Finite Group Databasebeta

← C3×#3314 #85178

Subgroups — C3×#3314 #85178

Order 384.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#554C211yesmaximal, characteristic, complemented
2C3×#546C211yesmaximal, characteristic
3C3×#489C211yesmaximal, characteristic, complemented
4C3×#484C211yesmaximal, characteristic, complemented
5C3×#480C211yesmaximal, characteristic, complemented
6C3×#474C211yesmaximal, characteristic, complemented
7C3×#468C211yesmaximal, characteristic, complemented
8C3×#467C211yesmaximal, characteristic, complemented
9C3×#464C211yesmaximal, characteristic, complemented
10C3×#452C211yesmaximal, characteristic, complemented
11C3×#450C211yesmaximal, characteristic, complemented
12C3×#440C211yesmaximal, characteristic, complemented
13C3×#435C211yesmaximal, characteristic, complemented
14C3×#417C211yesmaximal, characteristic, complemented
15C2×C3×#102C211yesmaximal, characteristic, complemented
16#3314C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#41C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C2×C3×Q16C2211yescharacteristic, complemented
20C2×C3×SD16C2211yescharacteristic
21C2×C3×SD16C2211yescharacteristic
22C2×C3×M16C2211yescharacteristic, complemented
23C22×C3×C8C2211yescharacteristic
24C3×C4⋊Q8C2211yescharacteristic, complemented
25C3×#125—21no—
26C3×#124C2211yescharacteristic
27C3×#123—21no—
28C3×C22⋊Q8—21no—
29C3×C22⋊Q8—21no—
30C3×C22⋊Q8C2211yescharacteristic
31C3×C22⋊Q8C2211yescharacteristic
32C3×C22⋊Q8C2211yescharacteristic, complemented
33C3×#121—21no—
34C3×#121C2211yescharacteristic
35C3×#120—21no—
36C3×C4×Q8C2211yescharacteristic, complemented
37C3×C4×D4—21no—
38C3×C4×D4C2211yescharacteristic
39C3×C4×D4C2211yescharacteristic
40C2×C3×C4⋊C4C2211yescharacteristic
41C2×C3×C4⋊C4C2211yescharacteristic, complemented
42C2×C3×C22⋊C4—21no—
43C3×#107C2211yescharacteristic, complemented
44C3×#107C2211yescharacteristic, complemented
45C3×#107C2211yescharacteristic, complemented
46C3×C4⋊C8C2211yescharacteristic, complemented
47C3×#103C2211yescharacteristic, complemented
48C3×#103C2211yescharacteristic, complemented
49C3×#103C2211yescharacteristic, complemented
50C3×#103C2211yescharacteristic, complemented
51C3×#102C2211yescharacteristic
52C3×#102C2211yescharacteristic
53C3×#102C2211yescharacteristic
54C3×#102C2211yescharacteristic
55C3×#102C2211yescharacteristic
56C3×#102C2211yescharacteristic
57C3×C22⋊C8C2211yescharacteristic
58C3×C22⋊C8C2211yescharacteristic, complemented
59C3×#97C2211yescharacteristic, complemented
60#554C2×C311yescharacteristic, complemented
61#546C2×C311yescharacteristic
62#489C2×C311yescharacteristic, complemented
63#484C2×C311yescharacteristic, complemented
64#480C2×C311yescharacteristic, complemented
65#474C2×C311yescharacteristic, complemented
66#468C2×C311yescharacteristic, complemented
67#467C2×C311yescharacteristic, complemented
68#464C2×C311yescharacteristic, complemented
69#452C2×C311yescharacteristic, complemented
70#450C2×C311yescharacteristic, complemented
71#440C2×C311yescharacteristic, complemented
72#435C2×C311yescharacteristic, complemented
73#417C2×C311yescharacteristic, complemented
74C2×#102C2×C311yescharacteristic, complemented
75C24×C3—21no—
76C3×#41—22no—
77C3×#41—41no—
78C2×C3×Q8—21no—
79C2×C3×Q8C2311yescharacteristic
80C2×C3×Q8C2311yescharacteristic
81C2×C3×D4—22no—
82C2×C3×D4—21no—
83C2×C3×D4—21no—
84C2×C3×D4—21no—
85C2×C3×D4—41no—
86C2×C3×D4D411yescharacteristic
87C2×C3×D4C2311yescharacteristic
88C2×C3×D4C2311yescharacteristic
89C22×C3×C4—21no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4C2311yescharacteristic
94C22×C3×C4C2311yescharacteristic
95C3×Q16—41no—
96C3×SD16—22no—
97C3×SD16—41no—
98C3×M16—41no—
99C2×C3×C8—41no—
100C2×C3×C8C2311yescharacteristic
101C2×C3×C8C2311yescharacteristic
102C2×C3×C8C2311yescharacteristic
103C2×C3×C8C2311yescharacteristic
104C3×C4⋊C4—21no—
105C3×C4⋊C4—21no—
106C3×C4⋊C4—21no—
107C3×C4⋊C4—21no—
108C3×C4⋊C4—21no—
109C3×C4⋊C4—21no—
110C3×C4⋊C4—21no—
111C3×C4⋊C4D411yescharacteristic
112C3×C4⋊C4C2311yescharacteristic
113C3×C4⋊C4C2311yescharacteristic
114C3×C4⋊C4C2311yescharacteristic
115C3×C4⋊C4C2311yescharacteristic
116C3×C22⋊C4—21no—
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⋊C4D411yescharacteristic
124C3×C22⋊C4D411yescharacteristic
125C3×C42—21no—
126C3×C42C2311yescharacteristic
127C2×#41C22×C311yescharacteristic
128C22×D4C22×C311yescharacteristic
129C2×Q16C22×C311yescharacteristic, complemented
130C2×SD16C22×C311yescharacteristic
131C2×SD16C22×C311yescharacteristic
132C2×M16C22×C311yescharacteristic, complemented
133C22×C8C22×C311yescharacteristic
134C4⋊Q8C22×C311yescharacteristic, complemented
135#125—21no—
136#124C22×C311yescharacteristic
137#123—21no—
138C22⋊Q8—21no—
139C22⋊Q8—21no—
140C22⋊Q8C22×C311yescharacteristic
141C22⋊Q8C22×C311yescharacteristic
142C22⋊Q8C22×C311yescharacteristic, complemented
143#121—21no—
144#121C22×C311yescharacteristic
145#120—21no—
146C4×Q8C22×C311yescharacteristic, complemented
147C4×D4—21no—
148C4×D4C22×C311yescharacteristic
149C4×D4C22×C311yescharacteristic
150C2×C4⋊C4C22×C311yescharacteristic
151C2×C4⋊C4C22×C311yescharacteristic, complemented
152C2×C22⋊C4—21no—
153#107C22×C311yescharacteristic, complemented
154#107C22×C311yescharacteristic, complemented
155#107C22×C311yescharacteristic, complemented
156C4⋊C8C22×C311yescharacteristic, complemented
157#103C22×C311yescharacteristic, complemented
158#103C22×C311yescharacteristic, complemented
159#103C22×C311yescharacteristic, complemented
160#103C22×C311yescharacteristic, complemented
161#102C22×C311yescharacteristic
162#102C22×C311yescharacteristic
163#102C22×C311yescharacteristic
164#102C22×C311yescharacteristic
165#102C22×C311yescharacteristic
166#102C22×C311yescharacteristic
167C22⋊C8C22×C311yescharacteristic
168C22⋊C8C22×C311yescharacteristic, complemented
169#97C22×C311yescharacteristic, complemented
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—42no—
173C23×C3—42no—
174C23×C3—81no—
175C23×C3C2×D411yescharacteristic
176C23×C3C2×D411yescharacteristic
177C3×Q8—21no—
178C3×Q8—21no—
179C3×Q8—21no—
180C3×Q8—21no—
181C3×Q8—81no—
182C3×D4—22no—
183C3×D4—21no—
184C3×D4—21no—
185C3×D4—21no—
186C3×D4—42no—
187C3×D4—42no—
188C3×D4—81no—
189C3×D4#4112yes—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—42no—
201C2×C3×C4—81no—
202C2×C3×C4—81no—
203C2×C3×C4—81no—
204C2×C3×C4C2×D411yescharacteristic
205C2×C3×C4C2×D411yescharacteristic
206C2×C3×C4C2×D411yescharacteristic
207C2×C3×C4C2×D411yescharacteristic
208C2×C3×C4C2411yescharacteristic
209C3×C8—21no—
210C3×C8—21no—
211C3×C8—21no—
212C3×C8—21no—
213C24—21no—
214#41—22no—
215#41—41no—
216C2×Q8—21no—
217C2×Q8C23×C311yescharacteristic
218C2×Q8C23×C311yescharacteristic
219C2×D4—22no—
220C2×D4—21no—
221C2×D4—21no—
222C2×D4—21no—
223C2×D4—41no—
224C2×D4C3×D411yescharacteristic
225C2×D4C23×C311yescharacteristic
226C2×D4C23×C311yescharacteristic
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4C23×C311yescharacteristic
232C22×C4C23×C311yescharacteristic
233Q16—41no—
234SD16—22no—
235SD16—41no—
236M16—41no—
237C2×C8—41no—
238C2×C8C23×C311yescharacteristic
239C2×C8C23×C311yescharacteristic
240C2×C8C23×C311yescharacteristic
241C2×C8C23×C311yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4C3×D411yescharacteristic
250C4⋊C4C23×C311yescharacteristic
251C4⋊C4C23×C311yescharacteristic
252C4⋊C4C23×C311yescharacteristic
253C4⋊C4C23×C311yescharacteristic
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4C3×D411yescharacteristic
262C22⋊C4C3×D411yescharacteristic
263C42—21no—
264C42C23×C311yescharacteristic
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—22no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—84no—
277C22×C3#13712yes—
278C22×C3C22×D411yescharacteristic
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—41no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4C2×#4111yescharacteristic
290C3×C4H(5,𝔽2)11yescharacteristic
291C23—21no—
292C23—21no—
293C23—42no—
294C23—42no—
295C23—81no—
296C23C2×C3×D411yescharacteristic
297C23C2×C3×D411yescharacteristic
298Q8—21no—
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—81no—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—42no—
309D4—81no—
310D4C3×#4112yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4C2×C3×D411yescharacteristic
326C2×C4C2×C3×D411yescharacteristic
327C2×C4C2×C3×D411yescharacteristic
328C2×C4C2×C3×D411yescharacteristic
329C2×C4C24×C311yescharacteristic
330C8—21no—
331C8—21no—
332C8—21no—
333C8—21no—
334C2×C3—22no—
335C2×C3—41no—
336C2×C3—42no—
337C2×C3—81no—
338C2×C3#54611yescharacteristic
339C2×C3C2×#13711yescharacteristic
340C2×C3#57611yescharacteristic
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—84no—
353C22C3×#13712yes—
354C22C22×C3×D411yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4C2×C3×#4111yescharacteristic
366C4C3×H(5,𝔽2)11yescharacteristic
367C3#331411yescharacteristic, direct product factor, Sylow
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2C3×#54611yescharacteristic
373C2C2×C3×#13711yescharacteristic
374C2C3×#57611yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
prime radicalC3×#546C2
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×#554C2semidirect
3. C3×#489C2semidirect
4. C3×#484C2semidirect
5. C3×#480C2semidirect
6. C3×#474C2semidirect
7. C3×#468C2semidirect
8. C3×#467C2semidirect
9. C3×#464C2semidirect
10. C3×#452C2semidirect
11. C3×#450C2semidirect
12. C3×#440C2semidirect
13. C3×#435C2semidirect
14. C3×#417C2semidirect
15. C2×C3×#102C2semidirect
16. #3314C3direct (N × H)
19. C2×C3×Q16C22semidirect
22. C2×C3×M16C22semidirect
24. C3×C4⋊Q8C22semidirect
32. C3×C22⋊Q8C22semidirect
36. C3×C4×Q8C22semidirect
41. C2×C3×C4⋊C4C22semidirect
43. C3×#107C22semidirect
44. C3×#107C22semidirect
45. C3×#107C22semidirect
46. C3×C4⋊C8C22semidirect
47. C3×#103C22semidirect
48. C3×#103C22semidirect
49. C3×#103C22semidirect
50. C3×#103C22semidirect
58. C3×C22⋊C8C22semidirect
59. C3×#97C22semidirect
60. #554C2×C3semidirect
62. #489C2×C3semidirect
63. #484C2×C3semidirect
64. #480C2×C3semidirect
65. #474C2×C3semidirect
66. #468C2×C3semidirect
67. #467C2×C3semidirect
68. #464C2×C3semidirect
69. #452C2×C3semidirect
70. #450C2×C3semidirect
71. #440C2×C3semidirect
72. #435C2×C3semidirect
73. #417C2×C3semidirect
74. C2×#102C2×C3semidirect
129. C2×Q16C22×C3semidirect
132. C2×M16C22×C3semidirect
134. C4⋊Q8C22×C3semidirect
142. C22⋊Q8C22×C3semidirect
146. C4×Q8C22×C3semidirect
151. C2×C4⋊C4C22×C3semidirect
153. #107C22×C3semidirect
154. #107C22×C3semidirect
155. #107C22×C3semidirect
156. C4⋊C8C22×C3semidirect
157. #103C22×C3semidirect
158. #103C22×C3semidirect
159. #103C22×C3semidirect
160. #103C22×C3semidirect
168. C22⋊C8C22×C3semidirect
169. #97C22×C3semidirect
367. C3#3314direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5542
C3×#5462
C3×#4892
C3×#4842
C3×#4802
C3×#4742
C3×#4682
C3×#4672
C3×#4642
C3×#4522
C3×#4502
C3×#4402
C3×#4352
C3×#4172
C2×C3×#1022
#33143