Subgroups — C₃×#67702 #11771080

Order 1152.

445 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#4935	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₃×#1296	—	3	1	no	maximal
5	#67702	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃²×C₈	—	2	1	no	—
7	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
9	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
10	C₂×C₃×C₄⋊Dic₃	C₄	1	2	yes	—
11	C₂²×C₃×C₃⋊C₈	—	2	1	no	—
12	C₃²×C₄⋊C₈	—	2	1	no	—
13	C₃²×C₄⋊C₈	C₄	1	2	yes	complemented
14	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
15	C₃×C₄⋊(C₃⋊C₈)	C₄	1	2	yes	complemented
16	C₂×C₃×C₄⋊C₈	—	2	1	no	—
17	C₂×C₃×C₄⋊C₈	—	3	1	no	—
18	C₂×C₃×C₄⋊C₈	D₃	1	1	yes	characteristic
19	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
20	C₃×#384	—	3	1	no	—
21	#4935	C₂×C₃	1	1	yes	characteristic
22	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
25	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
26	C₂²×C₃×Dic₃	—	2	2	no	—
27	C₂×C₃²×C₈	—	2	2	no	—
28	C₂×C₃²×C₈	—	4	1	no	—
29	C₂×C₃²×C₈	—	4	1	no	—
30	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
31	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
32	C₃²×C₄²	D₄	1	1	yes	characteristic
33	C₃²×C₄²	Q₈	1	1	yes	characteristic
34	C₃×C₄⋊Dic₃	—	4	1	no	—
35	C₃×C₄⋊Dic₃	—	4	1	no	—
36	C₃×C₄⋊Dic₃	—	4	1	no	—
37	C₃×C₄⋊Dic₃	—	4	1	no	—
38	C₃×C₄⋊Dic₃	—	4	2	no	—
39	C₂×C₃×C₃⋊C₈	—	2	2	no	—
40	C₂×C₃×C₃⋊C₈	—	4	1	no	—
41	C₂×C₃×C₃⋊C₈	—	4	1	no	—
42	#1296	—	3	1	no	Sylow
43	C₂²×C₃×C₈	—	2	2	no	—
44	C₂²×C₃×C₈	—	2	1	no	—
45	C₂²×C₃×C₈	—	2	1	no	—
46	C₂²×C₃×C₈	—	6	1	no	—
47	C₂×C₃×C₄⋊C₄	—	3	2	no	—
48	C₂×C₃×C₄⋊C₄	—	6	1	no	—
49	C₂×C₃×C₄⋊C₄	—	6	1	no	—
50	C₂×C₃×C₄²	—	2	1	no	—
51	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
52	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
53	C₂×C₄⋊Dic₃	—	2	1	no	—
54	C₂×C₄⋊Dic₃	—	2	1	no	—
55	C₂×C₄⋊Dic₃	C₃×C₄	1	2	yes	—
56	C₂²×C₃⋊C₈	—	2	1	no	—
57	C₃×C₄⋊C₈	—	2	2	no	—
58	C₃×C₄⋊C₈	—	2	1	no	—
59	C₃×C₄⋊C₈	—	2	1	no	—
60	C₃×C₄⋊C₈	—	2	2	no	—
61	C₃×C₄⋊C₈	—	3	2	no	—
62	C₃×C₄⋊C₈	—	6	1	no	—
63	C₃×C₄⋊C₈	Dic₃	1	2	yes	complemented
64	C₃×C₄⋊C₈	C₃×C₄	1	2	yes	complemented
65	C₄⋊(C₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₃⋊C₈)	C₃×C₄	1	2	yes	complemented
67	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₃²×C₄	—	2	1	no	—
69	C₂×C₃²×C₄	—	2	1	no	—
70	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
71	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
74	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
77	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
78	C₂×C₃²×C₄	SD₁₆	1	1	yes	characteristic
79	C₂×C₃²×C₄	SD₁₆	1	1	yes	characteristic
80	C₂×C₃²×C₄	SD₁₆	1	1	yes	characteristic
81	C₂×C₃²×C₄	SD₁₆	1	1	yes	characteristic
82	C₂×C₃²×C₄	Q₁₆	1	1	yes	characteristic
83	C₂×C₃²×C₄	Q₁₆	1	1	yes	characteristic
84	C₂×C₃×Dic₃	—	4	2	no	—
85	C₂×C₃×Dic₃	—	4	2	no	—
86	C₂×C₃×Dic₃	—	4	2	no	—
87	C₃²×C₈	—	4	2	no	—
88	C₃×C₃⋊C₈	—	4	2	no	—
89	C₂×C₄⋊C₈	—	3	1	no	—
90	C₂×C₄⋊C₈	C₃×D₃	1	1	yes	characteristic
91	#384	—	3	1	no	—
92	C₂²×C₃×C₄	—	2	1	no	—
93	C₂²×C₃×C₄	—	2	1	no	—
94	C₂²×C₃×C₄	—	2	1	no	—
95	C₂²×C₃×C₄	—	6	2	no	—
96	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
97	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
98	C₂²×C₃×C₄	#67	1	1	yes	characteristic
99	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
100	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
101	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
102	C₂²×Dic₃	—	2	2	no	—
103	C₂×C₃×C₈	—	2	4	no	—
104	C₂×C₃×C₈	—	2	2	no	—
105	C₂×C₃×C₈	—	2	2	no	—
106	C₂×C₃×C₈	—	4	2	no	—
107	C₂×C₃×C₈	—	4	2	no	—
108	C₂×C₃×C₈	—	4	1	no	—
109	C₂×C₃×C₈	—	4	1	no	—
110	C₂×C₃×C₈	—	4	1	no	—
111	C₂×C₃×C₈	—	4	1	no	—
112	C₂×C₃×C₈	—	6	2	no	—
113	C₂×C₃×C₈	—	12	1	no	—
114	C₂×C₃×C₈	—	12	1	no	—
115	C₃×C₄⋊C₄	—	12	2	no	—
116	C₃×C₄⋊C₄	—	12	1	no	—
117	C₃×C₄⋊C₄	—	12	1	no	—
118	C₃×C₄⋊C₄	—	12	1	no	—
119	C₃×C₄⋊C₄	—	12	1	no	—
120	C₃×C₄²	—	2	1	no	—
121	C₃×C₄²	—	2	1	no	—
122	C₃×C₄²	—	2	1	no	—
123	C₃×C₄²	—	2	1	no	—
124	C₃×C₄²	Dic₆	1	1	yes	characteristic
125	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
126	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
127	C₃×C₄²	#67	1	1	yes	characteristic
128	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
129	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
130	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
131	C₃×C₄²	C₃×Q₈	1	1	yes	characteristic
132	C₄⋊Dic₃	—	4	1	no	—
133	C₄⋊Dic₃	—	4	1	no	—
134	C₄⋊Dic₃	—	4	1	no	—
135	C₄⋊Dic₃	—	4	1	no	—
136	C₄⋊Dic₃	—	4	2	no	—
137	C₂×C₃⋊C₈	—	2	2	no	—
138	C₂×C₃⋊C₈	—	4	1	no	—
139	C₂×C₃⋊C₈	—	4	1	no	—
140	C₂²×C₃²	#95	1	1	yes	characteristic
141	C₂²×C₃²	#100	1	1	yes	characteristic
142	C₂²×C₃²	#101	1	1	yes	characteristic
143	C₂²×C₃²	#102	1	1	yes	characteristic
144	C₂²×C₃²	#102	1	1	yes	characteristic
145	C₂²×C₃²	#103	1	1	yes	characteristic
146	C₂²×C₃²	#103	1	1	yes	characteristic
147	C₃²×C₄	—	2	1	no	—
148	C₃²×C₄	—	2	1	no	—
149	C₃²×C₄	#102	1	1	yes	characteristic
150	C₃²×C₄	#102	1	1	yes	characteristic
151	C₃²×C₄	#103	1	1	yes	characteristic
152	C₃²×C₄	#103	1	1	yes	characteristic
153	C₃²×C₄	#106	1	1	yes	characteristic
154	C₃²×C₄	#106	1	1	yes	characteristic
155	C₃²×C₄	#107	1	1	yes	characteristic
156	C₃²×C₄	#107	1	1	yes	characteristic
157	C₃×Dic₃	—	8	2	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	6	1	no	—
160	C₂×C₄⋊C₄	—	3	2	no	—
161	C₂×C₄⋊C₄	—	6	1	no	—
162	C₂×C₄⋊C₄	—	6	1	no	—
163	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
164	C₄⋊C₈	—	2	1	no	—
165	C₄⋊C₈	—	3	2	no	—
166	C₄⋊C₈	—	6	1	no	—
167	C₄⋊C₈	C₃×Dic₃	1	2	yes	complemented
168	C₂³×C₃	—	2	1	no	—
169	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
170	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₃×C₄	—	2	1	no	—
172	C₂×C₃×C₄	—	2	1	no	—
173	C₂×C₃×C₄	—	2	1	no	—
174	C₂×C₃×C₄	—	2	1	no	—
175	C₂×C₃×C₄	—	2	1	no	—
176	C₂×C₃×C₄	—	2	1	no	—
177	C₂×C₃×C₄	—	2	1	no	—
178	C₂×C₃×C₄	—	2	1	no	—
179	C₂×C₃×C₄	—	2	1	no	—
180	C₂×C₃×C₄	—	2	1	no	—
181	C₂×C₃×C₄	—	2	1	no	—
182	C₂×C₃×C₄	—	2	1	no	—
183	C₂×C₃×C₄	—	2	1	no	—
184	C₂×C₃×C₄	—	2	1	no	—
185	C₂×C₃×C₄	—	2	1	no	—
186	C₂×C₃×C₄	—	2	1	no	—
187	C₂×C₃×C₄	—	2	1	no	—
188	C₂×C₃×C₄	—	2	1	no	—
189	C₂×C₃×C₄	—	4	1	no	—
190	C₂×C₃×C₄	—	4	1	no	—
191	C₂×C₃×C₄	—	12	2	no	—
192	C₂×C₃×C₄	—	12	2	no	—
193	C₂×C₃×C₄	—	12	2	no	—
194	C₂×C₃×C₄	#204	1	1	yes	characteristic
195	C₂×C₃×C₄	#204	1	1	yes	characteristic
196	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
197	C₂×C₃×C₄	Dic₁₂	1	1	yes	characteristic
198	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
199	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
200	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
201	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
202	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
203	C₂×C₃×C₄	#213	1	1	yes	characteristic
204	C₂×C₃×C₄	#214	1	1	yes	characteristic
205	C₂×C₃×C₄	#215	1	1	yes	characteristic
206	C₂×C₃×C₄	#216	1	1	yes	characteristic
207	C₂×C₃×C₄	#217	1	1	yes	characteristic
208	C₂×C₃×C₄	C₃×C₄²	1	1	yes	characteristic
209	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
214	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
215	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
216	C₂×C₃×C₄	C₃×SD₁₆	1	1	yes	characteristic
217	C₂×C₃×C₄	C₃×SD₁₆	1	1	yes	characteristic
218	C₂×C₃×C₄	C₃×SD₁₆	1	1	yes	characteristic
219	C₂×C₃×C₄	C₃×SD₁₆	1	1	yes	characteristic
220	C₂×C₃×C₄	C₃×Q₁₆	1	1	yes	characteristic
221	C₂×C₃×C₄	C₃×Q₁₆	1	1	yes	characteristic
222	C₂×Dic₃	—	4	2	no	—
223	C₂×Dic₃	—	4	2	no	—
224	C₂×Dic₃	—	4	2	no	—
225	C₃×C₈	—	4	4	no	—
226	C₃×C₈	—	4	2	no	—
227	C₃×C₈	—	4	2	no	—
228	C₃×C₈	—	12	2	no	—
229	C₃⋊C₈	—	4	2	no	—
230	C₂×C₃²	#331	1	1	yes	characteristic
231	C₂×C₃²	#332	1	1	yes	characteristic
232	C₂×C₃²	#332	1	1	yes	characteristic
233	C₂×C₃²	#333	1	1	yes	characteristic
234	C₂×C₃²	#340	1	1	yes	characteristic
235	C₂×C₃²	#340	1	1	yes	characteristic
236	C₂×C₃²	#343	1	1	yes	characteristic
237	C₂²×C₄	—	6	2	no	—
238	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
239	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
240	C₂²×C₄	C₃×#67	1	1	yes	characteristic
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	4	1	no	—
243	C₂×C₈	—	4	1	no	—
244	C₂×C₈	—	6	2	no	—
245	C₂×C₈	—	12	1	no	—
246	C₂×C₈	—	12	1	no	—
247	C₄⋊C₄	—	12	2	no	—
248	C₄⋊C₄	—	12	1	no	—
249	C₄⋊C₄	—	12	1	no	—
250	C₄⋊C₄	—	12	1	no	—
251	C₄⋊C₄	—	12	1	no	—
252	C₄²	C₃×Dic₆	1	1	yes	characteristic
253	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
254	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
255	C₄²	C₃×#67	1	1	yes	characteristic
256	C₂²×C₃	—	2	1	no	—
257	C₂²×C₃	—	2	1	no	—
258	C₂²×C₃	—	2	1	no	—
259	C₂²×C₃	—	2	1	no	—
260	C₂²×C₃	—	2	1	no	—
261	C₂²×C₃	—	2	1	no	—
262	C₂²×C₃	—	2	1	no	—
263	C₂²×C₃	#809	1	1	yes	characteristic
264	C₂²×C₃	#810	1	1	yes	characteristic
265	C₂²×C₃	#816	1	1	yes	characteristic
266	C₂²×C₃	#821	1	1	yes	characteristic
267	C₂²×C₃	#823	1	1	yes	characteristic
268	C₂²×C₃	#824	1	1	yes	characteristic
269	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
270	C₂²×C₃	C₃×#95	1	1	yes	characteristic
271	C₂²×C₃	C₃×#100	1	1	yes	characteristic
272	C₂²×C₃	C₃×#101	1	1	yes	characteristic
273	C₂²×C₃	C₃×#102	1	1	yes	characteristic
274	C₂²×C₃	C₃×#102	1	1	yes	characteristic
275	C₂²×C₃	C₃×#103	1	1	yes	characteristic
276	C₂²×C₃	C₃×#103	1	1	yes	characteristic
277	C₃×C₄	—	2	1	no	—
278	C₃×C₄	—	2	1	no	—
279	C₃×C₄	—	2	1	no	—
280	C₃×C₄	—	2	1	no	—
281	C₃×C₄	—	2	1	no	—
282	C₃×C₄	—	2	1	no	—
283	C₃×C₄	—	2	1	no	—
284	C₃×C₄	—	2	1	no	—
285	C₃×C₄	—	2	1	no	—
286	C₃×C₄	—	2	1	no	—
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	—	4	1	no	—
290	C₃×C₄	—	4	1	no	—
291	C₃×C₄	—	24	2	no	—
292	C₃×C₄	#807	1	1	yes	characteristic
293	C₃×C₄	#808	1	1	yes	characteristic
294	C₃×C₄	#816	1	1	yes	characteristic
295	C₃×C₄	#817	1	1	yes	characteristic
296	C₃×C₄	#818	1	1	yes	characteristic
297	C₃×C₄	#821	1	1	yes	characteristic
298	C₃×C₄	#832	1	1	yes	characteristic
299	C₃×C₄	#835	1	1	yes	characteristic
300	C₃×C₄	C₃×#102	1	1	yes	characteristic
301	C₃×C₄	C₃×#102	1	1	yes	characteristic
302	C₃×C₄	C₃×#103	1	1	yes	characteristic
303	C₃×C₄	C₃×#103	1	1	yes	characteristic
304	C₃×C₄	C₃×#106	1	1	yes	characteristic
305	C₃×C₄	C₃×#106	1	1	yes	characteristic
306	C₃×C₄	C₃×#107	1	1	yes	characteristic
307	C₃×C₄	C₃×#107	1	1	yes	characteristic
308	Dic₃	—	8	2	no	—
309	C₃²	#1296	1	1	yes	characteristic, complemented, Sylow
310	C₂³	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	12	2	no	—
314	C₂×C₄	—	12	2	no	—
315	C₂×C₄	—	12	2	no	—
316	C₂×C₄	C₃×#204	1	1	yes	characteristic
317	C₂×C₄	C₃×#204	1	1	yes	characteristic
318	C₂×C₄	C₃×D₂₄	1	1	yes	characteristic
319	C₂×C₄	C₃×Dic₁₂	1	1	yes	characteristic
320	C₂×C₄	C₃×C₄×Dic₃	1	1	yes	characteristic
321	C₂×C₄	C₃×Dic₃⋊C₄	1	1	yes	characteristic
322	C₂×C₄	C₃×Dic₃⋊C₄	1	1	yes	characteristic
323	C₂×C₄	C₃×C₄⋊Dic₃	1	1	yes	characteristic
324	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₃×#213	1	1	yes	characteristic
326	C₂×C₄	C₃×#214	1	1	yes	characteristic
327	C₂×C₄	C₃×#215	1	1	yes	characteristic
328	C₂×C₄	C₃×#216	1	1	yes	characteristic
329	C₂×C₄	C₃×#217	1	1	yes	characteristic
330	C₈	—	4	2	no	—
331	C₈	—	12	2	no	—
332	C₂×C₃	—	2	1	no	—
333	C₂×C₃	—	2	1	no	—
334	C₂×C₃	—	2	1	no	—
335	C₂×C₃	—	2	1	no	—
336	C₂×C₃	—	2	1	no	—
337	C₂×C₃	—	2	1	no	—
338	C₂×C₃	—	2	1	no	—
339	C₂×C₃	#4481	1	1	yes	characteristic
340	C₂×C₃	#4482	1	1	yes	characteristic
341	C₂×C₃	#4485	1	1	yes	characteristic
342	C₂×C₃	#4486	1	1	yes	characteristic
343	C₂×C₃	#4529	1	1	yes	characteristic
344	C₂×C₃	#4551	1	1	yes	characteristic
345	C₂×C₃	#4554	1	1	yes	characteristic
346	C₂×C₃	C₃×#331	1	1	yes	characteristic
347	C₂×C₃	C₃×#332	1	1	yes	characteristic
348	C₂×C₃	C₃×#332	1	1	yes	characteristic
349	C₂×C₃	C₃×#333	1	1	yes	characteristic
350	C₂×C₃	C₃×#340	1	1	yes	characteristic
351	C₂×C₃	C₃×#340	1	1	yes	characteristic
352	C₂×C₃	C₃×#343	1	1	yes	characteristic
353	C₂²	C₃×#809	1	1	yes	characteristic
354	C₂²	C₃×#810	1	1	yes	characteristic
355	C₂²	C₃×#816	1	1	yes	characteristic
356	C₂²	C₃×#821	1	1	yes	characteristic
357	C₂²	C₃×#823	1	1	yes	characteristic
358	C₂²	C₃×#824	1	1	yes	characteristic
359	C₂²	C₃×C₃⋊#95	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	24	2	no	—
363	C₄	C₃×#807	1	1	yes	characteristic
364	C₄	C₃×#808	1	1	yes	characteristic
365	C₄	C₃×#816	1	1	yes	characteristic
366	C₄	C₃×#817	1	1	yes	characteristic
367	C₄	C₃×#818	1	1	yes	characteristic
368	C₄	C₃×#821	1	1	yes	characteristic
369	C₄	C₃×#832	1	1	yes	characteristic
370	C₄	C₃×#835	1	1	yes	characteristic
371	C₃	—	2	1	no	—
372	C₃	#67702	1	1	yes	characteristic, direct product factor
373	C₃	C₃×#1296	1	1	yes	characteristic, complemented
374	C₂	C₃×#4481	1	1	yes	characteristic
375	C₂	C₃×#4482	1	1	yes	characteristic
376	C₂	C₃×#4485	1	1	yes	characteristic
377	C₂	C₃×#4486	1	1	yes	characteristic
378	C₂	C₃×#4529	1	1	yes	characteristic
379	C₂	C₃×#4551	1	1	yes	characteristic
380	C₂	C₃×#4554	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₃×C₄²
Frattini	C₂×C₄²	C₂×C₃×D₃
Fitting	C₂×C₃²×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₃²	C₂²⋊C₄
cosocle	C₂×C₃×C₄²	C₂²×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₃
hypocenter	C₃	C₃×#1296
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
5. #67702	C₃	direct (N × H)
13. C₃²×C₄⋊C₈	C₄	semidirect
15. C₃×C₄⋊(C₃⋊C₈)	C₄	semidirect
63. C₃×C₄⋊C₈	Dic₃	semidirect
64. C₃×C₄⋊C₈	C₃×C₄	semidirect
66. C₄⋊(C₃⋊C₈)	C₃×C₄	semidirect
167. C₄⋊C₈	C₃×Dic₃	semidirect
309. C₃²	#1296	semidirect
372. C₃	#67702	direct (N × H)
373. C₃	C₃×#1296	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄⋊C₈	2
C₃×#4935	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₃×#1296	3
#67702	3

Subgroups — C3×#67702 #11771080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#67702 #11771080