C3×#440C211yesmaximal, characteristic, complemented
15C3×#435C211yesmaximal, characteristic, complemented
16#3268C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#41C2211yescharacteristic
18C2×C3×#41C2211yescharacteristic
19C2×C3×#41C2211yescharacteristic, complemented
20C22×C3×D4C2211yescharacteristic
21C3×AGL(1,ℤ/8)—24no—
22C3×#135—24no—
23C2×C3×Q16C2211yescharacteristic, complemented
24C2×C3×SD16C2211yescharacteristic
25C2×C3×SD16C2211yescharacteristic
26C2×C3×SD16C2211yescharacteristic, complemented
27C2×C3×SD16C2211yescharacteristic, complemented
28C2×C3×D8C2211yescharacteristic
29C2×C3×D8C2211yescharacteristic
30C2×C3×D8C2211yescharacteristic
31C2×C3×D8C2211yescharacteristic
32C2×C3×M16C2211yescharacteristic
33C22×C3×C8C2211yescharacteristic, complemented
34C3×#127—21no—
35C3×#127C2211yescharacteristic, complemented
36C3×#124C2211yescharacteristic
37C3×#123—21no—
38C3×C22⋊Q8C2211yescharacteristic
39C3×#121—21no—
40C3×#121—21no—
41C3×#121—21no—
42C3×#121C2211yescharacteristic
43C3×#121C2211yescharacteristic
44C3×#121C2211yescharacteristic, complemented
45C3×#120—21no—
46C3×C4×Q8C2211yescharacteristic, complemented
47C3×C4×D4—21no—
48C3×C4×D4C2211yescharacteristic
49C3×C4×D4C2211yescharacteristic
50C2×C3×C22⋊C4—21no—
51C3×#107C2211yescharacteristic, complemented
52C3×C4⋊C8C2211yescharacteristic, complemented
53C3×#103C2211yescharacteristic, complemented
54C3×#103C2211yescharacteristic, complemented
55C3×#102C2211yescharacteristic
56C3×#102C2211yescharacteristic
57C3×#102C2211yescharacteristic, complemented
58C3×#102C2211yescharacteristic, complemented
59C3×C22⋊C8C2211yescharacteristic
60C3×C22⋊C8C2211yescharacteristic, complemented
61C3×#97C2211yescharacteristic, complemented
62C2×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
63C2×#135C2×C311yescharacteristic, complemented
64#550C2×C311yescharacteristic, complemented
65#546C2×C311yescharacteristic, complemented
66#496C2×C311yescharacteristic, complemented
67#468C2×C311yescharacteristic, complemented
68#466C2×C311yescharacteristic, complemented
69#464C2×C311yescharacteristic, complemented
70#459C2×C311yescharacteristic, complemented
71#452C2×C311yescharacteristic, complemented
72#449C2×C311yescharacteristic, complemented
73#449C2×C311yescharacteristic, complemented
74#447C2×C311yescharacteristic, complemented
75#440C2×C311yescharacteristic, complemented
76#435C2×C311yescharacteristic, complemented
77C24×C3—21no—
78C3×#41—22no—
79C3×#41—22no—
80C3×#41—22no—
81C3×#41—41no—
82C3×#41—41no—
83C3×#41—41no—
84C2×C3×Q8C2311yescharacteristic
85C2×C3×Q8C2311yescharacteristic
86C2×C3×D4—22no—
87C2×C3×D4—21no—
88C2×C3×D4—21no—
89C2×C3×D4—21no—
90C2×C3×D4—21no—
91C2×C3×D4—21no—
92C2×C3×D4—21no—
93C2×C3×D4—21no—
94C2×C3×D4—21no—
95C2×C3×D4—21no—
96C2×C3×D4—41no—
97C2×C3×D4D411yescharacteristic
98C2×C3×D4C2311yescharacteristic
99C2×C3×D4C2311yescharacteristic
100C2×C3×D4C2311yescharacteristic
101C2×C3×D4C2311yescharacteristic
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4—21no—
105C22×C3×C4—21no—
106C22×C3×C4C2311yescharacteristic
107C22×C3×C4C2311yescharacteristic
108C3×Q16—22no—
109C3×SD16—22no—
110C3×SD16—22no—
111C3×SD16—41no—
112C3×SD16D414yescomplemented
113C3×D8—22no—
114C3×D8—22no—
115C3×D8—22no—
116C3×D8—41no—
117C3×M16—22no—
118C2×C3×C8—22no—
119C2×C3×C8C2311yescharacteristic
120C2×C3×C8C2311yescharacteristic
121C2×C3×C8C2311yescharacteristic
122C2×C3×C8C2311yescharacteristic
123C3×C4⋊C4—21no—
124C3×C4⋊C4—21no—
125C3×C4⋊C4D411yescharacteristic
126C3×C4⋊C4C2311yescharacteristic
127C3×C4⋊C4C2311yescharacteristic
128C3×C22⋊C4—21no—
129C3×C22⋊C4—21no—
130C3×C22⋊C4—21no—
131C3×C22⋊C4—21no—
132C3×C22⋊C4—21no—
133C3×C22⋊C4—21no—
134C3×C22⋊C4—21no—
135C3×C22⋊C4D411yescharacteristic
136C3×C22⋊C4D411yescharacteristic
137C3×C42—21no—
138C3×C42C2311yescharacteristic
139C2×#41C22×C311yescharacteristic
140C2×#41C22×C311yescharacteristic
141C2×#41C22×C311yescharacteristic, complemented
142C22×D4C22×C311yescharacteristic
143AGL(1,ℤ/8)—24no—
144#135—24no—
145C2×Q16C22×C311yescharacteristic, complemented
146C2×SD16C22×C311yescharacteristic
147C2×SD16C22×C311yescharacteristic
148C2×SD16C22×C311yescharacteristic, complemented
149C2×SD16C22×C311yescharacteristic, complemented
150C2×D8C22×C311yescharacteristic
151C2×D8C22×C311yescharacteristic
152C2×D8C22×C311yescharacteristic
153C2×D8C22×C311yescharacteristic
154C2×M16C22×C311yescharacteristic
155C22×C8C22×C311yescharacteristic, complemented
156#127—21no—
157#127C22×C311yescharacteristic, complemented
158#124C22×C311yescharacteristic
159#123—21no—
160C22⋊Q8C22×C311yescharacteristic
161#121—21no—
162#121—21no—
163#121—21no—
164#121C22×C311yescharacteristic
165#121C22×C311yescharacteristic
166#121C22×C311yescharacteristic, complemented
167#120—21no—
168C4×Q8C22×C311yescharacteristic, complemented
169C4×D4—21no—
170C4×D4C22×C311yescharacteristic
171C4×D4C22×C311yescharacteristic
172C2×C22⋊C4—21no—
173#107C22×C311yescharacteristic, complemented
174C4⋊C8C22×C311yescharacteristic, complemented
175#103C22×C311yescharacteristic, complemented
176#103C22×C311yescharacteristic, complemented
177#102C22×C311yescharacteristic
178#102C22×C311yescharacteristic
179#102C22×C311yescharacteristic, complemented
180#102C22×C311yescharacteristic, complemented
181C22⋊C8C22×C311yescharacteristic
182C22⋊C8C22×C311yescharacteristic, complemented
183#97C22×C311yescharacteristic, complemented
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—42no—
189C23×C3—42no—
190C23×C3—81no—
191C23×C3C2×D411yescharacteristic
192C23×C3C2×D411yescharacteristic
193C3×Q8—21no—
194C3×Q8—21no—
195C3×Q8—21no—
196C3×Q8C2×D412yes—
197C3×D4—21no—
198C3×D4—21no—
199C3×D4—21no—
200C3×D4—21no—
201C3×D4—21no—
202C3×D4—21no—
203C3×D4—21no—
204C3×D4—41no—
205C3×D4—42no—
206C3×D4—42no—
207C3×D4—42no—
208C3×D4—42no—
209C3×D4—42no—
210C3×D4—81no—
211C3×D4—81no—
212C3×D4—81no—
213C3×D4—81no—
214C3×D4C2×D412yes—
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—42no—
224C2×C3×C4—42no—
225C2×C3×C4—42no—
226C2×C3×C4—81no—
227C2×C3×C4C2×D411yescharacteristic
228C2×C3×C4C2×D411yescharacteristic
229C2×C3×C4C2×D411yescharacteristic
230C2×C3×C4C2×D411yescharacteristic
231C2×C3×C4C2411yescharacteristic
232C3×C8—21no—
233C3×C8—21no—
234C3×C8—21no—
235C3×C8C2×D412yes—
236C24—21no—
237#41—22no—
238#41—22no—
239#41—22no—
240#41—41no—
241#41—41no—
242#41—41no—
243C2×Q8C23×C311yescharacteristic
244C2×Q8C23×C311yescharacteristic
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4C3×D411yescharacteristic
257C2×D4C23×C311yescharacteristic
258C2×D4C23×C311yescharacteristic
259C2×D4C23×C311yescharacteristic
260C2×D4C23×C311yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4C23×C311yescharacteristic
266C22×C4C23×C311yescharacteristic
267Q16—22no—
268SD16—22no—
269SD16—22no—
270SD16—41no—
271SD16C3×D414yescomplemented
272D8—22no—
273D8—22no—
274D8—22no—
275D8—41no—
276M16—22no—
277C2×C8—22no—
278C2×C8C23×C311yescharacteristic
279C2×C8C23×C311yescharacteristic
280C2×C8C23×C311yescharacteristic
281C2×C8C23×C311yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4C3×D411yescharacteristic
285C4⋊C4C23×C311yescharacteristic
286C4⋊C4C23×C311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4C3×D411yescharacteristic
295C22⋊C4C3×D411yescharacteristic
296C42—21no—
297C42C23×C311yescharacteristic
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—22no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—84no—
317C22×C3C22×D411yescharacteristic
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—22no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—41no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4C22×D411yescharacteristic
327C3×C4H(5,𝔽2)11yescharacteristic
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—42no—
333C23—42no—
334C23—81no—
335C23C2×C3×D411yescharacteristic
336C23C2×C3×D411yescharacteristic
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8C2×C3×D412yes—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—41no—
349D4—42no—
350D4—42no—
351D4—42no—
352D4—42no—
353D4—42no—
354D4—81no—
355D4—81no—
356D4—81no—
357D4—81no—
358D4C2×C3×D412yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—81no—
371C2×C4C2×C3×D411yescharacteristic
372C2×C4C2×C3×D411yescharacteristic
373C2×C4C2×C3×D411yescharacteristic
374C2×C4C2×C3×D411yescharacteristic
375C2×C4C24×C311yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8C2×C3×D412yes—
380C2×C3—41no—
381C2×C3—41no—
382C2×C3—42no—
383C2×C3—81no—
384C2×C3—81no—
385C2×C3—81no—
386C2×C3D4211yescharacteristic
387C2×C3#57511yescharacteristic
388C2×C3#57611yescharacteristic
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—22no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—84no—
408C22C22×C3×D411yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—22no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4C22×C3×D411yescharacteristic
418C4C3×H(5,𝔽2)11yescharacteristic
419C3#326811yescharacteristic, direct product factor, Sylow
420C2—41no—
421C2—41no—
422C2—42no—
423C2—81no—
424C2—81no—
425C2—81no—
426C2C3×D4211yescharacteristic
427C2C3×#57511yescharacteristic
428C2C3×#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. C2×C3×AGL(1,ℤ/8)C2semidirect
2. C2×C3×#135C2semidirect
3. C3×#550C2semidirect
4. C3×#546C2semidirect
5. C3×#496C2semidirect
6. C3×#468C2semidirect
7. C3×#466C2semidirect
8. C3×#464C2semidirect
9. C3×#459C2semidirect
10. C3×#452C2semidirect
11. C3×#449C2semidirect
12. C3×#449C2semidirect
13. C3×#447C2semidirect
14. C3×#440C2semidirect
15. C3×#435C2semidirect
16. #3268C3direct (N × H)
19. C2×C3×#41C22semidirect
23. C2×C3×Q16C22semidirect
26. C2×C3×SD16C22semidirect
27. C2×C3×SD16C22semidirect
33. C22×C3×C8C22semidirect
35. C3×#127C22semidirect
44. C3×#121C22semidirect
46. C3×C4×Q8C22semidirect
51. C3×#107C22semidirect
52. C3×C4⋊C8C22semidirect
53. C3×#103C22semidirect
54. C3×#103C22semidirect
57. C3×#102C22semidirect
58. C3×#102C22semidirect
60. C3×C22⋊C8C22semidirect
61. C3×#97C22semidirect
62. C2×AGL(1,ℤ/8)C2×C3semidirect
63. C2×#135C2×C3semidirect
64. #550C2×C3semidirect
65. #546C2×C3semidirect
66. #496C2×C3semidirect
67. #468C2×C3semidirect
68. #466C2×C3semidirect
69. #464C2×C3semidirect
70. #459C2×C3semidirect
71. #452C2×C3semidirect
72. #449C2×C3semidirect
73. #449C2×C3semidirect
74. #447C2×C3semidirect
75. #440C2×C3semidirect
76. #435C2×C3semidirect
112. C3×SD16D4semidirect
141. C2×#41C22×C3semidirect
145. C2×Q16C22×C3semidirect
148. C2×SD16C22×C3semidirect
149. C2×SD16C22×C3semidirect
155. C22×C8C22×C3semidirect
157. #127C22×C3semidirect
166. #121C22×C3semidirect
168. C4×Q8C22×C3semidirect
173. #107C22×C3semidirect
174. C4⋊C8C22×C3semidirect
175. #103C22×C3semidirect
176. #103C22×C3semidirect
179. #102C22×C3semidirect
180. #102C22×C3semidirect
182. C22⋊C8C22×C3semidirect
183. #97C22×C3semidirect
271. SD16C3×D4semidirect
419. C3#3268direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×AGL(1,ℤ/8)2
C2×C3×#1352
C3×#5502
C3×#5462
C3×#4962
C3×#4682
C3×#4662
C3×#4642
C3×#4592
C3×#4522
C3×#4492
C3×#4472
C3×#4402
C3×#4352
#32683