Subgroups — C₂×C₃×#63457 #13152404

Order 1728.

1370 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃₆	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×C₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×(C₂×D₉)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₃×#63457	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#895	—	3	1	no	maximal
8	C₂×#63457	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂³×C₃×D₉	C₂²	1	2	yes	—
10	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₃₆	—	2	8	no	—
15	C₂×C₃×D₃₆	—	2	4	no	—
16	C₂×C₃×D₃₆	C₂²	1	8	yes	complemented
17	C₂×C₃×D₃₆	C₂²	1	4	yes	complemented
18	C₂×C₃×C₄×D₉	—	2	4	no	—
19	C₂×C₃×C₄×D₉	C₂²	1	4	yes	complemented
20	C₃×C₉×C₄⋊C₄	C₂²	1	4	yes	complemented
21	C₃×(C₂×D₉)⋊C₄	C₂²	1	8	yes	complemented
22	C₂²×C₃×D₁₂	—	3	2	no	—
23	C₂²×C₃×D₁₂	—	3	1	no	—
24	C₂²×C₃×C₄×D₃	—	3	1	no	—
25	C₂×C₃²×C₄⋊C₄	D₃	1	1	yes	characteristic
26	C₂×C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
27	C₃×#895	—	3	8	no	—
28	C₂²×D₃₆	C₂×C₃	1	2	yes	complemented
29	C₂²×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×C₉×C₄⋊C₄	—	2	1	no	—
32	C₂×C₉×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×(C₂×D₉)⋊C₄	C₂×C₃	1	2	yes	complemented
34	#63457	C₂×C₃	1	8	yes	direct product factor
35	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
36	C₂²×C₃×D₉	—	2	2	no	—
37	C₂²×C₃×D₉	—	2	2	no	—
38	C₂²×C₃×D₉	—	2	4	no	—
39	C₂²×C₃×D₉	—	2	4	no	—
40	C₂²×C₃×D₉	—	2	4	no	—
41	C₂²×C₃×D₉	D₄	1	4	yes	complemented
42	C₂²×C₃×D₉	C₂³	1	4	yes	—
43	C₂²×C₃×D₉	C₂³	1	2	yes	—
44	C₂×C₃×C₄×C₉	—	2	4	no	—
45	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
46	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
48	C₂×C₃×Dic₉	—	2	2	no	—
49	C₂×C₃×Dic₉	C₂³	1	2	yes	—
50	C₃×D₃₆	—	2	16	no	—
51	C₃×D₃₆	—	2	8	no	—
52	C₃×C₄×D₉	—	2	8	no	—
53	C₂×C₃×#121	—	9	1	no	—
54	C₂×#895	—	3	1	no	—
55	C₂³×C₃×D₃	—	3	1	no	—
56	C₂³×C₃×D₃	—	3	2	no	—
57	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	—
58	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
59	C₂²×C₃×Dic₃	—	3	1	no	—
60	C₂×C₃×D₁₂	—	3	8	no	—
61	C₂×C₃×D₁₂	—	3	4	no	—
62	C₂×C₃×D₁₂	—	6	8	no	—
63	C₂×C₃×D₁₂	—	6	4	no	—
64	C₂×C₃×C₄×D₃	—	3	4	no	—
65	C₂×C₃×C₄×D₃	—	6	4	no	—
66	C₂³×D₉	C₂²×C₃	1	2	yes	—
67	C₂³×D₉	C₂²×C₃	1	1	yes	characteristic
68	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
69	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
70	C₂²×C₄×C₉	—	2	1	no	—
71	C₂²×C₄×C₉	—	2	2	no	—
72	C₂²×C₄×C₉	C₂²×C₃	1	2	yes	—
73	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
74	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
75	C₂×D₃₆	—	2	8	no	—
76	C₂×D₃₆	—	2	4	no	—
77	C₂×D₃₆	C₂²×C₃	1	8	yes	complemented
78	C₂×D₃₆	C₂²×C₃	1	4	yes	complemented
79	C₂×C₄×D₉	—	2	4	no	—
80	C₂×C₄×D₉	C₂²×C₃	1	4	yes	complemented
81	C₉×C₄⋊C₄	—	2	4	no	—
82	C₉×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
83	(C₂×D₉)⋊C₄	C₂²×C₃	1	8	yes	complemented
84	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
85	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
86	C₂²×C₃×C₉	#41	1	2	yes	—
87	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
88	C₂×C₃×D₉	—	2	8	no	—
89	C₂×C₃×D₉	—	2	2	no	—
90	C₂×C₃×D₉	—	2	2	no	—
91	C₂×C₃×D₉	—	2	4	no	—
92	C₂×C₃×D₉	—	2	4	no	—
93	C₂×C₃×D₉	—	2	4	no	—
94	C₂×C₃×D₉	—	4	8	no	—
95	C₂×C₃×D₉	C₂×D₄	1	4	yes	complemented
96	C₃×C₄×C₉	—	2	4	no	—
97	C₃×C₄×C₉	C₂×D₄	1	4	yes	complemented
98	C₃×Dic₉	—	2	2	no	—
99	C₂²×C₃×D₄	—	9	2	no	—
100	C₂²×C₃×D₄	—	9	1	no	—
101	C₂³×C₃×C₄	—	9	1	no	—
102	C₂²×D₁₂	—	3	2	no	—
103	C₂²×D₁₂	—	3	1	no	—
104	C₂²×C₄×D₃	—	3	1	no	—
105	C₃×#121	—	9	8	no	—
106	C₂×C₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₃×C₄⋊C₄	D₉	1	1	yes	characteristic, complemented
108	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
109	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
110	C₂×(C₂×D₃)⋊C₄	—	3	2	no	—
111	#895	—	3	8	no	—
112	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
113	C₂²×C₃×D₃	—	3	4	no	—
114	C₂²×C₃×D₃	—	3	2	no	—
115	C₂²×C₃×D₃	—	3	4	no	—
116	C₂²×C₃×D₃	—	6	2	no	—
117	C₂²×C₃×D₃	—	6	2	no	—
118	C₂²×C₃×D₃	—	6	4	no	—
119	C₂²×C₃×D₃	—	6	4	no	—
120	C₂²×C₃×D₃	—	6	4	no	—
121	C₂×C₃²×C₄	—	2	4	no	—
122	C₂×C₃²×C₄	D₁₂	1	4	yes	—
123	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
124	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
125	C₂×C₃×Dic₃	—	3	2	no	—
126	C₂×C₃×Dic₃	—	6	2	no	—
127	C₃×D₁₂	—	6	16	no	—
128	C₃×D₁₂	—	6	8	no	—
129	C₃×C₄×D₃	—	6	8	no	—
130	C₂³×C₉	—	2	1	no	—
131	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
132	C₂²×D₉	—	2	2	no	—
133	C₂²×D₉	—	2	2	no	—
134	C₂²×D₉	—	2	4	no	—
135	C₂²×D₉	—	2	4	no	—
136	C₂²×D₉	—	2	4	no	—
137	C₂²×D₉	C₃×D₄	1	4	yes	complemented
138	C₂²×D₉	C₂³×C₃	1	4	yes	—
139	C₂²×D₉	C₂³×C₃	1	2	yes	—
140	C₂×C₄×C₉	—	2	4	no	—
141	C₂×C₄×C₉	—	2	4	no	—
142	C₂×C₄×C₉	—	2	2	no	—
143	C₂×C₄×C₉	—	2	4	no	—
144	C₂×C₄×C₉	—	4	4	no	—
145	C₂×C₄×C₉	C₃×D₄	1	4	yes	complemented
146	C₂×C₄×C₉	C₂³×C₃	1	4	yes	—
147	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
148	C₂×Dic₉	—	2	2	no	—
149	C₂×Dic₉	C₂³×C₃	1	2	yes	—
150	D₃₆	—	2	16	no	—
151	D₃₆	—	2	8	no	—
152	C₄×D₉	—	2	8	no	—
153	C₂×#121	—	9	1	no	Sylow
154	C₂×C₃×C₉	#121	1	4	yes	complemented
155	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
158	C₃×D₉	—	2	4	no	—
159	C₃×D₉	—	4	4	no	—
160	C₂⁴×C₃	—	9	1	no	—
161	C₂⁴×C₃	—	9	2	no	—
162	C₂³×D₃	—	3	1	no	—
163	C₂³×D₃	—	3	2	no	—
164	C₂×C₃×D₄	—	9	8	no	—
165	C₂×C₃×D₄	—	9	4	no	—
166	C₂×C₃×D₄	—	18	8	no	—
167	C₂×C₃×D₄	—	18	4	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	—	2	2	no	—
170	C₂²×C₃×C₄	—	9	1	no	—
171	C₂²×C₃×C₄	—	9	4	no	—
172	C₂²×C₃×C₄	—	18	4	no	—
173	C₂²×C₃×C₄	C₂×D₉	1	2	yes	—
174	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
176	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
177	C₂²×Dic₃	—	3	1	no	—
178	C₂×D₁₂	—	3	8	no	—
179	C₂×D₁₂	—	3	4	no	—
180	C₂×D₁₂	—	6	8	no	—
181	C₂×D₁₂	—	6	4	no	—
182	C₂×C₄×D₃	—	3	4	no	—
183	C₂×C₄×D₃	—	6	4	no	—
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₄⋊C₄	C₂×D₉	1	4	yes	complemented
186	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
187	C₃×C₂²⋊C₄	—	9	8	no	—
188	(C₂×D₃)⋊C₄	—	3	8	no	—
189	C₂²×C₃²	C₂×D₁₂	1	2	yes	—
190	C₂²×C₃²	D₃×D₄	1	2	yes	—
191	C₂²×C₃²	#239	1	2	yes	—
192	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
193	C₂×C₃×D₃	—	3	4	no	—
194	C₂×C₃×D₃	—	6	8	no	—
195	C₂×C₃×D₃	—	6	2	no	—
196	C₂×C₃×D₃	—	6	2	no	—
197	C₂×C₃×D₃	—	6	4	no	—
198	C₂×C₃×D₃	—	6	4	no	—
199	C₂×C₃×D₃	—	6	4	no	—
200	C₂×C₃×D₃	—	12	8	no	—
201	C₃²×C₄	—	2	4	no	—
202	C₃²×C₄	C₂×D₁₂	1	4	yes	—
203	C₃×Dic₃	—	6	2	no	—
204	C₂²×C₉	—	2	1	no	—
205	C₂²×C₉	—	2	2	no	—
206	C₂²×C₉	—	2	2	no	—
207	C₂²×C₉	—	2	2	no	—
208	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
209	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
210	C₂²×C₉	C₃×#41	1	2	yes	—
211	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
212	C₂×D₉	—	2	8	no	—
213	C₂×D₉	—	2	2	no	—
214	C₂×D₉	—	2	2	no	—
215	C₂×D₉	—	2	4	no	—
216	C₂×D₉	—	2	4	no	—
217	C₂×D₉	—	2	4	no	—
218	C₂×D₉	—	4	8	no	—
219	C₂×D₉	C₂×C₃×D₄	1	4	yes	complemented
220	C₄×C₉	—	2	4	no	—
221	C₄×C₉	—	2	4	no	—
222	C₄×C₉	—	4	4	no	—
223	C₄×C₉	C₂×C₃×D₄	1	4	yes	complemented
224	Dic₉	—	2	2	no	—
225	C₂²×D₄	—	9	2	no	—
226	C₂²×D₄	—	9	1	no	—
227	C₂³×C₄	—	9	1	no	—
228	#121	—	9	8	no	—
229	C₂×C₄⋊C₄	C₃×D₉	1	1	yes	characteristic, complemented
230	C₂×C₂²⋊C₄	—	9	2	no	—
231	C₃×C₉	C₂×#121	1	1	yes	characteristic, complemented, Sylow
232	C₂³×C₃	—	2	1	no	—
233	C₂³×C₃	—	9	4	no	—
234	C₂³×C₃	—	9	2	no	—
235	C₂³×C₃	—	9	4	no	—
236	C₂³×C₃	—	18	2	no	—
237	C₂³×C₃	—	18	2	no	—
238	C₂³×C₃	—	18	4	no	—
239	C₂³×C₃	—	18	4	no	—
240	C₂³×C₃	—	18	4	no	—
241	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
242	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
243	C₂²×D₃	—	3	2	no	—
244	C₂²×D₃	—	3	4	no	—
245	C₂²×D₃	—	3	4	no	—
246	C₂²×D₃	—	6	2	no	—
247	C₂²×D₃	—	6	2	no	—
248	C₂²×D₃	—	6	4	no	—
249	C₂²×D₃	—	6	4	no	—
250	C₂²×D₃	—	6	4	no	—
251	C₃×D₄	—	18	16	no	—
252	C₃×D₄	—	18	8	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	4	4	no	—
259	C₂×C₃×C₄	—	9	2	no	—
260	C₂×C₃×C₄	—	18	2	no	—
261	C₂×C₃×C₄	—	18	8	no	—
262	C₂×C₃×C₄	D₃₆	1	4	yes	complemented
263	C₂×C₃×C₄	C₂²×D₉	1	4	yes	—
264	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
265	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
266	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
267	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
268	C₂×Dic₃	—	3	2	no	—
269	C₂×Dic₃	—	6	2	no	—
270	D₁₂	—	6	16	no	—
271	D₁₂	—	6	8	no	—
272	C₄×D₃	—	6	8	no	—
273	C₂×C₃²	#895	1	4	yes	—
274	C₂×C₃²	C₂²×D₁₂	1	1	yes	characteristic
275	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
276	C₂×C₃²	C₂×#239	1	1	yes	characteristic
277	C₃×D₃	—	6	4	no	—
278	C₃×D₃	—	12	4	no	—
279	C₂×C₉	—	2	4	no	—
280	C₂×C₉	—	2	1	no	—
281	C₂×C₉	—	2	1	no	—
282	C₂×C₉	—	2	1	no	—
283	C₂×C₉	C₃×#121	1	4	yes	complemented
284	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
285	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
286	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
287	D₉	—	2	4	no	—
288	D₉	—	4	4	no	—
289	C₂⁴	—	9	1	no	—
290	C₂⁴	—	9	2	no	—
291	C₂×D₄	—	9	8	no	—
292	C₂×D₄	—	9	4	no	—
293	C₂×D₄	—	18	8	no	—
294	C₂×D₄	—	18	4	no	—
295	C₂²×C₄	—	9	1	no	—
296	C₂²×C₄	—	9	4	no	—
297	C₂²×C₄	—	18	4	no	—
298	C₂²×C₄	C₂×C₃×D₉	1	2	yes	—
299	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
300	C₄⋊C₄	C₂×C₃×D₉	1	4	yes	complemented
301	C₂²⋊C₄	—	9	8	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	9	4	no	—
307	C₂²×C₃	—	18	2	no	—
308	C₂²×C₃	—	18	2	no	—
309	C₂²×C₃	—	18	8	no	—
310	C₂²×C₃	—	18	4	no	—
311	C₂²×C₃	—	18	4	no	—
312	C₂²×C₃	—	18	4	no	—
313	C₂²×C₃	—	36	8	no	—
314	C₂²×C₃	C₂×D₃₆	1	2	yes	—
315	C₂²×C₃	D₄×D₉	1	2	yes	—
316	C₂²×C₃	#3701	1	2	yes	—
317	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
318	C₂²×C₃	C₂×C₃×D₁₂	1	2	yes	—
319	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
320	C₂²×C₃	C₃×#239	1	2	yes	—
321	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
322	C₂×D₃	—	3	4	no	—
323	C₂×D₃	—	6	8	no	—
324	C₂×D₃	—	6	2	no	—
325	C₂×D₃	—	6	2	no	—
326	C₂×D₃	—	6	4	no	—
327	C₂×D₃	—	6	4	no	—
328	C₂×D₃	—	6	4	no	—
329	C₂×D₃	—	12	8	no	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	4	4	no	—
334	C₃×C₄	—	18	2	no	—
335	C₃×C₄	C₂×D₃₆	1	4	yes	complemented
336	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
337	Dic₃	—	6	2	no	—
338	C₃²	C₂×#895	1	1	yes	characteristic
339	C₉	—	2	1	no	—
340	C₉	C₂×C₃×#121	1	1	yes	characteristic, complemented
341	C₂³	—	9	2	no	—
342	C₂³	—	9	4	no	—
343	C₂³	—	9	4	no	—
344	C₂³	—	18	2	no	—
345	C₂³	—	18	2	no	—
346	C₂³	—	18	4	no	—
347	C₂³	—	18	4	no	—
348	C₂³	—	18	4	no	—
349	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
350	D₄	—	18	16	no	—
351	D₄	—	18	8	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	9	2	no	—
354	C₂×C₄	—	18	2	no	—
355	C₂×C₄	—	18	8	no	—
356	C₂×C₄	C₃×D₃₆	1	4	yes	complemented
357	C₂×C₄	C₂²×C₃×D₉	1	4	yes	—
358	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
359	C₂×C₃	—	2	1	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	4	no	—
363	C₂×C₃	—	18	4	no	—
364	C₂×C₃	—	36	4	no	—
365	C₂×C₃	#63457	1	4	yes	direct product factor
366	C₂×C₃	C₂²×D₃₆	1	1	yes	characteristic
367	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
368	C₂×C₃	C₂×#3701	1	1	yes	characteristic
369	C₂×C₃	C₃×#895	1	4	yes	—
370	C₂×C₃	C₂²×C₃×D₁₂	1	1	yes	characteristic
371	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
372	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
373	D₃	—	6	4	no	—
374	D₃	—	12	4	no	—
375	C₂²	—	9	4	no	—
376	C₂²	—	18	2	no	—
377	C₂²	—	18	2	no	—
378	C₂²	—	18	8	no	—
379	C₂²	—	18	4	no	—
380	C₂²	—	18	4	no	—
381	C₂²	—	18	4	no	—
382	C₂²	—	36	8	no	—
383	C₂²	C₂×C₃×D₃₆	1	2	yes	—
384	C₂²	C₃×D₄×D₉	1	2	yes	—
385	C₂²	C₃×#3701	1	2	yes	—
386	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
387	C₄	—	2	4	no	—
388	C₄	—	18	2	no	—
389	C₄	C₂×C₃×D₃₆	1	4	yes	complemented
390	C₃	—	2	1	no	—
391	C₃	C₂×#63457	1	1	yes	characteristic, direct product factor
392	C₃	C₂×C₃×#895	1	1	yes	characteristic
393	C₂	—	18	4	no	—
394	C₂	—	36	4	no	—
395	C₂	C₃×#63457	1	4	yes	direct product factor
396	C₂	C₂²×C₃×D₃₆	1	1	yes	characteristic
397	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic
398	C₂	C₂×C₃×#3701	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₄⋊C₄	C₂
socle	C₂³×C₃²	C₂²×D₃
hypercenter	C₂×C₃×C₄⋊C₄	D₉
hypocenter	C₉	C₂×C₃×#121
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₃₆	C₂	semidirect
2. C₂²×C₃×D₃₆	C₂	semidirect
3. C₂²×C₃×C₄×D₉	C₂	semidirect
4. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
5. C₂×C₃×(C₂×D₉)⋊C₄	C₂	semidirect
6. C₃×#63457	C₂	direct (N × H)
8. C₂×#63457	C₃	direct (N × H)
16. C₂×C₃×D₃₆	C₂²	semidirect
17. C₂×C₃×D₃₆	C₂²	semidirect
19. C₂×C₃×C₄×D₉	C₂²	semidirect
20. C₃×C₉×C₄⋊C₄	C₂²	semidirect
21. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
28. C₂²×D₃₆	C₂×C₃	semidirect
29. C₂²×D₃₆	C₂×C₃	semidirect
30. C₂²×C₄×D₉	C₂×C₃	semidirect
32. C₂×C₉×C₄⋊C₄	C₂×C₃	semidirect
33. C₂×(C₂×D₉)⋊C₄	C₂×C₃	semidirect
34. #63457	C₂×C₃	direct (N × H)
41. C₂²×C₃×D₉	D₄	semidirect
45. C₂×C₃×C₄×C₉	D₄	semidirect
77. C₂×D₃₆	C₂²×C₃	semidirect
78. C₂×D₃₆	C₂²×C₃	semidirect
80. C₂×C₄×D₉	C₂²×C₃	semidirect
82. C₉×C₄⋊C₄	C₂²×C₃	semidirect
83. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
95. C₂×C₃×D₉	C₂×D₄	semidirect
97. C₃×C₄×C₉	C₂×D₄	semidirect
107. C₂×C₃×C₄⋊C₄	D₉	semidirect
137. C₂²×D₉	C₃×D₄	semidirect
145. C₂×C₄×C₉	C₃×D₄	semidirect
154. C₂×C₃×C₉	#121	semidirect
185. C₃×C₄⋊C₄	C₂×D₉	semidirect
219. C₂×D₉	C₂×C₃×D₄	semidirect
223. C₄×C₉	C₂×C₃×D₄	semidirect
229. C₂×C₄⋊C₄	C₃×D₉	semidirect
231. C₃×C₉	C₂×#121	semidirect
262. C₂×C₃×C₄	D₃₆	semidirect
283. C₂×C₉	C₃×#121	semidirect
300. C₄⋊C₄	C₂×C₃×D₉	semidirect
335. C₃×C₄	C₂×D₃₆	semidirect
340. C₉	C₂×C₃×#121	semidirect
356. C₂×C₄	C₃×D₃₆	semidirect
365. C₂×C₃	#63457	direct (N × H)
389. C₄	C₂×C₃×D₃₆	semidirect
391. C₃	C₂×#63457	direct (N × H)
395. C₂	C₃×#63457	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃₆	2
C₂²×C₃×C₄×D₉	2
C₂×C₃×C₉×C₄⋊C₄	2
C₂×C₃×(C₂×D₉)⋊C₄	2
C₃×#63457	2
C₂×C₃×#895	3
C₂×#63457	3

Subgroups — C2×C3×#63457 #13152404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63457 #13152404