Subgroups — C₂×C₃×#5000 #11858777

Order 1152.

989 conjugacy classes of subgroups.

The subgroup lattice has 337 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#830	C₂	1	2	yes	maximal
3	C₃×#5000	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#803	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#433	—	3	1	no	maximal
8	C₂×#5000	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₃²×#117	C₄	1	4	yes	—
11	C₃²×#117	C₂²	1	4	yes	—
12	C₂×C₃²×C₄⋊C₄	C₄	1	2	yes	—
13	C₂×C₃²×C₂²⋊C₄	C₄	1	2	yes	—
14	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
15	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
17	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
18	C₃×#830	C₂²	1	8	yes	—
19	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	8	yes	complemented
20	C₃×#803	C₂²	1	4	yes	complemented
21	C₃×C₄×C₃⋊C₈	C₂²	1	4	yes	complemented
22	C₂×C₃×#117	—	2	1	no	—
23	C₂×C₃×#117	D₃	1	1	yes	characteristic
24	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
25	C₃×#433	—	3	8	no	—
26	C₂×C₃×C₄⋊C₈	—	3	2	no	—
27	C₂×C₃×C₂²⋊C₈	—	3	2	no	—
28	C₂×C₃×#97	—	3	1	no	—
29	C₂×C₃×C₄×C₈	—	3	1	no	—
30	C₂×#830	C₂×C₃	1	2	yes	—
31	#5000	C₂×C₃	1	8	yes	direct product factor
32	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	2	yes	complemented
33	C₂×#803	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂⁴×C₃²	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃²×C₄	—	2	4	no	—
37	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
39	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
40	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
41	C₂²×C₃²×C₄	C₂³	1	2	yes	—
42	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
43	C₃²×C₄⋊C₄	C₂×C₄	1	8	yes	—
44	C₃²×C₂²⋊C₄	C₂×C₄	1	8	yes	—
45	C₃²×C₄²	C₂×C₄	1	2	yes	—
46	C₃²×C₄²	C₂×C₄	1	2	yes	—
47	C₃²×C₄²	C₂³	1	2	yes	—
48	C₃²×C₄²	C₂³	1	2	yes	—
49	C₂×C₃×C₃⋊C₈	—	2	4	no	—
50	C₂×C₃×C₃⋊C₈	—	2	4	no	—
51	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
52	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
53	C₂×#433	—	3	1	no	Sylow
54	C₂³×C₃×C₄	—	2	1	no	—
55	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
56	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₃×C₈	—	3	2	no	—
58	C₂²×C₃×C₈	—	3	2	no	—
59	C₃×#117	—	2	4	no	—
60	C₃×#117	—	2	4	no	—
61	C₃×#117	Dic₃	1	4	yes	—
62	C₃×#117	C₃×C₄	1	4	yes	—
63	C₃×#117	C₂×D₃	1	4	yes	—
64	C₃×#117	C₂²×C₃	1	4	yes	—
65	C₂×C₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₃×C₄⋊C₄	Dic₃	1	2	yes	—
67	C₂×C₃×C₄⋊C₄	C₃×C₄	1	2	yes	—
68	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₃×C₂²⋊C₄	Dic₃	1	2	yes	—
70	C₂×C₃×C₂²⋊C₄	C₃×C₄	1	2	yes	—
71	C₂×C₃×C₄²	—	2	1	no	—
72	C₂×C₃×C₄²	—	2	1	no	—
73	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
74	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
75	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
78	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
79	C₃×C₄⋊C₈	—	3	8	no	—
80	C₃×C₂²⋊C₈	—	3	8	no	—
81	C₃×#97	—	3	4	no	—
82	C₃×C₄×C₈	—	3	4	no	—
83	#830	C₂²×C₃	1	8	yes	—
84	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	8	yes	complemented
85	#803	C₂²×C₃	1	4	yes	complemented
86	C₄×C₃⋊C₈	C₂²×C₃	1	4	yes	complemented
87	C₂³×C₃²	—	2	2	no	—
88	C₂³×C₃²	—	2	4	no	—
89	C₂³×C₃²	C₂²×C₄	1	2	yes	—
90	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃²×C₄	—	2	2	no	—
92	C₂×C₃²×C₄	—	2	4	no	—
93	C₂×C₃²×C₄	—	2	4	no	—
94	C₂×C₃²×C₄	—	2	4	no	—
95	C₂×C₃²×C₄	—	2	4	no	—
96	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
97	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
98	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
99	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃²×C₄	#41	1	4	yes	—
101	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
102	C₃×C₃⋊C₈	—	2	4	no	—
103	C₃×C₃⋊C₈	—	2	4	no	—
104	C₂×#117	C₃×D₃	1	1	yes	characteristic
105	#433	—	3	8	no	—
106	C₂×C₄⋊C₈	—	3	2	no	—
107	C₂×C₂²⋊C₈	—	3	2	no	—
108	C₂×#97	—	3	1	no	—
109	C₂×C₄×C₈	—	3	1	no	—
110	C₂⁴×C₃	—	2	1	no	—
111	C₂⁴×C₃	C₂×Dic₃	1	1	yes	characteristic
112	C₂⁴×C₃	C₂×C₃×C₄	1	1	yes	characteristic
113	C₂²×C₃×C₄	—	2	8	no	—
114	C₂²×C₃×C₄	—	2	4	no	—
115	C₂²×C₃×C₄	—	2	4	no	—
116	C₂²×C₃×C₄	—	2	1	no	—
117	C₂²×C₃×C₄	—	2	2	no	—
118	C₂²×C₃×C₄	—	2	2	no	—
119	C₂²×C₃×C₄	—	2	2	no	—
120	C₂²×C₃×C₄	—	2	1	no	—
121	C₂²×C₃×C₄	—	2	2	no	—
122	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
123	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
124	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
125	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
126	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
127	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
128	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
130	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
131	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
132	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
133	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
134	C₂×C₃×C₈	—	3	4	no	—
135	C₂×C₃×C₈	—	3	4	no	—
136	C₂×C₃×C₈	—	6	4	no	—
137	C₂×C₃×C₈	—	6	4	no	—
138	C₃×C₄⋊C₄	—	2	8	no	—
139	C₃×C₄⋊C₄	C₂×Dic₃	1	8	yes	—
140	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
141	C₃×C₂²⋊C₄	—	2	8	no	—
142	C₃×C₂²⋊C₄	C₂×Dic₃	1	8	yes	—
143	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
144	C₃×C₄²	—	2	2	no	—
145	C₃×C₄²	—	2	2	no	—
146	C₃×C₄²	—	2	2	no	—
147	C₃×C₄²	—	2	2	no	—
148	C₃×C₄²	C₂×Dic₃	1	2	yes	—
149	C₃×C₄²	C₂×Dic₃	1	2	yes	—
150	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
151	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
152	C₃×C₄²	C₂²×D₃	1	2	yes	—
153	C₃×C₄²	C₂²×D₃	1	2	yes	—
154	C₃×C₄²	C₂³×C₃	1	2	yes	—
155	C₃×C₄²	C₂³×C₃	1	2	yes	—
156	C₂×C₃⋊C₈	—	2	4	no	—
157	C₂×C₃⋊C₈	—	2	4	no	—
158	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
159	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
160	C₂²×C₃²	—	2	2	no	—
161	C₂²×C₃²	—	2	4	no	—
162	C₂²×C₃²	—	4	4	no	—
163	C₂²×C₃²	#117	1	2	yes	—
164	C₂²×C₃²	#131	1	4	yes	—
165	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
166	C₃²×C₄	—	2	2	no	—
167	C₃²×C₄	—	2	4	no	—
168	C₃²×C₄	—	2	4	no	—
169	C₃²×C₄	#117	1	2	yes	—
170	C₃²×C₄	C₂×#41	1	2	yes	—
171	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
172	C₂²×C₈	—	3	2	no	—
173	C₂²×C₈	—	3	2	no	—
174	#117	C₃×Dic₃	1	4	yes	—
175	#117	C₂×C₃×D₃	1	4	yes	—
176	C₂×C₄⋊C₄	C₃×Dic₃	1	2	yes	—
177	C₂×C₂²⋊C₄	C₃×Dic₃	1	2	yes	—
178	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
179	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
180	C₄⋊C₈	—	3	8	no	—
181	C₂²⋊C₈	—	3	8	no	—
182	#97	—	3	4	no	—
183	C₄×C₈	—	3	4	no	—
184	C₂³×C₃	—	2	4	no	—
185	C₂³×C₃	—	2	2	no	—
186	C₂³×C₃	—	2	4	no	—
187	C₂³×C₃	—	2	2	no	—
188	C₂³×C₃	—	2	4	no	—
189	C₂³×C₃	—	2	1	no	—
190	C₂³×C₃	—	2	2	no	—
191	C₂³×C₃	—	4	4	no	—
192	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
193	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
194	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
195	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
196	C₂×C₃×C₄	—	2	4	no	—
197	C₂×C₃×C₄	—	2	8	no	—
198	C₂×C₃×C₄	—	2	8	no	—
199	C₂×C₃×C₄	—	2	2	no	—
200	C₂×C₃×C₄	—	2	4	no	—
201	C₂×C₃×C₄	—	2	4	no	—
202	C₂×C₃×C₄	—	2	2	no	—
203	C₂×C₃×C₄	—	2	4	no	—
204	C₂×C₃×C₄	—	2	4	no	—
205	C₂×C₃×C₄	—	2	4	no	—
206	C₂×C₃×C₄	—	2	4	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	2	4	no	—
209	C₂×C₃×C₄	—	2	1	no	—
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	2	1	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	2	4	no	—
215	C₂×C₃×C₄	—	4	4	no	—
216	C₂×C₃×C₄	—	4	4	no	—
217	C₂×C₃×C₄	#235	1	4	yes	—
218	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
219	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
220	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
221	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
222	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
223	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
224	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
225	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
226	C₂×C₃×C₄	C₃×#41	1	4	yes	—
227	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
229	C₃×C₈	—	6	4	no	—
230	C₃×C₈	—	6	4	no	—
231	C₃⋊C₈	—	2	4	no	—
232	C₃⋊C₈	—	2	4	no	—
233	C₂×C₃²	—	4	2	no	—
234	C₂×C₃²	#433	1	4	yes	complemented
235	C₂×C₃²	C₂×#117	1	1	yes	characteristic
236	C₂×C₃²	C₂×#131	1	2	yes	—
237	C₂⁴	C₂×C₃×Dic₃	1	1	yes	characteristic
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
240	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
241	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
242	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
243	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
244	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
245	C₂×C₈	—	3	4	no	—
246	C₂×C₈	—	3	4	no	—
247	C₂×C₈	—	6	4	no	—
248	C₂×C₈	—	6	4	no	—
249	C₄⋊C₄	C₂×C₃×Dic₃	1	8	yes	—
250	C₂²⋊C₄	C₂×C₃×Dic₃	1	8	yes	—
251	C₄²	C₂×C₃×Dic₃	1	2	yes	—
252	C₄²	C₂×C₃×Dic₃	1	2	yes	—
253	C₄²	C₂²×C₃×D₃	1	2	yes	—
254	C₄²	C₂²×C₃×D₃	1	2	yes	—
255	C₂²×C₃	—	2	4	no	—
256	C₂²×C₃	—	2	4	no	—
257	C₂²×C₃	—	2	2	no	—
258	C₂²×C₃	—	2	4	no	—
259	C₂²×C₃	—	2	2	no	—
260	C₂²×C₃	—	2	2	no	—
261	C₂²×C₃	—	2	4	no	—
262	C₂²×C₃	—	2	1	no	—
263	C₂²×C₃	—	4	4	no	—
264	C₂²×C₃	—	4	8	no	—
265	C₂²×C₃	—	4	4	no	—
266	C₂²×C₃	—	4	4	no	—
267	C₂²×C₃	#926	1	2	yes	—
268	C₂²×C₃	#948	1	4	yes	—
269	C₂²×C₃	C₃×#117	1	2	yes	—
270	C₂²×C₃	C₃×#131	1	4	yes	—
271	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
272	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
273	C₃×C₄	—	2	4	no	—
274	C₃×C₄	—	2	4	no	—
275	C₃×C₄	—	2	4	no	—
276	C₃×C₄	—	2	2	no	—
277	C₃×C₄	—	2	4	no	—
278	C₃×C₄	—	2	4	no	—
279	C₃×C₄	—	2	2	no	—
280	C₃×C₄	—	2	2	no	—
281	C₃×C₄	—	2	2	no	—
282	C₃×C₄	—	4	4	no	—
283	C₃×C₄	—	4	4	no	—
284	C₃×C₄	#926	1	2	yes	—
285	C₃×C₄	C₃×#117	1	2	yes	—
286	C₃×C₄	C₂×#235	1	2	yes	—
287	C₃×C₄	C₂×C₃×#41	1	2	yes	—
288	C₃²	C₂×#433	1	1	yes	characteristic, complemented, Sylow
289	C₂³	—	2	2	no	—
290	C₂³	—	2	4	no	—
291	C₂³	C₂²×C₃×Dic₃	1	2	yes	—
292	C₂³	C₂²×C₃×Dic₃	1	1	yes	characteristic
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	C₃×#235	1	4	yes	—
299	C₂×C₄	C₂²×C₃×Dic₃	1	4	yes	—
300	C₂×C₄	C₂²×C₃×Dic₃	1	4	yes	—
301	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
302	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
303	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
304	C₈	—	6	4	no	—
305	C₈	—	6	4	no	—
306	C₂×C₃	—	2	1	no	—
307	C₂×C₃	—	2	2	no	—
308	C₂×C₃	—	2	4	no	—
309	C₂×C₃	—	4	4	no	—
310	C₂×C₃	—	4	2	no	—
311	C₂×C₃	—	4	2	no	—
312	C₂×C₃	#5000	1	4	yes	direct product factor
313	C₂×C₃	C₃×#433	1	4	yes	complemented
314	C₂×C₃	C₂×#926	1	1	yes	characteristic
315	C₂×C₃	C₂×#948	1	2	yes	—
316	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
317	C₂×C₃	C₂×C₃×#131	1	2	yes	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	4	4	no	—
321	C₂²	C₃×#926	1	2	yes	—
322	C₂²	C₃×#948	1	4	yes	—
323	C₂²	C₂³×C₃×Dic₃	1	1	yes	characteristic
324	C₄	—	2	2	no	—
325	C₄	—	2	4	no	—
326	C₄	—	2	4	no	—
327	C₄	C₃×#926	1	2	yes	—
328	C₄	C₂×C₃×#235	1	2	yes	—
329	C₃	—	2	1	no	—
330	C₃	C₂×#5000	1	1	yes	characteristic, direct product factor
331	C₃	C₂×C₃×#433	1	1	yes	characteristic, complemented
332	C₂	—	4	2	no	—
333	C₂	C₃×#5000	1	4	yes	direct product factor
334	C₂	C₂×C₃×#926	1	1	yes	characteristic
335	C₂	C₂×C₃×#948	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#117	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂⁴×C₃²	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#117	D₃
hypocenter	C₃	C₂×C₃×#433
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
3. C₃×#5000	C₂	direct (N × H)
4. C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
5. C₂×C₃×#803	C₂	semidirect
6. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
8. C₂×#5000	C₃	direct (N × H)
19. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
20. C₃×#803	C₂²	semidirect
21. C₃×C₄×C₃⋊C₈	C₂²	semidirect
31. #5000	C₂×C₃	direct (N × H)
32. C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
33. C₂×#803	C₂×C₃	semidirect
34. C₂×C₄×C₃⋊C₈	C₂×C₃	semidirect
84. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
85. #803	C₂²×C₃	semidirect
86. C₄×C₃⋊C₈	C₂²×C₃	semidirect
234. C₂×C₃²	#433	semidirect
288. C₃²	C₂×#433	semidirect
312. C₂×C₃	#5000	direct (N × H)
313. C₂×C₃	C₃×#433	semidirect
330. C₃	C₂×#5000	direct (N × H)
331. C₃	C₂×C₃×#433	semidirect
333. C₂	C₃×#5000	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×C₃²×#117	2
C₂×C₃×#830	2
C₃×#5000	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₂×C₃×#803	2
C₂×C₃×C₄×C₃⋊C₈	2
C₂×C₃×#433	3
C₂×#5000	3

Subgroups — C2×C3×#5000 #11858777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5000 #11858777