Subgroups — C₃×#35939 #10654546

Order 768.

2794 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic
3	C₃×#2640	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2639	C₂	1	2	yes	maximal, complemented
5	C₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2561	C₂	1	2	yes	maximal, complemented
8	C₃×#2492	C₂	1	2	yes	maximal, complemented
9	C₃×#2491	C₂	1	2	yes	maximal, complemented
10	C₃×#2488	C₂	1	4	yes	maximal, complemented
11	C₃×#2472	C₂	1	4	yes	maximal, complemented
12	C₃×#2436	C₂	1	2	yes	maximal, complemented
13	C₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#393	C₂	1	2	yes	maximal, complemented
15	C₃×#2339	C₂	1	2	yes	maximal, complemented
16	C₃×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
17	C₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
18	#35939	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂³×C₃×Q₈	C₂²	1	2	yes	complemented
21	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
22	C₃×D₄×Q₈	—	2	8	no	—
23	C₃×#546	—	2	8	no	—
24	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₃×#124	C₂²	1	4	yes	complemented
28	C₂×C₃×#123	C₂²	1	2	yes	—
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
32	C₂×C₃×#121	C₂²	1	2	yes	—
33	C₂×C₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₃×#120	C₂²	1	2	yes	—
35	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
38	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	—
42	C₃×#400	C₂²	1	4	yes	complemented
43	C₃×#400	C₂²	1	2	yes	complemented
44	C₃×#397	C₂²	1	1	yes	characteristic
45	C₃×#397	C₂²	1	1	yes	characteristic, complemented
46	C₃×#397	C₂²	1	2	yes	complemented
47	C₃×#397	C₂²	1	4	yes	complemented
48	C₃×#394	C₂²	1	2	yes	—
49	C₃×#394	C₂²	1	4	yes	complemented
50	C₃×#393	C₂²	1	1	yes	characteristic
51	C₃×#393	C₂²	1	4	yes	—
52	C₃×#393	C₂²	1	2	yes	—
53	C₃×#393	C₂²	1	2	yes	complemented
54	C₃×#393	C₂²	1	2	yes	complemented
55	C₃×#393	C₂²	1	2	yes	complemented
56	C₃×#393	C₂²	1	2	yes	complemented
57	C₃×#393	C₂²	1	4	yes	complemented
58	C₃×#393	C₂²	1	1	yes	characteristic, complemented
59	C₃×#391	C₂²	1	2	yes	complemented
60	C₃×#391	C₂²	1	4	yes	complemented
61	C₃×#391	C₂²	1	2	yes	complemented
62	C₃×#390	C₂²	1	2	yes	—
63	C₃×#390	C₂²	1	2	yes	—
64	C₃×#390	C₂²	1	2	yes	—
65	C₃×#388	C₂²	1	4	yes	—
66	C₃×#388	C₂²	1	4	yes	complemented
67	C₃×#388	C₂²	1	4	yes	complemented
68	C₃×#386	C₂²	1	4	yes	—
69	C₃×#386	C₂²	1	4	yes	—
70	C₃×#386	C₂²	1	4	yes	complemented
71	C₃×#386	C₂²	1	4	yes	complemented
72	C₃×#382	C₂²	1	2	yes	complemented
73	C₃×#381	C₂²	1	4	yes	complemented
74	C₃×#380	C₂²	1	2	yes	—
75	C₃×#380	C₂²	1	2	yes	complemented
76	C₃×#379	C₂²	1	4	yes	—
77	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
78	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
79	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
81	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
82	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
83	C₃×#376	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₃×#95	C₂²	1	2	yes	complemented
85	C₂×C₃×#95	C₂²	1	4	yes	complemented
86	C₂×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×#546	C₂×C₃	1	1	yes	characteristic
88	#2640	C₂×C₃	1	1	yes	characteristic, complemented
89	#2639	C₂×C₃	1	2	yes	complemented
90	#2592	C₂×C₃	1	1	yes	characteristic, complemented
91	#2563	C₂×C₃	1	1	yes	characteristic, complemented
92	#2561	C₂×C₃	1	2	yes	complemented
93	#2492	C₂×C₃	1	2	yes	complemented
94	#2491	C₂×C₃	1	2	yes	complemented
95	#2488	C₂×C₃	1	4	yes	complemented
96	#2472	C₂×C₃	1	4	yes	complemented
97	#2436	C₂×C₃	1	2	yes	complemented
98	#2398	C₂×C₃	1	1	yes	characteristic, complemented
99	C₂×#393	C₂×C₃	1	2	yes	complemented
100	#2339	C₂×C₃	1	2	yes	complemented
101	D₄×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
102	#2275	C₂×C₃	1	1	yes	characteristic, complemented
103	C₂⁵×C₃	C₂³	1	2	yes	—
104	C₂×C₃×#41	—	2	4	no	—
105	C₂×C₃×#41	—	2	8	no	—
106	C₂²×C₃×Q₈	—	2	8	no	—
107	C₂²×C₃×Q₈	—	4	8	no	—
108	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
110	C₂²×C₃×Q₈	C₂³	1	4	yes	—
111	C₂²×C₃×Q₈	C₂³	1	2	yes	—
112	C₂²×C₃×D₄	—	2	4	no	—
113	C₂²×C₃×D₄	—	2	8	no	—
114	C₂²×C₃×D₄	C₂³	1	2	yes	—
115	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
116	C₂²×C₃×D₄	C₂³	1	2	yes	—
117	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
118	C₂²×C₃×D₄	C₂³	1	2	yes	—
119	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
120	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
121	C₂³×C₃×C₄	C₂³	1	2	yes	—
122	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
123	C₂³×C₃×C₄	C₂³	1	4	yes	—
124	C₂³×C₃×C₄	C₂³	1	4	yes	—
125	C₂³×C₃×C₄	C₂³	1	2	yes	—
126	C₃×C₄⋊Q₈	—	2	8	no	—
127	C₃×C₄⋊Q₈	—	2	4	no	—
128	C₃×#124	—	2	4	no	—
129	C₃×#124	—	4	8	no	—
130	C₃×#123	—	2	8	no	—
131	C₃×C₂²⋊Q₈	—	2	8	no	—
132	C₃×C₂²⋊Q₈	—	2	4	no	—
133	C₃×C₂²⋊Q₈	—	2	16	no	—
134	C₃×#121	—	2	8	no	—
135	C₃×#121	—	2	4	no	—
136	C₃×#120	—	2	8	no	—
137	C₃×C₄×Q₈	—	2	4	no	—
138	C₃×C₄×D₄	—	2	8	no	—
139	C₃×C₄×D₄	—	2	8	no	—
140	C₃×C₄×D₄	—	2	4	no	—
141	C₃×C₄×D₄	D₄	1	8	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
152	C₂×C₃×C₂²⋊C₄	—	4	8	no	—
153	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄²	C₂³	1	2	yes	—
173	C₂×C₃×C₄²	C₂³	1	2	yes	—
174	C₂×C₃×C₄²	C₂³	1	2	yes	—
175	C₂×C₃×C₄²	C₂³	1	4	yes	—
176	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
177	C₃×#95	C₂³	1	1	yes	characteristic
178	C₃×#95	C₂³	1	2	yes	—
179	C₃×#95	C₂³	1	2	yes	—
180	C₃×#95	C₂³	1	4	yes	—
181	C₃×#95	C₂³	1	4	yes	—
182	C₃×#95	C₂³	1	4	yes	—
183	C₃×#95	C₂³	1	4	yes	—
184	C₃×#95	C₂³	1	1	yes	characteristic
185	C₃×#95	C₂³	1	2	yes	—
186	C₃×#95	C₂³	1	2	yes	—
187	C₃×#95	C₂³	1	2	yes	—
188	C₃×#95	C₂³	1	2	yes	—
189	C₃×#95	C₂³	1	4	yes	—
190	C₃×#95	C₂³	1	4	yes	—
191	C₃×#95	C₂³	1	4	yes	—
192	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
193	C₂³×Q₈	C₂²×C₃	1	2	yes	complemented
194	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
195	D₄×Q₈	—	2	8	no	—
196	#546	—	2	8	no	—
197	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
199	C₂×#124	C₂²×C₃	1	1	yes	characteristic
200	C₂×#124	C₂²×C₃	1	4	yes	complemented
201	C₂×#123	C₂²×C₃	1	2	yes	—
202	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
203	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
204	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
205	C₂×#121	C₂²×C₃	1	2	yes	—
206	C₂×#121	C₂²×C₃	1	1	yes	characteristic
207	C₂×#120	C₂²×C₃	1	2	yes	—
208	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
209	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
210	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
211	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
212	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
213	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
215	#400	C₂²×C₃	1	4	yes	complemented
216	#400	C₂²×C₃	1	2	yes	complemented
217	#397	C₂²×C₃	1	1	yes	characteristic
218	#397	C₂²×C₃	1	2	yes	complemented
219	#397	C₂²×C₃	1	1	yes	characteristic, complemented
220	#397	C₂²×C₃	1	4	yes	complemented
221	#394	C₂²×C₃	1	2	yes	—
222	#394	C₂²×C₃	1	4	yes	complemented
223	#393	C₂²×C₃	1	2	yes	—
224	#393	C₂²×C₃	1	1	yes	characteristic
225	#393	C₂²×C₃	1	4	yes	—
226	#393	C₂²×C₃	1	2	yes	complemented
227	#393	C₂²×C₃	1	2	yes	complemented
228	#393	C₂²×C₃	1	2	yes	complemented
229	#393	C₂²×C₃	1	2	yes	complemented
230	#393	C₂²×C₃	1	4	yes	complemented
231	#393	C₂²×C₃	1	1	yes	characteristic, complemented
232	#391	C₂²×C₃	1	2	yes	complemented
233	#391	C₂²×C₃	1	2	yes	complemented
234	#391	C₂²×C₃	1	4	yes	complemented
235	#390	C₂²×C₃	1	2	yes	—
236	#390	C₂²×C₃	1	2	yes	—
237	#390	C₂²×C₃	1	2	yes	—
238	#388	C₂²×C₃	1	4	yes	—
239	#388	C₂²×C₃	1	4	yes	complemented
240	#388	C₂²×C₃	1	4	yes	complemented
241	#386	C₂²×C₃	1	4	yes	—
242	#386	C₂²×C₃	1	4	yes	—
243	#386	C₂²×C₃	1	4	yes	complemented
244	#386	C₂²×C₃	1	4	yes	complemented
245	#382	C₂²×C₃	1	2	yes	complemented
246	#381	C₂²×C₃	1	4	yes	complemented
247	#380	C₂²×C₃	1	2	yes	—
248	#380	C₂²×C₃	1	2	yes	complemented
249	#379	C₂²×C₃	1	4	yes	—
250	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
251	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
252	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
253	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
254	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
255	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
256	#376	C₂²×C₃	1	1	yes	characteristic, complemented
257	C₂×#95	C₂²×C₃	1	4	yes	complemented
258	C₂×#95	C₂²×C₃	1	2	yes	complemented
259	C₂⁴×C₃	—	2	4	no	—
260	C₂⁴×C₃	—	2	4	no	—
261	C₂⁴×C₃	—	2	8	no	—
262	C₂⁴×C₃	—	4	2	no	—
263	C₂⁴×C₃	—	4	4	no	—
264	C₂⁴×C₃	C₂⁴	1	2	yes	—
265	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
266	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₃	C₂⁴	1	2	yes	—
268	C₃×#41	—	4	16	no	—
269	C₂×C₃×Q₈	—	2	2	no	—
270	C₂×C₃×Q₈	—	2	2	no	—
271	C₂×C₃×Q₈	—	2	8	no	—
272	C₂×C₃×Q₈	—	2	4	no	—
273	C₂×C₃×Q₈	—	2	4	no	—
274	C₂×C₃×Q₈	—	2	4	no	—
275	C₂×C₃×Q₈	—	2	8	no	—
276	C₂×C₃×Q₈	—	4	4	no	—
277	C₂×C₃×Q₈	—	4	4	no	—
278	C₂×C₃×Q₈	—	4	32	no	—
279	C₂×C₃×D₄	—	2	4	no	—
280	C₂×C₃×D₄	—	2	4	no	—
281	C₂×C₃×D₄	—	2	8	no	—
282	C₂×C₃×D₄	—	2	8	no	—
283	C₂×C₃×D₄	—	2	2	no	—
284	C₂×C₃×D₄	—	2	2	no	—
285	C₂×C₃×D₄	—	2	2	no	—
286	C₂×C₃×D₄	—	2	4	no	—
287	C₂×C₃×D₄	—	2	4	no	—
288	C₂×C₃×D₄	—	4	1	no	—
289	C₂×C₃×D₄	—	4	4	no	—
290	C₂×C₃×D₄	—	4	16	no	—
291	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
292	C₂×C₃×D₄	#41	1	8	yes	—
293	C₂²×C₃×C₄	—	2	4	no	—
294	C₂²×C₃×C₄	—	2	8	no	—
295	C₂²×C₃×C₄	—	2	8	no	—
296	C₂²×C₃×C₄	—	2	8	no	—
297	C₂²×C₃×C₄	—	2	2	no	—
298	C₂²×C₃×C₄	—	2	2	no	—
299	C₂²×C₃×C₄	—	2	4	no	—
300	C₂²×C₃×C₄	—	2	4	no	—
301	C₂²×C₃×C₄	—	2	8	no	—
302	C₂²×C₃×C₄	—	4	4	no	—
303	C₂²×C₃×C₄	—	4	4	no	—
304	C₂²×C₃×C₄	—	4	4	no	—
305	C₂²×C₃×C₄	—	4	4	no	—
306	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
307	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
308	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
309	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
310	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
312	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
313	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
314	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
315	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
317	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
318	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
319	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
320	C₃×C₄⋊C₄	—	2	2	no	—
321	C₃×C₄⋊C₄	—	2	4	no	—
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	2	no	—
324	C₃×C₄⋊C₄	—	2	4	no	—
325	C₃×C₄⋊C₄	—	2	8	no	—
326	C₃×C₄⋊C₄	—	2	4	no	—
327	C₃×C₄⋊C₄	—	2	4	no	—
328	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
329	C₃×C₂²⋊C₄	—	2	8	no	—
330	C₃×C₂²⋊C₄	—	2	8	no	—
331	C₃×C₂²⋊C₄	—	2	4	no	—
332	C₃×C₂²⋊C₄	—	2	2	no	—
333	C₃×C₂²⋊C₄	—	2	4	no	—
334	C₃×C₂²⋊C₄	—	2	4	no	—
335	C₃×C₂²⋊C₄	—	2	4	no	—
336	C₃×C₂²⋊C₄	—	2	2	no	—
337	C₃×C₂²⋊C₄	—	2	4	no	—
338	C₃×C₂²⋊C₄	—	2	4	no	—
339	C₃×C₂²⋊C₄	—	2	8	no	—
340	C₃×C₂²⋊C₄	—	2	4	no	—
341	C₃×C₂²⋊C₄	—	4	4	no	—
342	C₃×C₂²⋊C₄	—	4	4	no	—
343	C₃×C₂²⋊C₄	—	4	4	no	—
344	C₃×C₂²⋊C₄	—	4	2	no	—
345	C₃×C₂²⋊C₄	—	4	4	no	—
346	C₃×C₂²⋊C₄	—	4	4	no	—
347	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
348	C₃×C₄²	—	2	4	no	—
349	C₃×C₄²	—	2	4	no	—
350	C₃×C₄²	—	4	2	no	—
351	C₃×C₄²	—	4	4	no	—
352	C₃×C₄²	C₂×D₄	1	4	yes	—
353	C₂⁵	C₂³×C₃	1	2	yes	—
354	C₂×#41	—	2	4	no	—
355	C₂×#41	—	2	8	no	—
356	C₂²×Q₈	—	2	8	no	—
357	C₂²×Q₈	—	4	8	no	—
358	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
360	C₂²×Q₈	C₂³×C₃	1	4	yes	—
361	C₂²×Q₈	C₂³×C₃	1	2	yes	—
362	C₂²×D₄	—	2	4	no	—
363	C₂²×D₄	—	2	8	no	—
364	C₂²×D₄	C₂³×C₃	1	2	yes	—
365	C₂²×D₄	C₂³×C₃	1	2	yes	—
366	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
367	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₃	1	2	yes	—
369	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₃	1	2	yes	—
371	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₃	1	4	yes	—
374	C₂³×C₄	C₂³×C₃	1	4	yes	—
375	C₂³×C₄	C₂³×C₃	1	2	yes	—
376	C₄⋊Q₈	—	2	8	no	—
377	C₄⋊Q₈	—	2	4	no	—
378	#124	—	2	4	no	—
379	#124	—	4	8	no	—
380	#123	—	2	8	no	—
381	C₂²⋊Q₈	—	2	8	no	—
382	C₂²⋊Q₈	—	2	4	no	—
383	C₂²⋊Q₈	—	2	16	no	—
384	#121	—	2	8	no	—
385	#121	—	2	4	no	—
386	#120	—	2	8	no	—
387	C₄×Q₈	—	2	4	no	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	8	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	C₃×D₄	1	8	yes	—
392	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	2	8	no	—
402	C₂×C₂²⋊C₄	—	4	8	no	—
403	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₄²	C₂³×C₃	1	2	yes	—
423	C₂×C₄²	C₂³×C₃	1	2	yes	—
424	C₂×C₄²	C₂³×C₃	1	4	yes	—
425	C₂×C₄²	C₂³×C₃	1	2	yes	—
426	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
427	#95	C₂³×C₃	1	1	yes	characteristic
428	#95	C₂³×C₃	1	2	yes	—
429	#95	C₂³×C₃	1	2	yes	—
430	#95	C₂³×C₃	1	4	yes	—
431	#95	C₂³×C₃	1	4	yes	—
432	#95	C₂³×C₃	1	4	yes	—
433	#95	C₂³×C₃	1	4	yes	—
434	#95	C₂³×C₃	1	1	yes	characteristic
435	#95	C₂³×C₃	1	2	yes	—
436	#95	C₂³×C₃	1	2	yes	—
437	#95	C₂³×C₃	1	2	yes	—
438	#95	C₂³×C₃	1	2	yes	—
439	#95	C₂³×C₃	1	4	yes	—
440	#95	C₂³×C₃	1	4	yes	—
441	#95	C₂³×C₃	1	4	yes	—
442	C₂³×C₃	—	2	4	no	—
443	C₂³×C₃	—	2	2	no	—
444	C₂³×C₃	—	2	2	no	—
445	C₂³×C₃	—	2	1	no	—
446	C₂³×C₃	—	2	2	no	—
447	C₂³×C₃	—	2	2	no	—
448	C₂³×C₃	—	2	1	no	—
449	C₂³×C₃	—	2	2	no	—
450	C₂³×C₃	—	2	1	no	—
451	C₂³×C₃	—	2	2	no	—
452	C₂³×C₃	—	2	4	no	—
453	C₂³×C₃	—	2	2	no	—
454	C₂³×C₃	—	2	4	no	—
455	C₂³×C₃	—	2	1	no	—
456	C₂³×C₃	—	2	2	no	—
457	C₂³×C₃	—	2	1	no	—
458	C₂³×C₃	—	2	2	no	—
459	C₂³×C₃	—	4	8	no	—
460	C₂³×C₃	—	4	16	no	—
461	C₂³×C₃	—	4	8	no	—
462	C₂³×C₃	—	8	4	no	—
463	C₂³×C₃	—	8	8	no	—
464	C₂³×C₃	C₂²×D₄	1	4	yes	—
465	C₂³×C₃	C₂×#41	1	8	yes	—
466	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
467	C₂³×C₃	C₂⁵	1	1	yes	characteristic
468	C₃×Q₈	—	2	8	no	—
469	C₃×Q₈	—	4	16	no	—
470	C₃×Q₈	—	4	8	no	—
471	C₃×Q₈	—	4	4	no	—
472	C₃×D₄	—	4	4	no	—
473	C₃×D₄	—	4	8	no	—
474	C₃×D₄	—	4	8	no	—
475	C₃×D₄	—	4	4	no	—
476	C₃×D₄	—	8	4	no	—
477	C₃×D₄	#124	1	16	yes	complemented
478	C₂×C₃×C₄	—	2	2	no	—
479	C₂×C₃×C₄	—	2	4	no	—
480	C₂×C₃×C₄	—	2	2	no	—
481	C₂×C₃×C₄	—	2	2	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	2	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	2	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	4	no	—
489	C₂×C₃×C₄	—	2	2	no	—
490	C₂×C₃×C₄	—	2	2	no	—
491	C₂×C₃×C₄	—	2	4	no	—
492	C₂×C₃×C₄	—	2	2	no	—
493	C₂×C₃×C₄	—	2	2	no	—
494	C₂×C₃×C₄	—	2	4	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	4	no	—
497	C₂×C₃×C₄	—	2	2	no	—
498	C₂×C₃×C₄	—	2	4	no	—
499	C₂×C₃×C₄	—	2	4	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	2	no	—
502	C₂×C₃×C₄	—	2	4	no	—
503	C₂×C₃×C₄	—	2	2	no	—
504	C₂×C₃×C₄	—	2	2	no	—
505	C₂×C₃×C₄	—	4	8	no	—
506	C₂×C₃×C₄	—	4	16	no	—
507	C₂×C₃×C₄	—	4	8	no	—
508	C₂×C₃×C₄	—	4	4	no	—
509	C₂×C₃×C₄	—	4	4	no	—
510	C₂×C₃×C₄	—	8	8	no	—
511	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
512	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
513	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
514	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
515	C₂×C₃×C₄	C₂×#41	1	4	yes	—
516	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
517	C₂⁴	—	2	4	no	—
518	C₂⁴	—	2	4	no	—
519	C₂⁴	—	2	8	no	—
520	C₂⁴	—	4	4	no	—
521	C₂⁴	—	4	2	no	—
522	C₂⁴	C₂⁴×C₃	1	2	yes	—
523	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
524	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
525	C₂⁴	C₂⁴×C₃	1	2	yes	—
526	#41	—	4	16	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	8	no	—
530	C₂×Q₈	—	2	4	no	—
531	C₂×Q₈	—	2	4	no	—
532	C₂×Q₈	—	2	4	no	—
533	C₂×Q₈	—	2	8	no	—
534	C₂×Q₈	—	4	4	no	—
535	C₂×Q₈	—	4	4	no	—
536	C₂×Q₈	—	4	32	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	8	no	—
540	C₂×D₄	—	2	8	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	4	1	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	16	no	—
549	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
550	C₂×D₄	C₃×#41	1	8	yes	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	8	no	—
553	C₂²×C₄	—	2	8	no	—
554	C₂²×C₄	—	2	8	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	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	C₂×C₃×D₄	1	8	yes	—
565	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
571	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
587	C₂²⋊C₄	—	2	8	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	8	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	4	4	no	—
600	C₂²⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	—	4	4	no	—
602	C₂²⋊C₄	—	4	4	no	—
603	C₂²⋊C₄	—	4	4	no	—
604	C₂²⋊C₄	—	4	2	no	—
605	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	4	4	no	—
609	C₄²	—	4	2	no	—
610	C₄²	C₂×C₃×D₄	1	4	yes	—
611	C₂²×C₃	—	2	4	no	—
612	C₂²×C₃	—	2	4	no	—
613	C₂²×C₃	—	2	8	no	—
614	C₂²×C₃	—	2	8	no	—
615	C₂²×C₃	—	2	2	no	—
616	C₂²×C₃	—	2	4	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	—	4	1	no	—
619	C₂²×C₃	—	4	2	no	—
620	C₂²×C₃	—	4	1	no	—
621	C₂²×C₃	—	4	2	no	—
622	C₂²×C₃	—	4	1	no	—
623	C₂²×C₃	—	4	2	no	—
624	C₂²×C₃	—	4	1	no	—
625	C₂²×C₃	—	4	2	no	—
626	C₂²×C₃	—	4	2	no	—
627	C₂²×C₃	—	4	4	no	—
628	C₂²×C₃	—	4	2	no	—
629	C₂²×C₃	—	4	4	no	—
630	C₂²×C₃	—	8	16	no	—
631	C₂²×C₃	C₂×#124	1	8	yes	—
632	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
633	C₂²×C₃	C₂²×#41	1	2	yes	—
634	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
635	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
636	C₂²×C₃	#585	1	1	yes	characteristic
637	C₃×C₄	—	2	2	no	—
638	C₃×C₄	—	2	4	no	—
639	C₃×C₄	—	2	4	no	—
640	C₃×C₄	—	2	2	no	—
641	C₃×C₄	—	4	1	no	—
642	C₃×C₄	—	4	1	no	—
643	C₃×C₄	—	4	2	no	—
644	C₃×C₄	—	4	4	no	—
645	C₃×C₄	—	4	2	no	—
646	C₃×C₄	—	4	4	no	—
647	C₃×C₄	—	4	2	no	—
648	C₃×C₄	—	4	2	no	—
649	C₃×C₄	C₂×#124	1	4	yes	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	4	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	4	8	no	—
668	C₂³	—	4	16	no	—
669	C₂³	—	4	8	no	—
670	C₂³	—	8	4	no	—
671	C₂³	—	8	8	no	—
672	C₂³	C₂²×C₃×D₄	1	4	yes	—
673	C₂³	C₂×C₃×#41	1	8	yes	—
674	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
675	C₂³	C₂⁵×C₃	1	1	yes	characteristic
676	Q₈	—	2	8	no	—
677	Q₈	—	4	16	no	—
678	Q₈	—	4	8	no	—
679	Q₈	—	4	4	no	—
680	D₄	—	4	4	no	—
681	D₄	—	4	8	no	—
682	D₄	—	4	8	no	—
683	D₄	—	4	4	no	—
684	D₄	—	8	4	no	—
685	D₄	C₃×#124	1	16	yes	complemented
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	16	no	—
715	C₂×C₄	—	4	8	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	8	8	no	—
719	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
720	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
721	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
722	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
723	C₂×C₄	C₂×C₃×#41	1	4	yes	—
724	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
725	C₂×C₃	—	2	8	no	—
726	C₂×C₃	—	4	2	no	—
727	C₂×C₃	—	8	1	no	—
728	C₂×C₃	—	8	2	no	—
729	C₂×C₃	C₂²×#124	1	1	yes	characteristic
730	C₂×C₃	#3484	1	1	yes	characteristic
731	C₂×C₃	#3489	1	1	yes	characteristic
732	C₂×C₃	#3514	1	2	yes	—
733	C₂×C₃	#3520	1	2	yes	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	8	no	—
737	C₂²	—	2	8	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	8	16	no	—
754	C₂²	C₂×C₃×#124	1	8	yes	—
755	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
756	C₂²	C₂²×C₃×#41	1	2	yes	—
757	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
758	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
759	C₂²	C₃×#585	1	1	yes	characteristic
760	C₄	—	2	2	no	—
761	C₄	—	2	4	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	2	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	4	no	—
771	C₄	—	4	2	no	—
772	C₄	C₂×C₃×#124	1	4	yes	—
773	C₃	#35939	1	1	yes	characteristic, direct product factor, Sylow
774	C₂	—	2	8	no	—
775	C₂	—	4	2	no	—
776	C₂	—	8	2	no	—
777	C₂	—	8	1	no	—
778	C₂	C₂²×C₃×#124	1	1	yes	characteristic
779	C₂	C₃×#3484	1	1	yes	characteristic
780	C₂	C₃×#3489	1	1	yes	characteristic
781	C₂	C₃×#3514	1	2	yes	—
782	C₂	C₃×#3520	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#546	C₂
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×D₄×Q₈	C₂	semidirect
3. C₃×#2640	C₂	semidirect
4. C₃×#2639	C₂	semidirect
5. C₃×#2592	C₂	semidirect
6. C₃×#2563	C₂	semidirect
7. C₃×#2561	C₂	semidirect
8. C₃×#2492	C₂	semidirect
9. C₃×#2491	C₂	semidirect
10. C₃×#2488	C₂	semidirect
11. C₃×#2472	C₂	semidirect
12. C₃×#2436	C₂	semidirect
13. C₃×#2398	C₂	semidirect
14. C₂×C₃×#393	C₂	semidirect
15. C₃×#2339	C₂	semidirect
16. C₃×D₄×C₂²⋊C₄	C₂	semidirect
17. C₃×#2275	C₂	semidirect
18. #35939	C₃	direct (N × H)
20. C₂³×C₃×Q₈	C₂²	semidirect
24. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₃×#124	C₂²	semidirect
30. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
35. C₂×C₃×C₄×Q₈	C₂²	semidirect
42. C₃×#400	C₂²	semidirect
43. C₃×#400	C₂²	semidirect
45. C₃×#397	C₂²	semidirect
46. C₃×#397	C₂²	semidirect
47. C₃×#397	C₂²	semidirect
49. C₃×#394	C₂²	semidirect
53. C₃×#393	C₂²	semidirect
54. C₃×#393	C₂²	semidirect
55. C₃×#393	C₂²	semidirect
56. C₃×#393	C₂²	semidirect
57. C₃×#393	C₂²	semidirect
58. C₃×#393	C₂²	semidirect
59. C₃×#391	C₂²	semidirect
60. C₃×#391	C₂²	semidirect
61. C₃×#391	C₂²	semidirect
66. C₃×#388	C₂²	semidirect
67. C₃×#388	C₂²	semidirect
70. C₃×#386	C₂²	semidirect
71. C₃×#386	C₂²	semidirect
72. C₃×#382	C₂²	semidirect
73. C₃×#381	C₂²	semidirect
75. C₃×#380	C₂²	semidirect
77. C₃×C₄×C₄⋊C₄	C₂²	semidirect
78. C₃×C₄×C₄⋊C₄	C₂²	semidirect
80. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
81. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
82. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
83. C₃×#376	C₂²	semidirect
84. C₂×C₃×#95	C₂²	semidirect
85. C₂×C₃×#95	C₂²	semidirect
86. C₂×D₄×Q₈	C₂×C₃	semidirect
88. #2640	C₂×C₃	semidirect
89. #2639	C₂×C₃	semidirect
90. #2592	C₂×C₃	semidirect
91. #2563	C₂×C₃	semidirect
92. #2561	C₂×C₃	semidirect
93. #2492	C₂×C₃	semidirect
94. #2491	C₂×C₃	semidirect
95. #2488	C₂×C₃	semidirect
96. #2472	C₂×C₃	semidirect
97. #2436	C₂×C₃	semidirect
98. #2398	C₂×C₃	semidirect
99. C₂×#393	C₂×C₃	semidirect
100. #2339	C₂×C₃	semidirect
101. D₄×C₂²⋊C₄	C₂×C₃	semidirect
102. #2275	C₂×C₃	semidirect
193. C₂³×Q₈	C₂²×C₃	semidirect
197. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
198. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
200. C₂×#124	C₂²×C₃	semidirect
203. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
204. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
208. C₂×C₄×Q₈	C₂²×C₃	semidirect
215. #400	C₂²×C₃	semidirect
216. #400	C₂²×C₃	semidirect
218. #397	C₂²×C₃	semidirect
219. #397	C₂²×C₃	semidirect
220. #397	C₂²×C₃	semidirect
222. #394	C₂²×C₃	semidirect
226. #393	C₂²×C₃	semidirect
227. #393	C₂²×C₃	semidirect
228. #393	C₂²×C₃	semidirect
229. #393	C₂²×C₃	semidirect
230. #393	C₂²×C₃	semidirect
231. #393	C₂²×C₃	semidirect
232. #391	C₂²×C₃	semidirect
233. #391	C₂²×C₃	semidirect
234. #391	C₂²×C₃	semidirect
239. #388	C₂²×C₃	semidirect
240. #388	C₂²×C₃	semidirect
243. #386	C₂²×C₃	semidirect
244. #386	C₂²×C₃	semidirect
245. #382	C₂²×C₃	semidirect
246. #381	C₂²×C₃	semidirect
248. #380	C₂²×C₃	semidirect
250. C₄×C₄⋊C₄	C₂²×C₃	semidirect
251. C₄×C₄⋊C₄	C₂²×C₃	semidirect
253. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
254. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
255. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
256. #376	C₂²×C₃	semidirect
257. C₂×#95	C₂²×C₃	semidirect
258. C₂×#95	C₂²×C₃	semidirect
477. C₃×D₄	#124	semidirect
685. D₄	C₃×#124	semidirect
773. C₃	#35939	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×D₄×Q₈	2
C₂×C₃×#546	2
C₃×#2640	2
C₃×#2639	2
C₃×#2592	2
C₃×#2563	2
C₃×#2561	2
C₃×#2492	2
C₃×#2491	2
C₃×#2488	2
C₃×#2472	2
C₃×#2436	2
C₃×#2398	2
C₂×C₃×#393	2
C₃×#2339	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2275	2
#35939	3

Subgroups — C3×#35939 #10654546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35939 #10654546