Subgroups — C₂×C₃×#63384 #13143182

Order 1728.

578 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	C₂×C₃×#3697	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63384	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×#825	—	3	1	no	maximal
6	C₂×#63384	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₃×#611	—	2	1	no	—
9	C₂²×C₃×Dic₉	—	2	1	no	—
10	C₃×#3697	—	2	1	no	—
11	C₃×#3697	—	2	1	no	—
12	C₃×#3697	C₄	1	2	yes	complemented
13	C₃×#3697	C₂²	1	2	yes	—
14	C₂×C₃×D₃₆	C₄	1	1	yes	characteristic, complemented
15	C₂×C₃×C₄×D₉	—	2	1	no	—
16	C₂×C₃×Dic₁₈	C₄	1	1	yes	characteristic, complemented
17	C₃×C₉×M₁₆	—	2	1	no	—
18	C₃×C₉×M₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃×C₈×C₉	—	2	1	no	—
20	C₃×C₄×Dic₉	—	2	1	no	—
21	C₃×C₄×Dic₉	C₂²	1	2	yes	complemented
22	C₂×C₃×#235	—	3	1	no	—
23	C₂×C₃²×M₁₆	D₃	1	1	yes	characteristic
24	C₂×C₃×C₄×Dic₃	—	3	1	no	—
25	C₂×#3697	C₂×C₃	1	1	yes	characteristic
26	C₃×#825	—	3	4	no	—
27	C₂×C₉×M₁₆	—	2	1	no	—
28	C₂×C₉×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₄×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
30	#63384	C₂×C₃	1	4	yes	direct product factor
31	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
32	C₂²×C₃×D₉	—	2	1	no	—
33	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
36	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
37	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
38	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
39	C₃×#611	—	2	2	no	—
40	C₃×#611	—	2	2	no	—
41	C₂×C₃×Dic₉	—	2	4	no	—
42	C₂×C₃×Dic₉	—	2	1	no	—
43	C₂×C₃×Dic₉	—	2	2	no	—
44	C₃×D₃₆	—	2	1	no	—
45	C₃×D₃₆	C₂×C₄	1	2	yes	complemented
46	C₃×C₄×D₉	—	2	2	no	—
47	C₃×C₄×D₉	—	2	2	no	—
48	C₃×Dic₁₈	—	2	1	no	—
49	C₃×Dic₁₈	C₂×C₄	1	2	yes	complemented
50	C₃×C₈×C₉	—	2	2	no	—
51	C₂×C₃×#104	—	9	1	no	—
52	C₂×#825	—	3	1	no	—
53	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
54	C₂×C₃×#67	—	6	1	no	—
55	C₂²×C₃×Dic₃	—	6	1	no	—
56	C₃×#235	—	3	2	no	—
57	C₃×#235	—	3	2	no	—
58	C₃×#235	—	6	1	no	—
59	C₃×#235	—	6	1	no	—
60	C₂×C₃×D₁₂	—	3	1	no	—
61	C₂×C₃×C₄×D₃	—	6	1	no	—
62	C₂×C₃×Dic₆	—	3	1	no	—
63	C₃²×M₁₆	—	2	1	no	—
64	C₃²×M₁₆	C₂×D₃	1	2	yes	—
65	C₂×C₃²×C₈	—	2	1	no	—
66	C₃×C₄×Dic₃	—	3	2	no	—
67	C₃×C₄×Dic₃	—	6	1	no	—
68	C₂²×C₄×C₉	—	2	1	no	—
69	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
70	C₂×#611	—	2	1	no	—
71	C₂²×Dic₉	—	2	1	no	—
72	#3697	—	2	1	no	—
73	#3697	—	2	1	no	—
74	#3697	C₃×C₄	1	2	yes	complemented
75	#3697	C₂²×C₃	1	2	yes	—
76	C₂×D₃₆	C₃×C₄	1	1	yes	characteristic, complemented
77	C₂×C₄×D₉	—	2	1	no	—
78	C₂×Dic₁₈	C₃×C₄	1	1	yes	characteristic, complemented
79	C₉×M₁₆	—	2	2	no	—
80	C₉×M₁₆	—	2	2	no	—
81	C₉×M₁₆	—	2	1	no	—
82	C₉×M₁₆	C₂²×C₃	1	2	yes	complemented
83	C₂×C₈×C₉	—	2	2	no	—
84	C₂×C₈×C₉	—	2	1	no	—
85	C₄×Dic₉	—	2	1	no	—
86	C₄×Dic₉	C₂²×C₃	1	2	yes	complemented
87	C₂²×C₃×C₉	—	2	2	no	—
88	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×D₉	—	2	2	no	—
92	C₂×C₃×D₉	—	4	2	no	—
93	C₃×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₃×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
96	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
97	C₃×Dic₉	—	2	4	no	—
98	C₃×Dic₉	—	2	2	no	—
99	C₂×C₃×#41	—	9	1	no	—
100	C₂×#235	—	3	1	no	—
101	C₂×C₃×M₁₆	—	2	1	no	—
102	C₂×C₃×M₁₆	D₉	1	1	yes	characteristic, complemented
103	C₂×C₃×M₁₆	C₃×D₃	1	1	yes	characteristic
104	C₂×C₃×C₄²	—	9	1	no	—
105	C₂×C₄×Dic₃	—	3	1	no	—
106	C₃×#104	—	9	4	no	—
107	#825	—	3	4	no	—
108	C₂³×C₃²	D₁₂	1	1	yes	characteristic
109	C₂²×C₃×D₃	—	6	1	no	—
110	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
112	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
113	C₂×C₃²×C₄	#67	1	1	yes	characteristic
114	C₂×C₃²×C₄	#67	1	1	yes	characteristic
115	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
116	C₃×#67	—	6	2	no	—
117	C₃×#67	—	6	2	no	—
118	C₂×C₃×Dic₃	—	6	4	no	—
119	C₂×C₃×Dic₃	—	6	1	no	—
120	C₂×C₃×Dic₃	—	6	2	no	—
121	C₃×D₁₂	—	3	2	no	—
122	C₃×D₁₂	—	6	1	no	—
123	C₃×C₄×D₃	—	6	2	no	—
124	C₃×C₄×D₃	—	6	2	no	—
125	C₃×Dic₆	—	3	2	no	—
126	C₃×Dic₆	—	6	1	no	—
127	C₂³×C₉	—	2	1	no	—
128	C₂³×C₉	C₃×D₄	1	1	yes	characteristic
129	C₂²×D₉	—	2	1	no	—
130	C₃²×C₈	—	2	2	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
140	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
141	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
142	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
143	#611	—	2	2	no	—
144	#611	—	2	2	no	—
145	C₂×Dic₉	—	2	4	no	—
146	C₂×Dic₉	—	2	1	no	—
147	C₂×Dic₉	—	2	2	no	—
148	D₃₆	—	2	1	no	—
149	D₃₆	C₂×C₃×C₄	1	2	yes	complemented
150	C₄×D₉	—	2	2	no	—
151	C₄×D₉	—	2	2	no	—
152	Dic₁₈	—	2	1	no	—
153	Dic₁₈	C₂×C₃×C₄	1	2	yes	complemented
154	C₈×C₉	—	2	4	no	—
155	C₈×C₉	—	2	2	no	—
156	C₂×#104	—	9	1	no	Sylow
157	C₂×C₃×C₉	—	2	1	no	—
158	C₂×C₃×C₉	—	2	1	no	—
159	C₂×C₃×C₉	#104	1	2	yes	complemented
160	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₃×D₉	—	4	2	no	—
162	C₃×#41	—	9	2	no	—
163	C₃×#41	—	9	2	no	—
164	C₃×#41	—	18	1	no	—
165	C₃×#41	—	18	1	no	—
166	C₂×C₃×Q₈	—	9	1	no	—
167	C₂×C₃×D₄	—	9	1	no	—
168	C₂×C₃×D₄	—	18	1	no	—
169	C₂²×C₃×C₄	—	2	1	no	—
170	C₂²×C₃×C₄	—	18	1	no	—
171	C₂²×C₃×C₄	—	18	1	no	—
172	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
174	C₂×#67	—	6	1	no	—
175	C₂²×Dic₃	—	6	1	no	—
176	#235	—	3	2	no	—
177	#235	—	3	2	no	—
178	#235	—	6	1	no	—
179	#235	—	6	1	no	—
180	C₂×D₁₂	—	3	1	no	—
181	C₂×C₄×D₃	—	6	1	no	—
182	C₂×Dic₆	—	3	1	no	—
183	C₃×M₁₆	—	2	2	no	—
184	C₃×M₁₆	—	2	1	no	—
185	C₃×M₁₆	—	2	1	no	—
186	C₃×M₁₆	—	2	2	no	—
187	C₃×M₁₆	C₂×D₉	1	2	yes	complemented
188	C₃×M₁₆	C₂×C₃×D₃	1	2	yes	—
189	C₂×C₃×C₈	—	2	2	no	—
190	C₂×C₃×C₈	—	2	1	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₃×C₄²	—	9	2	no	—
193	C₃×C₄²	—	18	1	no	—
194	C₄×Dic₃	—	3	2	no	—
195	C₄×Dic₃	—	6	1	no	—
196	C₂²×C₃²	—	2	2	no	—
197	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
198	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
199	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
200	C₂×C₃×D₃	—	6	2	no	—
201	C₂×C₃×D₃	—	12	2	no	—
202	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
203	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
204	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
205	C₃²×C₄	C₂×#67	1	1	yes	characteristic
206	C₃×Dic₃	—	6	4	no	—
207	C₃×Dic₃	—	6	2	no	—
208	C₂²×C₉	—	2	2	no	—
209	C₂²×C₉	—	2	1	no	—
210	C₂²×C₉	—	2	1	no	—
211	C₂²×C₉	—	2	1	no	—
212	C₂²×C₉	—	4	2	no	—
213	C₂²×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
216	C₂×D₉	—	2	2	no	—
217	C₂×D₉	—	4	2	no	—
218	C₄×C₉	—	2	1	no	—
219	C₄×C₉	—	2	1	no	—
220	C₄×C₉	—	2	1	no	—
221	C₄×C₉	—	2	1	no	—
222	C₄×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
223	C₄×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
224	C₄×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
225	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
226	Dic₉	—	2	4	no	—
227	Dic₉	—	2	2	no	—
228	C₂×#41	—	9	1	no	—
229	C₂×M₁₆	C₃×D₉	1	1	yes	characteristic, complemented
230	C₂×C₄²	—	9	1	no	—
231	#104	—	9	4	no	—
232	C₃×C₉	C₂×#104	1	1	yes	characteristic, complemented, Sylow
233	C₂³×C₃	—	2	1	no	—
234	C₂³×C₃	—	18	1	no	—
235	C₂³×C₃	D₃₆	1	1	yes	characteristic
236	C₂³×C₃	C₃×D₁₂	1	1	yes	characteristic
237	C₂²×D₃	—	6	1	no	—
238	C₃×Q₈	—	9	2	no	—
239	C₃×Q₈	—	18	1	no	—
240	C₃×D₄	—	9	2	no	—
241	C₃×D₄	—	18	2	no	—
242	C₃×D₄	—	18	2	no	—
243	C₃×D₄	—	18	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	18	4	no	—
251	C₂×C₃×C₄	—	18	1	no	—
252	C₂×C₃×C₄	—	18	2	no	—
253	C₂×C₃×C₄	—	18	2	no	—
254	C₂×C₃×C₄	—	18	2	no	—
255	C₂×C₃×C₄	C₄×D₉	1	1	yes	characteristic
256	C₂×C₃×C₄	C₄×D₉	1	1	yes	characteristic
257	C₂×C₃×C₄	D₃₆	1	1	yes	characteristic
258	C₂×C₃×C₄	#611	1	1	yes	characteristic
259	C₂×C₃×C₄	#611	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
261	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
262	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
263	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
264	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
265	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
267	#67	—	6	2	no	—
268	#67	—	6	2	no	—
269	C₂×Dic₃	—	6	4	no	—
270	C₂×Dic₃	—	6	1	no	—
271	C₂×Dic₃	—	6	2	no	—
272	D₁₂	—	3	2	no	—
273	D₁₂	—	6	1	no	—
274	C₄×D₃	—	6	2	no	—
275	C₄×D₃	—	6	2	no	—
276	Dic₆	—	3	2	no	—
277	Dic₆	—	6	1	no	—
278	C₃×C₈	—	2	4	no	—
279	C₃×C₈	—	2	2	no	—
280	C₃×C₈	—	2	2	no	—
281	C₂×C₃²	—	2	1	no	—
282	C₂×C₃²	—	2	1	no	—
283	C₂×C₃²	#825	1	2	yes	—
284	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
285	C₃×D₃	—	12	2	no	—
286	C₂×C₉	—	2	1	no	—
287	C₂×C₉	—	2	1	no	—
288	C₂×C₉	—	2	1	no	—
289	C₂×C₉	—	2	2	no	—
290	C₂×C₉	—	4	1	no	—
291	C₂×C₉	—	4	1	no	—
292	C₂×C₉	C₃×#104	1	2	yes	complemented
293	C₂×C₉	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
294	D₉	—	4	2	no	—
295	#41	—	9	2	no	—
296	#41	—	9	2	no	—
297	#41	—	18	1	no	—
298	#41	—	18	1	no	—
299	C₂×Q₈	—	9	1	no	—
300	C₂×D₄	—	9	1	no	—
301	C₂×D₄	—	18	1	no	—
302	C₂²×C₄	—	18	1	no	—
303	C₂²×C₄	—	18	1	no	—
304	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
305	M₁₆	—	2	1	no	—
306	M₁₆	C₂×C₃×D₉	1	2	yes	complemented
307	C₂×C₈	—	2	1	no	—
308	C₄²	—	9	2	no	—
309	C₄²	—	18	1	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	1	no	—
313	C₂²×C₃	—	2	1	no	—
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	4	2	no	—
316	C₂²×C₃	—	18	2	no	—
317	C₂²×C₃	—	36	2	no	—
318	C₂²×C₃	(C₂×D₉)⋊C₄	1	1	yes	characteristic
319	C₂²×C₃	(C₂×D₉)⋊C₄	1	1	yes	characteristic
320	C₂²×C₃	C₂×D₃₆	1	1	yes	characteristic
321	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
322	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
323	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
324	C₂×D₃	—	6	2	no	—
325	C₂×D₃	—	12	2	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	2	1	no	—
330	C₃×C₄	—	18	4	no	—
331	C₃×C₄	—	18	2	no	—
332	C₃×C₄	(C₂×D₉)⋊C₄	1	1	yes	characteristic
333	C₃×C₄	(C₂×D₉)⋊C₄	1	1	yes	characteristic
334	C₃×C₄	C₂×C₄×D₉	1	1	yes	characteristic
335	C₃×C₄	C₂×#611	1	1	yes	characteristic
336	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
337	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
338	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
339	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
340	Dic₃	—	6	4	no	—
341	Dic₃	—	6	2	no	—
342	C₃²	C₂×#825	1	1	yes	characteristic
343	C₉	—	2	1	no	—
344	C₉	C₂×C₃×#104	1	1	yes	characteristic, complemented
345	C₂³	—	18	1	no	—
346	C₂³	C₃×D₃₆	1	1	yes	characteristic
347	Q₈	—	9	2	no	—
348	Q₈	—	18	1	no	—
349	D₄	—	9	2	no	—
350	D₄	—	18	2	no	—
351	D₄	—	18	2	no	—
352	D₄	—	18	1	no	—
353	C₂×C₄	—	18	4	no	—
354	C₂×C₄	—	18	2	no	—
355	C₂×C₄	—	18	1	no	—
356	C₂×C₄	—	18	2	no	—
357	C₂×C₄	—	18	2	no	—
358	C₂×C₄	C₃×C₄×D₉	1	1	yes	characteristic
359	C₂×C₄	C₃×C₄×D₉	1	1	yes	characteristic
360	C₂×C₄	C₃×D₃₆	1	1	yes	characteristic
361	C₂×C₄	C₃×#611	1	1	yes	characteristic
362	C₂×C₄	C₃×#611	1	1	yes	characteristic
363	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	2	1	no	—
367	C₂×C₃	—	2	1	no	—
368	C₂×C₃	—	2	1	no	—
369	C₂×C₃	—	2	1	no	—
370	C₂×C₃	—	2	2	no	—
371	C₂×C₃	—	4	1	no	—
372	C₂×C₃	—	4	1	no	—
373	C₂×C₃	—	36	2	no	—
374	C₂×C₃	#63384	1	2	yes	direct product factor
375	C₂×C₃	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
376	C₂×C₃	C₃×#825	1	2	yes	—
377	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
378	D₃	—	12	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	18	2	no	—
381	C₂²	—	36	2	no	—
382	C₂²	C₃×(C₂×D₉)⋊C₄	1	1	yes	characteristic
383	C₂²	C₃×(C₂×D₉)⋊C₄	1	1	yes	characteristic
384	C₂²	C₂×C₃×D₃₆	1	1	yes	characteristic
385	C₄	—	18	4	no	—
386	C₄	—	18	2	no	—
387	C₄	C₃×(C₂×D₉)⋊C₄	1	1	yes	characteristic
388	C₄	C₃×(C₂×D₉)⋊C₄	1	1	yes	characteristic
389	C₄	C₂×C₃×C₄×D₉	1	1	yes	characteristic
390	C₄	C₂×C₃×#611	1	1	yes	characteristic
391	C₃	—	2	1	no	—
392	C₃	C₂×#63384	1	1	yes	characteristic, direct product factor
393	C₃	C₂×C₃×#825	1	1	yes	characteristic
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	36	2	no	—
397	C₂	C₃×#63384	1	2	yes	direct product factor
398	C₂	C₂×C₃×(C₂×D₉)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	#611
commutator	C₄×C₉	C₂²×C₃×C₄
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×M₁₆	C₂
socle	C₂²×C₃²	(C₂×D₃)⋊C₄
prime radical	C₂×C₃×#3697	C₂
cosocle	C₂×C₄×C₉	C₂³×C₃
hypercenter	C₂×C₃×M₁₆	D₉
hypocenter	C₉	C₂×C₃×#104
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×M₁₆	C₂	semidirect
3. C₂×C₃×C₄×Dic₉	C₂	semidirect
4. C₃×#63384	C₂	direct (N × H)
6. C₂×#63384	C₃	direct (N × H)
12. C₃×#3697	C₄	semidirect
14. C₂×C₃×D₃₆	C₄	semidirect
16. C₂×C₃×Dic₁₈	C₄	semidirect
18. C₃×C₉×M₁₆	C₂²	semidirect
21. C₃×C₄×Dic₉	C₂²	semidirect
28. C₂×C₉×M₁₆	C₂×C₃	semidirect
29. C₂×C₄×Dic₉	C₂×C₃	semidirect
30. #63384	C₂×C₃	direct (N × H)
45. C₃×D₃₆	C₂×C₄	semidirect
49. C₃×Dic₁₈	C₂×C₄	semidirect
74. #3697	C₃×C₄	semidirect
76. C₂×D₃₆	C₃×C₄	semidirect
78. C₂×Dic₁₈	C₃×C₄	semidirect
82. C₉×M₁₆	C₂²×C₃	semidirect
86. C₄×Dic₉	C₂²×C₃	semidirect
102. C₂×C₃×M₁₆	D₉	semidirect
149. D₃₆	C₂×C₃×C₄	semidirect
153. Dic₁₈	C₂×C₃×C₄	semidirect
159. C₂×C₃×C₉	#104	semidirect
187. C₃×M₁₆	C₂×D₉	semidirect
229. C₂×M₁₆	C₃×D₉	semidirect
232. C₃×C₉	C₂×#104	semidirect
292. C₂×C₉	C₃×#104	semidirect
306. M₁₆	C₂×C₃×D₉	semidirect
344. C₉	C₂×C₃×#104	semidirect
374. C₂×C₃	#63384	direct (N × H)
392. C₃	C₂×#63384	direct (N × H)
397. C₂	C₃×#63384	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×#3697	2
C₂×C₃×C₉×M₁₆	2
C₂×C₃×C₄×Dic₉	2
C₃×#63384	2
C₂×C₃×#825	3
C₂×#63384	3

Subgroups — C2×C3×#63384 #13143182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63384 #13143182