Subgroups — C₃×#62905 #10681512

Order 768.

7326 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3560	C₂	1	12	yes	maximal, complemented
2	C₃×#3559	C₂	1	6	yes	maximal, complemented
3	C₃×#3537	C₂	1	6	yes	maximal, complemented
4	C₃×#3534	C₂	1	12	yes	maximal, complemented
5	C₃×#3519	C₂	1	6	yes	maximal, complemented
6	C₃×#3496	C₂	1	3	yes	maximal, complemented
7	C₃×#3496	C₂	1	6	yes	maximal, complemented
8	C₃×#3494	C₂	1	6	yes	maximal, complemented
9	C₂×C₃×#553	C₂	1	3	yes	maximal, complemented
10	C₃×#3459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3459	C₂	1	2	yes	maximal, complemented
12	#62905	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×H(5,𝔽₂)	C₂²	1	6	yes	complemented
14	C₃×#563	C₂²	1	12	yes	complemented
15	C₃×#562	C₂²	1	12	yes	complemented
16	C₃×#560	C₂²	1	24	yes	complemented
17	C₃×#555	C₂²	1	6	yes	complemented
18	C₃×#554	C₂²	1	6	yes	complemented
19	C₃×#553	C₂²	1	12	yes	complemented
20	C₃×#553	C₂²	1	24	yes	complemented
21	C₃×#553	C₂²	1	12	yes	complemented
22	C₃×#553	C₂²	1	12	yes	complemented
23	C₃×#553	C₂²	1	12	yes	complemented
24	C₃×#551	C₂²	1	24	yes	complemented
25	C₃×#550	C₂²	1	2	yes	complemented
26	C₃×#547	C₂²	1	12	yes	complemented
27	C₃×#547	C₂²	1	24	yes	complemented
28	C₃×#546	C₂²	1	24	yes	complemented
29	C₃×#546	C₂²	1	24	yes	complemented
30	C₃×#546	C₂²	1	24	yes	complemented
31	C₃×#546	C₂²	1	12	yes	complemented
32	C₃×D₄²	C₂²	1	12	yes	complemented
33	C₃×D₄²	C₂²	1	24	yes	complemented
34	C₃×D₄²	C₂²	1	6	yes	complemented
35	C₃×#544	C₂²	1	6	yes	complemented
36	C₃×#543	C₂²	1	1	yes	characteristic, complemented
37	C₃×#542	C₂²	1	12	yes	complemented
38	C₃×#540	C₂²	1	12	yes	complemented
39	C₃×#540	C₂²	1	12	yes	complemented
40	C₃×#539	C₂²	1	12	yes	complemented
41	C₃×#539	C₂²	1	6	yes	complemented
42	C₃×#539	C₂²	1	24	yes	complemented
43	C₃×#538	C₂²	1	6	yes	complemented
44	C₃×#538	C₂²	1	12	yes	complemented
45	C₃×#538	C₂²	1	24	yes	complemented
46	C₃×#538	C₂²	1	12	yes	complemented
47	C₃×#537	C₂²	1	12	yes	complemented
48	C₃×#537	C₂²	1	6	yes	complemented
49	C₃×#535	C₂²	1	6	yes	complemented
50	C₃×#534	C₂²	1	3	yes	complemented
51	C₃×#534	C₂²	1	6	yes	complemented
52	C₃×#534	C₂²	1	6	yes	complemented
53	C₃×#534	C₂²	1	12	yes	complemented
54	C₃×#534	C₂²	1	12	yes	complemented
55	C₃×#532	C₂²	1	12	yes	complemented
56	C₃×#532	C₂²	1	6	yes	complemented
57	C₃×#529	C₂²	1	12	yes	complemented
58	C₃×#529	C₂²	1	6	yes	complemented
59	C₂×C₃×#126	C₂²	1	6	yes	complemented
60	C₂×C₃×#125	C₂²	1	3	yes	complemented
61	C₃×#525	C₂²	1	6	yes	complemented
62	C₃×#525	C₂²	1	12	yes	complemented
63	C₂×C₃×#123	C₂²	1	6	yes	complemented
64	C₂×C₃×#121	C₂²	1	6	yes	complemented
65	C₂×C₃×#121	C₂²	1	3	yes	complemented
66	C₂×C₃×#121	C₂²	1	3	yes	complemented
67	C₂×C₃×#121	C₂²	1	6	yes	complemented
68	C₂×C₃×#121	C₂²	1	12	yes	complemented
69	C₃×#520	C₂²	1	2	yes	complemented
70	C₃×#518	C₂²	1	6	yes	complemented
71	C₂×C₃×C₄×D₄	C₂²	1	6	yes	complemented
72	C₂×C₃×C₄×D₄	C₂²	1	3	yes	complemented
73	C₂×C₃×C₄×D₄	C₂²	1	3	yes	complemented
74	C₂×C₃×#117	C₂²	1	3	yes	complemented
75	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
76	#3560	C₂×C₃	1	12	yes	complemented
77	#3559	C₂×C₃	1	6	yes	complemented
78	#3537	C₂×C₃	1	6	yes	complemented
79	#3534	C₂×C₃	1	12	yes	complemented
80	#3519	C₂×C₃	1	6	yes	complemented
81	#3496	C₂×C₃	1	3	yes	complemented
82	#3496	C₂×C₃	1	6	yes	complemented
83	#3494	C₂×C₃	1	6	yes	complemented
84	C₂×#553	C₂×C₃	1	3	yes	complemented
85	#3459	C₂×C₃	1	1	yes	characteristic, complemented
86	#3459	C₂×C₃	1	2	yes	complemented
87	C₃×H(5,𝔽₂)	—	4	24	no	—
88	C₂×C₃×#41	C₂³	1	24	yes	—
89	C₂×C₃×#41	C₂³	1	12	yes	—
90	C₂×C₃×#41	C₂³	1	2	yes	—
91	C₂×C₃×#41	C₂³	1	4	yes	—
92	C₂²×C₃×D₄	C₂³	1	6	yes	—
93	C₂²×C₃×D₄	C₂³	1	3	yes	—
94	C₂²×C₃×D₄	C₂³	1	12	yes	—
95	C₂²×C₃×D₄	C₂³	1	24	yes	—
96	C₂²×C₃×D₄	C₂³	1	3	yes	—
97	C₂²×C₃×D₄	C₂³	1	6	yes	—
98	C₂²×C₃×D₄	C₂³	1	6	yes	—
99	C₂²×C₃×D₄	C₂³	1	12	yes	—
100	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
101	C₂³×C₃×C₄	C₂³	1	3	yes	—
102	C₂³×C₃×C₄	C₂³	1	2	yes	—
103	C₂³×C₃×C₄	C₂³	1	6	yes	—
104	C₃×C₄⋊Q₈	C₂³	1	12	yes	—
105	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
106	C₃×#127	C₂³	1	12	yes	—
107	C₃×#127	C₂³	1	6	yes	—
108	C₃×#126	C₂³	1	24	yes	—
109	C₃×#126	C₂³	1	24	yes	—
110	C₃×#126	C₂³	1	24	yes	—
111	C₃×#126	C₂³	1	12	yes	—
112	C₃×#125	C₂³	1	12	yes	—
113	C₃×#125	C₂³	1	6	yes	—
114	C₃×#125	C₂³	1	12	yes	—
115	C₃×#125	C₂³	1	12	yes	—
116	C₃×#124	C₂³	1	6	yes	—
117	C₃×#124	C₂³	1	12	yes	—
118	C₃×#124	C₂³	1	12	yes	—
119	C₃×#124	C₂³	1	24	yes	—
120	C₃×#123	C₂³	1	12	yes	—
121	C₃×#123	C₂³	1	24	yes	—
122	C₃×#123	C₂³	1	24	yes	—
123	C₃×#123	C₂³	1	24	yes	—
124	C₃×#123	C₂³	1	24	yes	—
125	C₃×#123	C₂³	1	24	yes	—
126	C₃×#123	C₂³	1	24	yes	—
127	C₃×#123	C₂³	1	12	yes	—
128	C₃×#123	C₂³	1	24	yes	—
129	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
130	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
131	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
132	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
133	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
134	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
135	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
136	C₃×#121	C₂³	1	12	yes	—
137	C₃×#121	C₂³	1	12	yes	—
138	C₃×#121	C₂³	1	12	yes	—
139	C₃×#121	C₂³	1	24	yes	—
140	C₃×#121	C₂³	1	24	yes	—
141	C₃×#121	C₂³	1	24	yes	—
142	C₃×#121	C₂³	1	24	yes	—
143	C₃×#121	C₂³	1	6	yes	—
144	C₃×#121	C₂³	1	12	yes	—
145	C₃×#121	C₂³	1	24	yes	—
146	C₃×#121	C₂³	1	12	yes	—
147	C₃×#121	C₂³	1	12	yes	—
148	C₃×#121	C₂³	1	24	yes	—
149	C₃×#121	C₂³	1	12	yes	—
150	C₃×#121	C₂³	1	12	yes	—
151	C₃×#121	C₂³	1	12	yes	—
152	C₃×#121	C₂³	1	12	yes	—
153	C₃×#121	C₂³	1	12	yes	—
154	C₃×#121	C₂³	1	6	yes	—
155	C₃×#121	C₂³	1	6	yes	—
156	C₃×#120	C₂³	1	24	yes	—
157	C₃×#120	C₂³	1	24	yes	—
158	C₃×#120	C₂³	1	24	yes	—
159	C₃×#120	C₂³	1	12	yes	—
160	C₃×#120	C₂³	1	24	yes	—
161	C₃×C₄×Q₈	C₂³	1	4	yes	—
162	C₃×C₄×Q₈	C₂³	1	2	yes	—
163	C₃×C₄×D₄	C₂³	1	6	yes	—
164	C₃×C₄×D₄	C₂³	1	12	yes	—
165	C₃×C₄×D₄	C₂³	1	24	yes	—
166	C₃×C₄×D₄	C₂³	1	12	yes	—
167	C₃×C₄×D₄	C₂³	1	24	yes	—
168	C₃×C₄×D₄	C₂³	1	12	yes	—
169	C₃×C₄×D₄	C₂³	1	6	yes	—
170	C₃×C₄×D₄	C₂³	1	12	yes	—
171	C₃×C₄×D₄	C₂³	1	12	yes	—
172	C₃×C₄×D₄	C₂³	1	12	yes	—
173	C₃×C₄×D₄	C₂³	1	12	yes	—
174	C₃×C₄×D₄	C₂³	1	6	yes	—
175	C₃×C₄×D₄	C₂³	1	24	yes	—
176	C₃×C₄×D₄	C₂³	1	12	yes	—
177	C₃×#117	C₂³	1	6	yes	—
178	C₃×#117	C₂³	1	6	yes	—
179	C₃×#117	C₂³	1	12	yes	—
180	C₃×#117	C₂³	1	6	yes	—
181	C₃×#117	C₂³	1	12	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
185	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	3	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	3	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	24	yes	—
197	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
199	C₂×C₃×C₄²	C₂³	1	6	yes	—
200	C₂×C₃×C₄²	C₂³	1	3	yes	—
201	C₂×H(5,𝔽₂)	C₂²×C₃	1	6	yes	complemented
202	#563	C₂²×C₃	1	12	yes	complemented
203	#562	C₂²×C₃	1	12	yes	complemented
204	#560	C₂²×C₃	1	24	yes	complemented
205	#555	C₂²×C₃	1	6	yes	complemented
206	#554	C₂²×C₃	1	6	yes	complemented
207	#553	C₂²×C₃	1	12	yes	complemented
208	#553	C₂²×C₃	1	24	yes	complemented
209	#553	C₂²×C₃	1	12	yes	complemented
210	#553	C₂²×C₃	1	12	yes	complemented
211	#553	C₂²×C₃	1	12	yes	complemented
212	#551	C₂²×C₃	1	24	yes	complemented
213	#550	C₂²×C₃	1	2	yes	complemented
214	#547	C₂²×C₃	1	12	yes	complemented
215	#547	C₂²×C₃	1	24	yes	complemented
216	#546	C₂²×C₃	1	24	yes	complemented
217	#546	C₂²×C₃	1	24	yes	complemented
218	#546	C₂²×C₃	1	24	yes	complemented
219	#546	C₂²×C₃	1	12	yes	complemented
220	D₄²	C₂²×C₃	1	12	yes	complemented
221	D₄²	C₂²×C₃	1	24	yes	complemented
222	D₄²	C₂²×C₃	1	6	yes	complemented
223	#544	C₂²×C₃	1	6	yes	complemented
224	#543	C₂²×C₃	1	1	yes	characteristic, complemented
225	#542	C₂²×C₃	1	12	yes	complemented
226	#540	C₂²×C₃	1	12	yes	complemented
227	#540	C₂²×C₃	1	12	yes	complemented
228	#539	C₂²×C₃	1	12	yes	complemented
229	#539	C₂²×C₃	1	6	yes	complemented
230	#539	C₂²×C₃	1	24	yes	complemented
231	#538	C₂²×C₃	1	6	yes	complemented
232	#538	C₂²×C₃	1	12	yes	complemented
233	#538	C₂²×C₃	1	24	yes	complemented
234	#538	C₂²×C₃	1	12	yes	complemented
235	#537	C₂²×C₃	1	12	yes	complemented
236	#537	C₂²×C₃	1	6	yes	complemented
237	#535	C₂²×C₃	1	6	yes	complemented
238	#534	C₂²×C₃	1	3	yes	complemented
239	#534	C₂²×C₃	1	6	yes	complemented
240	#534	C₂²×C₃	1	6	yes	complemented
241	#534	C₂²×C₃	1	12	yes	complemented
242	#534	C₂²×C₃	1	12	yes	complemented
243	#532	C₂²×C₃	1	12	yes	complemented
244	#532	C₂²×C₃	1	6	yes	complemented
245	#529	C₂²×C₃	1	12	yes	complemented
246	#529	C₂²×C₃	1	6	yes	complemented
247	C₂×#126	C₂²×C₃	1	6	yes	complemented
248	C₂×#125	C₂²×C₃	1	3	yes	complemented
249	#525	C₂²×C₃	1	6	yes	complemented
250	#525	C₂²×C₃	1	12	yes	complemented
251	C₂×#123	C₂²×C₃	1	6	yes	complemented
252	C₂×#121	C₂²×C₃	1	6	yes	complemented
253	C₂×#121	C₂²×C₃	1	3	yes	complemented
254	C₂×#121	C₂²×C₃	1	3	yes	complemented
255	C₂×#121	C₂²×C₃	1	6	yes	complemented
256	C₂×#121	C₂²×C₃	1	12	yes	complemented
257	#520	C₂²×C₃	1	2	yes	complemented
258	#518	C₂²×C₃	1	6	yes	complemented
259	C₂×C₄×D₄	C₂²×C₃	1	6	yes	complemented
260	C₂×C₄×D₄	C₂²×C₃	1	3	yes	complemented
261	C₂×C₄×D₄	C₂²×C₃	1	3	yes	complemented
262	C₂×#117	C₂²×C₃	1	3	yes	complemented
263	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
264	C₂⁴×C₃	C₂⁴	1	3	yes	—
265	C₂⁴×C₃	C₂⁴	1	6	yes	—
266	C₂⁴×C₃	C₂⁴	1	12	yes	—
267	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
268	C₃×#41	—	4	4	no	—
269	C₃×#41	—	4	48	no	—
270	C₃×#41	—	4	24	no	—
271	C₃×#41	—	8	4	no	—
272	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
273	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
274	C₂×C₃×Q₈	C₂⁴	1	12	yes	—
275	C₂×C₃×D₄	—	2	24	no	—
276	C₂×C₃×D₄	—	2	12	no	—
277	C₂×C₃×D₄	—	4	6	no	—
278	C₂×C₃×D₄	—	4	12	no	—
279	C₂×C₃×D₄	—	4	24	no	—
280	C₂×C₃×D₄	—	4	48	no	—
281	C₂×C₃×D₄	—	8	6	no	—
282	C₂×C₃×D₄	—	8	12	no	—
283	C₂×C₃×D₄	C₂⁴	1	6	yes	—
284	C₂×C₃×D₄	C₂⁴	1	12	yes	—
285	C₂×C₃×D₄	C₂⁴	1	24	yes	—
286	C₂×C₃×D₄	C₂⁴	1	6	yes	—
287	C₂×C₃×D₄	C₂⁴	1	6	yes	—
288	C₂×C₃×D₄	C₂⁴	1	12	yes	—
289	C₂×C₃×D₄	C₂⁴	1	12	yes	—
290	C₂×C₃×D₄	C₂⁴	1	6	yes	—
291	C₂×C₃×D₄	C₂⁴	1	24	yes	—
292	C₂×C₃×D₄	C₂⁴	1	24	yes	—
293	C₂×C₃×D₄	C₂⁴	1	12	yes	—
294	C₂²×C₃×C₄	—	4	2	no	—
295	C₂²×C₃×C₄	—	4	6	no	—
296	C₂²×C₃×C₄	—	8	2	no	—
297	C₂²×C₃×C₄	—	8	6	no	—
298	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
299	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
300	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
301	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
302	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
303	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
304	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
305	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
306	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
307	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
308	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
309	C₂²×C₃×C₄	C₂⁴	1	24	yes	—
310	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
311	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
312	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
313	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
314	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
315	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
316	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
317	C₃×C₄⋊C₄	C₂⁴	1	24	yes	—
318	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
319	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
320	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
321	C₃×C₄⋊C₄	C₂⁴	1	24	yes	—
322	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
323	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
324	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
325	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
326	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
327	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
328	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
329	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
330	C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
331	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
332	C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
333	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
334	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
335	C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
336	C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
337	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
338	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
339	C₃×C₄²	C₂⁴	1	12	yes	—
340	C₃×C₄²	C₂⁴	1	6	yes	—
341	C₃×C₄²	C₂⁴	1	12	yes	—
342	C₃×C₄²	C₂⁴	1	6	yes	—
343	H(5,𝔽₂)	—	4	24	no	—
344	C₂×#41	C₂³×C₃	1	2	yes	—
345	C₂×#41	C₂³×C₃	1	24	yes	—
346	C₂×#41	C₂³×C₃	1	12	yes	—
347	C₂×#41	C₂³×C₃	1	4	yes	—
348	C₂²×D₄	C₂³×C₃	1	6	yes	—
349	C₂²×D₄	C₂³×C₃	1	3	yes	—
350	C₂²×D₄	C₂³×C₃	1	3	yes	—
351	C₂²×D₄	C₂³×C₃	1	6	yes	—
352	C₂²×D₄	C₂³×C₃	1	12	yes	—
353	C₂²×D₄	C₂³×C₃	1	24	yes	—
354	C₂²×D₄	C₂³×C₃	1	6	yes	—
355	C₂²×D₄	C₂³×C₃	1	12	yes	—
356	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₃	1	3	yes	—
358	C₂³×C₄	C₂³×C₃	1	2	yes	—
359	C₂³×C₄	C₂³×C₃	1	6	yes	—
360	C₄⋊Q₈	C₂³×C₃	1	12	yes	—
361	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
362	#127	C₂³×C₃	1	12	yes	—
363	#127	C₂³×C₃	1	6	yes	—
364	#126	C₂³×C₃	1	24	yes	—
365	#126	C₂³×C₃	1	24	yes	—
366	#126	C₂³×C₃	1	12	yes	—
367	#126	C₂³×C₃	1	24	yes	—
368	#125	C₂³×C₃	1	12	yes	—
369	#125	C₂³×C₃	1	12	yes	—
370	#125	C₂³×C₃	1	12	yes	—
371	#125	C₂³×C₃	1	6	yes	—
372	#124	C₂³×C₃	1	12	yes	—
373	#124	C₂³×C₃	1	6	yes	—
374	#124	C₂³×C₃	1	12	yes	—
375	#124	C₂³×C₃	1	24	yes	—
376	#123	C₂³×C₃	1	24	yes	—
377	#123	C₂³×C₃	1	24	yes	—
378	#123	C₂³×C₃	1	24	yes	—
379	#123	C₂³×C₃	1	12	yes	—
380	#123	C₂³×C₃	1	12	yes	—
381	#123	C₂³×C₃	1	24	yes	—
382	#123	C₂³×C₃	1	24	yes	—
383	#123	C₂³×C₃	1	24	yes	—
384	#123	C₂³×C₃	1	24	yes	—
385	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
386	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
387	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
388	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
389	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
390	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
391	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
392	#121	C₂³×C₃	1	6	yes	—
393	#121	C₂³×C₃	1	12	yes	—
394	#121	C₂³×C₃	1	24	yes	—
395	#121	C₂³×C₃	1	12	yes	—
396	#121	C₂³×C₃	1	12	yes	—
397	#121	C₂³×C₃	1	24	yes	—
398	#121	C₂³×C₃	1	12	yes	—
399	#121	C₂³×C₃	1	12	yes	—
400	#121	C₂³×C₃	1	12	yes	—
401	#121	C₂³×C₃	1	12	yes	—
402	#121	C₂³×C₃	1	12	yes	—
403	#121	C₂³×C₃	1	24	yes	—
404	#121	C₂³×C₃	1	12	yes	—
405	#121	C₂³×C₃	1	12	yes	—
406	#121	C₂³×C₃	1	6	yes	—
407	#121	C₂³×C₃	1	6	yes	—
408	#121	C₂³×C₃	1	12	yes	—
409	#121	C₂³×C₃	1	24	yes	—
410	#121	C₂³×C₃	1	24	yes	—
411	#121	C₂³×C₃	1	24	yes	—
412	#120	C₂³×C₃	1	12	yes	—
413	#120	C₂³×C₃	1	24	yes	—
414	#120	C₂³×C₃	1	24	yes	—
415	#120	C₂³×C₃	1	24	yes	—
416	#120	C₂³×C₃	1	24	yes	—
417	C₄×Q₈	C₂³×C₃	1	4	yes	—
418	C₄×Q₈	C₂³×C₃	1	2	yes	—
419	C₄×D₄	C₂³×C₃	1	6	yes	—
420	C₄×D₄	C₂³×C₃	1	12	yes	—
421	C₄×D₄	C₂³×C₃	1	24	yes	—
422	C₄×D₄	C₂³×C₃	1	12	yes	—
423	C₄×D₄	C₂³×C₃	1	24	yes	—
424	C₄×D₄	C₂³×C₃	1	12	yes	—
425	C₄×D₄	C₂³×C₃	1	6	yes	—
426	C₄×D₄	C₂³×C₃	1	12	yes	—
427	C₄×D₄	C₂³×C₃	1	12	yes	—
428	C₄×D₄	C₂³×C₃	1	12	yes	—
429	C₄×D₄	C₂³×C₃	1	12	yes	—
430	C₄×D₄	C₂³×C₃	1	6	yes	—
431	C₄×D₄	C₂³×C₃	1	24	yes	—
432	C₄×D₄	C₂³×C₃	1	12	yes	—
433	#117	C₂³×C₃	1	6	yes	—
434	#117	C₂³×C₃	1	6	yes	—
435	#117	C₂³×C₃	1	12	yes	—
436	#117	C₂³×C₃	1	6	yes	—
437	#117	C₂³×C₃	1	12	yes	—
438	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
439	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
440	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
441	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
442	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
443	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
444	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₃	1	3	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₃	1	3	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₃	1	24	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
455	C₂×C₄²	C₂³×C₃	1	6	yes	—
456	C₂×C₄²	C₂³×C₃	1	3	yes	—
457	C₂³×C₃	—	2	6	no	—
458	C₂³×C₃	—	2	12	no	—
459	C₂³×C₃	—	4	1	no	—
460	C₂³×C₃	—	4	1	no	—
461	C₂³×C₃	—	4	3	no	—
462	C₂³×C₃	—	4	6	no	—
463	C₂³×C₃	—	4	6	no	—
464	C₂³×C₃	—	4	3	no	—
465	C₂³×C₃	—	4	12	no	—
466	C₂³×C₃	—	4	12	no	—
467	C₂³×C₃	—	4	12	no	—
468	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
469	C₂³×C₃	C₂⁵	1	6	yes	—
470	C₂³×C₃	C₂⁵	1	12	yes	—
471	C₂³×C₃	C₂⁵	1	3	yes	—
472	C₃×Q₈	—	4	2	no	—
473	C₃×Q₈	—	4	12	no	—
474	C₃×Q₈	—	4	2	no	—
475	C₃×D₄	—	2	24	no	—
476	C₃×D₄	—	2	48	no	—
477	C₃×D₄	—	2	12	no	—
478	C₃×D₄	—	4	24	no	—
479	C₃×D₄	—	4	12	no	—
480	C₃×D₄	—	4	6	no	—
481	C₃×D₄	—	4	12	no	—
482	C₃×D₄	—	4	24	no	—
483	C₃×D₄	—	4	6	no	—
484	C₃×D₄	—	4	12	no	—
485	C₃×D₄	—	4	6	no	—
486	C₂×C₃×C₄	—	2	12	no	—
487	C₂×C₃×C₄	—	2	6	no	—
488	C₂×C₃×C₄	—	2	6	no	—
489	C₂×C₃×C₄	—	2	12	no	—
490	C₂×C₃×C₄	—	4	3	no	—
491	C₂×C₃×C₄	—	4	6	no	—
492	C₂×C₃×C₄	—	4	3	no	—
493	C₂×C₃×C₄	—	4	6	no	—
494	C₂×C₃×C₄	—	4	3	no	—
495	C₂×C₃×C₄	—	4	6	no	—
496	C₂×C₃×C₄	—	4	12	no	—
497	C₂×C₃×C₄	—	4	12	no	—
498	C₂×C₃×C₄	—	4	24	no	—
499	C₂×C₃×C₄	—	4	12	no	—
500	C₂×C₃×C₄	C₂⁵	1	2	yes	—
501	C₂×C₃×C₄	C₂⁵	1	6	yes	—
502	C₂×C₃×C₄	C₂⁵	1	3	yes	—
503	C₂×C₃×C₄	C₂⁵	1	6	yes	—
504	C₂×C₃×C₄	C₂⁵	1	6	yes	—
505	C₂×C₃×C₄	C₂⁵	1	12	yes	—
506	C₂×C₃×C₄	C₂⁵	1	6	yes	—
507	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
508	C₂⁴	C₂⁴×C₃	1	3	yes	—
509	C₂⁴	C₂⁴×C₃	1	6	yes	—
510	C₂⁴	C₂⁴×C₃	1	12	yes	—
511	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
512	#41	—	4	4	no	—
513	#41	—	4	48	no	—
514	#41	—	4	24	no	—
515	#41	—	8	4	no	—
516	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
517	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
518	C₂×Q₈	C₂⁴×C₃	1	12	yes	—
519	C₂×D₄	—	2	24	no	—
520	C₂×D₄	—	2	12	no	—
521	C₂×D₄	—	4	6	no	—
522	C₂×D₄	—	4	12	no	—
523	C₂×D₄	—	4	24	no	—
524	C₂×D₄	—	4	48	no	—
525	C₂×D₄	—	8	6	no	—
526	C₂×D₄	—	8	12	no	—
527	C₂×D₄	C₂⁴×C₃	1	6	yes	—
528	C₂×D₄	C₂⁴×C₃	1	12	yes	—
529	C₂×D₄	C₂⁴×C₃	1	24	yes	—
530	C₂×D₄	C₂⁴×C₃	1	6	yes	—
531	C₂×D₄	C₂⁴×C₃	1	6	yes	—
532	C₂×D₄	C₂⁴×C₃	1	12	yes	—
533	C₂×D₄	C₂⁴×C₃	1	12	yes	—
534	C₂×D₄	C₂⁴×C₃	1	6	yes	—
535	C₂×D₄	C₂⁴×C₃	1	24	yes	—
536	C₂×D₄	C₂⁴×C₃	1	24	yes	—
537	C₂×D₄	C₂⁴×C₃	1	12	yes	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	6	no	—
540	C₂²×C₄	—	8	2	no	—
541	C₂²×C₄	—	8	6	no	—
542	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
543	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
544	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
545	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
546	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
547	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
548	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
549	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
550	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
551	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
552	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
553	C₂²×C₄	C₂⁴×C₃	1	24	yes	—
554	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
555	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
556	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
557	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
558	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
559	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
560	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
561	C₄⋊C₄	C₂⁴×C₃	1	24	yes	—
562	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
563	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
564	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
565	C₄⋊C₄	C₂⁴×C₃	1	24	yes	—
566	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
567	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
568	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
569	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
570	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
571	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
572	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
573	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
574	C₂²⋊C₄	C₂⁴×C₃	1	24	yes	—
575	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
576	C₂²⋊C₄	C₂⁴×C₃	1	24	yes	—
577	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
578	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
579	C₂²⋊C₄	C₂⁴×C₃	1	24	yes	—
580	C₂²⋊C₄	C₂⁴×C₃	1	24	yes	—
581	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
582	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
583	C₄²	C₂⁴×C₃	1	12	yes	—
584	C₄²	C₂⁴×C₃	1	6	yes	—
585	C₄²	C₂⁴×C₃	1	12	yes	—
586	C₄²	C₂⁴×C₃	1	6	yes	—
587	C₂²×C₃	—	2	3	no	—
588	C₂²×C₃	—	2	3	no	—
589	C₂²×C₃	—	2	6	no	—
590	C₂²×C₃	—	2	12	no	—
591	C₂²×C₃	—	2	6	no	—
592	C₂²×C₃	—	2	12	no	—
593	C₂²×C₃	—	2	12	no	—
594	C₂²×C₃	—	2	6	no	—
595	C₂²×C₃	—	4	4	no	—
596	C₂²×C₃	—	8	6	no	—
597	C₂²×C₃	—	8	12	no	—
598	C₂²×C₃	—	16	12	no	—
599	C₂²×C₃	C₂×H(5,𝔽₂)	1	6	yes	—
600	C₂²×C₃	C₂⁶	1	1	yes	characteristic
601	C₃×C₄	—	2	12	no	—
602	C₃×C₄	—	2	6	no	—
603	C₃×C₄	—	2	3	no	—
604	C₃×C₄	—	2	6	no	—
605	C₃×C₄	—	2	2	no	—
606	C₃×C₄	—	2	6	no	—
607	C₃×C₄	—	2	6	no	—
608	C₃×C₄	#585	1	2	yes	—
609	C₂³	—	2	6	no	—
610	C₂³	—	2	12	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	3	no	—
614	C₂³	—	4	6	no	—
615	C₂³	—	4	6	no	—
616	C₂³	—	4	3	no	—
617	C₂³	—	4	12	no	—
618	C₂³	—	4	12	no	—
619	C₂³	—	4	12	no	—
620	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
621	C₂³	C₂⁵×C₃	1	6	yes	—
622	C₂³	C₂⁵×C₃	1	12	yes	—
623	C₂³	C₂⁵×C₃	1	3	yes	—
624	Q₈	—	4	12	no	—
625	Q₈	—	4	2	no	—
626	Q₈	—	4	2	no	—
627	D₄	—	2	24	no	—
628	D₄	—	2	48	no	—
629	D₄	—	2	12	no	—
630	D₄	—	4	24	no	—
631	D₄	—	4	12	no	—
632	D₄	—	4	6	no	—
633	D₄	—	4	12	no	—
634	D₄	—	4	24	no	—
635	D₄	—	4	6	no	—
636	D₄	—	4	12	no	—
637	D₄	—	4	6	no	—
638	C₂×C₄	—	2	12	no	—
639	C₂×C₄	—	2	6	no	—
640	C₂×C₄	—	2	6	no	—
641	C₂×C₄	—	2	12	no	—
642	C₂×C₄	—	4	3	no	—
643	C₂×C₄	—	4	6	no	—
644	C₂×C₄	—	4	3	no	—
645	C₂×C₄	—	4	6	no	—
646	C₂×C₄	—	4	3	no	—
647	C₂×C₄	—	4	6	no	—
648	C₂×C₄	—	4	12	no	—
649	C₂×C₄	—	4	12	no	—
650	C₂×C₄	—	4	24	no	—
651	C₂×C₄	—	4	12	no	—
652	C₂×C₄	C₂⁵×C₃	1	2	yes	—
653	C₂×C₄	C₂⁵×C₃	1	6	yes	—
654	C₂×C₄	C₂⁵×C₃	1	3	yes	—
655	C₂×C₄	C₂⁵×C₃	1	6	yes	—
656	C₂×C₄	C₂⁵×C₃	1	6	yes	—
657	C₂×C₄	C₂⁵×C₃	1	12	yes	—
658	C₂×C₄	C₂⁵×C₃	1	6	yes	—
659	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
660	C₂×C₃	—	2	6	no	—
661	C₂×C₃	—	4	6	no	—
662	C₂×C₃	—	4	12	no	—
663	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂×C₃	C₂×#585	1	1	yes	characteristic
665	C₂×C₃	H(7,𝔽₂)	1	1	yes	characteristic
666	C₂²	—	2	3	no	—
667	C₂²	—	2	3	no	—
668	C₂²	—	2	6	no	—
669	C₂²	—	2	12	no	—
670	C₂²	—	2	6	no	—
671	C₂²	—	2	12	no	—
672	C₂²	—	2	12	no	—
673	C₂²	—	2	6	no	—
674	C₂²	—	4	4	no	—
675	C₂²	—	8	6	no	—
676	C₂²	—	8	12	no	—
677	C₂²	—	16	12	no	—
678	C₂²	C₂×C₃×H(5,𝔽₂)	1	6	yes	—
679	C₂²	C₂⁶×C₃	1	1	yes	characteristic
680	C₄	—	2	12	no	—
681	C₄	—	2	6	no	—
682	C₄	—	2	3	no	—
683	C₄	—	2	6	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	6	no	—
686	C₄	—	2	6	no	—
687	C₄	C₃×#585	1	2	yes	—
688	C₃	#62905	1	1	yes	characteristic, direct product factor, Sylow
689	C₂	—	2	6	no	—
690	C₂	—	4	6	no	—
691	C₂	—	4	12	no	—
692	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂	C₂×C₃×#585	1	1	yes	characteristic
694	C₂	C₃×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3560	C₂	semidirect
2. C₃×#3559	C₂	semidirect
3. C₃×#3537	C₂	semidirect
4. C₃×#3534	C₂	semidirect
5. C₃×#3519	C₂	semidirect
6. C₃×#3496	C₂	semidirect
7. C₃×#3496	C₂	semidirect
8. C₃×#3494	C₂	semidirect
9. C₂×C₃×#553	C₂	semidirect
10. C₃×#3459	C₂	semidirect
11. C₃×#3459	C₂	semidirect
12. #62905	C₃	direct (N × H)
13. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
14. C₃×#563	C₂²	semidirect
15. C₃×#562	C₂²	semidirect
16. C₃×#560	C₂²	semidirect
17. C₃×#555	C₂²	semidirect
18. C₃×#554	C₂²	semidirect
19. C₃×#553	C₂²	semidirect
20. C₃×#553	C₂²	semidirect
21. C₃×#553	C₂²	semidirect
22. C₃×#553	C₂²	semidirect
23. C₃×#553	C₂²	semidirect
24. C₃×#551	C₂²	semidirect
25. C₃×#550	C₂²	semidirect
26. C₃×#547	C₂²	semidirect
27. C₃×#547	C₂²	semidirect
28. C₃×#546	C₂²	semidirect
29. C₃×#546	C₂²	semidirect
30. C₃×#546	C₂²	semidirect
31. C₃×#546	C₂²	semidirect
32. C₃×D₄²	C₂²	semidirect
33. C₃×D₄²	C₂²	semidirect
34. C₃×D₄²	C₂²	semidirect
35. C₃×#544	C₂²	semidirect
36. C₃×#543	C₂²	semidirect
37. C₃×#542	C₂²	semidirect
38. C₃×#540	C₂²	semidirect
39. C₃×#540	C₂²	semidirect
40. C₃×#539	C₂²	semidirect
41. C₃×#539	C₂²	semidirect
42. C₃×#539	C₂²	semidirect
43. C₃×#538	C₂²	semidirect
44. C₃×#538	C₂²	semidirect
45. C₃×#538	C₂²	semidirect
46. C₃×#538	C₂²	semidirect
47. C₃×#537	C₂²	semidirect
48. C₃×#537	C₂²	semidirect
49. C₃×#535	C₂²	semidirect
50. C₃×#534	C₂²	semidirect
51. C₃×#534	C₂²	semidirect
52. C₃×#534	C₂²	semidirect
53. C₃×#534	C₂²	semidirect
54. C₃×#534	C₂²	semidirect
55. C₃×#532	C₂²	semidirect
56. C₃×#532	C₂²	semidirect
57. C₃×#529	C₂²	semidirect
58. C₃×#529	C₂²	semidirect
59. C₂×C₃×#126	C₂²	semidirect
60. C₂×C₃×#125	C₂²	semidirect
61. C₃×#525	C₂²	semidirect
62. C₃×#525	C₂²	semidirect
63. C₂×C₃×#123	C₂²	semidirect
64. C₂×C₃×#121	C₂²	semidirect
65. C₂×C₃×#121	C₂²	semidirect
66. C₂×C₃×#121	C₂²	semidirect
67. C₂×C₃×#121	C₂²	semidirect
68. C₂×C₃×#121	C₂²	semidirect
69. C₃×#520	C₂²	semidirect
70. C₃×#518	C₂²	semidirect
71. C₂×C₃×C₄×D₄	C₂²	semidirect
72. C₂×C₃×C₄×D₄	C₂²	semidirect
73. C₂×C₃×C₄×D₄	C₂²	semidirect
74. C₂×C₃×#117	C₂²	semidirect
75. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
76. #3560	C₂×C₃	semidirect
77. #3559	C₂×C₃	semidirect
78. #3537	C₂×C₃	semidirect
79. #3534	C₂×C₃	semidirect
80. #3519	C₂×C₃	semidirect
81. #3496	C₂×C₃	semidirect
82. #3496	C₂×C₃	semidirect
83. #3494	C₂×C₃	semidirect
84. C₂×#553	C₂×C₃	semidirect
85. #3459	C₂×C₃	semidirect
86. #3459	C₂×C₃	semidirect
201. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
202. #563	C₂²×C₃	semidirect
203. #562	C₂²×C₃	semidirect
204. #560	C₂²×C₃	semidirect
205. #555	C₂²×C₃	semidirect
206. #554	C₂²×C₃	semidirect
207. #553	C₂²×C₃	semidirect
208. #553	C₂²×C₃	semidirect
209. #553	C₂²×C₃	semidirect
210. #553	C₂²×C₃	semidirect
211. #553	C₂²×C₃	semidirect
212. #551	C₂²×C₃	semidirect
213. #550	C₂²×C₃	semidirect
214. #547	C₂²×C₃	semidirect
215. #547	C₂²×C₃	semidirect
216. #546	C₂²×C₃	semidirect
217. #546	C₂²×C₃	semidirect
218. #546	C₂²×C₃	semidirect
219. #546	C₂²×C₃	semidirect
220. D₄²	C₂²×C₃	semidirect
221. D₄²	C₂²×C₃	semidirect
222. D₄²	C₂²×C₃	semidirect
223. #544	C₂²×C₃	semidirect
224. #543	C₂²×C₃	semidirect
225. #542	C₂²×C₃	semidirect
226. #540	C₂²×C₃	semidirect
227. #540	C₂²×C₃	semidirect
228. #539	C₂²×C₃	semidirect
229. #539	C₂²×C₃	semidirect
230. #539	C₂²×C₃	semidirect
231. #538	C₂²×C₃	semidirect
232. #538	C₂²×C₃	semidirect
233. #538	C₂²×C₃	semidirect
234. #538	C₂²×C₃	semidirect
235. #537	C₂²×C₃	semidirect
236. #537	C₂²×C₃	semidirect
237. #535	C₂²×C₃	semidirect
238. #534	C₂²×C₃	semidirect
239. #534	C₂²×C₃	semidirect
240. #534	C₂²×C₃	semidirect
241. #534	C₂²×C₃	semidirect
242. #534	C₂²×C₃	semidirect
243. #532	C₂²×C₃	semidirect
244. #532	C₂²×C₃	semidirect
245. #529	C₂²×C₃	semidirect
246. #529	C₂²×C₃	semidirect
247. C₂×#126	C₂²×C₃	semidirect
248. C₂×#125	C₂²×C₃	semidirect
249. #525	C₂²×C₃	semidirect
250. #525	C₂²×C₃	semidirect
251. C₂×#123	C₂²×C₃	semidirect
252. C₂×#121	C₂²×C₃	semidirect
253. C₂×#121	C₂²×C₃	semidirect
254. C₂×#121	C₂²×C₃	semidirect
255. C₂×#121	C₂²×C₃	semidirect
256. C₂×#121	C₂²×C₃	semidirect
257. #520	C₂²×C₃	semidirect
258. #518	C₂²×C₃	semidirect
259. C₂×C₄×D₄	C₂²×C₃	semidirect
260. C₂×C₄×D₄	C₂²×C₃	semidirect
261. C₂×C₄×D₄	C₂²×C₃	semidirect
262. C₂×#117	C₂²×C₃	semidirect
263. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
688. C₃	#62905	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3560	2
C₃×#3559	2
C₃×#3537	2
C₃×#3534	2
C₃×#3519	2
C₃×#3496	2
C₃×#3494	2
C₂×C₃×#553	2
C₃×#3459	2
#62905	3

Subgroups — C3×#62905 #10681512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#62905 #10681512