Subgroups — C₃×#69484 #11790029

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal
4	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₃×#4524	C₂	1	2	yes	maximal
6	C₃×#1939	—	3	1	no	maximal
7	#69484	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃²×C₄⋊C₄	C₄	1	1	yes	characteristic
9	C₂×C₃²×C₄⋊C₄	C₄	1	1	yes	characteristic
10	C₂×C₃²×C₄²	C₂²	1	2	yes	—
11	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
13	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₃²×#95	C₄	1	2	yes	—
16	C₃×C₄⋊(C₃⋊C₈)	—	2	2	no	—
17	C₃×C₄⋊(C₃⋊C₈)	—	2	4	no	—
18	C₃×C₄×C₃⋊C₈	—	2	2	no	—
19	C₂×C₃×C₄⋊C₈	—	3	2	no	—
20	C₂×C₃×C₄⋊C₈	—	3	1	no	—
21	C₂×C₃×C₄×C₈	—	3	1	no	—
22	C₃×C₄×C₄⋊C₄	—	2	1	no	—
23	C₃×C₄×C₄⋊C₄	D₃	1	1	yes	characteristic
24	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
25	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic
26	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	2	yes	—
27	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
28	C₃×#336	—	3	2	no	—
29	#4524	C₂×C₃	1	2	yes	—
30	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
31	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
33	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
35	C₃²×C₄⋊C₄	—	2	2	no	—
36	C₃²×C₄⋊C₄	C₈	1	4	yes	complemented
37	C₃²×C₄²	—	2	2	no	—
38	C₃²×C₄²	—	2	2	no	—
39	C₃²×C₄²	D₄	1	2	yes	—
40	C₃²×C₄²	Q₈	1	2	yes	—
41	C₂×C₃×C₃⋊C₈	—	2	1	no	—
42	C₂×C₃×C₃⋊C₈	—	2	1	no	—
43	C₂×C₃×C₃⋊C₈	—	2	1	no	—
44	C₂×C₃×C₃⋊C₈	—	2	1	no	—
45	C₂×C₃×C₃⋊C₈	—	2	2	no	—
46	C₂×C₃×C₃⋊C₈	—	2	2	no	—
47	C₂×C₃×C₃⋊C₈	—	2	2	no	—
48	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
49	C₂×C₃×C₃⋊C₈	Q₈	1	2	yes	—
50	#1939	—	3	1	no	Sylow
51	C₂²×C₃×C₈	—	3	1	no	—
52	C₂²×C₃×C₈	—	3	1	no	—
53	C₂²×C₃×C₈	—	3	2	no	—
54	C₂×C₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₃×C₄⋊C₄	Dic₃	1	1	yes	characteristic
57	C₂×C₃×C₄⋊C₄	Dic₃	1	1	yes	characteristic
58	C₂×C₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄²	—	2	1	no	—
61	C₂×C₃×C₄²	—	2	2	no	—
62	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
63	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
64	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
65	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
67	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
69	C₃×C₄⋊C₈	—	6	4	no	—
70	C₃×C₄⋊C₈	—	6	2	no	—
71	C₃×C₄×C₈	—	6	2	no	—
72	C₃×#95	—	2	2	no	—
73	C₃×#95	Dic₃	1	2	yes	—
74	C₃×#95	C₃×C₄	1	2	yes	—
75	C₄⋊(C₃⋊C₈)	—	2	2	no	—
76	C₄⋊(C₃⋊C₈)	—	2	4	no	—
77	C₄×C₃⋊C₈	—	2	2	no	—
78	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₃²×C₄	—	2	2	no	—
80	C₂×C₃²×C₄	—	2	2	no	—
81	C₂×C₃²×C₄	—	2	1	no	—
82	C₂×C₃²×C₄	—	2	1	no	—
83	C₂×C₃²×C₄	—	2	2	no	—
84	C₂×C₃²×C₄	—	2	2	no	—
85	C₂×C₃²×C₄	—	2	2	no	—
86	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
87	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
88	C₂×C₃²×C₄	C₂×C₈	1	4	yes	—
89	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
90	C₂×C₃²×C₄	M₁₆	1	2	yes	—
91	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
94	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₃²×C₄	#41	1	1	yes	characteristic
96	C₂×C₃²×C₄	#41	1	1	yes	characteristic
97	C₃×C₃⋊C₈	—	2	2	no	—
98	C₃×C₃⋊C₈	—	2	2	no	—
99	C₃×C₃⋊C₈	—	4	2	no	—
100	C₂×C₄⋊C₈	—	3	2	no	—
101	C₂×C₄⋊C₈	—	3	1	no	—
102	C₂×C₄×C₈	—	3	1	no	—
103	C₄×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
104	#336	—	3	2	no	—
105	C₂²×C₃×C₄	—	2	1	no	—
106	C₂²×C₃×C₄	—	2	1	no	—
107	C₂²×C₃×C₄	—	2	2	no	—
108	C₂²×C₃×C₄	—	2	2	no	—
109	C₂²×C₃×C₄	—	2	1	no	—
110	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
111	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
112	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
113	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
114	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
115	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
116	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
117	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
118	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
119	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
120	C₂×C₃×C₈	—	3	2	no	—
121	C₂×C₃×C₈	—	3	2	no	—
122	C₂×C₃×C₈	—	6	1	no	—
123	C₂×C₃×C₈	—	6	1	no	—
124	C₂×C₃×C₈	—	6	1	no	—
125	C₂×C₃×C₈	—	6	1	no	—
126	C₂×C₃×C₈	—	6	2	no	—
127	C₂×C₃×C₈	—	6	2	no	—
128	C₂×C₃×C₈	—	6	2	no	—
129	C₃×C₄⋊C₄	—	2	4	no	—
130	C₃×C₄⋊C₄	—	2	2	no	—
131	C₃×C₄⋊C₄	—	2	2	no	—
132	C₃×C₄⋊C₄	—	2	4	no	—
133	C₃×C₄⋊C₄	C₃⋊C₈	1	4	yes	complemented
134	C₃×C₄⋊C₄	C₃×C₈	1	4	yes	complemented
135	C₃×C₄²	—	2	2	no	—
136	C₃×C₄²	—	2	2	no	—
137	C₃×C₄²	—	2	2	no	—
138	C₃×C₄²	—	2	2	no	—
139	C₃×C₄²	—	2	2	no	—
140	C₃×C₄²	—	2	2	no	—
141	C₃×C₄²	—	4	2	no	—
142	C₃×C₄²	—	4	2	no	—
143	C₃×C₄²	Dic₆	1	2	yes	—
144	C₃×C₄²	D₁₂	1	2	yes	—
145	C₃×C₄²	C₃×D₄	1	2	yes	—
146	C₃×C₄²	C₃×Q₈	1	2	yes	—
147	C₂×C₃⋊C₈	—	2	1	no	—
148	C₂×C₃⋊C₈	—	2	1	no	—
149	C₂×C₃⋊C₈	—	2	1	no	—
150	C₂×C₃⋊C₈	—	2	1	no	—
151	C₂×C₃⋊C₈	—	2	2	no	—
152	C₂×C₃⋊C₈	—	2	2	no	—
153	C₂×C₃⋊C₈	—	2	2	no	—
154	C₂×C₃⋊C₈	C₃×D₄	1	2	yes	—
155	C₂×C₃⋊C₈	C₃×Q₈	1	2	yes	—
156	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
158	C₂²×C₃²	C₄×Q₈	1	1	yes	characteristic
159	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
160	C₂²×C₃²	C₂×M₁₆	1	1	yes	characteristic
161	C₂²×C₃²	#131	1	1	yes	characteristic
162	C₂²×C₃²	#131	1	1	yes	characteristic
163	C₃²×C₄	—	2	2	no	—
164	C₃²×C₄	—	2	4	no	—
165	C₃²×C₄	—	4	2	no	—
166	C₃²×C₄	C₄⋊C₈	1	4	yes	complemented
167	C₃²×C₄	#121	1	1	yes	characteristic
168	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
169	C₃²×C₄	#125	1	1	yes	characteristic
170	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
171	C₂²×C₈	—	3	1	no	—
172	C₂²×C₈	—	3	1	no	—
173	C₂²×C₈	—	3	2	no	—
174	C₂×C₄⋊C₄	C₃×Dic₃	1	1	yes	characteristic
175	C₂×C₄⋊C₄	C₃×Dic₃	1	1	yes	characteristic
176	C₂×C₄²	C₂×C₃×D₃	1	2	yes	—
177	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
178	C₄⋊C₈	—	6	4	no	—
179	C₄⋊C₈	—	6	2	no	—
180	C₄×C₈	—	6	2	no	—
181	#95	C₃×Dic₃	1	2	yes	—
182	C₂³×C₃	—	2	1	no	—
183	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
184	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
185	C₂×C₃×C₄	—	2	2	no	—
186	C₂×C₃×C₄	—	2	1	no	—
187	C₂×C₃×C₄	—	2	1	no	—
188	C₂×C₃×C₄	—	2	2	no	—
189	C₂×C₃×C₄	—	2	2	no	—
190	C₂×C₃×C₄	—	2	1	no	—
191	C₂×C₃×C₄	—	2	1	no	—
192	C₂×C₃×C₄	—	2	2	no	—
193	C₂×C₃×C₄	—	2	4	no	—
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	2	no	—
197	C₂×C₃×C₄	—	2	2	no	—
198	C₂×C₃×C₄	—	2	2	no	—
199	C₂×C₃×C₄	—	2	2	no	—
200	C₂×C₃×C₄	—	2	2	no	—
201	C₂×C₃×C₄	—	2	4	no	—
202	C₂×C₃×C₄	—	2	2	no	—
203	C₂×C₃×C₄	—	2	2	no	—
204	C₂×C₃×C₄	—	2	2	no	—
205	C₂×C₃×C₄	—	2	1	no	—
206	C₂×C₃×C₄	—	2	1	no	—
207	C₂×C₃×C₄	—	2	1	no	—
208	C₂×C₃×C₄	—	2	1	no	—
209	C₂×C₃×C₄	—	2	1	no	—
210	C₂×C₃×C₄	—	2	1	no	—
211	C₂×C₃×C₄	—	4	2	no	—
212	C₂×C₃×C₄	—	4	2	no	—
213	C₂×C₃×C₄	—	4	1	no	—
214	C₂×C₃×C₄	—	4	1	no	—
215	C₂×C₃×C₄	—	4	2	no	—
216	C₂×C₃×C₄	—	4	2	no	—
217	C₂×C₃×C₄	C₂×C₃⋊C₈	1	4	yes	—
218	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
219	C₂×C₃×C₄	#208	1	2	yes	—
220	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
221	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
222	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
223	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
224	C₂×C₃×C₄	C₂×C₃×C₈	1	4	yes	—
225	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
226	C₂×C₃×C₄	C₃×M₁₆	1	2	yes	—
227	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
229	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄	#237	1	1	yes	characteristic
231	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
232	C₂×C₃×C₄	#239	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
237	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
238	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
239	C₃×C₈	—	6	2	no	—
240	C₃×C₈	—	6	2	no	—
241	C₃×C₈	—	12	2	no	—
242	C₃⋊C₈	—	2	2	no	—
243	C₃⋊C₈	—	2	2	no	—
244	C₃⋊C₈	—	4	2	no	—
245	C₂×C₃²	#389	1	1	yes	characteristic
246	C₂×C₃²	C₂×C₄⋊C₈	1	1	yes	characteristic
247	C₂×C₃²	#424	1	1	yes	characteristic
248	C₂×C₃²	C₈×D₄	1	1	yes	characteristic
249	C₂×C₃²	#436	1	1	yes	characteristic
250	C₂×C₃²	C₈×Q₈	1	1	yes	characteristic
251	C₂×C₃²	#446	1	1	yes	characteristic
252	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
253	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
254	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
255	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
257	C₂×C₈	—	3	2	no	—
258	C₂×C₈	—	3	2	no	—
259	C₂×C₈	—	6	1	no	—
260	C₂×C₈	—	6	1	no	—
261	C₂×C₈	—	6	1	no	—
262	C₂×C₈	—	6	1	no	—
263	C₂×C₈	—	6	2	no	—
264	C₂×C₈	—	6	2	no	—
265	C₂×C₈	—	6	2	no	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	C₃×C₃⋊C₈	1	4	yes	complemented
268	C₄²	—	2	2	no	—
269	C₄²	—	2	2	no	—
270	C₄²	C₃×Dic₆	1	2	yes	—
271	C₄²	C₃×D₁₂	1	2	yes	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	—	2	1	no	—
279	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
280	C₂²×C₃	C₂×#208	1	1	yes	characteristic
281	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
282	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
283	C₂²×C₃	Q₈×Dic₃	1	1	yes	characteristic
284	C₂²×C₃	#948	1	1	yes	characteristic
285	C₂²×C₃	#948	1	1	yes	characteristic
286	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
287	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
288	C₂²×C₃	C₃×C₄×Q₈	1	1	yes	characteristic
289	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
290	C₂²×C₃	C₂×C₃×M₁₆	1	1	yes	characteristic
291	C₂²×C₃	C₃×#131	1	1	yes	characteristic
292	C₂²×C₃	C₃×#131	1	1	yes	characteristic
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	—	2	4	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	1	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	4	no	—
302	C₃×C₄	—	4	2	no	—
303	C₃×C₄	—	4	4	no	—
304	C₃×C₄	—	4	4	no	—
305	C₃×C₄	—	4	2	no	—
306	C₃×C₄	—	4	2	no	—
307	C₃×C₄	C₄⋊(C₃⋊C₈)	1	4	yes	complemented
308	C₃×C₄	C₃×C₄⋊C₈	1	4	yes	complemented
309	C₃×C₄	#888	1	1	yes	characteristic
310	C₃×C₄	#890	1	1	yes	characteristic
311	C₃×C₄	#895	1	1	yes	characteristic
312	C₃×C₄	#897	1	1	yes	characteristic
313	C₃×C₄	C₃×#121	1	1	yes	characteristic
314	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
315	C₃×C₄	C₃×#125	1	1	yes	characteristic
316	C₃×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
317	C₃²	#1939	1	1	yes	characteristic, complemented, Sylow
318	C₂³	C₂²×C₃×Dic₃	1	1	yes	characteristic
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	C₂×C₃×C₃⋊C₈	1	4	yes	—
327	C₂×C₄	C₂×C₃×C₃⋊C₈	1	2	yes	—
328	C₂×C₄	C₃×#208	1	2	yes	—
329	C₂×C₄	C₃×C₄⋊Dic₃	1	2	yes	—
330	C₂×C₄	C₃×C₄⋊Dic₃	1	2	yes	—
331	C₂×C₄	C₂×C₃×Dic₆	1	1	yes	characteristic
332	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
333	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
334	C₂×C₄	C₃×#237	1	1	yes	characteristic
335	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
336	C₂×C₄	C₃×#239	1	1	yes	characteristic
337	C₈	—	6	2	no	—
338	C₈	—	6	2	no	—
339	C₈	—	12	2	no	—
340	C₂×C₃	—	2	1	no	—
341	C₂×C₃	—	2	1	no	—
342	C₂×C₃	—	2	1	no	—
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	C₂×C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
348	C₂×C₃	#4984	1	1	yes	characteristic
349	C₂×C₃	#4999	1	1	yes	characteristic
350	C₂×C₃	D₄×C₃⋊C₈	1	1	yes	characteristic
351	C₂×C₃	#5012	1	1	yes	characteristic
352	C₂×C₃	Q₈×C₃⋊C₈	1	1	yes	characteristic
353	C₂×C₃	#5024	1	1	yes	characteristic
354	C₂×C₃	C₃×#389	1	1	yes	characteristic
355	C₂×C₃	C₂×C₃×C₄⋊C₈	1	1	yes	characteristic
356	C₂×C₃	C₃×#424	1	1	yes	characteristic
357	C₂×C₃	C₃×C₈×D₄	1	1	yes	characteristic
358	C₂×C₃	C₃×#436	1	1	yes	characteristic
359	C₂×C₃	C₃×C₈×Q₈	1	1	yes	characteristic
360	C₂×C₃	C₃×#446	1	1	yes	characteristic
361	C₂²	C₂²×C₃×C₃⋊C₈	1	1	yes	characteristic
362	C₂²	C₂×C₃×#208	1	1	yes	characteristic
363	C₂²	C₂×C₃×C₄⋊Dic₃	1	1	yes	characteristic
364	C₂²	C₃×D₄×Dic₃	1	1	yes	characteristic
365	C₂²	C₃×Q₈×Dic₃	1	1	yes	characteristic
366	C₂²	C₃×#948	1	1	yes	characteristic
367	C₂²	C₃×#948	1	1	yes	characteristic
368	C₄	—	2	2	no	—
369	C₄	—	2	4	no	—
370	C₄	—	4	2	no	—
371	C₄	C₃×C₄⋊(C₃⋊C₈)	1	4	yes	complemented
372	C₄	C₃×#888	1	1	yes	characteristic
373	C₄	C₃×#890	1	1	yes	characteristic
374	C₄	C₃×#895	1	1	yes	characteristic
375	C₄	C₃×#897	1	1	yes	characteristic
376	C₃	—	2	1	no	—
377	C₃	#69484	1	1	yes	characteristic, direct product factor
378	C₃	C₃×#1939	1	1	yes	characteristic, complemented
379	C₂	C₂×C₃×C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
380	C₂	C₃×#4984	1	1	yes	characteristic
381	C₂	C₃×#4999	1	1	yes	characteristic
382	C₂	C₃×D₄×C₃⋊C₈	1	1	yes	characteristic
383	C₂	C₃×#5012	1	1	yes	characteristic
384	C₂	C₃×Q₈×C₃⋊C₈	1	1	yes	characteristic
385	C₂	C₃×#5024	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₃×C₈
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×C₄×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₃
hypocenter	C₃	C₃×#1939
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
7. #69484	C₃	direct (N × H)
36. C₃²×C₄⋊C₄	C₈	semidirect
133. C₃×C₄⋊C₄	C₃⋊C₈	semidirect
134. C₃×C₄⋊C₄	C₃×C₈	semidirect
166. C₃²×C₄	C₄⋊C₈	semidirect
267. C₄⋊C₄	C₃×C₃⋊C₈	semidirect
307. C₃×C₄	C₄⋊(C₃⋊C₈)	semidirect
308. C₃×C₄	C₃×C₄⋊C₈	semidirect
317. C₃²	#1939	semidirect
371. C₄	C₃×C₄⋊(C₃⋊C₈)	semidirect
377. C₃	#69484	direct (N × H)
378. C₃	C₃×#1939	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄×C₄⋊C₄	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₂×C₃×C₄×C₃⋊C₈	2
C₃×#4524	2
C₃×#1939	3
#69484	3

Subgroups — C3×#69484 #11790029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69484 #11790029