Subgroups — C₃×#39375 #10657982

Order 768.

2624 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#538	C₂	1	2	yes	maximal, complemented
2	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2727	C₂	1	2	yes	maximal, complemented
4	C₃×#2710	C₂	1	4	yes	maximal, complemented
5	C₃×#2682	C₂	1	2	yes	maximal, complemented
6	C₃×#2626	C₂	1	2	yes	maximal, complemented
7	C₃×#2512	C₂	1	2	yes	maximal, complemented
8	C₃×#2501	C₂	1	2	yes	maximal, complemented
9	C₃×#2491	C₂	1	2	yes	maximal, complemented
10	C₃×#2418	C₂	1	4	yes	maximal, complemented
11	C₃×#2416	C₂	1	2	yes	maximal, complemented
12	C₃×#2408	C₂	1	2	yes	maximal, complemented
13	C₃×D₄×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
14	C₃×C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
16	#39375	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
18	C₃×#538	—	2	16	no	—
19	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×#126	C₂²	1	4	yes	complemented
21	C₂×C₃×#124	C₂²	1	4	yes	complemented
22	C₂×C₃×#123	C₂²	1	4	yes	complemented
23	C₂×C₃×#123	C₂²	1	4	yes	complemented
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃×#121	C₂²	1	2	yes	—
26	C₂×C₃×#121	C₂²	1	2	yes	—
27	C₂×C₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₃×#121	C₂²	1	4	yes	complemented
29	C₂×C₃×#120	C₂²	1	4	yes	—
30	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
31	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
35	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
38	C₃×#399	C₂²	1	4	yes	complemented
39	C₃×#399	C₂²	1	4	yes	complemented
40	C₃×#397	C₂²	1	4	yes	complemented
41	C₃×#396	C₂²	1	4	yes	complemented
42	C₃×#396	C₂²	1	4	yes	complemented
43	C₃×#394	C₂²	1	4	yes	—
44	C₃×#394	C₂²	1	4	yes	complemented
45	C₃×#394	C₂²	1	4	yes	complemented
46	C₃×#393	C₂²	1	4	yes	complemented
47	C₃×#392	C₂²	1	4	yes	—
48	C₃×#391	C₂²	1	2	yes	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×#390	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	4	yes	complemented
59	C₃×#389	C₂²	1	1	yes	characteristic, complemented
60	C₃×#388	C₂²	1	4	yes	complemented
61	C₃×#388	C₂²	1	4	yes	complemented
62	C₃×#388	C₂²	1	2	yes	complemented
63	C₃×#386	C₂²	1	2	yes	—
64	C₃×#386	C₂²	1	4	yes	complemented
65	C₃×#385	C₂²	1	4	yes	—
66	C₃×#385	C₂²	1	4	yes	complemented
67	C₃×#384	C₂²	1	1	yes	characteristic, complemented
68	C₃×#384	C₂²	1	2	yes	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	2	yes	complemented
73	C₃×#379	C₂²	1	4	yes	—
74	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
75	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
76	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
77	C₂×#538	C₂×C₃	1	2	yes	complemented
78	#2857	C₂×C₃	1	1	yes	characteristic, complemented
79	#2727	C₂×C₃	1	2	yes	complemented
80	#2710	C₂×C₃	1	4	yes	complemented
81	#2682	C₂×C₃	1	2	yes	complemented
82	#2626	C₂×C₃	1	2	yes	complemented
83	#2512	C₂×C₃	1	2	yes	complemented
84	#2501	C₂×C₃	1	2	yes	complemented
85	#2491	C₂×C₃	1	2	yes	complemented
86	#2418	C₂×C₃	1	4	yes	complemented
87	#2416	C₂×C₃	1	2	yes	complemented
88	#2408	C₂×C₃	1	2	yes	complemented
89	D₄×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
90	C₄×#121	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×#390	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂⁵×C₃	C₂³	1	2	yes	—
93	C₂²×C₃×Q₈	C₂³	1	2	yes	—
94	C₂²×C₃×D₄	—	2	4	no	—
95	C₂²×C₃×D₄	—	4	2	no	—
96	C₂²×C₃×D₄	—	4	2	no	—
97	C₂²×C₃×D₄	C₂³	1	2	yes	—
98	C₂²×C₃×D₄	C₂³	1	2	yes	—
99	C₂²×C₃×D₄	C₂³	1	2	yes	—
100	C₂²×C₃×D₄	C₂³	1	4	yes	—
101	C₂²×C₃×D₄	C₂³	1	4	yes	—
102	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
103	C₂³×C₃×C₄	C₂³	1	2	yes	—
104	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
105	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
106	C₂³×C₃×C₄	C₂³	1	2	yes	—
107	C₂³×C₃×C₄	C₂³	1	4	yes	—
108	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
109	C₃×C₄⋊Q₈	—	4	2	no	—
110	C₃×#126	—	2	16	no	—
111	C₃×#124	—	2	16	no	—
112	C₃×#123	—	2	16	no	—
113	C₃×#123	—	4	8	no	—
114	C₃×C₂²⋊Q₈	—	2	8	no	—
115	C₃×#121	—	2	16	no	—
116	C₃×#121	—	4	4	no	—
117	C₃×#121	—	4	4	no	—
118	C₃×#121	D₄	1	8	yes	complemented
119	C₃×#120	—	2	16	no	—
120	C₃×C₄×D₄	—	2	16	no	—
121	C₃×C₄×D₄	—	2	8	no	—
122	C₃×C₄×D₄	—	4	2	no	—
123	C₂×C₃×C₄⋊C₄	—	4	2	no	—
124	C₂×C₃×C₄⋊C₄	—	4	4	no	—
125	C₂×C₃×C₄⋊C₄	C₂³	1	2	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	2	yes	—
129	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₃×C₄⋊C₄	C₂³	1	4	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	1	yes	characteristic
136	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	4	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	—	4	4	no	—
142	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	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	4	yes	—
156	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄²	—	4	2	no	—
160	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₄²	C₂³	1	2	yes	—
162	C₂×C₃×C₄²	C₂³	1	4	yes	—
163	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	2	yes	—
170	C₃×#95	C₂³	1	4	yes	—
171	C₃×#95	C₂³	1	4	yes	—
172	C₃×#95	C₂³	1	4	yes	—
173	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
174	#538	—	2	16	no	—
175	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₂×#126	C₂²×C₃	1	4	yes	complemented
177	C₂×#124	C₂²×C₃	1	4	yes	complemented
178	C₂×#123	C₂²×C₃	1	4	yes	complemented
179	C₂×#123	C₂²×C₃	1	4	yes	complemented
180	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
181	C₂×#121	C₂²×C₃	1	2	yes	—
182	C₂×#121	C₂²×C₃	1	2	yes	—
183	C₂×#121	C₂²×C₃	1	1	yes	characteristic
184	C₂×#121	C₂²×C₃	1	4	yes	complemented
185	C₂×#120	C₂²×C₃	1	4	yes	—
186	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
187	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
188	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
190	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
191	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
192	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
193	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
194	#399	C₂²×C₃	1	4	yes	complemented
195	#399	C₂²×C₃	1	4	yes	complemented
196	#397	C₂²×C₃	1	4	yes	complemented
197	#396	C₂²×C₃	1	4	yes	complemented
198	#396	C₂²×C₃	1	4	yes	complemented
199	#394	C₂²×C₃	1	4	yes	—
200	#394	C₂²×C₃	1	4	yes	complemented
201	#394	C₂²×C₃	1	4	yes	complemented
202	#393	C₂²×C₃	1	4	yes	complemented
203	#392	C₂²×C₃	1	4	yes	—
204	#391	C₂²×C₃	1	2	yes	complemented
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	#390	C₂²×C₃	1	2	yes	—
211	#390	C₂²×C₃	1	1	yes	characteristic, complemented
212	#389	C₂²×C₃	1	2	yes	complemented
213	#389	C₂²×C₃	1	2	yes	complemented
214	#389	C₂²×C₃	1	4	yes	complemented
215	#389	C₂²×C₃	1	1	yes	characteristic, complemented
216	#388	C₂²×C₃	1	4	yes	complemented
217	#388	C₂²×C₃	1	4	yes	complemented
218	#388	C₂²×C₃	1	2	yes	complemented
219	#386	C₂²×C₃	1	2	yes	—
220	#386	C₂²×C₃	1	4	yes	complemented
221	#385	C₂²×C₃	1	4	yes	—
222	#385	C₂²×C₃	1	4	yes	complemented
223	#384	C₂²×C₃	1	1	yes	characteristic, complemented
224	#384	C₂²×C₃	1	2	yes	complemented
225	#380	C₂²×C₃	1	2	yes	—
226	#380	C₂²×C₃	1	2	yes	—
227	#380	C₂²×C₃	1	1	yes	characteristic
228	#380	C₂²×C₃	1	2	yes	complemented
229	#379	C₂²×C₃	1	4	yes	—
230	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
231	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
232	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
233	C₂⁴×C₃	—	2	4	no	—
234	C₂⁴×C₃	—	2	4	no	—
235	C₂⁴×C₃	—	2	4	no	—
236	C₂⁴×C₃	—	4	2	no	—
237	C₂⁴×C₃	—	4	2	no	—
238	C₂⁴×C₃	—	4	2	no	—
239	C₂⁴×C₃	—	4	2	no	—
240	C₂⁴×C₃	C₂⁴	1	4	yes	—
241	C₂⁴×C₃	C₂⁴	1	2	yes	—
242	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₃×Q₈	—	2	4	no	—
244	C₂×C₃×Q₈	—	4	2	no	—
245	C₂×C₃×Q₈	—	4	2	no	—
246	C₂×C₃×D₄	—	2	4	no	—
247	C₂×C₃×D₄	—	2	4	no	—
248	C₂×C₃×D₄	—	2	8	no	—
249	C₂×C₃×D₄	—	2	8	no	—
250	C₂×C₃×D₄	—	2	4	no	—
251	C₂×C₃×D₄	—	2	4	no	—
252	C₂×C₃×D₄	—	2	4	no	—
253	C₂×C₃×D₄	—	2	4	no	—
254	C₂×C₃×D₄	—	4	1	no	—
255	C₂×C₃×D₄	—	4	2	no	—
256	C₂×C₃×D₄	—	4	2	no	—
257	C₂×C₃×D₄	—	4	1	no	—
258	C₂×C₃×D₄	—	4	16	no	—
259	C₂×C₃×D₄	—	4	4	no	—
260	C₂×C₃×D₄	—	4	4	no	—
261	C₂×C₃×D₄	—	4	4	no	—
262	C₂×C₃×D₄	—	4	4	no	—
263	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
264	C₂×C₃×D₄	C₂×D₄	1	4	yes	complemented
265	C₂²×C₃×C₄	—	2	2	no	—
266	C₂²×C₃×C₄	—	2	2	no	—
267	C₂²×C₃×C₄	—	2	2	no	—
268	C₂²×C₃×C₄	—	2	4	no	—
269	C₂²×C₃×C₄	—	2	8	no	—
270	C₂²×C₃×C₄	—	2	4	no	—
271	C₂²×C₃×C₄	—	2	2	no	—
272	C₂²×C₃×C₄	—	2	4	no	—
273	C₂²×C₃×C₄	—	2	4	no	—
274	C₂²×C₃×C₄	—	4	1	no	—
275	C₂²×C₃×C₄	—	4	1	no	—
276	C₂²×C₃×C₄	—	4	1	no	—
277	C₂²×C₃×C₄	—	4	2	no	—
278	C₂²×C₃×C₄	—	4	4	no	—
279	C₂²×C₃×C₄	—	4	2	no	—
280	C₂²×C₃×C₄	—	4	4	no	—
281	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
282	C₂²×C₃×C₄	#41	1	4	yes	—
283	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
285	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
286	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
287	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
288	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
289	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
290	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
291	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
292	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
294	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
295	C₃×C₄⋊C₄	—	2	8	no	—
296	C₃×C₄⋊C₄	—	2	8	no	—
297	C₃×C₄⋊C₄	—	2	4	no	—
298	C₃×C₄⋊C₄	—	2	4	no	—
299	C₃×C₄⋊C₄	—	2	4	no	—
300	C₃×C₄⋊C₄	—	2	4	no	—
301	C₃×C₄⋊C₄	—	2	4	no	—
302	C₃×C₄⋊C₄	—	2	4	no	—
303	C₃×C₄⋊C₄	—	4	2	no	—
304	C₃×C₄⋊C₄	—	4	4	no	—
305	C₃×C₄⋊C₄	—	4	1	no	—
306	C₃×C₄⋊C₄	—	4	1	no	—
307	C₃×C₄⋊C₄	—	4	4	no	—
308	C₃×C₄⋊C₄	—	4	2	no	—
309	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
310	C₃×C₂²⋊C₄	—	2	8	no	—
311	C₃×C₂²⋊C₄	—	2	8	no	—
312	C₃×C₂²⋊C₄	—	2	4	no	—
313	C₃×C₂²⋊C₄	—	2	8	no	—
314	C₃×C₂²⋊C₄	—	2	8	no	—
315	C₃×C₂²⋊C₄	—	2	8	no	—
316	C₃×C₂²⋊C₄	—	2	8	no	—
317	C₃×C₂²⋊C₄	—	2	4	no	—
318	C₃×C₂²⋊C₄	—	2	8	no	—
319	C₃×C₂²⋊C₄	—	2	4	no	—
320	C₃×C₂²⋊C₄	—	4	4	no	—
321	C₃×C₂²⋊C₄	—	4	4	no	—
322	C₃×C₂²⋊C₄	—	4	2	no	—
323	C₃×C₂²⋊C₄	—	4	4	no	—
324	C₃×C₂²⋊C₄	—	4	4	no	—
325	C₃×C₂²⋊C₄	—	4	4	no	—
326	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
327	C₃×C₄²	—	2	8	no	—
328	C₃×C₄²	—	2	4	no	—
329	C₃×C₄²	—	2	2	no	—
330	C₃×C₄²	—	2	2	no	—
331	C₃×C₄²	—	4	1	no	—
332	C₃×C₄²	—	4	1	no	—
333	C₂⁵	C₂³×C₃	1	2	yes	—
334	C₂²×Q₈	C₂³×C₃	1	2	yes	—
335	C₂²×D₄	—	2	4	no	—
336	C₂²×D₄	—	4	2	no	—
337	C₂²×D₄	—	4	2	no	—
338	C₂²×D₄	C₂³×C₃	1	2	yes	—
339	C₂²×D₄	C₂³×C₃	1	2	yes	—
340	C₂²×D₄	C₂³×C₃	1	4	yes	—
341	C₂²×D₄	C₂³×C₃	1	4	yes	—
342	C₂²×D₄	C₂³×C₃	1	2	yes	—
343	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₃	1	2	yes	—
345	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₃	1	2	yes	—
348	C₂³×C₄	C₂³×C₃	1	4	yes	—
349	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
350	C₄⋊Q₈	—	4	2	no	—
351	#126	—	2	16	no	—
352	#124	—	2	16	no	—
353	#123	—	2	16	no	—
354	#123	—	4	8	no	—
355	C₂²⋊Q₈	—	2	8	no	—
356	#121	—	2	16	no	—
357	#121	—	4	4	no	—
358	#121	—	4	4	no	—
359	#121	C₃×D₄	1	8	yes	complemented
360	#120	—	2	16	no	—
361	C₄×D₄	—	2	16	no	—
362	C₄×D₄	—	2	8	no	—
363	C₄×D₄	—	4	2	no	—
364	C₂×C₄⋊C₄	—	4	2	no	—
365	C₂×C₄⋊C₄	—	4	4	no	—
366	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	8	no	—
382	C₂×C₂²⋊C₄	—	4	4	no	—
383	C₂×C₂²⋊C₄	C₂³×C₃	1	4	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	2	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
400	C₂×C₄²	—	4	2	no	—
401	C₂×C₄²	C₂³×C₃	1	4	yes	—
402	C₂×C₄²	C₂³×C₃	1	2	yes	—
403	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
407	#95	C₂³×C₃	1	2	yes	—
408	#95	C₂³×C₃	1	2	yes	—
409	#95	C₂³×C₃	1	4	yes	—
410	#95	C₂³×C₃	1	2	yes	—
411	#95	C₂³×C₃	1	4	yes	—
412	#95	C₂³×C₃	1	4	yes	—
413	#95	C₂³×C₃	1	4	yes	—
414	C₂³×C₃	—	2	1	no	—
415	C₂³×C₃	—	2	1	no	—
416	C₂³×C₃	—	2	1	no	—
417	C₂³×C₃	—	2	1	no	—
418	C₂³×C₃	—	2	2	no	—
419	C₂³×C₃	—	2	2	no	—
420	C₂³×C₃	—	2	2	no	—
421	C₂³×C₃	—	2	2	no	—
422	C₂³×C₃	—	2	2	no	—
423	C₂³×C₃	—	2	2	no	—
424	C₂³×C₃	—	2	4	no	—
425	C₂³×C₃	—	2	4	no	—
426	C₂³×C₃	—	2	4	no	—
427	C₂³×C₃	—	2	4	no	—
428	C₂³×C₃	—	2	4	no	—
429	C₂³×C₃	—	2	4	no	—
430	C₂³×C₃	—	2	4	no	—
431	C₂³×C₃	—	4	8	no	—
432	C₂³×C₃	—	4	8	no	—
433	C₂³×C₃	—	4	8	no	—
434	C₂³×C₃	—	8	4	no	—
435	C₂³×C₃	—	8	4	no	—
436	C₂³×C₃	—	8	4	no	—
437	C₂³×C₃	—	8	4	no	—
438	C₂³×C₃	C₂²×D₄	1	4	yes	—
439	C₂³×C₃	C₂²×D₄	1	2	yes	—
440	C₂³×C₃	C₂×#41	1	2	yes	—
441	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
442	C₂³×C₃	C₂⁵	1	1	yes	characteristic
443	C₃×Q₈	—	8	4	no	—
444	C₃×D₄	—	2	16	no	—
445	C₃×D₄	—	4	4	no	—
446	C₃×D₄	—	4	8	no	—
447	C₃×D₄	—	4	8	no	—
448	C₃×D₄	—	8	8	no	—
449	C₃×D₄	—	8	8	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	2	1	no	—
454	C₂×C₃×C₄	—	2	1	no	—
455	C₂×C₃×C₄	—	2	1	no	—
456	C₂×C₃×C₄	—	2	1	no	—
457	C₂×C₃×C₄	—	2	2	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	8	no	—
461	C₂×C₃×C₄	—	2	4	no	—
462	C₂×C₃×C₄	—	2	4	no	—
463	C₂×C₃×C₄	—	2	4	no	—
464	C₂×C₃×C₄	—	2	2	no	—
465	C₂×C₃×C₄	—	2	2	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	2	no	—
468	C₂×C₃×C₄	—	2	4	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	2	no	—
471	C₂×C₃×C₄	—	2	2	no	—
472	C₂×C₃×C₄	—	2	4	no	—
473	C₂×C₃×C₄	—	2	4	no	—
474	C₂×C₃×C₄	—	2	4	no	—
475	C₂×C₃×C₄	—	2	4	no	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	2	no	—
478	C₂×C₃×C₄	—	2	4	no	—
479	C₂×C₃×C₄	—	4	4	no	—
480	C₂×C₃×C₄	—	4	4	no	—
481	C₂×C₃×C₄	—	4	8	no	—
482	C₂×C₃×C₄	—	8	4	no	—
483	C₂×C₃×C₄	—	8	8	no	—
484	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
485	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
486	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
487	C₂×C₃×C₄	C₂×#41	1	2	yes	—
488	C₂×C₃×C₄	C₂×#41	1	2	yes	—
489	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
490	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
491	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
492	C₂⁴	—	2	4	no	—
493	C₂⁴	—	2	4	no	—
494	C₂⁴	—	2	4	no	—
495	C₂⁴	—	4	2	no	—
496	C₂⁴	—	4	2	no	—
497	C₂⁴	—	4	2	no	—
498	C₂⁴	—	4	2	no	—
499	C₂⁴	C₂⁴×C₃	1	4	yes	—
500	C₂⁴	C₂⁴×C₃	1	2	yes	—
501	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	4	2	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	4	no	—
507	C₂×D₄	—	2	8	no	—
508	C₂×D₄	—	2	8	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	4	1	no	—
514	C₂×D₄	—	4	2	no	—
515	C₂×D₄	—	4	2	no	—
516	C₂×D₄	—	4	1	no	—
517	C₂×D₄	—	4	16	no	—
518	C₂×D₄	—	4	4	no	—
519	C₂×D₄	—	4	4	no	—
520	C₂×D₄	—	4	4	no	—
521	C₂×D₄	—	4	4	no	—
522	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
523	C₂×D₄	C₂×C₃×D₄	1	4	yes	complemented
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	—	2	8	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	—	4	1	no	—
535	C₂²×C₄	—	4	1	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
541	C₂²×C₄	C₃×#41	1	4	yes	—
542	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
545	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	8	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	4	2	no	—
563	C₄⋊C₄	—	4	4	no	—
564	C₄⋊C₄	—	4	1	no	—
565	C₄⋊C₄	—	4	4	no	—
566	C₄⋊C₄	—	4	2	no	—
567	C₄⋊C₄	—	4	1	no	—
568	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	complemented
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	8	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	8	no	—
573	C₂²⋊C₄	—	2	8	no	—
574	C₂²⋊C₄	—	2	8	no	—
575	C₂²⋊C₄	—	2	8	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	4	4	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	4	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₂²⋊C₄	—	4	4	no	—
585	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	complemented
586	C₄²	—	2	8	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	4	1	no	—
591	C₄²	—	4	1	no	—
592	C₂²×C₃	—	2	2	no	—
593	C₂²×C₃	—	2	2	no	—
594	C₂²×C₃	—	2	2	no	—
595	C₂²×C₃	—	2	2	no	—
596	C₂²×C₃	—	2	2	no	—
597	C₂²×C₃	—	2	2	no	—
598	C₂²×C₃	—	2	4	no	—
599	C₂²×C₃	—	2	4	no	—
600	C₂²×C₃	—	2	4	no	—
601	C₂²×C₃	—	4	2	no	—
602	C₂²×C₃	—	4	2	no	—
603	C₂²×C₃	—	4	2	no	—
604	C₂²×C₃	—	4	2	no	—
605	C₂²×C₃	—	4	4	no	—
606	C₂²×C₃	—	4	4	no	—
607	C₂²×C₃	—	4	4	no	—
608	C₂²×C₃	—	4	4	no	—
609	C₂²×C₃	—	4	4	no	—
610	C₂²×C₃	—	4	4	no	—
611	C₂²×C₃	—	4	4	no	—
612	C₂²×C₃	—	8	16	no	—
613	C₂²×C₃	#547	1	4	yes	—
614	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
615	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
616	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
618	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
620	C₂²×C₃	#585	1	1	yes	characteristic
621	C₃×C₄	—	2	2	no	—
622	C₃×C₄	—	2	4	no	—
623	C₃×C₄	—	2	2	no	—
624	C₃×C₄	—	2	2	no	—
625	C₃×C₄	—	2	2	no	—
626	C₃×C₄	—	4	2	no	—
627	C₃×C₄	—	4	4	no	—
628	C₃×C₄	—	4	4	no	—
629	C₃×C₄	—	4	4	no	—
630	C₃×C₄	—	4	2	no	—
631	C₃×C₄	—	4	1	no	—
632	C₃×C₄	#538	1	4	yes	complemented
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	4	no	—
644	C₂³	—	2	4	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	4	8	no	—
651	C₂³	—	4	8	no	—
652	C₂³	—	4	8	no	—
653	C₂³	—	8	4	no	—
654	C₂³	—	8	4	no	—
655	C₂³	—	8	4	no	—
656	C₂³	—	8	4	no	—
657	C₂³	C₂²×C₃×D₄	1	4	yes	—
658	C₂³	C₂²×C₃×D₄	1	2	yes	—
659	C₂³	C₂×C₃×#41	1	2	yes	—
660	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
661	C₂³	C₂⁵×C₃	1	1	yes	characteristic
662	Q₈	—	8	4	no	—
663	D₄	—	2	16	no	—
664	D₄	—	4	4	no	—
665	D₄	—	4	8	no	—
666	D₄	—	4	8	no	—
667	D₄	—	8	8	no	—
668	D₄	—	8	8	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	8	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	8	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	8	no	—
703	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
704	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
705	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
706	C₂×C₄	C₂×C₃×#41	1	2	yes	—
707	C₂×C₄	C₂×C₃×#41	1	2	yes	—
708	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
709	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
710	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
711	C₂×C₃	—	2	4	no	—
712	C₂×C₃	—	4	4	no	—
713	C₂×C₃	—	8	4	no	—
714	C₂×C₃	C₂×#538	1	1	yes	characteristic
715	C₂×C₃	C₂×#547	1	1	yes	characteristic
716	C₂×C₃	#3496	1	1	yes	characteristic
717	C₂×C₃	#3498	1	1	yes	characteristic
718	C₂×C₃	#3506	1	1	yes	characteristic
719	C₂×C₃	#3536	1	1	yes	characteristic
720	C₂×C₃	#3561	1	1	yes	characteristic
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	8	16	no	—
742	C₂²	C₃×#547	1	4	yes	—
743	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
744	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
745	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
746	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
747	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
748	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
749	C₂²	C₃×#585	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	4	no	—
757	C₄	—	4	4	no	—
758	C₄	—	4	4	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	1	no	—
761	C₄	C₃×#538	1	4	yes	complemented
762	C₃	#39375	1	1	yes	characteristic, direct product factor, Sylow
763	C₂	—	2	4	no	—
764	C₂	—	4	4	no	—
765	C₂	—	8	4	no	—
766	C₂	C₂×C₃×#538	1	1	yes	characteristic
767	C₂	C₂×C₃×#547	1	1	yes	characteristic
768	C₂	C₃×#3496	1	1	yes	characteristic
769	C₂	C₃×#3498	1	1	yes	characteristic
770	C₂	C₃×#3506	1	1	yes	characteristic
771	C₂	C₃×#3536	1	1	yes	characteristic
772	C₂	C₃×#3561	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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×#538	C₂	semidirect
2. C₃×#2857	C₂	semidirect
3. C₃×#2727	C₂	semidirect
4. C₃×#2710	C₂	semidirect
5. C₃×#2682	C₂	semidirect
6. C₃×#2626	C₂	semidirect
7. C₃×#2512	C₂	semidirect
8. C₃×#2501	C₂	semidirect
9. C₃×#2491	C₂	semidirect
10. C₃×#2418	C₂	semidirect
11. C₃×#2416	C₂	semidirect
12. C₃×#2408	C₂	semidirect
13. C₃×D₄×C₄⋊C₄	C₂	semidirect
14. C₃×C₄×#121	C₂	semidirect
15. C₂×C₃×#390	C₂	semidirect
16. #39375	C₃	direct (N × H)
19. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
20. C₂×C₃×#126	C₂²	semidirect
21. C₂×C₃×#124	C₂²	semidirect
22. C₂×C₃×#123	C₂²	semidirect
23. C₂×C₃×#123	C₂²	semidirect
28. C₂×C₃×#121	C₂²	semidirect
32. C₂×C₃×C₄×D₄	C₂²	semidirect
34. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
38. C₃×#399	C₂²	semidirect
39. C₃×#399	C₂²	semidirect
40. C₃×#397	C₂²	semidirect
41. C₃×#396	C₂²	semidirect
42. C₃×#396	C₂²	semidirect
44. C₃×#394	C₂²	semidirect
45. C₃×#394	C₂²	semidirect
46. C₃×#393	C₂²	semidirect
48. C₃×#391	C₂²	semidirect
55. C₃×#390	C₂²	semidirect
56. C₃×#389	C₂²	semidirect
57. C₃×#389	C₂²	semidirect
58. C₃×#389	C₂²	semidirect
59. C₃×#389	C₂²	semidirect
60. C₃×#388	C₂²	semidirect
61. C₃×#388	C₂²	semidirect
62. C₃×#388	C₂²	semidirect
64. C₃×#386	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
76. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
77. C₂×#538	C₂×C₃	semidirect
78. #2857	C₂×C₃	semidirect
79. #2727	C₂×C₃	semidirect
80. #2710	C₂×C₃	semidirect
81. #2682	C₂×C₃	semidirect
82. #2626	C₂×C₃	semidirect
83. #2512	C₂×C₃	semidirect
84. #2501	C₂×C₃	semidirect
85. #2491	C₂×C₃	semidirect
86. #2418	C₂×C₃	semidirect
87. #2416	C₂×C₃	semidirect
88. #2408	C₂×C₃	semidirect
89. D₄×C₄⋊C₄	C₂×C₃	semidirect
90. C₄×#121	C₂×C₃	semidirect
91. C₂×#390	C₂×C₃	semidirect
118. C₃×#121	D₄	semidirect
175. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
176. C₂×#126	C₂²×C₃	semidirect
177. C₂×#124	C₂²×C₃	semidirect
178. C₂×#123	C₂²×C₃	semidirect
179. C₂×#123	C₂²×C₃	semidirect
184. C₂×#121	C₂²×C₃	semidirect
188. C₂×C₄×D₄	C₂²×C₃	semidirect
190. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
194. #399	C₂²×C₃	semidirect
195. #399	C₂²×C₃	semidirect
196. #397	C₂²×C₃	semidirect
197. #396	C₂²×C₃	semidirect
198. #396	C₂²×C₃	semidirect
200. #394	C₂²×C₃	semidirect
201. #394	C₂²×C₃	semidirect
202. #393	C₂²×C₃	semidirect
204. #391	C₂²×C₃	semidirect
211. #390	C₂²×C₃	semidirect
212. #389	C₂²×C₃	semidirect
213. #389	C₂²×C₃	semidirect
214. #389	C₂²×C₃	semidirect
215. #389	C₂²×C₃	semidirect
216. #388	C₂²×C₃	semidirect
217. #388	C₂²×C₃	semidirect
218. #388	C₂²×C₃	semidirect
220. #386	C₂²×C₃	semidirect
222. #385	C₂²×C₃	semidirect
223. #384	C₂²×C₃	semidirect
224. #384	C₂²×C₃	semidirect
228. #380	C₂²×C₃	semidirect
230. C₄×C₄⋊C₄	C₂²×C₃	semidirect
231. C₄×C₄⋊C₄	C₂²×C₃	semidirect
232. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
264. C₂×C₃×D₄	C₂×D₄	semidirect
309. C₃×C₄⋊C₄	C₂×D₄	semidirect
326. C₃×C₂²⋊C₄	C₂×D₄	semidirect
359. #121	C₃×D₄	semidirect
523. C₂×D₄	C₂×C₃×D₄	semidirect
568. C₄⋊C₄	C₂×C₃×D₄	semidirect
585. C₂²⋊C₄	C₂×C₃×D₄	semidirect
632. C₃×C₄	#538	semidirect
761. C₄	C₃×#538	semidirect
762. C₃	#39375	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×#538	2
C₃×#2857	2
C₃×#2727	2
C₃×#2710	2
C₃×#2682	2
C₃×#2626	2
C₃×#2512	2
C₃×#2501	2
C₃×#2491	2
C₃×#2418	2
C₃×#2416	2
C₃×#2408	2
C₃×D₄×C₄⋊C₄	2
C₃×C₄×#121	2
C₂×C₃×#390	2
#39375	3

Subgroups — C3×#39375 #10657982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#39375 #10657982