Subgroups — #86352

Order 384.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	#5834	C₂	1	1	yes	maximal, characteristic, complemented
3	#5829	C₂	1	1	yes	maximal, characteristic, complemented
4	#5817	C₂	1	1	yes	maximal, characteristic, complemented
5	#5817	C₂	1	1	yes	maximal, characteristic, complemented
6	#5732	C₂	1	1	yes	maximal, characteristic, complemented
7	#5731	C₂	1	1	yes	maximal, characteristic, complemented
8	#5726	C₂	1	1	yes	maximal, characteristic, complemented
9	#5725	C₂	1	1	yes	maximal, characteristic, complemented
10	#5681	C₂	1	1	yes	maximal, characteristic, complemented
11	#5680	C₂	1	1	yes	maximal, characteristic, complemented
12	#5676	C₂	1	1	yes	maximal, characteristic, complemented
13	#5674	C₂	1	1	yes	maximal, characteristic, complemented
14	#5666	C₂	1	2	yes	maximal, complemented
15	#5663	C₂	1	2	yes	maximal, complemented
16	#5661	C₂	1	2	yes	maximal, complemented
17	#5657	C₂	1	2	yes	maximal, complemented
18	#5647	C₂	1	2	yes	maximal, complemented
19	#5644	C₂	1	2	yes	maximal, complemented
20	#5638	C₂	1	2	yes	maximal, complemented
21	#5637	C₂	1	2	yes	maximal, complemented
22	#5535	C₂	1	1	yes	maximal, characteristic, complemented
23	#5528	C₂	1	1	yes	maximal, characteristic, complemented
24	#3562	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×#239	C₂²	1	1	yes	characteristic
28	C₂×#239	C₂²	1	1	yes	characteristic
29	C₂×#239	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×#124	C₂²	1	1	yes	characteristic
34	C₃×#124	C₂²	1	1	yes	characteristic
35	C₃×#123	C₂²	1	2	yes	complemented
36	C₃×#123	C₂²	1	2	yes	complemented
37	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
38	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₃×#117	C₂²	1	1	yes	characteristic, complemented
40	#947	C₂²	1	2	yes	—
41	#947	C₂²	1	1	yes	characteristic
42	#947	C₂²	1	1	yes	characteristic
43	#947	C₂²	1	2	yes	complemented
44	#947	C₂²	1	1	yes	characteristic, complemented
45	#946	C₂²	1	1	yes	characteristic
46	#946	C₂²	1	1	yes	characteristic
47	#946	C₂²	1	2	yes	complemented
48	#946	C₂²	1	2	yes	complemented
49	#946	C₂²	1	1	yes	characteristic, complemented
50	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
51	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
52	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
53	#940	C₂²	1	1	yes	characteristic
54	#940	C₂²	1	2	yes	complemented
55	#939	C₂²	1	2	yes	—
56	#938	C₂²	1	1	yes	characteristic
57	#938	C₂²	1	2	yes	complemented
58	#937	C₂²	1	2	yes	—
59	D₄×Dic₃	C₂²	1	1	yes	characteristic
60	#930	C₂²	1	2	yes	—
61	#930	C₂²	1	1	yes	characteristic
62	#930	C₂²	1	2	yes	complemented
63	#930	C₂²	1	2	yes	complemented
64	#930	C₂²	1	1	yes	characteristic, complemented
65	#929	C₂²	1	2	yes	—
66	C₄×#67	C₂²	1	1	yes	characteristic
67	C₄×#67	C₂²	1	2	yes	complemented
68	C₄×#67	C₂²	1	2	yes	complemented
69	C₄×#67	C₂²	1	2	yes	complemented
70	C₄×#67	C₂²	1	1	yes	characteristic, complemented
71	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
72	#898	C₂²	1	1	yes	characteristic
73	#898	C₂²	1	2	yes	—
74	#898	C₂²	1	2	yes	—
75	#898	C₂²	1	2	yes	complemented
76	#898	C₂²	1	2	yes	complemented
77	#897	C₂²	1	2	yes	complemented
78	#896	C₂²	1	1	yes	characteristic, complemented
79	#895	C₂²	1	2	yes	—
80	#895	C₂²	1	2	yes	complemented
81	#895	C₂²	1	2	yes	complemented
82	#894	C₂²	1	2	yes	—
83	#894	C₂²	1	1	yes	characteristic
84	#894	C₂²	1	2	yes	complemented
85	#894	C₂²	1	2	yes	complemented
86	#894	C₂²	1	2	yes	complemented
87	#893	C₂²	1	2	yes	complemented
88	#893	C₂²	1	2	yes	complemented
89	#892	C₂²	1	2	yes	complemented
90	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
91	#889	C₂²	1	1	yes	characteristic, complemented
92	#889	C₂²	1	2	yes	complemented
93	#889	C₂²	1	2	yes	complemented
94	#886	C₂²	1	2	yes	complemented
95	#885	C₂²	1	1	yes	characteristic
96	#885	C₂²	1	2	yes	complemented
97	#884	C₂²	1	2	yes	—
98	#884	C₂²	1	2	yes	—
99	#884	C₂²	1	2	yes	—
100	#884	C₂²	1	1	yes	characteristic
101	#884	C₂²	1	2	yes	complemented
102	#884	C₂²	1	2	yes	complemented
103	#883	C₂²	1	2	yes	—
104	#883	C₂²	1	2	yes	complemented
105	#883	C₂²	1	2	yes	complemented
106	#883	C₂²	1	1	yes	characteristic, complemented
107	#882	C₂²	1	2	yes	—
108	#882	C₂²	1	2	yes	—
109	#882	C₂²	1	2	yes	—
110	#67⋊C₄	C₂²	1	2	yes	complemented
111	#67⋊C₄	C₂²	1	2	yes	complemented
112	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
113	#879	C₂²	1	2	yes	complemented
114	#879	C₂²	1	1	yes	characteristic, complemented
115	#877	C₂²	1	2	yes	complemented
116	#874	C₂²	1	1	yes	characteristic
117	C₄×D₁₂	C₂²	1	1	yes	characteristic
118	C₄×D₁₂	C₂²	1	1	yes	characteristic
119	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
120	#872	C₂²	1	1	yes	characteristic
121	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
122	#870	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#562	—	3	2	no	—
125	#560	—	3	2	no	—
126	#559	—	3	1	no	—
127	#556	—	3	1	no	—
128	#553	—	3	2	no	—
129	#551	—	3	2	no	—
130	#550	—	3	1	no	—
131	#548	—	3	1	no	—
132	#548	—	3	1	no	—
133	#547	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#541	—	3	1	no	—
137	#540	—	3	2	no	—
138	#540	—	3	1	no	—
139	#539	—	3	2	no	—
140	#538	—	3	2	no	—
141	#538	—	3	2	no	—
142	#536	D₃	1	1	yes	characteristic, complemented
143	#535	—	3	1	no	—
144	#532	—	3	1	no	—
145	#529	—	3	1	no	—
146	#529	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₃×#41	—	4	2	no	—
149	C₂×C₃×Q₈	—	4	2	no	—
150	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂×C₃×Q₈	C₂³	1	2	yes	—
154	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×D₄	C₂³	1	2	yes	—
156	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³	1	2	yes	—
158	C₂²×C₃×C₄	C₂³	1	2	yes	—
159	C₂×#67	C₂³	1	2	yes	—
160	C₂×#67	C₂³	1	2	yes	—
161	C₂×#67	C₂³	1	2	yes	—
162	C₂×#67	C₂³	1	2	yes	—
163	C₂×#67	C₂³	1	1	yes	characteristic
164	C₂×#67	C₂³	1	1	yes	characteristic
165	C₂×#67	C₂³	1	2	yes	—
166	C₂×#67	C₂³	1	2	yes	—
167	C₂²×Dic₃	C₂³	1	2	yes	—
168	#239	—	4	2	no	—
169	#239	—	4	2	no	—
170	#239	—	4	2	no	—
171	D₃×D₄	—	4	2	no	—
172	C₂×D₁₂	C₂³	1	1	yes	characteristic
173	C₂×D₁₂	C₂³	1	1	yes	characteristic
174	C₂×D₁₂	C₂³	1	1	yes	characteristic
175	C₂×D₁₂	C₂³	1	2	yes	—
176	C₂×D₁₂	C₂³	1	2	yes	—
177	C₂×D₁₂	C₂³	1	2	yes	—
178	C₂×D₁₂	C₂³	1	2	yes	—
179	C₂×D₁₂	C₂³	1	2	yes	—
180	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂³	1	2	yes	—
185	C₂×C₄×D₃	C₂³	1	2	yes	—
186	C₂×C₄×D₃	C₂³	1	2	yes	—
187	C₂×C₄×D₃	C₂³	1	2	yes	—
188	C₂×C₄×D₃	C₂³	1	2	yes	—
189	C₂×Dic₆	C₂³	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₃×C₄²	C₂³	1	1	yes	characteristic
203	C₃×C₄²	C₂³	1	1	yes	characteristic
204	#217	C₂³	1	2	yes	—
205	#217	C₂³	1	2	yes	—
206	#217	C₂³	1	1	yes	characteristic
207	#217	C₂³	1	1	yes	characteristic
208	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
209	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
210	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
211	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
223	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
224	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
225	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₃	C₂³	1	2	yes	—
232	C₄⋊Dic₃	C₂³	1	2	yes	—
233	C₄⋊Dic₃	C₂³	1	2	yes	—
234	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	2	yes	—
238	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₃⋊C₄	C₂³	1	2	yes	—
241	Dic₃⋊C₄	C₂³	1	2	yes	—
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
245	C₄×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₃	C₂³	1	1	yes	characteristic
247	C₄×Dic₃	C₂³	1	1	yes	characteristic
248	C₄×Dic₃	C₂³	1	1	yes	characteristic
249	C₄×Dic₃	C₂³	1	2	yes	—
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₄×Dic₃	C₂³	1	2	yes	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	1	no	—
254	C₂×#41	—	3	1	no	—
255	C₂×#41	C₂×D₃	1	1	yes	characteristic
256	C₂²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
257	C₂²×D₄	—	3	1	no	—
258	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
259	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
260	#127	—	3	1	no	—
261	#127	—	3	2	no	—
262	#127	—	3	1	no	—
263	#126	—	3	1	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#126	—	3	2	no	—
268	#126	—	3	2	no	—
269	#126	—	3	1	no	—
270	#125	—	3	1	no	—
271	#125	—	3	2	no	—
272	#125	—	3	2	no	—
273	#125	—	3	1	no	—
274	#124	—	3	1	no	—
275	#124	—	3	1	no	—
276	#124	—	3	1	no	—
277	#124	—	3	2	no	—
278	#124	—	3	2	no	—
279	#124	—	3	1	no	—
280	#124	—	3	2	no	—
281	#124	C₂×D₃	1	1	yes	characteristic
282	#124	C₂×D₃	1	1	yes	characteristic
283	#123	—	3	2	no	—
284	#123	—	3	1	no	—
285	#123	—	3	2	no	—
286	#123	—	3	2	no	—
287	#123	—	3	2	no	—
288	#123	—	3	2	no	—
289	#123	—	3	1	no	—
290	#123	—	3	2	no	—
291	#123	—	3	2	no	—
292	#123	—	3	2	no	—
293	#123	—	3	2	no	—
294	#123	C₂×D₃	1	2	yes	complemented
295	#123	C₂×D₃	1	2	yes	complemented
296	C₂²⋊Q₈	—	3	1	no	—
297	C₂²⋊Q₈	—	3	2	no	—
298	C₂²⋊Q₈	—	3	2	no	—
299	C₂²⋊Q₈	—	3	1	no	—
300	C₂²⋊Q₈	—	3	1	no	—
301	C₂²⋊Q₈	—	3	1	no	—
302	C₂²⋊Q₈	—	3	2	no	—
303	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
304	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
305	#121	—	3	1	no	—
306	#121	—	3	2	no	—
307	#121	—	3	2	no	—
308	#121	—	3	2	no	—
309	#121	—	3	2	no	—
310	#121	—	3	1	no	—
311	#121	—	3	1	no	—
312	#121	—	3	2	no	—
313	#121	—	3	2	no	—
314	#121	—	3	2	no	—
315	#121	—	3	2	no	—
316	#121	—	3	1	no	—
317	#121	—	3	2	no	—
318	#121	—	3	2	no	—
319	#121	—	3	2	no	—
320	#121	—	3	2	no	—
321	#121	—	3	2	no	—
322	#120	—	3	2	no	—
323	#120	—	3	2	no	—
324	#120	—	3	2	no	—
325	#120	—	3	2	no	—
326	C₄×Q₈	—	3	1	no	—
327	C₄×Q₈	—	3	1	no	—
328	C₄×Q₈	—	3	1	no	—
329	C₄×Q₈	—	3	1	no	—
330	C₄×D₄	—	3	1	no	—
331	C₄×D₄	—	3	1	no	—
332	C₄×D₄	—	3	1	no	—
333	C₄×D₄	—	3	2	no	—
334	C₄×D₄	—	3	2	no	—
335	C₄×D₄	—	3	2	no	—
336	C₄×D₄	—	3	2	no	—
337	C₄×D₄	—	3	2	no	—
338	C₄×D₄	—	3	2	no	—
339	C₄×D₄	—	3	2	no	—
340	C₄×D₄	—	3	1	no	—
341	C₄×D₄	—	3	1	no	—
342	C₄×D₄	—	3	1	no	—
343	#117	—	3	2	no	—
344	#117	—	3	2	no	—
345	#117	—	3	1	no	—
346	#117	C₂×D₃	1	1	yes	characteristic, complemented
347	C₂×C₄⋊C₄	—	3	2	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂³×C₃	C₂⁴	1	2	yes	—
352	C₂³×C₃	C₂⁴	1	1	yes	characteristic
353	C₂²×D₃	—	4	2	no	—
354	C₂²×D₃	—	4	2	no	—
355	C₂²×D₃	—	4	2	no	—
356	C₂²×D₃	C₂⁴	1	1	yes	characteristic
357	C₂²×D₃	C₂⁴	1	2	yes	—
358	C₂²×D₃	C₂⁴	1	1	yes	characteristic
359	C₂²×D₃	C₂⁴	1	2	yes	—
360	C₃×Q₈	—	2	2	no	—
361	C₃×Q₈	—	2	2	no	—
362	C₃×Q₈	—	2	2	no	—
363	C₃×Q₈	—	4	2	no	—
364	C₃×D₄	—	2	2	no	—
365	C₃×D₄	—	4	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	4	2	no	—
368	C₂×C₃×C₄	—	4	2	no	—
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴	1	2	yes	—
372	C₂×C₃×C₄	C₂⁴	1	2	yes	—
373	C₂×C₃×C₄	C₂⁴	1	2	yes	—
374	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	#67	—	4	2	no	—
379	#67	—	4	1	no	—
380	#67	—	4	2	no	—
381	#67	—	4	2	no	—
382	#67	—	4	2	no	—
383	#67	—	4	2	no	—
384	#67	—	4	2	no	—
385	#67	—	4	1	no	—
386	C₂×Dic₃	—	4	2	no	—
387	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₃	C₂⁴	1	2	yes	—
391	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₃	C₂⁴	1	2	yes	—
394	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
395	D₁₂	—	2	2	no	—
396	D₁₂	—	2	2	no	—
397	D₁₂	—	4	1	no	—
398	D₁₂	—	4	2	no	—
399	D₁₂	—	4	2	no	—
400	D₁₂	—	4	2	no	—
401	D₁₂	—	4	2	no	—
402	D₁₂	—	4	2	no	—
403	C₄×D₃	—	2	2	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	4	1	no	—
406	C₄×D₃	—	4	1	no	—
407	C₄×D₃	—	4	2	no	—
408	C₄×D₃	—	4	2	no	—
409	C₄×D₃	—	4	2	no	—
410	C₄×D₃	—	4	2	no	—
411	C₄×D₃	—	4	2	no	—
412	Dic₆	—	4	1	no	—
413	C₂⁴	—	3	2	no	—
414	#41	—	4	2	no	—
415	#41	—	12	2	no	—
416	#41	—	12	2	no	—
417	#41	—	12	2	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	4	2	no	—
420	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
421	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
422	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
423	C₂×Q₈	C₂²×D₃	1	2	yes	—
424	C₂×D₄	—	3	1	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	2	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	1	no	—
431	C₂×D₄	—	3	2	no	—
432	C₂×D₄	—	3	1	no	—
433	C₂×D₄	—	3	1	no	—
434	C₂×D₄	—	3	1	no	—
435	C₂×D₄	—	3	2	no	—
436	C₂×D₄	—	3	2	no	—
437	C₂×D₄	—	3	2	no	—
438	C₂×D₄	—	3	2	no	—
439	C₂×D₄	—	3	2	no	—
440	C₂×D₄	—	12	2	no	—
441	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
442	C₂×D₄	C₂²×D₃	1	2	yes	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	3	1	no	—
447	C₂²×C₄	—	3	1	no	—
448	C₂²×C₄	—	3	2	no	—
449	C₂²×C₄	—	3	2	no	—
450	C₂²×C₄	—	3	2	no	—
451	C₂²×C₄	—	3	2	no	—
452	C₂²×C₄	—	3	2	no	—
453	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₃	1	2	yes	—
455	C₂²×C₄	C₂²×D₃	1	2	yes	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	2	no	—
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	—	3	1	no	—
461	C₄⋊C₄	—	3	1	no	—
462	C₄⋊C₄	—	3	2	no	—
463	C₄⋊C₄	—	3	1	no	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	1	no	—
466	C₄⋊C₄	—	3	1	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	2	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	1	no	—
474	C₄⋊C₄	C₂²×D₃	1	2	yes	—
475	C₄⋊C₄	C₂²×D₃	1	2	yes	—
476	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₃	1	2	yes	—
479	C₄⋊C₄	C₂²×D₃	1	2	yes	—
480	C₂²⋊C₄	—	3	2	no	—
481	C₂²⋊C₄	—	3	1	no	—
482	C₂²⋊C₄	—	3	1	no	—
483	C₂²⋊C₄	—	3	2	no	—
484	C₂²⋊C₄	—	3	1	no	—
485	C₂²⋊C₄	—	3	1	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	2	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	1	no	—
491	C₂²⋊C₄	—	3	1	no	—
492	C₂²⋊C₄	—	3	2	no	—
493	C₂²⋊C₄	—	3	2	no	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	—	3	1	no	—
498	C₂²⋊C₄	—	3	2	no	—
499	C₂²⋊C₄	—	3	2	no	—
500	C₂²⋊C₄	—	3	1	no	—
501	C₂²⋊C₄	—	3	2	no	—
502	C₂²⋊C₄	—	3	2	no	—
503	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
505	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
507	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
508	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
509	C₄²	—	3	1	no	—
510	C₄²	—	3	1	no	—
511	C₄²	—	3	1	no	—
512	C₄²	—	3	2	no	—
513	C₄²	—	3	1	no	—
514	C₄²	—	3	2	no	—
515	C₄²	—	3	2	no	—
516	C₄²	C₂²×D₃	1	1	yes	characteristic
517	C₄²	C₂²×D₃	1	1	yes	characteristic
518	C₂²×C₃	—	2	2	no	—
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	2	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	C₂⁵	1	1	yes	characteristic
525	C₂×D₃	—	2	1	no	—
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	2	2	no	—
528	C₂×D₃	—	2	2	no	—
529	C₂×D₃	—	2	1	no	—
530	C₂×D₃	—	2	2	no	—
531	C₂×D₃	—	2	2	no	—
532	C₂×D₃	—	2	1	no	—
533	C₂×D₃	—	2	2	no	—
534	C₂×D₃	—	2	2	no	—
535	C₂×D₃	—	2	1	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	8	4	no	—
538	C₃×C₄	—	2	2	no	—
539	C₃×C₄	—	2	2	no	—
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	1	no	—
544	C₃×C₄	—	2	1	no	—
545	C₃×C₄	—	2	1	no	—
546	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
547	Dic₃	—	2	1	no	—
548	Dic₃	—	2	1	no	—
549	Dic₃	—	2	1	no	—
550	Dic₃	—	2	1	no	—
551	Dic₃	—	2	1	no	—
552	Dic₃	—	2	2	no	—
553	Dic₃	—	2	2	no	—
554	Dic₃	—	2	1	no	—
555	C₂³	—	3	1	no	—
556	C₂³	—	3	2	no	—
557	C₂³	—	3	1	no	—
558	C₂³	—	3	2	no	—
559	C₂³	—	12	2	no	—
560	C₂³	—	12	2	no	—
561	C₂³	—	12	2	no	—
562	C₂³	C₂³×D₃	1	2	yes	—
563	C₂³	C₂³×D₃	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	12	1	no	—
569	D₄	—	2	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	6	2	no	—
572	D₄	—	6	2	no	—
573	D₄	—	12	2	no	—
574	D₄	—	12	2	no	—
575	D₄	—	12	2	no	—
576	D₄	—	12	1	no	—
577	D₄	—	12	2	no	—
578	D₄	—	12	2	no	—
579	D₄	—	12	2	no	—
580	D₄	—	12	2	no	—
581	D₄	—	12	2	no	—
582	D₄	—	12	2	no	—
583	D₄	—	12	1	no	—
584	D₄	—	12	2	no	—
585	D₄	—	12	1	no	—
586	D₄	—	12	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	3	1	no	—
589	C₂×C₄	—	3	1	no	—
590	C₂×C₄	—	3	1	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	3	2	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	2	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	6	2	no	—
599	C₂×C₄	—	6	2	no	—
600	C₂×C₄	—	12	2	no	—
601	C₂×C₄	—	12	2	no	—
602	C₂×C₄	—	12	2	no	—
603	C₂×C₄	—	12	2	no	—
604	C₂×C₄	—	12	2	no	—
605	C₂×C₄	—	12	1	no	—
606	C₂×C₄	—	12	1	no	—
607	C₂×C₄	—	12	2	no	—
608	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₃	1	2	yes	—
611	C₂×C₄	C₂³×D₃	1	2	yes	—
612	C₂×C₄	C₂³×D₃	1	2	yes	—
613	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
617	C₂×C₃	—	4	2	no	—
618	C₂×C₃	—	4	1	no	—
619	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
620	C₂×C₃	#585	1	1	yes	characteristic
621	C₂×C₃	#585	1	1	yes	characteristic
622	D₃	—	4	1	no	—
623	D₃	—	4	2	no	—
624	D₃	—	4	2	no	—
625	D₃	—	4	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	6	1	no	—
633	C₂²	—	6	1	no	—
634	C₂²	—	6	2	no	—
635	C₂²	—	6	2	no	—
636	C₂²	—	6	1	no	—
637	C₂²	—	6	2	no	—
638	C₂²	—	6	1	no	—
639	C₂²	—	6	2	no	—
640	C₂²	—	6	2	no	—
641	C₂²	—	6	2	no	—
642	C₂²	—	6	1	no	—
643	C₂²	—	6	1	no	—
644	C₂²	—	24	4	no	—
645	C₂²	C₂⁴×D₃	1	1	yes	characteristic
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	6	1	no	—
655	C₄	—	6	1	no	—
656	C₄	—	6	1	no	—
657	C₄	—	6	2	no	—
658	C₄	—	6	2	no	—
659	C₄	—	6	1	no	—
660	C₄	—	6	1	no	—
661	C₄	—	6	1	no	—
662	C₄	#1004	1	2	yes	—
663	C₃	#3562	1	1	yes	characteristic, complemented, Sylow
664	C₂	—	4	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	12	1	no	—
667	C₂	—	12	2	no	—
668	C₂	—	12	1	no	—
669	C₂	—	12	2	no	—
670	C₂	C₂×#1004	1	1	yes	characteristic
671	C₂	#5968	1	1	yes	characteristic
672	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#536	C₂
hypercenter	#536	D₃
hypocenter	C₃	#3562
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. C₃×#536	C₂	semidirect
2. #5834	C₂	semidirect
3. #5829	C₂	semidirect
4. #5817	C₂	semidirect
5. #5817	C₂	semidirect
6. #5732	C₂	semidirect
7. #5731	C₂	semidirect
8. #5726	C₂	semidirect
9. #5725	C₂	semidirect
10. #5681	C₂	semidirect
11. #5680	C₂	semidirect
12. #5676	C₂	semidirect
13. #5674	C₂	semidirect
14. #5666	C₂	semidirect
15. #5663	C₂	semidirect
16. #5661	C₂	semidirect
17. #5657	C₂	semidirect
18. #5647	C₂	semidirect
19. #5644	C₂	semidirect
20. #5638	C₂	semidirect
21. #5637	C₂	semidirect
22. #5535	C₂	semidirect
23. #5528	C₂	semidirect
26. C₂²×C₃×Q₈	C₂²	semidirect
29. C₂×#239	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×C₄⋊Q₈	C₂²	semidirect
35. C₃×#123	C₂²	semidirect
36. C₃×#123	C₂²	semidirect
37. C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₃×#117	C₂²	semidirect
43. #947	C₂²	semidirect
44. #947	C₂²	semidirect
47. #946	C₂²	semidirect
48. #946	C₂²	semidirect
49. #946	C₂²	semidirect
50. Q₈×Dic₃	C₂²	semidirect
51. Q₈×Dic₃	C₂²	semidirect
52. Q₈×Dic₃	C₂²	semidirect
54. #940	C₂²	semidirect
57. #938	C₂²	semidirect
62. #930	C₂²	semidirect
63. #930	C₂²	semidirect
64. #930	C₂²	semidirect
67. C₄×#67	C₂²	semidirect
68. C₄×#67	C₂²	semidirect
69. C₄×#67	C₂²	semidirect
70. C₄×#67	C₂²	semidirect
75. #898	C₂²	semidirect
76. #898	C₂²	semidirect
77. #897	C₂²	semidirect
78. #896	C₂²	semidirect
80. #895	C₂²	semidirect
81. #895	C₂²	semidirect
84. #894	C₂²	semidirect
85. #894	C₂²	semidirect
86. #894	C₂²	semidirect
87. #893	C₂²	semidirect
88. #893	C₂²	semidirect
89. #892	C₂²	semidirect
90. D₃×C₄⋊C₄	C₂²	semidirect
91. #889	C₂²	semidirect
92. #889	C₂²	semidirect
93. #889	C₂²	semidirect
94. #886	C₂²	semidirect
96. #885	C₂²	semidirect
101. #884	C₂²	semidirect
102. #884	C₂²	semidirect
104. #883	C₂²	semidirect
105. #883	C₂²	semidirect
106. #883	C₂²	semidirect
110. #67⋊C₄	C₂²	semidirect
111. #67⋊C₄	C₂²	semidirect
113. #879	C₂²	semidirect
114. #879	C₂²	semidirect
115. #877	C₂²	semidirect
119. C₄×D₁₂	C₂²	semidirect
121. C₄²×D₃	C₂²	semidirect
122. #870	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
142. #536	D₃	semidirect
256. C₂²×Q₈	C₂×D₃	semidirect
258. C₄⋊Q₈	C₂×D₃	semidirect
259. C₄⋊Q₈	C₂×D₃	semidirect
294. #123	C₂×D₃	semidirect
295. #123	C₂×D₃	semidirect
303. C₂²⋊Q₈	C₂×D₃	semidirect
304. C₂²⋊Q₈	C₂×D₃	semidirect
346. #117	C₂×D₃	semidirect
663. C₃	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₃×#536	2
#5834	2
#5829	2
#5817	2
#5732	2
#5731	2
#5726	2
#5725	2
#5681	2
#5680	2
#5676	2
#5674	2
#5666	2
#5663	2
#5661	2
#5657	2
#5647	2
#5644	2
#5638	2
#5637	2
#5535	2
#5528	2
#3562	3