Subgroups — C₂×C₃×#5116 #11866781

Order 1152.

1193 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#924	C₂	1	2	yes	maximal
3	C₂²×C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5116	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#816	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#467	—	3	1	no	maximal
8	C₂×#5116	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
11	C₂²×C₃²×C₈	—	2	4	no	—
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃²×C₈	C₂²	1	4	yes	—
14	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#217	—	2	2	no	—
16	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
17	C₃×#924	—	2	4	no	—
18	C₃×#924	C₂²	1	8	yes	—
19	C₂×C₃×Dic₃⋊C₄	—	2	2	no	—
20	C₂×C₃×Dic₁₂	—	2	4	no	—
21	C₂×C₃×Dic₁₂	C₂²	1	4	yes	complemented
22	C₃×#818	C₂²	1	4	yes	complemented
23	C₃×#816	C₂²	1	8	yes	complemented
24	C₂²×C₃×Q₁₆	—	3	1	no	—
25	C₂³×C₃×C₈	—	2	1	no	—
26	C₂³×C₃×C₈	D₃	1	1	yes	characteristic
27	C₂³×C₃×C₈	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
29	C₂×#924	C₂×C₃	1	2	yes	—
30	C₂²×Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
31	C₃×#467	—	3	8	no	—
32	C₂×C₃×#107	—	3	1	no	—
33	C₂×C₃×#103	—	3	2	no	—
34	#5116	C₂×C₃	1	8	yes	direct product factor
35	C₂×#818	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#816	C₂×C₃	1	2	yes	complemented
37	C₂⁴×C₃²	D₄	1	1	yes	characteristic
38	C₂²×C₃²×C₄	—	2	2	no	—
39	C₂²×C₃²×C₄	—	2	2	no	—
40	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
41	C₂²×C₃²×C₄	D₄	1	2	yes	—
42	C₂²×C₃²×C₄	C₂³	1	2	yes	—
43	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₃	—	2	2	no	—
45	C₂²×C₃×Dic₃	—	2	2	no	—
46	C₂×C₃×Dic₆	—	2	4	no	—
47	C₂×C₃×Dic₆	—	2	4	no	—
48	C₂×C₃×Dic₆	—	2	2	no	—
49	C₂×C₃×Dic₆	C₂³	1	4	yes	—
50	C₂×C₃²×C₈	—	2	2	no	—
51	C₂×C₃²×C₈	—	2	8	no	—
52	C₂×C₃²×C₈	D₄	1	4	yes	—
53	C₂×C₃²×C₈	C₂³	1	2	yes	—
54	C₂×C₃²×C₈	C₂³	1	2	yes	—
55	C₃×#217	—	2	8	no	—
56	C₃×C₄⋊Dic₃	—	2	2	no	—
57	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
58	C₃×Dic₃⋊C₄	—	2	8	no	—
59	C₃×Dic₁₂	—	2	8	no	—
60	C₂×#467	—	3	1	no	Sylow
61	C₂²×C₃×Q₈	—	3	2	no	—
62	C₂³×C₃×C₄	—	2	1	no	—
63	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
64	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
66	C₂×C₃×Q₁₆	—	3	4	no	—
67	C₂×C₃×Q₁₆	—	6	4	no	—
68	C₂²×C₃×C₈	—	2	8	no	—
69	C₂²×C₃×C₈	—	2	4	no	—
70	C₂²×C₃×C₈	—	2	4	no	—
71	C₂²×C₃×C₈	—	2	1	no	—
72	C₂²×C₃×C₈	—	2	4	no	—
73	C₂²×C₃×C₈	—	2	1	no	—
74	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
76	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
79	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
80	C₃×C₂²⋊Q₈	—	3	8	no	—
81	C₃×C₂²⋊Q₈	—	6	4	no	—
82	C₂×C₃×C₄⋊C₄	—	3	2	no	—
83	C₂×C₃×C₄⋊C₄	—	6	2	no	—
84	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
85	C₂×#217	—	2	2	no	—
86	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
87	#924	—	2	4	no	—
88	#924	C₂²×C₃	1	8	yes	—
89	C₂×Dic₃⋊C₄	—	2	2	no	—
90	C₂×Dic₁₂	—	2	4	no	—
91	C₂×Dic₁₂	C₂²×C₃	1	4	yes	complemented
92	C₃×#107	—	3	4	no	—
93	C₃×#103	—	3	8	no	—
94	#818	C₂²×C₃	1	4	yes	complemented
95	#816	C₂²×C₃	1	8	yes	complemented
96	C₂³×C₃²	—	2	2	no	—
97	C₂³×C₃²	—	2	2	no	—
98	C₂³×C₃²	Q₁₆	1	4	yes	complemented
99	C₂³×C₃²	C₂×D₄	1	2	yes	—
100	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	—	2	2	no	—
102	C₂×C₃²×C₄	—	2	4	no	—
103	C₂×C₃²×C₄	—	2	2	no	—
104	C₂×C₃²×C₄	—	2	2	no	—
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	#41	1	2	yes	—
109	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
110	C₂×C₃×Dic₃	—	2	4	no	—
111	C₂×C₃×Dic₃	—	2	4	no	—
112	C₂×C₃×Dic₃	—	4	4	no	—
113	C₂×C₃×Dic₃	—	4	4	no	—
114	C₃×Dic₆	—	2	4	no	—
115	C₃×Dic₆	—	2	4	no	—
116	C₃×Dic₆	—	4	4	no	—
117	C₃²×C₈	—	2	2	no	—
118	C₃²×C₈	C₂×D₄	1	4	yes	—
119	C₂²×Q₁₆	—	3	1	no	—
120	C₂³×C₈	C₃×D₃	1	1	yes	characteristic
121	C₂×C₂²⋊Q₈	—	3	2	no	—
122	#467	—	3	8	no	—
123	C₂×#107	—	3	1	no	—
124	C₂×#103	—	3	2	no	—
125	C₂⁴×C₃	—	2	1	no	—
126	C₂⁴×C₃	D₁₂	1	1	yes	characteristic
127	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
128	C₂×C₃×Q₈	—	3	4	no	—
129	C₂×C₃×Q₈	—	6	2	no	—
130	C₂×C₃×Q₈	—	6	4	no	—
131	C₂×C₃×Q₈	—	6	4	no	—
132	C₂²×C₃×C₄	—	2	4	no	—
133	C₂²×C₃×C₄	—	2	4	no	—
134	C₂²×C₃×C₄	—	2	2	no	—
135	C₂²×C₃×C₄	—	2	2	no	—
136	C₂²×C₃×C₄	—	2	2	no	—
137	C₂²×C₃×C₄	—	2	2	no	—
138	C₂²×C₃×C₄	—	2	1	no	—
139	C₂²×C₃×C₄	—	2	2	no	—
140	C₂²×C₃×C₄	—	2	2	no	—
141	C₂²×C₃×C₄	—	2	1	no	—
142	C₂²×C₃×C₄	—	6	2	no	—
143	C₂²×C₃×C₄	—	6	2	no	—
144	C₂²×C₃×C₄	D₁₂	1	2	yes	—
145	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
146	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
148	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
149	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
151	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
152	C₂²×Dic₃	—	2	2	no	—
153	C₂²×Dic₃	—	2	2	no	—
154	C₂×Dic₆	—	2	4	no	—
155	C₂×Dic₆	—	2	4	no	—
156	C₂×Dic₆	—	2	2	no	—
157	C₂×Dic₆	C₂³×C₃	1	4	yes	—
158	C₃×Q₁₆	—	6	8	no	—
159	C₂×C₃×C₈	—	2	4	no	—
160	C₂×C₃×C₈	—	2	16	no	—
161	C₂×C₃×C₈	—	2	2	no	—
162	C₂×C₃×C₈	—	2	2	no	—
163	C₂×C₃×C₈	—	2	8	no	—
164	C₂×C₃×C₈	—	2	8	no	—
165	C₂×C₃×C₈	—	2	4	no	—
166	C₂×C₃×C₈	—	2	2	no	—
167	C₂×C₃×C₈	—	2	2	no	—
168	C₂×C₃×C₈	#67	1	4	yes	—
169	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
170	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
171	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
172	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
173	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
174	C₃×C₄⋊C₄	—	3	4	no	—
175	C₃×C₄⋊C₄	—	6	8	no	—
176	C₃×C₄⋊C₄	—	6	2	no	—
177	C₃×C₂²⋊C₄	—	6	8	no	—
178	#217	—	2	8	no	—
179	C₄⋊Dic₃	—	2	2	no	—
180	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
181	Dic₃⋊C₄	—	2	8	no	—
182	Dic₁₂	—	2	8	no	—
183	C₂²×C₃²	—	2	2	no	—
184	C₂²×C₃²	—	2	2	no	—
185	C₂²×C₃²	—	2	8	no	—
186	C₂²×C₃²	#121	1	2	yes	—
187	C₂²×C₃²	C₂×Q₁₆	1	2	yes	—
188	C₂²×C₃²	C₂×Q₁₆	1	4	yes	complemented
189	C₂²×C₃²	#135	1	2	yes	—
190	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
191	C₃²×C₄	—	2	2	no	—
192	C₃²×C₄	#121	1	2	yes	—
193	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
194	C₃²×C₄	C₂×#41	1	1	yes	characteristic
195	C₃×Dic₃	—	4	4	no	—
196	C₃×Dic₃	—	4	4	no	—
197	C₂²×Q₈	—	3	2	no	—
198	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
199	C₂×Q₁₆	—	3	4	no	—
200	C₂×Q₁₆	—	6	4	no	—
201	C₂²×C₈	—	2	4	no	—
202	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
203	C₂²×C₈	C₂×C₃×D₃	1	4	yes	—
204	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
205	C₂²⋊Q₈	—	3	8	no	—
206	C₂²⋊Q₈	—	6	4	no	—
207	C₂×C₄⋊C₄	—	3	2	no	—
208	C₂×C₄⋊C₄	—	6	2	no	—
209	C₂×C₂²⋊C₄	—	6	2	no	—
210	#107	—	3	4	no	—
211	#103	—	3	8	no	—
212	C₂³×C₃	—	2	4	no	—
213	C₂³×C₃	—	2	4	no	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	2	2	no	—
216	C₂³×C₃	—	2	2	no	—
217	C₂³×C₃	—	2	2	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	2	2	no	—
220	C₂³×C₃	—	2	1	no	—
221	C₂³×C₃	Dic₁₂	1	4	yes	complemented
222	C₂³×C₃	C₃×Q₁₆	1	4	yes	complemented
223	C₂³×C₃	C₂×D₁₂	1	2	yes	—
224	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
225	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
226	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
227	C₃×Q₈	—	6	4	no	—
228	C₃×Q₈	—	6	4	no	—
229	C₃×Q₈	—	12	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	2	8	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	6	4	no	—
248	C₂×C₃×C₄	—	6	4	no	—
249	C₂×C₃×C₄	—	12	4	no	—
250	C₂×C₃×C₄	—	12	4	no	—
251	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
252	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
253	C₂×C₃×C₄	#235	1	2	yes	—
254	C₂×C₃×C₄	C₂×#67	1	2	yes	—
255	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
258	C₂×C₃×C₄	C₃×#41	1	2	yes	—
259	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
261	C₂×Dic₃	—	2	4	no	—
262	C₂×Dic₃	—	2	4	no	—
263	C₂×Dic₃	—	4	4	no	—
264	C₂×Dic₃	—	4	4	no	—
265	Dic₆	—	2	4	no	—
266	Dic₆	—	2	4	no	—
267	Dic₆	—	4	4	no	—
268	C₃×C₈	—	2	4	no	—
269	C₃×C₈	—	2	2	no	—
270	C₃×C₈	—	2	2	no	—
271	C₃×C₈	—	2	4	no	—
272	C₃×C₈	C₂×#67	1	4	yes	—
273	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
274	C₂×C₃²	—	2	4	no	—
275	C₂×C₃²	#467	1	4	yes	complemented
276	C₂×C₃²	C₂×#121	1	1	yes	characteristic
277	C₂×C₃²	C₂²×Q₁₆	1	1	yes	characteristic
278	C₂×C₃²	C₂×#135	1	1	yes	characteristic
279	C₂⁴	C₃×D₁₂	1	1	yes	characteristic
280	C₂×Q₈	—	3	4	no	—
281	C₂×Q₈	—	6	2	no	—
282	C₂×Q₈	—	6	4	no	—
283	C₂×Q₈	—	6	4	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	6	2	no	—
287	C₂²×C₄	—	6	2	no	—
288	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
289	C₂²×C₄	C₃×D₁₂	1	2	yes	—
290	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
291	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
292	Q₁₆	—	6	8	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	8	no	—
295	C₂×C₈	C₃×#67	1	4	yes	—
296	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
297	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
298	C₄⋊C₄	—	3	4	no	—
299	C₄⋊C₄	—	6	2	no	—
300	C₄⋊C₄	—	6	8	no	—
301	C₂²⋊C₄	—	6	8	no	—
302	C₂²×C₃	—	2	4	no	—
303	C₂²×C₃	—	2	16	no	—
304	C₂²×C₃	—	2	4	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	8	no	—
310	C₂²×C₃	—	2	8	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	2	2	no	—
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	#904	1	2	yes	—
317	C₂²×C₃	C₂×Dic₁₂	1	2	yes	—
318	C₂²×C₃	C₂×Dic₁₂	1	4	yes	complemented
319	C₂²×C₃	#930	1	2	yes	—
320	C₂²×C₃	C₃×#121	1	2	yes	—
321	C₂²×C₃	C₂×C₃×Q₁₆	1	2	yes	—
322	C₂²×C₃	C₂×C₃×Q₁₆	1	4	yes	complemented
323	C₂²×C₃	C₃×#135	1	2	yes	—
324	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
325	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
326	C₃×C₄	—	2	4	no	—
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	—	2	2	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	1	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	12	4	no	—
333	C₃×C₄	—	12	4	no	—
334	C₃×C₄	#930	1	2	yes	—
335	C₃×C₄	C₃×#121	1	2	yes	—
336	C₃×C₄	C₂×#235	1	1	yes	characteristic
337	C₃×C₄	C₂²×#67	1	1	yes	characteristic
338	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
339	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
340	Dic₃	—	4	4	no	—
341	Dic₃	—	4	4	no	—
342	C₃²	C₂×#467	1	1	yes	characteristic, complemented, Sylow
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	C₃×Dic₁₂	1	4	yes	complemented
346	C₂³	C₂×C₃×D₁₂	1	2	yes	—
347	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
348	Q₈	—	6	4	no	—
349	Q₈	—	6	4	no	—
350	Q₈	—	12	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	6	4	no	—
356	C₂×C₄	—	6	4	no	—
357	C₂×C₄	—	12	4	no	—
358	C₂×C₄	—	12	4	no	—
359	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
360	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
361	C₂×C₄	C₃×#235	1	2	yes	—
362	C₂×C₄	C₂×C₃×#67	1	2	yes	—
363	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	C₂×C₃×#67	1	4	yes	—
366	C₂×C₃	—	2	8	no	—
367	C₂×C₃	—	2	4	no	—
368	C₂×C₃	—	2	4	no	—
369	C₂×C₃	—	2	1	no	—
370	C₂×C₃	—	2	4	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	#5116	1	4	yes	direct product factor
374	C₂×C₃	C₃×#467	1	4	yes	complemented
375	C₂×C₃	C₂×#904	1	1	yes	characteristic
376	C₂×C₃	C₂²×Dic₁₂	1	1	yes	characteristic
377	C₂×C₃	C₂×#930	1	1	yes	characteristic
378	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
379	C₂×C₃	C₂²×C₃×Q₁₆	1	1	yes	characteristic
380	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
381	C₂²	—	2	2	no	—
382	C₂²	—	2	8	no	—
383	C₂²	—	2	2	no	—
384	C₂²	C₃×#904	1	2	yes	—
385	C₂²	C₂×C₃×Dic₁₂	1	2	yes	—
386	C₂²	C₂×C₃×Dic₁₂	1	4	yes	complemented
387	C₂²	C₃×#930	1	2	yes	—
388	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	12	4	no	—
391	C₄	—	12	4	no	—
392	C₄	C₃×#930	1	2	yes	—
393	C₄	C₂×C₃×#235	1	1	yes	characteristic
394	C₄	C₂²×C₃×#67	1	1	yes	characteristic
395	C₃	—	2	1	no	—
396	C₃	C₂×#5116	1	1	yes	characteristic, direct product factor
397	C₃	C₂×C₃×#467	1	1	yes	characteristic, complemented
398	C₂	—	2	4	no	—
399	C₂	C₃×#5116	1	4	yes	direct product factor
400	C₂	C₂×C₃×#904	1	1	yes	characteristic
401	C₂	C₂²×C₃×Dic₁₂	1	1	yes	characteristic
402	C₂	C₂×C₃×#930	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	C₂³×C₃²×C₈	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂⁴×C₃²	D₄
hypercenter	C₂³×C₃×C₈	D₃
hypocenter	C₃	C₂×C₃×#467
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂³×C₃×C₈

Complements

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

N	H ≅ G/N	type
3. C₂²×C₃×Dic₁₂	C₂	semidirect
4. C₃×#5116	C₂	direct (N × H)
5. C₂×C₃×#818	C₂	semidirect
6. C₂×C₃×#816	C₂	semidirect
8. C₂×#5116	C₃	direct (N × H)
21. C₂×C₃×Dic₁₂	C₂²	semidirect
22. C₃×#818	C₂²	semidirect
23. C₃×#816	C₂²	semidirect
30. C₂²×Dic₁₂	C₂×C₃	semidirect
34. #5116	C₂×C₃	direct (N × H)
35. C₂×#818	C₂×C₃	semidirect
36. C₂×#816	C₂×C₃	semidirect
91. C₂×Dic₁₂	C₂²×C₃	semidirect
94. #818	C₂²×C₃	semidirect
95. #816	C₂²×C₃	semidirect
98. C₂³×C₃²	Q₁₆	semidirect
188. C₂²×C₃²	C₂×Q₁₆	semidirect
221. C₂³×C₃	Dic₁₂	semidirect
222. C₂³×C₃	C₃×Q₁₆	semidirect
275. C₂×C₃²	#467	semidirect
318. C₂²×C₃	C₂×Dic₁₂	semidirect
322. C₂²×C₃	C₂×C₃×Q₁₆	semidirect
342. C₃²	C₂×#467	semidirect
345. C₂³	C₃×Dic₁₂	semidirect
373. C₂×C₃	#5116	direct (N × H)
374. C₂×C₃	C₃×#467	semidirect
386. C₂²	C₂×C₃×Dic₁₂	semidirect
396. C₃	C₂×#5116	direct (N × H)
397. C₃	C₂×C₃×#467	semidirect
399. C₂	C₃×#5116	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃²×C₈	2
C₂×C₃×#924	2
C₂²×C₃×Dic₁₂	2
C₃×#5116	2
C₂×C₃×#818	2
C₂×C₃×#816	2
C₂×C₃×#467	3
C₂×#5116	3

Subgroups — C2×C3×#5116 #11866781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5116 #11866781