Subgroups — C₃×C₄×#3697 #13152282

Order 1728.

1038 conjugacy classes of subgroups.

The subgroup lattice has 390 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×C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#611	C₂	1	4	yes	maximal, complemented
4	C₃×#63488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×D₃₆	C₂	1	2	yes	maximal, complemented
6	C₃×#63434	C₂	1	2	yes	maximal, complemented
7	C₃×C₄²×D₉	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×Dic₁₈	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×#235	—	3	1	no	maximal
10	C₄×#3697	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×#611	C₂²	1	2	yes	—
14	C₃×#3697	C₄	1	8	yes	direct product factor
15	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×D₉	C₂²	1	4	yes	—
17	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
18	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
19	C₃×C₄²×C₉	C₂²	1	2	yes	—
20	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₃×#3676	C₂²	1	2	yes	—
23	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	—
24	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
25	C₃×Dic₉⋊C₄	C₂²	1	4	yes	—
26	C₃×C₄×Dic₉	C₂²	1	2	yes	—
27	C₃×C₄×Dic₉	C₂²	1	4	yes	—
28	C₂×C₃×#235	—	3	1	no	—
29	C₂×C₃²×C₄²	D₃	1	1	yes	characteristic
30	C₃×C₄×#67	—	3	4	no	—
31	C₃×#926	—	3	1	no	—
32	C₃×C₄×D₁₂	—	3	2	no	—
33	C₃×#872	—	3	2	no	—
34	C₃×C₄²×D₃	—	3	2	no	—
35	C₃×C₄×Dic₆	—	3	2	no	—
36	C₂×#3697	C₂×C₃	1	1	yes	characteristic
37	C₂×C₄²×C₉	—	2	1	no	—
38	C₂×C₄²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
39	C₄×#611	C₂×C₃	1	4	yes	complemented
40	#63488	C₂×C₃	1	1	yes	characteristic, complemented
41	C₄×D₃₆	C₂×C₃	1	2	yes	complemented
42	#63434	C₂×C₃	1	2	yes	complemented
43	C₄²×D₉	C₂×C₃	1	2	yes	complemented
44	C₄×Dic₁₈	C₂×C₃	1	2	yes	complemented
45	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
46	C₂²×C₃×D₉	C₂³	1	2	yes	—
47	C₂×C₃×C₄×C₉	—	2	4	no	—
48	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
49	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
53	C₃×#611	C₂×C₄	1	8	yes	complemented
54	C₂×C₃×Dic₉	C₂³	1	4	yes	—
55	C₂×C₃×Dic₉	C₂³	1	2	yes	—
56	C₃×D₃₆	C₂×C₄	1	4	yes	complemented
57	C₃×C₄×D₉	—	2	8	no	—
58	C₃×C₄×D₉	C₂×C₄	1	8	yes	complemented
59	C₃×Dic₁₈	C₂×C₄	1	4	yes	complemented
60	C₃×C₄×#41	—	9	1	no	—
61	C₄×#235	—	3	1	no	—
62	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	—
63	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
64	C₂×C₃×#67	—	3	2	no	—
65	C₃×#235	—	3	8	no	—
66	C₂×C₃×D₁₂	—	3	1	no	—
67	C₂×C₃×C₄×D₃	—	3	2	no	—
68	C₂×C₃×C₄×D₃	—	3	4	no	—
69	C₂×C₃×Dic₆	—	3	1	no	—
70	C₃²×C₄²	C₂×D₃	1	2	yes	—
71	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
72	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
73	C₃×#217	—	3	2	no	—
74	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
75	C₃×C₄⋊Dic₃	—	3	2	no	—
76	C₃×Dic₃⋊C₄	—	3	4	no	—
77	C₃×C₄×Dic₃	—	3	2	no	—
78	C₃×C₄×Dic₃	—	3	4	no	—
79	C₂²×C₄×C₉	—	2	2	no	—
80	C₂²×C₄×C₉	—	2	1	no	—
81	C₂²×C₄×C₉	C₂²×C₃	1	2	yes	—
82	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
83	C₂×#611	C₂²×C₃	1	2	yes	—
84	#3697	C₃×C₄	1	8	yes	direct product factor
85	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
87	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
88	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
89	C₄²×C₉	—	2	2	no	—
90	C₄²×C₉	—	2	1	no	—
91	C₄²×C₉	—	2	1	no	—
92	C₄²×C₉	C₂²×C₃	1	2	yes	—
93	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
94	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
95	#3676	C₂²×C₃	1	2	yes	—
96	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
97	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
98	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
99	C₄×Dic₉	C₂²×C₃	1	2	yes	—
100	C₄×Dic₉	C₂²×C₃	1	4	yes	—
101	C₂²×C₃×C₉	—	2	2	no	—
102	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
104	C₂×C₃×D₉	—	2	4	no	—
105	C₂×C₃×D₉	C₂²×C₄	1	4	yes	—
106	C₃×C₄×C₉	—	2	2	no	—
107	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
108	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
109	C₃×C₄×C₉	#41	1	4	yes	complemented
110	C₃×Dic₉	—	2	4	no	—
111	C₃×Dic₉	C₂²×C₄	1	4	yes	—
112	C₂×C₃×#41	—	9	1	no	—
113	C₂×#235	—	3	1	no	—
114	C₃×C₄×Q₈	—	9	2	no	—
115	C₃×C₄×D₄	—	9	4	no	—
116	C₃×C₄×D₄	—	9	2	no	—
117	C₃×#117	—	9	1	no	—
118	C₃×#117	—	9	2	no	—
119	C₂×C₃×C₄²	—	2	1	no	—
120	C₂×C₃×C₄²	—	9	2	no	—
121	C₂×C₃×C₄²	D₉	1	1	yes	characteristic, complemented
122	C₂×C₃×C₄²	C₃×D₃	1	1	yes	characteristic
123	C₄×#67	—	3	4	no	—
124	#926	—	3	1	no	—
125	C₄×D₁₂	—	3	2	no	—
126	#872	—	3	2	no	—
127	C₄²×D₃	—	3	2	no	—
128	C₄×Dic₆	—	3	2	no	—
129	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
130	C₂²×C₃×D₃	—	3	2	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
133	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
134	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
137	C₃×#67	—	3	8	no	—
138	C₂×C₃×Dic₃	—	3	2	no	—
139	C₂×C₃×Dic₃	—	3	4	no	—
140	C₃×D₁₂	—	3	4	no	—
141	C₃×C₄×D₃	—	3	8	no	—
142	C₃×C₄×D₃	—	6	8	no	—
143	C₃×Dic₆	—	3	4	no	—
144	C₂³×C₉	—	2	1	no	—
145	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
146	C₂²×D₉	C₂³×C₃	1	2	yes	—
147	C₂×C₄×C₉	—	2	8	no	—
148	C₂×C₄×C₉	—	2	4	no	—
149	C₂×C₄×C₉	—	2	4	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	1	no	—
153	C₂×C₄×C₉	—	2	2	no	—
154	C₂×C₄×C₉	C₂×C₃×C₄	1	4	yes	complemented
155	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
156	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
158	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
159	#611	C₂×C₃×C₄	1	8	yes	complemented
160	C₂×Dic₉	C₂³×C₃	1	4	yes	—
161	C₂×Dic₉	C₂³×C₃	1	2	yes	—
162	D₃₆	C₂×C₃×C₄	1	4	yes	complemented
163	C₄×D₉	—	2	8	no	—
164	C₄×D₉	C₂×C₃×C₄	1	8	yes	complemented
165	Dic₁₈	C₂×C₃×C₄	1	4	yes	complemented
166	C₄×#41	—	9	1	no	Sylow
167	C₂×C₃×C₉	—	2	2	no	—
168	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₃×C₉	C₂×#41	1	2	yes	—
170	C₃×D₉	—	2	4	no	—
171	C₃×#41	—	9	8	no	—
172	C₂×C₃×Q₈	—	9	1	no	—
173	C₂×C₃×D₄	—	9	2	no	—
174	C₂×C₃×D₄	—	9	1	no	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	—	9	2	no	—
178	C₂²×C₃×C₄	—	9	4	no	—
179	C₂²×C₃×C₄	C₂×D₉	1	2	yes	—
180	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
182	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
183	C₂×#67	—	3	2	no	—
184	#235	—	3	8	no	—
185	C₂×D₁₂	—	3	1	no	—
186	C₂×C₄×D₃	—	3	2	no	—
187	C₂×C₄×D₃	—	3	4	no	—
188	C₂×Dic₆	—	3	1	no	—
189	C₃×C₄⋊C₄	—	9	4	no	—
190	C₃×C₄⋊C₄	—	9	2	no	—
191	C₃×C₂²⋊C₄	—	9	2	no	—
192	C₃×C₂²⋊C₄	—	9	4	no	—
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	—	2	2	no	—
196	C₃×C₄²	—	9	2	no	—
197	C₃×C₄²	—	9	4	no	—
198	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
199	C₃×C₄²	C₂×D₉	1	2	yes	—
200	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
201	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
202	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
203	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
204	#217	—	3	2	no	—
205	(C₂×D₃)⋊C₄	—	3	4	no	—
206	C₄⋊Dic₃	—	3	2	no	—
207	Dic₃⋊C₄	—	3	4	no	—
208	C₄×Dic₃	—	3	4	no	—
209	C₄×Dic₃	—	3	2	no	—
210	C₂²×C₃²	—	2	2	no	—
211	C₂²×C₃²	C₂×C₄×D₃	1	2	yes	—
212	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
213	C₂×C₃×D₃	—	3	4	no	—
214	C₂×C₃×D₃	—	6	4	no	—
215	C₃²×C₄	—	2	2	no	—
216	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
217	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
218	C₃²×C₄	#235	1	4	yes	—
219	C₃×Dic₃	—	3	4	no	—
220	C₃×Dic₃	—	6	4	no	—
221	C₂²×C₉	—	2	4	no	—
222	C₂²×C₉	—	2	2	no	—
223	C₂²×C₉	—	2	1	no	—
224	C₂²×C₉	—	2	2	no	—
225	C₂²×C₉	C₂²×C₃×C₄	1	2	yes	—
226	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
227	C₂×D₉	—	2	4	no	—
228	C₂×D₉	C₂²×C₃×C₄	1	4	yes	—
229	C₄×C₉	—	2	4	no	—
230	C₄×C₉	—	2	2	no	—
231	C₄×C₉	—	2	2	no	—
232	C₄×C₉	—	2	2	no	—
233	C₄×C₉	—	2	4	no	—
234	C₄×C₉	C₂²×C₃×C₄	1	2	yes	—
235	C₄×C₉	C₂²×C₃×C₄	1	2	yes	—
236	C₄×C₉	C₃×#41	1	4	yes	complemented
237	Dic₉	—	2	4	no	—
238	Dic₉	C₂²×C₃×C₄	1	4	yes	—
239	C₂×#41	—	9	1	no	—
240	C₄×Q₈	—	9	2	no	—
241	C₄×D₄	—	9	4	no	—
242	C₄×D₄	—	9	2	no	—
243	#117	—	9	1	no	—
244	#117	—	9	2	no	—
245	C₂×C₄²	—	9	2	no	—
246	C₂×C₄²	C₃×D₉	1	1	yes	characteristic, complemented
247	C₃×C₉	C₄×#41	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	—	9	2	no	—
250	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
251	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
252	C₂²×D₃	—	3	2	no	—
253	C₃×Q₈	—	9	4	no	—
254	C₃×D₄	—	9	8	no	—
255	C₃×D₄	—	9	4	no	—
256	C₂×C₃×C₄	—	2	8	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	9	2	no	—
265	C₂×C₃×C₄	—	9	8	no	—
266	C₂×C₃×C₄	—	9	4	no	—
267	C₂×C₃×C₄	—	18	8	no	—
268	C₂×C₃×C₄	C₄×D₉	1	4	yes	complemented
269	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
270	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
273	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
274	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
275	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
278	#67	—	3	8	no	—
279	C₂×Dic₃	—	3	2	no	—
280	C₂×Dic₃	—	3	4	no	—
281	D₁₂	—	3	4	no	—
282	C₄×D₃	—	3	8	no	—
283	C₄×D₃	—	6	8	no	—
284	Dic₆	—	3	4	no	—
285	C₂×C₃²	—	2	2	no	—
286	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
287	C₂×C₃²	C₂×#235	1	2	yes	—
288	C₃×D₃	—	6	4	no	—
289	C₂×C₉	—	2	4	no	—
290	C₂×C₉	—	2	2	no	—
291	C₂×C₉	—	2	1	no	—
292	C₂×C₉	—	2	2	no	—
293	C₂×C₉	C₂³×C₃×C₄	1	1	yes	characteristic
294	C₂×C₉	C₂×C₃×#41	1	2	yes	—
295	D₉	—	2	4	no	—
296	#41	—	9	8	no	—
297	C₂×Q₈	—	9	1	no	—
298	C₂×D₄	—	9	2	no	—
299	C₂×D₄	—	9	1	no	—
300	C₂²×C₄	—	9	2	no	—
301	C₂²×C₄	—	9	4	no	—
302	C₂²×C₄	C₂×C₃×D₉	1	2	yes	—
303	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
304	C₄⋊C₄	—	9	4	no	—
305	C₄⋊C₄	—	9	2	no	—
306	C₂²⋊C₄	—	9	2	no	—
307	C₂²⋊C₄	—	9	4	no	—
308	C₄²	—	9	2	no	—
309	C₄²	—	9	4	no	—
310	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
311	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
312	C₄²	C₂×C₃×D₉	1	2	yes	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	2	2	no	—
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	9	4	no	—
319	C₂²×C₃	—	18	4	no	—
320	C₂²×C₃	C₂×C₄×D₉	1	2	yes	—
321	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
322	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
323	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
324	C₂×D₃	—	3	4	no	—
325	C₂×D₃	—	6	4	no	—
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	2	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	9	4	no	—
333	C₃×C₄	—	18	4	no	—
334	C₃×C₄	C₂×C₄×D₉	1	2	yes	—
335	C₃×C₄	C₂×C₄×D₉	1	2	yes	—
336	C₃×C₄	#3697	1	4	yes	direct product factor
337	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
338	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
339	C₃×C₄	C₃×#235	1	4	yes	—
340	Dic₃	—	3	4	no	—
341	Dic₃	—	6	4	no	—
342	C₃²	C₄×#235	1	1	yes	characteristic
343	C₉	—	2	1	no	—
344	C₉	C₃×C₄×#41	1	1	yes	characteristic, complemented
345	C₂³	—	9	2	no	—
346	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
347	Q₈	—	9	4	no	—
348	D₄	—	9	8	no	—
349	D₄	—	9	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	9	2	no	—
352	C₂×C₄	—	9	8	no	—
353	C₂×C₄	—	9	4	no	—
354	C₂×C₄	—	18	8	no	—
355	C₂×C₄	C₃×C₄×D₉	1	4	yes	complemented
356	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
357	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
359	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
360	C₂×C₃	—	2	4	no	—
361	C₂×C₃	—	2	2	no	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	2	no	—
365	C₂×C₃	—	18	4	no	—
366	C₂×C₃	C₂²×C₄×D₉	1	1	yes	characteristic
367	C₂×C₃	C₂×#3697	1	2	yes	—
368	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
369	C₂×C₃	C₂×C₃×#235	1	2	yes	—
370	D₃	—	6	4	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	9	4	no	—
373	C₂²	—	18	4	no	—
374	C₂²	C₂×C₃×C₄×D₉	1	2	yes	—
375	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	9	4	no	—
378	C₄	—	18	4	no	—
379	C₄	C₂×C₃×C₄×D₉	1	2	yes	—
380	C₄	C₂×C₃×C₄×D₉	1	2	yes	—
381	C₄	C₃×#3697	1	4	yes	direct product factor
382	C₃	—	2	1	no	—
383	C₃	C₄×#3697	1	1	yes	characteristic, direct product factor
384	C₃	C₃×C₄×#235	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	18	4	no	—
387	C₂	C₂²×C₃×C₄×D₉	1	1	yes	characteristic
388	C₂	C₂×C₃×#3697	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂×D₉
commutator	C₂×C₉	C₂³×C₃×C₄
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₄²×C₉	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂×C₃×#3697	C₂
cosocle	C₂²×C₉	C₂⁴×C₃
hypercenter	C₂×C₃×C₄²	D₉
hypocenter	C₉	C₃×C₄×#41
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₃×C₄² ◁ C₂×C₃×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄²×C₉	C₂	semidirect
3. C₃×C₄×#611	C₂	semidirect
4. C₃×#63488	C₂	semidirect
5. C₃×C₄×D₃₆	C₂	semidirect
6. C₃×#63434	C₂	semidirect
7. C₃×C₄²×D₉	C₂	semidirect
8. C₃×C₄×Dic₁₈	C₂	semidirect
10. C₄×#3697	C₃	direct (N × H)
14. C₃×#3697	C₄	direct (N × H)
38. C₂×C₄²×C₉	C₂×C₃	semidirect
39. C₄×#611	C₂×C₃	semidirect
40. #63488	C₂×C₃	semidirect
41. C₄×D₃₆	C₂×C₃	semidirect
42. #63434	C₂×C₃	semidirect
43. C₄²×D₉	C₂×C₃	semidirect
44. C₄×Dic₁₈	C₂×C₃	semidirect
48. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
53. C₃×#611	C₂×C₄	semidirect
56. C₃×D₃₆	C₂×C₄	semidirect
58. C₃×C₄×D₉	C₂×C₄	semidirect
59. C₃×Dic₁₈	C₂×C₄	semidirect
84. #3697	C₃×C₄	direct (N × H)
109. C₃×C₄×C₉	#41	semidirect
121. C₂×C₃×C₄²	D₉	semidirect
154. C₂×C₄×C₉	C₂×C₃×C₄	semidirect
159. #611	C₂×C₃×C₄	semidirect
162. D₃₆	C₂×C₃×C₄	semidirect
164. C₄×D₉	C₂×C₃×C₄	semidirect
165. Dic₁₈	C₂×C₃×C₄	semidirect
236. C₄×C₉	C₃×#41	semidirect
246. C₂×C₄²	C₃×D₉	semidirect
247. C₃×C₉	C₄×#41	semidirect
268. C₂×C₃×C₄	C₄×D₉	semidirect
336. C₃×C₄	#3697	direct (N × H)
344. C₉	C₃×C₄×#41	semidirect
355. C₂×C₄	C₃×C₄×D₉	semidirect
381. C₄	C₃×#3697	direct (N × H)
383. C₃	C₄×#3697	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×C₄²×C₉	2
C₃×C₄×#611	2
C₃×#63488	2
C₃×C₄×D₃₆	2
C₃×#63434	2
C₃×C₄²×D₉	2
C₃×C₄×Dic₁₈	2
C₃×C₄×#235	3
C₄×#3697	3

Subgroups — C3×C4×#3697 #13152282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#3697 #13152282