Finite Group Databasebeta

← C3×#3327 #85191

Subgroups — C3×#3327 #85191

Order 384.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#552C211yesmaximal, characteristic, complemented
2C3×#548C211yesmaximal, characteristic
3C3×#488C211yesmaximal, characteristic, complemented
4C3×#484C211yesmaximal, characteristic, complemented
5C3×#482C211yesmaximal, characteristic, complemented
6C3×#479C211yesmaximal, characteristic, complemented
7C3×#470C211yesmaximal, characteristic, complemented
8C3×#468C211yesmaximal, characteristic, complemented
9C3×#464C211yesmaximal, characteristic, complemented
10C3×#452C211yesmaximal, characteristic, complemented
11C3×#451C211yesmaximal, characteristic, complemented
12C3×C4×Q16C211yesmaximal, characteristic, complemented
13C3×#436C211yesmaximal, characteristic, complemented
14C3×#419C211yesmaximal, characteristic, complemented
15C3×#417C211yesmaximal, characteristic, complemented
16#3327C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#41C2211yescharacteristic
18C22×C3×Q8C2211yescharacteristic
19C2×C3×Q16C2211yescharacteristic
20C2×C3×Q16C2211yescharacteristic
21C2×C3×SD16C2211yescharacteristic
22C2×C3×M16C2211yescharacteristic
23C2×C3×M16C2211yescharacteristic
24C3×#126—21no—
25C3×#125—21no—
26C3×#125C2211yescharacteristic
27C3×#124—21no—
28C3×#124C2211yescharacteristic
29C3×#123—21no—
30C3×C22⋊Q8—21no—
31C3×C22⋊Q8C2211yescharacteristic
32C3×C22⋊Q8C2211yescharacteristic
33C3×C22⋊Q8C2211yescharacteristic
34C3×#121—21no—
35C3×#121C2211yescharacteristic
36C3×C4×Q8C2211yescharacteristic
37C3×C4×Q8C2211yescharacteristic
38C3×C4×D4—21no—
39C3×C4×D4C2211yescharacteristic
40C3×#117—21no—
41C3×#117C2211yescharacteristic
42C2×C3×C4⋊C4C2211yescharacteristic
43C3×#107C2211yescharacteristic
44C3×#107C2211yescharacteristic
45C3×#106C2211yescharacteristic
46C3×C4⋊C8C2211yescharacteristic
47C3×#103C2211yescharacteristic
48C3×#103C2211yescharacteristic
49C3×#103C2211yescharacteristic
50C3×#103C2211yescharacteristic
51C3×#103C2211yescharacteristic
52C3×#103C2211yescharacteristic
53C3×#103C2211yescharacteristic
54C3×#102C2211yescharacteristic
55C3×#102C2211yescharacteristic
56C3×#102C2211yescharacteristic
57C3×C22⋊C8C2211yescharacteristic
58C3×C22⋊C8C2211yescharacteristic
59C3×C4×C8C2211yescharacteristic
60#552C2×C311yescharacteristic, complemented
61#548C2×C311yescharacteristic
62#488C2×C311yescharacteristic, complemented
63#484C2×C311yescharacteristic, complemented
64#482C2×C311yescharacteristic, complemented
65#479C2×C311yescharacteristic, complemented
66#470C2×C311yescharacteristic, complemented
67#468C2×C311yescharacteristic, complemented
68#464C2×C311yescharacteristic, complemented
69#452C2×C311yescharacteristic, complemented
70#451C2×C311yescharacteristic, complemented
71C4×Q16C2×C311yescharacteristic, complemented
72#436C2×C311yescharacteristic, complemented
73#419C2×C311yescharacteristic, complemented
74#417C2×C311yescharacteristic, complemented
75C3×#41—22no—
76C3×#41—41no—
77C2×C3×Q8—21no—
78C2×C3×Q8—22no—
79C2×C3×Q8—41no—
80C2×C3×Q8C2311yescharacteristic
81C2×C3×Q8C2311yescharacteristic
82C2×C3×Q8C2311yescharacteristic
83C2×C3×D4—21no—
84C2×C3×D4—21no—
85C2×C3×D4D411yescharacteristic
86C2×C3×D4C2311yescharacteristic
87C22×C3×C4—21no—
88C22×C3×C4—21no—
89C22×C3×C4—21no—
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C3×Q16—22no—
93C3×Q16—41no—
94C3×SD16—41no—
95C3×M16—41no—
96C3×M16—41no—
97C2×C3×C8C2311yescharacteristic
98C2×C3×C8C2311yescharacteristic
99C2×C3×C8C2311yescharacteristic
100C2×C3×C8C2311yescharacteristic
101C3×C4⋊C4—21no—
102C3×C4⋊C4—21no—
103C3×C4⋊C4—21no—
104C3×C4⋊C4—21no—
105C3×C4⋊C4—21no—
106C3×C4⋊C4—21no—
107C3×C4⋊C4—21no—
108C3×C4⋊C4—21no—
109C3×C4⋊C4D411yescharacteristic
110C3×C4⋊C4C2311yescharacteristic
111C3×C4⋊C4C2311yescharacteristic
112C3×C4⋊C4C2311yescharacteristic
113C3×C4⋊C4C2311yescharacteristic
114C3×C22⋊C4—21no—
115C3×C22⋊C4—21no—
116C3×C22⋊C4—21no—
117C3×C22⋊C4—21no—
118C3×C22⋊C4—21no—
119C3×C22⋊C4—21no—
120C3×C22⋊C4—21no—
121C3×C22⋊C4D411yescharacteristic
122C3×C22⋊C4D411yescharacteristic
123C3×C42—21no—
124C3×C42—21no—
125C3×C42—21no—
126C3×C42C2311yescharacteristic
127C2×#41C22×C311yescharacteristic
128C22×Q8C22×C311yescharacteristic
129C2×Q16C22×C311yescharacteristic
130C2×Q16C22×C311yescharacteristic
131C2×SD16C22×C311yescharacteristic
132C2×M16C22×C311yescharacteristic
133C2×M16C22×C311yescharacteristic
134#126—21no—
135#125—21no—
136#125C22×C311yescharacteristic
137#124—21no—
138#124C22×C311yescharacteristic
139#123—21no—
140C22⋊Q8—21no—
141C22⋊Q8C22×C311yescharacteristic
142C22⋊Q8C22×C311yescharacteristic
143C22⋊Q8C22×C311yescharacteristic
144#121—21no—
145#121C22×C311yescharacteristic
146C4×Q8C22×C311yescharacteristic
147C4×Q8C22×C311yescharacteristic
148C4×D4—21no—
149C4×D4C22×C311yescharacteristic
150#117—21no—
151#117C22×C311yescharacteristic
152C2×C4⋊C4C22×C311yescharacteristic
153#107C22×C311yescharacteristic
154#107C22×C311yescharacteristic
155#106C22×C311yescharacteristic
156C4⋊C8C22×C311yescharacteristic
157#103C22×C311yescharacteristic
158#103C22×C311yescharacteristic
159#103C22×C311yescharacteristic
160#103C22×C311yescharacteristic
161#103C22×C311yescharacteristic
162#103C22×C311yescharacteristic
163#103C22×C311yescharacteristic
164#102C22×C311yescharacteristic
165#102C22×C311yescharacteristic
166#102C22×C311yescharacteristic
167C22⋊C8C22×C311yescharacteristic
168C22⋊C8C22×C311yescharacteristic
169C4×C8C22×C311yescharacteristic
170C23×C3—21no—
171C23×C3C2×D411yescharacteristic
172C23×C3C2×D411yescharacteristic
173C3×Q8—21no—
174C3×Q8—21no—
175C3×Q8—21no—
176C3×Q8—21no—
177C3×Q8—21no—
178C3×Q8—42no—
179C3×Q8#4112yes—
180C3×D4—21no—
181C3×D4—21no—
182C3×D4—41no—
183C3×D4—42no—
184C3×D4—42no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
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—42no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4C2×D411yescharacteristic
200C2×C3×C4C2×D411yescharacteristic
201C2×C3×C4C2×D411yescharacteristic
202C2×C3×C4C2×D411yescharacteristic
203C2×C3×C4C2411yescharacteristic
204C3×C8—21no—
205C3×C8—21no—
206C3×C8—21no—
207C3×C8—21no—
208#41—22no—
209#41—41no—
210C2×Q8—21no—
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8C23×C311yescharacteristic
214C2×Q8C23×C311yescharacteristic
215C2×Q8C23×C311yescharacteristic
216C2×D4—21no—
217C2×D4—21no—
218C2×D4C3×D411yescharacteristic
219C2×D4C23×C311yescharacteristic
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4C23×C311yescharacteristic
224C22×C4C23×C311yescharacteristic
225Q16—22no—
226Q16—41no—
227SD16—41no—
228M16—41no—
229M16—41no—
230C2×C8C23×C311yescharacteristic
231C2×C8C23×C311yescharacteristic
232C2×C8C23×C311yescharacteristic
233C2×C8C23×C311yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4C3×D411yescharacteristic
243C4⋊C4C23×C311yescharacteristic
244C4⋊C4C23×C311yescharacteristic
245C4⋊C4C23×C311yescharacteristic
246C4⋊C4C23×C311yescharacteristic
247C22⋊C4—21no—
248C22⋊C4—21no—
249C22⋊C4—21no—
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4C3×D411yescharacteristic
255C22⋊C4C3×D411yescharacteristic
256C42—21no—
257C42—21no—
258C42—21no—
259C42C23×C311yescharacteristic
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3C22×D411yescharacteristic
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—22no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—41no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4C2×#4111yescharacteristic
282C3×C4H(5,𝔽2)11yescharacteristic
283C23—21no—
284C23C2×C3×D411yescharacteristic
285C23C2×C3×D411yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—42no—
292Q8C3×#4112yes—
293D4—21no—
294D4—21no—
295D4—41no—
296D4—42no—
297D4—42no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4C2×C3×D411yescharacteristic
313C2×C4C2×C3×D411yescharacteristic
314C2×C4C2×C3×D411yescharacteristic
315C2×C4C2×C3×D411yescharacteristic
316C2×C4C24×C311yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8—21no—
321C2×C3—41no—
322C2×C3—41no—
323C2×C3—81no—
324C2×C3#54611yescharacteristic
325C2×C3#57511yescharacteristic
326C2×C3#57811yescharacteristic
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22C22×C3×D411yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4C2×C3×#4111yescharacteristic
349C4C3×H(5,𝔽2)11yescharacteristic
350C3#332711yescharacteristic, direct product factor, Sylow
351C2—41no—
352C2—41no—
353C2—81no—
354C2C3×#54611yescharacteristic
355C2C3×#57511yescharacteristic
356C2C3×#57811yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
prime radicalC3×#548C2
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×#552C2semidirect
3. C3×#488C2semidirect
4. C3×#484C2semidirect
5. C3×#482C2semidirect
6. C3×#479C2semidirect
7. C3×#470C2semidirect
8. C3×#468C2semidirect
9. C3×#464C2semidirect
10. C3×#452C2semidirect
11. C3×#451C2semidirect
12. C3×C4×Q16C2semidirect
13. C3×#436C2semidirect
14. C3×#419C2semidirect
15. C3×#417C2semidirect
16. #3327C3direct (N × H)
60. #552C2×C3semidirect
62. #488C2×C3semidirect
63. #484C2×C3semidirect
64. #482C2×C3semidirect
65. #479C2×C3semidirect
66. #470C2×C3semidirect
67. #468C2×C3semidirect
68. #464C2×C3semidirect
69. #452C2×C3semidirect
70. #451C2×C3semidirect
71. C4×Q16C2×C3semidirect
72. #436C2×C3semidirect
73. #419C2×C3semidirect
74. #417C2×C3semidirect
350. C3#3327direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5522
C3×#5482
C3×#4882
C3×#4842
C3×#4822
C3×#4792
C3×#4702
C3×#4682
C3×#4642
C3×#4522
C3×#4512
C3×C4×Q162
C3×#4362
C3×#4192
C3×#4172
#33273