Subgroups — #11708411

Order 768.

7484 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3529	C₂	1	1	yes	maximal, characteristic, complemented
2	#87131	C₂	1	6	yes	maximal, complemented
3	#87113	C₂	1	12	yes	maximal, complemented
4	D₃×H(3,𝔽₄)	C₂	1	2	yes	maximal, complemented
5	#87080	C₂	1	12	yes	maximal, complemented
6	#86252	C₂	1	3	yes	maximal, complemented
7	#86244	C₂	1	3	yes	maximal, complemented
8	#86177	C₂	1	6	yes	maximal, complemented
9	#86163	C₂	1	6	yes	maximal, complemented
10	#86055	C₂	1	6	yes	maximal, complemented
11	#86039	C₂	1	6	yes	maximal, complemented
12	#63045	—	3	1	no	maximal, Sylow
13	C₂×#1010	C₂²	1	1	yes	characteristic, complemented
14	C₂×#1009	C₂²	1	3	yes	complemented
15	C₂³×D₁₂	C₂²	1	2	yes	complemented
16	C₃×#563	C₂²	1	3	yes	complemented
17	C₃×#562	C₂²	1	6	yes	complemented
18	C₃×H(3,𝔽₄)	C₂²	1	1	yes	characteristic, complemented
19	C₃×#560	C₂²	1	6	yes	complemented
20	C₃×#532	C₂²	1	3	yes	complemented
21	C₃×#529	C₂²	1	6	yes	complemented
22	C₃×#525	C₂²	1	6	yes	complemented
23	#5830	C₂²	1	6	yes	complemented
24	#5830	C₂²	1	3	yes	complemented
25	#5825	C₂²	1	3	yes	complemented
26	#5791	C₂²	1	6	yes	complemented
27	#5734	C₂²	1	6	yes	complemented
28	#5724	C₂²	1	6	yes	complemented
29	#5717	C₂²	1	6	yes	complemented
30	#5715	C₂²	1	6	yes	complemented
31	#5705	C₂²	1	24	yes	complemented
32	#5704	C₂²	1	24	yes	complemented
33	#5700	C₂²	1	12	yes	complemented
34	#5691	C₂²	1	12	yes	complemented
35	#5683	C₂²	1	12	yes	complemented
36	#5683	C₂²	1	6	yes	complemented
37	#5683	C₂²	1	6	yes	complemented
38	D₃×#124	C₂²	1	12	yes	complemented
39	D₃×#124	C₂²	1	6	yes	complemented
40	#5668	C₂²	1	6	yes	complemented
41	#5664	C₂²	1	12	yes	complemented
42	#5659	C₂²	1	12	yes	complemented
43	#5657	C₂²	1	24	yes	complemented
44	#5654	C₂²	1	24	yes	complemented
45	#5653	C₂²	1	12	yes	complemented
46	#5653	C₂²	1	12	yes	complemented
47	#5644	C₂²	1	12	yes	complemented
48	#5640	C₂²	1	24	yes	complemented
49	#5633	C₂²	1	12	yes	complemented
50	#5630	C₂²	1	24	yes	complemented
51	#5613	C₂²	1	24	yes	complemented
52	#5612	C₂²	1	12	yes	complemented
53	#5610	C₂²	1	24	yes	complemented
54	#5609	C₂²	1	24	yes	complemented
55	#5607	C₂²	1	24	yes	complemented
56	#5605	C₂²	1	12	yes	complemented
57	#5595	C₂²	1	12	yes	complemented
58	#5594	C₂²	1	12	yes	complemented
59	D₃×#120	C₂²	1	12	yes	complemented
60	D₃×#120	C₂²	1	12	yes	complemented
61	#5585	C₂²	1	6	yes	complemented
62	Q₈×D₁₂	C₂²	1	2	yes	complemented
63	#5563	C₂²	1	12	yes	complemented
64	#5552	C₂²	1	12	yes	complemented
65	#5550	C₂²	1	12	yes	complemented
66	#5550	C₂²	1	12	yes	complemented
67	D₄×D₁₂	C₂²	1	6	yes	complemented
68	D₄×D₁₂	C₂²	1	12	yes	complemented
69	#5542	C₂²	1	6	yes	complemented
70	#5534	C₂²	1	12	yes	complemented
71	#5525	C₂²	1	6	yes	complemented
72	#5521	C₂²	1	6	yes	complemented
73	#5477	C₂²	1	6	yes	complemented
74	C₂×#875	C₂²	1	3	yes	complemented
75	C₄×#235	C₂²	1	3	yes	complemented
76	#3558	—	3	12	no	—
77	#3558	—	3	6	no	—
78	#3549	—	3	3	no	—
79	#3545	—	3	6	no	—
80	#3540	—	3	6	no	—
81	#3532	—	3	12	no	—
82	#3529	D₃	1	1	yes	characteristic, complemented
83	C₂×H(3,𝔽₄)	—	3	2	no	—
84	#3514	—	3	6	no	—
85	#3500	—	3	3	no	—
86	#3484	—	3	6	no	—
87	C₂⁴×D₃	C₂³	1	4	yes	complemented
88	C₂×C₃×#41	C₂³	1	3	yes	—
89	C₂×C₃×#41	C₂³	1	1	yes	characteristic, complemented
90	C₂³×C₃×C₄	C₂³	1	2	yes	complemented
91	#1010	—	4	4	no	—
92	#1009	—	4	12	no	—
93	C₂×#239	C₂³	1	6	yes	—
94	C₂×D₃×Q₈	C₂³	1	2	yes	complemented
95	C₂×D₃×Q₈	C₂³	1	4	yes	complemented
96	C₂×#237	C₂³	1	6	yes	complemented
97	C₂×D₃×D₄	C₂³	1	6	yes	—
98	C₂×D₃×D₄	C₂³	1	12	yes	—
99	C₂×D₃×D₄	C₂³	1	12	yes	—
100	C₂×D₃×D₄	C₂³	1	24	yes	complemented
101	C₂×#235	C₂³	1	3	yes	—
102	C₂×#235	C₂³	1	6	yes	—
103	C₂×#235	C₂³	1	12	yes	complemented
104	C₂²×D₁₂	—	4	8	no	—
105	C₂²×D₁₂	C₂³	1	6	yes	—
106	C₂²×D₁₂	C₂³	1	3	yes	—
107	C₂²×D₁₂	C₂³	1	12	yes	complemented
108	C₂²×D₁₂	C₂³	1	6	yes	complemented
109	C₂²×Dic₆	C₂³	1	3	yes	complemented
110	C₃×C₄⋊Q₈	C₂³	1	3	yes	complemented
111	C₃×#127	C₂³	1	3	yes	—
112	C₃×#126	C₂³	1	12	yes	complemented
113	C₃×#125	C₂³	1	6	yes	complemented
114	C₃×#124	C₂³	1	6	yes	—
115	C₃×#124	C₂³	1	3	yes	—
116	C₃×#124	C₂³	1	3	yes	complemented
117	C₃×#123	C₂³	1	6	yes	—
118	C₃×#123	C₂³	1	12	yes	complemented
119	C₃×#123	C₂³	1	6	yes	complemented
120	C₃×C₂²⋊Q₈	C₂³	1	6	yes	complemented
121	C₃×C₂²⋊Q₈	C₂³	1	12	yes	complemented
122	C₃×#121	C₂³	1	6	yes	—
123	C₃×#121	C₂³	1	12	yes	—
124	C₃×#121	C₂³	1	12	yes	complemented
125	C₃×#120	C₂³	1	6	yes	—
126	C₃×#120	C₂³	1	6	yes	complemented
127	C₃×C₄×Q₈	C₂³	1	2	yes	complemented
128	C₃×C₄×D₄	C₂³	1	6	yes	—
129	C₃×C₄×D₄	C₂³	1	12	yes	complemented
130	C₃×#117	C₂³	1	6	yes	complemented
131	C₂×C₃×C₄²	C₂³	1	3	yes	complemented
132	#953	C₂³	1	12	yes	complemented
133	#947	C₂³	1	12	yes	complemented
134	#947	C₂³	1	12	yes	complemented
135	#947	C₂³	1	6	yes	complemented
136	#944	C₂³	1	6	yes	complemented
137	#940	C₂³	1	12	yes	—
138	#940	C₂³	1	6	yes	complemented
139	#939	C₂³	1	24	yes	complemented
140	#938	C₂³	1	24	yes	complemented
141	#937	C₂³	1	12	yes	—
142	#937	C₂³	1	24	yes	—
143	#937	C₂³	1	12	yes	complemented
144	#937	C₂³	1	24	yes	complemented
145	#937	C₂³	1	12	yes	complemented
146	#936	C₂³	1	6	yes	—
147	#936	C₂³	1	12	yes	—
148	#935	C₂³	1	12	yes	complemented
149	#930	C₂³	1	12	yes	—
150	#930	C₂³	1	12	yes	complemented
151	#930	C₂³	1	12	yes	complemented
152	#929	C₂³	1	12	yes	complemented
153	C₄×#67	C₂³	1	12	yes	complemented
154	C₄×#67	C₂³	1	24	yes	complemented
155	C₂×(C₂×D₃)⋊C₄	C₂³	1	12	yes	complemented
156	#926	C₂³	1	3	yes	complemented
157	#926	C₂³	1	6	yes	complemented
158	#924	C₂³	1	12	yes	complemented
159	#898	C₂³	1	24	yes	complemented
160	#897	C₂³	1	12	yes	complemented
161	#896	C₂³	1	24	yes	complemented
162	#896	C₂³	1	24	yes	complemented
163	#895	C₂³	1	12	yes	—
164	#895	C₂³	1	24	yes	complemented
165	#895	C₂³	1	24	yes	complemented
166	#894	C₂³	1	24	yes	complemented
167	#894	C₂³	1	24	yes	complemented
168	#894	C₂³	1	24	yes	complemented
169	#893	C₂³	1	24	yes	complemented
170	#893	C₂³	1	12	yes	complemented
171	#892	C₂³	1	24	yes	complemented
172	#887	C₂³	1	12	yes	complemented
173	#885	C₂³	1	24	yes	complemented
174	#885	C₂³	1	24	yes	complemented
175	#885	C₂³	1	24	yes	complemented
176	#885	C₂³	1	24	yes	complemented
177	#884	C₂³	1	24	yes	—
178	#884	C₂³	1	24	yes	complemented
179	#883	C₂³	1	24	yes	complemented
180	#882	C₂³	1	24	yes	—
181	#882	C₂³	1	24	yes	complemented
182	#882	C₂³	1	12	yes	complemented
183	#882	C₂³	1	12	yes	complemented
184	#882	C₂³	1	24	yes	complemented
185	#67⋊C₄	C₂³	1	24	yes	complemented
186	D₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
187	D₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
188	D₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
189	D₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
190	#879	C₂³	1	24	yes	complemented
191	#875	C₂³	1	6	yes	complemented
192	#875	C₂³	1	12	yes	complemented
193	#875	C₂³	1	6	yes	complemented
194	#875	C₂³	1	12	yes	complemented
195	#874	C₂³	1	6	yes	—
196	C₄×D₁₂	C₂³	1	6	yes	—
197	C₄×D₁₂	C₂³	1	12	yes	complemented
198	C₄×D₁₂	C₂³	1	12	yes	complemented
199	#872	C₂³	1	6	yes	complemented
200	C₄²×D₃	C₂³	1	6	yes	complemented
201	#869	C₂³	1	6	yes	complemented
202	C₄×Dic₆	C₂³	1	6	yes	complemented
203	C₂×2₋¹⁺⁴	—	3	1	no	—
204	C₂×H(5,𝔽₂)	—	3	3	no	—
205	C₂³×D₄	—	3	2	no	—
206	#563	C₂×D₃	1	3	yes	complemented
207	#562	—	3	12	no	—
208	#562	C₂×D₃	1	6	yes	complemented
209	H(3,𝔽₄)	—	3	6	no	—
210	H(3,𝔽₄)	—	3	12	no	—
211	H(3,𝔽₄)	—	3	6	no	—
212	H(3,𝔽₄)	—	3	12	no	—
213	H(3,𝔽₄)	C₂×D₃	1	1	yes	characteristic, complemented
214	#560	—	3	12	no	—
215	#560	C₂×D₃	1	6	yes	complemented
216	#559	—	3	12	no	—
217	#559	—	3	6	no	—
218	#556	—	3	6	no	—
219	#555	—	3	6	no	—
220	#555	—	3	12	no	—
221	#551	—	3	24	no	—
222	#551	—	3	12	no	—
223	D₄×Q₈	—	3	2	no	—
224	#548	—	3	12	no	—
225	#548	—	3	12	no	—
226	#546	—	3	24	no	—
227	#546	—	3	24	no	—
228	#546	—	3	12	no	—
229	#546	—	3	24	no	—
230	#546	—	3	12	no	—
231	#546	—	3	12	no	—
232	D₄²	—	3	6	no	—
233	D₄²	—	3	24	no	—
234	D₄²	—	3	6	no	—
235	D₄²	—	3	12	no	—
236	#542	—	3	24	no	—
237	#542	—	3	12	no	—
238	#538	—	3	24	no	—
239	#538	—	3	24	no	—
240	#538	—	3	12	no	—
241	#538	—	3	24	no	—
242	#536	—	3	3	no	—
243	#536	—	3	6	no	—
244	#535	—	3	6	no	—
245	#535	—	3	3	no	—
246	#535	—	3	6	no	—
247	#535	—	3	24	no	—
248	#535	—	3	6	no	—
249	#534	—	3	12	no	—
250	#534	—	3	12	no	—
251	#534	—	3	12	no	—
252	#532	—	3	6	no	—
253	#532	—	3	6	no	—
254	#532	C₂×D₃	1	3	yes	complemented
255	#529	—	3	12	no	—
256	#529	C₂×D₃	1	6	yes	complemented
257	C₂×#124	—	3	6	no	—
258	C₂×#124	—	3	12	no	—
259	C₂×#124	—	3	3	no	—
260	#525	—	3	6	no	—
261	#525	C₂×D₃	1	6	yes	complemented
262	C₂×#120	—	3	12	no	—
263	C₂×#120	—	3	12	no	—
264	#518	—	3	6	no	—
265	C₄×#41	—	3	3	no	—
266	C₂⁴×C₃	C₂⁴	1	2	yes	—
267	C₂³×D₃	—	4	8	no	—
268	C₂³×D₃	—	8	8	no	—
269	C₂³×D₃	C₂⁴	1	12	yes	—
270	C₂³×D₃	C₂⁴	1	12	yes	—
271	C₂³×D₃	C₂⁴	1	6	yes	—
272	C₃×#41	—	4	6	no	—
273	C₃×#41	—	4	2	no	—
274	C₂×C₃×Q₈	C₂⁴	1	3	yes	—
275	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
276	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
277	C₂×C₃×D₄	C₂⁴	1	6	yes	—
278	C₂×C₃×D₄	C₂⁴	1	6	yes	—
279	C₂×C₃×D₄	C₂⁴	1	3	yes	—
280	C₂×C₃×D₄	C₂⁴	1	3	yes	—
281	C₂×C₃×D₄	C₂⁴	1	12	yes	—
282	C₂²×C₃×C₄	—	4	4	no	—
283	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
284	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
285	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
286	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
287	C₂×#67	C₂⁴	1	6	yes	—
288	C₂×#67	C₂⁴	1	24	yes	—
289	C₂×#67	C₂⁴	1	24	yes	—
290	C₂×#67	C₂⁴	1	12	yes	—
291	C₂²×Dic₃	C₂⁴	1	6	yes	—
292	#239	—	4	12	no	—
293	D₃×Q₈	—	4	4	no	—
294	D₃×Q₈	—	8	4	no	—
295	#237	—	4	12	no	—
296	D₃×D₄	—	4	12	no	—
297	D₃×D₄	—	4	24	no	—
298	D₃×D₄	—	8	12	no	—
299	D₃×D₄	—	8	24	no	—
300	#235	—	2	12	no	—
301	#235	—	4	12	no	—
302	#235	—	8	12	no	—
303	C₂×D₁₂	—	2	24	no	—
304	C₂×D₁₂	—	4	12	no	—
305	C₂×D₁₂	—	4	6	no	—
306	C₂×D₁₂	—	4	24	no	—
307	C₂×D₁₂	C₂⁴	1	6	yes	—
308	C₂×D₁₂	C₂⁴	1	12	yes	—
309	C₂×D₁₂	C₂⁴	1	12	yes	—
310	C₂×D₁₂	C₂⁴	1	12	yes	—
311	C₂×D₁₂	C₂⁴	1	6	yes	—
312	C₂×D₁₂	C₂⁴	1	12	yes	—
313	C₂×D₁₂	C₂⁴	1	1	yes	characteristic
314	C₂×C₄×D₃	C₂⁴	1	6	yes	—
315	C₂×C₄×D₃	C₂⁴	1	12	yes	—
316	C₂×C₄×D₃	C₂⁴	1	24	yes	—
317	C₂×C₄×D₃	C₂⁴	1	12	yes	—
318	C₂×Dic₆	—	4	6	no	—
319	C₂×Dic₆	C₂⁴	1	3	yes	—
320	C₂×Dic₆	C₂⁴	1	12	yes	—
321	C₂×Dic₆	C₂⁴	1	6	yes	—
322	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
323	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
324	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
325	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
326	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
327	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
328	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
329	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
330	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
331	C₃×C₄²	C₂⁴	1	6	yes	—
332	C₃×C₄²	C₂⁴	1	3	yes	—
333	C₃×C₄²	C₂⁴	1	3	yes	—
334	#217	C₂⁴	1	12	yes	—
335	#217	C₂⁴	1	24	yes	—
336	#217	C₂⁴	1	6	yes	—
337	(C₂×D₃)⋊C₄	C₂⁴	1	12	yes	—
338	(C₂×D₃)⋊C₄	C₂⁴	1	24	yes	—
339	(C₂×D₃)⋊C₄	C₂⁴	1	24	yes	—
340	(C₂×D₃)⋊C₄	C₂⁴	1	24	yes	—
341	(C₂×D₃)⋊C₄	C₂⁴	1	24	yes	—
342	(C₂×D₃)⋊C₄	C₂⁴	1	24	yes	—
343	C₄⋊Dic₃	C₂⁴	1	6	yes	—
344	C₄⋊Dic₃	C₂⁴	1	12	yes	—
345	Dic₃⋊C₄	C₂⁴	1	12	yes	—
346	Dic₃⋊C₄	C₂⁴	1	24	yes	—
347	C₄×Dic₃	C₂⁴	1	12	yes	—
348	C₄×Dic₃	C₂⁴	1	6	yes	—
349	C₄×Dic₃	C₂⁴	1	12	yes	—
350	C₂⁵	—	3	4	no	—
351	2₋¹⁺⁴	—	12	4	no	—
352	H(5,𝔽₂)	—	12	12	no	—
353	C₂×#41	—	3	6	no	—
354	C₂×#41	—	3	6	no	—
355	C₂×#41	—	3	3	no	—
356	C₂×#41	—	3	6	no	—
357	C₂×#41	—	3	12	no	—
358	C₂×#41	C₂²×D₃	1	3	yes	—
359	C₂×#41	C₂²×D₃	1	1	yes	characteristic, complemented
360	C₂²×Q₈	—	3	2	no	—
361	C₂²×Q₈	—	3	4	no	—
362	C₂²×Q₈	—	3	3	no	—
363	C₂²×D₄	—	3	6	no	—
364	C₂²×D₄	—	3	12	no	—
365	C₂²×D₄	—	3	12	no	—
366	C₂²×D₄	—	3	24	no	—
367	C₂²×D₄	—	3	6	no	—
368	C₂²×D₄	—	3	3	no	—
369	C₂²×D₄	—	3	12	no	—
370	C₂²×D₄	—	3	6	no	—
371	C₂²×D₄	—	12	8	no	—
372	C₂³×C₄	C₂²×D₃	1	2	yes	complemented
373	C₄⋊Q₈	—	3	6	no	—
374	C₄⋊Q₈	—	3	6	no	—
375	C₄⋊Q₈	C₂²×D₃	1	3	yes	complemented
376	#127	—	3	6	no	—
377	#127	—	3	12	no	—
378	#127	—	3	6	no	—
379	#127	C₂²×D₃	1	3	yes	—
380	#126	—	3	24	no	—
381	#126	—	3	24	no	—
382	#126	C₂²×D₃	1	12	yes	complemented
383	#125	C₂²×D₃	1	6	yes	complemented
384	#124	—	3	6	no	—
385	#124	—	3	12	no	—
386	#124	—	3	12	no	—
387	#124	—	3	6	no	—
388	#124	—	3	12	no	—
389	#124	—	3	24	no	—
390	#124	—	3	24	no	—
391	#124	—	3	24	no	—
392	#124	—	3	24	no	—
393	#124	—	3	6	no	—
394	#124	—	3	12	no	—
395	#124	—	3	6	no	—
396	#124	—	3	12	no	—
397	#124	C₂²×D₃	1	6	yes	—
398	#124	C₂²×D₃	1	3	yes	—
399	#124	C₂²×D₃	1	3	yes	complemented
400	#123	—	3	12	no	—
401	#123	—	3	12	no	—
402	#123	—	3	24	no	—
403	#123	—	3	24	no	—
404	#123	—	3	24	no	—
405	#123	—	3	24	no	—
406	#123	C₂²×D₃	1	6	yes	—
407	#123	C₂²×D₃	1	6	yes	complemented
408	#123	C₂²×D₃	1	12	yes	complemented
409	C₂²⋊Q₈	—	3	12	no	—
410	C₂²⋊Q₈	—	3	12	no	—
411	C₂²⋊Q₈	—	3	24	no	—
412	C₂²⋊Q₈	—	3	24	no	—
413	C₂²⋊Q₈	C₂²×D₃	1	12	yes	complemented
414	C₂²⋊Q₈	C₂²×D₃	1	6	yes	complemented
415	#121	—	3	24	no	—
416	#121	—	3	24	no	—
417	#121	—	3	12	no	—
418	#121	—	3	12	no	—
419	#121	—	3	12	no	—
420	#121	—	3	12	no	—
421	#121	—	3	24	no	—
422	#121	—	3	24	no	—
423	#121	—	3	24	no	—
424	#121	—	3	24	no	—
425	#121	C₂²×D₃	1	12	yes	—
426	#121	C₂²×D₃	1	6	yes	—
427	#121	C₂²×D₃	1	12	yes	complemented
428	#120	—	3	12	no	—
429	#120	—	3	12	no	—
430	#120	—	3	12	no	—
431	#120	—	3	24	no	—
432	#120	—	3	24	no	—
433	#120	—	3	12	no	—
434	#120	—	3	12	no	—
435	#120	—	3	12	no	—
436	#120	—	3	24	no	—
437	#120	—	3	24	no	—
438	#120	—	3	24	no	—
439	#120	C₂²×D₃	1	6	yes	—
440	#120	C₂²×D₃	1	6	yes	complemented
441	C₄×Q₈	—	3	12	no	—
442	C₄×Q₈	—	3	6	no	—
443	C₄×Q₈	C₂²×D₃	1	2	yes	complemented
444	C₄×D₄	—	3	12	no	—
445	C₄×D₄	—	3	24	no	—
446	C₄×D₄	—	3	24	no	—
447	C₄×D₄	—	3	12	no	—
448	C₄×D₄	—	3	24	no	—
449	C₄×D₄	—	3	6	no	—
450	C₄×D₄	—	3	12	no	—
451	C₄×D₄	—	3	12	no	—
452	C₄×D₄	C₂²×D₃	1	6	yes	—
453	C₄×D₄	C₂²×D₃	1	12	yes	complemented
454	#117	—	3	3	no	—
455	#117	—	3	6	no	—
456	#117	—	3	24	no	—
457	#117	—	3	6	no	—
458	#117	C₂²×D₃	1	6	yes	complemented
459	C₂×C₂²⋊C₄	—	3	12	no	—
460	C₂×C₂²⋊C₄	—	3	12	no	—
461	C₂×C₂²⋊C₄	—	3	12	no	—
462	C₂×C₂²⋊C₄	—	3	24	no	—
463	C₂×C₂²⋊C₄	—	3	24	no	—
464	C₂×C₄²	—	3	6	no	—
465	C₂×C₄²	C₂²×D₃	1	3	yes	complemented
466	C₂³×C₃	—	4	2	no	—
467	C₂³×C₃	—	4	4	no	—
468	C₂³×C₃	C₂⁵	1	6	yes	—
469	C₂³×C₃	C₂⁵	1	3	yes	—
470	C₂²×D₃	—	2	24	no	—
471	C₂²×D₃	—	4	12	no	—
472	C₂²×D₃	—	4	24	no	—
473	C₂²×D₃	—	4	24	no	—
474	C₂²×D₃	—	4	6	no	—
475	C₂²×D₃	—	4	12	no	—
476	C₂²×D₃	—	8	32	no	—
477	C₂²×D₃	C₂⁵	1	12	yes	—
478	C₂²×D₃	C₂⁵	1	2	yes	—
479	C₃×Q₈	—	4	1	no	—
480	C₃×Q₈	—	4	2	no	—
481	C₃×Q₈	—	4	3	no	—
482	C₃×D₄	—	4	3	no	—
483	C₃×D₄	—	4	6	no	—
484	C₃×D₄	—	4	6	no	—
485	C₃×D₄	—	4	12	no	—
486	C₃×D₄	—	4	3	no	—
487	C₂×C₃×C₄	—	2	6	no	—
488	C₂×C₃×C₄	—	2	12	no	—
489	C₂×C₃×C₄	—	4	6	no	—
490	C₂×C₃×C₄	—	4	6	no	—
491	C₂×C₃×C₄	C₂⁵	1	6	yes	—
492	C₂×C₃×C₄	C₂⁵	1	6	yes	—
493	C₂×C₃×C₄	C₂⁵	1	3	yes	—
494	C₂×C₃×C₄	C₂⁵	1	6	yes	—
495	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
496	#67	—	2	12	no	—
497	#67	—	4	12	no	—
498	#67	—	4	24	no	—
499	#67	—	4	24	no	—
500	C₂×Dic₃	—	4	6	no	—
501	C₂×Dic₃	C₂⁵	1	12	yes	—
502	C₂×Dic₃	C₂⁵	1	6	yes	—
503	D₁₂	—	2	24	no	—
504	D₁₂	—	2	12	no	—
505	D₁₂	—	4	12	no	—
506	D₁₂	—	4	6	no	—
507	D₁₂	—	4	12	no	—
508	D₁₂	—	4	12	no	—
509	D₁₂	H(5,𝔽₂)	1	4	yes	—
510	C₄×D₃	—	2	12	no	—
511	C₄×D₃	—	4	12	no	—
512	C₄×D₃	—	4	24	no	—
513	C₄×D₃	—	4	12	no	—
514	Dic₆	—	2	6	no	—
515	Dic₆	—	4	6	no	—
516	Dic₆	—	4	12	no	—
517	C₂⁴	—	3	12	no	—
518	C₂⁴	—	3	12	no	—
519	C₂⁴	—	3	6	no	—
520	C₂⁴	—	12	8	no	—
521	C₂⁴	—	24	8	no	—
522	C₂⁴	C₂³×D₃	1	2	yes	—
523	#41	—	4	6	no	—
524	#41	—	4	2	no	—
525	#41	—	6	12	no	—
526	#41	—	12	12	no	—
527	#41	—	12	12	no	—
528	#41	—	12	12	no	—
529	#41	—	24	12	no	—
530	C₂×Q₈	—	3	3	no	—
531	C₂×Q₈	—	3	12	no	—
532	C₂×Q₈	—	3	6	no	—
533	C₂×Q₈	—	12	6	no	—
534	C₂×Q₈	—	12	4	no	—
535	C₂×Q₈	—	24	4	no	—
536	C₂×Q₈	C₂³×D₃	1	2	yes	—
537	C₂×Q₈	C₂³×D₃	1	3	yes	—
538	C₂×Q₈	C₂³×D₃	1	1	yes	characteristic
539	C₂×D₄	—	3	6	no	—
540	C₂×D₄	—	3	24	no	—
541	C₂×D₄	—	3	24	no	—
542	C₂×D₄	—	3	12	no	—
543	C₂×D₄	—	3	1	no	—
544	C₂×D₄	—	3	12	no	—
545	C₂×D₄	—	3	6	no	—
546	C₂×D₄	—	3	12	no	—
547	C₂×D₄	—	3	12	no	—
548	C₂×D₄	—	3	6	no	—
549	C₂×D₄	—	3	12	no	—
550	C₂×D₄	—	6	24	no	—
551	C₂×D₄	—	12	12	no	—
552	C₂×D₄	—	12	6	no	—
553	C₂×D₄	—	12	24	no	—
554	C₂×D₄	—	12	12	no	—
555	C₂×D₄	—	12	24	no	—
556	C₂×D₄	—	24	12	no	—
557	C₂×D₄	—	24	24	no	—
558	C₂×D₄	C₂³×D₃	1	6	yes	—
559	C₂×D₄	C₂³×D₃	1	12	yes	—
560	C₂×D₄	C₂³×D₃	1	3	yes	—
561	C₂×D₄	C₂³×D₃	1	3	yes	—
562	C₂×D₄	C₂³×D₃	1	6	yes	—
563	C₂²×C₄	—	3	6	no	—
564	C₂²×C₄	—	3	6	no	—
565	C₂²×C₄	—	3	12	no	—
566	C₂²×C₄	—	3	24	no	—
567	C₂²×C₄	—	3	12	no	—
568	C₂²×C₄	—	4	4	no	—
569	C₂²×C₄	C₂³×D₃	1	3	yes	—
570	C₂²×C₄	C₂³×D₃	1	6	yes	—
571	C₂²×C₄	C₂³×D₃	1	6	yes	—
572	C₂²×C₄	C₂³×D₃	1	6	yes	—
573	C₄⋊C₄	—	3	6	no	—
574	C₄⋊C₄	—	3	12	no	—
575	C₄⋊C₄	—	3	12	no	—
576	C₄⋊C₄	—	3	24	no	—
577	C₄⋊C₄	C₂³×D₃	1	12	yes	—
578	C₄⋊C₄	C₂³×D₃	1	12	yes	—
579	C₄⋊C₄	C₂³×D₃	1	6	yes	—
580	C₄⋊C₄	C₂³×D₃	1	6	yes	—
581	C₂²⋊C₄	—	3	12	no	—
582	C₂²⋊C₄	—	3	24	no	—
583	C₂²⋊C₄	—	3	6	no	—
584	C₂²⋊C₄	—	3	12	no	—
585	C₂²⋊C₄	—	3	24	no	—
586	C₂²⋊C₄	—	3	24	no	—
587	C₂²⋊C₄	—	3	24	no	—
588	C₂²⋊C₄	—	3	24	no	—
589	C₂²⋊C₄	—	3	24	no	—
590	C₂²⋊C₄	C₂³×D₃	1	6	yes	—
591	C₂²⋊C₄	C₂³×D₃	1	6	yes	—
592	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
593	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
594	C₂²⋊C₄	C₂³×D₃	1	12	yes	—
595	C₄²	—	3	6	no	—
596	C₄²	—	3	12	no	—
597	C₄²	—	3	12	no	—
598	C₄²	C₂³×D₃	1	3	yes	—
599	C₄²	C₂³×D₃	1	3	yes	—
600	C₄²	C₂³×D₃	1	6	yes	—
601	C₂²×C₃	—	2	3	no	—
602	C₂²×C₃	—	2	6	no	—
603	C₂²×C₃	—	2	6	no	—
604	C₂²×C₃	—	2	12	no	—
605	C₂²×C₃	—	4	8	no	—
606	C₂²×C₃	C₂⁶	1	1	yes	characteristic
607	C₂×D₃	—	2	4	no	—
608	C₂×D₃	—	2	12	no	—
609	C₂×D₃	—	2	24	no	—
610	C₂×D₃	—	8	24	no	—
611	C₂×D₃	—	8	24	no	—
612	C₂×D₃	—	16	6	no	—
613	C₂×D₃	C₂×H(5,𝔽₂)	1	4	yes	—
614	C₃×C₄	—	2	3	no	—
615	C₃×C₄	—	2	6	no	—
616	C₃×C₄	—	2	6	no	—
617	C₃×C₄	—	2	6	no	—
618	C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
619	Dic₃	—	2	6	no	—
620	Dic₃	—	2	12	no	—
621	C₂³	—	3	2	no	—
622	C₂³	—	3	12	no	—
623	C₂³	—	4	2	no	—
624	C₂³	—	4	4	no	—
625	C₂³	—	6	24	no	—
626	C₂³	—	12	12	no	—
627	C₂³	—	12	24	no	—
628	C₂³	—	12	24	no	—
629	C₂³	—	12	6	no	—
630	C₂³	—	12	12	no	—
631	C₂³	—	24	32	no	—
632	C₂³	C₂⁴×D₃	1	6	yes	—
633	C₂³	C₂⁴×D₃	1	3	yes	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	2	no	—
636	Q₈	—	4	3	no	—
637	Q₈	—	6	6	no	—
638	Q₈	—	12	6	no	—
639	Q₈	—	12	12	no	—
640	D₄	—	3	4	no	—
641	D₄	—	4	6	no	—
642	D₄	—	4	3	no	—
643	D₄	—	4	12	no	—
644	D₄	—	4	6	no	—
645	D₄	—	4	3	no	—
646	D₄	—	6	24	no	—
647	D₄	—	6	12	no	—
648	D₄	—	6	12	no	—
649	D₄	—	12	12	no	—
650	D₄	—	12	6	no	—
651	D₄	—	12	12	no	—
652	D₄	—	12	12	no	—
653	D₄	—	12	12	no	—
654	D₄	—	12	24	no	—
655	D₄	—	12	24	no	—
656	C₂×C₄	—	2	12	no	—
657	C₂×C₄	—	2	6	no	—
658	C₂×C₄	—	3	12	no	—
659	C₂×C₄	—	3	6	no	—
660	C₂×C₄	—	4	6	no	—
661	C₂×C₄	—	4	6	no	—
662	C₂×C₄	—	6	12	no	—
663	C₂×C₄	—	12	12	no	—
664	C₂×C₄	—	12	12	no	—
665	C₂×C₄	—	12	24	no	—
666	C₂×C₄	—	12	6	no	—
667	C₂×C₄	C₂⁴×D₃	1	6	yes	—
668	C₂×C₄	C₂⁴×D₃	1	3	yes	—
669	C₂×C₄	C₂⁴×D₃	1	6	yes	—
670	C₂×C₄	C₂⁴×D₃	1	6	yes	—
671	C₂×C₄	C₂⁴×D₃	1	1	yes	characteristic
672	C₂×C₃	—	4	6	no	—
673	C₂×C₃	—	4	3	no	—
674	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
675	C₂×C₃	H(7,𝔽₂)	1	2	yes	—
676	D₃	—	2	4	no	—
677	D₃	—	4	12	no	—
678	C₂²	—	2	6	no	—
679	C₂²	—	2	3	no	—
680	C₂²	—	2	6	no	—
681	C₂²	—	2	12	no	—
682	C₂²	—	3	4	no	—
683	C₂²	—	4	8	no	—
684	C₂²	—	6	4	no	—
685	C₂²	—	6	12	no	—
686	C₂²	—	6	24	no	—
687	C₂²	—	24	24	no	—
688	C₂²	—	24	24	no	—
689	C₂²	—	48	6	no	—
690	C₂²	C₂⁵×D₃	1	1	yes	characteristic
691	C₄	—	2	6	no	—
692	C₄	—	2	3	no	—
693	C₄	—	2	6	no	—
694	C₄	—	2	6	no	—
695	C₄	—	6	6	no	—
696	C₄	—	6	12	no	—
697	C₄	D₃×H(5,𝔽₂)	1	2	yes	—
698	C₃	#63045	1	1	yes	characteristic, complemented, Sylow
699	C₂	—	4	6	no	—
700	C₂	—	4	3	no	—
701	C₂	—	6	4	no	—
702	C₂	—	12	12	no	—
703	C₂	C₂×D₃×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂	#87574	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁶
Fitting	C₃×#3529	C₂
hypercenter	#3529	D₃
hypocenter	C₃	#63045
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #3529

Complements

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

N	H ≅ G/N	type
1. C₃×#3529	C₂	semidirect
2. #87131	C₂	semidirect
3. #87113	C₂	semidirect
4. D₃×H(3,𝔽₄)	C₂	semidirect
5. #87080	C₂	semidirect
6. #86252	C₂	semidirect
7. #86244	C₂	semidirect
8. #86177	C₂	semidirect
9. #86163	C₂	semidirect
10. #86055	C₂	semidirect
11. #86039	C₂	semidirect
13. C₂×#1010	C₂²	semidirect
14. C₂×#1009	C₂²	semidirect
15. C₂³×D₁₂	C₂²	semidirect
16. C₃×#563	C₂²	semidirect
17. C₃×#562	C₂²	semidirect
18. C₃×H(3,𝔽₄)	C₂²	semidirect
19. C₃×#560	C₂²	semidirect
20. C₃×#532	C₂²	semidirect
21. C₃×#529	C₂²	semidirect
22. C₃×#525	C₂²	semidirect
23. #5830	C₂²	semidirect
24. #5830	C₂²	semidirect
25. #5825	C₂²	semidirect
26. #5791	C₂²	semidirect
27. #5734	C₂²	semidirect
28. #5724	C₂²	semidirect
29. #5717	C₂²	semidirect
30. #5715	C₂²	semidirect
31. #5705	C₂²	semidirect
32. #5704	C₂²	semidirect
33. #5700	C₂²	semidirect
34. #5691	C₂²	semidirect
35. #5683	C₂²	semidirect
36. #5683	C₂²	semidirect
37. #5683	C₂²	semidirect
38. D₃×#124	C₂²	semidirect
39. D₃×#124	C₂²	semidirect
40. #5668	C₂²	semidirect
41. #5664	C₂²	semidirect
42. #5659	C₂²	semidirect
43. #5657	C₂²	semidirect
44. #5654	C₂²	semidirect
45. #5653	C₂²	semidirect
46. #5653	C₂²	semidirect
47. #5644	C₂²	semidirect
48. #5640	C₂²	semidirect
49. #5633	C₂²	semidirect
50. #5630	C₂²	semidirect
51. #5613	C₂²	semidirect
52. #5612	C₂²	semidirect
53. #5610	C₂²	semidirect
54. #5609	C₂²	semidirect
55. #5607	C₂²	semidirect
56. #5605	C₂²	semidirect
57. #5595	C₂²	semidirect
58. #5594	C₂²	semidirect
59. D₃×#120	C₂²	semidirect
60. D₃×#120	C₂²	semidirect
61. #5585	C₂²	semidirect
62. Q₈×D₁₂	C₂²	semidirect
63. #5563	C₂²	semidirect
64. #5552	C₂²	semidirect
65. #5550	C₂²	semidirect
66. #5550	C₂²	semidirect
67. D₄×D₁₂	C₂²	semidirect
68. D₄×D₁₂	C₂²	semidirect
69. #5542	C₂²	semidirect
70. #5534	C₂²	semidirect
71. #5525	C₂²	semidirect
72. #5521	C₂²	semidirect
73. #5477	C₂²	semidirect
74. C₂×#875	C₂²	semidirect
75. C₄×#235	C₂²	semidirect
82. #3529	D₃	semidirect
87. C₂⁴×D₃	C₂³	semidirect
89. C₂×C₃×#41	C₂³	semidirect
90. C₂³×C₃×C₄	C₂³	semidirect
94. C₂×D₃×Q₈	C₂³	semidirect
95. C₂×D₃×Q₈	C₂³	semidirect
96. C₂×#237	C₂³	semidirect
100. C₂×D₃×D₄	C₂³	semidirect
103. C₂×#235	C₂³	semidirect
107. C₂²×D₁₂	C₂³	semidirect
108. C₂²×D₁₂	C₂³	semidirect
109. C₂²×Dic₆	C₂³	semidirect
110. C₃×C₄⋊Q₈	C₂³	semidirect
112. C₃×#126	C₂³	semidirect
113. C₃×#125	C₂³	semidirect
116. C₃×#124	C₂³	semidirect
118. C₃×#123	C₂³	semidirect
119. C₃×#123	C₂³	semidirect
120. C₃×C₂²⋊Q₈	C₂³	semidirect
121. C₃×C₂²⋊Q₈	C₂³	semidirect
124. C₃×#121	C₂³	semidirect
126. C₃×#120	C₂³	semidirect
127. C₃×C₄×Q₈	C₂³	semidirect
129. C₃×C₄×D₄	C₂³	semidirect
130. C₃×#117	C₂³	semidirect
131. C₂×C₃×C₄²	C₂³	semidirect
132. #953	C₂³	semidirect
133. #947	C₂³	semidirect
134. #947	C₂³	semidirect
135. #947	C₂³	semidirect
136. #944	C₂³	semidirect
138. #940	C₂³	semidirect
139. #939	C₂³	semidirect
140. #938	C₂³	semidirect
143. #937	C₂³	semidirect
144. #937	C₂³	semidirect
145. #937	C₂³	semidirect
148. #935	C₂³	semidirect
150. #930	C₂³	semidirect
151. #930	C₂³	semidirect
152. #929	C₂³	semidirect
153. C₄×#67	C₂³	semidirect
154. C₄×#67	C₂³	semidirect
155. C₂×(C₂×D₃)⋊C₄	C₂³	semidirect
156. #926	C₂³	semidirect
157. #926	C₂³	semidirect
158. #924	C₂³	semidirect
159. #898	C₂³	semidirect
160. #897	C₂³	semidirect
161. #896	C₂³	semidirect
162. #896	C₂³	semidirect
164. #895	C₂³	semidirect
165. #895	C₂³	semidirect
166. #894	C₂³	semidirect
167. #894	C₂³	semidirect
168. #894	C₂³	semidirect
169. #893	C₂³	semidirect
170. #893	C₂³	semidirect
171. #892	C₂³	semidirect
172. #887	C₂³	semidirect
173. #885	C₂³	semidirect
174. #885	C₂³	semidirect
175. #885	C₂³	semidirect
176. #885	C₂³	semidirect
178. #884	C₂³	semidirect
179. #883	C₂³	semidirect
181. #882	C₂³	semidirect
182. #882	C₂³	semidirect
183. #882	C₂³	semidirect
184. #882	C₂³	semidirect
185. #67⋊C₄	C₂³	semidirect
186. D₃×C₂²⋊C₄	C₂³	semidirect
187. D₃×C₂²⋊C₄	C₂³	semidirect
188. D₃×C₂²⋊C₄	C₂³	semidirect
189. D₃×C₂²⋊C₄	C₂³	semidirect
190. #879	C₂³	semidirect
191. #875	C₂³	semidirect
192. #875	C₂³	semidirect
193. #875	C₂³	semidirect
194. #875	C₂³	semidirect
197. C₄×D₁₂	C₂³	semidirect
198. C₄×D₁₂	C₂³	semidirect
199. #872	C₂³	semidirect
200. C₄²×D₃	C₂³	semidirect
201. #869	C₂³	semidirect
202. C₄×Dic₆	C₂³	semidirect
206. #563	C₂×D₃	semidirect
208. #562	C₂×D₃	semidirect
213. H(3,𝔽₄)	C₂×D₃	semidirect
215. #560	C₂×D₃	semidirect
254. #532	C₂×D₃	semidirect
256. #529	C₂×D₃	semidirect
261. #525	C₂×D₃	semidirect
359. C₂×#41	C₂²×D₃	semidirect
372. C₂³×C₄	C₂²×D₃	semidirect
375. C₄⋊Q₈	C₂²×D₃	semidirect
382. #126	C₂²×D₃	semidirect
383. #125	C₂²×D₃	semidirect
399. #124	C₂²×D₃	semidirect
407. #123	C₂²×D₃	semidirect
408. #123	C₂²×D₃	semidirect
413. C₂²⋊Q₈	C₂²×D₃	semidirect
414. C₂²⋊Q₈	C₂²×D₃	semidirect
427. #121	C₂²×D₃	semidirect
440. #120	C₂²×D₃	semidirect
443. C₄×Q₈	C₂²×D₃	semidirect
453. C₄×D₄	C₂²×D₃	semidirect
458. #117	C₂²×D₃	semidirect
465. C₂×C₄²	C₂²×D₃	semidirect
698. C₃	#63045	semidirect

Maximal subgroups

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

subgroup	index
C₃×#3529	2
#87131	2
#87113	2
D₃×H(3,𝔽₄)	2
#87080	2
#86252	2
#86244	2
#86177	2
#86163	2
#86055	2
#86039	2
#63045	3