Finite Group Databasebeta

← C3×#3308 #85172

Subgroups — C3×#3308 #85172

Order 384.

420 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×#548C211yesmaximal, characteristic, complemented
2C3×#547C211yesmaximal, characteristic, complemented
3C3×#489C211yesmaximal, characteristic, complemented
4C3×#484C211yesmaximal, characteristic, complemented
5C3×#480C211yesmaximal, characteristic, complemented
6C3×#477C211yesmaximal, characteristic, complemented
7C3×#468C211yesmaximal, characteristic, complemented
8C3×#466C211yesmaximal, characteristic, complemented
9C3×#463C211yesmaximal, characteristic, complemented
10C3×#449C211yesmaximal, characteristic, complemented
11C3×#448C211yesmaximal, characteristic, complemented
12C3×#440C211yesmaximal, characteristic, complemented
13C3×#435C211yesmaximal, characteristic, complemented
14C3×#417C211yesmaximal, characteristic, complemented
15C2×C3×#103C211yesmaximal, characteristic, complemented
16#3308C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#41—21no—
18C2×C3×#41C2211yescharacteristic
19C22×C3×Q8C2211yescharacteristic
20C2×C3×SD16C2211yescharacteristic
21C2×C3×SD16C2211yescharacteristic
22C2×C3×D8C2211yescharacteristic
23C2×C3×M16C2211yescharacteristic
24C22×C3×C8C2211yescharacteristic
25C3×C4⋊Q8C2211yescharacteristic
26C3×#124—21no—
27C3×#124C2211yescharacteristic
28C3×#123—21no—
29C3×#123—21no—
30C3×C22⋊Q8—21no—
31C3×C22⋊Q8—21no—
32C3×C22⋊Q8C2211yescharacteristic
33C3×#121—21no—
34C3×#121C2211yescharacteristic
35C3×#121C2211yescharacteristic
36C3×#121C2211yescharacteristic
37C3×C4×Q8C2211yescharacteristic
38C3×C4×D4—21no—
39C3×C4×D4C2211yescharacteristic
40C3×C4×D4C2211yescharacteristic
41C2×C3×C4⋊C4C2211yescharacteristic
42C2×C3×C4⋊C4C2211yescharacteristic
43C3×#107C2211yescharacteristic
44C3×#107C2211yescharacteristic
45C3×#107C2211yescharacteristic
46C3×C4⋊C8C2211yescharacteristic
47C3×#103C2211yescharacteristic
48C3×#103C2211yescharacteristic
49C3×#103C2211yescharacteristic
50C3×#103C2211yescharacteristic
51C3×#103C2211yescharacteristic
52C3×#103C2211yescharacteristic
53C3×#102C2211yescharacteristic
54C3×#102C2211yescharacteristic
55C3×#102C2211yescharacteristic
56C3×#102C2211yescharacteristic
57C3×C22⋊C8C2211yescharacteristic
58C3×C22⋊C8C2211yescharacteristic
59C3×#97C2211yescharacteristic
60#548C2×C311yescharacteristic, complemented
61#547C2×C311yescharacteristic, complemented
62#489C2×C311yescharacteristic, complemented
63#484C2×C311yescharacteristic, complemented
64#480C2×C311yescharacteristic, complemented
65#477C2×C311yescharacteristic, complemented
66#468C2×C311yescharacteristic, complemented
67#466C2×C311yescharacteristic, complemented
68#463C2×C311yescharacteristic, complemented
69#449C2×C311yescharacteristic, complemented
70#448C2×C311yescharacteristic, complemented
71#440C2×C311yescharacteristic, complemented
72#435C2×C311yescharacteristic, complemented
73#417C2×C311yescharacteristic, complemented
74C2×#103C2×C311yescharacteristic, complemented
75C3×#41—22no—
76C3×#41—41no—
77C3×#41—44no—
78C2×C3×Q8—21no—
79C2×C3×Q8—21no—
80C2×C3×Q8—22no—
81C2×C3×Q8—41no—
82C2×C3×Q8C2311yescharacteristic
83C2×C3×Q8C2311yescharacteristic
84C2×C3×D4—21no—
85C2×C3×D4—21no—
86C2×C3×D4—21no—
87C2×C3×D4—21no—
88C2×C3×D4D411yescharacteristic
89C2×C3×D4C2311yescharacteristic
90C2×C3×D4C2311yescharacteristic
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4C2311yescharacteristic
97C22×C3×C4C2311yescharacteristic
98C3×SD16—22no—
99C3×SD16—41no—
100C3×D8—41no—
101C3×M16—41no—
102C2×C3×C8—41no—
103C2×C3×C8C2311yescharacteristic
104C2×C3×C8C2311yescharacteristic
105C2×C3×C8C2311yescharacteristic
106C2×C3×C8C2311yescharacteristic
107C3×C4⋊C4—21no—
108C3×C4⋊C4—21no—
109C3×C4⋊C4—21no—
110C3×C4⋊C4—21no—
111C3×C4⋊C4—21no—
112C3×C4⋊C4D411yescharacteristic
113C3×C4⋊C4C2311yescharacteristic
114C3×C4⋊C4C2311yescharacteristic
115C3×C4⋊C4C2311yescharacteristic
116C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
124C3×C22⋊C4D411yescharacteristic
125C3×C22⋊C4D411yescharacteristic
126C3×C42—21no—
127C3×C42C2311yescharacteristic
128C2×#41—21no—
129C2×#41C22×C311yescharacteristic
130C22×Q8C22×C311yescharacteristic
131C2×SD16C22×C311yescharacteristic
132C2×SD16C22×C311yescharacteristic
133C2×D8C22×C311yescharacteristic
134C2×M16C22×C311yescharacteristic
135C22×C8C22×C311yescharacteristic
136C4⋊Q8C22×C311yescharacteristic
137#124—21no—
138#124C22×C311yescharacteristic
139#123—21no—
140#123—21no—
141C22⋊Q8—21no—
142C22⋊Q8—21no—
143C22⋊Q8C22×C311yescharacteristic
144#121—21no—
145#121C22×C311yescharacteristic
146#121C22×C311yescharacteristic
147#121C22×C311yescharacteristic
148C4×Q8C22×C311yescharacteristic
149C4×D4—21no—
150C4×D4C22×C311yescharacteristic
151C4×D4C22×C311yescharacteristic
152C2×C4⋊C4C22×C311yescharacteristic
153C2×C4⋊C4C22×C311yescharacteristic
154#107C22×C311yescharacteristic
155#107C22×C311yescharacteristic
156#107C22×C311yescharacteristic
157C4⋊C8C22×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
167#102C22×C311yescharacteristic
168C22⋊C8C22×C311yescharacteristic
169C22⋊C8C22×C311yescharacteristic
170#97C22×C311yescharacteristic
171C23×C3—21no—
172C23×C3—21no—
173C23×C3C2×D411yescharacteristic
174C23×C3C2×D411yescharacteristic
175C3×Q8—21no—
176C3×Q8—21no—
177C3×Q8—21no—
178C3×Q8—42no—
179C3×Q8—42no—
180C3×Q8#4112yescomplemented
181C3×D4—22no—
182C3×D4—21no—
183C3×D4—21no—
184C3×D4—21no—
185C3×D4—21no—
186C3×D4—42no—
187C3×D4—42no—
188C3×D4—42no—
189C3×D4—42no—
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—42no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—42no—
205C2×C3×C4C2×D411yescharacteristic
206C2×C3×C4C2×D411yescharacteristic
207C2×C3×C4C2×D411yescharacteristic
208C2×C3×C4C2×D411yescharacteristic
209C2×C3×C4C2411yescharacteristic
210C3×C8—21no—
211C3×C8—21no—
212C3×C8—21no—
213C3×C8—21no—
214#41—22no—
215#41—41no—
216#41—44no—
217C2×Q8—21no—
218C2×Q8—21no—
219C2×Q8—22no—
220C2×Q8—41no—
221C2×Q8C23×C311yescharacteristic
222C2×Q8C23×C311yescharacteristic
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—21no—
227C2×D4C3×D411yescharacteristic
228C2×D4C23×C311yescharacteristic
229C2×D4C23×C311yescharacteristic
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C23×C311yescharacteristic
236C22×C4C23×C311yescharacteristic
237SD16—22no—
238SD16—41no—
239D8—41no—
240M16—41no—
241C2×C8—41no—
242C2×C8C23×C311yescharacteristic
243C2×C8C23×C311yescharacteristic
244C2×C8C23×C311yescharacteristic
245C2×C8C23×C311yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4C3×D411yescharacteristic
252C4⋊C4C23×C311yescharacteristic
253C4⋊C4C23×C311yescharacteristic
254C4⋊C4C23×C311yescharacteristic
255C4⋊C4C23×C311yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4C3×D411yescharacteristic
264C22⋊C4C3×D411yescharacteristic
265C42—21no—
266C42C23×C311yescharacteristic
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3AGL(1,ℤ/8)12yes—
279C22×C3C22×D411yescharacteristic
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4C2×#4111yescharacteristic
291C3×C4H(5,𝔽2)11yescharacteristic
292C23—21no—
293C23—21no—
294C23C2×C3×D411yescharacteristic
295C23C2×C3×D411yescharacteristic
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—42no—
300Q8—42no—
301Q8C3×#4112yescomplemented
302D4—22no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—42no—
309D4—42no—
310D4—42no—
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—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4C2×C3×D411yescharacteristic
327C2×C4C2×C3×D411yescharacteristic
328C2×C4C2×C3×D411yescharacteristic
329C2×C4C2×C3×D411yescharacteristic
330C2×C4C24×C311yescharacteristic
331C8—21no—
332C8—21no—
333C8—21no—
334C8—21no—
335C2×C3—22no—
336C2×C3—41no—
337C2×C3—81no—
338C2×C3—81no—
339C2×C3#54611yescharacteristic
340C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
341C2×C3#57811yescharacteristic
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22C3×AGL(1,ℤ/8)12yes—
354C22C22×C3×D411yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—22no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4C2×C3×#4111yescharacteristic
366C4C3×H(5,𝔽2)11yescharacteristic
367C3#330811yescharacteristic, direct product factor, Sylow
368C2—22no—
369C2—41no—
370C2—81no—
371C2—81no—
372C2C3×#54611yescharacteristic
373C2C2×C3×AGL(1,ℤ/8)11yescharacteristic
374C2C3×#57811yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
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×#548C2semidirect
2. C3×#547C2semidirect
3. C3×#489C2semidirect
4. C3×#484C2semidirect
5. C3×#480C2semidirect
6. C3×#477C2semidirect
7. C3×#468C2semidirect
8. C3×#466C2semidirect
9. C3×#463C2semidirect
10. C3×#449C2semidirect
11. C3×#448C2semidirect
12. C3×#440C2semidirect
13. C3×#435C2semidirect
14. C3×#417C2semidirect
15. C2×C3×#103C2semidirect
16. #3308C3direct (N × H)
60. #548C2×C3semidirect
61. #547C2×C3semidirect
62. #489C2×C3semidirect
63. #484C2×C3semidirect
64. #480C2×C3semidirect
65. #477C2×C3semidirect
66. #468C2×C3semidirect
67. #466C2×C3semidirect
68. #463C2×C3semidirect
69. #449C2×C3semidirect
70. #448C2×C3semidirect
71. #440C2×C3semidirect
72. #435C2×C3semidirect
73. #417C2×C3semidirect
74. C2×#103C2×C3semidirect
180. C3×Q8#41semidirect
301. Q8C3×#41semidirect
367. C3#3308direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5482
C3×#5472
C3×#4892
C3×#4842
C3×#4802
C3×#4772
C3×#4682
C3×#4662
C3×#4632
C3×#4492
C3×#4482
C3×#4402
C3×#4352
C3×#4172
C2×C3×#1032
#33083