Finite Group Databasebeta

← C3×#3111 #84975

Subgroups — C3×#3111 #84975

Order 384.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#529C211yesmaximal, characteristic, complemented
2C3×C4×#41C211yesmaximal, characteristic, complemented
3C3×#485C211yesmaximal, characteristic, complemented
4C3×#482C211yesmaximal, characteristic, complemented
5C3×#479C211yesmaximal, characteristic, complemented
6C3×#478C211yesmaximal, characteristic, complemented
7C3×#464C211yesmaximal, characteristic, complemented
8C3×#463C211yesmaximal, characteristic, complemented
9C3×#452C211yesmaximal, characteristic, complemented
10C3×#449C211yesmaximal, characteristic
11C3×#442C211yesmaximal, characteristic, complemented
12C3×#441C211yesmaximal, characteristic, complemented
13C3×#440C211yesmaximal, characteristic, complemented
14C3×#440C211yesmaximal, characteristic, complemented
15C3×#432C211yesmaximal, characteristic, complemented
16#3111C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#41C2211yescharacteristic
18C2×C3×Q16C2211yescharacteristic
19C2×C3×SD16C2211yescharacteristic
20C2×C3×SD16C2211yescharacteristic
21C2×C3×D8C2211yescharacteristic
22C3×#126—21no—
23C3×#125C2211yescharacteristic
24C3×#124C2211yescharacteristic
25C3×#123—21no—
26C3×C22⋊Q8C2211yescharacteristic
27C3×#121C2211yescharacteristic
28C3×C4×Q8C2211yescharacteristic
29C3×C4×Q8C2211yescharacteristic
30C3×C4×Q8C2211yescharacteristic
31C3×C4×D4—21no—
32C3×C4×D4—21no—
33C3×C4×D4—21no—
34C3×C4×D4C2211yescharacteristic
35C3×C4×D4C2211yescharacteristic
36C3×C4×D4C2211yescharacteristic
37C3×#117—21no—
38C3×#117—21no—
39C3×#117C2211yescharacteristic
40C2×C3×C42—21no—
41C2×C3×C42C2211yescharacteristic
42C3×#107C2211yescharacteristic
43C3×#107C2211yescharacteristic
44C3×#106C2211yescharacteristic
45C3×#106C2211yescharacteristic
46C3×C4⋊C8C2211yescharacteristic
47C3×C4⋊C8C2211yescharacteristic
48C3×#103C2211yescharacteristic
49C3×#103C2211yescharacteristic
50C3×#103C2211yescharacteristic
51C3×#103C2211yescharacteristic
52C3×#102C2211yescharacteristic
53C3×#102C2211yescharacteristic
54C3×#102C2211yescharacteristic
55C3×#102C2211yescharacteristic
56C3×C22⋊C8C2211yescharacteristic
57C3×C22⋊C8C2211yescharacteristic
58C3×#97C2211yescharacteristic
59C3×#97C2211yescharacteristic
60#529C2×C311yescharacteristic, complemented
61C4×#41C2×C311yescharacteristic, complemented
62#485C2×C311yescharacteristic, complemented
63#482C2×C311yescharacteristic, complemented
64#479C2×C311yescharacteristic, complemented
65#478C2×C311yescharacteristic, complemented
66#464C2×C311yescharacteristic, complemented
67#463C2×C311yescharacteristic, complemented
68#452C2×C311yescharacteristic, complemented
69#449C2×C311yescharacteristic
70#442C2×C311yescharacteristic, complemented
71#441C2×C311yescharacteristic, complemented
72#440C2×C311yescharacteristic, complemented
73#440C2×C311yescharacteristic, complemented
74#432C2×C311yescharacteristic, complemented
75C3×#41—22no—
76C3×#41—22no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×Q8C2311yescharacteristic
79C2×C3×D4—21no—
80C2×C3×D4—21no—
81C2×C3×D4C2311yescharacteristic
82C2×C3×D4C2311yescharacteristic
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C22×C3×C4—21no—
86C22×C3×C4—21no—
87C22×C3×C4D411yescharacteristic
88C22×C3×C4D411yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C3×Q16—22no—
91C3×SD16—22no—
92C3×SD16—22no—
93C3×D8—22no—
94C2×C3×C8C2311yescharacteristic
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C2×C3×C8C2311yescharacteristic
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⋊C4C2311yescharacteristic
105C3×C4⋊C4C2311yescharacteristic
106C3×C4⋊C4C2311yescharacteristic
107C3×C4⋊C4C2311yescharacteristic
108C3×C22⋊C4—21no—
109C3×C22⋊C4—21no—
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×C42—21no—
117C3×C42—21no—
118C3×C42—21no—
119C3×C42—21no—
120C3×C42D411yescharacteristic
121C3×C42D411yescharacteristic
122C3×C42C2311yescharacteristic
123C3×C42C2311yescharacteristic
124C2×#41C22×C311yescharacteristic
125C2×Q16C22×C311yescharacteristic
126C2×SD16C22×C311yescharacteristic
127C2×SD16C22×C311yescharacteristic
128C2×D8C22×C311yescharacteristic
129#126—21no—
130#125C22×C311yescharacteristic
131#124C22×C311yescharacteristic
132#123—21no—
133C22⋊Q8C22×C311yescharacteristic
134#121C22×C311yescharacteristic
135C4×Q8C22×C311yescharacteristic
136C4×Q8C22×C311yescharacteristic
137C4×Q8C22×C311yescharacteristic
138C4×D4—21no—
139C4×D4—21no—
140C4×D4—21no—
141C4×D4C22×C311yescharacteristic
142C4×D4C22×C311yescharacteristic
143C4×D4C22×C311yescharacteristic
144#117—21no—
145#117—21no—
146#117C22×C311yescharacteristic
147C2×C42—21no—
148C2×C42C22×C311yescharacteristic
149#107C22×C311yescharacteristic
150#107C22×C311yescharacteristic
151#106C22×C311yescharacteristic
152#106C22×C311yescharacteristic
153C4⋊C8C22×C311yescharacteristic
154C4⋊C8C22×C311yescharacteristic
155#103C22×C311yescharacteristic
156#103C22×C311yescharacteristic
157#103C22×C311yescharacteristic
158#103C22×C311yescharacteristic
159#102C22×C311yescharacteristic
160#102C22×C311yescharacteristic
161#102C22×C311yescharacteristic
162#102C22×C311yescharacteristic
163C22⋊C8C22×C311yescharacteristic
164C22⋊C8C22×C311yescharacteristic
165#97C22×C311yescharacteristic
166#97C22×C311yescharacteristic
167C23×C3—21no—
168C23×C3—21no—
169C23×C3C2×D411yescharacteristic
170C3×Q8—21no—
171C3×Q8—21no—
172C3×Q8—21no—
173C3×Q8#4112yes—
174C3×D4—24no—
175C3×D4—21no—
176C3×D4—21no—
177C3×D4—21no—
178C3×D4—42no—
179C3×D4#4112yes—
180C2×C3×C4—24no—
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—21no—
188C2×C3×C4—21no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4—42no—
192C2×C3×C4—42no—
193C2×C3×C4—42no—
194C2×C3×C4C2×D411yescharacteristic
195C2×C3×C4C2×D411yescharacteristic
196C2×C3×C4C2×D411yescharacteristic
197C2×C3×C4C2×D411yescharacteristic
198C2×C3×C4C2×D411yescharacteristic
199C2×C3×C4C2411yescharacteristic
200C3×C8—21no—
201C3×C8—21no—
202C3×C8—21no—
203C3×C8—21no—
204#41—22no—
205#41—22no—
206C2×Q8C23×C311yescharacteristic
207C2×Q8C23×C311yescharacteristic
208C2×D4—21no—
209C2×D4—21no—
210C2×D4C23×C311yescharacteristic
211C2×D4C23×C311yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4C3×D411yescharacteristic
217C22×C4C3×D411yescharacteristic
218C22×C4C23×C311yescharacteristic
219Q16—22no—
220SD16—22no—
221SD16—22no—
222D8—22no—
223C2×C8C23×C311yescharacteristic
224C2×C8C23×C311yescharacteristic
225C2×C8C23×C311yescharacteristic
226C2×C8C23×C311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4C23×C311yescharacteristic
234C4⋊C4C23×C311yescharacteristic
235C4⋊C4C23×C311yescharacteristic
236C4⋊C4C23×C311yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—21no—
242C22⋊C4—21no—
243C22⋊C4—21no—
244C22⋊C4—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42C3×D411yescharacteristic
250C42C3×D411yescharacteristic
251C42C23×C311yescharacteristic
252C42C23×C311yescharacteristic
253C22×C3—21no—
254C22×C3—22no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3C22×D411yescharacteristic
263C3×C4—21no—
264C3×C4—22no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4C2×#4111yescharacteristic
275C3×C4C2×#4111yescharacteristic
276C23—21no—
277C23—21no—
278C23C2×C3×D411yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8C3×#4112yes—
283D4—24no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4C3×#4112yes—
289C2×C4—24no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×C3×D411yescharacteristic
304C2×C4C2×C3×D411yescharacteristic
305C2×C4C2×C3×D411yescharacteristic
306C2×C4C2×C3×D411yescharacteristic
307C2×C4C2×C3×D411yescharacteristic
308C2×C4C24×C311yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8—21no—
313C2×C3—41no—
314C2×C3—42no—
315C2×C3—81no—
316C2×C3#52511yescharacteristic
317C2×C3#57511yescharacteristic
318C2×C3#57511yescharacteristic
319C22—21no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22C22×C3×D411yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4C2×C3×#4111yescharacteristic
341C4C2×C3×#4111yescharacteristic
342C3#311111yescharacteristic, direct product factor, Sylow
343C2—41no—
344C2—42no—
345C2—81no—
346C2C3×#52511yescharacteristic
347C2C3×#57511yescharacteristic
348C2C3×#57511yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
prime radicalC3×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#529C2semidirect
2. C3×C4×#41C2semidirect
3. C3×#485C2semidirect
4. C3×#482C2semidirect
5. C3×#479C2semidirect
6. C3×#478C2semidirect
7. C3×#464C2semidirect
8. C3×#463C2semidirect
9. C3×#452C2semidirect
11. C3×#442C2semidirect
12. C3×#441C2semidirect
13. C3×#440C2semidirect
14. C3×#440C2semidirect
15. C3×#432C2semidirect
16. #3111C3direct (N × H)
60. #529C2×C3semidirect
61. C4×#41C2×C3semidirect
62. #485C2×C3semidirect
63. #482C2×C3semidirect
64. #479C2×C3semidirect
65. #478C2×C3semidirect
66. #464C2×C3semidirect
67. #463C2×C3semidirect
68. #452C2×C3semidirect
70. #442C2×C3semidirect
71. #441C2×C3semidirect
72. #440C2×C3semidirect
73. #440C2×C3semidirect
74. #432C2×C3semidirect
342. C3#3111direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5292
C3×C4×#412
C3×#4852
C3×#4822
C3×#4792
C3×#4782
C3×#4642
C3×#4632
C3×#4522
C3×#4492
C3×#4422
C3×#4412
C3×#4402
C3×#4322
#31113