Subgroups — C₂×C₃×#4846 #11868241

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 399 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	C₂×C₃×#869	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#821	C₂	1	2	yes	maximal
5	C₂×C₃×#818	C₂	1	2	yes	maximal, complemented
6	C₃×#4846	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#474	—	3	1	no	maximal
8	C₂×#4846	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄×D₃	—	2	1	no	—
11	C₂²×C₃×Dic₆	—	2	1	no	—
12	C₂²×C₃²×C₈	C₂²	1	2	yes	—
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
15	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
16	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₃×C₄×D₁₂	—	2	2	no	—
19	C₃×C₄×D₁₂	C₂²	1	4	yes	—
20	C₃×#869	—	2	2	no	—
21	C₃×#869	C₂²	1	4	yes	complemented
22	C₃²×C₄⋊C₈	C₂²	1	4	yes	complemented
23	C₃×#821	C₂²	1	8	yes	—
24	C₃×#818	C₂²	1	8	yes	complemented
25	C₂×C₃×C₄⋊Q₈	—	3	1	no	—
26	C₂×C₃×C₄×D₄	—	3	1	no	—
27	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
28	C₂×#869	C₂×C₃	1	1	yes	characteristic, complemented
29	C₃×#474	—	3	8	no	—
30	C₂×C₃×#107	—	3	2	no	—
31	C₂×C₃×C₄⋊C₈	—	2	1	no	—
32	C₂×C₃×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
33	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×#102	—	3	2	no	—
35	C₂×#821	C₂×C₃	1	2	yes	—
36	C₂×#818	C₂×C₃	1	2	yes	complemented
37	#4846	C₂×C₃	1	8	yes	direct product factor
38	C₂³×C₃×D₃	—	2	1	no	—
39	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
40	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
41	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
42	C₂²×C₃×Dic₃	—	2	2	no	—
43	C₂²×C₃×Dic₃	—	2	1	no	—
44	C₂×C₃×D₁₂	—	2	1	no	—
45	C₂×C₃×D₁₂	—	2	2	no	—
46	C₂×C₃×D₁₂	Q₈	1	4	yes	complemented
47	C₂×C₃×D₁₂	C₂³	1	2	yes	—
48	C₂×C₃×C₄×D₃	—	2	4	no	—
49	C₂×C₃×C₄×D₃	—	4	4	no	—
50	C₂×C₃×Dic₆	—	2	4	no	—
51	C₂×C₃×Dic₆	—	4	4	no	—
52	C₂×C₃²×C₈	—	2	4	no	—
53	C₂×C₃²×C₈	C₂³	1	4	yes	—
54	C₃²×C₄²	D₄	1	2	yes	—
55	C₃²×C₄²	C₂³	1	2	yes	—
56	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
57	C₃×C₄⋊Dic₃	—	2	4	no	—
58	C₃×C₄⋊Dic₃	—	2	2	no	—
59	C₃×C₄⋊Dic₃	—	2	1	no	—
60	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
61	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
62	C₂×#474	—	3	1	no	Sylow
63	C₂²×C₃×Q₈	—	6	1	no	—
64	C₂²×C₃×D₄	—	3	1	no	—
65	C₂³×C₃×C₄	—	6	1	no	—
66	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₄×D₃	—	2	1	no	—
68	C₂²×Dic₆	—	2	1	no	—
69	C₂²×C₃×C₈	—	2	2	no	—
70	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
71	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
72	C₃×C₄⋊Q₈	—	3	4	no	—
73	C₃×C₄⋊Q₈	—	6	2	no	—
74	C₃×C₄×D₄	—	3	4	no	—
75	C₃×C₄×D₄	—	6	2	no	—
76	C₂×C₃×C₄⋊C₄	—	3	2	no	—
77	C₂×C₃×C₄⋊C₄	—	3	1	no	—
78	C₂×C₃×C₄⋊C₄	—	6	1	no	—
79	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
80	C₂×C₃×C₄²	—	2	1	no	—
81	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
82	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
83	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
84	C₂×C₄⋊Dic₃	—	2	1	no	—
85	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
86	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
87	C₄×D₁₂	—	2	2	no	—
88	C₄×D₁₂	C₂²×C₃	1	4	yes	—
89	#869	—	2	2	no	—
90	#869	C₂²×C₃	1	4	yes	complemented
91	C₃×#107	—	3	8	no	—
92	C₃×C₄⋊C₈	—	2	4	no	—
93	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
94	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
95	C₃×#102	—	3	8	no	—
96	#821	C₂²×C₃	1	8	yes	—
97	#818	C₂²×C₃	1	8	yes	complemented
98	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₃×D₃	—	2	4	no	—
100	C₂²×C₃×D₃	—	2	2	no	—
101	C₂²×C₃×D₃	—	4	2	no	—
102	C₂²×C₃×D₃	—	4	2	no	—
103	C₂×C₃²×C₄	—	2	2	no	—
104	C₂×C₃²×C₄	D₈	1	4	yes	—
105	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
106	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
108	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
109	C₂×C₃²×C₄	#41	1	2	yes	—
110	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
111	C₂×C₃×Dic₃	—	2	4	no	—
112	C₂×C₃×Dic₃	—	2	2	no	—
113	C₂×C₃×Dic₃	—	4	4	no	—
114	C₂×C₃×Dic₃	—	4	2	no	—
115	C₃×D₁₂	—	2	4	no	—
116	C₃×D₁₂	—	2	2	no	—
117	C₃×D₁₂	C₂×Q₈	1	4	yes	complemented
118	C₃×C₄×D₃	—	4	8	no	—
119	C₃×Dic₆	—	4	8	no	—
120	C₃²×C₈	—	2	4	no	—
121	C₂×C₄⋊Q₈	—	3	1	no	—
122	C₂×C₄×D₄	—	3	1	no	—
123	#474	—	3	8	no	—
124	C₂×#107	—	3	2	no	—
125	C₂×C₄⋊C₈	C₃×D₃	1	1	yes	characteristic, complemented
126	C₂×#102	—	3	2	no	—
127	C₂⁴×C₃	—	6	1	no	—
128	C₂³×D₃	—	2	1	no	—
129	C₂×C₃×Q₈	—	6	4	no	—
130	C₂×C₃×Q₈	—	12	4	no	—
131	C₂×C₃×D₄	—	3	4	no	—
132	C₂×C₃×D₄	—	3	2	no	—
133	C₂×C₃×D₄	—	6	1	no	—
134	C₂×C₃×D₄	—	6	2	no	—
135	C₂²×C₃×C₄	—	2	1	no	—
136	C₂²×C₃×C₄	—	2	1	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	6	1	no	—
139	C₂²×C₃×C₄	—	6	2	no	—
140	C₂²×C₃×C₄	—	6	4	no	—
141	C₂²×C₃×C₄	—	12	4	no	—
142	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
143	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
146	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
148	C₂²×Dic₃	—	2	2	no	—
149	C₂²×Dic₃	—	2	1	no	—
150	C₂×D₁₂	—	2	1	no	—
151	C₂×D₁₂	—	2	2	no	—
152	C₂×D₁₂	C₃×Q₈	1	4	yes	complemented
153	C₂×D₁₂	C₂³×C₃	1	2	yes	—
154	C₂×C₄×D₃	—	2	4	no	—
155	C₂×C₄×D₃	—	4	4	no	—
156	C₂×Dic₆	—	2	4	no	—
157	C₂×Dic₆	—	4	4	no	—
158	C₂×C₃×C₈	—	2	4	no	—
159	C₂×C₃×C₈	—	2	4	no	—
160	C₂×C₃×C₈	—	2	4	no	—
161	C₂×C₃×C₈	—	4	4	no	—
162	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
163	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
164	C₃×C₄⋊C₄	—	3	4	no	—
165	C₃×C₄⋊C₄	—	3	2	no	—
166	C₃×C₄⋊C₄	—	6	1	no	—
167	C₃×C₄⋊C₄	—	6	2	no	—
168	C₃×C₄⋊C₄	—	6	4	no	—
169	C₃×C₂²⋊C₄	—	6	4	no	—
170	C₃×C₄²	—	2	2	no	—
171	C₃×C₄²	—	2	2	no	—
172	C₃×C₄²	D₁₂	1	2	yes	—
173	C₃×C₄²	C₃×D₄	1	2	yes	—
174	C₃×C₄²	C₂²×D₃	1	2	yes	—
175	C₃×C₄²	C₂³×C₃	1	2	yes	—
176	(C₂×D₃)⋊C₄	—	2	4	no	—
177	C₄⋊Dic₃	—	2	2	no	—
178	C₄⋊Dic₃	—	2	4	no	—
179	C₄⋊Dic₃	—	2	1	no	—
180	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
181	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
182	C₂²×C₃²	C₂²⋊Q₈	1	2	yes	—
183	C₂²×C₃²	C₂×D₈	1	2	yes	—
184	C₂²×C₃²	#137	1	2	yes	—
185	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₃×D₃	—	2	4	no	—
187	C₂×C₃×D₃	—	4	2	no	—
188	C₂×C₃×D₃	—	4	2	no	—
189	C₂×C₃×D₃	—	4	8	no	—
190	C₃²×C₄	—	2	2	no	—
191	C₃²×C₄	C₂²⋊Q₈	1	2	yes	—
192	C₃²×C₄	C₂×D₈	1	4	yes	—
193	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
194	C₃²×C₄	C₂×#41	1	1	yes	characteristic
195	C₃×Dic₃	—	4	4	no	—
196	C₃×Dic₃	—	4	2	no	—
197	C₂²×Q₈	—	6	1	no	—
198	C₂²×D₄	—	3	1	no	—
199	C₂³×C₄	—	6	1	no	—
200	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
201	C₄⋊Q₈	—	3	4	no	—
202	C₄⋊Q₈	—	6	2	no	—
203	C₄×D₄	—	3	4	no	—
204	C₄×D₄	—	6	2	no	—
205	C₂×C₄⋊C₄	—	3	1	no	—
206	C₂×C₄⋊C₄	—	3	2	no	—
207	C₂×C₄⋊C₄	—	6	1	no	—
208	C₂×C₂²⋊C₄	—	6	1	no	—
209	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
210	#107	—	3	8	no	—
211	C₄⋊C₈	C₂×C₃×D₃	1	4	yes	complemented
212	#102	—	3	8	no	—
213	C₂³×C₃	—	2	1	no	—
214	C₂³×C₃	—	6	4	no	—
215	C₂³×C₃	—	6	2	no	—
216	C₂³×C₃	—	12	2	no	—
217	C₂³×C₃	—	12	2	no	—
218	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
219	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂²×D₃	—	2	4	no	—
221	C₂²×D₃	—	2	2	no	—
222	C₂²×D₃	—	4	2	no	—
223	C₂²×D₃	—	4	2	no	—
224	C₃×Q₈	—	12	8	no	—
225	C₃×D₄	—	3	4	no	—
226	C₃×D₄	—	6	4	no	—
227	C₃×D₄	—	6	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	4	2	no	—
238	C₂×C₃×C₄	—	6	2	no	—
239	C₂×C₃×C₄	—	6	4	no	—
240	C₂×C₃×C₄	—	12	2	no	—
241	C₂×C₃×C₄	—	12	4	no	—
242	C₂×C₃×C₄	—	12	8	no	—
243	C₂×C₃×C₄	D₂₄	1	4	yes	—
244	C₂×C₃×C₄	C₃×D₈	1	4	yes	—
245	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
246	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
248	C₂×C₃×C₄	#237	1	2	yes	—
249	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
250	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
251	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
253	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
254	C₂×C₃×C₄	C₃×#41	1	2	yes	—
255	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
257	C₂×Dic₃	—	2	4	no	—
258	C₂×Dic₃	—	2	2	no	—
259	C₂×Dic₃	—	4	4	no	—
260	C₂×Dic₃	—	4	2	no	—
261	D₁₂	—	2	4	no	—
262	D₁₂	—	2	2	no	—
263	D₁₂	C₂×C₃×Q₈	1	4	yes	complemented
264	C₄×D₃	—	4	8	no	—
265	Dic₆	—	4	8	no	—
266	C₃×C₈	—	2	4	no	—
267	C₃×C₈	—	2	4	no	—
268	C₃×C₈	—	4	4	no	—
269	C₂×C₃²	#474	1	4	yes	complemented
270	C₂×C₃²	C₂×C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
272	C₂×C₃²	C₂×#137	1	1	yes	characteristic
273	C₃×D₃	—	4	4	no	—
274	C₂⁴	—	6	1	no	—
275	C₂×Q₈	—	6	4	no	—
276	C₂×Q₈	—	12	4	no	—
277	C₂×D₄	—	3	2	no	—
278	C₂×D₄	—	3	4	no	—
279	C₂×D₄	—	6	1	no	—
280	C₂×D₄	—	6	2	no	—
281	C₂²×C₄	—	6	1	no	—
282	C₂²×C₄	—	6	2	no	—
283	C₂²×C₄	—	6	4	no	—
284	C₂²×C₄	—	12	4	no	—
285	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
286	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
290	C₄⋊C₄	—	3	4	no	—
291	C₄⋊C₄	—	3	2	no	—
292	C₄⋊C₄	—	6	1	no	—
293	C₄⋊C₄	—	6	2	no	—
294	C₄⋊C₄	—	6	4	no	—
295	C₂²⋊C₄	—	6	4	no	—
296	C₄²	C₃×D₁₂	1	2	yes	—
297	C₄²	C₂²×C₃×D₃	1	2	yes	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	6	4	no	—
303	C₂²×C₃	—	12	2	no	—
304	C₂²×C₃	—	12	2	no	—
305	C₂²×C₃	—	12	8	no	—
306	C₂²×C₃	#897	1	2	yes	—
307	C₂²×C₃	C₂×D₂₄	1	2	yes	—
308	C₂²×C₃	#909	1	2	yes	—
309	C₂²×C₃	C₃×C₂²⋊Q₈	1	2	yes	—
310	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
311	C₂²×C₃	C₃×#137	1	2	yes	—
312	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
313	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
314	C₂×D₃	—	2	4	no	—
315	C₂×D₃	—	4	2	no	—
316	C₂×D₃	—	4	2	no	—
317	C₂×D₃	—	4	8	no	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	2	2	no	—
321	C₃×C₄	—	2	4	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	—	12	2	no	—
326	C₃×C₄	—	12	4	no	—
327	C₃×C₄	#897	1	2	yes	—
328	C₃×C₄	C₂×D₂₄	1	4	yes	—
329	C₃×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
330	C₃×C₄	C₂×C₃×D₈	1	4	yes	—
331	C₃×C₄	C₂×#237	1	1	yes	characteristic
332	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
333	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
334	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
335	Dic₃	—	4	4	no	—
336	Dic₃	—	4	2	no	—
337	C₃²	C₂×#474	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	C₂×C₃×D₁₂	1	1	yes	characteristic
343	Q₈	—	12	8	no	—
344	D₄	—	3	4	no	—
345	D₄	—	6	4	no	—
346	D₄	—	6	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	6	2	no	—
349	C₂×C₄	—	6	4	no	—
350	C₂×C₄	—	12	2	no	—
351	C₂×C₄	—	12	4	no	—
352	C₂×C₄	—	12	8	no	—
353	C₂×C₄	C₃×D₂₄	1	4	yes	—
354	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
355	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
356	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
357	C₂×C₄	C₃×#237	1	2	yes	—
358	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
359	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
360	C₈	—	2	4	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	2	4	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	12	4	no	—
366	C₂×C₃	#4846	1	4	yes	direct product factor
367	C₂×C₃	C₃×#474	1	4	yes	complemented
368	C₂×C₃	C₂×#897	1	1	yes	characteristic
369	C₂×C₃	C₂²×D₂₄	1	1	yes	characteristic
370	C₂×C₃	C₂×#909	1	1	yes	characteristic
371	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
372	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
373	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
374	D₃	—	4	4	no	—
375	C₂²	—	6	4	no	—
376	C₂²	—	12	2	no	—
377	C₂²	—	12	8	no	—
378	C₂²	—	12	2	no	—
379	C₂²	C₃×#897	1	2	yes	—
380	C₂²	C₂×C₃×D₂₄	1	2	yes	—
381	C₂²	C₃×#909	1	2	yes	—
382	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
383	C₄	—	2	2	no	—
384	C₄	—	12	2	no	—
385	C₄	—	12	4	no	—
386	C₄	C₃×#897	1	2	yes	—
387	C₄	C₂×C₃×D₂₄	1	4	yes	—
388	C₄	C₂×C₃×#237	1	1	yes	characteristic
389	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
390	C₃	—	2	1	no	—
391	C₃	C₂×#4846	1	1	yes	characteristic, direct product factor
392	C₃	C₂×C₃×#474	1	1	yes	characteristic, complemented
393	C₂	—	12	4	no	—
394	C₂	C₃×#4846	1	4	yes	direct product factor
395	C₂	C₂×C₃×#897	1	1	yes	characteristic
396	C₂	C₂²×C₃×D₂₄	1	1	yes	characteristic
397	C₂	C₂×C₃×#909	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄⋊C₈	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₁₂	C₂²
hypercenter	C₂×C₃×C₄⋊C₈	D₃
hypocenter	C₃	C₂×C₃×#474
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×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
2. C₂×C₃×#869	C₂	semidirect
3. C₂×C₃²×C₄⋊C₈	C₂	semidirect
5. C₂×C₃×#818	C₂	semidirect
6. C₃×#4846	C₂	direct (N × H)
8. C₂×#4846	C₃	direct (N × H)
21. C₃×#869	C₂²	semidirect
22. C₃²×C₄⋊C₈	C₂²	semidirect
24. C₃×#818	C₂²	semidirect
28. C₂×#869	C₂×C₃	semidirect
32. C₂×C₃×C₄⋊C₈	D₃	semidirect
33. C₂×C₃×C₄⋊C₈	C₂×C₃	semidirect
36. C₂×#818	C₂×C₃	semidirect
37. #4846	C₂×C₃	direct (N × H)
46. C₂×C₃×D₁₂	Q₈	semidirect
90. #869	C₂²×C₃	semidirect
93. C₃×C₄⋊C₈	C₂×D₃	semidirect
94. C₃×C₄⋊C₈	C₂²×C₃	semidirect
97. #818	C₂²×C₃	semidirect
117. C₃×D₁₂	C₂×Q₈	semidirect
125. C₂×C₄⋊C₈	C₃×D₃	semidirect
152. C₂×D₁₂	C₃×Q₈	semidirect
211. C₄⋊C₈	C₂×C₃×D₃	semidirect
263. D₁₂	C₂×C₃×Q₈	semidirect
269. C₂×C₃²	#474	semidirect
337. C₃²	C₂×#474	semidirect
366. C₂×C₃	#4846	direct (N × H)
367. C₂×C₃	C₃×#474	semidirect
391. C₃	C₂×#4846	direct (N × H)
392. C₃	C₂×C₃×#474	semidirect
394. C₂	C₃×#4846	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×C₄×D₁₂	2
C₂×C₃×#869	2
C₂×C₃²×C₄⋊C₈	2
C₂×C₃×#821	2
C₂×C₃×#818	2
C₃×#4846	2
C₂×C₃×#474	3
C₂×#4846	3

Subgroups — C2×C3×#4846 #11868241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4846 #11868241