Finite Group Databasebeta

← C3×#3257 #85121

Subgroups — C3×#3257 #85121

Order 384.

358 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×#542C211yesmaximal, characteristic, complemented
2C3×#540C211yesmaximal, characteristic, complemented
3C3×#479C211yesmaximal, characteristic, complemented
4C3×#478C211yesmaximal, characteristic, complemented
5C3×#476C211yesmaximal, characteristic, complemented
6C3×#474C211yesmaximal, characteristic, complemented
7C3×#469C211yesmaximal, characteristic, complemented
8C3×#468C211yesmaximal, characteristic, complemented
9C3×#466C211yesmaximal, characteristic, complemented
10C3×#465C211yesmaximal, characteristic, complemented
11C3×#463C211yesmaximal, characteristic, complemented
12C3×#463C211yesmaximal, characteristic, complemented
13C3×#460C211yesmaximal, characteristic, complemented
14C3×#459C211yesmaximal, characteristic, complemented
15C3×#424C211yesmaximal, characteristic, complemented
16#3257C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×SD16C2211yescharacteristic
18C2×C3×SD16C2211yescharacteristic
19C2×C3×D8C2211yescharacteristic
20C2×C3×D8C2211yescharacteristic
21C2×C3×M16C2211yescharacteristic
22C22×C3×C8C2211yescharacteristic
23C3×C4⋊Q8C2211yescharacteristic
24C3×#127C2211yescharacteristic
25C3×#126—21no—
26C3×#125C2211yescharacteristic
27C3×#124—21no—
28C3×#124C2211yescharacteristic
29C3×#123—21no—
30C3×#123—21no—
31C3×#123—21no—
32C3×C22⋊Q8—21no—
33C3×C22⋊Q8C2211yescharacteristic
34C3×#121—21no—
35C3×#121—21no—
36C3×#121C2211yescharacteristic
37C3×#121C2211yescharacteristic
38C3×#121C2211yescharacteristic
39C3×C4×Q8C2211yescharacteristic
40C3×C4×D4C2211yescharacteristic
41C3×C4×D4C2211yescharacteristic
42C3×C4×D4C2211yescharacteristic
43C3×#117C2211yescharacteristic
44C3×#107C2211yescharacteristic
45C3×#107C2211yescharacteristic
46C3×#106C2211yescharacteristic
47C3×#106C2211yescharacteristic
48C3×C4⋊C8C2211yescharacteristic
49C3×C4⋊C8C2211yescharacteristic
50C3×C4⋊C8C2211yescharacteristic
51C3×C4⋊C8C2211yescharacteristic
52C3×#103C2211yescharacteristic
53C3×#103C2211yescharacteristic
54C3×#102C2211yescharacteristic
55C3×#102C2211yescharacteristic
56C3×#102C2211yescharacteristic
57C3×#102C2211yescharacteristic
58C3×#102C2211yescharacteristic
59C3×#102C2211yescharacteristic
60#542C2×C311yescharacteristic, complemented
61#540C2×C311yescharacteristic, complemented
62#479C2×C311yescharacteristic, complemented
63#478C2×C311yescharacteristic, complemented
64#476C2×C311yescharacteristic, complemented
65#474C2×C311yescharacteristic, complemented
66#469C2×C311yescharacteristic, complemented
67#468C2×C311yescharacteristic, complemented
68#466C2×C311yescharacteristic, complemented
69#465C2×C311yescharacteristic, complemented
70#463C2×C311yescharacteristic, complemented
71#463C2×C311yescharacteristic, complemented
72#460C2×C311yescharacteristic, complemented
73#459C2×C311yescharacteristic, complemented
74#424C2×C311yescharacteristic, complemented
75C2×C3×Q8—21no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×D4—21no—
78C2×C3×D4—21no—
79C2×C3×D4—21no—
80C2×C3×D4—21no—
81C2×C3×D4—21no—
82C2×C3×D4C2311yescharacteristic
83C2×C3×D4C2311yescharacteristic
84C2×C3×D4C2311yescharacteristic
85C22×C3×C4—21no—
86C22×C3×C4—21no—
87C22×C3×C4—21no—
88C22×C3×C4C2311yescharacteristic
89C3×SD16—41no—
90C3×SD16—41no—
91C3×D8—41no—
92C3×D8—41no—
93C3×M16—41no—
94C2×C3×C8—41no—
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C2×C3×C8C2311yescharacteristic
98C2×C3×C8C2311yescharacteristic
99C3×C4⋊C4—21no—
100C3×C4⋊C4—21no—
101C3×C4⋊C4—21no—
102C3×C4⋊C4—21no—
103C3×C4⋊C4—21no—
104C3×C4⋊C4D411yescharacteristic
105C3×C4⋊C4D411yescharacteristic
106C3×C4⋊C4C2311yescharacteristic
107C3×C4⋊C4C2311yescharacteristic
108C3×C4⋊C4C2311yescharacteristic
109C3×C4⋊C4C2311yescharacteristic
110C3×C22⋊C4—21no—
111C3×C22⋊C4—21no—
112C3×C22⋊C4—21no—
113C3×C22⋊C4—21no—
114C3×C22⋊C4—21no—
115C3×C22⋊C4—21no—
116C3×C22⋊C4—21no—
117C3×C22⋊C4—21no—
118C3×C22⋊C4—21no—
119C3×C22⋊C4D411yescharacteristic
120C3×C22⋊C4D411yescharacteristic
121C3×C42—21no—
122C3×C42C2311yescharacteristic
123C3×C42C2311yescharacteristic
124C2×SD16C22×C311yescharacteristic
125C2×SD16C22×C311yescharacteristic
126C2×D8C22×C311yescharacteristic
127C2×D8C22×C311yescharacteristic
128C2×M16C22×C311yescharacteristic
129C22×C8C22×C311yescharacteristic
130C4⋊Q8C22×C311yescharacteristic
131#127C22×C311yescharacteristic
132#126—21no—
133#125C22×C311yescharacteristic
134#124—21no—
135#124C22×C311yescharacteristic
136#123—21no—
137#123—21no—
138#123—21no—
139C22⋊Q8—21no—
140C22⋊Q8C22×C311yescharacteristic
141#121—21no—
142#121—21no—
143#121C22×C311yescharacteristic
144#121C22×C311yescharacteristic
145#121C22×C311yescharacteristic
146C4×Q8C22×C311yescharacteristic
147C4×D4C22×C311yescharacteristic
148C4×D4C22×C311yescharacteristic
149C4×D4C22×C311yescharacteristic
150#117C22×C311yescharacteristic
151#107C22×C311yescharacteristic
152#107C22×C311yescharacteristic
153#106C22×C311yescharacteristic
154#106C22×C311yescharacteristic
155C4⋊C8C22×C311yescharacteristic
156C4⋊C8C22×C311yescharacteristic
157C4⋊C8C22×C311yescharacteristic
158C4⋊C8C22×C311yescharacteristic
159#103C22×C311yescharacteristic
160#103C22×C311yescharacteristic
161#102C22×C311yescharacteristic
162#102C22×C311yescharacteristic
163#102C22×C311yescharacteristic
164#102C22×C311yescharacteristic
165#102C22×C311yescharacteristic
166#102C22×C311yescharacteristic
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3C2×D411yescharacteristic
171C3×Q8—21no—
172C3×Q8—21no—
173C3×Q8—81no—
174C3×D4—21no—
175C3×D4—21no—
176C3×D4—21no—
177C3×D4—21no—
178C3×D4—21no—
179C3×D4—21no—
180C3×D4—81no—
181C3×D4—81no—
182C3×D4—81no—
183C3×D4—81no—
184C3×D4—81no—
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—81no—
193C2×C3×C4—81no—
194C2×C3×C4—81no—
195C2×C3×C4C2×D411yescharacteristic
196C2×C3×C4C2×D411yescharacteristic
197C2×C3×C4C2×D411yescharacteristic
198C2×C3×C4C2×D411yescharacteristic
199C2×C3×C4C2×D411yescharacteristic
200C2×C3×C4C2411yescharacteristic
201C3×C8—21no—
202C3×C8—21no—
203C3×C8—21no—
204C3×C8—21no—
205C2×Q8—21no—
206C2×Q8C23×C311yescharacteristic
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4C23×C311yescharacteristic
213C2×D4C23×C311yescharacteristic
214C2×D4C23×C311yescharacteristic
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4C23×C311yescharacteristic
219SD16—41no—
220SD16—41no—
221D8—41no—
222D8—41no—
223M16—41no—
224C2×C8—41no—
225C2×C8C23×C311yescharacteristic
226C2×C8C23×C311yescharacteristic
227C2×C8C23×C311yescharacteristic
228C2×C8C23×C311yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4C3×D411yescharacteristic
235C4⋊C4C3×D411yescharacteristic
236C4⋊C4C23×C311yescharacteristic
237C4⋊C4C23×C311yescharacteristic
238C4⋊C4C23×C311yescharacteristic
239C4⋊C4C23×C311yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—21no—
242C22⋊C4—21no—
243C22⋊C4—21no—
244C22⋊C4—21no—
245C22⋊C4—21no—
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—21no—
249C22⋊C4C3×D411yescharacteristic
250C22⋊C4C3×D411yescharacteristic
251C42—21no—
252C42C23×C311yescharacteristic
253C42C23×C311yescharacteristic
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3C22×D411yescharacteristic
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4—41no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4H(5,𝔽2)11yescharacteristic
278C3×C42−1+411yescharacteristic
279C23—21no—
280C23—21no—
281C23—21no—
282C23C2×C3×D411yescharacteristic
283Q8—21no—
284Q8—21no—
285Q8—81no—
286D4—21no—
287D4—21no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—81no—
294D4—81no—
295D4—81no—
296D4—81no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4C2×C3×D411yescharacteristic
308C2×C4C2×C3×D411yescharacteristic
309C2×C4C2×C3×D411yescharacteristic
310C2×C4C2×C3×D411yescharacteristic
311C2×C4C2×C3×D411yescharacteristic
312C2×C4C24×C311yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—21no—
317C2×C3—41no—
318C2×C3—81no—
319C2×C3—81no—
320C2×C3—81no—
321C2×C3#53711yescharacteristic
322C2×C3#57611yescharacteristic
323C2×C3#57711yescharacteristic
324C22—21no—
325C22—21no—
326C22—21no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22C22×C3×D411yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4C3×H(5,𝔽2)11yescharacteristic
348C4C3×2−1+411yescharacteristic
349C3#325711yescharacteristic, direct product factor, Sylow
350C2—41no—
351C2—81no—
352C2—81no—
353C2—81no—
354C2C3×#53711yescharacteristic
355C2C3×#57611yescharacteristic
356C2C3×#57711yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#542C2semidirect
2. C3×#540C2semidirect
3. C3×#479C2semidirect
4. C3×#478C2semidirect
5. C3×#476C2semidirect
6. C3×#474C2semidirect
7. C3×#469C2semidirect
8. C3×#468C2semidirect
9. C3×#466C2semidirect
10. C3×#465C2semidirect
11. C3×#463C2semidirect
12. C3×#463C2semidirect
13. C3×#460C2semidirect
14. C3×#459C2semidirect
15. C3×#424C2semidirect
16. #3257C3direct (N × H)
60. #542C2×C3semidirect
61. #540C2×C3semidirect
62. #479C2×C3semidirect
63. #478C2×C3semidirect
64. #476C2×C3semidirect
65. #474C2×C3semidirect
66. #469C2×C3semidirect
67. #468C2×C3semidirect
68. #466C2×C3semidirect
69. #465C2×C3semidirect
70. #463C2×C3semidirect
71. #463C2×C3semidirect
72. #460C2×C3semidirect
73. #459C2×C3semidirect
74. #424C2×C3semidirect
349. C3#3257direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5422
C3×#5402
C3×#4792
C3×#4782
C3×#4762
C3×#4742
C3×#4692
C3×#4682
C3×#4662
C3×#4652
C3×#4632
C3×#4602
C3×#4592
C3×#4242
#32573