Subgroups — C₃×#70628 #11791024

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4988	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#809	C₂	1	2	yes	maximal, complemented
6	C₃×#1970	—	3	1	no	maximal
7	#70628	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
9	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
12	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₂₄	—	2	2	no	—
15	C₂×C₃×D₂₄	—	2	2	no	—
16	C₂×C₃×D₂₄	C₄	1	4	yes	complemented
17	C₃²×#107	—	2	2	no	—
18	C₃×C₈×Dic₃	—	2	2	no	—
19	C₃×#809	—	2	4	no	—
20	C₂²×C₃×D₈	—	3	1	no	—
21	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×#107	—	2	1	no	—
23	C₂×C₃×#107	D₃	1	1	yes	characteristic, complemented
24	C₂×C₃×#107	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×C₃×#102	—	3	2	no	—
26	C₂×C₃×C₄×C₈	—	3	1	no	—
27	C₃×#390	—	3	2	no	—
28	C₂×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
29	#4988	C₂×C₃	1	2	yes	complemented
30	C₂×#809	C₂×C₃	1	2	yes	complemented
31	C₂³×C₃×D₃	—	2	2	no	—
32	C₂²×C₃²×C₄	—	2	2	no	—
33	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
34	C₂²×C₃×Dic₃	D₄	1	2	yes	—
35	C₂×C₃×D₁₂	—	2	2	no	—
36	C₂×C₃×D₁₂	—	2	2	no	—
37	C₂×C₃×D₁₂	—	2	2	no	—
38	C₂×C₃×D₁₂	—	2	2	no	—
39	C₂×C₃×D₁₂	—	2	2	no	—
40	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	—
41	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
42	C₂×C₃²×C₈	D₄	1	2	yes	—
43	C₂×C₃²×C₈	D₄	1	2	yes	—
44	C₃²×C₄⋊C₄	—	2	2	no	—
45	C₃²×C₄⋊C₄	—	2	2	no	—
46	C₃×(C₂×D₃)⋊C₄	—	4	8	no	—
47	C₃×C₄×Dic₃	—	2	1	no	—
48	C₃×C₄×Dic₃	—	2	1	no	—
49	C₂×C₃×C₃⋊C₈	—	2	1	no	—
50	C₂×C₃×C₃⋊C₈	—	2	1	no	—
51	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
52	C₃×D₂₄	—	2	8	no	—
53	#1970	—	3	1	no	Sylow
54	C₂²×C₃×D₄	—	3	2	no	—
55	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
56	C₂×C₃×D₈	—	3	4	no	—
57	C₂×C₃×D₈	—	6	2	no	—
58	C₂×C₃×D₈	—	6	2	no	—
59	C₂²×C₃×C₈	—	2	1	no	—
60	C₂²×C₃×C₈	—	3	1	no	—
61	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
65	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₃×C₂²⋊C₄	—	6	4	no	—
67	C₂×C₃×C₄²	—	3	1	no	—
68	C₂×(C₂×D₃)⋊C₄	—	2	4	no	—
69	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
71	C₂×D₂₄	—	2	2	no	—
72	C₂×D₂₄	—	2	2	no	—
73	C₂×D₂₄	C₃×C₄	1	4	yes	complemented
74	C₃×#107	—	2	4	no	—
75	C₃×#107	—	2	2	no	—
76	C₃×#107	—	2	2	no	—
77	C₃×#102	—	6	4	no	—
78	C₃×C₄×C₈	—	6	2	no	—
79	C₈×Dic₃	—	2	2	no	—
80	#809	—	2	4	no	—
81	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₃×D₃	—	2	4	no	—
83	C₂²×C₃×D₃	—	4	2	no	—
84	C₂²×C₃×D₃	—	4	2	no	—
85	C₂²×C₃×D₃	—	4	4	no	—
86	C₂²×C₃×D₃	—	4	4	no	—
87	C₂×C₃²×C₄	—	4	2	no	—
88	C₂×C₃²×C₄	—	4	4	no	—
89	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃²×C₄	#41	1	1	yes	characteristic
94	C₂×C₃²×C₄	#41	1	1	yes	characteristic
95	C₂×C₃×Dic₃	—	2	2	no	—
96	C₂×C₃×Dic₃	—	2	2	no	—
97	C₂×C₃×Dic₃	D₈	1	4	yes	complemented
98	C₃×D₁₂	—	2	4	no	—
99	C₃×D₁₂	—	2	4	no	—
100	C₃×D₁₂	—	4	2	no	—
101	C₃×D₁₂	—	4	2	no	—
102	C₃²×C₈	C₂²⋊C₄	1	4	yes	complemented
103	C₃×C₃⋊C₈	—	2	2	no	—
104	C₂²×D₈	—	3	1	no	—
105	C₂×#107	C₃×D₃	1	1	yes	characteristic, complemented
106	C₂×#102	—	3	2	no	—
107	C₂×C₄×C₈	—	3	1	no	—
108	#390	—	3	2	no	—
109	C₂⁴×C₃	—	6	2	no	—
110	C₂³×D₃	—	2	2	no	—
111	C₂×C₃×D₄	—	3	4	no	—
112	C₂×C₃×D₄	—	6	2	no	—
113	C₂×C₃×D₄	—	6	2	no	—
114	C₂×C₃×D₄	—	6	2	no	—
115	C₂×C₃×D₄	—	6	2	no	—
116	C₂×C₃×D₄	—	6	2	no	—
117	C₂²×C₃×C₄	—	2	2	no	—
118	C₂²×C₃×C₄	—	2	2	no	—
119	C₂²×C₃×C₄	—	2	1	no	—
120	C₂²×C₃×C₄	—	3	2	no	—
121	C₂²×C₃×C₄	—	4	2	no	—
122	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
123	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
124	C₂²×Dic₃	C₃×D₄	1	2	yes	—
125	C₂×D₁₂	—	2	2	no	—
126	C₂×D₁₂	—	2	2	no	—
127	C₂×D₁₂	—	2	2	no	—
128	C₂×D₁₂	—	2	2	no	—
129	C₂×D₁₂	—	2	2	no	—
130	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	—
131	C₃×D₈	—	6	8	no	—
132	C₂×C₃×C₈	—	2	2	no	—
133	C₂×C₃×C₈	—	2	2	no	—
134	C₂×C₃×C₈	—	2	2	no	—
135	C₂×C₃×C₈	—	3	2	no	—
136	C₂×C₃×C₈	—	6	1	no	—
137	C₂×C₃×C₈	—	6	1	no	—
138	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
139	C₂×C₃×C₈	D₁₂	1	2	yes	—
140	C₂×C₃×C₈	#67	1	2	yes	—
141	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
142	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
143	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
144	C₃×C₄⋊C₄	—	2	4	no	—
145	C₃×C₄⋊C₄	—	2	2	no	—
146	C₃×C₄⋊C₄	—	2	2	no	—
147	C₃×C₄⋊C₄	—	2	2	no	—
148	C₃×C₄⋊C₄	—	2	2	no	—
149	C₃×C₄⋊C₄	—	4	2	no	—
150	C₃×C₂²⋊C₄	—	12	8	no	—
151	C₃×C₄²	—	6	1	no	—
152	C₃×C₄²	—	6	1	no	—
153	(C₂×D₃)⋊C₄	—	4	8	no	—
154	C₄×Dic₃	—	2	1	no	—
155	C₄×Dic₃	—	2	1	no	—
156	C₂×C₃⋊C₈	—	2	1	no	—
157	C₂×C₃⋊C₈	—	2	1	no	—
158	C₂×C₃⋊C₈	C₃×D₄	1	2	yes	—
159	D₂₄	—	2	8	no	—
160	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
161	C₂²×C₃²	#121	1	1	yes	characteristic
162	C₂²×C₃²	#127	1	1	yes	characteristic
163	C₂²×C₃²	C₂×D₈	1	2	yes	—
164	C₂²×C₃²	#135	1	2	yes	—
165	C₂×C₃×D₃	—	4	4	no	—
166	C₂×C₃×D₃	—	4	8	no	—
167	C₂×C₃×D₃	—	8	4	no	—
168	C₂×C₃×D₃	—	8	2	no	—
169	C₂×C₃×D₃	—	8	2	no	—
170	C₃²×C₄	—	8	2	no	—
171	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
173	C₃²×C₄	#121	1	1	yes	characteristic
174	C₃²×C₄	#124	1	1	yes	characteristic
175	C₃×Dic₃	—	2	4	no	—
176	C₂²×D₄	—	3	2	no	—
177	C₂×D₈	—	3	4	no	—
178	C₂×D₈	—	6	2	no	—
179	C₂×D₈	—	6	2	no	—
180	C₂²×C₈	—	3	1	no	—
181	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
182	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
183	C₂×C₂²⋊C₄	—	6	4	no	—
184	C₂×C₄²	—	3	1	no	—
185	#107	—	2	2	no	—
186	#102	—	6	4	no	—
187	C₄×C₈	—	6	2	no	—
188	C₂³×C₃	—	2	1	no	—
189	C₂³×C₃	—	6	4	no	—
190	C₂³×C₃	—	12	2	no	—
191	C₂³×C₃	—	12	4	no	—
192	C₂³×C₃	—	12	4	no	—
193	C₂³×C₃	—	12	2	no	—
194	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
195	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
196	C₂²×D₃	—	2	4	no	—
197	C₂²×D₃	—	4	2	no	—
198	C₂²×D₃	—	4	2	no	—
199	C₂²×D₃	—	4	4	no	—
200	C₂²×D₃	—	4	4	no	—
201	C₃×D₄	—	6	4	no	—
202	C₃×D₄	—	6	4	no	—
203	C₃×D₄	—	12	2	no	—
204	C₃×D₄	—	12	2	no	—
205	C₂×C₃×C₄	—	2	1	no	—
206	C₂×C₃×C₄	—	2	1	no	—
207	C₂×C₃×C₄	—	2	1	no	—
208	C₂×C₃×C₄	—	2	1	no	—
209	C₂×C₃×C₄	—	2	1	no	—
210	C₂×C₃×C₄	—	2	1	no	—
211	C₂×C₃×C₄	—	3	4	no	—
212	C₂×C₃×C₄	—	4	4	no	—
213	C₂×C₃×C₄	—	4	4	no	—
214	C₂×C₃×C₄	—	4	2	no	—
215	C₂×C₃×C₄	—	4	2	no	—
216	C₂×C₃×C₄	—	4	4	no	—
217	C₂×C₃×C₄	—	6	2	no	—
218	C₂×C₃×C₄	—	6	2	no	—
219	C₂×C₃×C₄	—	8	4	no	—
220	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
221	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
222	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄	#239	1	1	yes	characteristic
224	C₂×C₃×C₄	#239	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
231	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
232	C₂×Dic₃	—	2	2	no	—
233	C₂×Dic₃	—	2	2	no	—
234	C₂×Dic₃	C₃×D₈	1	4	yes	complemented
235	D₁₂	—	2	4	no	—
236	D₁₂	—	2	4	no	—
237	D₁₂	—	4	2	no	—
238	D₁₂	—	4	2	no	—
239	C₃×C₈	—	2	4	no	—
240	C₃×C₈	—	6	2	no	—
241	C₃×C₈	(C₂×D₃)⋊C₄	1	4	yes	complemented
242	C₃×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
243	C₃⋊C₈	—	2	2	no	—
244	C₂×C₃²	#390	1	1	yes	characteristic
245	C₂×C₃²	C₄×D₈	1	2	yes	—
246	C₂×C₃²	#466	1	2	yes	—
247	C₂×C₃²	#493	1	1	yes	characteristic
248	C₂×C₃²	#495	1	1	yes	characteristic
249	C₃×D₃	—	8	4	no	—
250	C₂⁴	—	6	2	no	—
251	C₂×D₄	—	3	4	no	—
252	C₂×D₄	—	6	2	no	—
253	C₂×D₄	—	6	2	no	—
254	C₂×D₄	—	6	2	no	—
255	C₂×D₄	—	6	2	no	—
256	C₂×D₄	—	6	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	3	2	no	—
259	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
260	D₈	—	6	8	no	—
261	C₂×C₈	—	3	2	no	—
262	C₂×C₈	—	6	1	no	—
263	C₂×C₈	—	6	1	no	—
264	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
265	C₂×C₈	C₃×D₁₂	1	2	yes	—
266	C₂×C₈	C₃×#67	1	2	yes	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	2	2	no	—
269	C₂²⋊C₄	—	12	8	no	—
270	C₄²	—	6	1	no	—
271	C₄²	—	6	1	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	12	8	no	—
278	C₂²×C₃	—	12	4	no	—
279	C₂²×C₃	—	24	4	no	—
280	C₂²×C₃	—	24	2	no	—
281	C₂²×C₃	—	24	2	no	—
282	C₂²×C₃	#893	1	1	yes	characteristic
283	C₂²×C₃	#895	1	1	yes	characteristic
284	C₂²×C₃	D₃×D₈	1	2	yes	—
285	C₂²×C₃	#919	1	2	yes	—
286	C₂²×C₃	#940	1	1	yes	characteristic
287	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
288	C₂²×C₃	C₃×#121	1	1	yes	characteristic
289	C₂²×C₃	C₃×#127	1	1	yes	characteristic
290	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
291	C₂²×C₃	C₃×#135	1	2	yes	—
292	C₂×D₃	—	4	4	no	—
293	C₂×D₃	—	4	8	no	—
294	C₂×D₃	—	8	4	no	—
295	C₂×D₃	—	8	2	no	—
296	C₂×D₃	—	8	2	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	1	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	6	4	no	—
302	C₃×C₄	—	8	4	no	—
303	C₃×C₄	—	8	2	no	—
304	C₃×C₄	—	8	2	no	—
305	C₃×C₄	#893	1	1	yes	characteristic
306	C₃×C₄	#895	1	1	yes	characteristic
307	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
308	C₃×C₄	#947	1	1	yes	characteristic
309	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
310	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
311	C₃×C₄	C₃×#121	1	1	yes	characteristic
312	C₃×C₄	C₃×#124	1	1	yes	characteristic
313	Dic₃	—	2	4	no	—
314	C₃²	#1970	1	1	yes	characteristic, complemented, Sylow
315	C₂³	—	6	4	no	—
316	C₂³	—	12	2	no	—
317	C₂³	—	12	4	no	—
318	C₂³	—	12	4	no	—
319	C₂³	—	12	2	no	—
320	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
321	D₄	—	6	4	no	—
322	D₄	—	6	4	no	—
323	D₄	—	12	2	no	—
324	D₄	—	12	2	no	—
325	C₂×C₄	—	3	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	6	2	no	—
329	C₂×C₄	—	6	2	no	—
330	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
331	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
332	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
333	C₂×C₄	C₃×#239	1	1	yes	characteristic
334	C₂×C₄	C₃×#239	1	1	yes	characteristic
335	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
336	C₈	—	6	2	no	—
337	C₈	C₃×(C₂×D₃)⋊C₄	1	4	yes	complemented
338	C₂×C₃	—	2	1	no	—
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	2	2	no	—
342	C₂×C₃	—	2	1	no	—
343	C₂×C₃	—	24	4	no	—
344	C₂×C₃	#4872	1	2	yes	—
345	C₂×C₃	#4883	1	2	yes	—
346	C₂×C₃	#4988	1	1	yes	characteristic
347	C₂×C₃	#5151	1	1	yes	characteristic
348	C₂×C₃	#5191	1	1	yes	characteristic
349	C₂×C₃	C₃×#390	1	1	yes	characteristic
350	C₂×C₃	C₃×C₄×D₈	1	2	yes	—
351	C₂×C₃	C₃×#466	1	2	yes	—
352	C₂×C₃	C₃×#493	1	1	yes	characteristic
353	C₂×C₃	C₃×#495	1	1	yes	characteristic
354	D₃	—	8	4	no	—
355	C₂²	—	12	4	no	—
356	C₂²	—	12	8	no	—
357	C₂²	—	24	2	no	—
358	C₂²	—	24	4	no	—
359	C₂²	—	24	2	no	—
360	C₂²	C₃×#893	1	1	yes	characteristic
361	C₂²	C₃×#895	1	1	yes	characteristic
362	C₂²	C₃×D₃×D₈	1	2	yes	—
363	C₂²	C₃×#919	1	2	yes	—
364	C₂²	C₃×#940	1	1	yes	characteristic
365	C₄	—	6	4	no	—
366	C₄	—	8	2	no	—
367	C₄	C₃×#893	1	1	yes	characteristic
368	C₄	C₃×#895	1	1	yes	characteristic
369	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
370	C₄	C₃×#947	1	1	yes	characteristic
371	C₃	—	2	1	no	—
372	C₃	#70628	1	1	yes	characteristic, direct product factor
373	C₃	C₃×#1970	1	1	yes	characteristic, complemented
374	C₂	—	24	4	no	—
375	C₂	C₃×#4872	1	2	yes	—
376	C₂	C₃×#4883	1	2	yes	—
377	C₂	C₃×#4988	1	1	yes	characteristic
378	C₂	C₃×#5151	1	1	yes	characteristic
379	C₂	C₃×#5191	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×#107	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₂₄	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×#107	D₃
hypocenter	C₃	C₃×#1970
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#107

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×#107	C₂	semidirect
3. C₂×C₃×C₈×Dic₃	C₂	semidirect
4. C₃×#4988	C₂	semidirect
5. C₂×C₃×#809	C₂	semidirect
7. #70628	C₃	direct (N × H)
16. C₂×C₃×D₂₄	C₄	semidirect
23. C₂×C₃×#107	D₃	semidirect
24. C₂×C₃×#107	C₂×C₃	semidirect
28. C₂×C₈×Dic₃	C₂×C₃	semidirect
29. #4988	C₂×C₃	semidirect
30. C₂×#809	C₂×C₃	semidirect
73. C₂×D₂₄	C₃×C₄	semidirect
97. C₂×C₃×Dic₃	D₈	semidirect
102. C₃²×C₈	C₂²⋊C₄	semidirect
105. C₂×#107	C₃×D₃	semidirect
234. C₂×Dic₃	C₃×D₈	semidirect
241. C₃×C₈	(C₂×D₃)⋊C₄	semidirect
242. C₃×C₈	C₃×C₂²⋊C₄	semidirect
314. C₃²	#1970	semidirect
337. C₈	C₃×(C₂×D₃)⋊C₄	semidirect
372. C₃	#70628	direct (N × H)
373. C₃	C₃×#1970	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₂₄	2
C₂×C₃²×#107	2
C₂×C₃×C₈×Dic₃	2
C₃×#4988	2
C₂×C₃×#809	2
C₃×#1970	3
#70628	3

Subgroups — C3×#70628 #11791024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70628 #11791024