Subgroups — C₃×#62824 #10681431

Order 768.

7330 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3561	C₂	1	8	yes	maximal, complemented
2	C₃×#3558	C₂	1	8	yes	maximal, complemented
3	C₃×#3545	C₂	1	8	yes	maximal, complemented
4	C₃×#3514	C₂	1	16	yes	maximal, complemented
5	C₃×#3510	C₂	1	4	yes	maximal, complemented
6	C₃×#3500	C₂	1	4	yes	maximal, complemented
7	C₃×#3490	C₂	1	8	yes	maximal, complemented
8	C₃×#3486	C₂	1	2	yes	maximal, complemented
9	C₃×#3484	C₂	1	2	yes	maximal, complemented
10	C₃×#3444	C₂	1	2	yes	maximal, complemented
11	C₂²×C₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
12	#62824	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
14	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
15	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
17	C₃×#563	C₂²	1	8	yes	complemented
18	C₃×#562	C₂²	1	16	yes	complemented
19	C₃×H(3,𝔽₄)	C₂²	1	8	yes	complemented
20	C₃×#559	C₂²	1	16	yes	complemented
21	C₃×#556	C₂²	1	16	yes	complemented
22	C₃×#555	C₂²	1	16	yes	complemented
23	C₃×#551	C₂²	1	32	yes	complemented
24	C₃×#551	C₂²	1	32	yes	complemented
25	C₃×#551	C₂²	1	16	yes	complemented
26	C₃×D₄×Q₈	C₂²	1	16	yes	complemented
27	C₃×#548	C₂²	1	16	yes	complemented
28	C₃×#548	C₂²	1	16	yes	complemented
29	C₃×#546	C₂²	1	16	yes	complemented
30	C₃×#546	C₂²	1	32	yes	complemented
31	C₃×#546	C₂²	1	32	yes	complemented
32	C₃×#546	C₂²	1	16	yes	complemented
33	C₃×D₄²	C₂²	1	16	yes	complemented
34	C₃×#543	C₂²	1	8	yes	complemented
35	C₃×#542	C₂²	1	16	yes	complemented
36	C₃×#542	C₂²	1	32	yes	complemented
37	C₃×#538	C₂²	1	16	yes	complemented
38	C₃×#538	C₂²	1	16	yes	complemented
39	C₃×#538	C₂²	1	32	yes	complemented
40	C₃×#536	C₂²	1	4	yes	complemented
41	C₃×#536	C₂²	1	8	yes	complemented
42	C₃×#536	C₂²	1	8	yes	complemented
43	C₃×#535	C₂²	1	4	yes	—
44	C₃×#535	C₂²	1	8	yes	complemented
45	C₃×#534	C₂²	1	8	yes	complemented
46	C₃×#534	C₂²	1	8	yes	complemented
47	C₃×#533	C₂²	1	2	yes	complemented
48	C₃×#533	C₂²	1	4	yes	complemented
49	C₃×#532	C₂²	1	2	yes	complemented
50	C₃×#532	C₂²	1	4	yes	complemented
51	C₃×#532	C₂²	1	8	yes	complemented
52	C₃×#529	C₂²	1	8	yes	complemented
53	C₃×#529	C₂²	1	8	yes	complemented
54	C₃×#529	C₂²	1	8	yes	complemented
55	C₃×#529	C₂²	1	16	yes	complemented
56	C₂×C₃×#124	C₂²	1	4	yes	complemented
57	C₂×C₃×#124	C₂²	1	8	yes	complemented
58	C₂×C₃×#124	C₂²	1	4	yes	complemented
59	C₂×C₃×#124	C₂²	1	8	yes	complemented
60	C₂×C₃×#124	C₂²	1	8	yes	complemented
61	C₃×#525	C₂²	1	4	yes	complemented
62	C₃×#525	C₂²	1	8	yes	complemented
63	C₃×#525	C₂²	1	8	yes	complemented
64	C₂×C₃×#120	C₂²	1	8	yes	complemented
65	C₃×#519	C₂²	1	2	yes	complemented
66	C₃×#518	C₂²	1	2	yes	complemented
67	C₃×#518	C₂²	1	16	yes	complemented
68	C₃×C₄×#41	C₂²	1	4	yes	complemented
69	C₃×C₄×#41	C₂²	1	8	yes	complemented
70	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
71	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
72	#3561	C₂×C₃	1	8	yes	complemented
73	#3558	C₂×C₃	1	8	yes	complemented
74	#3545	C₂×C₃	1	8	yes	complemented
75	#3514	C₂×C₃	1	16	yes	complemented
76	#3510	C₂×C₃	1	4	yes	complemented
77	#3500	C₂×C₃	1	4	yes	complemented
78	#3490	C₂×C₃	1	8	yes	complemented
79	#3486	C₂×C₃	1	2	yes	complemented
80	#3484	C₂×C₃	1	2	yes	complemented
81	#3444	C₂×C₃	1	2	yes	complemented
82	C₂²×#124	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂⁵×C₃	C₂³	1	2	yes	—
84	C₃×2₋¹⁺⁴	—	4	8	no	—
85	C₃×H(5,𝔽₂)	—	4	8	no	—
86	C₂×C₃×#41	C₂³	1	4	yes	—
87	C₂×C₃×#41	C₂³	1	8	yes	—
88	C₂×C₃×#41	C₂³	1	8	yes	—
89	C₂×C₃×#41	C₂³	1	8	yes	—
90	C₂×C₃×#41	C₂³	1	8	yes	complemented
91	C₂²×C₃×Q₈	—	4	4	no	—
92	C₂²×C₃×Q₈	C₂³	1	2	yes	—
93	C₂²×C₃×Q₈	C₂³	1	2	yes	—
94	C₂²×C₃×Q₈	C₂³	1	8	yes	—
95	C₂²×C₃×Q₈	C₂³	1	8	yes	complemented
96	C₂²×C₃×D₄	—	4	4	no	—
97	C₂²×C₃×D₄	C₂³	1	2	yes	—
98	C₂²×C₃×D₄	C₂³	1	2	yes	—
99	C₂²×C₃×D₄	C₂³	1	8	yes	—
100	C₂²×C₃×D₄	C₂³	1	8	yes	—
101	C₂²×C₃×D₄	C₂³	1	8	yes	—
102	C₂²×C₃×D₄	C₂³	1	16	yes	—
103	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
104	C₂³×C₃×C₄	C₂³	1	2	yes	—
105	C₂³×C₃×C₄	C₂³	1	2	yes	—
106	C₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
107	C₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
108	C₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
109	C₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
110	C₃×#127	C₂³	1	8	yes	—
111	C₃×#127	C₂³	1	2	yes	complemented
112	C₃×#126	C₂³	1	32	yes	complemented
113	C₃×#126	C₂³	1	16	yes	complemented
114	C₃×#126	C₂³	1	32	yes	complemented
115	C₃×#125	C₂³	1	8	yes	complemented
116	C₃×#125	C₂³	1	4	yes	complemented
117	C₃×#124	C₂³	1	16	yes	—
118	C₃×#124	C₂³	1	8	yes	—
119	C₃×#124	C₂³	1	8	yes	—
120	C₃×#124	C₂³	1	8	yes	—
121	C₃×#124	C₂³	1	16	yes	—
122	C₃×#124	C₂³	1	8	yes	—
123	C₃×#124	C₂³	1	8	yes	—
124	C₃×#124	C₂³	1	8	yes	complemented
125	C₃×#124	C₂³	1	32	yes	complemented
126	C₃×#124	C₂³	1	8	yes	complemented
127	C₃×#124	C₂³	1	16	yes	complemented
128	C₃×#124	C₂³	1	4	yes	complemented
129	C₃×#124	C₂³	1	32	yes	complemented
130	C₃×#123	C₂³	1	16	yes	—
131	C₃×#123	C₂³	1	8	yes	—
132	C₃×#123	C₂³	1	16	yes	—
133	C₃×#123	C₂³	1	16	yes	—
134	C₃×#123	C₂³	1	32	yes	complemented
135	C₃×#123	C₂³	1	32	yes	complemented
136	C₃×#123	C₂³	1	32	yes	complemented
137	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
138	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
139	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
140	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
141	C₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
142	C₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
143	C₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
144	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
145	C₃×#121	C₂³	1	32	yes	—
146	C₃×#121	C₂³	1	8	yes	—
147	C₃×#121	C₂³	1	8	yes	—
148	C₃×#121	C₂³	1	8	yes	—
149	C₃×#121	C₂³	1	16	yes	—
150	C₃×#121	C₂³	1	16	yes	—
151	C₃×#121	C₂³	1	32	yes	complemented
152	C₃×#121	C₂³	1	32	yes	complemented
153	C₃×#120	C₂³	1	16	yes	—
154	C₃×#120	C₂³	1	8	yes	—
155	C₃×#120	C₂³	1	16	yes	—
156	C₃×#120	C₂³	1	32	yes	—
157	C₃×#120	C₂³	1	32	yes	complemented
158	C₃×C₄×Q₈	C₂³	1	8	yes	complemented
159	C₃×C₄×Q₈	C₂³	1	16	yes	complemented
160	C₃×C₄×Q₈	C₂³	1	8	yes	complemented
161	C₃×C₄×Q₈	C₂³	1	8	yes	complemented
162	C₃×C₄×D₄	C₂³	1	16	yes	—
163	C₃×C₄×D₄	C₂³	1	16	yes	—
164	C₃×C₄×D₄	C₂³	1	16	yes	—
165	C₃×C₄×D₄	C₂³	1	16	yes	—
166	C₃×C₄×D₄	C₂³	1	32	yes	—
167	C₃×C₄×D₄	C₂³	1	8	yes	complemented
168	C₃×C₄×D₄	C₂³	1	32	yes	complemented
169	C₃×C₄×D₄	C₂³	1	8	yes	complemented
170	C₃×C₄×D₄	C₂³	1	8	yes	complemented
171	C₃×C₄×D₄	C₂³	1	32	yes	complemented
172	C₃×#117	C₂³	1	4	yes	—
173	C₃×#117	C₂³	1	8	yes	—
174	C₃×#117	C₂³	1	8	yes	—
175	C₃×#117	C₂³	1	8	yes	complemented
176	C₃×#117	C₂³	1	16	yes	complemented
177	C₃×#117	C₂³	1	32	yes	complemented
178	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
185	C₂×C₃×C₄²	C₂³	1	4	yes	—
186	C₂×C₃×C₄²	C₂³	1	2	yes	—
187	C₂×C₃×C₄²	C₂³	1	2	yes	—
188	C₂×C₃×C₄²	C₂³	1	4	yes	—
189	C₂×C₃×C₄²	C₂³	1	8	yes	complemented
190	C₂×2₋¹⁺⁴	C₂²×C₃	1	2	yes	complemented
191	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
192	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
194	#563	C₂²×C₃	1	8	yes	complemented
195	#562	C₂²×C₃	1	16	yes	complemented
196	H(3,𝔽₄)	C₂²×C₃	1	8	yes	complemented
197	#559	C₂²×C₃	1	16	yes	complemented
198	#556	C₂²×C₃	1	16	yes	complemented
199	#555	C₂²×C₃	1	16	yes	complemented
200	#551	C₂²×C₃	1	32	yes	complemented
201	#551	C₂²×C₃	1	32	yes	complemented
202	#551	C₂²×C₃	1	16	yes	complemented
203	D₄×Q₈	C₂²×C₃	1	16	yes	complemented
204	#548	C₂²×C₃	1	16	yes	complemented
205	#548	C₂²×C₃	1	16	yes	complemented
206	#546	C₂²×C₃	1	16	yes	complemented
207	#546	C₂²×C₃	1	32	yes	complemented
208	#546	C₂²×C₃	1	32	yes	complemented
209	#546	C₂²×C₃	1	16	yes	complemented
210	D₄²	C₂²×C₃	1	16	yes	complemented
211	#543	C₂²×C₃	1	8	yes	complemented
212	#542	C₂²×C₃	1	16	yes	complemented
213	#542	C₂²×C₃	1	32	yes	complemented
214	#538	C₂²×C₃	1	16	yes	complemented
215	#538	C₂²×C₃	1	16	yes	complemented
216	#538	C₂²×C₃	1	32	yes	complemented
217	#536	C₂²×C₃	1	4	yes	complemented
218	#536	C₂²×C₃	1	8	yes	complemented
219	#536	C₂²×C₃	1	8	yes	complemented
220	#535	C₂²×C₃	1	4	yes	—
221	#535	C₂²×C₃	1	8	yes	complemented
222	#534	C₂²×C₃	1	8	yes	complemented
223	#534	C₂²×C₃	1	8	yes	complemented
224	#533	C₂²×C₃	1	2	yes	complemented
225	#533	C₂²×C₃	1	4	yes	complemented
226	#532	C₂²×C₃	1	2	yes	complemented
227	#532	C₂²×C₃	1	4	yes	complemented
228	#532	C₂²×C₃	1	8	yes	complemented
229	#529	C₂²×C₃	1	8	yes	complemented
230	#529	C₂²×C₃	1	8	yes	complemented
231	#529	C₂²×C₃	1	8	yes	complemented
232	#529	C₂²×C₃	1	16	yes	complemented
233	C₂×#124	C₂²×C₃	1	4	yes	complemented
234	C₂×#124	C₂²×C₃	1	8	yes	complemented
235	C₂×#124	C₂²×C₃	1	4	yes	complemented
236	C₂×#124	C₂²×C₃	1	8	yes	complemented
237	C₂×#124	C₂²×C₃	1	8	yes	complemented
238	#525	C₂²×C₃	1	4	yes	complemented
239	#525	C₂²×C₃	1	8	yes	complemented
240	#525	C₂²×C₃	1	8	yes	complemented
241	C₂×#120	C₂²×C₃	1	8	yes	complemented
242	#519	C₂²×C₃	1	2	yes	complemented
243	#518	C₂²×C₃	1	2	yes	complemented
244	#518	C₂²×C₃	1	16	yes	complemented
245	C₄×#41	C₂²×C₃	1	4	yes	complemented
246	C₄×#41	C₂²×C₃	1	8	yes	complemented
247	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
248	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
249	C₂⁴×C₃	—	4	8	no	—
250	C₂⁴×C₃	—	4	4	no	—
251	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₃	C₂⁴	1	4	yes	—
253	C₂⁴×C₃	C₂⁴	1	8	yes	—
254	C₂⁴×C₃	C₂⁴	1	8	yes	—
255	C₃×#41	—	2	16	no	—
256	C₃×#41	—	4	16	no	—
257	C₃×#41	—	4	16	no	—
258	C₃×#41	—	4	16	no	—
259	C₃×#41	—	4	16	no	—
260	C₂×C₃×Q₈	—	2	8	no	—
261	C₂×C₃×Q₈	—	4	4	no	—
262	C₂×C₃×Q₈	—	4	16	no	—
263	C₂×C₃×Q₈	—	4	16	no	—
264	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
265	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
266	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
267	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
268	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
269	C₂×C₃×D₄	—	2	8	no	—
270	C₂×C₃×D₄	—	4	16	no	—
271	C₂×C₃×D₄	—	4	16	no	—
272	C₂×C₃×D₄	—	4	4	no	—
273	C₂×C₃×D₄	—	4	32	no	—
274	C₂×C₃×D₄	—	4	16	no	—
275	C₂×C₃×D₄	C₂⁴	1	16	yes	—
276	C₂×C₃×D₄	C₂⁴	1	8	yes	—
277	C₂×C₃×D₄	C₂⁴	1	8	yes	—
278	C₂×C₃×D₄	C₂⁴	1	4	yes	—
279	C₂×C₃×D₄	C₂⁴	1	32	yes	—
280	C₂×C₃×D₄	C₂⁴	1	8	yes	—
281	C₂×C₃×D₄	C₂⁴	1	8	yes	—
282	C₂×C₃×D₄	C₂⁴	1	16	yes	—
283	C₂×C₃×D₄	C₂⁴	1	8	yes	—
284	C₂²×C₃×C₄	—	2	4	no	—
285	C₂²×C₃×C₄	—	4	4	no	—
286	C₂²×C₃×C₄	—	4	4	no	—
287	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
288	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
289	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
290	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
291	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
292	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
293	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
294	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
295	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
296	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
297	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
298	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
299	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
300	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
301	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
302	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
303	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
304	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
305	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
306	C₃×C₄⋊C₄	C₂⁴	1	32	yes	—
307	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
308	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
309	C₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
310	C₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
311	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
312	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
313	C₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
314	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
315	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
316	C₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
317	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
318	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
319	C₃×C₄²	C₂⁴	1	2	yes	—
320	C₃×C₄²	C₂⁴	1	2	yes	—
321	C₃×C₄²	C₂⁴	1	2	yes	—
322	C₃×C₄²	C₂⁴	1	4	yes	—
323	C₃×C₄²	C₂⁴	1	4	yes	—
324	C₃×C₄²	C₂⁴	1	2	yes	—
325	C₃×C₄²	C₂⁴	1	16	yes	—
326	C₃×C₄²	C₂⁴	1	8	yes	—
327	C₃×C₄²	C₂⁴	1	16	yes	—
328	C₂⁵	C₂³×C₃	1	2	yes	—
329	2₋¹⁺⁴	—	4	8	no	—
330	H(5,𝔽₂)	—	4	8	no	—
331	C₂×#41	C₂³×C₃	1	4	yes	—
332	C₂×#41	C₂³×C₃	1	8	yes	—
333	C₂×#41	C₂³×C₃	1	8	yes	—
334	C₂×#41	C₂³×C₃	1	8	yes	—
335	C₂×#41	C₂³×C₃	1	8	yes	complemented
336	C₂²×Q₈	—	4	4	no	—
337	C₂²×Q₈	C₂³×C₃	1	2	yes	—
338	C₂²×Q₈	C₂³×C₃	1	2	yes	—
339	C₂²×Q₈	C₂³×C₃	1	8	yes	—
340	C₂²×Q₈	C₂³×C₃	1	8	yes	complemented
341	C₂²×D₄	—	4	4	no	—
342	C₂²×D₄	C₂³×C₃	1	2	yes	—
343	C₂²×D₄	C₂³×C₃	1	16	yes	—
344	C₂²×D₄	C₂³×C₃	1	8	yes	—
345	C₂²×D₄	C₂³×C₃	1	2	yes	—
346	C₂²×D₄	C₂³×C₃	1	8	yes	—
347	C₂²×D₄	C₂³×C₃	1	8	yes	—
348	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₃	1	2	yes	—
350	C₂³×C₄	C₂³×C₃	1	2	yes	—
351	C₄⋊Q₈	C₂³×C₃	1	2	yes	complemented
352	C₄⋊Q₈	C₂³×C₃	1	4	yes	complemented
353	C₄⋊Q₈	C₂³×C₃	1	8	yes	complemented
354	C₄⋊Q₈	C₂³×C₃	1	16	yes	complemented
355	#127	C₂³×C₃	1	8	yes	—
356	#127	C₂³×C₃	1	2	yes	complemented
357	#126	C₂³×C₃	1	16	yes	complemented
358	#126	C₂³×C₃	1	32	yes	complemented
359	#126	C₂³×C₃	1	32	yes	complemented
360	#125	C₂³×C₃	1	4	yes	complemented
361	#125	C₂³×C₃	1	8	yes	complemented
362	#124	C₂³×C₃	1	8	yes	—
363	#124	C₂³×C₃	1	8	yes	—
364	#124	C₂³×C₃	1	16	yes	—
365	#124	C₂³×C₃	1	16	yes	—
366	#124	C₂³×C₃	1	8	yes	—
367	#124	C₂³×C₃	1	8	yes	—
368	#124	C₂³×C₃	1	8	yes	—
369	#124	C₂³×C₃	1	4	yes	complemented
370	#124	C₂³×C₃	1	8	yes	complemented
371	#124	C₂³×C₃	1	32	yes	complemented
372	#124	C₂³×C₃	1	8	yes	complemented
373	#124	C₂³×C₃	1	16	yes	complemented
374	#124	C₂³×C₃	1	32	yes	complemented
375	#123	C₂³×C₃	1	8	yes	—
376	#123	C₂³×C₃	1	16	yes	—
377	#123	C₂³×C₃	1	16	yes	—
378	#123	C₂³×C₃	1	16	yes	—
379	#123	C₂³×C₃	1	32	yes	complemented
380	#123	C₂³×C₃	1	32	yes	complemented
381	#123	C₂³×C₃	1	32	yes	complemented
382	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
383	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
384	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
385	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
386	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
387	C₂²⋊Q₈	C₂³×C₃	1	32	yes	complemented
388	C₂²⋊Q₈	C₂³×C₃	1	32	yes	complemented
389	C₂²⋊Q₈	C₂³×C₃	1	32	yes	complemented
390	#121	C₂³×C₃	1	8	yes	—
391	#121	C₂³×C₃	1	8	yes	—
392	#121	C₂³×C₃	1	8	yes	—
393	#121	C₂³×C₃	1	16	yes	—
394	#121	C₂³×C₃	1	16	yes	—
395	#121	C₂³×C₃	1	32	yes	—
396	#121	C₂³×C₃	1	32	yes	complemented
397	#121	C₂³×C₃	1	32	yes	complemented
398	#120	C₂³×C₃	1	8	yes	—
399	#120	C₂³×C₃	1	16	yes	—
400	#120	C₂³×C₃	1	32	yes	—
401	#120	C₂³×C₃	1	16	yes	—
402	#120	C₂³×C₃	1	32	yes	complemented
403	C₄×Q₈	C₂³×C₃	1	8	yes	complemented
404	C₄×Q₈	C₂³×C₃	1	8	yes	complemented
405	C₄×Q₈	C₂³×C₃	1	8	yes	complemented
406	C₄×Q₈	C₂³×C₃	1	16	yes	complemented
407	C₄×D₄	C₂³×C₃	1	16	yes	—
408	C₄×D₄	C₂³×C₃	1	16	yes	—
409	C₄×D₄	C₂³×C₃	1	16	yes	—
410	C₄×D₄	C₂³×C₃	1	32	yes	—
411	C₄×D₄	C₂³×C₃	1	16	yes	—
412	C₄×D₄	C₂³×C₃	1	8	yes	complemented
413	C₄×D₄	C₂³×C₃	1	8	yes	complemented
414	C₄×D₄	C₂³×C₃	1	8	yes	complemented
415	C₄×D₄	C₂³×C₃	1	32	yes	complemented
416	C₄×D₄	C₂³×C₃	1	32	yes	complemented
417	#117	C₂³×C₃	1	4	yes	—
418	#117	C₂³×C₃	1	8	yes	—
419	#117	C₂³×C₃	1	8	yes	—
420	#117	C₂³×C₃	1	8	yes	complemented
421	#117	C₂³×C₃	1	16	yes	complemented
422	#117	C₂³×C₃	1	32	yes	complemented
423	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₃	1	32	yes	complemented
430	C₂×C₄²	C₂³×C₃	1	4	yes	—
431	C₂×C₄²	C₂³×C₃	1	2	yes	—
432	C₂×C₄²	C₂³×C₃	1	2	yes	—
433	C₂×C₄²	C₂³×C₃	1	4	yes	—
434	C₂×C₄²	C₂³×C₃	1	8	yes	complemented
435	C₂³×C₃	—	2	2	no	—
436	C₂³×C₃	—	2	4	no	—
437	C₂³×C₃	—	2	8	no	—
438	C₂³×C₃	—	2	16	no	—
439	C₂³×C₃	—	4	8	no	—
440	C₂³×C₃	—	4	8	no	—
441	C₂³×C₃	—	4	8	no	—
442	C₂³×C₃	—	4	8	no	—
443	C₂³×C₃	—	4	16	no	—
444	C₂³×C₃	—	8	16	no	—
445	C₂³×C₃	C₂⁵	1	8	yes	—
446	C₂³×C₃	C₂⁵	1	8	yes	—
447	C₂³×C₃	C₂⁵	1	1	yes	characteristic
448	C₂³×C₃	C₂⁵	1	2	yes	—
449	C₃×Q₈	—	2	16	no	—
450	C₃×Q₈	—	2	8	no	—
451	C₃×Q₈	—	4	8	no	—
452	C₃×Q₈	—	4	8	no	—
453	C₃×Q₈	—	4	8	no	—
454	C₃×D₄	—	2	16	no	—
455	C₃×D₄	—	2	32	no	—
456	C₃×D₄	—	2	16	no	—
457	C₃×D₄	—	2	8	no	—
458	C₃×D₄	—	4	8	no	—
459	C₃×D₄	—	4	16	no	—
460	C₃×D₄	—	4	32	no	—
461	C₃×D₄	—	4	8	no	—
462	C₃×D₄	—	4	8	no	—
463	C₂×C₃×C₄	—	2	2	no	—
464	C₂×C₃×C₄	—	2	8	no	—
465	C₂×C₃×C₄	—	2	8	no	—
466	C₂×C₃×C₄	—	2	8	no	—
467	C₂×C₃×C₄	—	2	16	no	—
468	C₂×C₃×C₄	—	4	2	no	—
469	C₂×C₃×C₄	—	4	4	no	—
470	C₂×C₃×C₄	—	4	2	no	—
471	C₂×C₃×C₄	—	4	8	no	—
472	C₂×C₃×C₄	—	4	16	no	—
473	C₂×C₃×C₄	—	4	8	no	—
474	C₂×C₃×C₄	—	4	16	no	—
475	C₂×C₃×C₄	—	4	16	no	—
476	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
477	C₂×C₃×C₄	C₂⁵	1	4	yes	—
478	C₂×C₃×C₄	C₂⁵	1	4	yes	—
479	C₂×C₃×C₄	C₂⁵	1	16	yes	—
480	C₂×C₃×C₄	C₂⁵	1	2	yes	—
481	C₂×C₃×C₄	C₂⁵	1	8	yes	—
482	C₂×C₃×C₄	C₂⁵	1	8	yes	—
483	C₂×C₃×C₄	C₂⁵	1	2	yes	—
484	C₂⁴	—	4	4	no	—
485	C₂⁴	—	4	8	no	—
486	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
487	C₂⁴	C₂⁴×C₃	1	4	yes	—
488	C₂⁴	C₂⁴×C₃	1	8	yes	—
489	C₂⁴	C₂⁴×C₃	1	8	yes	—
490	#41	—	2	16	no	—
491	#41	—	4	16	no	—
492	#41	—	4	16	no	—
493	#41	—	4	16	no	—
494	#41	—	4	16	no	—
495	C₂×Q₈	—	2	8	no	—
496	C₂×Q₈	—	4	4	no	—
497	C₂×Q₈	—	4	16	no	—
498	C₂×Q₈	—	4	16	no	—
499	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
500	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
501	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
502	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
503	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
504	C₂×D₄	—	2	8	no	—
505	C₂×D₄	—	4	16	no	—
506	C₂×D₄	—	4	16	no	—
507	C₂×D₄	—	4	4	no	—
508	C₂×D₄	—	4	16	no	—
509	C₂×D₄	—	4	32	no	—
510	C₂×D₄	C₂⁴×C₃	1	16	yes	—
511	C₂×D₄	C₂⁴×C₃	1	8	yes	—
512	C₂×D₄	C₂⁴×C₃	1	8	yes	—
513	C₂×D₄	C₂⁴×C₃	1	4	yes	—
514	C₂×D₄	C₂⁴×C₃	1	32	yes	—
515	C₂×D₄	C₂⁴×C₃	1	8	yes	—
516	C₂×D₄	C₂⁴×C₃	1	8	yes	—
517	C₂×D₄	C₂⁴×C₃	1	16	yes	—
518	C₂×D₄	C₂⁴×C₃	1	8	yes	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	4	4	no	—
521	C₂²×C₄	—	4	4	no	—
522	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
524	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
526	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
527	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
531	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
532	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
533	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
534	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
535	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
536	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
537	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
538	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
539	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
540	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
541	C₄⋊C₄	C₂⁴×C₃	1	32	yes	—
542	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
543	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
544	C₂²⋊C₄	C₂⁴×C₃	1	32	yes	—
545	C₂²⋊C₄	C₂⁴×C₃	1	32	yes	—
546	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
547	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
548	C₂²⋊C₄	C₂⁴×C₃	1	32	yes	—
549	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
550	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
551	C₂²⋊C₄	C₂⁴×C₃	1	32	yes	—
552	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
553	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
554	C₄²	C₂⁴×C₃	1	2	yes	—
555	C₄²	C₂⁴×C₃	1	2	yes	—
556	C₄²	C₂⁴×C₃	1	2	yes	—
557	C₄²	C₂⁴×C₃	1	4	yes	—
558	C₄²	C₂⁴×C₃	1	4	yes	—
559	C₄²	C₂⁴×C₃	1	2	yes	—
560	C₄²	C₂⁴×C₃	1	16	yes	—
561	C₄²	C₂⁴×C₃	1	8	yes	—
562	C₄²	C₂⁴×C₃	1	16	yes	—
563	C₂²×C₃	—	2	8	no	—
564	C₂²×C₃	—	2	2	no	—
565	C₂²×C₃	—	2	2	no	—
566	C₂²×C₃	—	2	2	no	—
567	C₂²×C₃	—	2	8	no	—
568	C₂²×C₃	—	2	8	no	—
569	C₂²×C₃	—	2	16	no	—
570	C₂²×C₃	—	2	16	no	—
571	C₂²×C₃	—	8	8	no	—
572	C₂²×C₃	—	8	16	no	—
573	C₂²×C₃	—	16	8	no	—
574	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
575	C₂²×C₃	#585	1	4	yes	—
576	C₂²×C₃	C₂⁶	1	1	yes	characteristic
577	C₃×C₄	—	2	2	no	—
578	C₃×C₄	—	2	8	no	—
579	C₃×C₄	—	2	8	no	—
580	C₃×C₄	—	2	4	no	—
581	C₃×C₄	—	2	4	no	—
582	C₃×C₄	—	2	16	no	—
583	C₃×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	8	no	—
587	C₂³	—	2	16	no	—
588	C₂³	—	4	8	no	—
589	C₂³	—	4	8	no	—
590	C₂³	—	4	8	no	—
591	C₂³	—	4	8	no	—
592	C₂³	—	4	16	no	—
593	C₂³	—	8	16	no	—
594	C₂³	C₂⁵×C₃	1	8	yes	—
595	C₂³	C₂⁵×C₃	1	8	yes	—
596	C₂³	C₂⁵×C₃	1	1	yes	characteristic
597	C₂³	C₂⁵×C₃	1	2	yes	—
598	Q₈	—	2	16	no	—
599	Q₈	—	2	8	no	—
600	Q₈	—	4	8	no	—
601	Q₈	—	4	8	no	—
602	Q₈	—	4	8	no	—
603	D₄	—	2	16	no	—
604	D₄	—	2	32	no	—
605	D₄	—	2	16	no	—
606	D₄	—	2	8	no	—
607	D₄	—	4	8	no	—
608	D₄	—	4	16	no	—
609	D₄	—	4	32	no	—
610	D₄	—	4	8	no	—
611	D₄	—	4	8	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	8	no	—
614	C₂×C₄	—	2	8	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	16	no	—
617	C₂×C₄	—	4	8	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	8	no	—
622	C₂×C₄	—	4	16	no	—
623	C₂×C₄	—	4	16	no	—
624	C₂×C₄	—	4	16	no	—
625	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
626	C₂×C₄	C₂⁵×C₃	1	4	yes	—
627	C₂×C₄	C₂⁵×C₃	1	4	yes	—
628	C₂×C₄	C₂⁵×C₃	1	16	yes	—
629	C₂×C₄	C₂⁵×C₃	1	2	yes	—
630	C₂×C₄	C₂⁵×C₃	1	8	yes	—
631	C₂×C₄	C₂⁵×C₃	1	8	yes	—
632	C₂×C₄	C₂⁵×C₃	1	2	yes	—
633	C₂×C₃	—	2	2	no	—
634	C₂×C₃	—	2	4	no	—
635	C₂×C₃	—	4	8	no	—
636	C₂×C₃	—	4	8	no	—
637	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
638	C₂×C₃	C₂×#585	1	2	yes	—
639	C₂²	—	2	8	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	8	no	—
644	C₂²	—	2	8	no	—
645	C₂²	—	2	16	no	—
646	C₂²	—	2	16	no	—
647	C₂²	—	8	8	no	—
648	C₂²	—	8	16	no	—
649	C₂²	—	16	8	no	—
650	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
651	C₂²	C₃×#585	1	4	yes	—
652	C₂²	C₂⁶×C₃	1	1	yes	characteristic
653	C₄	—	2	2	no	—
654	C₄	—	2	8	no	—
655	C₄	—	2	8	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	16	no	—
659	C₄	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
660	C₃	#62824	1	1	yes	characteristic, direct product factor, Sylow
661	C₂	—	2	2	no	—
662	C₂	—	2	4	no	—
663	C₂	—	4	8	no	—
664	C₂	—	4	8	no	—
665	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂	C₂×C₃×#585	1	2	yes	—

	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×#3561	C₂	semidirect
2. C₃×#3558	C₂	semidirect
3. C₃×#3545	C₂	semidirect
4. C₃×#3514	C₂	semidirect
5. C₃×#3510	C₂	semidirect
6. C₃×#3500	C₂	semidirect
7. C₃×#3490	C₂	semidirect
8. C₃×#3486	C₂	semidirect
9. C₃×#3484	C₂	semidirect
10. C₃×#3444	C₂	semidirect
11. C₂²×C₃×#124	C₂	semidirect
12. #62824	C₃	direct (N × H)
13. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
14. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
15. C₂³×C₃×Q₈	C₂²	semidirect
17. C₃×#563	C₂²	semidirect
18. C₃×#562	C₂²	semidirect
19. C₃×H(3,𝔽₄)	C₂²	semidirect
20. C₃×#559	C₂²	semidirect
21. C₃×#556	C₂²	semidirect
22. C₃×#555	C₂²	semidirect
23. C₃×#551	C₂²	semidirect
24. C₃×#551	C₂²	semidirect
25. C₃×#551	C₂²	semidirect
26. C₃×D₄×Q₈	C₂²	semidirect
27. C₃×#548	C₂²	semidirect
28. C₃×#548	C₂²	semidirect
29. C₃×#546	C₂²	semidirect
30. C₃×#546	C₂²	semidirect
31. C₃×#546	C₂²	semidirect
32. C₃×#546	C₂²	semidirect
33. C₃×D₄²	C₂²	semidirect
34. C₃×#543	C₂²	semidirect
35. C₃×#542	C₂²	semidirect
36. C₃×#542	C₂²	semidirect
37. C₃×#538	C₂²	semidirect
38. C₃×#538	C₂²	semidirect
39. C₃×#538	C₂²	semidirect
40. C₃×#536	C₂²	semidirect
41. C₃×#536	C₂²	semidirect
42. C₃×#536	C₂²	semidirect
44. C₃×#535	C₂²	semidirect
45. C₃×#534	C₂²	semidirect
46. C₃×#534	C₂²	semidirect
47. C₃×#533	C₂²	semidirect
48. C₃×#533	C₂²	semidirect
49. C₃×#532	C₂²	semidirect
50. C₃×#532	C₂²	semidirect
51. C₃×#532	C₂²	semidirect
52. C₃×#529	C₂²	semidirect
53. C₃×#529	C₂²	semidirect
54. C₃×#529	C₂²	semidirect
55. C₃×#529	C₂²	semidirect
56. C₂×C₃×#124	C₂²	semidirect
57. C₂×C₃×#124	C₂²	semidirect
58. C₂×C₃×#124	C₂²	semidirect
59. C₂×C₃×#124	C₂²	semidirect
60. C₂×C₃×#124	C₂²	semidirect
61. C₃×#525	C₂²	semidirect
62. C₃×#525	C₂²	semidirect
63. C₃×#525	C₂²	semidirect
64. C₂×C₃×#120	C₂²	semidirect
65. C₃×#519	C₂²	semidirect
66. C₃×#518	C₂²	semidirect
67. C₃×#518	C₂²	semidirect
68. C₃×C₄×#41	C₂²	semidirect
69. C₃×C₄×#41	C₂²	semidirect
70. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
71. C₂²×C₃×C₄²	C₂²	semidirect
72. #3561	C₂×C₃	semidirect
73. #3558	C₂×C₃	semidirect
74. #3545	C₂×C₃	semidirect
75. #3514	C₂×C₃	semidirect
76. #3510	C₂×C₃	semidirect
77. #3500	C₂×C₃	semidirect
78. #3490	C₂×C₃	semidirect
79. #3486	C₂×C₃	semidirect
80. #3484	C₂×C₃	semidirect
81. #3444	C₂×C₃	semidirect
82. C₂²×#124	C₂×C₃	semidirect
90. C₂×C₃×#41	C₂³	semidirect
95. C₂²×C₃×Q₈	C₂³	semidirect
106. C₃×C₄⋊Q₈	C₂³	semidirect
107. C₃×C₄⋊Q₈	C₂³	semidirect
108. C₃×C₄⋊Q₈	C₂³	semidirect
109. C₃×C₄⋊Q₈	C₂³	semidirect
111. C₃×#127	C₂³	semidirect
112. C₃×#126	C₂³	semidirect
113. C₃×#126	C₂³	semidirect
114. C₃×#126	C₂³	semidirect
115. C₃×#125	C₂³	semidirect
116. C₃×#125	C₂³	semidirect
124. C₃×#124	C₂³	semidirect
125. C₃×#124	C₂³	semidirect
126. C₃×#124	C₂³	semidirect
127. C₃×#124	C₂³	semidirect
128. C₃×#124	C₂³	semidirect
129. C₃×#124	C₂³	semidirect
134. C₃×#123	C₂³	semidirect
135. C₃×#123	C₂³	semidirect
136. C₃×#123	C₂³	semidirect
141. C₃×C₂²⋊Q₈	C₂³	semidirect
142. C₃×C₂²⋊Q₈	C₂³	semidirect
143. C₃×C₂²⋊Q₈	C₂³	semidirect
144. C₃×C₂²⋊Q₈	C₂³	semidirect
151. C₃×#121	C₂³	semidirect
152. C₃×#121	C₂³	semidirect
157. C₃×#120	C₂³	semidirect
158. C₃×C₄×Q₈	C₂³	semidirect
159. C₃×C₄×Q₈	C₂³	semidirect
160. C₃×C₄×Q₈	C₂³	semidirect
161. C₃×C₄×Q₈	C₂³	semidirect
167. C₃×C₄×D₄	C₂³	semidirect
168. C₃×C₄×D₄	C₂³	semidirect
169. C₃×C₄×D₄	C₂³	semidirect
170. C₃×C₄×D₄	C₂³	semidirect
171. C₃×C₄×D₄	C₂³	semidirect
175. C₃×#117	C₂³	semidirect
176. C₃×#117	C₂³	semidirect
177. C₃×#117	C₂³	semidirect
184. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
189. C₂×C₃×C₄²	C₂³	semidirect
190. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
191. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
192. C₂³×Q₈	C₂²×C₃	semidirect
194. #563	C₂²×C₃	semidirect
195. #562	C₂²×C₃	semidirect
196. H(3,𝔽₄)	C₂²×C₃	semidirect
197. #559	C₂²×C₃	semidirect
198. #556	C₂²×C₃	semidirect
199. #555	C₂²×C₃	semidirect
200. #551	C₂²×C₃	semidirect
201. #551	C₂²×C₃	semidirect
202. #551	C₂²×C₃	semidirect
203. D₄×Q₈	C₂²×C₃	semidirect
204. #548	C₂²×C₃	semidirect
205. #548	C₂²×C₃	semidirect
206. #546	C₂²×C₃	semidirect
207. #546	C₂²×C₃	semidirect
208. #546	C₂²×C₃	semidirect
209. #546	C₂²×C₃	semidirect
210. D₄²	C₂²×C₃	semidirect
211. #543	C₂²×C₃	semidirect
212. #542	C₂²×C₃	semidirect
213. #542	C₂²×C₃	semidirect
214. #538	C₂²×C₃	semidirect
215. #538	C₂²×C₃	semidirect
216. #538	C₂²×C₃	semidirect
217. #536	C₂²×C₃	semidirect
218. #536	C₂²×C₃	semidirect
219. #536	C₂²×C₃	semidirect
221. #535	C₂²×C₃	semidirect
222. #534	C₂²×C₃	semidirect
223. #534	C₂²×C₃	semidirect
224. #533	C₂²×C₃	semidirect
225. #533	C₂²×C₃	semidirect
226. #532	C₂²×C₃	semidirect
227. #532	C₂²×C₃	semidirect
228. #532	C₂²×C₃	semidirect
229. #529	C₂²×C₃	semidirect
230. #529	C₂²×C₃	semidirect
231. #529	C₂²×C₃	semidirect
232. #529	C₂²×C₃	semidirect
233. C₂×#124	C₂²×C₃	semidirect
234. C₂×#124	C₂²×C₃	semidirect
235. C₂×#124	C₂²×C₃	semidirect
236. C₂×#124	C₂²×C₃	semidirect
237. C₂×#124	C₂²×C₃	semidirect
238. #525	C₂²×C₃	semidirect
239. #525	C₂²×C₃	semidirect
240. #525	C₂²×C₃	semidirect
241. C₂×#120	C₂²×C₃	semidirect
242. #519	C₂²×C₃	semidirect
243. #518	C₂²×C₃	semidirect
244. #518	C₂²×C₃	semidirect
245. C₄×#41	C₂²×C₃	semidirect
246. C₄×#41	C₂²×C₃	semidirect
247. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
248. C₂²×C₄²	C₂²×C₃	semidirect
335. C₂×#41	C₂³×C₃	semidirect
340. C₂²×Q₈	C₂³×C₃	semidirect
351. C₄⋊Q₈	C₂³×C₃	semidirect
352. C₄⋊Q₈	C₂³×C₃	semidirect
353. C₄⋊Q₈	C₂³×C₃	semidirect
354. C₄⋊Q₈	C₂³×C₃	semidirect
356. #127	C₂³×C₃	semidirect
357. #126	C₂³×C₃	semidirect
358. #126	C₂³×C₃	semidirect
359. #126	C₂³×C₃	semidirect
360. #125	C₂³×C₃	semidirect
361. #125	C₂³×C₃	semidirect
369. #124	C₂³×C₃	semidirect
370. #124	C₂³×C₃	semidirect
371. #124	C₂³×C₃	semidirect
372. #124	C₂³×C₃	semidirect
373. #124	C₂³×C₃	semidirect
374. #124	C₂³×C₃	semidirect
379. #123	C₂³×C₃	semidirect
380. #123	C₂³×C₃	semidirect
381. #123	C₂³×C₃	semidirect
386. C₂²⋊Q₈	C₂³×C₃	semidirect
387. C₂²⋊Q₈	C₂³×C₃	semidirect
388. C₂²⋊Q₈	C₂³×C₃	semidirect
389. C₂²⋊Q₈	C₂³×C₃	semidirect
396. #121	C₂³×C₃	semidirect
397. #121	C₂³×C₃	semidirect
402. #120	C₂³×C₃	semidirect
403. C₄×Q₈	C₂³×C₃	semidirect
404. C₄×Q₈	C₂³×C₃	semidirect
405. C₄×Q₈	C₂³×C₃	semidirect
406. C₄×Q₈	C₂³×C₃	semidirect
412. C₄×D₄	C₂³×C₃	semidirect
413. C₄×D₄	C₂³×C₃	semidirect
414. C₄×D₄	C₂³×C₃	semidirect
415. C₄×D₄	C₂³×C₃	semidirect
416. C₄×D₄	C₂³×C₃	semidirect
420. #117	C₂³×C₃	semidirect
421. #117	C₂³×C₃	semidirect
422. #117	C₂³×C₃	semidirect
429. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
434. C₂×C₄²	C₂³×C₃	semidirect
660. C₃	#62824	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×#3561	2
C₃×#3558	2
C₃×#3545	2
C₃×#3514	2
C₃×#3510	2
C₃×#3500	2
C₃×#3490	2
C₃×#3486	2
C₃×#3484	2
C₃×#3444	2
C₂²×C₃×#124	2
#62824	3

Subgroups — C3×#62824 #10681431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#62824 #10681431