Subgroups — C₂×D₃×#798 #11899365

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#63625	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#798	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#63544	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#63543	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×#798	C₂	1	8	yes	maximal, direct product factor
9	C₂×D₃×M₃₂	—	3	1	no	maximal
10	C₂²×#798	—	3	1	no	maximal
11	C₂×C₄×D₃²	C₄	1	1	yes	characteristic
12	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
15	C₂×#3710	C₄	1	1	yes	characteristic
16	C₂×D₃×C₃⋊C₈	C₄	1	1	yes	characteristic
17	C₂×D₃×C₃⋊C₈	C₄	1	1	yes	characteristic
18	D₃²×C₈	C₄	1	4	yes	—
19	D₃²×C₈	C₂²	1	4	yes	—
20	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
22	#63625	C₂²	1	4	yes	complemented
23	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₃×#798	C₂²	1	4	yes	complemented
26	C₃×D₃×C₁₆	C₂²	1	4	yes	complemented
27	#63544	C₂²	1	4	yes	complemented
28	#63543	C₂²	1	4	yes	complemented
29	D₃×C₃⋊C₁₆	C₂²	1	4	yes	complemented
30	C₂²×D₃×C₈	—	3	1	no	—
31	C₂²×D₃×C₈	—	3	1	no	—
32	C₂×C₃×M₃₂	—	3	1	no	—
33	C₂²×C₃×C₁₆	—	3	1	no	—
34	C₂×#812	—	3	1	no	—
35	C₂²×C₃⋊C₁₆	—	3	1	no	—
36	D₃×M₃₂	—	3	8	no	—
37	C₂×#798	—	3	1	no	—
38	C₂×#798	—	3	1	no	—
39	C₂×#798	—	3	1	no	—
40	C₂×#798	—	3	1	no	—
41	C₂×#798	—	3	1	no	—
42	C₂×#798	—	3	8	no	—
43	C₂×#798	—	6	1	no	—
44	C₂×#798	D₃	1	1	yes	characteristic, direct product factor
45	C₂×D₃×C₁₆	—	3	1	no	—
46	C₂×D₃×C₁₆	D₃	1	1	yes	characteristic, complemented
47	C₂²×D₃²	C₈	1	1	yes	characteristic
48	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
51	C₂×#624	C₈	1	1	yes	characteristic
52	C₂×D₃×Dic₃	C₈	1	1	yes	characteristic
53	C₂×D₃×Dic₃	C₈	1	1	yes	characteristic
54	C₄×D₃²	C₈	1	4	yes	—
55	C₄×D₃²	C₂×C₄	1	4	yes	—
56	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
57	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
58	C₈×C₃⋊D₃	C₂×C₄	1	2	yes	—
59	C₈×C₃⋊D₃	C₂³	1	2	yes	—
60	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
62	C₃×D₃×C₈	C₂×C₄	1	2	yes	—
63	C₃×D₃×C₈	C₂×C₄	1	2	yes	—
64	C₃×D₃×C₈	C₂³	1	2	yes	—
65	C₃×D₃×C₈	C₂³	1	2	yes	—
66	#3710	C₂×C₄	1	4	yes	—
67	D₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
68	D₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
69	C₃²×C₁₆	C₂³	1	2	yes	complemented
70	C₃⋊(C₃⋊C₁₆)	C₂³	1	2	yes	complemented
71	C₃×C₃⋊C₁₆	C₂³	1	2	yes	complemented
72	C₃×C₃⋊C₁₆	C₂³	1	2	yes	complemented
73	C₂²×M₃₂	—	9	1	no	Sylow
74	C₂²×C₄×D₃	—	3	1	no	—
75	C₂²×C₄×D₃	—	3	1	no	—
76	C₂²×C₃×C₈	—	3	1	no	—
77	C₂²×C₃×C₈	—	3	1	no	—
78	C₂²×C₃⋊C₈	—	3	1	no	—
79	C₂²×C₃⋊C₈	—	3	1	no	—
80	C₂×D₃×C₈	—	3	1	no	—
81	C₂×D₃×C₈	—	3	1	no	—
82	C₂×D₃×C₈	—	3	1	no	—
83	C₂×D₃×C₈	—	3	1	no	—
84	C₂×D₃×C₈	—	3	1	no	—
85	C₂×D₃×C₈	—	3	1	no	—
86	C₂×D₃×C₈	—	3	4	no	—
87	C₂×D₃×C₈	—	3	4	no	—
88	C₂×D₃×C₈	—	3	4	no	—
89	C₂×D₃×C₈	—	3	4	no	—
90	C₂×D₃×C₈	—	6	1	no	—
91	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
92	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
93	C₃×M₃₂	—	3	4	no	—
94	C₂×C₃×C₁₆	—	2	1	no	—
95	C₂×C₃×C₁₆	—	3	1	no	—
96	C₂×C₃×C₁₆	—	3	1	no	—
97	C₂×C₃×C₁₆	—	3	4	no	—
98	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
99	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
100	#812	—	3	4	no	—
101	C₂×C₃⋊C₁₆	—	3	1	no	—
102	C₂×C₃⋊C₁₆	—	3	1	no	—
103	C₂×C₃⋊C₁₆	—	3	4	no	—
104	C₂×C₃⋊C₁₆	—	6	1	no	—
105	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
106	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
107	#798	—	3	4	no	—
108	#798	—	3	4	no	—
109	#798	—	3	4	no	—
110	#798	—	3	4	no	—
111	#798	—	3	4	no	—
112	#798	—	6	4	no	—
113	#798	C₂×D₃	1	4	yes	direct product factor
114	D₃×C₁₆	—	3	4	no	—
115	D₃×C₁₆	C₂×D₃	1	4	yes	complemented
116	C₂²×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
117	C₂²×C₃×D₃	C₂×C₈	1	1	yes	characteristic
118	C₂²×C₃×D₃	C₂×C₈	1	1	yes	characteristic
119	C₂×D₃²	—	2	4	no	—
120	C₂×D₃²	C₂×C₈	1	4	yes	—
121	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃⋊Dic₃	C₂×C₈	1	1	yes	characteristic
123	C₄×C₃⋊D₃	C₂×C₈	1	2	yes	—
124	C₄×C₃⋊D₃	C₂²×C₄	1	2	yes	—
125	C₂×C₃×Dic₃	C₂×C₈	1	1	yes	characteristic
126	C₂×C₃×Dic₃	C₂×C₈	1	1	yes	characteristic
127	C₃×C₄×D₃	C₂×C₈	1	2	yes	—
128	C₃×C₄×D₃	C₂×C₈	1	2	yes	—
129	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
130	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
131	#624	C₂×C₈	1	4	yes	—
132	D₃×Dic₃	C₂×C₈	1	4	yes	—
133	D₃×Dic₃	C₂×C₈	1	4	yes	—
134	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
135	C₃²×C₈	C₂⁴	1	1	yes	characteristic
136	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	2	yes	—
137	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
138	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
139	C₂³×C₈	—	9	1	no	—
140	C₂×M₃₂	—	3	1	no	—
141	C₂×M₃₂	—	9	1	no	—
142	C₂×M₃₂	—	9	8	no	—
143	C₂×M₃₂	—	9	1	no	—
144	C₂×M₃₂	—	9	1	no	—
145	C₂²×C₁₆	—	3	1	no	—
146	C₂²×C₁₆	—	9	1	no	—
147	C₂³×D₃	—	3	1	no	—
148	C₂³×D₃	—	3	1	no	—
149	C₂²×C₃×C₄	—	3	1	no	—
150	C₂²×C₃×C₄	—	3	1	no	—
151	C₂²×Dic₃	—	3	1	no	—
152	C₂²×Dic₃	—	3	1	no	—
153	C₂×C₄×D₃	—	3	1	no	—
154	C₂×C₄×D₃	—	3	1	no	—
155	C₂×C₄×D₃	—	3	1	no	—
156	C₂×C₄×D₃	—	3	1	no	—
157	C₂×C₄×D₃	—	3	1	no	—
158	C₂×C₄×D₃	—	3	1	no	—
159	C₂×C₄×D₃	—	3	4	no	—
160	C₂×C₄×D₃	—	3	4	no	—
161	C₂×C₄×D₃	—	3	4	no	—
162	C₂×C₄×D₃	—	3	4	no	—
163	C₂×C₄×D₃	—	6	1	no	—
164	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
165	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
166	C₂×C₃×C₈	—	2	1	no	—
167	C₂×C₃×C₈	—	3	1	no	—
168	C₂×C₃×C₈	—	3	1	no	—
169	C₂×C₃×C₈	—	3	2	no	—
170	C₂×C₃×C₈	—	3	2	no	—
171	C₂×C₃×C₈	—	3	2	no	—
172	C₂×C₃×C₈	—	3	2	no	—
173	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
174	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
175	C₂×C₃⋊C₈	—	3	1	no	—
176	C₂×C₃⋊C₈	—	3	1	no	—
177	C₂×C₃⋊C₈	—	3	4	no	—
178	C₂×C₃⋊C₈	—	3	4	no	—
179	C₂×C₃⋊C₈	—	6	1	no	—
180	C₂×C₃⋊C₈	C₄×D₃	1	1	yes	characteristic
181	C₂×C₃⋊C₈	C₄×D₃	1	1	yes	characteristic
182	D₃×C₈	—	3	4	no	—
183	D₃×C₈	—	3	4	no	—
184	D₃×C₈	—	3	2	no	—
185	D₃×C₈	—	3	2	no	—
186	D₃×C₈	—	3	2	no	—
187	D₃×C₈	—	3	2	no	—
188	D₃×C₈	—	3	4	no	—
189	D₃×C₈	—	3	4	no	—
190	D₃×C₈	—	6	2	no	—
191	D₃×C₈	—	6	2	no	—
192	D₃×C₈	C₄×D₃	1	2	yes	—
193	D₃×C₈	C₄×D₃	1	2	yes	—
194	D₃×C₈	C₂²×D₃	1	2	yes	—
195	D₃×C₈	C₂²×D₃	1	2	yes	—
196	C₃×C₁₆	—	2	2	no	—
197	C₃×C₁₆	—	3	2	no	—
198	C₃×C₁₆	—	3	2	no	—
199	C₃×C₁₆	C₂²×D₃	1	2	yes	complemented
200	C₃×C₁₆	C₂²×D₃	1	2	yes	complemented
201	C₃⋊C₁₆	—	3	2	no	—
202	C₃⋊C₁₆	—	3	2	no	—
203	C₃⋊C₁₆	—	6	2	no	—
204	C₃⋊C₁₆	C₂²×D₃	1	2	yes	complemented
205	C₃⋊C₁₆	C₂²×D₃	1	2	yes	complemented
206	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
207	C₂×C₃⋊D₃	—	2	2	no	—
208	C₂×C₃⋊D₃	C₂²×C₈	1	2	yes	—
209	C₂×C₃×D₃	—	2	2	no	—
210	C₂×C₃×D₃	M₃₂	1	4	yes	complemented
211	C₂×C₃×D₃	C₂²×C₈	1	2	yes	—
212	C₂×C₃×D₃	C₂²×C₈	1	2	yes	—
213	D₃²	—	2	8	no	—
214	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
215	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
216	C₃⋊Dic₃	C₂²×C₈	1	2	yes	—
217	C₃×Dic₃	C₂²×C₈	1	2	yes	—
218	C₃×Dic₃	C₂²×C₈	1	2	yes	—
219	C₂³×C₄	—	9	1	no	—
220	C₂²×C₈	—	3	1	no	—
221	C₂²×C₈	—	3	1	no	—
222	C₂²×C₈	—	9	1	no	—
223	C₂²×C₈	—	9	4	no	—
224	C₂²×C₈	—	9	4	no	—
225	C₂²×C₈	—	9	1	no	—
226	C₂²×C₈	—	9	1	no	—
227	C₂²×C₈	—	9	1	no	—
228	M₃₂	—	3	4	no	—
229	M₃₂	—	9	4	no	—
230	M₃₂	—	9	4	no	—
231	M₃₂	—	9	4	no	—
232	C₂×C₁₆	—	3	1	no	—
233	C₂×C₁₆	—	3	1	no	—
234	C₂×C₁₆	—	3	4	no	—
235	C₂×C₁₆	—	9	4	no	—
236	C₂×C₁₆	—	9	1	no	—
237	C₂×C₁₆	D₃²	1	1	yes	characteristic, complemented
238	C₂³×C₃	—	3	1	no	—
239	C₂³×C₃	—	3	1	no	—
240	C₂²×D₃	—	3	1	no	—
241	C₂²×D₃	—	3	1	no	—
242	C₂²×D₃	—	3	4	no	—
243	C₂²×D₃	—	3	4	no	—
244	C₂²×D₃	—	6	1	no	—
245	C₂²×D₃	—	6	4	no	—
246	C₂²×D₃	—	6	4	no	—
247	C₂²×D₃	D₃×C₈	1	1	yes	characteristic
248	C₂²×D₃	D₃×C₈	1	1	yes	characteristic
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	3	1	no	—
251	C₂×C₃×C₄	—	3	1	no	—
252	C₂×C₃×C₄	—	3	2	no	—
253	C₂×C₃×C₄	—	3	2	no	—
254	C₂×C₃×C₄	—	3	2	no	—
255	C₂×C₃×C₄	—	3	2	no	—
256	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
258	C₂×Dic₃	—	3	1	no	—
259	C₂×Dic₃	—	3	1	no	—
260	C₂×Dic₃	—	3	4	no	—
261	C₂×Dic₃	—	3	4	no	—
262	C₂×Dic₃	—	6	1	no	—
263	C₂×Dic₃	D₃×C₈	1	1	yes	characteristic
264	C₂×Dic₃	D₃×C₈	1	1	yes	characteristic
265	C₄×D₃	—	3	4	no	—
266	C₄×D₃	—	3	4	no	—
267	C₄×D₃	—	3	2	no	—
268	C₄×D₃	—	3	2	no	—
269	C₄×D₃	—	3	2	no	—
270	C₄×D₃	—	3	2	no	—
271	C₄×D₃	—	3	4	no	—
272	C₄×D₃	—	3	4	no	—
273	C₄×D₃	—	6	2	no	—
274	C₄×D₃	—	6	2	no	—
275	C₄×D₃	D₃×C₈	1	2	yes	—
276	C₄×D₃	D₃×C₈	1	2	yes	—
277	C₄×D₃	C₂×C₄×D₃	1	2	yes	—
278	C₄×D₃	C₂×C₄×D₃	1	2	yes	—
279	C₃×C₈	—	2	1	no	—
280	C₃×C₈	—	2	1	no	—
281	C₃×C₈	—	3	2	no	—
282	C₃×C₈	—	3	2	no	—
283	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
284	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
285	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
286	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
287	C₃⋊C₈	—	3	2	no	—
288	C₃⋊C₈	—	3	2	no	—
289	C₃⋊C₈	—	6	2	no	—
290	C₃⋊C₈	C₂×C₄×D₃	1	2	yes	—
291	C₃⋊C₈	C₂×C₄×D₃	1	2	yes	—
292	C₂×C₃²	C₂×M₃₂	1	2	yes	complemented
293	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
294	C₃⋊D₃	—	2	2	no	—
295	C₃×D₃	—	2	2	no	—
296	C₃×D₃	C₂×M₃₂	1	4	yes	complemented
297	C₂⁴	—	9	1	no	—
298	C₂²×C₄	—	3	1	no	—
299	C₂²×C₄	—	3	1	no	—
300	C₂²×C₄	—	9	4	no	—
301	C₂²×C₄	—	9	1	no	—
302	C₂²×C₄	—	9	4	no	—
303	C₂²×C₄	—	9	1	no	—
304	C₂²×C₄	—	9	1	no	—
305	C₂²×C₄	—	9	1	no	—
306	C₂×C₈	—	3	1	no	—
307	C₂×C₈	—	3	1	no	—
308	C₂×C₈	—	3	2	no	—
309	C₂×C₈	—	3	2	no	—
310	C₂×C₈	—	3	2	no	—
311	C₂×C₈	—	3	2	no	—
312	C₂×C₈	—	9	4	no	—
313	C₂×C₈	—	9	4	no	—
314	C₂×C₈	—	9	4	no	—
315	C₂×C₈	—	9	1	no	—
316	C₂×C₈	—	9	2	no	—
317	C₂×C₈	—	9	2	no	—
318	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
319	C₁₆	—	3	2	no	—
320	C₁₆	—	3	2	no	—
321	C₁₆	—	9	2	no	—
322	C₁₆	C₂×D₃²	1	2	yes	complemented
323	C₂²×C₃	—	2	1	no	—
324	C₂²×C₃	—	3	4	no	—
325	C₂²×C₃	—	3	2	no	—
326	C₂²×C₃	—	3	2	no	—
327	C₂²×C₃	—	6	2	no	—
328	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
329	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
330	C₂×D₃	—	2	2	no	—
331	C₂×D₃	—	3	2	no	—
332	C₂×D₃	—	3	2	no	—
333	C₂×D₃	—	6	2	no	—
334	C₂×D₃	—	6	8	no	—
335	C₂×D₃	—	6	2	no	—
336	C₂×D₃	—	6	2	no	—
337	C₂×D₃	—	6	8	no	—
338	C₂×D₃	—	12	2	no	—
339	C₂×D₃	#798	1	4	yes	direct product factor
340	C₂×D₃	C₂×D₃×C₈	1	2	yes	—
341	C₂×D₃	C₂×D₃×C₈	1	2	yes	—
342	C₃×C₄	—	2	1	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	3	2	no	—
345	C₃×C₄	—	3	2	no	—
346	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
347	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
348	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
349	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
350	Dic₃	—	3	2	no	—
351	Dic₃	—	3	2	no	—
352	Dic₃	—	6	2	no	—
353	Dic₃	C₂×D₃×C₈	1	2	yes	—
354	Dic₃	C₂×D₃×C₈	1	2	yes	—
355	C₃²	C₂²×M₃₂	1	1	yes	characteristic, complemented, Sylow
356	C₂³	—	3	1	no	—
357	C₂³	—	3	1	no	—
358	C₂³	—	9	4	no	—
359	C₂³	—	9	1	no	—
360	C₂³	—	18	4	no	—
361	C₂×C₄	—	3	1	no	—
362	C₂×C₄	—	3	1	no	—
363	C₂×C₄	—	3	2	no	—
364	C₂×C₄	—	3	2	no	—
365	C₂×C₄	—	3	2	no	—
366	C₂×C₄	—	3	2	no	—
367	C₂×C₄	—	9	4	no	—
368	C₂×C₄	—	9	4	no	—
369	C₂×C₄	—	9	4	no	—
370	C₂×C₄	—	9	1	no	—
371	C₂×C₄	—	9	2	no	—
372	C₂×C₄	—	9	2	no	—
373	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
374	C₈	—	3	2	no	—
375	C₈	—	3	2	no	—
376	C₈	—	9	2	no	—
377	C₈	C₄×D₃²	1	1	yes	characteristic
378	C₈	C₂²×D₃²	1	1	yes	characteristic
379	C₂×C₃	—	2	2	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	3	4	no	—
382	C₂×C₃	—	6	2	no	—
383	C₂×C₃	C₂×#798	1	2	yes	complemented
384	C₂×C₃	D₃×M₃₂	1	2	yes	complemented
385	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
386	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
387	D₃	—	2	2	no	—
388	D₃	—	6	2	no	—
389	D₃	—	6	2	no	—
390	D₃	—	12	2	no	—
391	D₃	C₂×#798	1	4	yes	direct product factor
392	C₂²	—	3	4	no	—
393	C₂²	—	3	2	no	—
394	C₂²	—	3	2	no	—
395	C₂²	—	6	2	no	—
396	C₂²	—	9	2	no	—
397	C₂²	—	18	8	no	—
398	C₂²	—	18	2	no	—
399	C₂²	D₃²×C₈	1	1	yes	characteristic
400	C₄	—	3	2	no	—
401	C₄	—	3	2	no	—
402	C₄	—	9	2	no	—
403	C₄	D₃²×C₈	1	1	yes	characteristic
404	C₄	C₂×C₄×D₃²	1	1	yes	characteristic
405	C₃	—	2	1	no	—
406	C₃	C₂²×#798	1	1	yes	characteristic, complemented
407	C₃	C₂×D₃×M₃₂	1	1	yes	characteristic, complemented
408	C₂	—	3	4	no	—
409	C₂	—	6	2	no	—
410	C₂	—	18	2	no	—
411	C₂	D₃×#798	1	2	yes	direct product factor
412	C₂	C₂×D₃²×C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃²
commutator	C₂×C₃²	C₂³×C₈
Frattini	C₈	C₂²×D₃²
Fitting	C₂×C₃²×C₁₆	C₂²
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂²×D₃²	C₈
cosocle	C₃²×C₈	C₂⁴
hypercenter	C₂×C₁₆	D₃²
hypocenter	C₃²	C₂²×M₃₂
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#63625	C₂	semidirect
3. C₂×C₃×#798	C₂	semidirect
4. C₂×C₃×D₃×C₁₆	C₂	semidirect
5. C₂×#63544	C₂	semidirect
6. C₂×#63543	C₂	semidirect
7. C₂×D₃×C₃⋊C₁₆	C₂	semidirect
8. D₃×#798	C₂	direct (N × H)
20. C₂×C₃²×C₁₆	C₂²	semidirect
21. C₂×C₃⋊(C₃⋊C₁₆)	C₂²	semidirect
22. #63625	C₂²	semidirect
23. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
24. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
25. C₃×#798	C₂²	semidirect
26. C₃×D₃×C₁₆	C₂²	semidirect
27. #63544	C₂²	semidirect
28. #63543	C₂²	semidirect
29. D₃×C₃⋊C₁₆	C₂²	semidirect
44. C₂×#798	D₃	direct (N × H)
46. C₂×D₃×C₁₆	D₃	semidirect
69. C₃²×C₁₆	C₂³	semidirect
70. C₃⋊(C₃⋊C₁₆)	C₂³	semidirect
71. C₃×C₃⋊C₁₆	C₂³	semidirect
72. C₃×C₃⋊C₁₆	C₂³	semidirect
98. C₂×C₃×C₁₆	C₂×D₃	semidirect
99. C₂×C₃×C₁₆	C₂×D₃	semidirect
105. C₂×C₃⋊C₁₆	C₂×D₃	semidirect
106. C₂×C₃⋊C₁₆	C₂×D₃	semidirect
113. #798	C₂×D₃	direct (N × H)
115. D₃×C₁₆	C₂×D₃	semidirect
199. C₃×C₁₆	C₂²×D₃	semidirect
200. C₃×C₁₆	C₂²×D₃	semidirect
204. C₃⋊C₁₆	C₂²×D₃	semidirect
205. C₃⋊C₁₆	C₂²×D₃	semidirect
210. C₂×C₃×D₃	M₃₂	semidirect
237. C₂×C₁₆	D₃²	semidirect
292. C₂×C₃²	C₂×M₃₂	semidirect
296. C₃×D₃	C₂×M₃₂	semidirect
322. C₁₆	C₂×D₃²	semidirect
339. C₂×D₃	#798	direct (N × H)
355. C₃²	C₂²×M₃₂	semidirect
383. C₂×C₃	C₂×#798	semidirect
384. C₂×C₃	D₃×M₃₂	semidirect
391. D₃	C₂×#798	direct (N × H)
406. C₃	C₂²×#798	semidirect
407. C₃	C₂×D₃×M₃₂	semidirect
411. C₂	D₃×#798	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×D₃²×C₈	2
C₂×#63625	2
C₂×C₃×#798	2
C₂×C₃×D₃×C₁₆	2
C₂×#63544	2
C₂×#63543	2
C₂×D₃×C₃⋊C₁₆	2
D₃×#798	2
C₂×D₃×M₃₂	3
C₂²×#798	3

Subgroups — C2×D3×#798 #11899365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×#798 #11899365