Subgroups — C₃×C₄×#121 #84164

Order 384.

824 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×D₄	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#388	C₂	1	2	yes	maximal, complemented
8	C₃×#386	C₂	1	2	yes	maximal, complemented
9	C₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₄×#121	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄	C₂²	1	2	yes	—
17	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
19	C₃×#121	C₄	1	8	yes	direct product factor
20	C₃×C₄×D₄	—	2	8	no	—
21	C₃×C₄×D₄	—	2	4	no	—
22	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₄²	—	2	4	no	—
32	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄²	C₂²	1	2	yes	—
36	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
37	C₃×#95	C₂²	1	2	yes	—
38	C₃×#95	C₂²	1	2	yes	—
39	C₃×#95	C₂²	1	2	yes	—
40	C₂×#121	C₂×C₃	1	1	yes	characteristic
41	C₂×C₄×D₄	C₂×C₃	1	2	yes	complemented
42	C₂×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂²×C₄²	C₂×C₃	1	1	yes	characteristic, complemented
44	#390	C₂×C₃	1	1	yes	characteristic, complemented
45	#389	C₂×C₃	1	1	yes	characteristic, complemented
46	#388	C₂×C₃	1	2	yes	complemented
47	#386	C₂×C₃	1	2	yes	complemented
48	#380	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
50	C₄×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
51	C₂⁴×C₃	C₂³	1	2	yes	—
52	C₂⁴×C₃	C₂³	1	1	yes	characteristic
53	C₂×C₃×D₄	—	2	4	no	—
54	C₂×C₃×D₄	—	2	4	no	—
55	C₂×C₃×D₄	—	2	2	no	—
56	C₂×C₃×D₄	—	2	2	no	—
57	C₂×C₃×D₄	C₂×C₄	1	8	yes	complemented
58	C₂×C₃×D₄	C₂×C₄	1	4	yes	complemented
59	C₂²×C₃×C₄	—	2	2	no	—
60	C₂²×C₃×C₄	—	2	2	no	—
61	C₂²×C₃×C₄	—	2	2	no	—
62	C₂²×C₃×C₄	—	2	2	no	—
63	C₂²×C₃×C₄	—	2	2	no	—
64	C₂²×C₃×C₄	—	2	2	no	—
65	C₂²×C₃×C₄	—	2	2	no	—
66	C₂²×C₃×C₄	—	2	4	no	—
67	C₂²×C₃×C₄	—	2	4	no	—
68	C₂²×C₃×C₄	—	2	4	no	—
69	C₂²×C₃×C₄	C₂×C₄	1	4	yes	complemented
70	C₂²×C₃×C₄	D₄	1	4	yes	complemented
71	C₂²×C₃×C₄	C₂³	1	2	yes	—
72	C₂²×C₃×C₄	C₂³	1	2	yes	—
73	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄	C₂³	1	2	yes	—
75	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
80	C₃×C₄⋊C₄	—	2	4	no	—
81	C₃×C₄⋊C₄	—	2	2	no	—
82	C₃×C₄⋊C₄	—	2	2	no	—
83	C₃×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
84	C₃×C₂²⋊C₄	—	2	4	no	—
85	C₃×C₂²⋊C₄	—	2	4	no	—
86	C₃×C₂²⋊C₄	—	2	4	no	—
87	C₃×C₂²⋊C₄	—	2	4	no	—
88	C₃×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
89	C₃×C₄²	—	2	2	no	—
90	C₃×C₄²	—	2	2	no	—
91	C₃×C₄²	—	2	2	no	—
92	C₃×C₄²	—	2	4	no	—
93	C₃×C₄²	D₄	1	4	yes	complemented
94	C₂²×D₄	C₂²×C₃	1	2	yes	—
95	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
96	C₂³×C₄	C₂²×C₃	1	2	yes	—
97	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
99	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
100	#121	C₃×C₄	1	8	yes	direct product factor
101	C₄×D₄	—	2	8	no	—
102	C₄×D₄	—	2	4	no	—
103	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
105	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂×C₄²	—	2	4	no	—
113	C₂×C₄²	C₂²×C₃	1	2	yes	—
114	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
118	#95	C₂²×C₃	1	2	yes	—
119	#95	C₂²×C₃	1	2	yes	—
120	#95	C₂²×C₃	1	2	yes	—
121	C₂³×C₃	—	2	1	no	—
122	C₂³×C₃	—	2	1	no	—
123	C₂³×C₃	—	2	1	no	—
124	C₂³×C₃	—	2	1	no	—
125	C₂³×C₃	—	2	2	no	—
126	C₂³×C₃	—	2	2	no	—
127	C₂³×C₃	—	2	2	no	—
128	C₂³×C₃	—	2	2	no	—
129	C₂³×C₃	—	2	2	no	—
130	C₂³×C₃	—	2	2	no	—
131	C₂³×C₃	C₂²×C₄	1	4	yes	—
132	C₂³×C₃	C₂²×C₄	1	2	yes	—
133	C₂³×C₃	C₂×D₄	1	2	yes	—
134	C₂³×C₃	#41	1	2	yes	—
135	C₂³×C₃	C₂⁴	1	1	yes	characteristic
136	C₃×D₄	—	2	16	no	—
137	C₃×D₄	—	2	8	no	—
138	C₂×C₃×C₄	—	2	8	no	—
139	C₂×C₃×C₄	—	2	1	no	—
140	C₂×C₃×C₄	—	2	1	no	—
141	C₂×C₃×C₄	—	2	1	no	—
142	C₂×C₃×C₄	—	2	2	no	—
143	C₂×C₃×C₄	—	2	1	no	—
144	C₂×C₃×C₄	—	2	1	no	—
145	C₂×C₃×C₄	—	2	1	no	—
146	C₂×C₃×C₄	—	2	1	no	—
147	C₂×C₃×C₄	—	2	1	no	—
148	C₂×C₃×C₄	—	2	2	no	—
149	C₂×C₃×C₄	—	2	8	no	—
150	C₂×C₃×C₄	—	2	8	no	—
151	C₂×C₃×C₄	—	2	2	no	—
152	C₂×C₃×C₄	—	2	2	no	—
153	C₂×C₃×C₄	—	2	2	no	—
154	C₂×C₃×C₄	—	2	2	no	—
155	C₂×C₃×C₄	—	2	2	no	—
156	C₂×C₃×C₄	—	2	2	no	—
157	C₂×C₃×C₄	—	4	8	no	—
158	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
159	C₂×C₃×C₄	C₂²×C₄	1	4	yes	—
160	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
161	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
163	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
164	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
165	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
166	C₂×C₃×C₄	#41	1	2	yes	—
167	C₂×C₃×C₄	#41	1	2	yes	—
168	C₂×C₃×C₄	#41	1	2	yes	—
169	C₂⁴	C₂³×C₃	1	2	yes	—
170	C₂⁴	C₂³×C₃	1	1	yes	characteristic
171	C₂×D₄	—	2	4	no	—
172	C₂×D₄	—	2	4	no	—
173	C₂×D₄	—	2	2	no	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	C₂×C₃×C₄	1	8	yes	complemented
176	C₂×D₄	C₂×C₃×C₄	1	4	yes	complemented
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	2	4	no	—
185	C₂²×C₄	—	2	4	no	—
186	C₂²×C₄	—	2	4	no	—
187	C₂²×C₄	C₂×C₃×C₄	1	4	yes	complemented
188	C₂²×C₄	C₃×D₄	1	4	yes	complemented
189	C₂²×C₄	C₂³×C₃	1	2	yes	—
190	C₂²×C₄	C₂³×C₃	1	2	yes	—
191	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
192	C₂²×C₄	C₂³×C₃	1	2	yes	—
193	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
196	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
197	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
198	C₄⋊C₄	—	2	4	no	—
199	C₄⋊C₄	—	2	2	no	—
200	C₄⋊C₄	—	2	2	no	—
201	C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
202	C₂²⋊C₄	—	2	4	no	—
203	C₂²⋊C₄	—	2	4	no	—
204	C₂²⋊C₄	—	2	4	no	—
205	C₂²⋊C₄	—	2	4	no	—
206	C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
207	C₄²	—	2	2	no	—
208	C₄²	—	2	2	no	—
209	C₄²	—	2	2	no	—
210	C₄²	—	2	4	no	—
211	C₄²	C₃×D₄	1	4	yes	complemented
212	C₂²×C₃	—	2	2	no	—
213	C₂²×C₃	—	2	2	no	—
214	C₂²×C₃	—	2	2	no	—
215	C₂²×C₃	—	2	2	no	—
216	C₂²×C₃	—	2	2	no	—
217	C₂²×C₃	—	2	2	no	—
218	C₂²×C₃	—	2	4	no	—
219	C₂²×C₃	—	2	4	no	—
220	C₂²×C₃	—	2	4	no	—
221	C₂²×C₃	—	4	2	no	—
222	C₂²×C₃	—	4	2	no	—
223	C₂²×C₃	—	4	2	no	—
224	C₂²×C₃	—	4	2	no	—
225	C₂²×C₃	C₄×D₄	1	4	yes	complemented
226	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
227	C₂²×C₃	C₂²×D₄	1	1	yes	characteristic
228	C₂²×C₃	C₂²×D₄	1	1	yes	characteristic
229	C₂²×C₃	C₂×#41	1	1	yes	characteristic
230	C₂²×C₃	C₂×#41	1	1	yes	characteristic
231	C₂²×C₃	C₂×#41	1	1	yes	characteristic
232	C₂²×C₃	C₂×#41	1	1	yes	characteristic
233	C₃×C₄	—	2	2	no	—
234	C₃×C₄	—	2	4	no	—
235	C₃×C₄	—	2	2	no	—
236	C₃×C₄	—	2	2	no	—
237	C₃×C₄	—	2	2	no	—
238	C₃×C₄	—	4	2	no	—
239	C₃×C₄	—	4	2	no	—
240	C₃×C₄	C₄×D₄	1	4	yes	complemented
241	C₃×C₄	#121	1	4	yes	direct product factor
242	C₂³	—	2	1	no	—
243	C₂³	—	2	1	no	—
244	C₂³	—	2	1	no	—
245	C₂³	—	2	1	no	—
246	C₂³	—	2	2	no	—
247	C₂³	—	2	2	no	—
248	C₂³	—	2	2	no	—
249	C₂³	—	2	2	no	—
250	C₂³	—	2	2	no	—
251	C₂³	—	2	2	no	—
252	C₂³	C₂²×C₃×C₄	1	4	yes	—
253	C₂³	C₂²×C₃×C₄	1	2	yes	—
254	C₂³	C₂×C₃×D₄	1	2	yes	—
255	C₂³	C₃×#41	1	2	yes	—
256	C₂³	C₂⁴×C₃	1	1	yes	characteristic
257	D₄	—	2	16	no	—
258	D₄	—	2	8	no	—
259	C₂×C₄	—	2	8	no	—
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	2	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	8	no	—
271	C₂×C₄	—	2	8	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	4	8	no	—
279	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
280	C₂×C₄	C₂²×C₃×C₄	1	4	yes	—
281	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
282	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
283	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
284	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
285	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
286	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
287	C₂×C₄	C₃×#41	1	2	yes	—
288	C₂×C₄	C₃×#41	1	2	yes	—
289	C₂×C₄	C₃×#41	1	2	yes	—
290	C₂×C₃	—	2	4	no	—
291	C₂×C₃	—	4	4	no	—
292	C₂×C₃	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂×C₃	C₂×C₄×D₄	1	1	yes	characteristic
294	C₂×C₃	C₄×#41	1	1	yes	characteristic
295	C₂×C₃	C₂×#121	1	1	yes	characteristic
296	C₂×C₃	#525	1	1	yes	characteristic
297	C₂×C₃	#529	1	1	yes	characteristic
298	C₂×C₃	#532	1	1	yes	characteristic
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	2	no	—
302	C₂²	—	2	2	no	—
303	C₂²	—	2	2	no	—
304	C₂²	—	2	2	no	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	4	2	no	—
309	C₂²	—	4	2	no	—
310	C₂²	—	4	2	no	—
311	C₂²	—	4	2	no	—
312	C₂²	C₃×C₄×D₄	1	4	yes	complemented
313	C₂²	C₂³×C₃×C₄	1	1	yes	characteristic
314	C₂²	C₂²×C₃×D₄	1	1	yes	characteristic
315	C₂²	C₂²×C₃×D₄	1	1	yes	characteristic
316	C₂²	C₂×C₃×#41	1	1	yes	characteristic
317	C₂²	C₂×C₃×#41	1	1	yes	characteristic
318	C₂²	C₂×C₃×#41	1	1	yes	characteristic
319	C₂²	C₂×C₃×#41	1	1	yes	characteristic
320	C₄	—	2	2	no	—
321	C₄	—	2	4	no	—
322	C₄	—	2	2	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	4	2	no	—
326	C₄	—	4	2	no	—
327	C₄	C₃×C₄×D₄	1	4	yes	complemented
328	C₄	C₃×#121	1	4	yes	direct product factor
329	C₃	C₄×#121	1	1	yes	characteristic, direct product factor, Sylow
330	C₂	—	2	4	no	—
331	C₂	—	4	4	no	—
332	C₂	C₂×C₃×C₄×D₄	1	1	yes	characteristic
333	C₂	C₂×C₃×C₄×D₄	1	1	yes	characteristic
334	C₂	C₃×C₄×#41	1	1	yes	characteristic
335	C₂	C₂×C₃×#121	1	1	yes	characteristic
336	C₂	C₃×#525	1	1	yes	characteristic
337	C₂	C₃×#529	1	1	yes	characteristic
338	C₂	C₃×#532	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂³
commutator	C₂²	C₂³×C₃×C₄
Frattini, cosocle	C₂³	C₂⁴×C₃
socle	C₂³×C₃	C₂⁴
prime radical	C₂×C₃×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×D₄	C₂	semidirect
3. C₂×C₃×C₄×D₄	C₂	semidirect
4. C₂²×C₃×C₄²	C₂	semidirect
5. C₃×#390	C₂	semidirect
6. C₃×#389	C₂	semidirect
7. C₃×#388	C₂	semidirect
8. C₃×#386	C₂	semidirect
9. C₃×#380	C₂	semidirect
10. C₃×C₄×C₄⋊C₄	C₂	semidirect
11. C₃×C₄×C₂²⋊C₄	C₂	semidirect
12. C₄×#121	C₃	direct (N × H)
19. C₃×#121	C₄	direct (N × H)
41. C₂×C₄×D₄	C₂×C₃	semidirect
42. C₂×C₄×D₄	C₂×C₃	semidirect
43. C₂²×C₄²	C₂×C₃	semidirect
44. #390	C₂×C₃	semidirect
45. #389	C₂×C₃	semidirect
46. #388	C₂×C₃	semidirect
47. #386	C₂×C₃	semidirect
48. #380	C₂×C₃	semidirect
49. C₄×C₄⋊C₄	C₂×C₃	semidirect
50. C₄×C₂²⋊C₄	C₂×C₃	semidirect
57. C₂×C₃×D₄	C₂×C₄	semidirect
58. C₂×C₃×D₄	C₂×C₄	semidirect
69. C₂²×C₃×C₄	C₂×C₄	semidirect
70. C₂²×C₃×C₄	D₄	semidirect
83. C₃×C₄⋊C₄	C₂×C₄	semidirect
88. C₃×C₂²⋊C₄	C₂×C₄	semidirect
93. C₃×C₄²	D₄	semidirect
100. #121	C₃×C₄	direct (N × H)
175. C₂×D₄	C₂×C₃×C₄	semidirect
176. C₂×D₄	C₂×C₃×C₄	semidirect
187. C₂²×C₄	C₂×C₃×C₄	semidirect
188. C₂²×C₄	C₃×D₄	semidirect
201. C₄⋊C₄	C₂×C₃×C₄	semidirect
206. C₂²⋊C₄	C₂×C₃×C₄	semidirect
211. C₄²	C₃×D₄	semidirect
225. C₂²×C₃	C₄×D₄	semidirect
240. C₃×C₄	C₄×D₄	semidirect
241. C₃×C₄	#121	direct (N × H)
312. C₂²	C₃×C₄×D₄	semidirect
327. C₄	C₃×C₄×D₄	semidirect
328. C₄	C₃×#121	direct (N × H)
329. C₃	C₄×#121	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#121	2
C₂×C₃×C₄×D₄	2
C₂²×C₃×C₄²	2
C₃×#390	2
C₃×#389	2
C₃×#388	2
C₃×#386	2
C₃×#380	2
C₃×C₄×C₄⋊C₄	2
C₃×C₄×C₂²⋊C₄	2
C₄×#121	3

Subgroups — C3×C4×#121 #84164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#121 #84164