Subgroups — C₃×#70496 #11774545

Order 1152.

687 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃²×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4483	C₂	1	4	yes	maximal, complemented
5	C₃×#1486	—	3	1	no	maximal
6	#70496	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂²×C₃×D₁₂	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₄×D₃	—	2	1	no	—
9	C₂×C₃²×M₁₆	—	2	1	no	—
10	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
11	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
12	C₂×C₃×C₄⋊Dic₃	C₄	1	1	yes	characteristic
13	C₃×C₄×D₁₂	—	2	1	no	—
14	C₃×C₄×D₁₂	—	2	1	no	—
15	C₃×C₄×D₁₂	C₄	1	2	yes	—
16	C₃×C₄×D₁₂	C₂²	1	2	yes	—
17	C₃²×C₄⋊C₈	—	2	1	no	—
18	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
19	C₃×#830	—	2	1	no	—
20	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
21	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₃×C₄×D₄	—	3	1	no	—
23	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
24	C₃×#431	—	3	1	no	—
25	C₃×#423	—	2	1	no	—
26	C₃×#423	D₃	1	1	yes	characteristic, complemented
27	C₃×#423	C₂×C₃	1	1	yes	characteristic, complemented
28	#4925	C₂×C₃	1	1	yes	characteristic, complemented
29	C₃×D₄⋊C₈	—	3	4	no	—
30	#4483	C₂×C₃	1	4	yes	complemented
31	C₂³×C₃×D₃	—	2	1	no	—
32	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
34	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
35	C₂²×C₃×Dic₃	—	2	1	no	—
36	C₂×C₃×D₁₂	—	2	1	no	—
37	C₂×C₃×D₁₂	—	2	4	no	—
38	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
39	C₂×C₃×C₄×D₃	—	2	2	no	—
40	C₂×C₃×C₄×D₃	—	2	2	no	—
41	C₂×C₃×C₄×D₃	—	4	2	no	—
42	C₂×C₃×C₄×D₃	—	4	2	no	—
43	C₃²×M₁₆	—	4	2	no	—
44	C₂×C₃²×C₈	—	2	2	no	—
45	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
46	C₃²×C₄²	D₄	1	1	yes	characteristic
47	C₃²×C₄²	D₄	1	1	yes	characteristic
48	C₃²×C₄²	C₂³	1	1	yes	characteristic
49	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
50	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₃×C₄⋊Dic₃	—	2	1	no	—
52	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
53	C₂×C₃×C₃⋊C₈	—	2	2	no	—
54	#1486	—	3	1	no	Sylow
55	C₂²×C₃×D₄	—	3	1	no	—
56	C₂³×C₃×C₄	—	6	1	no	—
57	C₂²×D₁₂	C₃×C₄	1	1	yes	characteristic
58	C₂²×C₄×D₃	—	2	1	no	—
59	C₂×C₃×M₁₆	—	2	2	no	—
60	C₂×C₃×M₁₆	—	2	1	no	—
61	C₂×C₃×M₁₆	—	2	1	no	—
62	C₃×C₄×D₄	—	3	2	no	—
63	C₃×C₄×D₄	—	3	2	no	—
64	C₃×C₄×D₄	—	6	1	no	—
65	C₃×C₄×D₄	—	6	1	no	—
66	C₂×C₃×C₄⋊C₄	—	3	1	no	—
67	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
68	C₂×C₃×C₄²	—	2	1	no	—
69	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
70	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
71	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
72	C₂×C₄⋊Dic₃	C₃×C₄	1	1	yes	characteristic
73	C₄×D₁₂	—	2	1	no	—
74	C₄×D₁₂	—	2	1	no	—
75	C₄×D₁₂	C₃×C₄	1	2	yes	—
76	C₄×D₁₂	C₂²×C₃	1	2	yes	—
77	C₃×C₄⋊C₈	—	2	2	no	—
78	C₃×C₄⋊C₈	—	2	1	no	—
79	C₃×C₄⋊C₈	—	2	1	no	—
80	C₃×C₄⋊C₈	—	2	2	no	—
81	C₃×C₄⋊C₈	—	6	1	no	—
82	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
83	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
84	C₃×C₂²⋊C₈	—	6	1	no	—
85	C₃×C₄×C₈	—	3	2	no	—
86	#830	—	2	1	no	—
87	C₄⋊(C₃⋊C₈)	—	2	1	no	—
88	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
89	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₃×D₃	—	2	4	no	—
91	C₂²×C₃×D₃	—	2	2	no	—
92	C₂²×C₃×D₃	—	4	2	no	—
93	C₂²×C₃×D₃	—	4	2	no	—
94	C₂×C₃²×C₄	—	2	2	no	—
95	C₂×C₃²×C₄	—	4	1	no	—
96	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃²×C₄	D₈	1	2	yes	—
100	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
101	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×Dic₃	—	2	2	no	—
105	C₂×C₃×Dic₃	—	4	2	no	—
106	C₃×D₁₂	—	2	4	no	—
107	C₃×D₁₂	—	2	2	no	—
108	C₃×D₁₂	M₁₆	1	4	yes	complemented
109	C₃×C₄×D₃	—	4	4	no	—
110	C₃×C₄×D₃	—	4	2	no	—
111	C₃×C₄×D₃	—	4	2	no	—
112	C₃²×C₈	—	4	2	no	—
113	C₃×C₃⋊C₈	—	4	2	no	—
114	C₂×C₄×D₄	—	3	1	no	—
115	#431	—	3	1	no	—
116	#423	C₃×D₃	1	1	yes	characteristic, complemented
117	D₄⋊C₈	—	3	4	no	—
118	C₂⁴×C₃	—	6	1	no	—
119	C₂³×D₃	—	2	1	no	—
120	C₂×C₃×D₄	—	3	2	no	—
121	C₂×C₃×D₄	—	6	4	no	—
122	C₂×C₃×D₄	—	6	1	no	—
123	C₂²×C₃×C₄	—	2	1	no	—
124	C₂²×C₃×C₄	—	2	1	no	—
125	C₂²×C₃×C₄	—	2	1	no	—
126	C₂²×C₃×C₄	—	6	1	no	—
127	C₂²×C₃×C₄	—	6	2	no	—
128	C₂²×C₃×C₄	—	6	2	no	—
129	C₂²×C₃×C₄	—	12	2	no	—
130	C₂²×C₃×C₄	—	12	2	no	—
131	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
132	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
133	C₂²×C₃×C₄	#67	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
137	C₂²×Dic₃	—	2	1	no	—
138	C₂×D₁₂	—	2	1	no	—
139	C₂×D₁₂	—	2	4	no	—
140	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
141	C₂×C₄×D₃	—	2	2	no	—
142	C₂×C₄×D₃	—	2	2	no	—
143	C₂×C₄×D₃	—	4	2	no	—
144	C₂×C₄×D₃	—	4	2	no	—
145	C₃×M₁₆	—	4	4	no	—
146	C₃×M₁₆	—	4	2	no	—
147	C₃×M₁₆	—	4	2	no	—
148	C₂×C₃×C₈	—	2	4	no	—
149	C₂×C₃×C₈	—	2	2	no	—
150	C₂×C₃×C₈	—	2	2	no	—
151	C₂×C₃×C₈	—	6	2	no	—
152	C₃×C₄⋊C₄	—	3	2	no	—
153	C₃×C₄⋊C₄	—	6	1	no	—
154	C₃×C₂²⋊C₄	—	6	2	no	—
155	C₃×C₂²⋊C₄	—	6	2	no	—
156	C₃×C₄²	—	2	1	no	—
157	C₃×C₄²	—	2	1	no	—
158	C₃×C₄²	—	2	1	no	—
159	C₃×C₄²	—	2	1	no	—
160	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
161	C₃×C₄²	D₁₂	1	1	yes	characteristic
162	C₃×C₄²	#67	1	1	yes	characteristic
163	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
164	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
165	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
166	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
167	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
168	(C₂×D₃)⋊C₄	—	2	2	no	—
169	(C₂×D₃)⋊C₄	—	2	2	no	—
170	C₄⋊Dic₃	—	2	1	no	—
171	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
172	C₂×C₃⋊C₈	—	2	2	no	—
173	C₂²×C₃²	—	2	1	no	—
174	C₂²×C₃²	—	2	1	no	—
175	C₂²×C₃²	#102	1	2	yes	—
176	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₃×D₃	—	2	4	no	—
178	C₂×C₃×D₃	—	4	8	no	—
179	C₂×C₃×D₃	—	4	2	no	—
180	C₂×C₃×D₃	—	4	2	no	—
181	C₃²×C₄	—	2	1	no	—
182	C₃²×C₄	—	2	1	no	—
183	C₃²×C₄	—	2	1	no	—
184	C₃²×C₄	#102	1	2	yes	—
185	C₃²×C₄	C₂×M₁₆	1	2	yes	—
186	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
187	C₃²×C₄	C₂×SD₁₆	1	1	yes	characteristic
188	C₃×Dic₃	—	4	2	no	—
189	C₂²×D₄	—	3	1	no	—
190	C₂³×C₄	—	6	1	no	—
191	C₂×M₁₆	—	2	1	no	—
192	C₄×D₄	—	3	2	no	—
193	C₄×D₄	—	3	2	no	—
194	C₄×D₄	—	6	1	no	—
195	C₄×D₄	—	6	1	no	—
196	C₂×C₄⋊C₄	—	3	1	no	—
197	C₂×C₂²⋊C₄	—	6	1	no	—
198	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
199	C₄⋊C₈	—	2	1	no	—
200	C₄⋊C₈	—	6	1	no	—
201	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	complemented
202	C₂²⋊C₈	—	6	1	no	—
203	C₄×C₈	—	3	2	no	—
204	C₂³×C₃	—	2	1	no	—
205	C₂³×C₃	—	6	4	no	—
206	C₂³×C₃	—	6	2	no	—
207	C₂³×C₃	—	12	2	no	—
208	C₂³×C₃	—	12	2	no	—
209	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
210	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×D₃	—	2	4	no	—
212	C₂²×D₃	—	2	2	no	—
213	C₂²×D₃	—	4	2	no	—
214	C₂²×D₃	—	4	2	no	—
215	C₃×D₄	—	3	4	no	—
216	C₃×D₄	—	6	4	no	—
217	C₃×D₄	—	6	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	4	2	no	—
229	C₂×C₃×C₄	—	4	1	no	—
230	C₂×C₃×C₄	—	4	1	no	—
231	C₂×C₃×C₄	—	4	2	no	—
232	C₂×C₃×C₄	—	6	2	no	—
233	C₂×C₃×C₄	—	12	2	no	—
234	C₂×C₃×C₄	—	12	4	no	—
235	C₂×C₃×C₄	—	12	2	no	—
236	C₂×C₃×C₄	—	12	2	no	—
237	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
238	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
239	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
240	C₂×C₃×C₄	#213	1	2	yes	—
241	C₂×C₃×C₄	#215	1	2	yes	—
242	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
246	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
247	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
253	C₂×Dic₃	—	2	2	no	—
254	C₂×Dic₃	—	4	2	no	—
255	D₁₂	—	2	4	no	—
256	D₁₂	—	2	2	no	—
257	D₁₂	C₃×M₁₆	1	4	yes	complemented
258	C₄×D₃	—	4	4	no	—
259	C₄×D₃	—	4	2	no	—
260	C₄×D₃	—	4	2	no	—
261	C₃×C₈	—	4	4	no	—
262	C₃×C₈	—	4	2	no	—
263	C₃×C₈	—	4	2	no	—
264	C₃×C₈	—	12	2	no	—
265	C₃⋊C₈	—	4	2	no	—
266	C₂×C₃²	—	2	2	no	—
267	C₂×C₃²	#407	1	1	yes	characteristic
268	C₂×C₃²	C₂×#102	1	1	yes	characteristic
269	C₂×C₃²	#421	1	1	yes	characteristic
270	C₃×D₃	—	4	4	no	—
271	C₂⁴	—	6	1	no	—
272	C₂×D₄	—	3	2	no	—
273	C₂×D₄	—	6	4	no	—
274	C₂×D₄	—	6	1	no	—
275	C₂²×C₄	—	6	1	no	—
276	C₂²×C₄	—	6	2	no	—
277	C₂²×C₄	—	6	2	no	—
278	C₂²×C₄	—	12	2	no	—
279	C₂²×C₄	—	12	2	no	—
280	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
281	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
282	C₂²×C₄	C₃×#67	1	1	yes	characteristic
283	M₁₆	—	4	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	6	2	no	—
286	C₄⋊C₄	—	3	2	no	—
287	C₄⋊C₄	—	6	1	no	—
288	C₂²⋊C₄	—	6	2	no	—
289	C₂²⋊C₄	—	6	2	no	—
290	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
291	C₄²	C₃×D₁₂	1	1	yes	characteristic
292	C₄²	C₃×#67	1	1	yes	characteristic
293	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	4	1	no	—
302	C₂²×C₃	—	6	4	no	—
303	C₂²×C₃	—	12	8	no	—
304	C₂²×C₃	—	12	2	no	—
305	C₂²×C₃	—	12	2	no	—
306	C₂²×C₃	#809	1	2	yes	—
307	C₂²×C₃	C₃×#102	1	2	yes	—
308	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
309	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×D₃	—	2	4	no	—
311	C₂×D₃	—	4	8	no	—
312	C₂×D₃	—	4	2	no	—
313	C₂×D₃	—	4	2	no	—
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	2	1	no	—
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	4	1	no	—
326	C₃×C₄	—	4	1	no	—
327	C₃×C₄	—	12	2	no	—
328	C₃×C₄	#809	1	2	yes	—
329	C₃×C₄	C₃×#102	1	2	yes	—
330	C₃×C₄	D₃×M₁₆	1	2	yes	—
331	C₃×C₄	C₂×#213	1	1	yes	characteristic
332	C₃×C₄	C₂×#215	1	1	yes	characteristic
333	C₃×C₄	C₂×C₃×M₁₆	1	2	yes	—
334	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
335	C₃×C₄	C₂×C₃×SD₁₆	1	1	yes	characteristic
336	Dic₃	—	4	2	no	—
337	C₃²	#1486	1	1	yes	characteristic, complemented, Sylow
338	C₂³	—	6	4	no	—
339	C₂³	—	6	2	no	—
340	C₂³	—	12	2	no	—
341	C₂³	—	12	2	no	—
342	C₂³	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	D₄	—	3	4	no	—
344	D₄	—	6	4	no	—
345	D₄	—	6	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	6	2	no	—
349	C₂×C₄	—	12	2	no	—
350	C₂×C₄	—	12	2	no	—
351	C₂×C₄	—	12	2	no	—
352	C₂×C₄	—	12	4	no	—
353	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₃×#213	1	2	yes	—
357	C₂×C₄	C₃×#215	1	2	yes	—
358	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
360	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
361	C₈	—	4	2	no	—
362	C₈	—	12	2	no	—
363	C₂×C₃	—	2	2	no	—
364	C₂×C₃	—	2	2	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	2	1	no	—
367	C₂×C₃	—	2	1	no	—
368	C₂×C₃	—	4	2	no	—
369	C₂×C₃	—	12	4	no	—
370	C₂×C₃	C₂×#809	1	1	yes	characteristic
371	C₂×C₃	#5126	1	1	yes	characteristic
372	C₂×C₃	#5139	1	1	yes	characteristic
373	C₂×C₃	C₃×#407	1	1	yes	characteristic
374	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
375	C₂×C₃	C₃×#421	1	1	yes	characteristic
376	D₃	—	4	4	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	6	4	no	—
380	C₂²	—	12	8	no	—
381	C₂²	—	12	2	no	—
382	C₂²	—	12	2	no	—
383	C₂²	C₃×#809	1	2	yes	—
384	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	12	2	no	—
389	C₄	C₃×#809	1	2	yes	—
390	C₄	C₃×D₃×M₁₆	1	2	yes	—
391	C₄	C₂×C₃×#213	1	1	yes	characteristic
392	C₄	C₂×C₃×#215	1	1	yes	characteristic
393	C₃	—	2	1	no	—
394	C₃	#70496	1	1	yes	characteristic, direct product factor
395	C₃	C₃×#1486	1	1	yes	characteristic, complemented
396	C₂	—	2	2	no	—
397	C₂	—	12	4	no	—
398	C₂	C₂×C₃×#809	1	1	yes	characteristic
399	C₂	C₃×#5126	1	1	yes	characteristic
400	C₂	C₃×#5139	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₃
Fitting	C₃²×#423	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×D₁₂	C₄
cosocle	C₃×C₄²	C₂³×C₃
hypercenter	C₃×#423	D₃
hypocenter	C₃	C₃×#1486
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#423

Complements

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

N	H ≅ G/N	type
2. C₃²×#423	C₂	semidirect
3. C₃×#4925	C₂	semidirect
4. C₃×#4483	C₂	semidirect
6. #70496	C₃	direct (N × H)
18. C₃²×C₄⋊C₈	C₂²	semidirect
21. C₃×C₄×C₃⋊C₈	C₂²	semidirect
26. C₃×#423	D₃	semidirect
27. C₃×#423	C₂×C₃	semidirect
28. #4925	C₂×C₃	semidirect
30. #4483	C₂×C₃	semidirect
82. C₃×C₄⋊C₈	C₂×D₃	semidirect
83. C₃×C₄⋊C₈	C₂²×C₃	semidirect
88. C₄×C₃⋊C₈	C₂²×C₃	semidirect
108. C₃×D₁₂	M₁₆	semidirect
116. #423	C₃×D₃	semidirect
201. C₄⋊C₈	C₂×C₃×D₃	semidirect
257. D₁₂	C₃×M₁₆	semidirect
337. C₃²	#1486	semidirect
394. C₃	#70496	direct (N × H)
395. C₃	C₃×#1486	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×D₁₂	2
C₃²×#423	2
C₃×#4925	2
C₃×#4483	2
C₃×#1486	3
#70496	3

Subgroups — C3×#70496 #11774545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70496 #11774545