Finite Group Databasebeta

← C3×#3270 #85134

Subgroups — C3×#3270 #85134

Order 384.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#137C211yesmaximal, characteristic, complemented
2C22×C3×Q16C211yesmaximal, characteristic, complemented
3C3×D4×Q8C211yesmaximal, characteristic, complemented
4C3×#548C211yesmaximal, characteristic
5C3×#497C211yesmaximal, characteristic, complemented
6C3×#470C211yesmaximal, characteristic, complemented
7C3×#465C211yesmaximal, characteristic, complemented
8C3×#464C211yesmaximal, characteristic, complemented
9C3×#462C211yesmaximal, characteristic, complemented
10C3×#452C211yesmaximal, characteristic, complemented
11C3×#451C211yesmaximal, characteristic, complemented
12C3×#451C211yesmaximal, characteristic, complemented
13C3×#448C211yesmaximal, characteristic, complemented
14C3×#441C211yesmaximal, characteristic, complemented
15C3×#435C211yesmaximal, characteristic, complemented
16#3270C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#41C2211yescharacteristic
18C22×C3×Q8C2211yescharacteristic
19C22×C3×Q8C2211yescharacteristic
20C22×C3×Q8C2211yescharacteristic
21C3×#137—24no—
22C2×C3×Q16—24no—
23C2×C3×Q16C2211yescharacteristic
24C2×C3×Q16C2211yescharacteristic
25C2×C3×Q16C2211yescharacteristic
26C2×C3×Q16C2211yescharacteristic
27C2×C3×Q16C2211yescharacteristic
28C2×C3×Q16C2211yescharacteristic
29C2×C3×SD16C2211yescharacteristic
30C2×C3×SD16C2211yescharacteristic
31C2×C3×SD16C2211yescharacteristic
32C2×C3×M16C2211yescharacteristic
33C22×C3×C8C2211yescharacteristic
34C3×C4⋊Q8—21no—
35C3×C4⋊Q8C2211yescharacteristic
36C3×#124—21no—
37C3×#124C2211yescharacteristic
38C3×C22⋊Q8—21no—
39C3×C22⋊Q8—21no—
40C3×C22⋊Q8—21no—
41C3×C22⋊Q8C2211yescharacteristic
42C3×C22⋊Q8C2211yescharacteristic
43C3×C22⋊Q8C2211yescharacteristic
44C3×#121—21no—
45C3×#121C2211yescharacteristic
46C3×C4×Q8C2211yescharacteristic
47C3×C4×Q8C2211yescharacteristic
48C3×C4×D4—21no—
49C3×C4×D4—21no—
50C3×C4×D4C2211yescharacteristic
51C3×#106C2211yescharacteristic
52C3×C4⋊C8C2211yescharacteristic
53C3×#103C2211yescharacteristic
54C3×#103C2211yescharacteristic
55C3×#103C2211yescharacteristic
56C3×#103C2211yescharacteristic
57C3×#103C2211yescharacteristic
58C3×#102C2211yescharacteristic
59C3×C22⋊C8C2211yescharacteristic
60C3×C22⋊C8C2211yescharacteristic
61C3×#97C2211yescharacteristic
62C2×#137C2×C311yescharacteristic, complemented
63C22×Q16C2×C311yescharacteristic, complemented
64D4×Q8C2×C311yescharacteristic, complemented
65#548C2×C311yescharacteristic
66#497C2×C311yescharacteristic, complemented
67#470C2×C311yescharacteristic, complemented
68#465C2×C311yescharacteristic, complemented
69#464C2×C311yescharacteristic, complemented
70#462C2×C311yescharacteristic, complemented
71#452C2×C311yescharacteristic, complemented
72#451C2×C311yescharacteristic, complemented
73#451C2×C311yescharacteristic, complemented
74#448C2×C311yescharacteristic, complemented
75#441C2×C311yescharacteristic, complemented
76#435C2×C311yescharacteristic, complemented
77C3×#41—22no—
78C3×#41—41no—
79C2×C3×Q8—21no—
80C2×C3×Q8—21no—
81C2×C3×Q8—21no—
82C2×C3×Q8—22no—
83C2×C3×Q8—22no—
84C2×C3×Q8—22no—
85C2×C3×Q8—41no—
86C2×C3×Q8—41no—
87C2×C3×Q8—41no—
88C2×C3×Q8C2311yescharacteristic
89C2×C3×Q8C2311yescharacteristic
90C2×C3×Q8C2311yescharacteristic
91C2×C3×Q8C2311yescharacteristic
92C2×C3×Q8C2311yescharacteristic
93C2×C3×D4—21no—
94C2×C3×D4—21no—
95C2×C3×D4D411yescharacteristic
96C2×C3×D4C2311yescharacteristic
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—21no—
101C22×C3×C4C2311yescharacteristic
102C22×C3×C4C2311yescharacteristic
103C3×Q16—22no—
104C3×Q16—22no—
105C3×Q16—22no—
106C3×Q16—22no—
107C3×Q16—41no—
108C3×Q16D414yescomplemented
109C3×SD16—22no—
110C3×SD16—22no—
111C3×SD16—41no—
112C3×M16—22no—
113C2×C3×C8—22no—
114C2×C3×C8C2311yescharacteristic
115C2×C3×C8C2311yescharacteristic
116C2×C3×C8C2311yescharacteristic
117C2×C3×C8C2311yescharacteristic
118C3×C4⋊C4—21no—
119C3×C4⋊C4—21no—
120C3×C4⋊C4—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4—21no—
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⋊C4D411yescharacteristic
135C3×C22⋊C4D411yescharacteristic
136C3×C42—21no—
137C3×C42—21no—
138C3×C42C2311yescharacteristic
139C2×#41C22×C311yescharacteristic
140C22×Q8C22×C311yescharacteristic
141C22×Q8C22×C311yescharacteristic
142C22×Q8C22×C311yescharacteristic
143#137—24no—
144C2×Q16—24no—
145C2×Q16C22×C311yescharacteristic
146C2×Q16C22×C311yescharacteristic
147C2×Q16C22×C311yescharacteristic
148C2×Q16C22×C311yescharacteristic
149C2×Q16C22×C311yescharacteristic
150C2×Q16C22×C311yescharacteristic
151C2×SD16C22×C311yescharacteristic
152C2×SD16C22×C311yescharacteristic
153C2×SD16C22×C311yescharacteristic
154C2×M16C22×C311yescharacteristic
155C22×C8C22×C311yescharacteristic
156C4⋊Q8—21no—
157C4⋊Q8C22×C311yescharacteristic
158#124—21no—
159#124C22×C311yescharacteristic
160C22⋊Q8—21no—
161C22⋊Q8—21no—
162C22⋊Q8—21no—
163C22⋊Q8C22×C311yescharacteristic
164C22⋊Q8C22×C311yescharacteristic
165C22⋊Q8C22×C311yescharacteristic
166#121—21no—
167#121C22×C311yescharacteristic
168C4×Q8C22×C311yescharacteristic
169C4×Q8C22×C311yescharacteristic
170C4×D4—21no—
171C4×D4—21no—
172C4×D4C22×C311yescharacteristic
173#106C22×C311yescharacteristic
174C4⋊C8C22×C311yescharacteristic
175#103C22×C311yescharacteristic
176#103C22×C311yescharacteristic
177#103C22×C311yescharacteristic
178#103C22×C311yescharacteristic
179#103C22×C311yescharacteristic
180#102C22×C311yescharacteristic
181C22⋊C8C22×C311yescharacteristic
182C22⋊C8C22×C311yescharacteristic
183#97C22×C311yescharacteristic
184C23×C3—21no—
185C23×C3C2×D411yescharacteristic
186C23×C3C2×D411yescharacteristic
187C3×Q8—21no—
188C3×Q8—21no—
189C3×Q8—21no—
190C3×Q8—21no—
191C3×Q8—21no—
192C3×Q8—21no—
193C3×Q8—21no—
194C3×Q8—21no—
195C3×Q8—42no—
196C3×Q8—42no—
197C3×Q8—42no—
198C3×Q8C2×D412yes—
199C3×Q8C2×D412yes—
200C3×D4—22no—
201C3×D4—21no—
202C3×D4—21no—
203C3×D4—42no—
204C3×D4—42no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—42no—
217C2×C3×C4—42no—
218C2×C3×C4—42no—
219C2×C3×C4—42no—
220C2×C3×C4C2×D411yescharacteristic
221C2×C3×C4C2×D411yescharacteristic
222C2×C3×C4C2×D411yescharacteristic
223C2×C3×C4C2×D411yescharacteristic
224C2×C3×C4C2411yescharacteristic
225C3×C8—21no—
226C3×C8—21no—
227C3×C8—21no—
228C3×C8C2×D412yes—
229#41—22no—
230#41—41no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8C23×C311yescharacteristic
241C2×Q8C23×C311yescharacteristic
242C2×Q8C23×C311yescharacteristic
243C2×Q8C23×C311yescharacteristic
244C2×Q8C23×C311yescharacteristic
245C2×D4—21no—
246C2×D4—21no—
247C2×D4C3×D411yescharacteristic
248C2×D4C23×C311yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C23×C311yescharacteristic
254C22×C4C23×C311yescharacteristic
255Q16—22no—
256Q16—22no—
257Q16—22no—
258Q16—22no—
259Q16—41no—
260Q16C3×D414yescomplemented
261SD16—22no—
262SD16—22no—
263SD16—41no—
264M16—22no—
265C2×C8—22no—
266C2×C8C23×C311yescharacteristic
267C2×C8C23×C311yescharacteristic
268C2×C8C23×C311yescharacteristic
269C2×C8C23×C311yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4C3×D411yescharacteristic
278C4⋊C4C23×C311yescharacteristic
279C4⋊C4C23×C311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4C3×D411yescharacteristic
287C22⋊C4C3×D411yescharacteristic
288C42—21no—
289C42—21no—
290C42C23×C311yescharacteristic
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3#13712yescomplemented
300C22×C3C22×D411yescharacteristic
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4C22×D411yescharacteristic
313C3×C4H(5,𝔽2)11yescharacteristic
314C23—21no—
315C23C2×C3×D411yescharacteristic
316C23C2×C3×D411yescharacteristic
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—42no—
326Q8—42no—
327Q8—42no—
328Q8C2×C3×D412yes—
329Q8C2×C3×D412yes—
330D4—22no—
331D4—21no—
332D4—21no—
333D4—42no—
334D4—42no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4C2×C3×D411yescharacteristic
351C2×C4C2×C3×D411yescharacteristic
352C2×C4C2×C3×D411yescharacteristic
353C2×C4C2×C3×D411yescharacteristic
354C2×C4C24×C311yescharacteristic
355C8—21no—
356C8—21no—
357C8—21no—
358C8C2×C3×D412yes—
359C2×C3—22no—
360C2×C3—41no—
361C2×C3—81no—
362C2×C3D4211yescharacteristic
363C2×C3C2×#13711yescharacteristic
364C2×C3#57811yescharacteristic
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22C3×#13712yescomplemented
374C22C22×C3×D411yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—22no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4C22×C3×D411yescharacteristic
387C4C3×H(5,𝔽2)11yescharacteristic
388C3#327011yescharacteristic, direct product factor, Sylow
389C2—22no—
390C2—41no—
391C2—81no—
392C2C3×D4211yescharacteristic
393C2C2×C3×#13711yescharacteristic
394C2C3×#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. C2×C3×#137C2semidirect
2. C22×C3×Q16C2semidirect
3. C3×D4×Q8C2semidirect
5. C3×#497C2semidirect
6. C3×#470C2semidirect
7. C3×#465C2semidirect
8. C3×#464C2semidirect
9. C3×#462C2semidirect
10. C3×#452C2semidirect
11. C3×#451C2semidirect
12. C3×#451C2semidirect
13. C3×#448C2semidirect
14. C3×#441C2semidirect
15. C3×#435C2semidirect
16. #3270C3direct (N × H)
62. C2×#137C2×C3semidirect
63. C22×Q16C2×C3semidirect
64. D4×Q8C2×C3semidirect
66. #497C2×C3semidirect
67. #470C2×C3semidirect
68. #465C2×C3semidirect
69. #464C2×C3semidirect
70. #462C2×C3semidirect
71. #452C2×C3semidirect
72. #451C2×C3semidirect
73. #451C2×C3semidirect
74. #448C2×C3semidirect
75. #441C2×C3semidirect
76. #435C2×C3semidirect
108. C3×Q16D4semidirect
260. Q16C3×D4semidirect
299. C22×C3#137semidirect
373. C22C3×#137semidirect
388. C3#3270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1372
C22×C3×Q162
C3×D4×Q82
C3×#5482
C3×#4972
C3×#4702
C3×#4652
C3×#4642
C3×#4622
C3×#4522
C3×#4512
C3×#4482
C3×#4412
C3×#4352
#32703