Finite Group Databasebeta

← C3×#3343 #85207

Subgroups — C3×#3343 #85207

Order 384.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#552C211yesmaximal, characteristic, complemented
2C3×#547C211yesmaximal, characteristic
3C3×#501C211yesmaximal, characteristic, complemented
4C3×#484C211yesmaximal, characteristic, complemented
5C3×#483C211yesmaximal, characteristic, complemented
6C3×#482C211yesmaximal, characteristic, complemented
7C3×#480C211yesmaximal, characteristic, complemented
8C3×#478C211yesmaximal, characteristic, complemented
9C3×#477C211yesmaximal, characteristic, complemented
10C3×#468C211yesmaximal, characteristic, complemented
11C3×#465C211yesmaximal, characteristic, complemented
12C3×#440C211yesmaximal, characteristic, complemented
13C3×#435C211yesmaximal, characteristic, complemented
14C3×#428C211yesmaximal, characteristic, complemented
15C2×C3×#107C211yesmaximal, characteristic, complemented
16#3343C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#41—21no—
18C2×C3×SD16C2211yescharacteristic
19C2×C3×M16C2211yescharacteristic
20C22×C3×C8C2211yescharacteristic
21C3×C4⋊Q8C2211yescharacteristic
22C3×#126—21no—
23C3×#125—21no—
24C3×#125C2211yescharacteristic
25C3×#123—21no—
26C3×#123—21no—
27C3×#123—21no—
28C3×C22⋊Q8—21no—
29C3×C22⋊Q8C2211yescharacteristic
30C3×C22⋊Q8C2211yescharacteristic
31C3×#121C2211yescharacteristic
32C3×#121C2211yescharacteristic
33C3×C4×Q8C2211yescharacteristic
34C3×C4×D4C2211yescharacteristic
35C3×C4×D4C2211yescharacteristic
36C3×#117—21no—
37C3×#117C2211yescharacteristic
38C2×C3×C4⋊C4C2211yescharacteristic
39C2×C3×C4⋊C4C2211yescharacteristic
40C2×C3×C4⋊C4C2211yescharacteristic
41C3×#107C2211yescharacteristic
42C3×#107C2211yescharacteristic
43C3×#107C2211yescharacteristic
44C3×#107C2211yescharacteristic
45C3×#107C2211yescharacteristic
46C3×#107C2211yescharacteristic
47C3×#106C2211yescharacteristic
48C3×#106C2211yescharacteristic
49C3×#106C2211yescharacteristic
50C3×C4⋊C8C2211yescharacteristic
51C3×#103C2211yescharacteristic
52C3×#103C2211yescharacteristic
53C3×#103C2211yescharacteristic
54C3×#102C2211yescharacteristic
55C3×#102C2211yescharacteristic
56C3×#102C2211yescharacteristic
57C3×C22⋊C8C2211yescharacteristic
58C3×C22⋊C8C2211yescharacteristic
59C3×#97C2211yescharacteristic
60#552C2×C311yescharacteristic, complemented
61#547C2×C311yescharacteristic
62#501C2×C311yescharacteristic, complemented
63#484C2×C311yescharacteristic, complemented
64#483C2×C311yescharacteristic, complemented
65#482C2×C311yescharacteristic, complemented
66#480C2×C311yescharacteristic, complemented
67#478C2×C311yescharacteristic, complemented
68#477C2×C311yescharacteristic, complemented
69#468C2×C311yescharacteristic, complemented
70#465C2×C311yescharacteristic, complemented
71#440C2×C311yescharacteristic, complemented
72#435C2×C311yescharacteristic, complemented
73#428C2×C311yescharacteristic, complemented
74C2×#107C2×C311yescharacteristic, complemented
75C3×#41—44no—
76C2×C3×Q8—21no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×D4—21no—
79C2×C3×D4—21no—
80C2×C3×D4D411yescharacteristic
81C2×C3×D4C2311yescharacteristic
82C22×C3×C4—21no—
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C22×C3×C4—21no—
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C3×SD16—22no—
89C3×M16—22no—
90C2×C3×C8—22no—
91C2×C3×C8C2311yescharacteristic
92C2×C3×C8C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C3×C4⋊C4—21no—
96C3×C4⋊C4—21no—
97C3×C4⋊C4—21no—
98C3×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
106C3×C4⋊C4C2311yescharacteristic
107C3×C4⋊C4C2311yescharacteristic
108C3×C4⋊C4C2311yescharacteristic
109C3×C4⋊C4C2311yescharacteristic
110C3×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
118C3×C22⋊C4D411yescharacteristic
119C3×C42—21no—
120C3×C42—21no—
121C3×C42C2311yescharacteristic
122C2×#41—21no—
123C2×SD16C22×C311yescharacteristic
124C2×M16C22×C311yescharacteristic
125C22×C8C22×C311yescharacteristic
126C4⋊Q8C22×C311yescharacteristic
127#126—21no—
128#125—21no—
129#125C22×C311yescharacteristic
130#123—21no—
131#123—21no—
132#123—21no—
133C22⋊Q8—21no—
134C22⋊Q8C22×C311yescharacteristic
135C22⋊Q8C22×C311yescharacteristic
136#121C22×C311yescharacteristic
137#121C22×C311yescharacteristic
138C4×Q8C22×C311yescharacteristic
139C4×D4C22×C311yescharacteristic
140C4×D4C22×C311yescharacteristic
141#117—21no—
142#117C22×C311yescharacteristic
143C2×C4⋊C4C22×C311yescharacteristic
144C2×C4⋊C4C22×C311yescharacteristic
145C2×C4⋊C4C22×C311yescharacteristic
146#107C22×C311yescharacteristic
147#107C22×C311yescharacteristic
148#107C22×C311yescharacteristic
149#107C22×C311yescharacteristic
150#107C22×C311yescharacteristic
151#107C22×C311yescharacteristic
152#106C22×C311yescharacteristic
153#106C22×C311yescharacteristic
154#106C22×C311yescharacteristic
155C4⋊C8C22×C311yescharacteristic
156#103C22×C311yescharacteristic
157#103C22×C311yescharacteristic
158#103C22×C311yescharacteristic
159#102C22×C311yescharacteristic
160#102C22×C311yescharacteristic
161#102C22×C311yescharacteristic
162C22⋊C8C22×C311yescharacteristic
163C22⋊C8C22×C311yescharacteristic
164#97C22×C311yescharacteristic
165C23×C3—21no—
166C23×C3C2×D411yescharacteristic
167C23×C3C2×D411yescharacteristic
168C3×Q8—21no—
169C3×Q8—21no—
170C3×Q8—42no—
171C3×D4—22no—
172C3×D4—21no—
173C3×D4—21no—
174C3×D4—42no—
175C3×D4—42no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—42no—
188C2×C3×C4—42no—
189C2×C3×C4—42no—
190C2×C3×C4—42no—
191C2×C3×C4C2×D411yescharacteristic
192C2×C3×C4C2×D411yescharacteristic
193C2×C3×C4C2×D411yescharacteristic
194C2×C3×C4C2×D411yescharacteristic
195C2×C3×C4C2411yescharacteristic
196C3×C8—21no—
197C3×C8—21no—
198C3×C8—21no—
199C3×C8#4112yescomplemented
200#41—44no—
201C2×Q8—21no—
202C2×Q8C23×C311yescharacteristic
203C2×D4—21no—
204C2×D4—21no—
205C2×D4C3×D411yescharacteristic
206C2×D4C23×C311yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4C23×C311yescharacteristic
212C22×C4C23×C311yescharacteristic
213SD16—22no—
214M16—22no—
215C2×C8—22no—
216C2×C8C23×C311yescharacteristic
217C2×C8C23×C311yescharacteristic
218C2×C8C23×C311yescharacteristic
219C2×C8C23×C311yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4C3×D411yescharacteristic
230C4⋊C4C23×C311yescharacteristic
231C4⋊C4C23×C311yescharacteristic
232C4⋊C4C23×C311yescharacteristic
233C4⋊C4C23×C311yescharacteristic
234C4⋊C4C23×C311yescharacteristic
235C4⋊C4C23×C311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—21no—
242C22⋊C4C3×D411yescharacteristic
243C22⋊C4C3×D411yescharacteristic
244C42—21no—
245C42—21no—
246C42C23×C311yescharacteristic
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3—41no—
255C22×C3AGL(1,ℤ/8)12yes—
256C22×C3C22×D411yescharacteristic
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—41no—
262C3×C4—41no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4C2×#4111yescharacteristic
269C3×C42−1+411yescharacteristic
270C23—21no—
271C23C2×C3×D411yescharacteristic
272C23C2×C3×D411yescharacteristic
273Q8—21no—
274Q8—21no—
275Q8—42no—
276D4—22no—
277D4—21no—
278D4—21no—
279D4—42no—
280D4—42no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4C2×C3×D411yescharacteristic
297C2×C4C2×C3×D411yescharacteristic
298C2×C4C2×C3×D411yescharacteristic
299C2×C4C2×C3×D411yescharacteristic
300C2×C4C24×C311yescharacteristic
301C8—21no—
302C8—21no—
303C8—21no—
304C8C3×#4112yescomplemented
305C2×C3—22no—
306C2×C3—41no—
307C2×C3—81no—
308C2×C3#54711yescharacteristic
309C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
310C2×C3#57811yescharacteristic
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22C3×AGL(1,ℤ/8)12yes—
320C22C22×C3×D411yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4C2×C3×#4111yescharacteristic
333C4C3×2−1+411yescharacteristic
334C3#334311yescharacteristic, direct product factor, Sylow
335C2—22no—
336C2—41no—
337C2—81no—
338C2C3×#54711yescharacteristic
339C2C2×C3×AGL(1,ℤ/8)11yescharacteristic
340C2C3×#57811yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
prime radicalC3×#547C2
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×#501C2semidirect
4. C3×#484C2semidirect
5. C3×#483C2semidirect
6. C3×#482C2semidirect
7. C3×#480C2semidirect
8. C3×#478C2semidirect
9. C3×#477C2semidirect
10. C3×#468C2semidirect
11. C3×#465C2semidirect
12. C3×#440C2semidirect
13. C3×#435C2semidirect
14. C3×#428C2semidirect
15. C2×C3×#107C2semidirect
16. #3343C3direct (N × H)
60. #552C2×C3semidirect
62. #501C2×C3semidirect
63. #484C2×C3semidirect
64. #483C2×C3semidirect
65. #482C2×C3semidirect
66. #480C2×C3semidirect
67. #478C2×C3semidirect
68. #477C2×C3semidirect
69. #468C2×C3semidirect
70. #465C2×C3semidirect
71. #440C2×C3semidirect
72. #435C2×C3semidirect
73. #428C2×C3semidirect
74. C2×#107C2×C3semidirect
199. C3×C8#41semidirect
304. C8C3×#41semidirect
334. C3#3343direct (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×#5472
C3×#5012
C3×#4842
C3×#4832
C3×#4822
C3×#4802
C3×#4782
C3×#4772
C3×#4682
C3×#4652
C3×#4402
C3×#4352
C3×#4282
C2×C3×#1072
#33433