Subgroups — C₃×#39367 #10657974

Order 768.

2560 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	C₂×C₃×#543	C₂	1	2	yes	maximal, complemented
2	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2732	C₂	1	2	yes	maximal, complemented
4	C₃×#2692	C₂	1	4	yes	maximal, complemented
5	C₃×#2683	C₂	1	2	yes	maximal, complemented
6	C₃×#2626	C₂	1	2	yes	maximal, complemented
7	C₃×#2542	C₂	1	2	yes	maximal, complemented
8	C₃×#2538	C₂	1	2	yes	maximal, complemented
9	C₃×#2452	C₂	1	2	yes	maximal, complemented
10	C₃×#2452	C₂	1	2	yes	maximal, complemented
11	C₃×#2440	C₂	1	2	yes	maximal, complemented
12	C₃×#2437	C₂	1	4	yes	maximal, complemented
13	C₃×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal
14	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#390	C₂	1	1	yes	maximal, characteristic
16	#39367	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
18	C₃×#543	—	2	16	no	—
19	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
29	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
31	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
32	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	—
35	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
37	C₃×#399	C₂²	1	4	yes	complemented
38	C₃×#399	C₂²	1	4	yes	complemented
39	C₃×#398	C₂²	1	4	yes	complemented
40	C₃×#396	C₂²	1	4	yes	complemented
41	C₃×#396	C₂²	1	4	yes	complemented
42	C₃×#396	C₂²	1	4	yes	complemented
43	C₃×#396	C₂²	1	4	yes	complemented
44	C₃×#395	C₂²	1	4	yes	complemented
45	C₃×#393	C₂²	1	4	yes	complemented
46	C₃×#393	C₂²	1	4	yes	complemented
47	C₃×#391	C₂²	1	2	yes	complemented
48	C₃×#391	C₂²	1	1	yes	characteristic, complemented
49	C₃×#390	C₂²	1	2	yes	—
50	C₃×#390	C₂²	1	2	yes	—
51	C₃×#390	C₂²	1	2	yes	—
52	C₃×#390	C₂²	1	2	yes	—
53	C₃×#390	C₂²	1	2	yes	—
54	C₃×#390	C₂²	1	2	yes	—
55	C₃×#389	C₂²	1	1	yes	characteristic, complemented
56	C₃×#389	C₂²	1	2	yes	complemented
57	C₃×#389	C₂²	1	2	yes	complemented
58	C₃×#389	C₂²	1	2	yes	complemented
59	C₃×#389	C₂²	1	2	yes	complemented
60	C₃×#387	C₂²	1	2	yes	complemented
61	C₃×#386	C₂²	1	4	yes	—
62	C₃×#386	C₂²	1	4	yes	—
63	C₃×#385	C₂²	1	4	yes	—
64	C₃×#385	C₂²	1	2	yes	—
65	C₃×#385	C₂²	1	4	yes	complemented
66	C₃×#385	C₂²	1	4	yes	complemented
67	C₃×#384	C₂²	1	2	yes	complemented
68	C₃×#384	C₂²	1	1	yes	characteristic, complemented
69	C₃×#380	C₂²	1	1	yes	characteristic
70	C₃×#380	C₂²	1	2	yes	—
71	C₃×#380	C₂²	1	2	yes	—
72	C₃×#380	C₂²	1	4	yes	complemented
73	C₃×#379	C₂²	1	4	yes	—
74	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
75	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
76	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
77	C₂×#543	C₂×C₃	1	2	yes	complemented
78	#2857	C₂×C₃	1	1	yes	characteristic, complemented
79	#2732	C₂×C₃	1	2	yes	complemented
80	#2692	C₂×C₃	1	4	yes	complemented
81	#2683	C₂×C₃	1	2	yes	complemented
82	#2626	C₂×C₃	1	2	yes	complemented
83	#2542	C₂×C₃	1	2	yes	complemented
84	#2538	C₂×C₃	1	2	yes	complemented
85	#2452	C₂×C₃	1	2	yes	complemented
86	#2452	C₂×C₃	1	2	yes	complemented
87	#2440	C₂×C₃	1	2	yes	complemented
88	#2437	C₂×C₃	1	4	yes	complemented
89	D₄×C₂²⋊C₄	C₂×C₃	1	2	yes	—
90	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×#390	C₂×C₃	1	1	yes	characteristic
92	C₂⁵×C₃	C₂³	1	2	yes	—
93	C₂²×C₃×Q₈	C₂³	1	2	yes	—
94	C₂²×C₃×Q₈	C₂³	1	4	yes	—
95	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
96	C₂²×C₃×D₄	—	4	2	no	—
97	C₂²×C₃×D₄	—	4	2	no	—
98	C₂²×C₃×D₄	Q₈	1	8	yes	complemented
99	C₂²×C₃×D₄	C₂³	1	2	yes	—
100	C₂²×C₃×D₄	C₂³	1	2	yes	—
101	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
102	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
103	C₂³×C₃×C₄	C₂³	1	4	yes	—
104	C₂³×C₃×C₄	C₂³	1	2	yes	—
105	C₂³×C₃×C₄	C₂³	1	4	yes	—
106	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
107	C₃×C₄⋊Q₈	—	4	2	no	—
108	C₃×C₄⋊Q₈	—	4	4	no	—
109	C₃×C₂²⋊Q₈	—	2	16	no	—
110	C₃×C₂²⋊Q₈	—	2	8	no	—
111	C₃×C₂²⋊Q₈	—	2	16	no	—
112	C₃×C₂²⋊Q₈	—	2	16	no	—
113	C₃×C₂²⋊Q₈	—	2	16	no	—
114	C₃×C₂²⋊Q₈	—	2	16	no	—
115	C₃×C₂²⋊Q₈	—	4	8	no	—
116	C₃×C₂²⋊Q₈	D₄	1	8	yes	complemented
117	C₃×C₄×Q₈	—	4	2	no	—
118	C₃×C₄×D₄	—	4	4	no	—
119	C₃×C₄×D₄	—	4	4	no	—
120	C₂×C₃×C₄⋊C₄	—	4	2	no	—
121	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
141	C₂×C₃×C₂²⋊C₄	—	2	16	no	—
142	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
143	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄²	—	4	2	no	—
157	C₂×C₃×C₄²	C₂³	1	2	yes	—
158	C₂×C₃×C₄²	C₂³	1	2	yes	—
159	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
163	C₃×#95	C₂³	1	2	yes	—
164	C₃×#95	C₂³	1	2	yes	—
165	C₃×#95	C₂³	1	2	yes	—
166	C₃×#95	C₂³	1	2	yes	—
167	C₃×#95	C₂³	1	2	yes	—
168	C₃×#95	C₂³	1	4	yes	—
169	C₃×#95	C₂³	1	4	yes	—
170	C₃×#95	C₂³	1	4	yes	—
171	C₃×#95	C₂³	1	4	yes	—
172	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
173	#543	—	2	16	no	—
174	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
176	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
177	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
178	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
179	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
180	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
181	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
182	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
183	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
184	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
186	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
187	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
188	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
189	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
190	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
191	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
192	#399	C₂²×C₃	1	4	yes	complemented
193	#399	C₂²×C₃	1	4	yes	complemented
194	#398	C₂²×C₃	1	4	yes	complemented
195	#396	C₂²×C₃	1	4	yes	complemented
196	#396	C₂²×C₃	1	4	yes	complemented
197	#396	C₂²×C₃	1	4	yes	complemented
198	#396	C₂²×C₃	1	4	yes	complemented
199	#395	C₂²×C₃	1	4	yes	complemented
200	#393	C₂²×C₃	1	4	yes	complemented
201	#393	C₂²×C₃	1	4	yes	complemented
202	#391	C₂²×C₃	1	2	yes	complemented
203	#391	C₂²×C₃	1	1	yes	characteristic, complemented
204	#390	C₂²×C₃	1	2	yes	—
205	#390	C₂²×C₃	1	2	yes	—
206	#390	C₂²×C₃	1	2	yes	—
207	#390	C₂²×C₃	1	2	yes	—
208	#390	C₂²×C₃	1	2	yes	—
209	#390	C₂²×C₃	1	2	yes	—
210	#389	C₂²×C₃	1	2	yes	complemented
211	#389	C₂²×C₃	1	2	yes	complemented
212	#389	C₂²×C₃	1	1	yes	characteristic, complemented
213	#389	C₂²×C₃	1	2	yes	complemented
214	#389	C₂²×C₃	1	2	yes	complemented
215	#387	C₂²×C₃	1	2	yes	complemented
216	#386	C₂²×C₃	1	4	yes	—
217	#386	C₂²×C₃	1	4	yes	—
218	#385	C₂²×C₃	1	4	yes	—
219	#385	C₂²×C₃	1	2	yes	—
220	#385	C₂²×C₃	1	4	yes	complemented
221	#385	C₂²×C₃	1	4	yes	complemented
222	#384	C₂²×C₃	1	1	yes	characteristic, complemented
223	#384	C₂²×C₃	1	2	yes	complemented
224	#380	C₂²×C₃	1	2	yes	—
225	#380	C₂²×C₃	1	2	yes	—
226	#380	C₂²×C₃	1	1	yes	characteristic
227	#380	C₂²×C₃	1	4	yes	complemented
228	#379	C₂²×C₃	1	4	yes	—
229	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
230	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
231	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
232	C₂⁴×C₃	—	2	4	no	—
233	C₂⁴×C₃	—	2	4	no	—
234	C₂⁴×C₃	—	4	2	no	—
235	C₂⁴×C₃	—	4	2	no	—
236	C₂⁴×C₃	—	4	2	no	—
237	C₂⁴×C₃	—	4	2	no	—
238	C₂⁴×C₃	C₂×Q₈	1	8	yes	—
239	C₂⁴×C₃	C₂⁴	1	4	yes	—
240	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₃×Q₈	—	2	4	no	—
242	C₂×C₃×Q₈	—	2	8	no	—
243	C₂×C₃×Q₈	—	4	1	no	—
244	C₂×C₃×Q₈	—	4	1	no	—
245	C₂×C₃×Q₈	—	4	4	no	—
246	C₂×C₃×Q₈	—	4	2	no	—
247	C₂×C₃×Q₈	—	4	4	no	—
248	C₂×C₃×Q₈	—	4	2	no	—
249	C₂×C₃×Q₈	C₂×D₄	1	4	yes	complemented
250	C₂×C₃×D₄	—	2	4	no	—
251	C₂×C₃×D₄	—	2	4	no	—
252	C₂×C₃×D₄	—	4	16	no	—
253	C₂×C₃×D₄	—	4	2	no	—
254	C₂×C₃×D₄	—	4	2	no	—
255	C₂×C₃×D₄	C₂×Q₈	1	8	yes	—
256	C₂×C₃×D₄	C₂×Q₈	1	8	yes	—
257	C₂²×C₃×C₄	—	2	2	no	—
258	C₂²×C₃×C₄	—	2	2	no	—
259	C₂²×C₃×C₄	—	2	2	no	—
260	C₂²×C₃×C₄	—	2	4	no	—
261	C₂²×C₃×C₄	—	2	2	no	—
262	C₂²×C₃×C₄	—	2	8	no	—
263	C₂²×C₃×C₄	—	2	8	no	—
264	C₂²×C₃×C₄	—	4	1	no	—
265	C₂²×C₃×C₄	—	4	1	no	—
266	C₂²×C₃×C₄	—	4	1	no	—
267	C₂²×C₃×C₄	—	4	2	no	—
268	C₂²×C₃×C₄	—	4	2	no	—
269	C₂²×C₃×C₄	—	4	4	no	—
270	C₂²×C₃×C₄	—	4	4	no	—
271	C₂²×C₃×C₄	—	4	4	no	—
272	C₂²×C₃×C₄	—	4	4	no	—
273	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
274	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
275	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
277	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
278	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
279	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
280	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
281	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
283	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
284	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
286	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
287	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
288	C₃×C₄⋊C₄	—	2	8	no	—
289	C₃×C₄⋊C₄	—	2	4	no	—
290	C₃×C₄⋊C₄	—	2	8	no	—
291	C₃×C₄⋊C₄	—	2	8	no	—
292	C₃×C₄⋊C₄	—	2	8	no	—
293	C₃×C₄⋊C₄	—	2	4	no	—
294	C₃×C₄⋊C₄	—	2	4	no	—
295	C₃×C₄⋊C₄	—	2	4	no	—
296	C₃×C₄⋊C₄	—	2	4	no	—
297	C₃×C₄⋊C₄	—	2	4	no	—
298	C₃×C₄⋊C₄	—	4	2	no	—
299	C₃×C₄⋊C₄	—	4	1	no	—
300	C₃×C₄⋊C₄	—	4	1	no	—
301	C₃×C₄⋊C₄	—	4	2	no	—
302	C₃×C₄⋊C₄	—	4	4	no	—
303	C₃×C₄⋊C₄	—	4	2	no	—
304	C₃×C₄⋊C₄	—	4	4	no	—
305	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
306	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	complemented
307	C₃×C₂²⋊C₄	—	2	8	no	—
308	C₃×C₂²⋊C₄	—	2	4	no	—
309	C₃×C₂²⋊C₄	—	2	8	no	—
310	C₃×C₂²⋊C₄	—	2	8	no	—
311	C₃×C₂²⋊C₄	—	2	8	no	—
312	C₃×C₂²⋊C₄	—	2	8	no	—
313	C₃×C₂²⋊C₄	—	2	8	no	—
314	C₃×C₂²⋊C₄	—	4	4	no	—
315	C₃×C₂²⋊C₄	—	4	4	no	—
316	C₃×C₂²⋊C₄	—	4	4	no	—
317	C₃×C₂²⋊C₄	—	4	4	no	—
318	C₃×C₂²⋊C₄	—	4	4	no	—
319	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
320	C₃×C₄²	—	2	2	no	—
321	C₃×C₄²	—	2	2	no	—
322	C₃×C₄²	—	2	4	no	—
323	C₃×C₄²	—	2	4	no	—
324	C₃×C₄²	—	4	1	no	—
325	C₃×C₄²	—	4	1	no	—
326	C₂⁵	C₂³×C₃	1	2	yes	—
327	C₂²×Q₈	C₂³×C₃	1	4	yes	—
328	C₂²×Q₈	C₂³×C₃	1	2	yes	—
329	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
330	C₂²×D₄	—	4	2	no	—
331	C₂²×D₄	—	4	2	no	—
332	C₂²×D₄	C₃×Q₈	1	8	yes	complemented
333	C₂²×D₄	C₂³×C₃	1	2	yes	—
334	C₂²×D₄	C₂³×C₃	1	2	yes	—
335	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₃	1	4	yes	—
339	C₂³×C₄	C₂³×C₃	1	4	yes	—
340	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
341	C₄⋊Q₈	—	4	2	no	—
342	C₄⋊Q₈	—	4	4	no	—
343	C₂²⋊Q₈	—	2	16	no	—
344	C₂²⋊Q₈	—	2	8	no	—
345	C₂²⋊Q₈	—	2	16	no	—
346	C₂²⋊Q₈	—	2	16	no	—
347	C₂²⋊Q₈	—	2	16	no	—
348	C₂²⋊Q₈	—	2	16	no	—
349	C₂²⋊Q₈	—	4	8	no	—
350	C₂²⋊Q₈	C₃×D₄	1	8	yes	complemented
351	C₄×Q₈	—	4	2	no	—
352	C₄×D₄	—	4	4	no	—
353	C₄×D₄	—	4	4	no	—
354	C₂×C₄⋊C₄	—	4	2	no	—
355	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
363	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	—	2	8	no	—
375	C₂×C₂²⋊C₄	—	2	16	no	—
376	C₂×C₂²⋊C₄	—	4	4	no	—
377	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
390	C₂×C₄²	—	4	2	no	—
391	C₂×C₄²	C₂³×C₃	1	2	yes	—
392	C₂×C₄²	C₂³×C₃	1	2	yes	—
393	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
397	#95	C₂³×C₃	1	2	yes	—
398	#95	C₂³×C₃	1	2	yes	—
399	#95	C₂³×C₃	1	2	yes	—
400	#95	C₂³×C₃	1	2	yes	—
401	#95	C₂³×C₃	1	2	yes	—
402	#95	C₂³×C₃	1	4	yes	—
403	#95	C₂³×C₃	1	4	yes	—
404	#95	C₂³×C₃	1	4	yes	—
405	#95	C₂³×C₃	1	4	yes	—
406	C₂³×C₃	—	2	1	no	—
407	C₂³×C₃	—	2	1	no	—
408	C₂³×C₃	—	2	1	no	—
409	C₂³×C₃	—	2	1	no	—
410	C₂³×C₃	—	2	4	no	—
411	C₂³×C₃	—	2	4	no	—
412	C₂³×C₃	—	2	4	no	—
413	C₂³×C₃	—	2	4	no	—
414	C₂³×C₃	—	2	4	no	—
415	C₂³×C₃	—	2	4	no	—
416	C₂³×C₃	—	2	16	no	—
417	C₂³×C₃	—	4	8	no	—
418	C₂³×C₃	—	4	8	no	—
419	C₂³×C₃	—	8	4	no	—
420	C₂³×C₃	—	8	4	no	—
421	C₂³×C₃	—	8	4	no	—
422	C₂³×C₃	—	8	4	no	—
423	C₂³×C₃	C₂²×D₄	1	2	yes	—
424	C₂³×C₃	C₂²×Q₈	1	8	yes	—
425	C₂³×C₃	C₂²×Q₈	1	2	yes	—
426	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
427	C₂³×C₃	C₂⁵	1	1	yes	characteristic
428	C₃×Q₈	—	4	4	no	—
429	C₃×Q₈	—	8	4	no	—
430	C₃×Q₈	—	8	8	no	—
431	C₃×D₄	—	2	16	no	—
432	C₃×D₄	—	4	8	no	—
433	C₂×C₃×C₄	—	2	1	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	2	2	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	2	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	1	no	—
442	C₂×C₃×C₄	—	2	1	no	—
443	C₂×C₃×C₄	—	2	2	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	8	no	—
446	C₂×C₃×C₄	—	2	4	no	—
447	C₂×C₃×C₄	—	2	4	no	—
448	C₂×C₃×C₄	—	2	4	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	4	no	—
453	C₂×C₃×C₄	—	2	1	no	—
454	C₂×C₃×C₄	—	2	2	no	—
455	C₂×C₃×C₄	—	2	4	no	—
456	C₂×C₃×C₄	—	2	4	no	—
457	C₂×C₃×C₄	—	2	4	no	—
458	C₂×C₃×C₄	—	2	4	no	—
459	C₂×C₃×C₄	—	2	2	no	—
460	C₂×C₃×C₄	—	2	2	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	2	no	—
463	C₂×C₃×C₄	—	2	4	no	—
464	C₂×C₃×C₄	—	4	4	no	—
465	C₂×C₃×C₄	—	4	4	no	—
466	C₂×C₃×C₄	—	8	8	no	—
467	C₂×C₃×C₄	—	8	8	no	—
468	C₂×C₃×C₄	—	8	4	no	—
469	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
470	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
471	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
472	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
473	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
474	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
475	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
476	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
477	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
478	C₂⁴	—	2	4	no	—
479	C₂⁴	—	2	4	no	—
480	C₂⁴	—	4	2	no	—
481	C₂⁴	—	4	2	no	—
482	C₂⁴	—	4	2	no	—
483	C₂⁴	—	4	2	no	—
484	C₂⁴	C₂×C₃×Q₈	1	8	yes	—
485	C₂⁴	C₂⁴×C₃	1	4	yes	—
486	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
487	C₂×Q₈	—	2	4	no	—
488	C₂×Q₈	—	2	8	no	—
489	C₂×Q₈	—	4	1	no	—
490	C₂×Q₈	—	4	1	no	—
491	C₂×Q₈	—	4	4	no	—
492	C₂×Q₈	—	4	2	no	—
493	C₂×Q₈	—	4	4	no	—
494	C₂×Q₈	—	4	2	no	—
495	C₂×Q₈	C₂×C₃×D₄	1	4	yes	complemented
496	C₂×D₄	—	2	4	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	4	16	no	—
499	C₂×D₄	—	4	2	no	—
500	C₂×D₄	—	4	2	no	—
501	C₂×D₄	C₂×C₃×Q₈	1	8	yes	—
502	C₂×D₄	C₂×C₃×Q₈	1	8	yes	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	8	no	—
509	C₂²×C₄	—	2	8	no	—
510	C₂²×C₄	—	4	1	no	—
511	C₂²×C₄	—	4	1	no	—
512	C₂²×C₄	—	4	1	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	—	4	4	no	—
518	C₂²×C₄	—	4	4	no	—
519	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
520	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
526	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
527	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
534	C₄⋊C₄	—	2	8	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	8	no	—
537	C₄⋊C₄	—	2	8	no	—
538	C₄⋊C₄	—	2	8	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	1	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	4	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	4	no	—
550	C₄⋊C₄	—	4	1	no	—
551	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	complemented
552	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	complemented
553	C₂²⋊C₄	—	2	8	no	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	—	2	8	no	—
556	C₂²⋊C₄	—	2	8	no	—
557	C₂²⋊C₄	—	2	8	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	2	8	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₂²⋊C₄	—	4	4	no	—
563	C₂²⋊C₄	—	4	4	no	—
564	C₂²⋊C₄	—	4	4	no	—
565	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	4	1	no	—
571	C₄²	—	4	1	no	—
572	C₂²×C₃	—	2	2	no	—
573	C₂²×C₃	—	2	2	no	—
574	C₂²×C₃	—	2	2	no	—
575	C₂²×C₃	—	2	2	no	—
576	C₂²×C₃	—	2	2	no	—
577	C₂²×C₃	—	2	2	no	—
578	C₂²×C₃	—	2	8	no	—
579	C₂²×C₃	—	2	8	no	—
580	C₂²×C₃	—	2	8	no	—
581	C₂²×C₃	—	4	4	no	—
582	C₂²×C₃	—	4	4	no	—
583	C₂²×C₃	—	4	4	no	—
584	C₂²×C₃	—	4	4	no	—
585	C₂²×C₃	—	8	16	no	—
586	C₂²×C₃	D₄×Q₈	1	4	yes	—
587	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
588	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
589	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
593	C₂²×C₃	#585	1	1	yes	characteristic
594	C₃×C₄	—	2	2	no	—
595	C₃×C₄	—	2	2	no	—
596	C₃×C₄	—	2	2	no	—
597	C₃×C₄	—	2	4	no	—
598	C₃×C₄	—	2	4	no	—
599	C₃×C₄	—	2	2	no	—
600	C₃×C₄	—	4	4	no	—
601	C₃×C₄	—	4	4	no	—
602	C₃×C₄	—	4	4	no	—
603	C₃×C₄	—	4	2	no	—
604	C₃×C₄	—	4	1	no	—
605	C₃×C₄	—	4	2	no	—
606	C₃×C₄	#543	1	4	yes	complemented
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	4	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	4	no	—
615	C₂³	—	2	4	no	—
616	C₂³	—	2	4	no	—
617	C₂³	—	2	16	no	—
618	C₂³	—	4	8	no	—
619	C₂³	—	4	8	no	—
620	C₂³	—	8	4	no	—
621	C₂³	—	8	4	no	—
622	C₂³	—	8	4	no	—
623	C₂³	—	8	4	no	—
624	C₂³	C₂²×C₃×D₄	1	2	yes	—
625	C₂³	C₂²×C₃×Q₈	1	8	yes	—
626	C₂³	C₂²×C₃×Q₈	1	2	yes	—
627	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
628	C₂³	C₂⁵×C₃	1	1	yes	characteristic
629	Q₈	—	4	4	no	—
630	Q₈	—	8	4	no	—
631	Q₈	—	8	8	no	—
632	D₄	—	2	16	no	—
633	D₄	—	4	8	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	8	8	no	—
668	C₂×C₄	—	8	8	no	—
669	C₂×C₄	—	8	4	no	—
670	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
671	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
672	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
673	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
674	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
675	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
676	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
677	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
678	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
679	C₂×C₃	—	2	4	no	—
680	C₂×C₃	—	4	8	no	—
681	C₂×C₃	C₂×#543	1	1	yes	characteristic
682	C₂×C₃	C₂×D₄×Q₈	1	1	yes	characteristic
683	C₂×C₃	#3496	1	1	yes	characteristic
684	C₂×C₃	#3498	1	1	yes	characteristic
685	C₂×C₃	#3501	1	1	yes	characteristic
686	C₂×C₃	#3536	1	1	yes	characteristic
687	C₂×C₃	#3561	1	1	yes	characteristic
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	8	no	—
695	C₂²	—	2	8	no	—
696	C₂²	—	2	8	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	8	16	no	—
702	C₂²	C₃×D₄×Q₈	1	4	yes	—
703	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
704	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
705	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
708	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
709	C₂²	C₃×#585	1	1	yes	characteristic
710	C₄	—	2	2	no	—
711	C₄	—	2	2	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	4	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	2	no	—
716	C₄	—	4	4	no	—
717	C₄	—	4	4	no	—
718	C₄	—	4	4	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	C₃×#543	1	4	yes	complemented
723	C₃	#39367	1	1	yes	characteristic, direct product factor, Sylow
724	C₂	—	2	4	no	—
725	C₂	—	4	8	no	—
726	C₂	C₂×C₃×#543	1	1	yes	characteristic
727	C₂	C₂×C₃×D₄×Q₈	1	1	yes	characteristic
728	C₂	C₃×#3496	1	1	yes	characteristic
729	C₂	C₃×#3498	1	1	yes	characteristic
730	C₂	C₃×#3501	1	1	yes	characteristic
731	C₂	C₃×#3536	1	1	yes	characteristic
732	C₂	C₃×#3561	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#543	C₂	semidirect
2. C₃×#2857	C₂	semidirect
3. C₃×#2732	C₂	semidirect
4. C₃×#2692	C₂	semidirect
5. C₃×#2683	C₂	semidirect
6. C₃×#2626	C₂	semidirect
7. C₃×#2542	C₂	semidirect
8. C₃×#2538	C₂	semidirect
9. C₃×#2452	C₂	semidirect
10. C₃×#2452	C₂	semidirect
11. C₃×#2440	C₂	semidirect
12. C₃×#2437	C₂	semidirect
14. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
16. #39367	C₃	direct (N × H)
19. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
20. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₃×C₄×Q₈	C₂²	semidirect
37. C₃×#399	C₂²	semidirect
38. C₃×#399	C₂²	semidirect
39. C₃×#398	C₂²	semidirect
40. C₃×#396	C₂²	semidirect
41. C₃×#396	C₂²	semidirect
42. C₃×#396	C₂²	semidirect
43. C₃×#396	C₂²	semidirect
44. C₃×#395	C₂²	semidirect
45. C₃×#393	C₂²	semidirect
46. C₃×#393	C₂²	semidirect
47. C₃×#391	C₂²	semidirect
48. C₃×#391	C₂²	semidirect
55. C₃×#389	C₂²	semidirect
56. C₃×#389	C₂²	semidirect
57. C₃×#389	C₂²	semidirect
58. C₃×#389	C₂²	semidirect
59. C₃×#389	C₂²	semidirect
60. C₃×#387	C₂²	semidirect
65. C₃×#385	C₂²	semidirect
66. C₃×#385	C₂²	semidirect
67. C₃×#384	C₂²	semidirect
68. C₃×#384	C₂²	semidirect
72. C₃×#380	C₂²	semidirect
74. C₃×C₄×C₄⋊C₄	C₂²	semidirect
75. C₃×C₄×C₄⋊C₄	C₂²	semidirect
77. C₂×#543	C₂×C₃	semidirect
78. #2857	C₂×C₃	semidirect
79. #2732	C₂×C₃	semidirect
80. #2692	C₂×C₃	semidirect
81. #2683	C₂×C₃	semidirect
82. #2626	C₂×C₃	semidirect
83. #2542	C₂×C₃	semidirect
84. #2538	C₂×C₃	semidirect
85. #2452	C₂×C₃	semidirect
86. #2452	C₂×C₃	semidirect
87. #2440	C₂×C₃	semidirect
88. #2437	C₂×C₃	semidirect
90. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
98. C₂²×C₃×D₄	Q₈	semidirect
116. C₃×C₂²⋊Q₈	D₄	semidirect
174. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
175. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
179. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
180. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
181. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
182. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
183. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
184. C₂×C₄×Q₈	C₂²×C₃	semidirect
192. #399	C₂²×C₃	semidirect
193. #399	C₂²×C₃	semidirect
194. #398	C₂²×C₃	semidirect
195. #396	C₂²×C₃	semidirect
196. #396	C₂²×C₃	semidirect
197. #396	C₂²×C₃	semidirect
198. #396	C₂²×C₃	semidirect
199. #395	C₂²×C₃	semidirect
200. #393	C₂²×C₃	semidirect
201. #393	C₂²×C₃	semidirect
202. #391	C₂²×C₃	semidirect
203. #391	C₂²×C₃	semidirect
210. #389	C₂²×C₃	semidirect
211. #389	C₂²×C₃	semidirect
212. #389	C₂²×C₃	semidirect
213. #389	C₂²×C₃	semidirect
214. #389	C₂²×C₃	semidirect
215. #387	C₂²×C₃	semidirect
220. #385	C₂²×C₃	semidirect
221. #385	C₂²×C₃	semidirect
222. #384	C₂²×C₃	semidirect
223. #384	C₂²×C₃	semidirect
227. #380	C₂²×C₃	semidirect
229. C₄×C₄⋊C₄	C₂²×C₃	semidirect
230. C₄×C₄⋊C₄	C₂²×C₃	semidirect
249. C₂×C₃×Q₈	C₂×D₄	semidirect
305. C₃×C₄⋊C₄	C₂×D₄	semidirect
306. C₃×C₄⋊C₄	C₂×D₄	semidirect
332. C₂²×D₄	C₃×Q₈	semidirect
350. C₂²⋊Q₈	C₃×D₄	semidirect
495. C₂×Q₈	C₂×C₃×D₄	semidirect
551. C₄⋊C₄	C₂×C₃×D₄	semidirect
552. C₄⋊C₄	C₂×C₃×D₄	semidirect
606. C₃×C₄	#543	semidirect
722. C₄	C₃×#543	semidirect
723. C₃	#39367	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×#543	2
C₃×#2857	2
C₃×#2732	2
C₃×#2692	2
C₃×#2683	2
C₃×#2626	2
C₃×#2542	2
C₃×#2538	2
C₃×#2452	2
C₃×#2440	2
C₃×#2437	2
C₃×D₄×C₂²⋊C₄	2
C₃×C₄×C₂²⋊Q₈	2
C₂×C₃×#390	2
#39367	3

Subgroups — C3×#39367 #10657974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#39367 #10657974