Subgroups — #10801654

Order 768.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3035	C₂	1	1	yes	maximal, characteristic
2	C₂×#5197	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#5196	C₂	1	1	yes	maximal, characteristic, complemented
4	#83276	C₂	1	1	yes	maximal, characteristic, complemented
5	#82511	C₂	1	1	yes	maximal, characteristic, complemented
6	#72087	C₂	1	1	yes	maximal, characteristic, complemented
7	#72087	C₂	1	1	yes	maximal, characteristic, complemented
8	#71818	C₂	1	1	yes	maximal, characteristic, complemented
9	#71646	C₂	1	1	yes	maximal, characteristic, complemented
10	#70474	C₂	1	1	yes	maximal, characteristic, complemented
11	#70467	C₂	1	1	yes	maximal, characteristic, complemented
12	#70291	C₂	1	1	yes	maximal, characteristic, complemented
13	#70291	C₂	1	1	yes	maximal, characteristic, complemented
14	#70290	C₂	1	1	yes	maximal, characteristic, complemented
15	#70289	C₂	1	1	yes	maximal, characteristic, complemented
16	#21519	—	3	1	no	maximal, Sylow
17	C₂×C₃×#135	C₂²	1	1	yes	characteristic
18	C₂×C₃×#135	C₂²	1	1	yes	characteristic
19	C₃×#532	C₂²	1	1	yes	characteristic
20	C₃×C₄×#41	C₂²	1	1	yes	characteristic
21	C₂×#948	C₂²	1	1	yes	characteristic
22	C₂×#948	C₂²	1	1	yes	characteristic
23	C₂×#948	C₂²	1	1	yes	characteristic
24	C₂×#948	C₂²	1	1	yes	characteristic
25	C₃×#464	C₄	1	1	yes	characteristic, complemented
26	C₃×#464	C₄	1	1	yes	characteristic, complemented
27	C₃×#463	C₄	1	1	yes	characteristic, complemented
28	C₃×#463	C₄	1	1	yes	characteristic, complemented
29	C₃×#462	C₄	1	1	yes	characteristic, complemented
30	C₃×#461	C₄	1	1	yes	characteristic, complemented
31	C₃×#460	C₄	1	1	yes	characteristic, complemented
32	C₃×#459	C₄	1	1	yes	characteristic, complemented
33	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₃×#416	C₂²	1	1	yes	characteristic
35	C₃×#416	C₂²	1	1	yes	characteristic
36	C₂×#837	C₂²	1	1	yes	characteristic
37	C₂×#837	C₂²	1	1	yes	characteristic
38	C₂×#837	C₂²	1	1	yes	characteristic
39	C₂×#837	C₂²	1	1	yes	characteristic
40	C₂×#837	C₂²	1	1	yes	characteristic
41	C₂×#837	C₂²	1	1	yes	characteristic
42	#5234	C₂²	1	1	yes	characteristic
43	#5234	C₂²	1	1	yes	characteristic
44	#5197	—	2	4	no	—
45	#5196	—	2	4	no	—
46	C₂×#819	C₂²	1	1	yes	characteristic
47	C₂×#819	C₂²	1	1	yes	characteristic
48	C₂×#815	C₂²	1	1	yes	characteristic
49	C₂×C₈×Dic₃	C₂²	1	1	yes	characteristic
50	#5011	—	2	1	no	—
51	#5011	—	2	1	no	—
52	#5011	—	2	1	no	—
53	#5011	—	2	1	no	—
54	#4997	—	2	1	no	—
55	#4997	—	2	1	no	—
56	#4997	C₂²	1	1	yes	characteristic
57	#4997	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
59	#4924	C₂²	1	1	yes	characteristic
60	C₄×#208	—	2	1	no	—
61	C₄×#208	C₂²	1	1	yes	characteristic
62	C₂×#803	—	2	1	no	—
63	C₂×#803	C₂²	1	1	yes	characteristic
64	#4552	C₂²	1	1	yes	characteristic
65	#4552	C₂²	1	1	yes	characteristic
66	#4550	C₂²	1	1	yes	characteristic
67	#4550	C₂²	1	1	yes	characteristic
68	#4532	C₂²	1	1	yes	characteristic
69	#4532	C₂²	1	1	yes	characteristic
70	#3035	D₃	1	1	yes	characteristic
71	C₂×#444	—	3	1	no	—
72	C₂×#443	—	3	1	no	—
73	#2932	—	3	1	no	—
74	#2875	—	3	1	no	—
75	#1980	—	3	1	no	—
76	#1950	—	3	1	no	—
77	#1929	—	3	1	no	—
78	#1929	—	3	1	no	—
79	#1876	—	3	1	no	—
80	#1876	—	3	1	no	—
81	#1806	—	3	1	no	—
82	#1771	—	3	1	no	—
83	#1765	—	3	1	no	—
84	#1764	—	3	1	no	—
85	C₂×C₃×#41	C₂³	1	1	yes	characteristic
86	C₂×C₃×#41	C₂³	1	1	yes	characteristic
87	C₂×C₃×#41	C₂³	1	1	yes	characteristic
88	C₃×#135	—	2	2	no	—
89	C₃×#135	—	2	2	no	—
90	C₃×#135	—	2	2	no	—
91	C₃×#135	—	2	2	no	—
92	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
93	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
95	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
97	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
98	C₂×C₃×D₈	C₂×C₄	1	1	yes	characteristic
99	C₂×C₃×D₈	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
101	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
102	C₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
103	C₃×#127	C₂×C₄	1	1	yes	characteristic
104	C₃×#124	C₂×C₄	1	1	yes	characteristic
105	C₃×#124	C₂×C₄	1	1	yes	characteristic
106	C₃×#121	—	2	1	no	—
107	C₃×#121	—	2	1	no	—
108	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
109	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
110	C₃×C₄×D₄	—	2	1	no	—
111	C₃×C₄×D₄	—	2	1	no	—
112	C₃×C₄×D₄	—	2	1	no	—
113	C₃×C₄×D₄	—	2	1	no	—
114	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
115	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
116	C₃×#117	—	2	1	no	—
117	C₃×#117	C₂³	1	1	yes	characteristic
118	C₂×C₃×C₄²	—	2	1	no	—
119	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
120	#948	—	2	2	no	—
121	#948	—	2	2	no	—
122	#948	—	2	2	no	—
123	#948	—	2	2	no	—
124	#948	—	2	2	no	—
125	#948	—	2	2	no	—
126	#948	—	2	2	no	—
127	#948	D₄	1	4	yes	complemented
128	C₂×C₄⋊Dic₃	—	2	1	no	—
129	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
130	C₂×C₄×Dic₃	C₂³	1	1	yes	characteristic
131	C₂×#208	—	2	1	no	—
132	C₂×#208	—	2	1	no	—
133	C₂×#208	—	2	1	no	—
134	C₂×#208	—	2	1	no	—
135	C₂×#208	C₂³	1	1	yes	characteristic
136	C₂×#208	C₂³	1	1	yes	characteristic
137	C₂×#208	C₂³	1	1	yes	characteristic
138	C₂×#208	C₂³	1	1	yes	characteristic
139	C₂²×C₃⋊C₈	—	2	1	no	—
140	C₂²×C₃⋊C₈	—	2	1	no	—
141	C₂²×C₃⋊C₈	—	2	1	no	—
142	C₂²×C₃⋊C₈	—	2	1	no	—
143	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
144	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
145	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
146	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
147	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
148	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
149	C₃×#103	C₂×C₄	1	1	yes	characteristic
150	C₃×#103	C₂×C₄	1	1	yes	characteristic
151	C₃×#103	C₂×C₄	1	1	yes	characteristic
152	C₃×#103	C₂×C₄	1	1	yes	characteristic
153	C₃×#102	C₂×C₄	1	1	yes	characteristic
154	C₃×#102	C₂×C₄	1	1	yes	characteristic
155	C₃×#102	C₂×C₄	1	1	yes	characteristic
156	C₃×#102	C₂×C₄	1	1	yes	characteristic
157	#837	—	2	2	no	—
158	#837	—	2	2	no	—
159	#837	—	2	2	no	—
160	#837	—	2	2	no	—
161	#837	—	2	2	no	—
162	#837	—	2	2	no	—
163	C₃⋊#95	—	2	1	no	—
164	#830	—	2	1	no	—
165	#830	—	2	1	no	—
166	#830	—	2	1	no	—
167	#830	—	2	1	no	—
168	#819	—	2	2	no	—
169	#819	—	2	2	no	—
170	#815	—	2	2	no	—
171	C₈×Dic₃	—	2	2	no	—
172	C₄⋊(C₃⋊C₈)	—	2	1	no	—
173	C₄⋊(C₃⋊C₈)	—	2	1	no	—
174	#803	—	2	1	no	—
175	#803	—	2	1	no	—
176	#803	—	2	1	no	—
177	#803	D₄	1	1	yes	characteristic
178	#803	D₄	1	1	yes	characteristic
179	#803	D₄	1	1	yes	characteristic
180	#803	D₄	1	1	yes	characteristic
181	C₄×C₃⋊C₈	—	2	1	no	—
182	C₄×C₃⋊C₈	—	2	1	no	—
183	C₄×C₃⋊C₈	—	2	1	no	—
184	C₂×#135	C₂×D₃	1	1	yes	characteristic
185	C₂×#135	C₂×D₃	1	1	yes	characteristic
186	C₂×#131	—	3	1	no	—
187	C₂×#131	—	3	1	no	—
188	C₂×#131	—	3	1	no	—
189	C₂×#131	—	3	1	no	—
190	#532	C₂×D₃	1	1	yes	characteristic
191	C₄×#41	C₂×D₃	1	1	yes	characteristic
192	#464	Dic₃	1	1	yes	characteristic, complemented
193	#464	Dic₃	1	1	yes	characteristic, complemented
194	#463	Dic₃	1	1	yes	characteristic, complemented
195	#463	Dic₃	1	1	yes	characteristic, complemented
196	#462	Dic₃	1	1	yes	characteristic, complemented
197	#461	Dic₃	1	1	yes	characteristic, complemented
198	#460	Dic₃	1	1	yes	characteristic, complemented
199	#459	Dic₃	1	1	yes	characteristic, complemented
200	#444	—	6	4	no	—
201	#443	—	6	4	no	—
202	#435	—	6	1	no	—
203	#435	—	6	1	no	—
204	#435	—	6	1	no	—
205	#435	—	6	1	no	—
206	C₂×#108	—	3	1	no	—
207	C₂×#108	—	3	1	no	—
208	#423	—	3	1	no	—
209	C₂×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
210	C₂×#104	—	3	1	no	—
211	C₂×#104	—	3	1	no	—
212	C₂×#104	—	3	1	no	—
213	C₂×#104	—	3	1	no	—
214	C₂×#104	—	3	1	no	—
215	C₂×#104	—	3	1	no	—
216	#416	C₂×D₃	1	1	yes	characteristic
217	#416	C₂×D₃	1	1	yes	characteristic
218	#408	—	3	1	no	—
219	#408	—	3	1	no	—
220	#405	—	3	1	no	—
221	#405	—	3	1	no	—
222	#405	—	6	1	no	—
223	#405	—	6	1	no	—
224	C₄×M₁₆	—	3	1	no	—
225	C₄×M₁₆	—	6	1	no	—
226	C₂×#97	—	3	1	no	—
227	C₂×#97	—	3	1	no	—
228	C₂×#97	—	6	1	no	—
229	C₂×C₄×C₈	—	3	1	no	—
230	C₄×C₄⋊C₄	—	3	1	no	—
231	#341	—	3	1	no	—
232	#341	—	3	1	no	—
233	#339	—	3	1	no	—
234	#339	—	3	1	no	—
235	#336	—	3	1	no	—
236	#336	—	3	1	no	—
237	C₃×#41	—	2	1	no	—
238	C₃×#41	—	2	1	no	—
239	C₃×#41	—	2	1	no	—
240	C₃×#41	—	2	1	no	—
241	C₃×#41	—	2	1	no	—
242	C₃×#41	—	2	1	no	—
243	C₃×#41	—	2	1	no	—
244	C₃×#41	—	2	1	no	—
245	C₃×#41	—	2	1	no	—
246	C₃×#41	—	2	1	no	—
247	C₃×#41	C₂×D₄	1	2	yes	—
248	C₃×#41	#41	1	2	yes	—
249	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
250	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
251	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
252	C₂×C₃×D₄	—	2	1	no	—
253	C₂×C₃×D₄	—	2	1	no	—
254	C₂×C₃×D₄	—	2	1	no	—
255	C₂×C₃×D₄	—	2	1	no	—
256	C₂×C₃×D₄	—	2	1	no	—
257	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
258	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
259	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
260	C₂²×C₃×C₄	—	2	1	no	—
261	C₂²×C₃×C₄	—	2	1	no	—
262	C₂²×C₃×C₄	—	2	1	no	—
263	C₂²×C₃×C₄	—	2	1	no	—
264	C₂²×C₃×C₄	—	2	1	no	—
265	C₂²×C₃×C₄	#41	1	1	yes	characteristic
266	C₂²×C₃×C₄	#41	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
268	C₂²×Dic₃	—	2	1	no	—
269	C₂²×Dic₃	—	2	1	no	—
270	C₃×Q₁₆	—	2	2	no	—
271	C₃×Q₁₆	—	2	2	no	—
272	C₃×SD₁₆	—	2	2	no	—
273	C₃×SD₁₆	—	2	2	no	—
274	C₃×SD₁₆	—	2	2	no	—
275	C₃×SD₁₆	—	2	2	no	—
276	C₃×D₈	—	2	2	no	—
277	C₃×D₈	—	2	2	no	—
278	C₂×C₃×C₈	—	2	1	no	—
279	C₂×C₃×C₈	—	2	1	no	—
280	C₂×C₃×C₈	—	2	1	no	—
281	C₂×C₃×C₈	—	2	1	no	—
282	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
283	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
284	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
285	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	—	2	1	no	—
288	C₃×C₄⋊C₄	—	2	1	no	—
289	C₃×C₄⋊C₄	—	2	1	no	—
290	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
291	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
292	C₃×C₂²⋊C₄	—	2	1	no	—
293	C₃×C₂²⋊C₄	—	2	1	no	—
294	C₃×C₂²⋊C₄	—	2	1	no	—
295	C₃×C₂²⋊C₄	—	2	1	no	—
296	C₃×C₂²⋊C₄	—	2	1	no	—
297	C₃×C₂²⋊C₄	—	2	1	no	—
298	C₃×C₂²⋊C₄	—	2	1	no	—
299	C₃×C₄²	—	2	1	no	—
300	C₃×C₄²	—	2	1	no	—
301	C₃×C₄²	—	2	1	no	—
302	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
303	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
304	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
305	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
306	C₄⋊Dic₃	—	4	2	no	—
307	C₄×Dic₃	—	2	1	no	—
308	C₄×Dic₃	—	2	1	no	—
309	C₄×Dic₃	—	2	1	no	—
310	C₄×Dic₃	—	2	1	no	—
311	#208	—	2	4	no	—
312	#208	—	2	1	no	—
313	#208	—	2	1	no	—
314	#208	—	2	4	no	—
315	#208	—	2	1	no	—
316	#208	—	2	1	no	—
317	#208	—	2	1	no	—
318	#208	—	2	1	no	—
319	#208	—	4	2	no	—
320	#208	—	4	2	no	—
321	#208	C₂×D₄	1	2	yes	—
322	#208	#41	1	2	yes	—
323	C₂×C₃⋊C₈	—	2	4	no	—
324	C₂×C₃⋊C₈	—	2	1	no	—
325	C₂×C₃⋊C₈	—	2	1	no	—
326	C₂×C₃⋊C₈	—	2	1	no	—
327	C₂×C₃⋊C₈	—	2	1	no	—
328	C₂×C₃⋊C₈	—	2	4	no	—
329	C₂×C₃⋊C₈	—	2	1	no	—
330	C₂×C₃⋊C₈	—	2	1	no	—
331	C₂×C₃⋊C₈	—	4	2	no	—
332	C₂×C₃⋊C₈	—	4	2	no	—
333	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
334	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
335	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
336	C₂×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
337	C₂×C₃⋊C₈	C₂×D₄	1	2	yes	—
338	C₂×C₃⋊C₈	#41	1	2	yes	—
339	C₂×#41	C₂²×D₃	1	1	yes	characteristic
340	C₂×#41	C₂²×D₃	1	1	yes	characteristic
341	C₂×#41	C₂²×D₃	1	1	yes	characteristic
342	#135	—	2	2	no	—
343	#135	—	2	2	no	—
344	#135	—	2	2	no	—
345	#135	—	2	2	no	—
346	C₂×Q₁₆	C₂×Dic₃	1	1	yes	characteristic
347	C₂×Q₁₆	C₂×Dic₃	1	1	yes	characteristic
348	C₂×SD₁₆	C₂×Dic₃	1	1	yes	characteristic
349	C₂×SD₁₆	C₂×Dic₃	1	1	yes	characteristic
350	C₂×SD₁₆	C₂×Dic₃	1	1	yes	characteristic
351	C₂×SD₁₆	C₂×Dic₃	1	1	yes	characteristic
352	C₂×D₈	C₂×Dic₃	1	1	yes	characteristic
353	C₂×D₈	C₂×Dic₃	1	1	yes	characteristic
354	#131	—	3	4	no	—
355	#131	—	6	2	no	—
356	#131	—	6	2	no	—
357	#131	—	6	2	no	—
358	#131	—	6	2	no	—
359	#131	—	6	2	no	—
360	#131	—	6	2	no	—
361	#131	—	6	2	no	—
362	C₂×M₁₆	—	3	1	no	—
363	C₂×M₁₆	—	3	1	no	—
364	C₂×M₁₆	—	3	1	no	—
365	C₂×M₁₆	—	3	1	no	—
366	C₂×M₁₆	—	6	1	no	—
367	C₂×M₁₆	—	6	1	no	—
368	C₂×M₁₆	—	6	1	no	—
369	C₂×M₁₆	—	6	1	no	—
370	C₂²×C₈	—	3	1	no	—
371	C₂²×C₈	—	3	1	no	—
372	C₂²×C₈	—	6	1	no	—
373	C₂²×C₈	—	6	1	no	—
374	C₂²×C₈	—	6	1	no	—
375	C₂²×C₈	—	6	1	no	—
376	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
377	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
378	C₄⋊Q₈	C₂×Dic₃	1	1	yes	characteristic
379	#127	C₂×Dic₃	1	1	yes	characteristic
380	#124	C₂×Dic₃	1	1	yes	characteristic
381	#124	C₂×Dic₃	1	1	yes	characteristic
382	#121	—	2	1	no	—
383	#121	—	2	1	no	—
384	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
385	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
391	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
392	#117	—	2	1	no	—
393	#117	C₂²×D₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	—	6	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	3	1	no	—
397	C₂×C₄²	—	3	1	no	—
398	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
399	#108	—	6	2	no	—
400	#108	—	6	2	no	—
401	C₄⋊C₈	—	6	1	no	—
402	C₄⋊C₈	—	6	1	no	—
403	C₄⋊C₈	C₂×Dic₃	1	1	yes	characteristic
404	C₄⋊C₈	C₂×Dic₃	1	1	yes	characteristic
405	C₄⋊C₈	C₂×Dic₃	1	1	yes	characteristic
406	C₄⋊C₈	C₂×Dic₃	1	1	yes	characteristic
407	#104	—	6	2	no	—
408	#104	—	6	2	no	—
409	#104	—	6	2	no	—
410	#104	—	6	2	no	—
411	#104	—	6	2	no	—
412	#104	—	6	2	no	—
413	#103	C₂×Dic₃	1	1	yes	characteristic
414	#103	C₂×Dic₃	1	1	yes	characteristic
415	#103	C₂×Dic₃	1	1	yes	characteristic
416	#103	C₂×Dic₃	1	1	yes	characteristic
417	#102	C₂×Dic₃	1	1	yes	characteristic
418	#102	C₂×Dic₃	1	1	yes	characteristic
419	#102	C₂×Dic₃	1	1	yes	characteristic
420	#102	C₂×Dic₃	1	1	yes	characteristic
421	C₂²⋊C₈	—	6	1	no	—
422	C₂²⋊C₈	—	6	1	no	—
423	C₂²⋊C₈	—	6	1	no	—
424	C₂²⋊C₈	—	6	1	no	—
425	#97	—	3	1	no	—
426	#97	—	3	1	no	—
427	#97	—	3	1	no	—
428	#97	—	3	1	no	—
429	#97	—	6	1	no	—
430	#97	—	6	1	no	—
431	#97	—	6	2	no	—
432	#97	—	6	1	no	—
433	C₄×C₈	—	6	1	no	—
434	C₄×C₈	—	6	1	no	—
435	C₄×C₈	—	6	2	no	—
436	C₄×C₈	—	6	1	no	—
437	#95	—	6	1	no	—
438	C₂³×C₃	—	2	1	no	—
439	C₂³×C₃	—	2	1	no	—
440	C₂³×C₃	—	2	1	no	—
441	C₂³×C₃	C₂×#41	1	1	yes	characteristic
442	C₃×Q₈	—	2	1	no	—
443	C₃×Q₈	—	2	1	no	—
444	C₃×Q₈	—	2	1	no	—
445	C₃×Q₈	—	2	1	no	—
446	C₃×Q₈	—	2	1	no	—
447	C₃×Q₈	C₄×D₄	1	2	yes	—
448	C₃×D₄	—	2	2	no	—
449	C₃×D₄	—	2	2	no	—
450	C₃×D₄	—	2	1	no	—
451	C₃×D₄	—	2	1	no	—
452	C₃×D₄	—	2	1	no	—
453	C₃×D₄	—	2	1	no	—
454	C₃×D₄	—	2	1	no	—
455	C₃×D₄	—	4	1	no	—
456	C₃×D₄	—	4	1	no	—
457	C₃×D₄	—	4	1	no	—
458	C₃×D₄	—	4	1	no	—
459	C₃×D₄	—	8	1	no	—
460	C₃×D₄	—	8	1	no	—
461	C₃×D₄	C₄×D₄	1	2	yes	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	2	2	no	—
464	C₂×C₃×C₄	—	2	2	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	1	no	—
469	C₂×C₃×C₄	—	4	1	no	—
470	C₂×C₃×C₄	—	4	1	no	—
471	C₂×C₃×C₄	—	4	1	no	—
472	C₂×C₃×C₄	—	4	1	no	—
473	C₂×C₃×C₄	—	4	1	no	—
474	C₂×C₃×C₄	—	4	1	no	—
475	C₂×C₃×C₄	—	8	1	no	—
476	C₂×C₃×C₄	—	8	1	no	—
477	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
478	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
479	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
480	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
481	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
482	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
485	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
486	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
487	C₂×Dic₃	—	2	2	no	—
488	C₂×Dic₃	—	4	1	no	—
489	C₂×Dic₃	—	4	1	no	—
490	C₂×Dic₃	—	4	1	no	—
491	C₂×Dic₃	—	4	1	no	—
492	C₂×Dic₃	—	4	1	no	—
493	C₃×C₈	—	2	1	no	—
494	C₃×C₈	—	2	1	no	—
495	C₃×C₈	—	2	1	no	—
496	C₃×C₈	—	2	1	no	—
497	C₃⋊C₈	—	2	2	no	—
498	C₃⋊C₈	—	2	1	no	—
499	C₃⋊C₈	—	2	2	no	—
500	C₃⋊C₈	—	2	1	no	—
501	C₃⋊C₈	—	4	1	no	—
502	C₃⋊C₈	—	4	1	no	—
503	C₃⋊C₈	#121	1	2	yes	—
504	C₃⋊C₈	#121	1	2	yes	—
505	#41	—	2	1	no	—
506	#41	—	2	1	no	—
507	#41	—	2	1	no	—
508	#41	—	2	1	no	—
509	#41	—	2	1	no	—
510	#41	—	2	1	no	—
511	#41	—	2	1	no	—
512	#41	—	2	1	no	—
513	#41	—	2	1	no	—
514	#41	—	2	1	no	—
515	#41	D₃×D₄	1	2	yes	—
516	#41	#237	1	2	yes	—
517	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
518	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
519	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
526	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
527	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	6	1	no	—
534	C₂²×C₄	—	6	1	no	—
535	C₂²×C₄	#237	1	1	yes	characteristic
536	C₂²×C₄	#237	1	1	yes	characteristic
537	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
538	Q₁₆	—	2	2	no	—
539	Q₁₆	—	2	2	no	—
540	SD₁₆	—	2	2	no	—
541	SD₁₆	—	2	2	no	—
542	SD₁₆	—	2	2	no	—
543	SD₁₆	—	2	2	no	—
544	D₈	—	2	2	no	—
545	D₈	—	2	2	no	—
546	M₁₆	—	3	2	no	—
547	M₁₆	—	3	2	no	—
548	M₁₆	—	6	4	no	—
549	M₁₆	—	6	4	no	—
550	M₁₆	—	6	1	no	—
551	M₁₆	—	6	1	no	—
552	M₁₆	—	6	1	no	—
553	M₁₆	—	6	1	no	—
554	M₁₆	—	6	1	no	—
555	M₁₆	—	6	1	no	—
556	M₁₆	—	12	2	no	—
557	M₁₆	—	12	2	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	3	2	no	—
563	C₂×C₈	—	3	1	no	—
564	C₂×C₈	—	3	1	no	—
565	C₂×C₈	—	3	2	no	—
566	C₂×C₈	—	3	1	no	—
567	C₂×C₈	—	3	1	no	—
568	C₂×C₈	—	6	4	no	—
569	C₂×C₈	—	6	4	no	—
570	C₂×C₈	—	6	1	no	—
571	C₂×C₈	—	6	1	no	—
572	C₂×C₈	—	6	1	no	—
573	C₂×C₈	—	6	1	no	—
574	C₂×C₈	—	6	1	no	—
575	C₂×C₈	—	6	1	no	—
576	C₂×C₈	—	12	2	no	—
577	C₂×C₈	—	12	2	no	—
578	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
579	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
580	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
581	C₂×C₈	C₂²×Dic₃	1	1	yes	characteristic
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	12	2	no	—
587	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
588	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
589	C₂²⋊C₄	—	2	1	no	—
590	C₂²⋊C₄	—	2	1	no	—
591	C₂²⋊C₄	—	2	1	no	—
592	C₂²⋊C₄	—	2	1	no	—
593	C₂²⋊C₄	—	2	1	no	—
594	C₂²⋊C₄	—	2	1	no	—
595	C₂²⋊C₄	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	6	1	no	—
600	C₄²	—	6	1	no	—
601	C₄²	—	6	1	no	—
602	C₄²	—	6	1	no	—
603	C₄²	D₃×D₄	1	1	yes	characteristic
604	C₄²	D₃×D₄	1	1	yes	characteristic
605	C₄²	C₂²×Dic₃	1	1	yes	characteristic
606	C₄²	C₂²×Dic₃	1	1	yes	characteristic
607	C₂²×C₃	—	2	1	no	—
608	C₂²×C₃	—	2	1	no	—
609	C₂²×C₃	—	2	2	no	—
610	C₂²×C₃	—	4	1	no	—
611	C₂²×C₃	—	4	1	no	—
612	C₂²×C₃	—	4	1	no	—
613	C₂²×C₃	—	4	1	no	—
614	C₂²×C₃	—	4	1	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
619	C₂²×C₃	#529	1	1	yes	characteristic
620	C₂²×C₃	#532	1	1	yes	characteristic
621	C₃×C₄	—	2	1	no	—
622	C₃×C₄	—	2	1	no	—
623	C₃×C₄	—	2	1	no	—
624	C₃×C₄	—	2	1	no	—
625	C₃×C₄	—	2	2	no	—
626	C₃×C₄	—	4	1	no	—
627	C₃×C₄	—	4	1	no	—
628	C₃×C₄	—	4	1	no	—
629	C₃×C₄	—	4	1	no	—
630	C₃×C₄	C₂×C₄×D₄	1	1	yes	characteristic
631	C₃×C₄	C₄×#41	1	1	yes	characteristic
632	C₃×C₄	C₂×#121	1	1	yes	characteristic
633	C₃×C₄	#525	1	1	yes	characteristic
634	Dic₃	—	4	2	no	—
635	Dic₃	—	8	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	C₂×#237	1	1	yes	characteristic
640	Q₈	—	2	1	no	—
641	Q₈	—	2	1	no	—
642	Q₈	—	2	1	no	—
643	Q₈	—	2	1	no	—
644	Q₈	—	2	1	no	—
645	Q₈	D₄×Dic₃	1	2	yes	—
646	D₄	—	2	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	1	no	—
649	D₄	—	2	1	no	—
650	D₄	—	2	1	no	—
651	D₄	—	2	1	no	—
652	D₄	—	2	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	8	1	no	—
658	D₄	—	8	1	no	—
659	D₄	D₄×Dic₃	1	2	yes	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	6	2	no	—
674	C₂×C₄	—	8	1	no	—
675	C₂×C₄	—	8	1	no	—
676	C₂×C₄	—	12	1	no	—
677	C₂×C₄	—	12	1	no	—
678	C₂×C₄	—	12	1	no	—
679	C₂×C₄	—	12	1	no	—
680	C₂×C₄	—	12	1	no	—
681	C₂×C₄	D₄×Dic₃	1	1	yes	characteristic
682	C₂×C₄	D₄×Dic₃	1	1	yes	characteristic
683	C₂×C₄	D₄×Dic₃	1	1	yes	characteristic
684	C₂×C₄	D₄×Dic₃	1	1	yes	characteristic
685	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
686	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
687	C₂×C₄	C₂×#237	1	1	yes	characteristic
688	C₂×C₄	D₃×#41	1	1	yes	characteristic
689	C₂×C₄	D₃×#41	1	1	yes	characteristic
690	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
691	C₈	—	2	1	no	—
692	C₈	—	2	1	no	—
693	C₈	—	2	1	no	—
694	C₈	—	2	1	no	—
695	C₈	—	3	2	no	—
696	C₈	—	3	2	no	—
697	C₈	—	6	2	no	—
698	C₈	—	6	1	no	—
699	C₈	—	6	1	no	—
700	C₈	—	6	2	no	—
701	C₈	—	12	1	no	—
702	C₈	—	12	1	no	—
703	C₂×C₃	—	2	1	no	—
704	C₂×C₃	—	2	1	no	—
705	C₂×C₃	—	4	2	no	—
706	C₂×C₃	—	8	1	no	—
707	C₂×C₃	—	8	1	no	—
708	C₂×C₃	C₄×#121	1	1	yes	characteristic
709	C₂×C₃	#2956	1	1	yes	characteristic
710	C₂×C₃	#2957	1	1	yes	characteristic
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	#5596	1	1	yes	characteristic
723	C₂²	#5600	1	1	yes	characteristic
724	C₂²	C₂×D₄×Dic₃	1	1	yes	characteristic
725	C₄	—	2	1	no	—
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	2	no	—
730	C₄	—	4	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	12	2	no	—
735	C₄	—	24	1	no	—
736	C₄	D₃×#121	1	1	yes	characteristic
737	C₄	#5606	1	1	yes	characteristic
738	C₄	C₂×D₄×Dic₃	1	1	yes	characteristic
739	C₄	Dic₃×#41	1	1	yes	characteristic
740	C₃	#21519	1	1	yes	characteristic, complemented, Sylow
741	C₂	—	2	1	no	—
742	C₂	—	2	1	no	—
743	C₂	—	4	2	no	—
744	C₂	—	8	1	no	—
745	C₂	—	8	1	no	—
746	C₂	Dic₃×#121	1	1	yes	characteristic
747	C₂	#83910	1	1	yes	characteristic
748	C₂	#84000	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₄
commutator	C₂×C₃×C₄	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₃
Fitting, prime radical	C₃×#3035	C₂
socle	C₂²×C₃	C₂×C₄×D₄
cosocle	C₂²×C₃×C₄	C₂⁴
hypercenter	#3035	D₃
hypocenter	C₃	#21519
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
2. C₂×#5197	C₂	semidirect
3. C₂×#5196	C₂	semidirect
4. #83276	C₂	semidirect
5. #82511	C₂	semidirect
6. #72087	C₂	semidirect
7. #72087	C₂	semidirect
8. #71818	C₂	semidirect
9. #71646	C₂	semidirect
10. #70474	C₂	semidirect
11. #70467	C₂	semidirect
12. #70291	C₂	semidirect
13. #70291	C₂	semidirect
14. #70290	C₂	semidirect
15. #70289	C₂	semidirect
25. C₃×#464	C₄	semidirect
26. C₃×#464	C₄	semidirect
27. C₃×#463	C₄	semidirect
28. C₃×#463	C₄	semidirect
29. C₃×#462	C₄	semidirect
30. C₃×#461	C₄	semidirect
31. C₃×#460	C₄	semidirect
32. C₃×#459	C₄	semidirect
127. #948	D₄	semidirect
192. #464	Dic₃	semidirect
193. #464	Dic₃	semidirect
194. #463	Dic₃	semidirect
195. #463	Dic₃	semidirect
196. #462	Dic₃	semidirect
197. #461	Dic₃	semidirect
198. #460	Dic₃	semidirect
199. #459	Dic₃	semidirect
740. C₃	#21519	semidirect

Maximal subgroups

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

subgroup	index
C₃×#3035	2
C₂×#5197	2
C₂×#5196	2
#83276	2
#82511	2
#72087	2
#71818	2
#71646	2
#70474	2
#70467	2
#70291	2
#70290	2
#70289	2
#21519	3