Finite Group Databasebeta

← C3×#3320 #85184

Subgroups — C3×#3320 #85184

Order 384.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#553C211yesmaximal, characteristic
2C3×D4×Q8C211yesmaximal, characteristic, complemented
3C3×#491C211yesmaximal, characteristic, complemented
4C3×#485C211yesmaximal, characteristic, complemented
5C3×#484C211yesmaximal, characteristic, complemented
6C3×#479C211yesmaximal, characteristic, complemented
7C3×#468C211yesmaximal, characteristic, complemented
8C3×#465C211yesmaximal, characteristic, complemented
9C3×#461C211yesmaximal, characteristic, complemented
10C3×#448C211yesmaximal, characteristic, complemented
11C3×#448C211yesmaximal, characteristic, complemented
12C3×#440C211yesmaximal, characteristic, complemented
13C3×#435C211yesmaximal, characteristic, complemented
14C3×#419C211yesmaximal, characteristic, complemented
15C2×C3×#103C211yesmaximal, characteristic, complemented
16#3320C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q8C2211yescharacteristic
18C22×C3×Q8C2211yescharacteristic
19C2×C3×SD16C2211yescharacteristic
20C2×C3×SD16C2211yescharacteristic
21C2×C3×SD16C2211yescharacteristic
22C2×C3×M16C2211yescharacteristic
23C22×C3×C8C2211yescharacteristic
24C3×C4⋊Q8—21no—
25C3×C4⋊Q8C2211yescharacteristic
26C3×#126—21no—
27C3×#125C2211yescharacteristic
28C3×#123—21no—
29C3×C22⋊Q8—21no—
30C3×C22⋊Q8—21no—
31C3×C22⋊Q8C2211yescharacteristic
32C3×C22⋊Q8C2211yescharacteristic
33C3×#121—21no—
34C3×#121C2211yescharacteristic
35C3×#121C2211yescharacteristic
36C3×C4×Q8C2211yescharacteristic
37C3×C4×D4—21no—
38C3×C4×D4—21no—
39C3×C4×D4C2211yescharacteristic
40C3×C4×D4C2211yescharacteristic
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×#103C2211yescharacteristic
55C3×#103C2211yescharacteristic
56C3×#102C2211yescharacteristic
57C3×C22⋊C8C2211yescharacteristic
58C3×C22⋊C8C2211yescharacteristic
59C3×#97C2211yescharacteristic
60#553C2×C311yescharacteristic
61D4×Q8C2×C311yescharacteristic, complemented
62#491C2×C311yescharacteristic, complemented
63#485C2×C311yescharacteristic, complemented
64#484C2×C311yescharacteristic, complemented
65#479C2×C311yescharacteristic, complemented
66#468C2×C311yescharacteristic, complemented
67#465C2×C311yescharacteristic, complemented
68#461C2×C311yescharacteristic, complemented
69#448C2×C311yescharacteristic, complemented
70#448C2×C311yescharacteristic, complemented
71#440C2×C311yescharacteristic, complemented
72#435C2×C311yescharacteristic, complemented
73#419C2×C311yescharacteristic, complemented
74C2×#103C2×C311yescharacteristic, complemented
75C2×C3×Q8—21no—
76C2×C3×Q8—21no—
77C2×C3×Q8—22no—
78C2×C3×Q8—22no—
79C2×C3×Q8—41no—
80C2×C3×Q8—41no—
81C2×C3×Q8C2311yescharacteristic
82C2×C3×Q8C2311yescharacteristic
83C2×C3×Q8C2311yescharacteristic
84C2×C3×D4—21no—
85C2×C3×D4—21no—
86C2×C3×D4D411yescharacteristic
87C2×C3×D4C2311yescharacteristic
88C22×C3×C4—21no—
89C22×C3×C4—21no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C3×SD16—22no—
95C3×SD16—41no—
96C3×SD16—41no—
97C3×M16—41no—
98C2×C3×C8—41no—
99C2×C3×C8C2311yescharacteristic
100C2×C3×C8C2311yescharacteristic
101C2×C3×C8C2311yescharacteristic
102C2×C3×C8C2311yescharacteristic
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⋊C4—21no—
110C3×C4⋊C4—21no—
111C3×C4⋊C4D411yescharacteristic
112C3×C4⋊C4C2311yescharacteristic
113C3×C4⋊C4C2311yescharacteristic
114C3×C4⋊C4C2311yescharacteristic
115C3×C4⋊C4C2311yescharacteristic
116C3×C22⋊C4—21no—
117C3×C22⋊C4—21no—
118C3×C22⋊C4—21no—
119C3×C22⋊C4—21no—
120C3×C22⋊C4—21no—
121C3×C22⋊C4—21no—
122C3×C22⋊C4D411yescharacteristic
123C3×C22⋊C4D411yescharacteristic
124C3×C42—21no—
125C3×C42—21no—
126C3×C42C2311yescharacteristic
127C22×Q8C22×C311yescharacteristic
128C22×Q8C22×C311yescharacteristic
129C2×SD16C22×C311yescharacteristic
130C2×SD16C22×C311yescharacteristic
131C2×SD16C22×C311yescharacteristic
132C2×M16C22×C311yescharacteristic
133C22×C8C22×C311yescharacteristic
134C4⋊Q8—21no—
135C4⋊Q8C22×C311yescharacteristic
136#126—21no—
137#125C22×C311yescharacteristic
138#123—21no—
139C22⋊Q8—21no—
140C22⋊Q8—21no—
141C22⋊Q8C22×C311yescharacteristic
142C22⋊Q8C22×C311yescharacteristic
143#121—21no—
144#121C22×C311yescharacteristic
145#121C22×C311yescharacteristic
146C4×Q8C22×C311yescharacteristic
147C4×D4—21no—
148C4×D4—21no—
149C4×D4C22×C311yescharacteristic
150C4×D4C22×C311yescharacteristic
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#103C22×C311yescharacteristic
165#103C22×C311yescharacteristic
166#102C22×C311yescharacteristic
167C22⋊C8C22×C311yescharacteristic
168C22⋊C8C22×C311yescharacteristic
169#97C22×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—42no—
180C3×Q8#4112yes—
181C3×D4—22no—
182C3×D4—21no—
183C3×D4—21no—
184C3×D4—42no—
185C3×D4—81no—
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—21no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4—81no—
200C2×C3×C4—81no—
201C2×C3×C4C2×D411yescharacteristic
202C2×C3×C4C2×D411yescharacteristic
203C2×C3×C4C2×D411yescharacteristic
204C2×C3×C4C2×D411yescharacteristic
205C2×C3×C4C2411yescharacteristic
206C3×C8—21no—
207C3×C8—21no—
208C3×C8—21no—
209C3×C8—21no—
210C2×Q8—21no—
211C2×Q8—21no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8C23×C311yescharacteristic
217C2×Q8C23×C311yescharacteristic
218C2×Q8C23×C311yescharacteristic
219C2×D4—21no—
220C2×D4—21no—
221C2×D4C3×D411yescharacteristic
222C2×D4C23×C311yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4C23×C311yescharacteristic
228C22×C4C23×C311yescharacteristic
229SD16—22no—
230SD16—41no—
231SD16—41no—
232M16—41no—
233C2×C8—41no—
234C2×C8C23×C311yescharacteristic
235C2×C8C23×C311yescharacteristic
236C2×C8C23×C311yescharacteristic
237C2×C8C23×C311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4C3×D411yescharacteristic
247C4⋊C4C23×C311yescharacteristic
248C4⋊C4C23×C311yescharacteristic
249C4⋊C4C23×C311yescharacteristic
250C4⋊C4C23×C311yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4C3×D411yescharacteristic
258C22⋊C4C3×D411yescharacteristic
259C42—21no—
260C42—21no—
261C42C23×C311yescharacteristic
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3#13712yes—
271C22×C3C22×D411yescharacteristic
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—22no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—41no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4C2×#4111yescharacteristic
284C3×C4H(5,𝔽2)11yescharacteristic
285C23—21no—
286C23C2×C3×D411yescharacteristic
287C23C2×C3×D411yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—42no—
295Q8C3×#4112yes—
296D4—22no—
297D4—21no—
298D4—21no—
299D4—42no—
300D4—81no—
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—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4C2×C3×D411yescharacteristic
317C2×C4C2×C3×D411yescharacteristic
318C2×C4C2×C3×D411yescharacteristic
319C2×C4C2×C3×D411yescharacteristic
320C2×C4C24×C311yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—21no—
325C2×C3—22no—
326C2×C3—41no—
327C2×C3—81no—
328C2×C3#54611yescharacteristic
329C2×C3C2×#13711yescharacteristic
330C2×C3#57711yescharacteristic
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22C3×#13712yes—
340C22C22×C3×D411yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4C2×C3×#4111yescharacteristic
353C4C3×H(5,𝔽2)11yescharacteristic
354C3#332011yescharacteristic, direct product factor, Sylow
355C2—22no—
356C2—41no—
357C2—81no—
358C2C3×#54611yescharacteristic
359C2C2×C3×#13711yescharacteristic
360C2C3×#57711yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
prime radicalC3×#553C2
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
2. C3×D4×Q8C2semidirect
3. C3×#491C2semidirect
4. C3×#485C2semidirect
5. C3×#484C2semidirect
6. C3×#479C2semidirect
7. C3×#468C2semidirect
8. C3×#465C2semidirect
9. C3×#461C2semidirect
10. C3×#448C2semidirect
11. C3×#448C2semidirect
12. C3×#440C2semidirect
13. C3×#435C2semidirect
14. C3×#419C2semidirect
15. C2×C3×#103C2semidirect
16. #3320C3direct (N × H)
61. D4×Q8C2×C3semidirect
62. #491C2×C3semidirect
63. #485C2×C3semidirect
64. #484C2×C3semidirect
65. #479C2×C3semidirect
66. #468C2×C3semidirect
67. #465C2×C3semidirect
68. #461C2×C3semidirect
69. #448C2×C3semidirect
70. #448C2×C3semidirect
71. #440C2×C3semidirect
72. #435C2×C3semidirect
73. #419C2×C3semidirect
74. C2×#103C2×C3semidirect
354. C3#3320direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5532
C3×D4×Q82
C3×#4912
C3×#4852
C3×#4842
C3×#4792
C3×#4682
C3×#4652
C3×#4612
C3×#4482
C3×#4402
C3×#4352
C3×#4192
C2×C3×#1032
#33203