Subgroups — C₂×C₃×#3290 #10679708

Order 768.

2650 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#577	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3290	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#471	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#454	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#455	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#3290	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×C₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
15	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	—
16	C₃×#578	—	2	4	no	—
17	C₃×#578	C₂²	1	8	yes	complemented
18	C₃×#577	—	2	8	no	—
19	C₃×#577	C₂²	1	16	yes	complemented
20	C₃×#576	—	2	4	no	—
21	C₃×#576	C₂²	1	8	yes	complemented
22	C₂×C₃×#137	—	2	2	no	—
23	C₂×C₃×#137	—	2	2	no	—
24	C₂×C₃×#137	C₂²	1	2	yes	—
25	C₂×C₃×#137	C₂²	1	2	yes	complemented
26	C₂×C₃×AGL(1,ℤ/8)	—	2	2	no	—
27	C₂×C₃×AGL(1,ℤ/8)	—	2	2	no	—
28	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
29	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
30	C₂×C₃×#135	—	2	1	no	—
31	C₂×C₃×#135	—	2	2	no	—
32	C₂×C₃×#135	—	2	1	no	—
33	C₂×C₃×#135	C₂²	1	1	yes	characteristic
34	C₂×C₃×#135	C₂²	1	1	yes	characteristic
35	C₂²×C₃×Q₁₆	—	2	1	no	—
36	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₃×SD₁₆	—	2	2	no	—
38	C₂²×C₃×SD₁₆	C₂²	1	2	yes	complemented
39	C₂²×C₃×D₈	—	2	1	no	—
40	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic
41	C₂×C₃×#131	C₂²	1	1	yes	characteristic
42	C₂×C₃×#131	C₂²	1	2	yes	complemented
43	C₂×C₃×#131	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×#124	C₂²	1	2	yes	complemented
45	C₃×#495	C₂²	1	8	yes	complemented
46	C₃×#473	C₂²	1	8	yes	complemented
47	C₃×#472	C₂²	1	8	yes	complemented
48	C₃×#471	C₂²	1	16	yes	complemented
49	C₃×#455	C₂²	1	16	yes	complemented
50	C₃×#454	C₂²	1	16	yes	complemented
51	C₃×#443	C₂²	1	8	yes	complemented
52	C₃×#443	C₂²	1	8	yes	complemented
53	C₂×C₃×#108	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃×#108	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×#104	C₂²	1	1	yes	characteristic
56	C₂×C₃×#104	C₂²	1	2	yes	complemented
57	C₂×C₃×#104	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×#101	C₂²	1	2	yes	complemented
59	C₂×C₃×#100	C₂²	1	2	yes	complemented
60	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
61	C₂×#578	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×#577	C₂×C₃	1	2	yes	complemented
63	C₂×#576	C₂×C₃	1	1	yes	characteristic, complemented
64	#3290	C₂×C₃	1	16	yes	direct product factor
65	C₂×#495	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×#473	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂×#472	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×#471	C₂×C₃	1	2	yes	complemented
69	C₂×#454	C₂×C₃	1	2	yes	complemented
70	C₂×#455	C₂×C₃	1	2	yes	complemented
71	C₂×#443	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂×#443	C₂×C₃	1	1	yes	characteristic, complemented
73	C₃×2₋¹⁺⁴	—	2	4	no	—
74	C₃×2₋¹⁺⁴	—	2	4	no	—
75	C₃×2₋¹⁺⁴	—	4	2	no	—
76	C₃×2₋¹⁺⁴	C₂³	1	8	yes	complemented
77	C₃×H(5,𝔽₂)	—	2	4	no	—
78	C₃×H(5,𝔽₂)	—	2	4	no	—
79	C₃×H(5,𝔽₂)	—	4	2	no	—
80	C₃×H(5,𝔽₂)	C₂³	1	8	yes	—
81	C₂×C₃×#41	—	2	2	no	—
82	C₂×C₃×#41	—	2	2	no	—
83	C₂×C₃×#41	—	2	2	no	—
84	C₂×C₃×#41	—	2	2	no	—
85	C₂×C₃×#41	—	4	2	no	—
86	C₂×C₃×#41	C₂³	1	1	yes	characteristic
87	C₂×C₃×#41	C₂³	1	2	yes	—
88	C₂×C₃×#41	C₂³	1	1	yes	characteristic
89	C₂²×C₃×Q₈	—	2	2	no	—
90	C₂²×C₃×Q₈	—	2	2	no	—
91	C₂²×C₃×Q₈	C₂³	1	2	yes	—
92	C₂²×C₃×D₄	—	2	2	no	—
93	C₂²×C₃×D₄	—	2	2	no	—
94	C₂²×C₃×D₄	—	4	2	no	—
95	C₂²×C₃×D₄	C₂³	1	2	yes	—
96	C₃×#137	—	2	4	no	—
97	C₃×#137	—	2	4	no	—
98	C₃×#137	—	2	16	no	—
99	C₃×#137	—	2	16	no	—
100	C₃×#137	C₂³	1	8	yes	—
101	C₃×#137	C₂³	1	8	yes	complemented
102	C₃×AGL(1,ℤ/8)	—	2	4	no	—
103	C₃×AGL(1,ℤ/8)	—	2	4	no	—
104	C₃×AGL(1,ℤ/8)	—	2	16	no	—
105	C₃×AGL(1,ℤ/8)	—	2	16	no	—
106	C₃×AGL(1,ℤ/8)	C₂³	1	8	yes	—
107	C₃×AGL(1,ℤ/8)	C₂³	1	8	yes	complemented
108	C₃×#135	—	2	8	no	—
109	C₃×#135	—	2	16	no	—
110	C₃×#135	—	2	8	no	—
111	C₃×#135	D₄	1	4	yes	—
112	C₃×#135	D₄	1	4	yes	—
113	C₃×#135	C₂³	1	4	yes	—
114	C₃×#135	C₂³	1	4	yes	—
115	C₂×C₃×Q₁₆	—	2	2	no	—
116	C₂×C₃×Q₁₆	—	2	2	no	—
117	C₂×C₃×Q₁₆	—	2	8	no	—
118	C₂×C₃×Q₁₆	—	2	1	no	—
119	C₂×C₃×Q₁₆	—	2	1	no	—
120	C₂×C₃×Q₁₆	—	2	2	no	—
121	C₂×C₃×Q₁₆	D₄	1	1	yes	characteristic
122	C₂×C₃×Q₁₆	D₄	1	1	yes	characteristic
123	C₂×C₃×Q₁₆	C₂³	1	4	yes	complemented
124	C₂×C₃×SD₁₆	—	2	2	no	—
125	C₂×C₃×SD₁₆	—	2	2	no	—
126	C₂×C₃×SD₁₆	—	2	2	no	—
127	C₂×C₃×SD₁₆	—	2	2	no	—
128	C₂×C₃×SD₁₆	—	2	16	no	—
129	C₂×C₃×SD₁₆	—	2	2	no	—
130	C₂×C₃×SD₁₆	—	2	2	no	—
131	C₂×C₃×SD₁₆	—	2	4	no	—
132	C₂×C₃×SD₁₆	D₄	1	1	yes	characteristic
133	C₂×C₃×SD₁₆	D₄	1	1	yes	characteristic
134	C₂×C₃×SD₁₆	D₄	1	2	yes	—
135	C₂×C₃×SD₁₆	C₂³	1	8	yes	complemented
136	C₂×C₃×D₈	—	2	2	no	—
137	C₂×C₃×D₈	—	2	2	no	—
138	C₂×C₃×D₈	—	2	8	no	—
139	C₂×C₃×D₈	—	2	1	no	—
140	C₂×C₃×D₈	—	2	1	no	—
141	C₂×C₃×D₈	—	2	2	no	—
142	C₂×C₃×D₈	D₄	1	1	yes	characteristic
143	C₂×C₃×D₈	D₄	1	1	yes	characteristic
144	C₂×C₃×D₈	C₂³	1	4	yes	—
145	C₃×#131	—	2	2	no	—
146	C₃×#131	—	2	4	no	—
147	C₃×#131	—	2	2	no	—
148	C₃×#131	C₂³	1	4	yes	—
149	C₃×#131	C₂³	1	8	yes	complemented
150	C₃×#131	C₂³	1	4	yes	complemented
151	C₂×C₃×M₁₆	—	2	1	no	—
152	C₂×C₃×M₁₆	—	2	2	no	—
153	C₂×C₃×M₁₆	—	2	1	no	—
154	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₃×M₁₆	C₂³	1	2	yes	—
156	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₈	—	2	1	no	—
158	C₂²×C₃×C₈	—	2	2	no	—
159	C₂²×C₃×C₈	—	2	1	no	—
160	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
161	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
162	C₃×#124	—	4	2	no	—
163	C₃×#124	C₂³	1	8	yes	complemented
164	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
165	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
166	C₃×#108	C₂³	1	4	yes	complemented
167	C₃×#108	C₂³	1	4	yes	complemented
168	C₃×#104	C₂³	1	4	yes	—
169	C₃×#104	C₂³	1	4	yes	complemented
170	C₃×#104	C₂³	1	8	yes	complemented
171	C₃×#101	C₂³	1	8	yes	complemented
172	C₃×#100	C₂³	1	8	yes	complemented
173	C₃×C₄×C₈	C₂³	1	4	yes	complemented
174	C₂×2₋¹⁺⁴	C₂²×C₃	1	2	yes	complemented
175	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	—
176	#578	—	2	4	no	—
177	#578	C₂²×C₃	1	8	yes	complemented
178	#577	—	2	8	no	—
179	#577	C₂²×C₃	1	16	yes	complemented
180	#576	—	2	4	no	—
181	#576	C₂²×C₃	1	8	yes	complemented
182	C₂×#137	—	2	2	no	—
183	C₂×#137	—	2	2	no	—
184	C₂×#137	C₂²×C₃	1	2	yes	—
185	C₂×#137	C₂²×C₃	1	2	yes	complemented
186	C₂×AGL(1,ℤ/8)	—	2	2	no	—
187	C₂×AGL(1,ℤ/8)	—	2	2	no	—
188	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
189	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
190	C₂×#135	—	2	1	no	—
191	C₂×#135	—	2	2	no	—
192	C₂×#135	—	2	1	no	—
193	C₂×#135	C₂²×C₃	1	1	yes	characteristic
194	C₂×#135	C₂²×C₃	1	1	yes	characteristic
195	C₂²×Q₁₆	—	2	1	no	—
196	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₂²×SD₁₆	—	2	2	no	—
198	C₂²×SD₁₆	C₂²×C₃	1	2	yes	complemented
199	C₂²×D₈	—	2	1	no	—
200	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic
201	C₂×#131	C₂²×C₃	1	1	yes	characteristic
202	C₂×#131	C₂²×C₃	1	2	yes	complemented
203	C₂×#131	C₂²×C₃	1	1	yes	characteristic, complemented
204	C₂×#124	C₂²×C₃	1	2	yes	complemented
205	#495	C₂²×C₃	1	8	yes	complemented
206	#473	C₂²×C₃	1	8	yes	complemented
207	#472	C₂²×C₃	1	8	yes	complemented
208	#471	C₂²×C₃	1	16	yes	complemented
209	#455	C₂²×C₃	1	16	yes	complemented
210	#454	C₂²×C₃	1	16	yes	complemented
211	#443	C₂²×C₃	1	8	yes	complemented
212	#443	C₂²×C₃	1	8	yes	complemented
213	C₂×#108	C₂²×C₃	1	1	yes	characteristic, complemented
214	C₂×#108	C₂²×C₃	1	1	yes	characteristic, complemented
215	C₂×#104	C₂²×C₃	1	1	yes	characteristic
216	C₂×#104	C₂²×C₃	1	2	yes	complemented
217	C₂×#104	C₂²×C₃	1	1	yes	characteristic, complemented
218	C₂×#101	C₂²×C₃	1	2	yes	complemented
219	C₂×#100	C₂²×C₃	1	2	yes	complemented
220	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
221	C₂⁴×C₃	—	2	2	no	—
222	C₂⁴×C₃	—	4	2	no	—
223	C₃×#41	—	2	1	no	—
224	C₃×#41	—	2	2	no	—
225	C₃×#41	—	2	1	no	—
226	C₃×#41	—	2	1	no	—
227	C₃×#41	—	2	2	no	—
228	C₃×#41	—	2	1	no	—
229	C₃×#41	—	2	8	no	—
230	C₃×#41	—	2	8	no	—
231	C₃×#41	—	2	8	no	—
232	C₃×#41	—	2	8	no	—
233	C₃×#41	—	4	8	no	—
234	C₃×#41	—	4	4	no	—
235	C₃×#41	—	4	4	no	—
236	C₃×#41	—	4	4	no	—
237	C₃×#41	—	4	4	no	—
238	C₃×#41	—	4	8	no	—
239	C₃×#41	C₂×D₄	1	2	yes	—
240	C₃×#41	C₂×D₄	1	4	yes	—
241	C₃×#41	C₂×D₄	1	2	yes	—
242	C₃×#41	C₂⁴	1	2	yes	—
243	C₃×#41	C₂⁴	1	4	yes	—
244	C₃×#41	C₂⁴	1	2	yes	—
245	C₂×C₃×Q₈	—	2	2	no	—
246	C₂×C₃×Q₈	—	2	8	no	—
247	C₂×C₃×Q₈	—	2	8	no	—
248	C₂×C₃×Q₈	—	2	2	no	—
249	C₂×C₃×Q₈	—	2	2	no	—
250	C₂×C₃×Q₈	—	2	2	no	—
251	C₂×C₃×Q₈	—	2	2	no	—
252	C₂×C₃×Q₈	—	4	2	no	—
253	C₂×C₃×Q₈	—	4	4	no	—
254	C₂×C₃×Q₈	—	4	4	no	—
255	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
256	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
257	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
258	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
259	C₂×C₃×D₄	—	2	1	no	—
260	C₂×C₃×D₄	—	2	2	no	—
261	C₂×C₃×D₄	—	2	1	no	—
262	C₂×C₃×D₄	—	2	8	no	—
263	C₂×C₃×D₄	—	2	8	no	—
264	C₂×C₃×D₄	—	2	2	no	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	—	2	2	no	—
267	C₂×C₃×D₄	—	2	2	no	—
268	C₂×C₃×D₄	—	2	2	no	—
269	C₂×C₃×D₄	—	4	4	no	—
270	C₂×C₃×D₄	—	4	4	no	—
271	C₂×C₃×D₄	—	4	2	no	—
272	C₂×C₃×D₄	—	4	2	no	—
273	C₂×C₃×D₄	—	4	8	no	—
274	C₂×C₃×D₄	—	4	8	no	—
275	C₂×C₃×D₄	—	4	2	no	—
276	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
277	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
278	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
279	C₂×C₃×D₄	C₂⁴	1	4	yes	—
280	C₂²×C₃×C₄	—	2	1	no	—
281	C₂²×C₃×C₄	—	2	2	no	—
282	C₂²×C₃×C₄	—	2	1	no	—
283	C₂²×C₃×C₄	—	2	1	no	—
284	C₂²×C₃×C₄	—	2	2	no	—
285	C₂²×C₃×C₄	—	4	2	no	—
286	C₂²×C₃×C₄	—	4	2	no	—
287	C₂²×C₃×C₄	—	4	2	no	—
288	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
289	C₃×Q₁₆	—	2	8	no	—
290	C₃×Q₁₆	—	2	8	no	—
291	C₃×Q₁₆	—	2	4	no	—
292	C₃×Q₁₆	—	2	4	no	—
293	C₃×Q₁₆	C₂×D₄	1	4	yes	—
294	C₃×Q₁₆	C₂×D₄	1	4	yes	—
295	C₃×SD₁₆	—	2	8	no	—
296	C₃×SD₁₆	—	2	8	no	—
297	C₃×SD₁₆	—	2	8	no	—
298	C₃×SD₁₆	—	2	8	no	—
299	C₃×SD₁₆	—	2	8	no	—
300	C₃×SD₁₆	—	2	8	no	—
301	C₃×SD₁₆	C₂×D₄	1	4	yes	—
302	C₃×SD₁₆	C₂×D₄	1	4	yes	—
303	C₃×SD₁₆	C₂×D₄	1	8	yes	—
304	C₃×D₈	—	2	8	no	—
305	C₃×D₈	—	2	8	no	—
306	C₃×D₈	—	2	4	no	—
307	C₃×D₈	—	2	4	no	—
308	C₃×D₈	C₂×D₄	1	4	yes	—
309	C₃×D₈	C₂×D₄	1	4	yes	—
310	C₃×M₁₆	—	2	1	no	—
311	C₃×M₁₆	—	2	2	no	—
312	C₃×M₁₆	—	2	1	no	—
313	C₃×M₁₆	—	2	4	no	—
314	C₃×M₁₆	—	2	8	no	—
315	C₃×M₁₆	—	2	4	no	—
316	C₃×M₁₆	C₂⁴	1	2	yes	—
317	C₃×M₁₆	C₂⁴	1	4	yes	—
318	C₃×M₁₆	C₂⁴	1	2	yes	—
319	C₂×C₃×C₈	—	2	1	no	—
320	C₂×C₃×C₈	—	2	2	no	—
321	C₂×C₃×C₈	—	2	1	no	—
322	C₂×C₃×C₈	—	2	4	no	—
323	C₂×C₃×C₈	—	2	8	no	—
324	C₂×C₃×C₈	—	2	4	no	—
325	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
326	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
327	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
328	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
329	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
330	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
331	C₂×C₃×C₈	C₂⁴	1	2	yes	—
332	C₂×C₃×C₈	C₂⁴	1	2	yes	—
333	C₃×C₂²⋊C₄	—	4	8	no	—
334	C₃×C₄²	—	2	1	no	—
335	C₃×C₄²	C₂⁴	1	2	yes	—
336	2₋¹⁺⁴	—	2	4	no	—
337	2₋¹⁺⁴	—	2	4	no	—
338	2₋¹⁺⁴	—	4	2	no	—
339	2₋¹⁺⁴	C₂³×C₃	1	8	yes	complemented
340	H(5,𝔽₂)	—	2	4	no	—
341	H(5,𝔽₂)	—	2	4	no	—
342	H(5,𝔽₂)	—	4	2	no	—
343	H(5,𝔽₂)	C₂³×C₃	1	8	yes	—
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	—	4	2	no	—
349	C₂×#41	C₂³×C₃	1	1	yes	characteristic
350	C₂×#41	C₂³×C₃	1	2	yes	—
351	C₂×#41	C₂³×C₃	1	1	yes	characteristic
352	C₂²×Q₈	—	2	2	no	—
353	C₂²×Q₈	—	2	2	no	—
354	C₂²×Q₈	C₂³×C₃	1	2	yes	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	2	no	—
357	C₂²×D₄	—	4	2	no	—
358	C₂²×D₄	C₂³×C₃	1	2	yes	—
359	#137	—	2	4	no	—
360	#137	—	2	4	no	—
361	#137	—	2	16	no	—
362	#137	—	2	16	no	—
363	#137	C₂³×C₃	1	8	yes	—
364	#137	C₂³×C₃	1	8	yes	complemented
365	AGL(1,ℤ/8)	—	2	4	no	—
366	AGL(1,ℤ/8)	—	2	4	no	—
367	AGL(1,ℤ/8)	—	2	16	no	—
368	AGL(1,ℤ/8)	—	2	16	no	—
369	AGL(1,ℤ/8)	C₂³×C₃	1	8	yes	—
370	AGL(1,ℤ/8)	C₂³×C₃	1	8	yes	complemented
371	#135	—	2	8	no	—
372	#135	—	2	16	no	—
373	#135	—	2	8	no	—
374	#135	C₃×D₄	1	4	yes	—
375	#135	C₃×D₄	1	4	yes	—
376	#135	C₂³×C₃	1	4	yes	—
377	#135	C₂³×C₃	1	4	yes	—
378	C₂×Q₁₆	—	2	2	no	—
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×Q₁₆	—	2	8	no	—
381	C₂×Q₁₆	—	2	1	no	—
382	C₂×Q₁₆	—	2	1	no	—
383	C₂×Q₁₆	—	2	2	no	—
384	C₂×Q₁₆	C₃×D₄	1	1	yes	characteristic
385	C₂×Q₁₆	C₃×D₄	1	1	yes	characteristic
386	C₂×Q₁₆	C₂³×C₃	1	4	yes	complemented
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×SD₁₆	—	2	2	no	—
389	C₂×SD₁₆	—	2	2	no	—
390	C₂×SD₁₆	—	2	2	no	—
391	C₂×SD₁₆	—	2	16	no	—
392	C₂×SD₁₆	—	2	2	no	—
393	C₂×SD₁₆	—	2	2	no	—
394	C₂×SD₁₆	—	2	4	no	—
395	C₂×SD₁₆	C₃×D₄	1	1	yes	characteristic
396	C₂×SD₁₆	C₃×D₄	1	1	yes	characteristic
397	C₂×SD₁₆	C₃×D₄	1	2	yes	—
398	C₂×SD₁₆	C₂³×C₃	1	8	yes	complemented
399	C₂×D₈	—	2	2	no	—
400	C₂×D₈	—	2	2	no	—
401	C₂×D₈	—	2	8	no	—
402	C₂×D₈	—	2	1	no	—
403	C₂×D₈	—	2	1	no	—
404	C₂×D₈	—	2	2	no	—
405	C₂×D₈	C₃×D₄	1	1	yes	characteristic
406	C₂×D₈	C₃×D₄	1	1	yes	characteristic
407	C₂×D₈	C₂³×C₃	1	4	yes	—
408	#131	—	2	2	no	—
409	#131	—	2	4	no	—
410	#131	—	2	2	no	—
411	#131	C₂³×C₃	1	4	yes	—
412	#131	C₂³×C₃	1	8	yes	complemented
413	#131	C₂³×C₃	1	4	yes	complemented
414	C₂×M₁₆	—	2	1	no	—
415	C₂×M₁₆	—	2	2	no	—
416	C₂×M₁₆	—	2	1	no	—
417	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
418	C₂×M₁₆	C₂³×C₃	1	2	yes	—
419	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
420	C₂²×C₈	—	2	1	no	—
421	C₂²×C₈	—	2	2	no	—
422	C₂²×C₈	—	2	1	no	—
423	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
425	#124	—	4	2	no	—
426	#124	C₂³×C₃	1	8	yes	complemented
427	C₂×C₂²⋊C₄	—	4	2	no	—
428	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
429	#108	C₂³×C₃	1	4	yes	complemented
430	#108	C₂³×C₃	1	4	yes	complemented
431	#104	C₂³×C₃	1	4	yes	—
432	#104	C₂³×C₃	1	4	yes	complemented
433	#104	C₂³×C₃	1	8	yes	complemented
434	#101	C₂³×C₃	1	8	yes	complemented
435	#100	C₂³×C₃	1	8	yes	complemented
436	C₄×C₈	C₂³×C₃	1	4	yes	complemented
437	C₂³×C₃	—	2	1	no	—
438	C₂³×C₃	—	2	2	no	—
439	C₂³×C₃	—	2	1	no	—
440	C₂³×C₃	—	2	4	no	—
441	C₂³×C₃	—	4	8	no	—
442	C₂³×C₃	—	4	2	no	—
443	C₂³×C₃	—	4	2	no	—
444	C₂³×C₃	—	8	4	no	—
445	C₂³×C₃	—	16	4	no	—
446	C₂³×C₃	H(5,𝔽₂)	1	1	yes	characteristic
447	C₃×Q₈	—	2	1	no	—
448	C₃×Q₈	—	2	2	no	—
449	C₃×Q₈	—	2	1	no	—
450	C₃×Q₈	—	2	4	no	—
451	C₃×Q₈	—	2	4	no	—
452	C₃×Q₈	—	4	8	no	—
453	C₃×Q₈	—	4	2	no	—
454	C₃×Q₈	—	4	2	no	—
455	C₃×Q₈	C₂²×D₄	1	2	yes	—
456	C₃×Q₈	C₂²×D₄	1	4	yes	—
457	C₃×Q₈	C₂²×D₄	1	2	yes	—
458	C₃×D₄	—	2	2	no	—
459	C₃×D₄	—	2	4	no	—
460	C₃×D₄	—	2	2	no	—
461	C₃×D₄	—	2	2	no	—
462	C₃×D₄	—	2	4	no	—
463	C₃×D₄	—	2	2	no	—
464	C₃×D₄	—	2	1	no	—
465	C₃×D₄	—	2	2	no	—
466	C₃×D₄	—	2	1	no	—
467	C₃×D₄	—	2	4	no	—
468	C₃×D₄	—	2	4	no	—
469	C₃×D₄	—	4	8	no	—
470	C₃×D₄	—	4	8	no	—
471	C₃×D₄	—	4	8	no	—
472	C₃×D₄	—	4	2	no	—
473	C₃×D₄	—	4	2	no	—
474	C₃×D₄	C₂²×D₄	1	2	yes	—
475	C₃×D₄	C₂²×D₄	1	4	yes	—
476	C₃×D₄	C₂²×D₄	1	2	yes	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	2	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	2	no	—
481	C₂×C₃×C₄	—	2	4	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	2	2	no	—
484	C₂×C₃×C₄	—	2	4	no	—
485	C₂×C₃×C₄	—	2	2	no	—
486	C₂×C₃×C₄	—	2	2	no	—
487	C₂×C₃×C₄	—	2	4	no	—
488	C₂×C₃×C₄	—	4	8	no	—
489	C₂×C₃×C₄	—	4	8	no	—
490	C₂×C₃×C₄	—	4	8	no	—
491	C₂×C₃×C₄	—	4	2	no	—
492	C₂×C₃×C₄	—	4	2	no	—
493	C₂×C₃×C₄	—	4	2	no	—
494	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
499	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
500	C₃×C₈	—	2	2	no	—
501	C₃×C₈	—	2	4	no	—
502	C₃×C₈	—	2	2	no	—
503	C₃×C₈	C₂²×D₄	1	2	yes	—
504	C₃×C₈	C₂²×D₄	1	2	yes	—
505	C₃×C₈	C₂²×D₄	1	2	yes	—
506	C₃×C₈	C₂²×D₄	1	2	yes	—
507	C₂⁴	—	2	2	no	—
508	C₂⁴	—	4	2	no	—
509	#41	—	2	1	no	—
510	#41	—	2	2	no	—
511	#41	—	2	1	no	—
512	#41	—	2	1	no	—
513	#41	—	2	2	no	—
514	#41	—	2	1	no	—
515	#41	—	2	8	no	—
516	#41	—	2	8	no	—
517	#41	—	2	8	no	—
518	#41	—	2	8	no	—
519	#41	—	4	8	no	—
520	#41	—	4	4	no	—
521	#41	—	4	4	no	—
522	#41	—	4	4	no	—
523	#41	—	4	4	no	—
524	#41	—	4	8	no	—
525	#41	C₂×C₃×D₄	1	2	yes	—
526	#41	C₂×C₃×D₄	1	4	yes	—
527	#41	C₂×C₃×D₄	1	2	yes	—
528	#41	C₂⁴×C₃	1	2	yes	—
529	#41	C₂⁴×C₃	1	4	yes	—
530	#41	C₂⁴×C₃	1	2	yes	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	2	8	no	—
533	C₂×Q₈	—	2	8	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	4	2	no	—
539	C₂×Q₈	—	4	4	no	—
540	C₂×Q₈	—	4	4	no	—
541	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
542	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
543	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
544	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	8	no	—
560	C₂×D₄	—	4	8	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
563	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
564	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
565	C₂×D₄	C₂⁴×C₃	1	4	yes	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
575	Q₁₆	—	2	8	no	—
576	Q₁₆	—	2	8	no	—
577	Q₁₆	—	2	4	no	—
578	Q₁₆	—	2	4	no	—
579	Q₁₆	C₂×C₃×D₄	1	4	yes	—
580	Q₁₆	C₂×C₃×D₄	1	4	yes	—
581	SD₁₆	—	2	8	no	—
582	SD₁₆	—	2	8	no	—
583	SD₁₆	—	2	8	no	—
584	SD₁₆	—	2	8	no	—
585	SD₁₆	—	2	8	no	—
586	SD₁₆	—	2	8	no	—
587	SD₁₆	C₂×C₃×D₄	1	4	yes	—
588	SD₁₆	C₂×C₃×D₄	1	4	yes	—
589	SD₁₆	C₂×C₃×D₄	1	8	yes	—
590	D₈	—	2	8	no	—
591	D₈	—	2	8	no	—
592	D₈	—	2	4	no	—
593	D₈	—	2	4	no	—
594	D₈	C₂×C₃×D₄	1	4	yes	—
595	D₈	C₂×C₃×D₄	1	4	yes	—
596	M₁₆	—	2	1	no	—
597	M₁₆	—	2	2	no	—
598	M₁₆	—	2	1	no	—
599	M₁₆	—	2	4	no	—
600	M₁₆	—	2	8	no	—
601	M₁₆	—	2	4	no	—
602	M₁₆	C₂⁴×C₃	1	2	yes	—
603	M₁₆	C₂⁴×C₃	1	4	yes	—
604	M₁₆	C₂⁴×C₃	1	2	yes	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	4	no	—
609	C₂×C₈	—	2	8	no	—
610	C₂×C₈	—	2	4	no	—
611	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
612	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
613	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
614	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
615	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
616	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
617	C₂×C₈	C₂⁴×C₃	1	2	yes	—
618	C₂×C₈	C₂⁴×C₃	1	2	yes	—
619	C₂²⋊C₄	—	4	8	no	—
620	C₄²	—	2	1	no	—
621	C₄²	C₂⁴×C₃	1	2	yes	—
622	C₂²×C₃	—	2	2	no	—
623	C₂²×C₃	—	2	2	no	—
624	C₂²×C₃	—	2	4	no	—
625	C₂²×C₃	—	2	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	4	no	—
631	C₂²×C₃	—	8	4	no	—
632	C₂²×C₃	—	16	2	no	—
633	C₂²×C₃	—	16	8	no	—
634	C₂²×C₃	D₄²	1	1	yes	characteristic
635	C₂²×C₃	D₄²	1	1	yes	characteristic
636	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
637	C₃×C₄	—	2	2	no	—
638	C₃×C₄	—	2	4	no	—
639	C₃×C₄	—	2	2	no	—
640	C₃×C₄	—	4	2	no	—
641	C₃×C₄	—	4	4	no	—
642	C₃×C₄	D₄²	1	1	yes	characteristic
643	C₃×C₄	D₄²	1	1	yes	characteristic
644	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
645	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
646	C₂³	—	2	1	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	4	8	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	8	4	no	—
654	C₂³	—	16	4	no	—
655	C₂³	C₃×H(5,𝔽₂)	1	1	yes	characteristic
656	Q₈	—	2	1	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	1	no	—
659	Q₈	—	2	4	no	—
660	Q₈	—	2	4	no	—
661	Q₈	—	4	8	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	4	2	no	—
664	Q₈	C₂²×C₃×D₄	1	2	yes	—
665	Q₈	C₂²×C₃×D₄	1	4	yes	—
666	Q₈	C₂²×C₃×D₄	1	2	yes	—
667	D₄	—	2	2	no	—
668	D₄	—	2	4	no	—
669	D₄	—	2	2	no	—
670	D₄	—	2	2	no	—
671	D₄	—	2	4	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	1	no	—
676	D₄	—	2	2	no	—
677	D₄	—	2	1	no	—
678	D₄	—	4	8	no	—
679	D₄	—	4	8	no	—
680	D₄	—	4	8	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	2	no	—
683	D₄	C₂²×C₃×D₄	1	2	yes	—
684	D₄	C₂²×C₃×D₄	1	4	yes	—
685	D₄	C₂²×C₃×D₄	1	2	yes	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	4	8	no	—
698	C₂×C₄	—	4	8	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	—	4	2	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
704	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
705	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
706	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
707	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
708	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
709	C₈	—	2	2	no	—
710	C₈	—	2	4	no	—
711	C₈	—	2	2	no	—
712	C₈	C₂²×C₃×D₄	1	2	yes	—
713	C₈	C₂²×C₃×D₄	1	2	yes	—
714	C₈	C₂²×C₃×D₄	1	2	yes	—
715	C₈	C₂²×C₃×D₄	1	2	yes	—
716	C₂×C₃	—	2	1	no	—
717	C₂×C₃	—	2	1	no	—
718	C₂×C₃	—	4	2	no	—
719	C₂×C₃	—	4	4	no	—
720	C₂×C₃	—	4	2	no	—
721	C₂×C₃	—	8	4	no	—
722	C₂×C₃	#3290	1	2	yes	direct product factor
723	C₂×C₃	C₂×D₄²	1	1	yes	characteristic
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	8	4	no	—
733	C₂²	—	8	4	no	—
734	C₂²	—	16	2	no	—
735	C₂²	—	16	8	no	—
736	C₂²	C₃×D₄²	1	1	yes	characteristic
737	C₂²	C₃×D₄²	1	1	yes	characteristic
738	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
739	C₄	—	2	2	no	—
740	C₄	—	2	4	no	—
741	C₄	—	2	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	4	no	—
744	C₄	C₃×D₄²	1	1	yes	characteristic
745	C₄	C₃×D₄²	1	1	yes	characteristic
746	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
747	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
748	C₃	C₂×#3290	1	1	yes	characteristic, direct product factor, Sylow
749	C₂	—	2	1	no	—
750	C₂	—	2	1	no	—
751	C₂	—	4	2	no	—
752	C₂	—	4	4	no	—
753	C₂	—	4	2	no	—
754	C₂	—	8	4	no	—
755	C₂	C₃×#3290	1	2	yes	direct product factor
756	C₂	C₂×C₃×D₄²	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#578	C₂	semidirect
2. C₂×C₃×#577	C₂	semidirect
3. C₂×C₃×#576	C₂	semidirect
4. C₃×#3290	C₂	direct (N × H)
5. C₂×C₃×#495	C₂	semidirect
6. C₂×C₃×#473	C₂	semidirect
7. C₂×C₃×#472	C₂	semidirect
8. C₂×C₃×#471	C₂	semidirect
9. C₂×C₃×#454	C₂	semidirect
10. C₂×C₃×#455	C₂	semidirect
11. C₂×C₃×#443	C₂	semidirect
12. C₂×C₃×#443	C₂	semidirect
13. C₂×#3290	C₃	direct (N × H)
14. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
17. C₃×#578	C₂²	semidirect
19. C₃×#577	C₂²	semidirect
21. C₃×#576	C₂²	semidirect
25. C₂×C₃×#137	C₂²	semidirect
29. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
36. C₂²×C₃×Q₁₆	C₂²	semidirect
38. C₂²×C₃×SD₁₆	C₂²	semidirect
42. C₂×C₃×#131	C₂²	semidirect
43. C₂×C₃×#131	C₂²	semidirect
44. C₂×C₃×#124	C₂²	semidirect
45. C₃×#495	C₂²	semidirect
46. C₃×#473	C₂²	semidirect
47. C₃×#472	C₂²	semidirect
48. C₃×#471	C₂²	semidirect
49. C₃×#455	C₂²	semidirect
50. C₃×#454	C₂²	semidirect
51. C₃×#443	C₂²	semidirect
52. C₃×#443	C₂²	semidirect
53. C₂×C₃×#108	C₂²	semidirect
54. C₂×C₃×#108	C₂²	semidirect
56. C₂×C₃×#104	C₂²	semidirect
57. C₂×C₃×#104	C₂²	semidirect
58. C₂×C₃×#101	C₂²	semidirect
59. C₂×C₃×#100	C₂²	semidirect
60. C₂×C₃×C₄×C₈	C₂²	semidirect
61. C₂×#578	C₂×C₃	semidirect
62. C₂×#577	C₂×C₃	semidirect
63. C₂×#576	C₂×C₃	semidirect
64. #3290	C₂×C₃	direct (N × H)
65. C₂×#495	C₂×C₃	semidirect
66. C₂×#473	C₂×C₃	semidirect
67. C₂×#472	C₂×C₃	semidirect
68. C₂×#471	C₂×C₃	semidirect
69. C₂×#454	C₂×C₃	semidirect
70. C₂×#455	C₂×C₃	semidirect
71. C₂×#443	C₂×C₃	semidirect
72. C₂×#443	C₂×C₃	semidirect
76. C₃×2₋¹⁺⁴	C₂³	semidirect
101. C₃×#137	C₂³	semidirect
107. C₃×AGL(1,ℤ/8)	C₂³	semidirect
123. C₂×C₃×Q₁₆	C₂³	semidirect
135. C₂×C₃×SD₁₆	C₂³	semidirect
149. C₃×#131	C₂³	semidirect
150. C₃×#131	C₂³	semidirect
163. C₃×#124	C₂³	semidirect
166. C₃×#108	C₂³	semidirect
167. C₃×#108	C₂³	semidirect
169. C₃×#104	C₂³	semidirect
170. C₃×#104	C₂³	semidirect
171. C₃×#101	C₂³	semidirect
172. C₃×#100	C₂³	semidirect
173. C₃×C₄×C₈	C₂³	semidirect
174. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
177. #578	C₂²×C₃	semidirect
179. #577	C₂²×C₃	semidirect
181. #576	C₂²×C₃	semidirect
185. C₂×#137	C₂²×C₃	semidirect
189. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
196. C₂²×Q₁₆	C₂²×C₃	semidirect
198. C₂²×SD₁₆	C₂²×C₃	semidirect
202. C₂×#131	C₂²×C₃	semidirect
203. C₂×#131	C₂²×C₃	semidirect
204. C₂×#124	C₂²×C₃	semidirect
205. #495	C₂²×C₃	semidirect
206. #473	C₂²×C₃	semidirect
207. #472	C₂²×C₃	semidirect
208. #471	C₂²×C₃	semidirect
209. #455	C₂²×C₃	semidirect
210. #454	C₂²×C₃	semidirect
211. #443	C₂²×C₃	semidirect
212. #443	C₂²×C₃	semidirect
213. C₂×#108	C₂²×C₃	semidirect
214. C₂×#108	C₂²×C₃	semidirect
216. C₂×#104	C₂²×C₃	semidirect
217. C₂×#104	C₂²×C₃	semidirect
218. C₂×#101	C₂²×C₃	semidirect
219. C₂×#100	C₂²×C₃	semidirect
220. C₂×C₄×C₈	C₂²×C₃	semidirect
339. 2₋¹⁺⁴	C₂³×C₃	semidirect
364. #137	C₂³×C₃	semidirect
370. AGL(1,ℤ/8)	C₂³×C₃	semidirect
386. C₂×Q₁₆	C₂³×C₃	semidirect
398. C₂×SD₁₆	C₂³×C₃	semidirect
412. #131	C₂³×C₃	semidirect
413. #131	C₂³×C₃	semidirect
426. #124	C₂³×C₃	semidirect
429. #108	C₂³×C₃	semidirect
430. #108	C₂³×C₃	semidirect
432. #104	C₂³×C₃	semidirect
433. #104	C₂³×C₃	semidirect
434. #101	C₂³×C₃	semidirect
435. #100	C₂³×C₃	semidirect
436. C₄×C₈	C₂³×C₃	semidirect
722. C₂×C₃	#3290	direct (N × H)
748. C₃	C₂×#3290	direct (N × H)
755. C₂	C₃×#3290	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×#578	2
C₂×C₃×#577	2
C₂×C₃×#576	2
C₃×#3290	2
C₂×C₃×#495	2
C₂×C₃×#473	2
C₂×C₃×#472	2
C₂×C₃×#471	2
C₂×C₃×#454	2
C₂×C₃×#455	2
C₂×C₃×#443	2
C₂×#3290	3

Subgroups — C2×C3×#3290 #10679708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3290 #10679708