Subgroups — #10818166

Order 768.

824 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#5024	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#4925	C₂	1	1	yes	maximal, characteristic
4	#71635	C₂	1	1	yes	maximal, characteristic, complemented
5	#71529	C₂	1	1	yes	maximal, characteristic
6	#69485	C₂	1	1	yes	maximal, characteristic, complemented
7	#69482	C₂	1	1	yes	maximal, characteristic, complemented
8	#69482	C₂	1	1	yes	maximal, characteristic, complemented
9	#69478	C₂	1	1	yes	maximal, characteristic, complemented
10	#69478	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#69452	C₂	1	1	yes	maximal, characteristic
13	#69452	C₂	1	1	yes	maximal, characteristic
14	#69451	C₂	1	1	yes	maximal, characteristic
15	#69451	C₂	1	1	yes	maximal, characteristic
16	#23052	—	3	1	no	maximal, Sylow
17	C₂×C₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
18	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
20	C₃×#391	C₄	1	1	yes	characteristic
21	C₃×#389	C₄	1	1	yes	characteristic
22	C₃×#387	C₄	1	1	yes	characteristic
23	C₃×#387	C₄	1	1	yes	characteristic
24	C₃×#385	C₄	1	1	yes	characteristic
25	C₃×#385	C₄	1	1	yes	characteristic
26	C₃×#380	C₄	1	1	yes	characteristic
27	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×#830	C₂²	1	1	yes	characteristic
33	C₂×#830	C₂²	1	1	yes	characteristic
34	C₂×#830	C₂²	1	1	yes	characteristic
35	C₂×#830	C₂²	1	1	yes	characteristic
36	#5024	—	2	4	no	—
37	#4925	—	2	4	no	—
38	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
44	C₂×#803	C₂²	1	1	yes	characteristic
45	C₂×#803	C₂²	1	1	yes	characteristic
46	C₂×#803	C₂²	1	1	yes	characteristic
47	C₂×#803	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
52	#4524	C₂²	1	1	yes	characteristic
53	#4524	C₂²	1	1	yes	characteristic
54	#4524	C₂²	1	1	yes	characteristic
55	#4524	C₂²	1	1	yes	characteristic
56	#4524	C₂²	1	1	yes	characteristic
57	#4524	C₂²	1	1	yes	characteristic
58	#4524	C₂²	1	1	yes	characteristic
59	#4524	C₂²	1	1	yes	characteristic
60	#4524	C₂²	1	1	yes	characteristic
61	#4524	C₂²	1	1	yes	characteristic
62	C₂×#446	—	3	1	no	—
63	C₂×#431	—	3	1	no	—
64	C₄×C₂²⋊Q₈	D₃	1	1	yes	characteristic
65	#1985	—	3	1	no	—
66	#1940	—	3	1	no	—
67	#1924	—	3	1	no	—
68	#1924	—	3	1	no	—
69	#1923	—	3	1	no	—
70	#1923	—	3	1	no	—
71	#1916	—	3	1	no	—
72	#1916	—	3	1	no	—
73	#1771	—	3	1	no	—
74	#1771	—	3	1	no	—
75	C₈×C₄⋊C₄	—	3	1	no	—
76	#1749	—	3	1	no	—
77	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
78	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
81	C₃×C₂²⋊Q₈	—	2	4	no	—
82	C₃×C₄×Q₈	—	2	2	no	—
83	C₃×C₄×Q₈	—	2	2	no	—
84	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄²	—	2	2	no	—
98	C₂×C₃×C₄²	—	2	2	no	—
99	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
107	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
110	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
111	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
113	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
114	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
115	C₃×#95	C₂×C₄	1	1	yes	characteristic
116	C₃×#95	C₂×C₄	1	1	yes	characteristic
117	C₃×#95	C₂×C₄	1	1	yes	characteristic
118	C₃×#95	C₂×C₄	1	1	yes	characteristic
119	C₃×#95	C₂×C₄	1	1	yes	characteristic
120	C₃×#95	C₂×C₄	1	1	yes	characteristic
121	C₃×#95	C₂×C₄	1	1	yes	characteristic
122	C₃×#95	C₂×C₄	1	1	yes	characteristic
123	C₃×#95	C₂×C₄	1	1	yes	characteristic
124	C₃×#95	C₂×C₄	1	1	yes	characteristic
125	#830	—	2	2	no	—
126	#830	—	2	2	no	—
127	#830	—	2	2	no	—
128	#830	—	2	2	no	—
129	C₄⋊(C₃⋊C₈)	—	2	2	no	—
130	C₄⋊(C₃⋊C₈)	—	2	2	no	—
131	C₄⋊(C₃⋊C₈)	—	2	2	no	—
132	C₄⋊(C₃⋊C₈)	—	2	2	no	—
133	C₄⋊(C₃⋊C₈)	—	2	2	no	—
134	C₄⋊(C₃⋊C₈)	D₄	1	4	yes	—
135	#803	—	2	2	no	—
136	#803	—	2	2	no	—
137	#803	—	2	2	no	—
138	#803	—	2	2	no	—
139	C₄×C₃⋊C₈	—	2	2	no	—
140	C₄×C₃⋊C₈	—	2	2	no	—
141	C₄×C₃⋊C₈	—	2	2	no	—
142	C₄×C₃⋊C₈	—	2	2	no	—
143	C₂×C₂²⋊Q₈	Dic₃	1	1	yes	characteristic
144	C₂×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
145	C₂²×C₄²	C₂×D₃	1	1	yes	characteristic
146	#446	—	6	4	no	—
147	#431	—	6	4	no	—
148	C₂×C₄⋊C₈	—	3	1	no	—
149	C₂×C₄⋊C₈	—	3	1	no	—
150	C₂×C₄⋊C₈	—	3	1	no	—
151	C₂×C₄⋊C₈	—	3	1	no	—
152	C₂×C₄⋊C₈	—	3	1	no	—
153	C₂×C₄⋊C₈	—	3	1	no	—
154	C₂×C₂²⋊C₈	—	3	1	no	—
155	C₂×C₂²⋊C₈	—	3	1	no	—
156	C₂×C₂²⋊C₈	—	3	1	no	—
157	C₂×C₂²⋊C₈	—	3	1	no	—
158	C₂×#97	—	3	1	no	—
159	C₂×#97	—	3	1	no	—
160	C₂×#97	—	3	1	no	—
161	C₂×#97	—	3	1	no	—
162	C₂×C₄×C₈	—	3	1	no	—
163	C₂×C₄×C₈	—	3	1	no	—
164	C₂×C₄×C₈	—	3	1	no	—
165	C₂×C₄×C₈	—	3	1	no	—
166	#391	Dic₃	1	1	yes	characteristic
167	#389	Dic₃	1	1	yes	characteristic
168	#387	Dic₃	1	1	yes	characteristic
169	#387	Dic₃	1	1	yes	characteristic
170	#385	Dic₃	1	1	yes	characteristic
171	#385	Dic₃	1	1	yes	characteristic
172	#380	Dic₃	1	1	yes	characteristic
173	C₄×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
174	C₄×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
175	C₄×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
176	C₄×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
177	C₄×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
178	#336	—	3	1	no	—
179	#336	—	3	1	no	—
180	#336	—	3	1	no	—
181	#336	—	3	1	no	—
182	#336	—	3	1	no	—
183	#336	—	3	1	no	—
184	#336	—	3	1	no	—
185	#336	—	3	1	no	—
186	#336	—	3	1	no	—
187	#336	—	3	1	no	—
188	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₃×Q₈	—	2	2	no	—
190	C₂×C₃×Q₈	—	2	2	no	—
191	C₂×C₃×Q₈	—	4	1	no	—
192	C₂²×C₃×C₄	—	2	2	no	—
193	C₂²×C₃×C₄	—	2	2	no	—
194	C₂²×C₃×C₄	—	2	2	no	—
195	C₂²×C₃×C₄	—	2	2	no	—
196	C₂²×C₃×C₄	—	2	2	no	—
197	C₂²×C₃×C₄	—	2	1	no	—
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	—	2	1	no	—
203	C₂²×C₃×C₄	—	4	1	no	—
204	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
218	C₃×C₄⋊C₄	—	2	2	no	—
219	C₃×C₄⋊C₄	—	2	2	no	—
220	C₃×C₄⋊C₄	—	2	2	no	—
221	C₃×C₄⋊C₄	—	2	2	no	—
222	C₃×C₄⋊C₄	—	2	2	no	—
223	C₃×C₄⋊C₄	—	2	2	no	—
224	C₃×C₄⋊C₄	—	2	2	no	—
225	C₃×C₄⋊C₄	—	4	1	no	—
226	C₃×C₄⋊C₄	M₁₆	1	4	yes	—
227	C₃×C₂²⋊C₄	—	2	2	no	—
228	C₃×C₂²⋊C₄	—	2	2	no	—
229	C₃×C₂²⋊C₄	—	2	2	no	—
230	C₃×C₂²⋊C₄	—	2	2	no	—
231	C₃×C₄²	—	2	2	no	—
232	C₃×C₄²	—	2	2	no	—
233	C₃×C₄²	—	2	1	no	—
234	C₃×C₄²	—	2	1	no	—
235	C₃×C₄²	—	2	1	no	—
236	C₃×C₄²	—	2	1	no	—
237	C₃×C₄²	—	2	1	no	—
238	C₃×C₄²	—	2	1	no	—
239	C₃×C₄²	—	2	1	no	—
240	C₃×C₄²	—	2	1	no	—
241	C₃×C₄²	—	2	1	no	—
242	C₃×C₄²	—	2	1	no	—
243	C₃×C₄²	C₂×D₄	1	2	yes	—
244	C₃×C₄²	#41	1	2	yes	—
245	C₂×C₃⋊C₈	—	2	1	no	—
246	C₂×C₃⋊C₈	—	2	1	no	—
247	C₂×C₃⋊C₈	—	2	1	no	—
248	C₂×C₃⋊C₈	—	2	1	no	—
249	C₂×C₃⋊C₈	—	2	1	no	—
250	C₂×C₃⋊C₈	—	2	1	no	—
251	C₂×C₃⋊C₈	—	2	1	no	—
252	C₂×C₃⋊C₈	—	2	1	no	—
253	C₂×C₃⋊C₈	—	2	1	no	—
254	C₂×C₃⋊C₈	—	2	1	no	—
255	C₂×C₃⋊C₈	—	2	1	no	—
256	C₂×C₃⋊C₈	—	2	1	no	—
257	C₂×C₃⋊C₈	—	2	1	no	—
258	C₂×C₃⋊C₈	—	2	1	no	—
259	C₂×C₃⋊C₈	—	2	1	no	—
260	C₂×C₃⋊C₈	—	2	1	no	—
261	C₂×C₃⋊C₈	—	2	1	no	—
262	C₂×C₃⋊C₈	—	2	1	no	—
263	C₂×C₃⋊C₈	—	2	1	no	—
264	C₂×C₃⋊C₈	—	2	1	no	—
265	C₂×C₃⋊C₈	C₂×D₄	1	2	yes	—
266	C₂×C₃⋊C₈	C₂×D₄	1	2	yes	—
267	C₂×C₃⋊C₈	#41	1	2	yes	—
268	C₂×C₃⋊C₈	#41	1	2	yes	—
269	C₂²×Q₈	C₂×Dic₃	1	1	yes	characteristic
270	C₂³×C₄	C₂×Dic₃	1	1	yes	characteristic
271	C₂³×C₄	C₂×Dic₃	1	1	yes	characteristic
272	C₂³×C₄	C₂²×D₃	1	1	yes	characteristic
273	C₂²×C₈	—	3	1	no	—
274	C₂²×C₈	—	3	1	no	—
275	C₂²×C₈	—	3	1	no	—
276	C₂²×C₈	—	3	1	no	—
277	C₂²×C₈	—	3	1	no	—
278	C₂²×C₈	—	3	1	no	—
279	C₂²×C₈	—	3	1	no	—
280	C₂²×C₈	—	3	1	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	C₂×Dic₃	1	1	yes	characteristic
300	C₂×C₄²	C₂×Dic₃	1	1	yes	characteristic
301	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
302	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
303	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
304	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
305	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
306	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
307	C₄⋊C₈	—	3	4	no	—
308	C₄⋊C₈	—	6	2	no	—
309	C₄⋊C₈	—	6	2	no	—
310	C₄⋊C₈	—	6	2	no	—
311	C₄⋊C₈	—	6	2	no	—
312	C₄⋊C₈	—	6	2	no	—
313	C₂²⋊C₈	—	6	2	no	—
314	C₂²⋊C₈	—	6	2	no	—
315	C₂²⋊C₈	—	6	2	no	—
316	C₂²⋊C₈	—	6	2	no	—
317	#97	—	6	2	no	—
318	#97	—	6	2	no	—
319	#97	—	6	2	no	—
320	#97	—	6	2	no	—
321	C₄×C₈	—	6	2	no	—
322	C₄×C₈	—	6	2	no	—
323	C₄×C₈	—	6	2	no	—
324	C₄×C₈	—	6	2	no	—
325	#95	C₂×Dic₃	1	1	yes	characteristic
326	#95	C₂×Dic₃	1	1	yes	characteristic
327	#95	C₂×Dic₃	1	1	yes	characteristic
328	#95	C₂×Dic₃	1	1	yes	characteristic
329	#95	C₂×Dic₃	1	1	yes	characteristic
330	#95	C₂×Dic₃	1	1	yes	characteristic
331	#95	C₂×Dic₃	1	1	yes	characteristic
332	#95	C₂×Dic₃	1	1	yes	characteristic
333	#95	C₂×Dic₃	1	1	yes	characteristic
334	#95	C₂×Dic₃	1	1	yes	characteristic
335	C₂³×C₃	—	2	1	no	—
336	C₂³×C₃	—	2	1	no	—
337	C₂³×C₃	—	2	1	no	—
338	C₂³×C₃	—	2	1	no	—
339	C₂³×C₃	—	2	1	no	—
340	C₂³×C₃	—	2	1	no	—
341	C₂³×C₃	#131	1	2	yes	—
342	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
343	C₃×Q₈	—	4	4	no	—
344	C₂×C₃×C₄	—	2	8	no	—
345	C₂×C₃×C₄	—	2	1	no	—
346	C₂×C₃×C₄	—	2	1	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	1	no	—
364	C₂×C₃×C₄	—	2	1	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	4	4	no	—
379	C₂×C₃×C₄	—	4	1	no	—
380	C₂×C₃×C₄	—	4	1	no	—
381	C₂×C₃×C₄	—	4	1	no	—
382	C₂×C₃×C₄	—	4	1	no	—
383	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
384	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
385	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
386	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
387	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
388	C₂×C₃×C₄	#131	1	2	yes	—
389	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
392	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
393	C₂×C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
394	C₂×C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
395	C₃⋊C₈	—	2	2	no	—
396	C₃⋊C₈	—	2	2	no	—
397	C₃⋊C₈	—	2	2	no	—
398	C₃⋊C₈	—	2	2	no	—
399	C₃⋊C₈	—	4	1	no	—
400	C₃⋊C₈	—	4	1	no	—
401	C₃⋊C₈	—	4	1	no	—
402	C₃⋊C₈	—	4	1	no	—
403	C₂⁴	C₂²×Dic₃	1	1	yes	characteristic
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	4	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	4	1	no	—
419	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
420	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
421	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
422	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
423	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
424	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
426	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
432	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
433	C₂×C₈	—	3	2	no	—
434	C₂×C₈	—	3	2	no	—
435	C₂×C₈	—	3	2	no	—
436	C₂×C₈	—	3	2	no	—
437	C₂×C₈	—	6	1	no	—
438	C₂×C₈	—	6	1	no	—
439	C₂×C₈	—	6	1	no	—
440	C₂×C₈	—	6	1	no	—
441	C₂×C₈	—	6	1	no	—
442	C₂×C₈	—	6	1	no	—
443	C₂×C₈	—	6	1	no	—
444	C₂×C₈	—	6	1	no	—
445	C₂×C₈	—	6	1	no	—
446	C₂×C₈	—	6	1	no	—
447	C₂×C₈	—	6	1	no	—
448	C₂×C₈	—	6	1	no	—
449	C₂×C₈	—	6	1	no	—
450	C₂×C₈	—	6	1	no	—
451	C₂×C₈	—	6	1	no	—
452	C₂×C₈	—	6	1	no	—
453	C₂×C₈	—	6	1	no	—
454	C₂×C₈	—	6	1	no	—
455	C₂×C₈	—	6	1	no	—
456	C₂×C₈	—	6	1	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	#208	1	4	yes	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	D₃×D₄	1	2	yes	—
483	C₄²	#237	1	2	yes	—
484	C₂²×C₃	—	2	2	no	—
485	C₂²×C₃	—	2	2	no	—
486	C₂²×C₃	—	2	2	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	1	no	—
489	C₂²×C₃	—	4	1	no	—
490	C₂²×C₃	—	4	1	no	—
491	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
492	C₂²×C₃	C₄×#41	1	1	yes	characteristic
493	C₂²×C₃	#519	1	1	yes	characteristic
494	C₂²×C₃	C₂²×M₁₆	1	1	yes	characteristic
495	C₂²×C₃	C₂×#131	1	1	yes	characteristic
496	C₂²×C₃	C₂×#131	1	1	yes	characteristic
497	C₂²×C₃	#568	1	1	yes	characteristic
498	C₃×C₄	—	2	2	no	—
499	C₃×C₄	—	2	2	no	—
500	C₃×C₄	—	2	2	no	—
501	C₃×C₄	—	2	2	no	—
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	—	2	2	no	—
504	C₃×C₄	—	4	1	no	—
505	C₃×C₄	—	4	1	no	—
506	C₃×C₄	—	4	1	no	—
507	C₃×C₄	—	4	1	no	—
508	C₃×C₄	—	4	1	no	—
509	C₃×C₄	—	4	1	no	—
510	C₃×C₄	—	4	1	no	—
511	C₃×C₄	#547	1	1	yes	characteristic
512	C₃×C₄	#548	1	1	yes	characteristic
513	C₃×C₄	#552	1	1	yes	characteristic
514	C₃×C₄	#556	1	1	yes	characteristic
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	#948	1	2	yes	—
522	C₂³	C₂³×Dic₃	1	1	yes	characteristic
523	Q₈	—	4	4	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	C₂×#208	1	2	yes	—
564	C₂×C₄	C₂×#208	1	2	yes	—
565	C₂×C₄	C₂×#208	1	2	yes	—
566	C₂×C₄	D₄×Dic₃	1	2	yes	—
567	C₂×C₄	D₄×Dic₃	1	2	yes	—
568	C₂×C₄	#948	1	2	yes	—
569	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
570	C₂×C₄	C₂×#237	1	1	yes	characteristic
571	C₂×C₄	#1007	1	1	yes	characteristic
572	C₂×C₄	#1007	1	1	yes	characteristic
573	C₂×C₄	D₃×#41	1	1	yes	characteristic
574	C₂×C₄	D₃×#41	1	1	yes	characteristic
575	C₈	—	6	2	no	—
576	C₈	—	6	2	no	—
577	C₈	—	6	2	no	—
578	C₈	—	6	2	no	—
579	C₈	—	12	1	no	—
580	C₈	—	12	1	no	—
581	C₈	—	12	1	no	—
582	C₈	—	12	1	no	—
583	C₂×C₃	—	4	2	no	—
584	C₂×C₃	#2362	1	1	yes	characteristic
585	C₂×C₃	#2929	1	1	yes	characteristic
586	C₂×C₃	D₄×M₁₆	1	1	yes	characteristic
587	C₂×C₃	#2965	1	1	yes	characteristic
588	C₂×C₃	#2968	1	1	yes	characteristic
589	C₂×C₃	#2984	1	1	yes	characteristic
590	C₂×C₃	#2985	1	1	yes	characteristic
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	C₂²×#208	1	1	yes	characteristic
599	C₂²	C₂×D₄×Dic₃	1	1	yes	characteristic
600	C₂²	#5812	1	1	yes	characteristic
601	C₂²	C₂×#948	1	1	yes	characteristic
602	C₂²	C₂×#948	1	1	yes	characteristic
603	C₂²	#5819	1	1	yes	characteristic
604	C₂²	Dic₃×#41	1	1	yes	characteristic
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	#5631	1	1	yes	characteristic
619	C₄	#5633	1	1	yes	characteristic
620	C₄	#5639	1	1	yes	characteristic
621	C₄	#5641	1	1	yes	characteristic
622	C₃	#23052	1	1	yes	characteristic, complemented, Sylow
623	C₂	—	4	2	no	—
624	C₂	D₄×#208	1	1	yes	characteristic
625	C₂	#82437	1	1	yes	characteristic
626	C₂	#82517	1	1	yes	characteristic
627	C₂	#82748	1	1	yes	characteristic
628	C₂	#82916	1	1	yes	characteristic
629	C₂	#83128	1	1	yes	characteristic
630	C₂	#83331	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₃
commutator, socle	C₂³×C₃	C₂³×C₄
Fitting	C₃×C₄×C₂²⋊Q₈	C₂
prime radical	C₂⁴×C₃	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂⁴
hypercenter	C₄×C₂²⋊Q₈	D₃
hypocenter	C₃	#23052
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×#5024	C₂	semidirect
4. #71635	C₂	semidirect
6. #69485	C₂	semidirect
7. #69482	C₂	semidirect
8. #69482	C₂	semidirect
9. #69478	C₂	semidirect
10. #69478	C₂	semidirect
11. C₄⋊C₄×C₃⋊C₈	C₂	semidirect
622. C₃	#23052	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₂²⋊Q₈	2
C₂×#5024	2
C₂×#4925	2
#71635	2
#71529	2
#69485	2
#69482	2
#69478	2
C₄⋊C₄×C₃⋊C₈	2
#69452	2
#69451	2
#23052	3