Subgroups — C₃×#60141 #10678748

Order 768.

2862 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#525	C₂	1	1	yes	maximal, characteristic
4	C₃×D₄×M₁₆	C₂	1	8	yes	maximal, complemented
5	C₃×#2933	C₂	1	8	yes	maximal, complemented
6	C₃×#2930	C₂	1	4	yes	maximal, complemented
7	C₃×#2929	C₂	1	4	yes	maximal, complemented
8	C₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
12	#60141	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
14	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
15	C₃×#568	—	2	8	no	—
16	C₂×C₃×#131	C₂²	1	4	yes	complemented
17	C₂×C₃×#131	C₂²	1	4	yes	complemented
18	C₂²×C₃×M₁₆	—	2	8	no	—
19	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×M₁₆	C₂²	1	4	yes	—
23	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₃×M₁₆	C₂²	1	2	yes	complemented
25	C₂²×C₃×M₁₆	C₂²	1	4	yes	complemented
26	C₂²×C₃×M₁₆	C₂²	1	4	yes	complemented
27	C₂³×C₃×C₈	C₂²	1	2	yes	complemented
28	C₃×#525	C₄	1	2	yes	—
29	C₃×#525	C₄	1	4	yes	—
30	C₃×#525	C₄	1	2	yes	—
31	C₃×#525	C₂²	1	2	yes	—
32	C₃×#525	C₂²	1	2	yes	—
33	C₃×#525	C₂²	1	4	yes	—
34	C₂×C₃×#123	C₄	1	2	yes	—
35	C₂×C₃×C₂²⋊Q₈	C₄	1	2	yes	—
36	C₂×C₃×#121	C₄	1	2	yes	—
37	C₂×C₃×#120	C₄	1	2	yes	—
38	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
39	C₂×C₃×#117	C₂²	1	1	yes	characteristic
40	C₃×#436	C₂²	1	16	yes	complemented
41	C₃×#435	C₂²	1	16	yes	complemented
42	C₃×#435	C₂²	1	16	yes	complemented
43	C₃×C₈×D₄	C₂²	1	16	yes	complemented
44	C₃×#424	C₂²	1	4	yes	complemented
45	C₃×#424	C₂²	1	4	yes	complemented
46	C₃×#423	C₂²	1	4	yes	complemented
47	C₃×#408	C₂²	1	4	yes	complemented
48	C₃×#408	C₂²	1	4	yes	complemented
49	C₃×#407	C₂²	1	4	yes	—
50	C₃×#407	C₂²	1	2	yes	complemented
51	C₃×#407	C₂²	1	2	yes	complemented
52	C₃×#407	C₂²	1	4	yes	complemented
53	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
54	C₃×#405	C₂²	1	4	yes	complemented
55	C₃×#405	C₂²	1	4	yes	complemented
56	C₃×C₄×M₁₆	C₂²	1	4	yes	complemented
57	C₂×#568	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂³×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×#525	C₂×C₃	1	1	yes	characteristic
60	D₄×M₁₆	C₂×C₃	1	8	yes	complemented
61	#2933	C₂×C₃	1	8	yes	complemented
62	#2930	C₂×C₃	1	4	yes	complemented
63	#2929	C₂×C₃	1	4	yes	complemented
64	#2905	C₂×C₃	1	1	yes	characteristic, complemented
65	#2879	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×#407	C₂×C₃	1	1	yes	characteristic, complemented
67	#2873	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂⁵×C₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×#41	—	2	4	no	—
70	C₂×C₃×#41	—	2	4	no	—
71	C₂×C₃×#41	C₂×C₄	1	2	yes	—
72	C₂×C₃×#41	C₂×C₄	1	2	yes	—
73	C₂×C₃×#41	C₂³	1	2	yes	—
74	C₂×C₃×#41	C₂³	1	2	yes	—
75	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
77	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₃×D₄	C₂×C₄	1	4	yes	—
79	C₂³×C₃×C₄	—	2	4	no	—
80	C₂³×C₃×C₄	—	2	4	no	—
81	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
82	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
85	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
86	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
87	C₂³×C₃×C₄	C₂³	1	2	yes	—
88	C₂³×C₃×C₄	C₂³	1	2	yes	—
89	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
90	C₂³×C₃×C₄	C₂³	1	2	yes	—
91	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
92	C₃×#131	—	2	16	no	—
93	C₃×#131	—	2	16	no	—
94	C₂×C₃×M₁₆	—	2	4	no	—
95	C₂×C₃×M₁₆	—	2	4	no	—
96	C₂×C₃×M₁₆	—	2	4	no	—
97	C₂×C₃×M₁₆	—	2	16	no	—
98	C₂×C₃×M₁₆	—	2	16	no	—
99	C₂×C₃×M₁₆	—	2	16	no	—
100	C₂×C₃×M₁₆	—	2	8	no	—
101	C₂×C₃×M₁₆	D₄	1	8	yes	complemented
102	C₂×C₃×M₁₆	C₂³	1	2	yes	—
103	C₂×C₃×M₁₆	C₂³	1	2	yes	—
104	C₂×C₃×M₁₆	C₂³	1	2	yes	—
105	C₂×C₃×M₁₆	C₂³	1	8	yes	—
106	C₂×C₃×M₁₆	C₂³	1	2	yes	—
107	C₂×C₃×M₁₆	C₂³	1	2	yes	—
108	C₂×C₃×M₁₆	C₂³	1	2	yes	—
109	C₂×C₃×M₁₆	C₂³	1	2	yes	—
110	C₂×C₃×M₁₆	C₂³	1	2	yes	—
111	C₂×C₃×M₁₆	C₂³	1	8	yes	complemented
112	C₂²×C₃×C₈	—	2	8	no	—
113	C₂²×C₃×C₈	C₂³	1	2	yes	—
114	C₂²×C₃×C₈	C₂³	1	8	yes	—
115	C₂²×C₃×C₈	C₂³	1	2	yes	—
116	C₂²×C₃×C₈	C₂³	1	2	yes	—
117	C₂²×C₃×C₈	C₂³	1	2	yes	—
118	C₂²×C₃×C₈	C₂³	1	8	yes	complemented
119	C₃×#123	C₂×C₄	1	4	yes	—
120	C₃×#123	C₂×C₄	1	4	yes	—
121	C₃×#123	C₂×C₄	1	8	yes	—
122	C₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
123	C₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
124	C₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
125	C₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
126	C₃×#121	C₂×C₄	1	4	yes	—
127	C₃×#121	C₂×C₄	1	4	yes	—
128	C₃×#121	C₂×C₄	1	4	yes	—
129	C₃×#121	C₂×C₄	1	4	yes	—
130	C₃×#120	C₂×C₄	1	4	yes	—
131	C₃×#120	C₂×C₄	1	8	yes	—
132	C₃×#120	C₂×C₄	1	4	yes	—
133	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
134	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
135	C₃×C₄×D₄	C₂³	1	8	yes	—
136	C₃×C₄×D₄	C₂³	1	8	yes	—
137	C₃×#117	C₂×C₄	1	2	yes	—
138	C₃×#117	C₂×C₄	1	2	yes	—
139	C₃×#117	C₂³	1	2	yes	—
140	C₃×#117	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
143	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
146	C₂×C₃×C₄²	C₂³	1	2	yes	—
147	C₃×C₄⋊C₈	C₂³	1	16	yes	complemented
148	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
149	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
150	C₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
151	C₃×#97	C₂³	1	8	yes	complemented
152	C₃×C₄×C₈	C₂³	1	8	yes	complemented
153	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
154	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
155	#568	—	2	8	no	—
156	C₂×#131	C₂²×C₃	1	4	yes	complemented
157	C₂×#131	C₂²×C₃	1	4	yes	complemented
158	C₂²×M₁₆	—	2	8	no	—
159	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
160	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
161	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
162	C₂²×M₁₆	C₂²×C₃	1	4	yes	—
163	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
164	C₂²×M₁₆	C₂²×C₃	1	2	yes	complemented
165	C₂²×M₁₆	C₂²×C₃	1	4	yes	complemented
166	C₂²×M₁₆	C₂²×C₃	1	4	yes	complemented
167	C₂³×C₈	C₂²×C₃	1	2	yes	complemented
168	#525	C₃×C₄	1	2	yes	—
169	#525	C₃×C₄	1	4	yes	—
170	#525	C₃×C₄	1	2	yes	—
171	#525	C₂²×C₃	1	2	yes	—
172	#525	C₂²×C₃	1	2	yes	—
173	#525	C₂²×C₃	1	4	yes	—
174	C₂×#123	C₃×C₄	1	2	yes	—
175	C₂×C₂²⋊Q₈	C₃×C₄	1	2	yes	—
176	C₂×#121	C₃×C₄	1	2	yes	—
177	C₂×#120	C₃×C₄	1	2	yes	—
178	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
179	C₂×#117	C₂²×C₃	1	1	yes	characteristic
180	#436	C₂²×C₃	1	16	yes	complemented
181	#435	C₂²×C₃	1	16	yes	complemented
182	#435	C₂²×C₃	1	16	yes	complemented
183	C₈×D₄	C₂²×C₃	1	16	yes	complemented
184	#424	C₂²×C₃	1	4	yes	complemented
185	#424	C₂²×C₃	1	4	yes	complemented
186	#423	C₂²×C₃	1	4	yes	complemented
187	#408	C₂²×C₃	1	4	yes	complemented
188	#408	C₂²×C₃	1	4	yes	complemented
189	#407	C₂²×C₃	1	4	yes	—
190	#407	C₂²×C₃	1	2	yes	complemented
191	#407	C₂²×C₃	1	2	yes	complemented
192	#407	C₂²×C₃	1	4	yes	complemented
193	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	complemented
194	#405	C₂²×C₃	1	4	yes	complemented
195	#405	C₂²×C₃	1	4	yes	complemented
196	C₄×M₁₆	C₂²×C₃	1	4	yes	complemented
197	C₂⁴×C₃	—	2	4	no	—
198	C₂⁴×C₃	—	4	4	no	—
199	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
200	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
201	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
202	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
203	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
204	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
205	C₃×#41	—	2	8	no	—
206	C₃×#41	—	2	8	no	—
207	C₃×#41	—	2	4	no	—
208	C₃×#41	—	2	4	no	—
209	C₃×#41	—	2	4	no	—
210	C₃×#41	—	2	4	no	—
211	C₂×C₃×Q₈	—	2	4	no	—
212	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
213	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
214	C₂×C₃×D₄	—	2	8	no	—
215	C₂×C₃×D₄	—	2	4	no	—
216	C₂×C₃×D₄	—	4	8	no	—
217	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
218	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
219	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
220	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
221	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
222	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
223	C₂²×C₃×C₄	—	2	4	no	—
224	C₂²×C₃×C₄	—	2	8	no	—
225	C₂²×C₃×C₄	—	2	4	no	—
226	C₂²×C₃×C₄	—	2	4	no	—
227	C₂²×C₃×C₄	—	2	8	no	—
228	C₂²×C₃×C₄	—	2	2	no	—
229	C₂²×C₃×C₄	—	2	4	no	—
230	C₂²×C₃×C₄	—	2	4	no	—
231	C₂²×C₃×C₄	—	2	2	no	—
232	C₂²×C₃×C₄	—	2	4	no	—
233	C₂²×C₃×C₄	—	2	4	no	—
234	C₂²×C₃×C₄	—	2	4	no	—
235	C₂²×C₃×C₄	—	2	2	no	—
236	C₂²×C₃×C₄	—	2	2	no	—
237	C₂²×C₃×C₄	—	2	4	no	—
238	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
239	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
240	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
241	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
242	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
243	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
244	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
245	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
246	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
247	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
249	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
251	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
254	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
255	C₂²×C₃×C₄	#41	1	4	yes	—
256	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
257	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
258	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
259	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
262	C₃×M₁₆	—	2	4	no	—
263	C₃×M₁₆	—	2	4	no	—
264	C₃×M₁₆	—	2	4	no	—
265	C₃×M₁₆	—	2	4	no	—
266	C₃×M₁₆	—	2	4	no	—
267	C₃×M₁₆	—	2	4	no	—
268	C₃×M₁₆	—	2	16	no	—
269	C₃×M₁₆	—	2	16	no	—
270	C₃×M₁₆	C₂×D₄	1	8	yes	—
271	C₃×M₁₆	C₂×D₄	1	8	yes	complemented
272	C₂×C₃×C₈	—	2	4	no	—
273	C₂×C₃×C₈	—	2	4	no	—
274	C₂×C₃×C₈	—	2	4	no	—
275	C₂×C₃×C₈	—	2	16	no	—
276	C₂×C₃×C₈	—	2	16	no	—
277	C₂×C₃×C₈	C₂×D₄	1	8	yes	complemented
278	C₂×C₃×C₈	C₂⁴	1	4	yes	—
279	C₂×C₃×C₈	C₂⁴	1	4	yes	—
280	C₂×C₃×C₈	C₂⁴	1	4	yes	—
281	C₂×C₃×C₈	C₂⁴	1	4	yes	—
282	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
283	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
284	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
285	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
286	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
287	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
288	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
289	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
290	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
291	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
292	C₃×C₄²	C₂²×C₄	1	4	yes	—
293	C₃×C₄²	C₂⁴	1	4	yes	—
294	C₂⁵	C₂×C₃×C₄	1	1	yes	characteristic
295	C₂×#41	—	2	4	no	—
296	C₂×#41	—	2	4	no	—
297	C₂×#41	C₂×C₃×C₄	1	2	yes	—
298	C₂×#41	C₂×C₃×C₄	1	2	yes	—
299	C₂×#41	C₂³×C₃	1	2	yes	—
300	C₂×#41	C₂³×C₃	1	2	yes	—
301	C₂²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
302	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
303	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
304	C₂²×D₄	C₂×C₃×C₄	1	4	yes	—
305	C₂³×C₄	—	2	4	no	—
306	C₂³×C₄	—	2	4	no	—
307	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
308	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
309	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
310	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
311	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₃	1	2	yes	—
313	C₂³×C₄	C₂³×C₃	1	2	yes	—
314	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₃	1	2	yes	—
316	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
318	#131	—	2	16	no	—
319	#131	—	2	16	no	—
320	C₂×M₁₆	—	2	4	no	—
321	C₂×M₁₆	—	2	4	no	—
322	C₂×M₁₆	—	2	4	no	—
323	C₂×M₁₆	—	2	16	no	—
324	C₂×M₁₆	—	2	16	no	—
325	C₂×M₁₆	—	2	16	no	—
326	C₂×M₁₆	—	2	8	no	—
327	C₂×M₁₆	C₃×D₄	1	8	yes	complemented
328	C₂×M₁₆	C₂³×C₃	1	2	yes	—
329	C₂×M₁₆	C₂³×C₃	1	2	yes	—
330	C₂×M₁₆	C₂³×C₃	1	2	yes	—
331	C₂×M₁₆	C₂³×C₃	1	8	yes	—
332	C₂×M₁₆	C₂³×C₃	1	2	yes	—
333	C₂×M₁₆	C₂³×C₃	1	2	yes	—
334	C₂×M₁₆	C₂³×C₃	1	2	yes	—
335	C₂×M₁₆	C₂³×C₃	1	2	yes	—
336	C₂×M₁₆	C₂³×C₃	1	2	yes	—
337	C₂×M₁₆	C₂³×C₃	1	8	yes	complemented
338	C₂²×C₈	—	2	8	no	—
339	C₂²×C₈	C₂³×C₃	1	2	yes	—
340	C₂²×C₈	C₂³×C₃	1	8	yes	—
341	C₂²×C₈	C₂³×C₃	1	2	yes	—
342	C₂²×C₈	C₂³×C₃	1	2	yes	—
343	C₂²×C₈	C₂³×C₃	1	2	yes	—
344	C₂²×C₈	C₂³×C₃	1	8	yes	complemented
345	#123	C₂×C₃×C₄	1	4	yes	—
346	#123	C₂×C₃×C₄	1	4	yes	—
347	#123	C₂×C₃×C₄	1	8	yes	—
348	C₂²⋊Q₈	C₂×C₃×C₄	1	4	yes	—
349	C₂²⋊Q₈	C₂×C₃×C₄	1	4	yes	—
350	C₂²⋊Q₈	C₂×C₃×C₄	1	4	yes	—
351	C₂²⋊Q₈	C₂×C₃×C₄	1	4	yes	—
352	#121	C₂×C₃×C₄	1	4	yes	—
353	#121	C₂×C₃×C₄	1	4	yes	—
354	#121	C₂×C₃×C₄	1	4	yes	—
355	#121	C₂×C₃×C₄	1	4	yes	—
356	#120	C₂×C₃×C₄	1	4	yes	—
357	#120	C₂×C₃×C₄	1	8	yes	—
358	#120	C₂×C₃×C₄	1	4	yes	—
359	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
360	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
361	C₄×D₄	C₂³×C₃	1	8	yes	—
362	C₄×D₄	C₂³×C₃	1	8	yes	—
363	#117	C₂×C₃×C₄	1	2	yes	—
364	#117	C₂×C₃×C₄	1	2	yes	—
365	#117	C₂³×C₃	1	2	yes	—
366	#117	C₂³×C₃	1	2	yes	—
367	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
368	C₂×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
370	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
372	C₂×C₄²	C₂³×C₃	1	2	yes	—
373	C₄⋊C₈	C₂³×C₃	1	16	yes	complemented
374	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
375	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
376	C₂²⋊C₈	C₂³×C₃	1	16	yes	complemented
377	#97	C₂³×C₃	1	8	yes	complemented
378	C₄×C₈	C₂³×C₃	1	8	yes	complemented
379	C₂³×C₃	—	2	2	no	—
380	C₂³×C₃	—	2	4	no	—
381	C₂³×C₃	—	2	4	no	—
382	C₂³×C₃	—	2	4	no	—
383	C₂³×C₃	—	2	2	no	—
384	C₂³×C₃	—	2	4	no	—
385	C₂³×C₃	—	2	4	no	—
386	C₂³×C₃	—	2	4	no	—
387	C₂³×C₃	—	4	2	no	—
388	C₂³×C₃	—	4	2	no	—
389	C₂³×C₃	—	4	2	no	—
390	C₂³×C₃	—	4	2	no	—
391	C₂³×C₃	—	4	4	no	—
392	C₂³×C₃	—	4	16	no	—
393	C₂³×C₃	C₄×D₄	1	4	yes	—
394	C₂³×C₃	C₂³×C₄	1	2	yes	—
395	C₂³×C₃	C₂³×C₄	1	4	yes	—
396	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
397	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
398	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
399	C₂³×C₃	C₂³×C₄	1	2	yes	—
400	C₃×Q₈	—	2	4	no	—
401	C₃×Q₈	—	2	4	no	—
402	C₃×D₄	—	2	8	no	—
403	C₃×D₄	—	2	8	no	—
404	C₃×D₄	—	2	16	no	—
405	C₃×D₄	—	2	4	no	—
406	C₃×D₄	—	2	4	no	—
407	C₃×D₄	—	4	8	no	—
408	C₂×C₃×C₄	—	2	4	no	—
409	C₂×C₃×C₄	—	2	2	no	—
410	C₂×C₃×C₄	—	2	4	no	—
411	C₂×C₃×C₄	—	2	2	no	—
412	C₂×C₃×C₄	—	2	4	no	—
413	C₂×C₃×C₄	—	2	4	no	—
414	C₂×C₃×C₄	—	2	4	no	—
415	C₂×C₃×C₄	—	2	4	no	—
416	C₂×C₃×C₄	—	2	4	no	—
417	C₂×C₃×C₄	—	2	4	no	—
418	C₂×C₃×C₄	—	2	4	no	—
419	C₂×C₃×C₄	—	2	8	no	—
420	C₂×C₃×C₄	—	2	2	no	—
421	C₂×C₃×C₄	—	2	4	no	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	2	2	no	—
424	C₂×C₃×C₄	—	2	2	no	—
425	C₂×C₃×C₄	—	2	4	no	—
426	C₂×C₃×C₄	—	4	4	no	—
427	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
428	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
429	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
430	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
431	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
432	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
433	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
434	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
435	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
436	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
437	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
438	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
439	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
440	C₂×C₃×C₄	C₂×#41	1	2	yes	—
441	C₂×C₃×C₄	C₂×#41	1	2	yes	—
442	C₂×C₃×C₄	C₂×#41	1	2	yes	—
443	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
444	C₃×C₈	—	2	4	no	—
445	C₃×C₈	—	2	4	no	—
446	C₃×C₈	—	2	4	no	—
447	C₃×C₈	C₂²×D₄	1	8	yes	—
448	C₂⁴	—	2	4	no	—
449	C₂⁴	—	4	4	no	—
450	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
451	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
452	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
453	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
454	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
455	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
456	#41	—	2	8	no	—
457	#41	—	2	8	no	—
458	#41	—	2	4	no	—
459	#41	—	2	4	no	—
460	#41	—	2	4	no	—
461	#41	—	2	4	no	—
462	C₂×Q₈	—	2	4	no	—
463	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
464	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
465	C₂×D₄	—	2	8	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	4	8	no	—
468	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
469	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
470	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
471	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
472	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
473	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	8	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	8	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
490	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
491	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
492	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
493	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
494	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
495	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
496	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
497	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
498	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
499	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
500	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
501	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
502	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
503	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
506	C₂²×C₄	C₃×#41	1	4	yes	—
507	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
510	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
513	M₁₆	—	2	4	no	—
514	M₁₆	—	2	4	no	—
515	M₁₆	—	2	4	no	—
516	M₁₆	—	2	4	no	—
517	M₁₆	—	2	4	no	—
518	M₁₆	—	2	4	no	—
519	M₁₆	—	2	16	no	—
520	M₁₆	—	2	16	no	—
521	M₁₆	C₂×C₃×D₄	1	8	yes	—
522	M₁₆	C₂×C₃×D₄	1	8	yes	complemented
523	C₂×C₈	—	2	4	no	—
524	C₂×C₈	—	2	4	no	—
525	C₂×C₈	—	2	4	no	—
526	C₂×C₈	—	2	16	no	—
527	C₂×C₈	—	2	16	no	—
528	C₂×C₈	C₂×C₃×D₄	1	8	yes	complemented
529	C₂×C₈	C₂⁴×C₃	1	4	yes	—
530	C₂×C₈	C₂⁴×C₃	1	4	yes	—
531	C₂×C₈	C₂⁴×C₃	1	4	yes	—
532	C₂×C₈	C₂⁴×C₃	1	4	yes	—
533	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
534	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
535	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
536	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
537	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
538	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
539	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
540	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
541	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
542	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
543	C₄²	C₂²×C₃×C₄	1	4	yes	—
544	C₄²	C₂⁴×C₃	1	4	yes	—
545	C₂²×C₃	—	2	8	no	—
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	—	2	2	no	—
549	C₂²×C₃	—	2	2	no	—
550	C₂²×C₃	—	2	2	no	—
551	C₂²×C₃	—	2	2	no	—
552	C₂²×C₃	—	2	4	no	—
553	C₂²×C₃	—	2	8	no	—
554	C₂²×C₃	—	2	2	no	—
555	C₂²×C₃	—	2	2	no	—
556	C₂²×C₃	—	4	4	no	—
557	C₂²×C₃	—	4	8	no	—
558	C₂²×C₃	—	4	8	no	—
559	C₂²×C₃	—	4	4	no	—
560	C₂²×C₃	—	8	4	no	—
561	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
562	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
563	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
564	C₂²×C₃	#568	1	4	yes	complemented
565	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
566	C₃×C₄	—	2	2	no	—
567	C₃×C₄	—	2	2	no	—
568	C₃×C₄	—	2	4	no	—
569	C₃×C₄	—	2	8	no	—
570	C₃×C₄	C₂×C₄×D₄	1	2	yes	—
571	C₃×C₄	C₂×C₄×D₄	1	2	yes	—
572	C₃×C₄	C₂×C₄×D₄	1	2	yes	—
573	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
574	C₃×C₄	C₂²×#41	1	1	yes	characteristic
575	C₂³	—	2	4	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	4	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	4	no	—
583	C₂³	—	4	2	no	—
584	C₂³	—	4	2	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	4	no	—
588	C₂³	—	4	16	no	—
589	C₂³	C₃×C₄×D₄	1	4	yes	—
590	C₂³	C₂³×C₃×C₄	1	2	yes	—
591	C₂³	C₂³×C₃×C₄	1	4	yes	—
592	C₂³	C₂³×C₃×C₄	1	2	yes	—
593	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
594	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
595	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
596	Q₈	—	2	4	no	—
597	Q₈	—	2	4	no	—
598	D₄	—	2	16	no	—
599	D₄	—	2	8	no	—
600	D₄	—	2	8	no	—
601	D₄	—	2	4	no	—
602	D₄	—	2	4	no	—
603	D₄	—	4	8	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
624	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
625	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
626	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
627	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
628	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
629	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
630	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
631	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
632	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
633	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
634	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
635	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
636	C₂×C₄	C₂×C₃×#41	1	2	yes	—
637	C₂×C₄	C₂×C₃×#41	1	2	yes	—
638	C₂×C₄	C₂×C₃×#41	1	2	yes	—
639	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
640	C₈	—	2	4	no	—
641	C₈	—	2	4	no	—
642	C₈	—	2	4	no	—
643	C₈	C₂²×C₃×D₄	1	8	yes	—
644	C₂×C₃	—	2	2	no	—
645	C₂×C₃	—	2	4	no	—
646	C₂×C₃	—	2	2	no	—
647	C₂×C₃	—	2	2	no	—
648	C₂×C₃	—	4	2	no	—
649	C₂×C₃	—	4	4	no	—
650	C₂×C₃	C₂²×C₄×D₄	1	1	yes	characteristic
651	C₂×C₃	C₂×#568	1	2	yes	—
652	C₂²	—	2	8	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	2	8	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	8	no	—
665	C₂²	—	4	8	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	8	4	no	—
668	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
669	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
670	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
671	C₂²	C₃×#568	1	4	yes	complemented
672	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
673	C₄	—	2	2	no	—
674	C₄	—	2	2	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	8	no	—
677	C₄	C₂×C₃×C₄×D₄	1	2	yes	—
678	C₄	C₂×C₃×C₄×D₄	1	2	yes	—
679	C₄	C₂×C₃×C₄×D₄	1	2	yes	—
680	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
681	C₄	C₂²×C₃×#41	1	1	yes	characteristic
682	C₃	#60141	1	1	yes	characteristic, direct product factor, Sylow
683	C₂	—	2	4	no	—
684	C₂	—	2	2	no	—
685	C₂	—	2	2	no	—
686	C₂	—	2	2	no	—
687	C₂	—	4	2	no	—
688	C₂	—	4	4	no	—
689	C₂	C₂²×C₃×C₄×D₄	1	1	yes	characteristic
690	C₂	C₂×C₃×#568	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂⁴×C₄
prime radical	C₂×C₃×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#568	C₂	semidirect
2. C₂³×C₃×M₁₆	C₂	semidirect
4. C₃×D₄×M₁₆	C₂	semidirect
5. C₃×#2933	C₂	semidirect
6. C₃×#2930	C₂	semidirect
7. C₃×#2929	C₂	semidirect
8. C₃×#2905	C₂	semidirect
9. C₃×#2879	C₂	semidirect
10. C₂×C₃×#407	C₂	semidirect
11. C₃×#2873	C₂	semidirect
12. #60141	C₃	direct (N × H)
16. C₂×C₃×#131	C₂²	semidirect
17. C₂×C₃×#131	C₂²	semidirect
24. C₂²×C₃×M₁₆	C₂²	semidirect
25. C₂²×C₃×M₁₆	C₂²	semidirect
26. C₂²×C₃×M₁₆	C₂²	semidirect
27. C₂³×C₃×C₈	C₂²	semidirect
40. C₃×#436	C₂²	semidirect
41. C₃×#435	C₂²	semidirect
42. C₃×#435	C₂²	semidirect
43. C₃×C₈×D₄	C₂²	semidirect
44. C₃×#424	C₂²	semidirect
45. C₃×#424	C₂²	semidirect
46. C₃×#423	C₂²	semidirect
47. C₃×#408	C₂²	semidirect
48. C₃×#408	C₂²	semidirect
50. C₃×#407	C₂²	semidirect
51. C₃×#407	C₂²	semidirect
52. C₃×#407	C₂²	semidirect
53. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
54. C₃×#405	C₂²	semidirect
55. C₃×#405	C₂²	semidirect
56. C₃×C₄×M₁₆	C₂²	semidirect
57. C₂×#568	C₂×C₃	semidirect
58. C₂³×M₁₆	C₂×C₃	semidirect
60. D₄×M₁₆	C₂×C₃	semidirect
61. #2933	C₂×C₃	semidirect
62. #2930	C₂×C₃	semidirect
63. #2929	C₂×C₃	semidirect
64. #2905	C₂×C₃	semidirect
65. #2879	C₂×C₃	semidirect
66. C₂×#407	C₂×C₃	semidirect
67. #2873	C₂×C₃	semidirect
101. C₂×C₃×M₁₆	D₄	semidirect
111. C₂×C₃×M₁₆	C₂³	semidirect
118. C₂²×C₃×C₈	C₂³	semidirect
147. C₃×C₄⋊C₈	C₂³	semidirect
150. C₃×C₂²⋊C₈	C₂³	semidirect
151. C₃×#97	C₂³	semidirect
152. C₃×C₄×C₈	C₂³	semidirect
156. C₂×#131	C₂²×C₃	semidirect
157. C₂×#131	C₂²×C₃	semidirect
164. C₂²×M₁₆	C₂²×C₃	semidirect
165. C₂²×M₁₆	C₂²×C₃	semidirect
166. C₂²×M₁₆	C₂²×C₃	semidirect
167. C₂³×C₈	C₂²×C₃	semidirect
180. #436	C₂²×C₃	semidirect
181. #435	C₂²×C₃	semidirect
182. #435	C₂²×C₃	semidirect
183. C₈×D₄	C₂²×C₃	semidirect
184. #424	C₂²×C₃	semidirect
185. #424	C₂²×C₃	semidirect
186. #423	C₂²×C₃	semidirect
187. #408	C₂²×C₃	semidirect
188. #408	C₂²×C₃	semidirect
190. #407	C₂²×C₃	semidirect
191. #407	C₂²×C₃	semidirect
192. #407	C₂²×C₃	semidirect
193. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
194. #405	C₂²×C₃	semidirect
195. #405	C₂²×C₃	semidirect
196. C₄×M₁₆	C₂²×C₃	semidirect
271. C₃×M₁₆	C₂×D₄	semidirect
277. C₂×C₃×C₈	C₂×D₄	semidirect
327. C₂×M₁₆	C₃×D₄	semidirect
337. C₂×M₁₆	C₂³×C₃	semidirect
344. C₂²×C₈	C₂³×C₃	semidirect
373. C₄⋊C₈	C₂³×C₃	semidirect
376. C₂²⋊C₈	C₂³×C₃	semidirect
377. #97	C₂³×C₃	semidirect
378. C₄×C₈	C₂³×C₃	semidirect
522. M₁₆	C₂×C₃×D₄	semidirect
528. C₂×C₈	C₂×C₃×D₄	semidirect
564. C₂²×C₃	#568	semidirect
671. C₂²	C₃×#568	semidirect
682. C₃	#60141	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×#568	2
C₂³×C₃×M₁₆	2
C₂×C₃×#525	2
C₃×D₄×M₁₆	2
C₃×#2933	2
C₃×#2930	2
C₃×#2929	2
C₃×#2905	2
C₃×#2879	2
C₂×C₃×#407	2
C₃×#2873	2
#60141	3

Subgroups — C3×#60141 #10678748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60141 #10678748