Subgroups — D₃×#23412 #72253874

Order 1536.

At least 6768 conjugacy classes of subgroups; only the 1167 normal subgroups are shown.

The subgroup lattice has 789 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃×#410	C₂	1	1	yes	maximal, characteristic, complemented
7	#10822200	C₂	1	1	yes	maximal, characteristic, complemented
8	#10822199	C₂	1	1	yes	maximal, characteristic, complemented
9	#10822198	C₂	1	1	yes	maximal, characteristic, complemented
10	#10822197	C₂	1	1	yes	maximal, characteristic, complemented
11	#10822196	C₂	1	1	yes	maximal, characteristic, complemented
12	#10822195	C₂	1	1	yes	maximal, characteristic, complemented
13	#10822194	C₂	1	4	yes	maximal, complemented
14	#10822193	C₂	1	1	yes	maximal, characteristic, complemented
15	#10822192	C₂	1	4	yes	maximal, complemented
16	D₃×#2009	C₂	1	4	yes	maximal, complemented
17	D₃×#2008	C₂	1	4	yes	maximal, complemented
18	C₂×D₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#23412	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×D₃×#41	C₂²	1	1	yes	characteristic
21	C₂²×D₃×#41	C₂²	1	1	yes	characteristic
22	C₂²×D₃×#41	C₂²	1	1	yes	characteristic
23	C₂×C₃×#575	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#575	C₂²	1	1	yes	characteristic, complemented
25	C₃×#3449	C₂²	1	1	yes	characteristic, complemented
26	#87268	C₂²	1	1	yes	characteristic, complemented
27	#87268	C₂²	1	1	yes	characteristic, complemented
28	C₂×#5822	C₂²	1	1	yes	characteristic, complemented
29	C₂×#5822	C₂²	1	1	yes	characteristic, complemented
30	C₂×#5822	C₂²	1	1	yes	characteristic, complemented
31	C₂×#5822	C₂²	1	1	yes	characteristic, complemented
32	D₃×#575	C₂²	1	4	yes	—
33	D₃×#575	C₂²	1	4	yes	complemented
34	C₂×#5777	C₂²	1	2	yes	complemented
35	C₂×D₃×#137	C₂²	1	2	yes	complemented
36	C₂×#5773	C₂²	1	2	yes	complemented
37	C₂×D₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
38	C₂×#5748	C₂²	1	1	yes	characteristic, complemented
39	C₂×#5748	C₂²	1	1	yes	characteristic, complemented
40	C₂²×D₃×M₁₆	C₂²	1	1	yes	characteristic
41	C₂²×D₃×M₁₆	C₂²	1	1	yes	characteristic
42	D₃×#536	C₂²	1	2	yes	complemented
43	#86338	C₂²	1	2	yes	complemented
44	D₃×#535	C₂²	1	2	yes	complemented
45	#86313	C₂²	1	2	yes	complemented
46	#85735	C₂²	1	1	yes	characteristic, complemented
47	C₂×D₃×#117	C₂²	1	1	yes	characteristic
48	C₂×D₃×#117	C₂²	1	1	yes	characteristic
49	C₂×C₃×#421	C₂²	1	1	yes	characteristic, complemented
50	C₃×#2896	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×#410	C₂²	1	1	yes	characteristic, complemented
52	C₂×#5240	C₂²	1	1	yes	characteristic, complemented
53	C₂×#5236	C₂²	1	1	yes	characteristic, complemented
54	#84072	C₂²	1	1	yes	characteristic, complemented
55	C₂×#5139	C₂²	1	1	yes	characteristic, complemented
56	#83768	C₂²	1	1	yes	characteristic, complemented
57	C₂×#5006	C₂²	1	1	yes	characteristic, complemented
58	C₂×#5006	C₂²	1	1	yes	characteristic, complemented
59	C₂×#5005	C₂²	1	1	yes	characteristic, complemented
60	#82213	C₂²	1	1	yes	characteristic, complemented
61	D₃×#421	C₂²	1	4	yes	complemented
62	D₃×#421	C₂²	1	4	yes	complemented
63	#78956	C₂²	1	2	yes	complemented
64	D₃×#419	C₂²	1	2	yes	complemented
65	#78924	C₂²	1	2	yes	complemented
66	D₃×#418	C₂²	1	2	yes	complemented
67	D₃×#410	C₂²	1	4	yes	complemented
68	D₃×#410	C₂²	1	4	yes	complemented
69	C₃×#2009	C₂²	1	4	yes	complemented
70	C₃×#2008	C₂²	1	4	yes	complemented
71	C₂×C₃×#344	C₂²	1	1	yes	characteristic, complemented
72	#72120	C₂²	1	4	yes	complemented
73	#72119	C₂²	1	4	yes	complemented
74	#72111	C₂²	1	4	yes	complemented
75	#72099	C₂²	1	4	yes	complemented
76	C₂×#4559	C₂²	1	1	yes	characteristic, complemented
77	C₂×#4556	C₂²	1	1	yes	characteristic, complemented
78	#71869	C₂²	1	4	yes	complemented
79	#71858	C₂²	1	4	yes	complemented
80	C₂×#4533	C₂²	1	1	yes	characteristic, complemented
81	#70412	C₂²	1	4	yes	complemented
82	#70409	C₂²	1	4	yes	complemented
83	#70351	C₂²	1	4	yes	complemented
84	#70331	C₂²	1	4	yes	complemented
85	#70053	C₂²	1	4	yes	complemented
86	#70050	C₂²	1	4	yes	complemented
87	#69031	C₂²	1	4	yes	complemented
88	#69028	C₂²	1	4	yes	complemented
89	D₃×#344	C₂²	1	4	yes	complemented
90	D₃×#344	C₂²	1	4	yes	complemented
91	#23412	D₃	1	1	yes	characteristic, direct product factor
92	C₂²×C₃×#41	C₂³	1	1	yes	characteristic
93	C₂²×C₃×#41	C₂³	1	1	yes	characteristic
94	C₂²×C₃×#41	C₂³	1	1	yes	characteristic
95	C₂×D₃×#41	D₄	1	2	yes	—
96	C₂×D₃×#41	D₄	1	2	yes	—
97	C₂×D₃×#41	D₄	1	2	yes	—
98	C₂×D₃×#41	D₄	1	2	yes	—
99	C₂×D₃×#41	D₄	1	2	yes	—
100	C₂×D₃×#41	D₄	1	2	yes	—
101	C₂×D₃×#41	D₄	1	2	yes	complemented
102	C₂×D₃×#41	D₄	1	2	yes	complemented
103	C₂×D₃×#41	C₂³	1	2	yes	—
104	C₂×D₃×#41	C₂³	1	2	yes	—
105	C₂×D₃×#41	C₂³	1	2	yes	—
106	C₂×D₃×#41	C₂³	1	2	yes	—
107	C₂²×#239	D₄	1	1	yes	characteristic
108	C₂²×#239	D₄	1	1	yes	characteristic, complemented
109	C₂²×#239	C₂³	1	1	yes	characteristic
110	C₂²×D₃×Q₈	D₄	1	1	yes	characteristic
111	C₂²×D₃×Q₈	D₄	1	1	yes	characteristic, complemented
112	C₂²×D₃×Q₈	C₂³	1	1	yes	characteristic
113	C₂²×#237	D₄	1	1	yes	characteristic
114	C₂²×#237	D₄	1	1	yes	characteristic, complemented
115	C₂²×#237	C₂³	1	1	yes	characteristic
116	C₂²×D₃×D₄	D₄	1	1	yes	characteristic
117	C₂²×D₃×D₄	D₄	1	1	yes	characteristic, complemented
118	C₂²×D₃×D₄	C₂³	1	1	yes	characteristic
119	C₂²×#235	C₂³	1	1	yes	characteristic
120	C₂²×#235	C₂³	1	1	yes	characteristic
121	C₂²×#235	C₂³	1	1	yes	characteristic
122	C₂³×C₄×D₃	C₂³	1	1	yes	characteristic
123	C₃×#575	C₂³	1	4	yes	—
124	C₂×C₃×#137	C₂³	1	2	yes	complemented
125	C₂×C₃×AGL(1,ℤ/8)	C₂³	1	2	yes	complemented
126	C₂²×C₃×M₁₆	C₂³	1	1	yes	characteristic
127	C₂²×C₃×M₁₆	C₂³	1	1	yes	characteristic
128	C₃×#536	C₂³	1	2	yes	complemented
129	C₃×#535	C₂³	1	2	yes	complemented
130	C₂×C₃×#117	C₂³	1	1	yes	characteristic
131	C₂×C₃×#117	C₂³	1	1	yes	characteristic
132	#5830	C₂³	1	2	yes	complemented
133	#5825	C₂³	1	2	yes	complemented
134	C₂×#951	C₂³	1	2	yes	complemented
135	#5822	C₂³	1	4	yes	—
136	#5822	C₂³	1	4	yes	—
137	C₂×#949	C₂³	1	2	yes	complemented
138	#5816	C₂³	1	2	yes	complemented
139	C₂×#942	C₂³	1	2	yes	complemented
140	#5805	C₂³	1	2	yes	complemented
141	C₂×#932	C₂³	1	2	yes	complemented
142	C₂×#926	C₂³	1	1	yes	characteristic
143	C₂×#926	C₂³	1	1	yes	characteristic
144	C₂²×#208	C₂³	1	1	yes	characteristic
145	C₂²×#208	C₂³	1	1	yes	characteristic
146	#5748	C₂³	1	4	yes	—
147	C₂×#909	C₂³	1	2	yes	complemented
148	C₂×#908	C₂³	1	2	yes	complemented
149	C₂×D₃×M₁₆	D₄	1	2	yes	complemented
150	C₂×D₃×M₁₆	D₄	1	2	yes	complemented
151	C₂×D₃×M₁₆	D₄	1	2	yes	complemented
152	C₂×D₃×M₁₆	D₄	1	2	yes	complemented
153	C₂×D₃×M₁₆	D₄	1	2	yes	complemented
154	C₂×D₃×M₁₆	D₄	1	2	yes	complemented
155	C₂×D₃×M₁₆	C₂³	1	2	yes	—
156	C₂×D₃×M₁₆	C₂³	1	2	yes	—
157	C₂×D₃×M₁₆	C₂³	1	2	yes	—
158	C₂×D₃×M₁₆	C₂³	1	2	yes	—
159	C₂²×ΓL(1,𝔽₂₅)	D₄	1	2	yes	complemented
160	C₂²×D₃×C₈	D₄	1	2	yes	complemented
161	#5526	C₂³	1	2	yes	complemented
162	#5525	C₂³	1	2	yes	complemented
163	D₃×#117	D₄	1	2	yes	—
164	D₃×#117	D₄	1	2	yes	—
165	D₃×#117	C₂³	1	2	yes	—
166	D₃×#117	C₂³	1	2	yes	—
167	D₃×#117	C₂³	1	2	yes	—
168	D₃×#117	C₂³	1	2	yes	—
169	C₂×D₃×C₂²⋊C₄	D₄	1	2	yes	—
170	C₂×#877	D₄	1	2	yes	—
171	C₃×#421	C₂³	1	4	yes	complemented
172	C₃×#419	C₂³	1	2	yes	complemented
173	C₃×#418	C₂³	1	2	yes	complemented
174	C₃×#410	C₂³	1	4	yes	complemented
175	#5240	C₂³	1	4	yes	complemented
176	#5236	C₂³	1	4	yes	complemented
177	#5225	C₂³	1	2	yes	complemented
178	#5215	C₂³	1	2	yes	complemented
179	#5139	C₂³	1	4	yes	complemented
180	#5131	C₂³	1	2	yes	complemented
181	#5120	C₂³	1	2	yes	complemented
182	#5006	C₂³	1	4	yes	complemented
183	#5006	C₂³	1	4	yes	complemented
184	#5005	C₂³	1	4	yes	complemented
185	#5004	C₂³	1	2	yes	complemented
186	#5001	C₂³	1	2	yes	complemented
187	C₃×#344	C₂³	1	4	yes	complemented
188	#4559	C₂³	1	4	yes	complemented
189	#4556	C₂³	1	4	yes	complemented
190	#4533	C₂³	1	4	yes	complemented
191	C₂×#575	C₂×D₃	1	1	yes	characteristic, complemented
192	C₂×#575	C₂×D₃	1	1	yes	characteristic, complemented
193	#3449	C₂×D₃	1	1	yes	characteristic, complemented
194	C₂×#421	C₂×D₃	1	1	yes	characteristic, complemented
195	#2896	C₂×D₃	1	1	yes	characteristic, complemented
196	C₂×#410	C₂×D₃	1	1	yes	characteristic, complemented
197	#2009	C₂×D₃	1	4	yes	complemented
198	#2008	C₂×D₃	1	4	yes	complemented
199	C₂×#344	C₂×D₃	1	1	yes	characteristic, complemented
200	C₂⁴×D₃	C₂×D₄	1	1	yes	characteristic
201	C₂×C₃×#41	C₂×D₄	1	2	yes	—
202	C₂×C₃×#41	C₂×D₄	1	2	yes	—
203	C₂×C₃×#41	C₂×D₄	1	2	yes	—
204	C₂×C₃×#41	C₂×D₄	1	2	yes	complemented
205	C₂×C₃×#41	C₂⁴	1	2	yes	—
206	C₂×C₃×#41	C₂⁴	1	2	yes	—
207	C₂²×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₃×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
209	C₂²×C₃×Q₈	C₂⁴	1	1	yes	characteristic
210	C₂²×C₃×D₄	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₃×D₄	C₂×D₄	1	1	yes	characteristic, complemented
212	C₂²×C₃×D₄	C₂⁴	1	1	yes	characteristic
213	C₂³×C₃×C₄	C₂⁴	1	1	yes	characteristic
214	C₂³×Dic₃	C₂×D₄	1	1	yes	characteristic
215	C₂×#239	C₂×D₄	1	2	yes	—
216	C₂×#239	C₂×D₄	1	2	yes	—
217	C₂×#239	C₂×D₄	1	2	yes	—
218	C₂×#239	C₂×D₄	1	2	yes	—
219	C₂×#239	C₂×D₄	1	2	yes	—
220	C₂×#239	C₂×D₄	1	2	yes	complemented
221	C₂×D₃×Q₈	C₂×D₄	1	2	yes	—
222	C₂×D₃×Q₈	C₂×D₄	1	2	yes	—
223	C₂×D₃×Q₈	C₂×D₄	1	2	yes	—
224	C₂×D₃×Q₈	C₂×D₄	1	2	yes	—
225	C₂×D₃×Q₈	C₂×D₄	1	2	yes	—
226	C₂×D₃×Q₈	C₂×D₄	1	2	yes	complemented
227	C₂×#237	C₂×D₄	1	2	yes	—
228	C₂×#237	C₂×D₄	1	2	yes	—
229	C₂×#237	C₂×D₄	1	2	yes	—
230	C₂×#237	C₂×D₄	1	2	yes	—
231	C₂×#237	C₂×D₄	1	2	yes	—
232	C₂×#237	C₂×D₄	1	2	yes	complemented
233	C₂×D₃×D₄	C₂×D₄	1	2	yes	—
234	C₂×D₃×D₄	C₂×D₄	1	2	yes	—
235	C₂×D₃×D₄	C₂×D₄	1	2	yes	—
236	C₂×D₃×D₄	C₂×D₄	1	2	yes	—
237	C₂×D₃×D₄	C₂×D₄	1	2	yes	—
238	C₂×D₃×D₄	C₂×D₄	1	2	yes	complemented
239	C₂×#235	C₂×D₄	1	2	yes	—
240	C₂×#235	C₂×D₄	1	2	yes	—
241	C₂×#235	C₂×D₄	1	2	yes	—
242	C₂×#235	C₂×D₄	1	2	yes	complemented
243	C₂×#235	C₂⁴	1	2	yes	—
244	C₂×#235	C₂⁴	1	2	yes	—
245	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic
246	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic, complemented
247	C₂²×D₁₂	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×D₃	#41	1	1	yes	characteristic
271	C₂²×C₄×D₃	#41	1	1	yes	characteristic
272	C₂²×C₄×D₃	#41	1	1	yes	characteristic
273	C₂²×C₄×D₃	#41	1	1	yes	characteristic
274	C₂²×C₄×D₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×D₃	C₂⁴	1	1	yes	characteristic
276	C₂²×Dic₆	C₂×D₄	1	1	yes	characteristic
277	C₂²×Dic₆	C₂×D₄	1	1	yes	characteristic, complemented
278	C₂²×Dic₆	C₂⁴	1	1	yes	characteristic
279	C₂×C₃×M₁₆	C₂×D₄	1	2	yes	complemented
280	C₂×C₃×M₁₆	C₂×D₄	1	2	yes	complemented
281	C₂×C₃×M₁₆	C₂×D₄	1	2	yes	complemented
282	C₂×C₃×M₁₆	C₂⁴	1	2	yes	—
283	C₂×C₃×M₁₆	C₂⁴	1	2	yes	—
284	C₂²×C₃×C₈	C₂×D₄	1	2	yes	complemented
285	C₃×#117	C₂×D₄	1	2	yes	—
286	C₃×#117	C₂⁴	1	2	yes	—
287	C₃×#117	C₂⁴	1	2	yes	—
288	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
289	C₂×#217	C₂×D₄	1	2	yes	—
290	#926	C₂×D₄	1	2	yes	—
291	#926	C₂⁴	1	2	yes	—
292	#926	C₂⁴	1	2	yes	—
293	C₂×#208	C₂×D₄	1	2	yes	complemented
294	C₂×#208	C₂×D₄	1	2	yes	complemented
295	C₂×#208	C₂×D₄	1	2	yes	complemented
296	C₂×#208	C₂⁴	1	2	yes	—
297	C₂×#208	C₂⁴	1	2	yes	—
298	C₂²×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
299	D₃×M₁₆	C₂×D₄	1	4	yes	—
300	D₃×M₁₆	C₂×D₄	1	4	yes	—
301	D₃×M₁₆	C₂×D₄	1	4	yes	complemented
302	D₃×M₁₆	C₂×D₄	1	4	yes	complemented
303	C₂×ΓL(1,𝔽₂₅)	C₂×D₄	1	4	yes	—
304	C₂×ΓL(1,𝔽₂₅)	C₂×D₄	1	4	yes	complemented
305	C₂×D₃×C₈	C₂×D₄	1	4	yes	—
306	C₂×D₃×C₈	C₂×D₄	1	4	yes	complemented
307	D₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
308	D₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
309	#877	C₂×D₄	1	4	yes	—
310	#877	C₂×D₄	1	4	yes	—
311	C₂²×#41	C₂²×D₃	1	1	yes	characteristic
312	C₂²×#41	C₂²×D₃	1	1	yes	characteristic
313	C₂²×#41	C₂²×D₃	1	1	yes	characteristic
314	#575	C₂²×D₃	1	4	yes	—
315	C₂×#137	C₂²×D₃	1	2	yes	complemented
316	C₂×AGL(1,ℤ/8)	C₂²×D₃	1	2	yes	complemented
317	C₂²×M₁₆	C₂²×D₃	1	1	yes	characteristic
318	C₂²×M₁₆	C₂²×D₃	1	1	yes	characteristic
319	#536	C₂²×D₃	1	2	yes	complemented
320	#535	C₂²×D₃	1	2	yes	complemented
321	C₂×#117	C₂²×D₃	1	1	yes	characteristic
322	C₂×#117	C₂²×D₃	1	1	yes	characteristic
323	#421	C₂²×D₃	1	4	yes	complemented
324	#419	C₂²×D₃	1	2	yes	complemented
325	#418	C₂²×D₃	1	2	yes	complemented
326	#410	C₂²×D₃	1	4	yes	complemented
327	#344	C₂²×D₃	1	4	yes	complemented
328	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
329	C₂³×D₃	#120	1	1	yes	characteristic
330	C₂³×D₃	#120	1	1	yes	characteristic
331	C₂³×D₃	#120	1	1	yes	characteristic
332	C₂³×D₃	#120	1	1	yes	characteristic
333	C₂³×D₃	#121	1	1	yes	characteristic
334	C₂³×D₃	#121	1	1	yes	characteristic
335	C₂³×D₃	#121	1	1	yes	characteristic
336	C₂³×D₃	#121	1	1	yes	characteristic
337	C₂³×D₃	#127	1	1	yes	characteristic
338	C₂³×D₃	#127	1	1	yes	characteristic
339	C₂³×D₃	#127	1	1	yes	characteristic
340	C₂³×D₃	#127	1	1	yes	characteristic
341	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
342	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₃×Q₈	C₂²×D₄	1	2	yes	—
344	C₂×C₃×Q₈	C₂²×D₄	1	2	yes	—
345	C₂×C₃×Q₈	C₂²×D₄	1	2	yes	—
346	C₂×C₃×D₄	C₂²×D₄	1	2	yes	—
347	C₂×C₃×D₄	C₂²×D₄	1	2	yes	—
348	C₂×C₃×D₄	C₂²×D₄	1	2	yes	—
349	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
351	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
352	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
353	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
355	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
356	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
357	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
358	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
360	C₂²×C₃×C₄	C₂×#41	1	1	yes	characteristic
361	C₂²×C₃×C₄	C₂×#41	1	1	yes	characteristic
362	C₂²×C₃×C₄	C₂⁵	1	1	yes	characteristic
363	C₂²×Dic₃	#120	1	1	yes	characteristic
364	C₂²×Dic₃	#120	1	1	yes	characteristic
365	C₂²×Dic₃	#120	1	1	yes	characteristic
366	C₂²×Dic₃	#120	1	1	yes	characteristic
367	C₂²×Dic₃	#121	1	1	yes	characteristic
368	C₂²×Dic₃	#121	1	1	yes	characteristic
369	C₂²×Dic₃	#121	1	1	yes	characteristic
370	C₂²×Dic₃	#121	1	1	yes	characteristic
371	C₂²×Dic₃	#127	1	1	yes	characteristic
372	C₂²×Dic₃	#127	1	1	yes	characteristic
373	C₂²×Dic₃	#127	1	1	yes	characteristic
374	C₂²×Dic₃	#127	1	1	yes	characteristic
375	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
376	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×D₁₂	C₂²×D₄	1	2	yes	—
378	C₂×D₁₂	C₂²×D₄	1	2	yes	—
379	C₂×D₁₂	C₂²×D₄	1	2	yes	—
380	C₂×C₄×D₃	#120	1	1	yes	characteristic
381	C₂×C₄×D₃	#120	1	1	yes	characteristic
382	C₂×C₄×D₃	#120	1	1	yes	characteristic
383	C₂×C₄×D₃	#120	1	1	yes	characteristic
384	C₂×C₄×D₃	#120	1	1	yes	characteristic
385	C₂×C₄×D₃	#120	1	1	yes	characteristic
386	C₂×C₄×D₃	#120	1	1	yes	characteristic
387	C₂×C₄×D₃	#120	1	1	yes	characteristic
388	C₂×C₄×D₃	#120	1	1	yes	characteristic
389	C₂×C₄×D₃	#120	1	1	yes	characteristic
390	C₂×C₄×D₃	#120	1	1	yes	characteristic
391	C₂×C₄×D₃	#120	1	1	yes	characteristic
392	C₂×C₄×D₃	#120	1	1	yes	characteristic
393	C₂×C₄×D₃	#120	1	1	yes	characteristic
394	C₂×C₄×D₃	#120	1	1	yes	characteristic
395	C₂×C₄×D₃	#120	1	1	yes	characteristic
396	C₂×C₄×D₃	#120	1	1	yes	characteristic
397	C₂×C₄×D₃	#120	1	1	yes	characteristic
398	C₂×C₄×D₃	#120	1	1	yes	characteristic
399	C₂×C₄×D₃	#120	1	1	yes	characteristic
400	C₂×C₄×D₃	#120	1	1	yes	characteristic
401	C₂×C₄×D₃	#120	1	1	yes	characteristic
402	C₂×C₄×D₃	#120	1	1	yes	characteristic
403	C₂×C₄×D₃	#120	1	1	yes	characteristic
404	C₂×C₄×D₃	#120	1	1	yes	characteristic
405	C₂×C₄×D₃	#120	1	1	yes	characteristic
406	C₂×C₄×D₃	#120	1	1	yes	characteristic
407	C₂×C₄×D₃	#120	1	1	yes	characteristic
408	C₂×C₄×D₃	#120	1	1	yes	characteristic
409	C₂×C₄×D₃	#120	1	1	yes	characteristic
410	C₂×C₄×D₃	#120	1	1	yes	characteristic
411	C₂×C₄×D₃	#120	1	1	yes	characteristic
412	C₂×C₄×D₃	#120	1	1	yes	characteristic
413	C₂×C₄×D₃	#120	1	1	yes	characteristic
414	C₂×C₄×D₃	#120	1	1	yes	characteristic
415	C₂×C₄×D₃	#120	1	1	yes	characteristic
416	C₂×C₄×D₃	#120	1	1	yes	characteristic
417	C₂×C₄×D₃	#120	1	1	yes	characteristic
418	C₂×C₄×D₃	#120	1	1	yes	characteristic
419	C₂×C₄×D₃	#120	1	1	yes	characteristic
420	C₂×C₄×D₃	#121	1	1	yes	characteristic
421	C₂×C₄×D₃	#121	1	1	yes	characteristic
422	C₂×C₄×D₃	#121	1	1	yes	characteristic
423	C₂×C₄×D₃	#121	1	1	yes	characteristic
424	C₂×C₄×D₃	#121	1	1	yes	characteristic
425	C₂×C₄×D₃	#121	1	1	yes	characteristic
426	C₂×C₄×D₃	#121	1	1	yes	characteristic
427	C₂×C₄×D₃	#121	1	1	yes	characteristic
428	C₂×C₄×D₃	#121	1	1	yes	characteristic
429	C₂×C₄×D₃	#121	1	1	yes	characteristic
430	C₂×C₄×D₃	#121	1	1	yes	characteristic
431	C₂×C₄×D₃	#121	1	1	yes	characteristic
432	C₂×C₄×D₃	#121	1	1	yes	characteristic
433	C₂×C₄×D₃	#121	1	1	yes	characteristic
434	C₂×C₄×D₃	#121	1	1	yes	characteristic
435	C₂×C₄×D₃	#121	1	1	yes	characteristic
436	C₂×C₄×D₃	#121	1	1	yes	characteristic
437	C₂×C₄×D₃	#121	1	1	yes	characteristic
438	C₂×C₄×D₃	#121	1	1	yes	characteristic
439	C₂×C₄×D₃	#121	1	1	yes	characteristic
440	C₂×C₄×D₃	#121	1	1	yes	characteristic
441	C₂×C₄×D₃	#121	1	1	yes	characteristic
442	C₂×C₄×D₃	#121	1	1	yes	characteristic
443	C₂×C₄×D₃	#121	1	1	yes	characteristic
444	C₂×C₄×D₃	#121	1	1	yes	characteristic
445	C₂×C₄×D₃	#121	1	1	yes	characteristic
446	C₂×C₄×D₃	#121	1	1	yes	characteristic
447	C₂×C₄×D₃	#121	1	1	yes	characteristic
448	C₂×C₄×D₃	#121	1	1	yes	characteristic
449	C₂×C₄×D₃	#121	1	1	yes	characteristic
450	C₂×C₄×D₃	#121	1	1	yes	characteristic
451	C₂×C₄×D₃	#121	1	1	yes	characteristic
452	C₂×C₄×D₃	#121	1	1	yes	characteristic
453	C₂×C₄×D₃	#121	1	1	yes	characteristic
454	C₂×C₄×D₃	#121	1	1	yes	characteristic
455	C₂×C₄×D₃	#121	1	1	yes	characteristic
456	C₂×C₄×D₃	#121	1	1	yes	characteristic
457	C₂×C₄×D₃	#121	1	1	yes	characteristic
458	C₂×C₄×D₃	#121	1	1	yes	characteristic
459	C₂×C₄×D₃	#121	1	1	yes	characteristic
460	C₂×C₄×D₃	#127	1	1	yes	characteristic
461	C₂×C₄×D₃	#127	1	1	yes	characteristic
462	C₂×C₄×D₃	#127	1	1	yes	characteristic
463	C₂×C₄×D₃	#127	1	1	yes	characteristic
464	C₂×C₄×D₃	#127	1	1	yes	characteristic
465	C₂×C₄×D₃	#127	1	1	yes	characteristic
466	C₂×C₄×D₃	#127	1	1	yes	characteristic
467	C₂×C₄×D₃	#127	1	1	yes	characteristic
468	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×D₃	C₂×#41	1	1	yes	characteristic
489	C₂×C₄×D₃	C₂×#41	1	1	yes	characteristic
490	C₂×C₄×D₃	C₂×#41	1	1	yes	characteristic
491	C₂×C₄×D₃	C₂×#41	1	1	yes	characteristic
492	C₂×Dic₆	C₂²×D₄	1	2	yes	—
493	C₂×Dic₆	C₂²×D₄	1	2	yes	—
494	C₂×Dic₆	C₂²×D₄	1	2	yes	—
495	C₃×M₁₆	C₂²×D₄	1	4	yes	—
496	C₂×C₃×C₈	C₂²×D₄	1	4	yes	—
497	C₃×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
498	#217	C₂²×D₄	1	4	yes	—
499	#208	C₂²×D₄	1	4	yes	—
500	C₂×C₃⋊C₈	C₂²×D₄	1	4	yes	—
501	C₂×#41	D₃×D₄	1	2	yes	—
502	C₂×#41	D₃×D₄	1	2	yes	—
503	C₂×#41	D₃×D₄	1	2	yes	—
504	C₂×#41	D₃×D₄	1	2	yes	complemented
505	C₂×#41	C₂³×D₃	1	2	yes	—
506	C₂×#41	C₂³×D₃	1	2	yes	—
507	C₂²×Q₈	D₃×D₄	1	1	yes	characteristic
508	C₂²×Q₈	D₃×D₄	1	1	yes	characteristic, complemented
509	C₂²×Q₈	C₂³×D₃	1	1	yes	characteristic
510	C₂²×D₄	D₃×D₄	1	1	yes	characteristic
511	C₂²×D₄	D₃×D₄	1	1	yes	characteristic, complemented
512	C₂²×D₄	C₂³×D₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×D₃	1	1	yes	characteristic
514	C₂×M₁₆	D₃×D₄	1	2	yes	complemented
515	C₂×M₁₆	D₃×D₄	1	2	yes	complemented
516	C₂×M₁₆	D₃×D₄	1	2	yes	complemented
517	C₂×M₁₆	C₂³×D₃	1	2	yes	—
518	C₂×M₁₆	C₂³×D₃	1	2	yes	—
519	C₂²×C₈	D₃×D₄	1	2	yes	complemented
520	#117	D₃×D₄	1	2	yes	—
521	#117	C₂³×D₃	1	2	yes	—
522	#117	C₂³×D₃	1	2	yes	—
523	C₂×C₂²⋊C₄	D₃×D₄	1	2	yes	—
524	C₂³×C₃	C₂×#120	1	1	yes	characteristic
525	C₂³×C₃	C₂×#120	1	1	yes	characteristic
526	C₂³×C₃	C₂×#121	1	1	yes	characteristic
527	C₂³×C₃	C₂×#121	1	1	yes	characteristic
528	C₂³×C₃	C₂×#127	1	1	yes	characteristic
529	C₂³×C₃	C₂×#127	1	1	yes	characteristic
530	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
531	C₂²×D₃	#392	1	1	yes	characteristic
532	C₂²×D₃	#392	1	1	yes	characteristic
533	C₂²×D₃	#392	1	1	yes	characteristic
534	C₂²×D₃	#392	1	1	yes	characteristic
535	C₂²×D₃	#392	1	1	yes	characteristic
536	C₂²×D₃	#392	1	1	yes	characteristic
537	C₂²×D₃	#392	1	1	yes	characteristic
538	C₂²×D₃	#392	1	1	yes	characteristic
539	C₂²×D₃	#392	1	1	yes	characteristic
540	C₂²×D₃	#392	1	1	yes	characteristic
541	C₂²×D₃	#392	1	1	yes	characteristic
542	C₂²×D₃	#392	1	1	yes	characteristic
543	C₂²×D₃	#392	1	1	yes	characteristic
544	C₂²×D₃	#392	1	1	yes	characteristic
545	C₂²×D₃	#392	1	1	yes	characteristic
546	C₂²×D₃	#392	1	1	yes	characteristic
547	C₂²×D₃	C₂×#120	1	1	yes	characteristic
548	C₂²×D₃	C₂×#120	1	1	yes	characteristic
549	C₂²×D₃	C₂×#120	1	1	yes	characteristic
550	C₂²×D₃	C₂×#120	1	1	yes	characteristic
551	C₂²×D₃	C₂×#121	1	1	yes	characteristic
552	C₂²×D₃	C₂×#121	1	1	yes	characteristic
553	C₂²×D₃	C₂×#121	1	1	yes	characteristic
554	C₂²×D₃	C₂×#121	1	1	yes	characteristic
555	C₂²×D₃	C₂×#127	1	1	yes	characteristic
556	C₂²×D₃	C₂×#127	1	1	yes	characteristic
557	C₂²×D₃	C₂×#127	1	1	yes	characteristic
558	C₂²×D₃	C₂×#127	1	1	yes	characteristic
559	C₂×C₃×C₄	C₂×#120	1	1	yes	characteristic
560	C₂×C₃×C₄	C₂×#120	1	1	yes	characteristic
561	C₂×C₃×C₄	C₂×#120	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂×#120	1	1	yes	characteristic
563	C₂×C₃×C₄	C₂×#120	1	1	yes	characteristic
564	C₂×C₃×C₄	C₂×#120	1	1	yes	characteristic
565	C₂×C₃×C₄	C₂×#120	1	1	yes	characteristic
566	C₂×C₃×C₄	C₂×#120	1	1	yes	characteristic
567	C₂×C₃×C₄	C₂×#120	1	1	yes	characteristic
568	C₂×C₃×C₄	C₂×#120	1	1	yes	characteristic
569	C₂×C₃×C₄	C₂×#121	1	1	yes	characteristic
570	C₂×C₃×C₄	C₂×#121	1	1	yes	characteristic
571	C₂×C₃×C₄	C₂×#121	1	1	yes	characteristic
572	C₂×C₃×C₄	C₂×#121	1	1	yes	characteristic
573	C₂×C₃×C₄	C₂×#121	1	1	yes	characteristic
574	C₂×C₃×C₄	C₂×#121	1	1	yes	characteristic
575	C₂×C₃×C₄	C₂×#121	1	1	yes	characteristic
576	C₂×C₃×C₄	C₂×#121	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂×#121	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂×#121	1	1	yes	characteristic
579	C₂×C₃×C₄	C₂×#127	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂×#127	1	1	yes	characteristic
581	C₂×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
582	C₂×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
583	C₂×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
584	C₂×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
585	C₂×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
586	C₂×C₃×C₄	C₂²×#41	1	1	yes	characteristic
587	C₂×Dic₃	#392	1	1	yes	characteristic
588	C₂×Dic₃	#392	1	1	yes	characteristic
589	C₂×Dic₃	#392	1	1	yes	characteristic
590	C₂×Dic₃	#392	1	1	yes	characteristic
591	C₂×Dic₃	#392	1	1	yes	characteristic
592	C₂×Dic₃	#392	1	1	yes	characteristic
593	C₂×Dic₃	#392	1	1	yes	characteristic
594	C₂×Dic₃	#392	1	1	yes	characteristic
595	C₂×Dic₃	#392	1	1	yes	characteristic
596	C₂×Dic₃	#392	1	1	yes	characteristic
597	C₂×Dic₃	#392	1	1	yes	characteristic
598	C₂×Dic₃	#392	1	1	yes	characteristic
599	C₂×Dic₃	#392	1	1	yes	characteristic
600	C₂×Dic₃	#392	1	1	yes	characteristic
601	C₂×Dic₃	#392	1	1	yes	characteristic
602	C₂×Dic₃	#392	1	1	yes	characteristic
603	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
604	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
605	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
606	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
607	C₂×Dic₃	C₂×#121	1	1	yes	characteristic
608	C₂×Dic₃	C₂×#121	1	1	yes	characteristic
609	C₂×Dic₃	C₂×#121	1	1	yes	characteristic
610	C₂×Dic₃	C₂×#121	1	1	yes	characteristic
611	C₂×Dic₃	C₂×#127	1	1	yes	characteristic
612	C₂×Dic₃	C₂×#127	1	1	yes	characteristic
613	C₂×Dic₃	C₂×#127	1	1	yes	characteristic
614	C₂×Dic₃	C₂×#127	1	1	yes	characteristic
615	C₄×D₃	#392	1	1	yes	characteristic
616	C₄×D₃	#392	1	1	yes	characteristic
617	C₄×D₃	#392	1	1	yes	characteristic
618	C₄×D₃	#392	1	1	yes	characteristic
619	C₄×D₃	#392	1	1	yes	characteristic
620	C₄×D₃	#392	1	1	yes	characteristic
621	C₄×D₃	#392	1	1	yes	characteristic
622	C₄×D₃	#392	1	1	yes	characteristic
623	C₄×D₃	#392	1	1	yes	characteristic
624	C₄×D₃	#392	1	1	yes	characteristic
625	C₄×D₃	#392	1	1	yes	characteristic
626	C₄×D₃	#392	1	1	yes	characteristic
627	C₄×D₃	#392	1	1	yes	characteristic
628	C₄×D₃	#392	1	1	yes	characteristic
629	C₄×D₃	#392	1	1	yes	characteristic
630	C₄×D₃	#392	1	1	yes	characteristic
631	C₄×D₃	#392	1	1	yes	characteristic
632	C₄×D₃	#392	1	1	yes	characteristic
633	C₄×D₃	#392	1	1	yes	characteristic
634	C₄×D₃	#392	1	1	yes	characteristic
635	C₄×D₃	#392	1	1	yes	characteristic
636	C₄×D₃	#392	1	1	yes	characteristic
637	C₄×D₃	#392	1	1	yes	characteristic
638	C₄×D₃	#392	1	1	yes	characteristic
639	C₄×D₃	#392	1	1	yes	characteristic
640	C₄×D₃	#392	1	1	yes	characteristic
641	C₄×D₃	#392	1	1	yes	characteristic
642	C₄×D₃	#392	1	1	yes	characteristic
643	C₄×D₃	#392	1	1	yes	characteristic
644	C₄×D₃	#392	1	1	yes	characteristic
645	C₄×D₃	#392	1	1	yes	characteristic
646	C₄×D₃	#392	1	1	yes	characteristic
647	C₄×D₃	C₂×#120	1	1	yes	characteristic
648	C₄×D₃	C₂×#120	1	1	yes	characteristic
649	C₄×D₃	C₂×#120	1	1	yes	characteristic
650	C₄×D₃	C₂×#120	1	1	yes	characteristic
651	C₄×D₃	C₂×#120	1	1	yes	characteristic
652	C₄×D₃	C₂×#120	1	1	yes	characteristic
653	C₄×D₃	C₂×#120	1	1	yes	characteristic
654	C₄×D₃	C₂×#120	1	1	yes	characteristic
655	C₄×D₃	C₂×#120	1	1	yes	characteristic
656	C₄×D₃	C₂×#120	1	1	yes	characteristic
657	C₄×D₃	C₂×#120	1	1	yes	characteristic
658	C₄×D₃	C₂×#120	1	1	yes	characteristic
659	C₄×D₃	C₂×#120	1	1	yes	characteristic
660	C₄×D₃	C₂×#120	1	1	yes	characteristic
661	C₄×D₃	C₂×#120	1	1	yes	characteristic
662	C₄×D₃	C₂×#120	1	1	yes	characteristic
663	C₄×D₃	C₂×#121	1	1	yes	characteristic
664	C₄×D₃	C₂×#121	1	1	yes	characteristic
665	C₄×D₃	C₂×#121	1	1	yes	characteristic
666	C₄×D₃	C₂×#121	1	1	yes	characteristic
667	C₄×D₃	C₂×#121	1	1	yes	characteristic
668	C₄×D₃	C₂×#121	1	1	yes	characteristic
669	C₄×D₃	C₂×#121	1	1	yes	characteristic
670	C₄×D₃	C₂×#121	1	1	yes	characteristic
671	C₄×D₃	C₂×#121	1	1	yes	characteristic
672	C₄×D₃	C₂×#121	1	1	yes	characteristic
673	C₄×D₃	C₂×#121	1	1	yes	characteristic
674	C₄×D₃	C₂×#121	1	1	yes	characteristic
675	C₄×D₃	C₂×#121	1	1	yes	characteristic
676	C₄×D₃	C₂×#121	1	1	yes	characteristic
677	C₄×D₃	C₂×#121	1	1	yes	characteristic
678	C₄×D₃	C₂×#121	1	1	yes	characteristic
679	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
680	C₂×Q₈	C₂×D₃×D₄	1	2	yes	—
681	C₂×Q₈	C₂×D₃×D₄	1	2	yes	—
682	C₂×Q₈	C₂×D₃×D₄	1	2	yes	—
683	C₂×D₄	C₂×D₃×D₄	1	2	yes	—
684	C₂×D₄	C₂×D₃×D₄	1	2	yes	—
685	C₂×D₄	C₂×D₃×D₄	1	2	yes	—
686	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
697	C₂²×C₄	D₃×#41	1	1	yes	characteristic
698	C₂²×C₄	D₃×#41	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×D₃	1	1	yes	characteristic
700	M₁₆	C₂×D₃×D₄	1	4	yes	—
701	C₂×C₈	C₂×D₃×D₄	1	4	yes	—
702	C₂²⋊C₄	C₂×D₃×D₄	1	4	yes	—
703	C₂²×C₃	C₂×#392	1	1	yes	characteristic
704	C₂²×C₃	C₂×#392	1	1	yes	characteristic
705	C₂²×C₃	C₂×#392	1	1	yes	characteristic
706	C₂²×C₃	C₂×#392	1	1	yes	characteristic
707	C₂²×C₃	C₂²×#120	1	1	yes	characteristic
708	C₂²×C₃	C₂²×#121	1	1	yes	characteristic
709	C₂²×C₃	C₂²×#127	1	1	yes	characteristic
710	C₂×D₃	C₂×#392	1	1	yes	characteristic
711	C₂×D₃	C₂×#392	1	1	yes	characteristic
712	C₂×D₃	C₂×#392	1	1	yes	characteristic
713	C₂×D₃	C₂×#392	1	1	yes	characteristic
714	C₂×D₃	C₂×#392	1	1	yes	characteristic
715	C₂×D₃	C₂×#392	1	1	yes	characteristic
716	C₂×D₃	C₂×#392	1	1	yes	characteristic
717	C₂×D₃	C₂×#392	1	1	yes	characteristic
718	C₃×C₄	C₂×#392	1	1	yes	characteristic
719	C₃×C₄	C₂×#392	1	1	yes	characteristic
720	C₃×C₄	C₂×#392	1	1	yes	characteristic
721	C₃×C₄	C₂×#392	1	1	yes	characteristic
722	C₃×C₄	C₂²×#120	1	1	yes	characteristic
723	C₃×C₄	C₂²×#120	1	1	yes	characteristic
724	C₃×C₄	C₂²×#121	1	1	yes	characteristic
725	C₃×C₄	C₂²×#121	1	1	yes	characteristic
726	Dic₃	C₂×#392	1	1	yes	characteristic
727	Dic₃	C₂×#392	1	1	yes	characteristic
728	Dic₃	C₂×#392	1	1	yes	characteristic
729	Dic₃	C₂×#392	1	1	yes	characteristic
730	Dic₃	C₂×#392	1	1	yes	characteristic
731	Dic₃	C₂×#392	1	1	yes	characteristic
732	Dic₃	C₂×#392	1	1	yes	characteristic
733	Dic₃	C₂×#392	1	1	yes	characteristic
734	C₂³	D₃×#120	1	1	yes	characteristic
735	C₂³	D₃×#120	1	1	yes	characteristic
736	C₂³	D₃×#121	1	1	yes	characteristic
737	C₂³	D₃×#121	1	1	yes	characteristic
738	C₂³	D₃×#127	1	1	yes	characteristic
739	C₂³	D₃×#127	1	1	yes	characteristic
740	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
741	C₂×C₄	D₃×#120	1	1	yes	characteristic
742	C₂×C₄	D₃×#120	1	1	yes	characteristic
743	C₂×C₄	D₃×#120	1	1	yes	characteristic
744	C₂×C₄	D₃×#120	1	1	yes	characteristic
745	C₂×C₄	D₃×#120	1	1	yes	characteristic
746	C₂×C₄	D₃×#120	1	1	yes	characteristic
747	C₂×C₄	D₃×#120	1	1	yes	characteristic
748	C₂×C₄	D₃×#120	1	1	yes	characteristic
749	C₂×C₄	D₃×#120	1	1	yes	characteristic
750	C₂×C₄	D₃×#120	1	1	yes	characteristic
751	C₂×C₄	D₃×#121	1	1	yes	characteristic
752	C₂×C₄	D₃×#121	1	1	yes	characteristic
753	C₂×C₄	D₃×#121	1	1	yes	characteristic
754	C₂×C₄	D₃×#121	1	1	yes	characteristic
755	C₂×C₄	D₃×#121	1	1	yes	characteristic
756	C₂×C₄	D₃×#121	1	1	yes	characteristic
757	C₂×C₄	D₃×#121	1	1	yes	characteristic
758	C₂×C₄	D₃×#121	1	1	yes	characteristic
759	C₂×C₄	D₃×#121	1	1	yes	characteristic
760	C₂×C₄	D₃×#121	1	1	yes	characteristic
761	C₂×C₄	D₃×#127	1	1	yes	characteristic
762	C₂×C₄	D₃×#127	1	1	yes	characteristic
763	C₂×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
767	C₂×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
768	C₂×C₄	C₂×D₃×#41	1	1	yes	characteristic
769	C₂×C₃	C₂²×#392	1	1	yes	characteristic
770	D₃	#23412	1	2	yes	direct product factor
771	C₂²	D₃×#392	1	1	yes	characteristic
772	C₂²	D₃×#392	1	1	yes	characteristic
773	C₂²	D₃×#392	1	1	yes	characteristic
774	C₂²	D₃×#392	1	1	yes	characteristic
775	C₂²	C₂×D₃×#120	1	1	yes	characteristic
776	C₂²	C₂×D₃×#121	1	1	yes	characteristic
777	C₂²	C₂×D₃×#127	1	1	yes	characteristic
778	C₄	D₃×#392	1	1	yes	characteristic
779	C₄	D₃×#392	1	1	yes	characteristic
780	C₄	D₃×#392	1	1	yes	characteristic
781	C₄	D₃×#392	1	1	yes	characteristic
782	C₄	C₂×D₃×#120	1	1	yes	characteristic
783	C₄	C₂×D₃×#120	1	1	yes	characteristic
784	C₄	C₂×D₃×#121	1	1	yes	characteristic
785	C₄	C₂×D₃×#121	1	1	yes	characteristic
786	C₃	C₂×#23412	1	1	yes	characteristic, complemented, Sylow
787	C₂	C₂×D₃×#392	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃×#392
commutator, cosocle	C₂²×C₃×C₄	C₂⁵
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₃×#23412	C₂
socle	C₂×C₃	C₂²×#392
hypercenter	#23412	D₃
hypocenter	C₃	C₂×#23412
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #23412

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×#575	C₂	semidirect
2. C₂×D₃×#575	C₂	semidirect
3. D₃×#3449	C₂	semidirect
4. C₂×D₃×#421	C₂	semidirect
5. D₃×#2896	C₂	semidirect
6. C₂×D₃×#410	C₂	semidirect
7. #10822200	C₂	semidirect
8. #10822199	C₂	semidirect
9. #10822198	C₂	semidirect
10. #10822197	C₂	semidirect
11. #10822196	C₂	semidirect
12. #10822195	C₂	semidirect
13. #10822194	C₂	semidirect
14. #10822193	C₂	semidirect
15. #10822192	C₂	semidirect
16. D₃×#2009	C₂	semidirect
17. D₃×#2008	C₂	semidirect
18. C₂×D₃×#344	C₂	semidirect
19. C₃×#23412	C₂	semidirect
23. C₂×C₃×#575	C₂²	semidirect
24. C₂×C₃×#575	C₂²	semidirect
25. C₃×#3449	C₂²	semidirect
26. #87268	C₂²	semidirect
27. #87268	C₂²	semidirect
28. C₂×#5822	C₂²	semidirect
29. C₂×#5822	C₂²	semidirect
30. C₂×#5822	C₂²	semidirect
31. C₂×#5822	C₂²	semidirect
33. D₃×#575	C₂²	semidirect
34. C₂×#5777	C₂²	semidirect
35. C₂×D₃×#137	C₂²	semidirect
36. C₂×#5773	C₂²	semidirect
37. C₂×D₃×AGL(1,ℤ/8)	C₂²	semidirect
38. C₂×#5748	C₂²	semidirect
39. C₂×#5748	C₂²	semidirect
42. D₃×#536	C₂²	semidirect
43. #86338	C₂²	semidirect
44. D₃×#535	C₂²	semidirect
45. #86313	C₂²	semidirect
46. #85735	C₂²	semidirect
49. C₂×C₃×#421	C₂²	semidirect
50. C₃×#2896	C₂²	semidirect
51. C₂×C₃×#410	C₂²	semidirect
52. C₂×#5240	C₂²	semidirect
53. C₂×#5236	C₂²	semidirect
54. #84072	C₂²	semidirect
55. C₂×#5139	C₂²	semidirect
56. #83768	C₂²	semidirect
57. C₂×#5006	C₂²	semidirect
58. C₂×#5006	C₂²	semidirect
59. C₂×#5005	C₂²	semidirect
60. #82213	C₂²	semidirect
61. D₃×#421	C₂²	semidirect
62. D₃×#421	C₂²	semidirect
63. #78956	C₂²	semidirect
64. D₃×#419	C₂²	semidirect
65. #78924	C₂²	semidirect
66. D₃×#418	C₂²	semidirect
67. D₃×#410	C₂²	semidirect
68. D₃×#410	C₂²	semidirect
69. C₃×#2009	C₂²	semidirect
70. C₃×#2008	C₂²	semidirect
71. C₂×C₃×#344	C₂²	semidirect
72. #72120	C₂²	semidirect
73. #72119	C₂²	semidirect
74. #72111	C₂²	semidirect
75. #72099	C₂²	semidirect
76. C₂×#4559	C₂²	semidirect
77. C₂×#4556	C₂²	semidirect
78. #71869	C₂²	semidirect
79. #71858	C₂²	semidirect
80. C₂×#4533	C₂²	semidirect
81. #70412	C₂²	semidirect
82. #70409	C₂²	semidirect
83. #70351	C₂²	semidirect
84. #70331	C₂²	semidirect
85. #70053	C₂²	semidirect
86. #70050	C₂²	semidirect
87. #69031	C₂²	semidirect
88. #69028	C₂²	semidirect
89. D₃×#344	C₂²	semidirect
90. D₃×#344	C₂²	semidirect
91. #23412	D₃	direct (N × H)
101. C₂×D₃×#41	D₄	semidirect
102. C₂×D₃×#41	D₄	semidirect
108. C₂²×#239	D₄	semidirect
111. C₂²×D₃×Q₈	D₄	semidirect
114. C₂²×#237	D₄	semidirect
117. C₂²×D₃×D₄	D₄	semidirect
124. C₂×C₃×#137	C₂³	semidirect
125. C₂×C₃×AGL(1,ℤ/8)	C₂³	semidirect
128. C₃×#536	C₂³	semidirect
129. C₃×#535	C₂³	semidirect
132. #5830	C₂³	semidirect
133. #5825	C₂³	semidirect
134. C₂×#951	C₂³	semidirect
137. C₂×#949	C₂³	semidirect
138. #5816	C₂³	semidirect
139. C₂×#942	C₂³	semidirect
140. #5805	C₂³	semidirect
141. C₂×#932	C₂³	semidirect
147. C₂×#909	C₂³	semidirect
148. C₂×#908	C₂³	semidirect
149. C₂×D₃×M₁₆	D₄	semidirect
150. C₂×D₃×M₁₆	D₄	semidirect
151. C₂×D₃×M₁₆	D₄	semidirect
152. C₂×D₃×M₁₆	D₄	semidirect
153. C₂×D₃×M₁₆	D₄	semidirect
154. C₂×D₃×M₁₆	D₄	semidirect
159. C₂²×ΓL(1,𝔽₂₅)	D₄	semidirect
160. C₂²×D₃×C₈	D₄	semidirect
161. #5526	C₂³	semidirect
162. #5525	C₂³	semidirect
171. C₃×#421	C₂³	semidirect
172. C₃×#419	C₂³	semidirect
173. C₃×#418	C₂³	semidirect
174. C₃×#410	C₂³	semidirect
175. #5240	C₂³	semidirect
176. #5236	C₂³	semidirect
177. #5225	C₂³	semidirect
178. #5215	C₂³	semidirect
179. #5139	C₂³	semidirect
180. #5131	C₂³	semidirect
181. #5120	C₂³	semidirect
182. #5006	C₂³	semidirect
183. #5006	C₂³	semidirect
184. #5005	C₂³	semidirect
185. #5004	C₂³	semidirect
186. #5001	C₂³	semidirect
187. C₃×#344	C₂³	semidirect
188. #4559	C₂³	semidirect
189. #4556	C₂³	semidirect
190. #4533	C₂³	semidirect
191. C₂×#575	C₂×D₃	semidirect
192. C₂×#575	C₂×D₃	semidirect
193. #3449	C₂×D₃	semidirect
194. C₂×#421	C₂×D₃	semidirect
195. #2896	C₂×D₃	semidirect
196. C₂×#410	C₂×D₃	semidirect
197. #2009	C₂×D₃	semidirect
198. #2008	C₂×D₃	semidirect
199. C₂×#344	C₂×D₃	semidirect
204. C₂×C₃×#41	C₂×D₄	semidirect
208. C₂²×C₃×Q₈	C₂×D₄	semidirect
211. C₂²×C₃×D₄	C₂×D₄	semidirect
220. C₂×#239	C₂×D₄	semidirect
226. C₂×D₃×Q₈	C₂×D₄	semidirect
232. C₂×#237	C₂×D₄	semidirect
238. C₂×D₃×D₄	C₂×D₄	semidirect
242. C₂×#235	C₂×D₄	semidirect
246. C₂²×D₁₂	C₂×D₄	semidirect
277. C₂²×Dic₆	C₂×D₄	semidirect
279. C₂×C₃×M₁₆	C₂×D₄	semidirect
280. C₂×C₃×M₁₆	C₂×D₄	semidirect
281. C₂×C₃×M₁₆	C₂×D₄	semidirect
284. C₂²×C₃×C₈	C₂×D₄	semidirect
293. C₂×#208	C₂×D₄	semidirect
294. C₂×#208	C₂×D₄	semidirect
295. C₂×#208	C₂×D₄	semidirect
298. C₂²×C₃⋊C₈	C₂×D₄	semidirect
301. D₃×M₁₆	C₂×D₄	semidirect
302. D₃×M₁₆	C₂×D₄	semidirect
304. C₂×ΓL(1,𝔽₂₅)	C₂×D₄	semidirect
306. C₂×D₃×C₈	C₂×D₄	semidirect
315. C₂×#137	C₂²×D₃	semidirect
316. C₂×AGL(1,ℤ/8)	C₂²×D₃	semidirect
319. #536	C₂²×D₃	semidirect
320. #535	C₂²×D₃	semidirect
323. #421	C₂²×D₃	semidirect
324. #419	C₂²×D₃	semidirect
325. #418	C₂²×D₃	semidirect
326. #410	C₂²×D₃	semidirect
327. #344	C₂²×D₃	semidirect
504. C₂×#41	D₃×D₄	semidirect
508. C₂²×Q₈	D₃×D₄	semidirect
511. C₂²×D₄	D₃×D₄	semidirect
514. C₂×M₁₆	D₃×D₄	semidirect
515. C₂×M₁₆	D₃×D₄	semidirect
516. C₂×M₁₆	D₃×D₄	semidirect
519. C₂²×C₈	D₃×D₄	semidirect
770. D₃	#23412	direct (N × H)
786. C₃	C₂×#23412	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×#575	2
D₃×#3449	2
C₂×D₃×#421	2
D₃×#2896	2
C₂×D₃×#410	2
#10822200	2
#10822199	2
#10822198	2
#10822197	2
#10822196	2
#10822195	2
#10822194	2
#10822193	2
#10822192	2
D₃×#2009	2
D₃×#2008	2
C₂×D₃×#344	2
C₃×#23412	2
C₂×#23412	3

Subgroups — D3×#23412 #72253874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#23412 #72253874