Subgroups — C₃×#86281 #11906315

Order 1152.

2231 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5728	C₂	1	2	yes	maximal, complemented
3	C₃×D₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
4	C₃×#5689	C₂	1	4	yes	maximal, complemented
5	C₃×#5635	C₂	1	4	yes	maximal, complemented
6	C₃×#5632	C₂	1	4	yes	maximal, complemented
7	C₃×#5579	C₂	1	2	yes	maximal, complemented
8	C₃×Q₈×D₁₂	C₂	1	2	yes	maximal, complemented
9	C₃×#5567	C₂	1	2	yes	maximal, complemented
10	C₃×Q₈×Dic₆	C₂	1	2	yes	maximal, complemented
11	C₃×#5523	C₂	1	2	yes	maximal
12	C₃×#5519	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic
14	C₂×C₃×#869	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3503	—	3	1	no	maximal
16	#86281	C₃	1	1	yes	maximal, characteristic, direct product factor
17	C₂×C₃×D₃×Q₈	C₂²	1	4	yes	—
18	C₂×C₃×#235	C₂²	1	1	yes	characteristic
19	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
20	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₃²×#125	C₂²	1	2	yes	—
23	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃²×C₄×Q₈	C₂²	1	2	yes	—
26	C₃²×C₄×Q₈	C₂²	1	2	yes	—
27	C₃²×#117	C₂²	1	2	yes	—
28	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
29	C₃×#946	C₂²	1	4	yes	—
30	C₃×Q₈×Dic₃	C₂²	1	4	yes	—
31	C₃×#944	C₂²	1	4	yes	—
32	C₃×C₄×#67	C₂²	1	2	yes	—
33	C₃×C₄×#67	C₂²	1	2	yes	—
34	C₃×#926	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
36	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
37	C₃×#897	C₂²	1	4	yes	—
38	C₃×#897	C₂²	1	8	yes	—
39	C₃×#896	C₂²	1	8	yes	—
40	C₃×#892	C₂²	1	4	yes	—
41	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
42	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
43	C₃×#890	C₂²	1	4	yes	—
44	C₃×#889	C₂²	1	8	yes	—
45	C₃×#888	C₂²	1	4	yes	—
46	C₃×#888	C₂²	1	8	yes	—
47	C₃×#888	C₂²	1	4	yes	—
48	C₃×#887	C₂²	1	4	yes	—
49	C₃×#67⋊C₄	C₂²	1	8	yes	—
50	C₃×#878	C₂²	1	8	yes	—
51	C₃×C₄×D₁₂	C₂²	1	4	yes	—
52	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
53	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
54	C₃×#872	C₂²	1	2	yes	—
55	C₃×C₄²×D₃	C₂²	1	2	yes	—
56	C₃×#870	C₂²	1	4	yes	—
57	C₃×#869	C₂²	1	4	yes	—
58	C₃×#869	C₂²	1	2	yes	—
59	C₃×#869	C₂²	1	2	yes	—
60	C₃×#869	C₂²	1	2	yes	—
61	C₃×#869	C₂²	1	2	yes	—
62	C₃×C₄×Dic₆	C₂²	1	4	yes	—
63	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
64	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
65	C₃×Q₈²	—	3	2	no	—
66	C₃×#557	—	3	2	no	—
67	C₃×#554	—	3	4	no	—
68	C₃×#554	—	3	2	no	—
69	C₃×D₄×Q₈	—	3	4	no	—
70	C₃×D₄×Q₈	—	3	2	no	—
71	C₃×#544	—	3	4	no	—
72	C₃×#544	—	3	2	no	—
73	C₃×#533	—	2	1	no	—
74	C₃×#533	—	3	2	no	—
75	C₃×#533	D₃	1	1	yes	characteristic, complemented
76	C₃×#533	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×C₃×C₄⋊Q₈	—	3	2	no	—
78	C₂×C₃×C₄⋊Q₈	—	3	1	no	—
79	C₃×#520	—	3	2	no	—
80	C₃×C₄×#41	—	3	1	no	—
81	#5728	C₂×C₃	1	2	yes	complemented
82	D₃×C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
83	#5689	C₂×C₃	1	4	yes	complemented
84	#5635	C₂×C₃	1	4	yes	complemented
85	#5632	C₂×C₃	1	4	yes	complemented
86	#5579	C₂×C₃	1	2	yes	complemented
87	Q₈×D₁₂	C₂×C₃	1	2	yes	complemented
88	#5567	C₂×C₃	1	2	yes	complemented
89	Q₈×Dic₆	C₂×C₃	1	2	yes	complemented
90	#5523	C₂×C₃	1	2	yes	—
91	#5519	C₂×C₃	1	2	yes	complemented
92	C₄×#235	C₂×C₃	1	1	yes	characteristic
93	C₂×#869	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×C₃²×Q₈	C₂³	1	2	yes	—
95	C₂×C₃²×Q₈	C₂³	1	2	yes	—
96	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
97	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
98	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
99	C₂×C₃×#67	C₂³	1	2	yes	—
100	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
101	C₃×D₃×Q₈	—	4	8	no	—
102	C₃×#235	Q₈	1	8	yes	complemented
103	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
105	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
106	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
107	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
108	C₂×C₃×Dic₆	—	4	4	no	—
109	C₂×C₃×Dic₆	C₂³	1	4	yes	—
110	C₂×C₃×Dic₆	C₂³	1	8	yes	—
111	C₂×C₃×Dic₆	C₂³	1	4	yes	—
112	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
113	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
114	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
115	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
116	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
117	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
118	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
119	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₃²×C₄²	C₂³	1	1	yes	characteristic
121	C₃²×C₄²	C₂³	1	1	yes	characteristic
122	C₃²×C₄²	C₂³	1	1	yes	characteristic
123	C₃²×C₄²	C₂³	1	1	yes	characteristic
124	C₃²×C₄²	C₂³	1	4	yes	—
125	C₃×#217	C₂³	1	2	yes	—
126	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
127	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
128	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
129	C₃×C₄⋊Dic₃	C₂³	1	8	yes	—
130	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
131	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
132	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
133	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
134	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
135	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
136	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
137	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
138	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
139	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
140	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
141	C₃×C₄×Dic₃	C₂³	1	8	yes	—
142	C₃×C₄×Dic₃	C₂³	1	2	yes	—
143	C₃×C₄×Dic₃	C₂³	1	2	yes	—
144	C₃×C₄×Dic₃	C₂³	1	2	yes	—
145	#3503	—	3	1	no	Sylow
146	C₂×C₃×#41	—	3	1	no	—
147	C₂²×C₃×Q₈	—	3	4	no	—
148	C₂²×C₃×Q₈	—	3	2	no	—
149	C₂×D₃×Q₈	C₂²×C₃	1	4	yes	—
150	C₂×#235	C₂²×C₃	1	1	yes	characteristic
151	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
152	C₃×C₄⋊Q₈	—	2	1	no	—
153	C₃×C₄⋊Q₈	—	2	1	no	—
154	C₃×C₄⋊Q₈	—	3	4	no	—
155	C₃×C₄⋊Q₈	—	3	4	no	—
156	C₃×C₄⋊Q₈	—	3	8	no	—
157	C₃×C₄⋊Q₈	—	3	4	no	—
158	C₃×C₄⋊Q₈	—	3	2	no	—
159	C₃×C₄⋊Q₈	—	3	4	no	—
160	C₃×C₄⋊Q₈	—	3	2	no	—
161	C₃×C₄⋊Q₈	—	3	2	no	—
162	C₃×C₄⋊Q₈	—	3	2	no	—
163	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
164	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
165	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
166	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
167	C₃×#125	—	2	2	no	—
168	C₃×#125	—	3	8	no	—
169	C₃×#125	—	3	4	no	—
170	C₃×#125	—	3	4	no	—
171	C₃×#125	C₂×D₃	1	2	yes	—
172	C₃×#125	C₂²×C₃	1	2	yes	—
173	C₃×C₂²⋊Q₈	—	2	2	no	—
174	C₃×C₂²⋊Q₈	—	2	2	no	—
175	C₃×C₂²⋊Q₈	—	3	4	no	—
176	C₃×C₂²⋊Q₈	—	3	8	no	—
177	C₃×C₂²⋊Q₈	—	3	4	no	—
178	C₃×C₂²⋊Q₈	—	3	8	no	—
179	C₃×C₂²⋊Q₈	—	3	8	no	—
180	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
181	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
182	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
183	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
184	C₃×C₄×Q₈	—	2	2	no	—
185	C₃×C₄×Q₈	—	2	2	no	—
186	C₃×C₄×Q₈	—	3	4	no	—
187	C₃×C₄×Q₈	—	3	4	no	—
188	C₃×C₄×Q₈	—	3	1	no	—
189	C₃×C₄×Q₈	—	3	4	no	—
190	C₃×C₄×Q₈	—	3	1	no	—
191	C₃×C₄×Q₈	C₂×D₃	1	2	yes	—
192	C₃×C₄×Q₈	C₂×D₃	1	2	yes	—
193	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
194	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
195	C₃×C₄×D₄	—	3	2	no	—
196	C₃×C₄×D₄	—	3	2	no	—
197	C₃×C₄×D₄	—	3	8	no	—
198	C₃×C₄×D₄	—	3	1	no	—
199	C₃×C₄×D₄	—	3	1	no	—
200	C₃×C₄×D₄	—	3	4	no	—
201	C₃×#117	—	2	2	no	—
202	C₃×#117	—	3	1	no	—
203	C₃×#117	—	3	4	no	—
204	C₃×#117	—	3	2	no	—
205	C₃×#117	C₂×D₃	1	2	yes	—
206	C₃×#117	C₂²×C₃	1	2	yes	—
207	C₂×C₃×C₄⋊C₄	—	3	2	no	—
208	C₂×C₃×C₄⋊C₄	—	3	2	no	—
209	C₂×C₃×C₄⋊C₄	—	3	4	no	—
210	C₂×C₃×C₄⋊C₄	—	3	4	no	—
211	C₂×C₃×C₄²	—	2	1	no	—
212	C₂×C₃×C₄²	—	3	2	no	—
213	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
214	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
215	#946	C₂²×C₃	1	4	yes	—
216	Q₈×Dic₃	C₂²×C₃	1	4	yes	—
217	#944	C₂²×C₃	1	4	yes	—
218	C₄×#67	C₂²×C₃	1	2	yes	—
219	C₄×#67	C₂²×C₃	1	2	yes	—
220	#926	C₂²×C₃	1	1	yes	characteristic
221	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
222	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
223	#897	C₂²×C₃	1	4	yes	—
224	#897	C₂²×C₃	1	8	yes	—
225	#896	C₂²×C₃	1	8	yes	—
226	#892	C₂²×C₃	1	4	yes	—
227	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
228	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
229	#890	C₂²×C₃	1	4	yes	—
230	#889	C₂²×C₃	1	8	yes	—
231	#888	C₂²×C₃	1	8	yes	—
232	#888	C₂²×C₃	1	4	yes	—
233	#888	C₂²×C₃	1	4	yes	—
234	#887	C₂²×C₃	1	4	yes	—
235	#67⋊C₄	C₂²×C₃	1	8	yes	—
236	#878	C₂²×C₃	1	8	yes	—
237	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
238	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
239	C₄×D₁₂	C₂²×C₃	1	4	yes	—
240	#872	C₂²×C₃	1	2	yes	—
241	C₄²×D₃	C₂²×C₃	1	2	yes	—
242	#870	C₂²×C₃	1	4	yes	—
243	#869	C₂²×C₃	1	2	yes	—
244	#869	C₂²×C₃	1	2	yes	—
245	#869	C₂²×C₃	1	2	yes	—
246	#869	C₂²×C₃	1	2	yes	—
247	#869	C₂²×C₃	1	4	yes	—
248	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
249	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
250	C₄×Dic₆	C₂²×C₃	1	4	yes	—
251	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
252	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
253	C₃²×Q₈	—	2	4	no	—
254	C₃²×Q₈	—	2	4	no	—
255	C₂×C₃²×C₄	—	2	2	no	—
256	C₂×C₃²×C₄	—	2	2	no	—
257	C₂×C₃²×C₄	C₂×Q₈	1	4	yes	complemented
258	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
259	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
260	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
261	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
262	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
263	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
264	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
265	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
266	C₃×#67	C₂×Q₈	1	8	yes	complemented
267	C₂×C₃×Dic₃	—	4	4	no	—
268	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
269	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
270	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
271	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
272	C₃×D₁₂	C₂×Q₈	1	4	yes	complemented
273	C₃×C₄×D₃	—	2	4	no	—
274	C₃×C₄×D₃	—	2	4	no	—
275	C₃×C₄×D₃	—	4	8	no	—
276	C₃×C₄×D₃	C₂×Q₈	1	8	yes	complemented
277	C₃×Dic₆	—	2	8	no	—
278	C₃×Dic₆	—	4	4	no	—
279	C₃×Dic₆	—	4	8	no	—
280	C₃×Dic₆	C₂×Q₈	1	4	yes	complemented
281	Q₈²	—	3	2	no	—
282	#557	—	3	2	no	—
283	#554	—	3	4	no	—
284	#554	—	3	2	no	—
285	D₄×Q₈	—	3	4	no	—
286	D₄×Q₈	—	3	2	no	—
287	#544	—	3	4	no	—
288	#544	—	3	2	no	—
289	#533	—	3	2	no	—
290	#533	C₃×D₃	1	1	yes	characteristic, complemented
291	C₂×C₄⋊Q₈	—	3	2	no	—
292	C₂×C₄⋊Q₈	—	3	1	no	—
293	#520	—	3	2	no	—
294	C₄×#41	—	3	1	no	—
295	C₃×#41	—	3	8	no	—
296	C₂×C₃×Q₈	—	2	2	no	—
297	C₂×C₃×Q₈	—	2	2	no	—
298	C₂×C₃×Q₈	—	3	1	no	—
299	C₂×C₃×Q₈	—	3	4	no	—
300	C₂×C₃×Q₈	—	3	8	no	—
301	C₂×C₃×Q₈	—	3	4	no	—
302	C₂×C₃×Q₈	—	12	4	no	—
303	C₂×C₃×Q₈	—	12	8	no	—
304	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
305	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
306	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
307	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
308	C₂×C₃×D₄	—	3	2	no	—
309	C₂×C₃×D₄	—	3	1	no	—
310	C₂²×C₃×C₄	—	2	1	no	—
311	C₂²×C₃×C₄	—	2	1	no	—
312	C₂²×C₃×C₄	—	2	1	no	—
313	C₂²×C₃×C₄	—	3	2	no	—
314	C₂²×C₃×C₄	—	3	4	no	—
315	C₂²×C₃×C₄	—	3	2	no	—
316	C₂²×C₃×C₄	—	3	2	no	—
317	C₂²×C₃×C₄	—	3	8	no	—
318	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
321	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
323	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
324	C₂×#67	C₂³×C₃	1	2	yes	—
325	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
326	D₃×Q₈	—	4	8	no	—
327	#235	C₃×Q₈	1	8	yes	complemented
328	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
329	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
330	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
331	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
332	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
333	C₂×Dic₆	—	4	4	no	—
334	C₂×Dic₆	C₂³×C₃	1	4	yes	—
335	C₂×Dic₆	C₂³×C₃	1	4	yes	—
336	C₂×Dic₆	C₂³×C₃	1	8	yes	—
337	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
338	C₃×C₄⋊C₄	—	2	2	no	—
339	C₃×C₄⋊C₄	—	2	2	no	—
340	C₃×C₄⋊C₄	—	2	4	no	—
341	C₃×C₄⋊C₄	—	2	4	no	—
342	C₃×C₄⋊C₄	—	2	2	no	—
343	C₃×C₄⋊C₄	—	2	2	no	—
344	C₃×C₄⋊C₄	—	3	8	no	—
345	C₃×C₄⋊C₄	—	3	8	no	—
346	C₃×C₄⋊C₄	—	3	2	no	—
347	C₃×C₄⋊C₄	—	3	2	no	—
348	C₃×C₄⋊C₄	—	3	8	no	—
349	C₃×C₄⋊C₄	—	3	4	no	—
350	C₃×C₄⋊C₄	—	3	4	no	—
351	C₃×C₄⋊C₄	—	3	4	no	—
352	C₃×C₄⋊C₄	—	3	4	no	—
353	C₃×C₄⋊C₄	—	3	1	no	—
354	C₃×C₄⋊C₄	—	3	1	no	—
355	C₃×C₄⋊C₄	—	3	8	no	—
356	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
357	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
358	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
359	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
360	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
361	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
362	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
363	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
364	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
365	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
366	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
367	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
368	C₃×C₂²⋊C₄	—	2	4	no	—
369	C₃×C₂²⋊C₄	—	3	2	no	—
370	C₃×C₂²⋊C₄	—	3	2	no	—
371	C₃×C₂²⋊C₄	—	3	2	no	—
372	C₃×C₂²⋊C₄	—	3	8	no	—
373	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
374	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
375	C₃×C₄²	—	2	1	no	—
376	C₃×C₄²	—	2	1	no	—
377	C₃×C₄²	—	2	1	no	—
378	C₃×C₄²	—	2	1	no	—
379	C₃×C₄²	—	2	4	no	—
380	C₃×C₄²	—	3	2	no	—
381	C₃×C₄²	—	3	2	no	—
382	C₃×C₄²	—	3	2	no	—
383	C₃×C₄²	—	3	8	no	—
384	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
385	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
386	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
387	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
388	C₃×C₄²	C₂²×D₃	1	4	yes	—
389	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
390	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
391	C₃×C₄²	C₂³×C₃	1	4	yes	—
392	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
393	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
394	#217	C₂³×C₃	1	2	yes	—
395	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
396	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
397	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
398	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
399	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
400	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
401	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
402	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
403	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
404	C₄⋊Dic₃	C₂³×C₃	1	8	yes	—
405	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
406	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
407	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
408	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
409	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
410	C₄×Dic₃	C₂³×C₃	1	2	yes	—
411	C₄×Dic₃	C₂³×C₃	1	2	yes	—
412	C₄×Dic₃	C₂³×C₃	1	8	yes	—
413	C₄×Dic₃	C₂³×C₃	1	2	yes	—
414	C₂²×C₃²	—	2	1	no	—
415	C₂²×C₃²	—	2	1	no	—
416	C₂²×C₃²	C₂²×Q₈	1	2	yes	—
417	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
418	C₂×C₃×D₃	—	2	2	no	—
419	C₂×C₃×D₃	—	2	2	no	—
420	C₂×C₃×D₃	C₂²×Q₈	1	4	yes	—
421	C₃²×C₄	—	2	1	no	—
422	C₃²×C₄	—	2	4	no	—
423	C₃²×C₄	—	2	1	no	—
424	C₃²×C₄	—	2	4	no	—
425	C₃²×C₄	C₂²×Q₈	1	2	yes	—
426	C₃²×C₄	C₂²×Q₈	1	2	yes	—
427	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
428	C₃²×C₄	2₋¹⁺⁴	1	2	yes	—
429	C₃×Dic₃	—	2	8	no	—
430	C₃×Dic₃	—	2	2	no	—
431	C₃×Dic₃	—	2	2	no	—
432	C₃×Dic₃	C₂²×Q₈	1	4	yes	—
433	C₂×#41	—	3	1	no	—
434	C₂²×Q₈	—	3	4	no	—
435	C₂²×Q₈	—	3	2	no	—
436	C₄⋊Q₈	—	3	4	no	—
437	C₄⋊Q₈	—	3	4	no	—
438	C₄⋊Q₈	—	3	4	no	—
439	C₄⋊Q₈	—	3	8	no	—
440	C₄⋊Q₈	—	3	2	no	—
441	C₄⋊Q₈	—	3	2	no	—
442	C₄⋊Q₈	—	3	2	no	—
443	C₄⋊Q₈	—	3	2	no	—
444	C₄⋊Q₈	—	3	4	no	—
445	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
446	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
447	#125	—	3	4	no	—
448	#125	—	3	8	no	—
449	#125	—	3	4	no	—
450	#125	C₂×C₃×D₃	1	2	yes	—
451	C₂²⋊Q₈	—	3	4	no	—
452	C₂²⋊Q₈	—	3	4	no	—
453	C₂²⋊Q₈	—	3	8	no	—
454	C₂²⋊Q₈	—	3	8	no	—
455	C₂²⋊Q₈	—	3	8	no	—
456	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
457	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
458	C₄×Q₈	—	3	4	no	—
459	C₄×Q₈	—	3	4	no	—
460	C₄×Q₈	—	3	1	no	—
461	C₄×Q₈	—	3	1	no	—
462	C₄×Q₈	—	3	4	no	—
463	C₄×Q₈	C₂×C₃×D₃	1	2	yes	—
464	C₄×Q₈	C₂×C₃×D₃	1	2	yes	—
465	C₄×D₄	—	3	2	no	—
466	C₄×D₄	—	3	2	no	—
467	C₄×D₄	—	3	8	no	—
468	C₄×D₄	—	3	1	no	—
469	C₄×D₄	—	3	1	no	—
470	C₄×D₄	—	3	4	no	—
471	#117	—	3	1	no	—
472	#117	—	3	4	no	—
473	#117	—	3	2	no	—
474	#117	C₂×C₃×D₃	1	2	yes	—
475	C₂×C₄⋊C₄	—	3	2	no	—
476	C₂×C₄⋊C₄	—	3	2	no	—
477	C₂×C₄⋊C₄	—	3	4	no	—
478	C₂×C₄⋊C₄	—	3	4	no	—
479	C₂×C₄²	—	3	2	no	—
480	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
481	C₂³×C₃	—	2	1	no	—
482	C₂³×C₃	—	3	2	no	—
483	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
484	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
485	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
486	C₃×Q₈	—	2	4	no	—
487	C₃×Q₈	—	2	4	no	—
488	C₃×Q₈	—	2	4	no	—
489	C₃×Q₈	—	2	4	no	—
490	C₃×Q₈	—	3	4	no	—
491	C₃×Q₈	—	4	4	no	—
492	C₃×Q₈	—	4	4	no	—
493	C₃×Q₈	—	6	8	no	—
494	C₃×Q₈	—	12	4	no	—
495	C₃×Q₈	—	12	8	no	—
496	C₃×D₄	—	3	8	no	—
497	C₃×D₄	—	3	4	no	—
498	C₂×C₃×C₄	—	2	2	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	2	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	4	no	—
509	C₂×C₃×C₄	—	2	4	no	—
510	C₂×C₃×C₄	—	2	4	no	—
511	C₂×C₃×C₄	—	3	2	no	—
512	C₂×C₃×C₄	—	3	8	no	—
513	C₂×C₃×C₄	—	3	2	no	—
514	C₂×C₃×C₄	—	3	2	no	—
515	C₂×C₃×C₄	—	3	8	no	—
516	C₂×C₃×C₄	—	4	2	no	—
517	C₂×C₃×C₄	—	4	2	no	—
518	C₂×C₃×C₄	—	6	4	no	—
519	C₂×C₃×C₄	—	6	4	no	—
520	C₂×C₃×C₄	—	12	8	no	—
521	C₂×C₃×C₄	—	12	4	no	—
522	C₂×C₃×C₄	D₃×Q₈	1	4	yes	complemented
523	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	complemented
524	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
525	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
526	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
527	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
528	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
529	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
530	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
531	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
532	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
533	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
534	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
535	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
536	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
537	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
538	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
540	#67	C₂×C₃×Q₈	1	8	yes	complemented
541	C₂×Dic₃	—	4	4	no	—
542	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
543	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
544	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
545	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
546	D₁₂	C₂×C₃×Q₈	1	4	yes	complemented
547	C₄×D₃	—	2	4	no	—
548	C₄×D₃	—	2	4	no	—
549	C₄×D₃	—	4	8	no	—
550	C₄×D₃	C₂×C₃×Q₈	1	8	yes	complemented
551	Dic₆	—	2	8	no	—
552	Dic₆	—	4	4	no	—
553	Dic₆	—	4	8	no	—
554	Dic₆	C₂×C₃×Q₈	1	4	yes	complemented
555	C₂×C₃²	—	2	2	no	—
556	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
557	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
558	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
559	C₃×D₃	—	2	4	no	—
560	#41	—	3	8	no	—
561	C₂×Q₈	—	3	1	no	—
562	C₂×Q₈	—	3	4	no	—
563	C₂×Q₈	—	3	8	no	—
564	C₂×Q₈	—	3	4	no	—
565	C₂×Q₈	—	12	4	no	—
566	C₂×Q₈	—	12	8	no	—
567	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
568	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
569	C₂×D₄	—	3	2	no	—
570	C₂×D₄	—	3	1	no	—
571	C₂²×C₄	—	3	2	no	—
572	C₂²×C₄	—	3	4	no	—
573	C₂²×C₄	—	3	2	no	—
574	C₂²×C₄	—	3	2	no	—
575	C₂²×C₄	—	3	8	no	—
576	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
577	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
578	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
579	C₄⋊C₄	—	3	4	no	—
580	C₄⋊C₄	—	3	4	no	—
581	C₄⋊C₄	—	3	8	no	—
582	C₄⋊C₄	—	3	4	no	—
583	C₄⋊C₄	—	3	8	no	—
584	C₄⋊C₄	—	3	4	no	—
585	C₄⋊C₄	—	3	2	no	—
586	C₄⋊C₄	—	3	1	no	—
587	C₄⋊C₄	—	3	2	no	—
588	C₄⋊C₄	—	3	1	no	—
589	C₄⋊C₄	—	3	8	no	—
590	C₄⋊C₄	—	3	8	no	—
591	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
592	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
593	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
594	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
595	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
596	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
597	C₂²⋊C₄	—	3	2	no	—
598	C₂²⋊C₄	—	3	2	no	—
599	C₂²⋊C₄	—	3	2	no	—
600	C₂²⋊C₄	—	3	8	no	—
601	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
602	C₄²	—	3	2	no	—
603	C₄²	—	3	2	no	—
604	C₄²	—	3	2	no	—
605	C₄²	—	3	8	no	—
606	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
607	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
608	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
609	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
610	C₄²	C₂²×C₃×D₃	1	4	yes	—
611	C₂²×C₃	—	2	1	no	—
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	2	1	no	—
615	C₂²×C₃	—	2	2	no	—
616	C₂²×C₃	—	2	1	no	—
617	C₂²×C₃	—	3	4	no	—
618	C₂²×C₃	—	4	1	no	—
619	C₂²×C₃	—	4	1	no	—
620	C₂²×C₃	—	6	2	no	—
621	C₂²×C₃	—	6	2	no	—
622	C₂²×C₃	C₂×D₃×Q₈	1	2	yes	—
623	C₂²×C₃	C₂²×C₃×Q₈	1	2	yes	—
624	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
625	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
626	C₂×D₃	—	2	2	no	—
627	C₂×D₃	—	2	2	no	—
628	C₂×D₃	C₂²×C₃×Q₈	1	4	yes	—
629	C₃×C₄	—	2	1	no	—
630	C₃×C₄	—	2	4	no	—
631	C₃×C₄	—	2	1	no	—
632	C₃×C₄	—	2	4	no	—
633	C₃×C₄	—	2	1	no	—
634	C₃×C₄	—	2	4	no	—
635	C₃×C₄	—	2	1	no	—
636	C₃×C₄	—	2	4	no	—
637	C₃×C₄	—	2	2	no	—
638	C₃×C₄	—	2	2	no	—
639	C₃×C₄	—	2	2	no	—
640	C₃×C₄	—	2	2	no	—
641	C₃×C₄	—	3	4	no	—
642	C₃×C₄	—	4	1	no	—
643	C₃×C₄	—	4	1	no	—
644	C₃×C₄	—	4	4	no	—
645	C₃×C₄	—	4	4	no	—
646	C₃×C₄	—	6	2	no	—
647	C₃×C₄	—	6	8	no	—
648	C₃×C₄	—	6	2	no	—
649	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
650	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
651	C₃×C₄	#1009	1	2	yes	—
652	C₃×C₄	#1010	1	2	yes	—
653	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
654	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
655	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
656	C₃×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
657	Dic₃	—	2	8	no	—
658	Dic₃	—	2	2	no	—
659	Dic₃	—	2	2	no	—
660	Dic₃	C₂²×C₃×Q₈	1	4	yes	—
661	C₃²	#3503	1	1	yes	characteristic, complemented, Sylow
662	C₂³	—	3	2	no	—
663	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
664	Q₈	—	2	4	no	—
665	Q₈	—	2	4	no	—
666	Q₈	—	3	4	no	—
667	Q₈	—	6	8	no	—
668	Q₈	—	12	4	no	—
669	Q₈	—	12	8	no	—
670	D₄	—	3	8	no	—
671	D₄	—	3	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	3	2	no	—
675	C₂×C₄	—	3	8	no	—
676	C₂×C₄	—	3	2	no	—
677	C₂×C₄	—	3	2	no	—
678	C₂×C₄	—	3	8	no	—
679	C₂×C₄	—	6	4	no	—
680	C₂×C₄	—	6	4	no	—
681	C₂×C₄	—	12	8	no	—
682	C₂×C₄	—	12	4	no	—
683	C₂×C₄	C₃×D₃×Q₈	1	4	yes	complemented
684	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
685	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
686	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
687	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
688	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
689	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
690	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
691	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
692	C₂×C₃	—	2	2	no	—
693	C₂×C₃	—	2	2	no	—
694	C₂×C₃	—	2	1	no	—
695	C₂×C₃	—	2	1	no	—
696	C₂×C₃	—	2	1	no	—
697	C₂×C₃	—	4	2	no	—
698	C₂×C₃	—	6	4	no	—
699	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
700	C₂×C₃	C₂×#1009	1	1	yes	characteristic
701	C₂×C₃	C₂×#1010	1	1	yes	characteristic
702	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
703	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
705	D₃	—	2	4	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	3	4	no	—
709	C₂²	—	6	2	no	—
710	C₂²	—	6	2	no	—
711	C₂²	C₂×C₃×D₃×Q₈	1	2	yes	—
712	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	4	no	—
717	C₄	—	3	4	no	—
718	C₄	—	6	2	no	—
719	C₄	—	6	8	no	—
720	C₄	—	6	2	no	—
721	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
722	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
723	C₄	C₃×#1009	1	2	yes	—
724	C₄	C₃×#1010	1	2	yes	—
725	C₃	—	2	1	no	—
726	C₃	#86281	1	1	yes	characteristic, direct product factor
727	C₃	C₃×#3503	1	1	yes	characteristic, complemented
728	C₂	—	2	2	no	—
729	C₂	—	6	4	no	—
730	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic
731	C₂	C₂×C₃×#1009	1	1	yes	characteristic
732	C₂	C₂×C₃×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#533	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂×C₃×#235	C₂²
hypercenter	C₃×#533	D₃
hypocenter	C₃	C₃×#3503
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#533

Complements

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

N	H ≅ G/N	type
1. C₃²×#533	C₂	semidirect
2. C₃×#5728	C₂	semidirect
3. C₃×D₃×C₄⋊Q₈	C₂	semidirect
4. C₃×#5689	C₂	semidirect
5. C₃×#5635	C₂	semidirect
6. C₃×#5632	C₂	semidirect
7. C₃×#5579	C₂	semidirect
8. C₃×Q₈×D₁₂	C₂	semidirect
9. C₃×#5567	C₂	semidirect
10. C₃×Q₈×Dic₆	C₂	semidirect
12. C₃×#5519	C₂	semidirect
14. C₂×C₃×#869	C₂	semidirect
16. #86281	C₃	direct (N × H)
75. C₃×#533	D₃	semidirect
76. C₃×#533	C₂×C₃	semidirect
81. #5728	C₂×C₃	semidirect
82. D₃×C₄⋊Q₈	C₂×C₃	semidirect
83. #5689	C₂×C₃	semidirect
84. #5635	C₂×C₃	semidirect
85. #5632	C₂×C₃	semidirect
86. #5579	C₂×C₃	semidirect
87. Q₈×D₁₂	C₂×C₃	semidirect
88. #5567	C₂×C₃	semidirect
89. Q₈×Dic₆	C₂×C₃	semidirect
91. #5519	C₂×C₃	semidirect
93. C₂×#869	C₂×C₃	semidirect
102. C₃×#235	Q₈	semidirect
257. C₂×C₃²×C₄	C₂×Q₈	semidirect
266. C₃×#67	C₂×Q₈	semidirect
272. C₃×D₁₂	C₂×Q₈	semidirect
276. C₃×C₄×D₃	C₂×Q₈	semidirect
280. C₃×Dic₆	C₂×Q₈	semidirect
290. #533	C₃×D₃	semidirect
327. #235	C₃×Q₈	semidirect
522. C₂×C₃×C₄	D₃×Q₈	semidirect
523. C₂×C₃×C₄	C₂×C₃×Q₈	semidirect
540. #67	C₂×C₃×Q₈	semidirect
546. D₁₂	C₂×C₃×Q₈	semidirect
550. C₄×D₃	C₂×C₃×Q₈	semidirect
554. Dic₆	C₂×C₃×Q₈	semidirect
661. C₃²	#3503	semidirect
683. C₂×C₄	C₃×D₃×Q₈	semidirect
726. C₃	#86281	direct (N × H)
727. C₃	C₃×#3503	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#533	2
C₃×#5728	2
C₃×D₃×C₄⋊Q₈	2
C₃×#5689	2
C₃×#5635	2
C₃×#5632	2
C₃×#5579	2
C₃×Q₈×D₁₂	2
C₃×#5567	2
C₃×Q₈×Dic₆	2
C₃×#5523	2
C₃×#5519	2
C₃×C₄×#235	2
C₂×C₃×#869	2
C₃×#3503	3
#86281	3

Subgroups — C3×#86281 #11906315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86281 #11906315