Subgroups — C₃×#86280 #11906172

Order 1152.

2311 conjugacy classes of subgroups.

The subgroup lattice has 710 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×#5730	C₂	1	2	yes	maximal, complemented
3	C₃×#5727	C₂	1	2	yes	maximal, complemented
4	C₃×#5690	C₂	1	4	yes	maximal, complemented
5	C₃×#5634	C₂	1	4	yes	maximal, complemented
6	C₃×D₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
7	C₃×#5579	C₂	1	4	yes	maximal, complemented
8	C₃×#5579	C₂	1	2	yes	maximal, complemented
9	C₃×Q₈×D₁₂	C₂	1	2	yes	maximal, complemented
10	C₃×#5521	C₂	1	2	yes	maximal
11	C₃×#5519	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
13	C₃×#5470	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3501	—	3	1	no	maximal
15	#86280	C₃	1	1	yes	maximal, characteristic, direct product factor
16	C₂×C₃×D₃×Q₈	C₂²	1	4	yes	complemented
17	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
19	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₃²×#125	C₂²	1	2	yes	complemented
22	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
25	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
26	C₃²×#117	C₂²	1	2	yes	—
27	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
28	C₃×#946	C₂²	1	4	yes	complemented
29	C₃×#946	C₂²	1	8	yes	complemented
30	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₃×#926	C₂²	1	2	yes	—
32	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₃×#924	C₂²	1	2	yes	—
34	C₃×#924	C₂²	1	2	yes	—
35	C₃×#897	C₂²	1	4	yes	complemented
36	C₃×#897	C₂²	1	8	yes	complemented
37	C₃×#896	C₂²	1	8	yes	complemented
38	C₃×#896	C₂²	1	8	yes	complemented
39	C₃×#896	C₂²	1	8	yes	complemented
40	C₃×#893	C₂²	1	4	yes	—
41	C₃×#893	C₂²	1	4	yes	—
42	C₃×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
43	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	complemented
44	C₃×#890	C₂²	1	4	yes	complemented
45	C₃×#888	C₂²	1	4	yes	complemented
46	C₃×D₃×C₂²⋊C₄	C₂²	1	8	yes	—
47	C₃×#878	C₂²	1	8	yes	—
48	C₃×C₄×D₁₂	C₂²	1	4	yes	—
49	C₃×C₄×D₁₂	C₂²	1	4	yes	—
50	C₃×C₄×D₁₂	C₂²	1	2	yes	—
51	C₃×C₄×D₁₂	C₂²	1	2	yes	—
52	C₃×C₄×D₁₂	C₂²	1	2	yes	—
53	C₃×C₄×D₁₂	C₂²	1	2	yes	—
54	C₃×#870	C₂²	1	4	yes	complemented
55	C₃×#870	C₂²	1	2	yes	complemented
56	C₃×#869	C₂²	1	4	yes	complemented
57	C₃×#869	C₂²	1	1	yes	characteristic, complemented
58	C₃×#869	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
60	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
61	C₃×#554	—	3	2	no	—
62	C₃×#554	—	3	4	no	—
63	C₃×#554	—	3	2	no	—
64	C₃×#554	—	3	4	no	—
65	C₃×D₄×Q₈	—	3	2	no	—
66	C₃×D₄×Q₈	—	3	2	no	—
67	C₃×#544	—	3	2	no	—
68	C₃×#543	—	3	4	no	—
69	C₃×#533	—	2	1	no	—
70	C₃×#533	—	3	1	no	—
71	C₃×#533	D₃	1	1	yes	characteristic, complemented
72	C₃×#533	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×C₃×C₂²⋊Q₈	—	3	4	no	—
74	C₃×#518	—	3	2	no	—
75	C₂×C₃×C₄×D₄	—	3	1	no	—
76	#5730	C₂×C₃	1	2	yes	complemented
77	#5727	C₂×C₃	1	2	yes	complemented
78	#5690	C₂×C₃	1	4	yes	complemented
79	#5634	C₂×C₃	1	4	yes	complemented
80	D₃×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
81	#5579	C₂×C₃	1	2	yes	complemented
82	#5579	C₂×C₃	1	4	yes	complemented
83	Q₈×D₁₂	C₂×C₃	1	2	yes	complemented
84	#5521	C₂×C₃	1	2	yes	—
85	#5519	C₂×C₃	1	2	yes	complemented
86	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
87	#5470	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂³×C₃×D₃	C₂³	1	2	yes	—
89	C₂×C₃²×Q₈	C₂³	1	2	yes	—
90	C₂×C₃²×Q₈	C₂³	1	2	yes	—
91	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
92	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
93	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
94	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
95	C₃×D₃×Q₈	—	4	8	no	—
96	C₂×C₃×D₁₂	Q₈	1	8	yes	complemented
97	C₂×C₃×D₁₂	C₂³	1	2	yes	—
98	C₂×C₃×D₁₂	C₂³	1	2	yes	—
99	C₂×C₃×C₄×D₃	—	4	4	no	—
100	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
101	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
102	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
103	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
104	C₂×C₃×Dic₆	C₂³	1	2	yes	—
105	C₂×C₃×Dic₆	C₂³	1	8	yes	—
106	C₂×C₃×Dic₆	C₂³	1	2	yes	—
107	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
108	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
109	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
110	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
111	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
112	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
113	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₃²×C₄²	C₂³	1	1	yes	characteristic
115	C₃²×C₄²	C₂³	1	1	yes	characteristic
116	C₃²×C₄²	C₂³	1	1	yes	characteristic
117	C₃²×C₄²	C₂³	1	1	yes	characteristic
118	C₃²×C₄²	C₂³	1	4	yes	—
119	C₃×#217	C₂³	1	4	yes	—
120	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
121	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
122	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
123	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
124	C₃×C₄⋊Dic₃	C₂³	1	8	yes	—
125	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
126	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
127	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
128	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
129	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
130	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
131	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
132	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
133	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
134	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
135	C₃×C₄×Dic₃	C₂³	1	4	yes	—
136	#3501	—	3	1	no	Sylow
137	C₂²×C₃×Q₈	—	3	4	no	—
138	C₂²×C₃×D₄	—	3	1	no	—
139	C₂³×C₃×C₄	—	3	2	no	—
140	C₂×D₃×Q₈	C₂²×C₃	1	4	yes	complemented
141	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
142	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
143	C₃×C₄⋊Q₈	—	2	1	no	—
144	C₃×C₄⋊Q₈	—	2	1	no	—
145	C₃×C₄⋊Q₈	—	3	4	no	—
146	C₃×C₄⋊Q₈	—	3	1	no	—
147	C₃×C₄⋊Q₈	—	3	1	no	—
148	C₃×C₄⋊Q₈	—	3	4	no	—
149	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
150	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
151	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₃×#125	—	2	2	no	—
154	C₃×#125	—	3	4	no	—
155	C₃×#125	—	3	2	no	—
156	C₃×#125	—	3	4	no	—
157	C₃×#125	C₂×D₃	1	2	yes	complemented
158	C₃×#125	C₂²×C₃	1	2	yes	complemented
159	C₃×C₂²⋊Q₈	—	2	2	no	—
160	C₃×C₂²⋊Q₈	—	2	2	no	—
161	C₃×C₂²⋊Q₈	—	3	4	no	—
162	C₃×C₂²⋊Q₈	—	3	8	no	—
163	C₃×C₂²⋊Q₈	—	3	2	no	—
164	C₃×C₂²⋊Q₈	—	3	2	no	—
165	C₃×C₂²⋊Q₈	—	3	8	no	—
166	C₃×C₂²⋊Q₈	—	3	8	no	—
167	C₃×C₂²⋊Q₈	—	3	8	no	—
168	C₃×C₂²⋊Q₈	—	3	4	no	—
169	C₃×C₂²⋊Q₈	—	3	8	no	—
170	C₃×C₂²⋊Q₈	—	3	8	no	—
171	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
172	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
173	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
174	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
175	C₃×C₄×Q₈	—	2	2	no	—
176	C₃×C₄×Q₈	—	2	2	no	—
177	C₃×C₄×Q₈	—	3	2	no	—
178	C₃×C₄×Q₈	—	3	2	no	—
179	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
180	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
181	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
182	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
183	C₃×C₄×D₄	—	3	4	no	—
184	C₃×C₄×D₄	—	3	4	no	—
185	C₃×C₄×D₄	—	3	2	no	—
186	C₃×C₄×D₄	—	3	2	no	—
187	C₃×C₄×D₄	—	3	2	no	—
188	C₃×C₄×D₄	—	3	2	no	—
189	C₃×C₄×D₄	—	3	4	no	—
190	C₃×C₄×D₄	—	3	4	no	—
191	C₃×#117	—	2	2	no	—
192	C₃×#117	—	3	2	no	—
193	C₃×#117	C₂×D₃	1	2	yes	—
194	C₃×#117	C₂²×C₃	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	—	3	1	no	—
196	C₂×C₃×C₄⋊C₄	—	3	8	no	—
197	C₂×C₃×C₄⋊C₄	—	3	4	no	—
198	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
199	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
200	C₂×C₃×C₄²	—	2	1	no	—
201	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
202	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
203	#946	C₂²×C₃	1	8	yes	complemented
204	#946	C₂²×C₃	1	4	yes	complemented
205	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
206	#926	C₂²×C₃	1	2	yes	—
207	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
208	#924	C₂²×C₃	1	2	yes	—
209	#924	C₂²×C₃	1	2	yes	—
210	#897	C₂²×C₃	1	8	yes	complemented
211	#897	C₂²×C₃	1	4	yes	complemented
212	#896	C₂²×C₃	1	8	yes	complemented
213	#896	C₂²×C₃	1	8	yes	complemented
214	#896	C₂²×C₃	1	8	yes	complemented
215	#893	C₂²×C₃	1	4	yes	—
216	#893	C₂²×C₃	1	4	yes	—
217	D₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
218	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
219	#890	C₂²×C₃	1	4	yes	complemented
220	#888	C₂²×C₃	1	4	yes	complemented
221	D₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
222	#878	C₂²×C₃	1	8	yes	—
223	C₄×D₁₂	C₂²×C₃	1	2	yes	—
224	C₄×D₁₂	C₂²×C₃	1	2	yes	—
225	C₄×D₁₂	C₂²×C₃	1	2	yes	—
226	C₄×D₁₂	C₂²×C₃	1	2	yes	—
227	C₄×D₁₂	C₂²×C₃	1	4	yes	—
228	C₄×D₁₂	C₂²×C₃	1	4	yes	—
229	#870	C₂²×C₃	1	2	yes	complemented
230	#870	C₂²×C₃	1	4	yes	complemented
231	#869	C₂²×C₃	1	1	yes	characteristic, complemented
232	#869	C₂²×C₃	1	1	yes	characteristic, complemented
233	#869	C₂²×C₃	1	4	yes	complemented
234	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
235	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
236	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
237	C₂²×C₃×D₃	—	4	2	no	—
238	C₂²×C₃×D₃	—	4	2	no	—
239	C₂²×C₃×D₃	C₂×Q₈	1	8	yes	complemented
240	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
241	C₃²×Q₈	—	2	4	no	—
242	C₃²×Q₈	—	4	2	no	—
243	C₂×C₃²×C₄	—	2	2	no	—
244	C₂×C₃²×C₄	—	4	1	no	—
245	C₂×C₃²×C₄	C₂×Q₈	1	4	yes	complemented
246	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
247	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
248	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
249	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
250	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
251	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
252	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
253	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
254	C₂×C₃×Dic₃	—	4	2	no	—
255	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
256	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
257	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
258	C₃×D₁₂	C₂×Q₈	1	8	yes	complemented
259	C₃×D₁₂	C₂×Q₈	1	8	yes	complemented
260	C₃×C₄×D₃	—	2	8	no	—
261	C₃×C₄×D₃	—	4	4	no	—
262	C₃×C₄×D₃	—	4	8	no	—
263	C₃×C₄×D₃	—	4	8	no	—
264	C₃×Dic₆	—	2	4	no	—
265	C₃×Dic₆	—	4	2	no	—
266	C₃×Dic₆	—	4	8	no	—
267	#554	—	3	2	no	—
268	#554	—	3	4	no	—
269	#554	—	3	2	no	—
270	#554	—	3	4	no	—
271	D₄×Q₈	—	3	2	no	—
272	D₄×Q₈	—	3	2	no	—
273	#544	—	3	2	no	—
274	#543	—	3	4	no	—
275	#533	—	3	1	no	—
276	#533	C₃×D₃	1	1	yes	characteristic, complemented
277	C₂×C₂²⋊Q₈	—	3	4	no	—
278	#518	—	3	2	no	—
279	C₂×C₄×D₄	—	3	1	no	—
280	C₂⁴×C₃	—	3	2	no	—
281	C₂³×D₃	C₂³×C₃	1	2	yes	—
282	C₂×C₃×Q₈	—	2	2	no	—
283	C₂×C₃×Q₈	—	2	2	no	—
284	C₂×C₃×Q₈	—	3	2	no	—
285	C₂×C₃×Q₈	—	3	2	no	—
286	C₂×C₃×Q₈	—	3	8	no	—
287	C₂×C₃×Q₈	—	12	8	no	—
288	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
289	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
290	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
291	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
292	C₂×C₃×D₄	—	3	8	no	—
293	C₂×C₃×D₄	—	3	2	no	—
294	C₂×C₃×D₄	—	3	2	no	—
295	C₂²×C₃×C₄	—	2	1	no	—
296	C₂²×C₃×C₄	—	2	1	no	—
297	C₂²×C₃×C₄	—	2	1	no	—
298	C₂²×C₃×C₄	—	3	2	no	—
299	C₂²×C₃×C₄	—	3	4	no	—
300	C₂²×C₃×C₄	—	3	8	no	—
301	C₂²×C₃×C₄	—	3	8	no	—
302	C₂²×C₃×C₄	—	3	4	no	—
303	C₂²×C₃×C₄	—	12	4	no	—
304	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
306	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
307	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
308	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
309	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
310	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
311	D₃×Q₈	—	4	8	no	—
312	C₂×D₁₂	C₃×Q₈	1	8	yes	complemented
313	C₂×D₁₂	C₂³×C₃	1	2	yes	—
314	C₂×D₁₂	C₂³×C₃	1	2	yes	—
315	C₂×C₄×D₃	—	4	4	no	—
316	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
317	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
318	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
319	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
320	C₂×Dic₆	C₂³×C₃	1	2	yes	—
321	C₂×Dic₆	C₂³×C₃	1	2	yes	—
322	C₂×Dic₆	C₂³×C₃	1	8	yes	—
323	C₃×C₄⋊C₄	—	2	2	no	—
324	C₃×C₄⋊C₄	—	2	2	no	—
325	C₃×C₄⋊C₄	—	2	4	no	—
326	C₃×C₄⋊C₄	—	2	4	no	—
327	C₃×C₄⋊C₄	—	2	2	no	—
328	C₃×C₄⋊C₄	—	2	2	no	—
329	C₃×C₄⋊C₄	—	3	4	no	—
330	C₃×C₄⋊C₄	—	3	8	no	—
331	C₃×C₄⋊C₄	—	3	8	no	—
332	C₃×C₄⋊C₄	—	3	4	no	—
333	C₃×C₄⋊C₄	—	3	2	no	—
334	C₃×C₄⋊C₄	—	3	2	no	—
335	C₃×C₄⋊C₄	—	3	2	no	—
336	C₃×C₄⋊C₄	—	3	8	no	—
337	C₃×C₄⋊C₄	—	3	2	no	—
338	C₃×C₄⋊C₄	—	3	2	no	—
339	C₃×C₄⋊C₄	—	3	2	no	—
340	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
341	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
342	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
343	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
344	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
345	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
346	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
347	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
348	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
349	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
350	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
351	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	3	4	no	—
354	C₃×C₂²⋊C₄	—	3	8	no	—
355	C₃×C₂²⋊C₄	—	3	8	no	—
356	C₃×C₂²⋊C₄	—	3	4	no	—
357	C₃×C₂²⋊C₄	—	3	4	no	—
358	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
359	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
360	C₃×C₄²	—	2	1	no	—
361	C₃×C₄²	—	2	1	no	—
362	C₃×C₄²	—	2	1	no	—
363	C₃×C₄²	—	2	1	no	—
364	C₃×C₄²	—	2	4	no	—
365	C₃×C₄²	—	3	4	no	—
366	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
367	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
368	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
369	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
370	C₃×C₄²	C₂²×D₃	1	4	yes	—
371	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
372	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
373	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
374	C₃×C₄²	C₂³×C₃	1	4	yes	—
375	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
376	#217	C₂³×C₃	1	4	yes	—
377	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
378	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
379	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
380	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
381	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
382	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
383	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
384	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
385	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
386	C₄⋊Dic₃	C₂³×C₃	1	8	yes	—
387	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
388	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
389	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
390	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
391	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
392	C₄×Dic₃	C₂³×C₃	1	4	yes	—
393	C₂²×C₃²	—	2	1	no	—
394	C₂²×C₃²	—	2	1	no	—
395	C₂²×C₃²	C₂²×Q₈	1	2	yes	—
396	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
397	C₂×C₃×D₃	—	2	4	no	—
398	C₂×C₃×D₃	—	2	4	no	—
399	C₂×C₃×D₃	—	4	8	no	—
400	C₂×C₃×D₃	C₂²×Q₈	1	8	yes	—
401	C₃²×C₄	—	2	1	no	—
402	C₃²×C₄	—	2	4	no	—
403	C₃²×C₄	—	2	1	no	—
404	C₃²×C₄	—	2	1	no	—
405	C₃²×C₄	—	2	4	no	—
406	C₃²×C₄	C₂²×Q₈	1	2	yes	—
407	C₃²×C₄	C₂²×Q₈	1	2	yes	—
408	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
409	C₃×Dic₃	—	2	4	no	—
410	C₃×Dic₃	—	2	4	no	—
411	C₃×Dic₃	—	2	4	no	—
412	C₂²×Q₈	—	3	4	no	—
413	C₂²×D₄	—	3	1	no	—
414	C₂³×C₄	—	3	2	no	—
415	C₄⋊Q₈	—	3	4	no	—
416	C₄⋊Q₈	—	3	1	no	—
417	C₄⋊Q₈	—	3	1	no	—
418	C₄⋊Q₈	—	3	4	no	—
419	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
420	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
421	#125	—	3	4	no	—
422	#125	—	3	2	no	—
423	#125	—	3	4	no	—
424	#125	C₂×C₃×D₃	1	2	yes	complemented
425	C₂²⋊Q₈	—	3	4	no	—
426	C₂²⋊Q₈	—	3	8	no	—
427	C₂²⋊Q₈	—	3	2	no	—
428	C₂²⋊Q₈	—	3	2	no	—
429	C₂²⋊Q₈	—	3	4	no	—
430	C₂²⋊Q₈	—	3	8	no	—
431	C₂²⋊Q₈	—	3	8	no	—
432	C₂²⋊Q₈	—	3	8	no	—
433	C₂²⋊Q₈	—	3	8	no	—
434	C₂²⋊Q₈	—	3	8	no	—
435	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
436	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
437	C₄×Q₈	—	3	2	no	—
438	C₄×Q₈	—	3	2	no	—
439	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
440	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
441	C₄×D₄	—	3	4	no	—
442	C₄×D₄	—	3	4	no	—
443	C₄×D₄	—	3	2	no	—
444	C₄×D₄	—	3	2	no	—
445	C₄×D₄	—	3	2	no	—
446	C₄×D₄	—	3	2	no	—
447	C₄×D₄	—	3	4	no	—
448	C₄×D₄	—	3	4	no	—
449	#117	—	3	2	no	—
450	#117	C₂×C₃×D₃	1	2	yes	—
451	C₂×C₄⋊C₄	—	3	1	no	—
452	C₂×C₄⋊C₄	—	3	8	no	—
453	C₂×C₄⋊C₄	—	3	4	no	—
454	C₂×C₂²⋊C₄	—	3	2	no	—
455	C₂×C₂²⋊C₄	—	3	8	no	—
456	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
457	C₂³×C₃	—	2	1	no	—
458	C₂³×C₃	—	3	4	no	—
459	C₂³×C₃	—	3	8	no	—
460	C₂³×C₃	—	12	2	no	—
461	C₂³×C₃	—	12	2	no	—
462	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
463	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
464	C₂²×D₃	—	4	2	no	—
465	C₂²×D₃	—	4	2	no	—
466	C₂²×D₃	C₂×C₃×Q₈	1	8	yes	complemented
467	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
468	C₃×Q₈	—	2	4	no	—
469	C₃×Q₈	—	2	4	no	—
470	C₃×Q₈	—	4	4	no	—
471	C₃×Q₈	—	4	2	no	—
472	C₃×Q₈	—	4	2	no	—
473	C₃×Q₈	—	4	4	no	—
474	C₃×Q₈	—	6	4	no	—
475	C₃×Q₈	—	12	2	no	—
476	C₃×Q₈	—	12	8	no	—
477	C₃×D₄	—	3	8	no	—
478	C₃×D₄	—	3	8	no	—
479	C₂×C₃×C₄	—	2	2	no	—
480	C₂×C₃×C₄	—	2	2	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	4	no	—
488	C₂×C₃×C₄	—	2	4	no	—
489	C₂×C₃×C₄	—	2	4	no	—
490	C₂×C₃×C₄	—	3	4	no	—
491	C₂×C₃×C₄	—	3	4	no	—
492	C₂×C₃×C₄	—	3	4	no	—
493	C₂×C₃×C₄	—	4	2	no	—
494	C₂×C₃×C₄	—	4	1	no	—
495	C₂×C₃×C₄	—	4	1	no	—
496	C₂×C₃×C₄	—	4	2	no	—
497	C₂×C₃×C₄	—	6	8	no	—
498	C₂×C₃×C₄	—	12	8	no	—
499	C₂×C₃×C₄	—	12	4	no	—
500	C₂×C₃×C₄	—	12	8	no	—
501	C₂×C₃×C₄	—	12	2	no	—
502	C₂×C₃×C₄	D₃×Q₈	1	4	yes	complemented
503	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	complemented
504	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
507	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
508	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
509	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
510	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
511	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
512	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
513	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
514	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
515	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
516	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
517	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
518	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
519	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
520	C₂×Dic₃	—	4	2	no	—
521	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
522	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
523	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
524	D₁₂	C₂×C₃×Q₈	1	8	yes	complemented
525	D₁₂	C₂×C₃×Q₈	1	8	yes	complemented
526	C₄×D₃	—	2	8	no	—
527	C₄×D₃	—	4	4	no	—
528	C₄×D₃	—	4	8	no	—
529	C₄×D₃	—	4	8	no	—
530	Dic₆	—	2	4	no	—
531	Dic₆	—	4	2	no	—
532	Dic₆	—	4	8	no	—
533	C₂×C₃²	—	2	2	no	—
534	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
535	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
536	C₂×C₃²	#585	1	1	yes	characteristic
537	C₃×D₃	—	2	8	no	—
538	C₂⁴	—	3	2	no	—
539	C₂×Q₈	—	3	2	no	—
540	C₂×Q₈	—	3	2	no	—
541	C₂×Q₈	—	3	8	no	—
542	C₂×Q₈	—	12	8	no	—
543	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
544	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
545	C₂×D₄	—	3	2	no	—
546	C₂×D₄	—	3	2	no	—
547	C₂×D₄	—	3	8	no	—
548	C₂²×C₄	—	3	2	no	—
549	C₂²×C₄	—	3	4	no	—
550	C₂²×C₄	—	3	8	no	—
551	C₂²×C₄	—	3	8	no	—
552	C₂²×C₄	—	3	4	no	—
553	C₂²×C₄	—	12	4	no	—
554	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
555	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
556	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
557	C₄⋊C₄	—	3	4	no	—
558	C₄⋊C₄	—	3	2	no	—
559	C₄⋊C₄	—	3	2	no	—
560	C₄⋊C₄	—	3	2	no	—
561	C₄⋊C₄	—	3	8	no	—
562	C₄⋊C₄	—	3	8	no	—
563	C₄⋊C₄	—	3	8	no	—
564	C₄⋊C₄	—	3	2	no	—
565	C₄⋊C₄	—	3	2	no	—
566	C₄⋊C₄	—	3	4	no	—
567	C₄⋊C₄	—	3	2	no	—
568	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
569	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
570	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
571	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
572	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
573	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
574	C₂²⋊C₄	—	3	4	no	—
575	C₂²⋊C₄	—	3	8	no	—
576	C₂²⋊C₄	—	3	8	no	—
577	C₂²⋊C₄	—	3	4	no	—
578	C₂²⋊C₄	—	3	4	no	—
579	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
580	C₄²	—	3	4	no	—
581	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
582	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
583	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
584	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
585	C₄²	C₂²×C₃×D₃	1	4	yes	—
586	C₂²×C₃	—	2	1	no	—
587	C₂²×C₃	—	2	1	no	—
588	C₂²×C₃	—	2	1	no	—
589	C₂²×C₃	—	2	1	no	—
590	C₂²×C₃	—	2	2	no	—
591	C₂²×C₃	—	2	1	no	—
592	C₂²×C₃	—	3	8	no	—
593	C₂²×C₃	—	4	1	no	—
594	C₂²×C₃	—	4	1	no	—
595	C₂²×C₃	—	6	4	no	—
596	C₂²×C₃	—	6	4	no	—
597	C₂²×C₃	—	12	8	no	—
598	C₂²×C₃	C₂×D₃×Q₈	1	2	yes	—
599	C₂²×C₃	C₂²×C₃×Q₈	1	2	yes	—
600	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
601	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
602	C₂×D₃	—	2	4	no	—
603	C₂×D₃	—	2	4	no	—
604	C₂×D₃	—	4	8	no	—
605	C₂×D₃	C₂²×C₃×Q₈	1	8	yes	—
606	C₃×C₄	—	2	2	no	—
607	C₃×C₄	—	2	1	no	—
608	C₃×C₄	—	2	4	no	—
609	C₃×C₄	—	2	1	no	—
610	C₃×C₄	—	2	1	no	—
611	C₃×C₄	—	2	4	no	—
612	C₃×C₄	—	2	4	no	—
613	C₃×C₄	—	2	1	no	—
614	C₃×C₄	—	2	1	no	—
615	C₃×C₄	—	2	4	no	—
616	C₃×C₄	—	2	1	no	—
617	C₃×C₄	—	2	2	no	—
618	C₃×C₄	—	2	2	no	—
619	C₃×C₄	—	2	2	no	—
620	C₃×C₄	—	4	1	no	—
621	C₃×C₄	—	4	1	no	—
622	C₃×C₄	—	4	4	no	—
623	C₃×C₄	—	4	4	no	—
624	C₃×C₄	—	6	4	no	—
625	C₃×C₄	—	6	4	no	—
626	C₃×C₄	—	6	4	no	—
627	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
628	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
629	C₃×C₄	#1009	1	2	yes	—
630	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
631	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
632	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
633	Dic₃	—	2	4	no	—
634	Dic₃	—	2	4	no	—
635	Dic₃	—	2	4	no	—
636	C₃²	#3501	1	1	yes	characteristic, complemented, Sylow
637	C₂³	—	3	4	no	—
638	C₂³	—	3	8	no	—
639	C₂³	—	12	2	no	—
640	C₂³	—	12	2	no	—
641	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
642	Q₈	—	2	4	no	—
643	Q₈	—	4	2	no	—
644	Q₈	—	6	4	no	—
645	Q₈	—	12	8	no	—
646	Q₈	—	12	2	no	—
647	D₄	—	3	8	no	—
648	D₄	—	3	8	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	3	4	no	—
651	C₂×C₄	—	3	4	no	—
652	C₂×C₄	—	3	4	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	6	8	no	—
655	C₂×C₄	—	12	4	no	—
656	C₂×C₄	—	12	8	no	—
657	C₂×C₄	—	12	8	no	—
658	C₂×C₄	—	12	2	no	—
659	C₂×C₄	C₃×D₃×Q₈	1	4	yes	complemented
660	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
661	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
662	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
663	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
664	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
665	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
666	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
667	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
668	C₂×C₃	—	2	2	no	—
669	C₂×C₃	—	2	2	no	—
670	C₂×C₃	—	2	1	no	—
671	C₂×C₃	—	2	1	no	—
672	C₂×C₃	—	2	1	no	—
673	C₂×C₃	—	4	2	no	—
674	C₂×C₃	—	6	8	no	—
675	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
676	C₂×C₃	C₂×#1009	1	1	yes	characteristic
677	C₂×C₃	#5964	1	1	yes	characteristic
678	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
679	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂×C₃	C₃×#585	1	1	yes	characteristic
681	D₃	—	2	8	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	3	8	no	—
685	C₂²	—	6	4	no	—
686	C₂²	—	6	4	no	—
687	C₂²	—	12	8	no	—
688	C₂²	C₂×C₃×D₃×Q₈	1	2	yes	—
689	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
690	C₄	—	2	1	no	—
691	C₄	—	2	4	no	—
692	C₄	—	2	1	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	4	no	—
695	C₄	—	6	4	no	—
696	C₄	—	6	4	no	—
697	C₄	—	6	4	no	—
698	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
699	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
700	C₄	C₃×#1009	1	2	yes	—
701	C₃	—	2	1	no	—
702	C₃	#86280	1	1	yes	characteristic, direct product factor
703	C₃	C₃×#3501	1	1	yes	characteristic, complemented
704	C₂	—	2	2	no	—
705	C₂	—	6	8	no	—
706	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic
707	C₂	C₂×C₃×#1009	1	1	yes	characteristic
708	C₂	C₃×#5964	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	C₂²×C₃×D₁₂	C₂²
hypercenter	C₃×#533	D₃
hypocenter	C₃	C₃×#3501
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×#5730	C₂	semidirect
3. C₃×#5727	C₂	semidirect
4. C₃×#5690	C₂	semidirect
5. C₃×#5634	C₂	semidirect
6. C₃×D₃×C₂²⋊Q₈	C₂	semidirect
7. C₃×#5579	C₂	semidirect
8. C₃×#5579	C₂	semidirect
9. C₃×Q₈×D₁₂	C₂	semidirect
11. C₃×#5519	C₂	semidirect
13. C₃×#5470	C₂	semidirect
15. #86280	C₃	direct (N × H)
16. C₂×C₃×D₃×Q₈	C₂²	semidirect
19. C₃²×C₄⋊Q₈	C₂²	semidirect
20. C₃²×C₄⋊Q₈	C₂²	semidirect
21. C₃²×#125	C₂²	semidirect
24. C₃²×C₄×Q₈	C₂²	semidirect
25. C₃²×C₄×Q₈	C₂²	semidirect
28. C₃×#946	C₂²	semidirect
29. C₃×#946	C₂²	semidirect
35. C₃×#897	C₂²	semidirect
36. C₃×#897	C₂²	semidirect
37. C₃×#896	C₂²	semidirect
38. C₃×#896	C₂²	semidirect
39. C₃×#896	C₂²	semidirect
42. C₃×D₃×C₄⋊C₄	C₂²	semidirect
43. C₃×D₃×C₄⋊C₄	C₂²	semidirect
44. C₃×#890	C₂²	semidirect
45. C₃×#888	C₂²	semidirect
54. C₃×#870	C₂²	semidirect
55. C₃×#870	C₂²	semidirect
56. C₃×#869	C₂²	semidirect
57. C₃×#869	C₂²	semidirect
58. C₃×#869	C₂²	semidirect
59. C₃×C₄×Dic₆	C₂²	semidirect
60. C₃×C₄×Dic₆	C₂²	semidirect
71. C₃×#533	D₃	semidirect
72. C₃×#533	C₂×C₃	semidirect
76. #5730	C₂×C₃	semidirect
77. #5727	C₂×C₃	semidirect
78. #5690	C₂×C₃	semidirect
79. #5634	C₂×C₃	semidirect
80. D₃×C₂²⋊Q₈	C₂×C₃	semidirect
81. #5579	C₂×C₃	semidirect
82. #5579	C₂×C₃	semidirect
83. Q₈×D₁₂	C₂×C₃	semidirect
85. #5519	C₂×C₃	semidirect
87. #5470	C₂×C₃	semidirect
96. C₂×C₃×D₁₂	Q₈	semidirect
140. C₂×D₃×Q₈	C₂²×C₃	semidirect
149. C₃×C₄⋊Q₈	C₂×D₃	semidirect
150. C₃×C₄⋊Q₈	C₂×D₃	semidirect
151. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
152. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
157. C₃×#125	C₂×D₃	semidirect
158. C₃×#125	C₂²×C₃	semidirect
179. C₃×C₄×Q₈	C₂×D₃	semidirect
180. C₃×C₄×Q₈	C₂×D₃	semidirect
181. C₃×C₄×Q₈	C₂²×C₃	semidirect
182. C₃×C₄×Q₈	C₂²×C₃	semidirect
203. #946	C₂²×C₃	semidirect
204. #946	C₂²×C₃	semidirect
210. #897	C₂²×C₃	semidirect
211. #897	C₂²×C₃	semidirect
212. #896	C₂²×C₃	semidirect
213. #896	C₂²×C₃	semidirect
214. #896	C₂²×C₃	semidirect
217. D₃×C₄⋊C₄	C₂²×C₃	semidirect
218. D₃×C₄⋊C₄	C₂²×C₃	semidirect
219. #890	C₂²×C₃	semidirect
220. #888	C₂²×C₃	semidirect
229. #870	C₂²×C₃	semidirect
230. #870	C₂²×C₃	semidirect
231. #869	C₂²×C₃	semidirect
232. #869	C₂²×C₃	semidirect
233. #869	C₂²×C₃	semidirect
234. C₄×Dic₆	C₂²×C₃	semidirect
235. C₄×Dic₆	C₂²×C₃	semidirect
239. C₂²×C₃×D₃	C₂×Q₈	semidirect
245. C₂×C₃²×C₄	C₂×Q₈	semidirect
258. C₃×D₁₂	C₂×Q₈	semidirect
259. C₃×D₁₂	C₂×Q₈	semidirect
276. #533	C₃×D₃	semidirect
312. C₂×D₁₂	C₃×Q₈	semidirect
419. C₄⋊Q₈	C₂×C₃×D₃	semidirect
420. C₄⋊Q₈	C₂×C₃×D₃	semidirect
424. #125	C₂×C₃×D₃	semidirect
439. C₄×Q₈	C₂×C₃×D₃	semidirect
440. C₄×Q₈	C₂×C₃×D₃	semidirect
466. C₂²×D₃	C₂×C₃×Q₈	semidirect
502. C₂×C₃×C₄	D₃×Q₈	semidirect
503. C₂×C₃×C₄	C₂×C₃×Q₈	semidirect
524. D₁₂	C₂×C₃×Q₈	semidirect
525. D₁₂	C₂×C₃×Q₈	semidirect
636. C₃²	#3501	semidirect
659. C₂×C₄	C₃×D₃×Q₈	semidirect
702. C₃	#86280	direct (N × H)
703. C₃	C₃×#3501	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×#5730	2
C₃×#5727	2
C₃×#5690	2
C₃×#5634	2
C₃×D₃×C₂²⋊Q₈	2
C₃×#5579	2
C₃×Q₈×D₁₂	2
C₃×#5521	2
C₃×#5519	2
C₂×C₃×C₄×D₁₂	2
C₃×#5470	2
C₃×#3501	3
#86280	3

Subgroups — C3×#86280 #11906172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86280 #11906172