Subgroups — #86170

Order 384.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#5706	C₂	1	2	yes	maximal, complemented
3	D₃×#126	C₂	1	2	yes	maximal, complemented
4	#5693	C₂	1	2	yes	maximal, complemented
5	#5679	C₂	1	2	yes	maximal, complemented
6	#5661	C₂	1	2	yes	maximal, complemented
7	#5659	C₂	1	2	yes	maximal, complemented
8	#5638	C₂	1	2	yes	maximal, complemented
9	#5613	C₂	1	2	yes	maximal, complemented
10	#5584	C₂	1	1	yes	maximal, characteristic, complemented
11	#5579	C₂	1	1	yes	maximal, characteristic, complemented
12	#5565	C₂	1	1	yes	maximal, characteristic, complemented
13	#5551	C₂	1	1	yes	maximal, characteristic, complemented
14	#5550	C₂	1	1	yes	maximal, characteristic, complemented
15	#5550	C₂	1	1	yes	maximal, characteristic, complemented
16	#5542	C₂	1	1	yes	maximal, characteristic, complemented
17	#5541	C₂	1	1	yes	maximal, characteristic, complemented
18	#5534	C₂	1	1	yes	maximal, characteristic, complemented
19	#5523	C₂	1	1	yes	maximal, characteristic, complemented
20	#5521	C₂	1	1	yes	maximal, characteristic, complemented
21	#5518	C₂	1	1	yes	maximal, characteristic, complemented
22	#5479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
24	#3521	—	3	1	no	maximal, Sylow
25	C₂×#235	C₂²	1	1	yes	characteristic
26	C₂×#235	C₂²	1	1	yes	characteristic
27	C₂²×D₁₂	C₂²	1	1	yes	characteristic
28	C₃×#126	C₂²	1	1	yes	characteristic
29	C₃×#126	C₂²	1	1	yes	characteristic, complemented
30	C₃×#125	C₂²	1	1	yes	characteristic, complemented
31	C₃×#124	C₂²	1	1	yes	characteristic
32	C₃×#123	C₂²	1	1	yes	characteristic
33	C₃×#123	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×#121	C₂²	1	1	yes	characteristic
36	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×#117	C₂²	1	1	yes	characteristic
41	C₃×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
43	#946	C₂²	1	2	yes	complemented
44	#946	C₂²	1	2	yes	complemented
45	#939	C₂²	1	2	yes	complemented
46	#938	C₂²	1	2	yes	complemented
47	#937	C₂²	1	2	yes	—
48	#937	C₂²	1	2	yes	—
49	#936	C₂²	1	2	yes	—
50	#935	C₂²	1	2	yes	—
51	#930	C₂²	1	1	yes	characteristic
52	#930	C₂²	1	1	yes	characteristic
53	#929	C₂²	1	2	yes	complemented
54	C₄×#67	C₂²	1	2	yes	complemented
55	C₄×#67	C₂²	1	2	yes	complemented
56	C₄×#67	C₂²	1	2	yes	complemented
57	#926	C₂²	1	1	yes	characteristic
58	#926	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
60	#924	C₂²	1	1	yes	characteristic
61	#924	C₂²	1	1	yes	characteristic
62	#924	C₂²	1	1	yes	characteristic, complemented
63	#924	C₂²	1	1	yes	characteristic, complemented
64	#898	C₂²	1	2	yes	complemented
65	#898	C₂²	1	2	yes	complemented
66	#898	C₂²	1	2	yes	complemented
67	#898	C₂²	1	2	yes	complemented
68	#896	C₂²	1	2	yes	complemented
69	#896	C₂²	1	2	yes	complemented
70	#896	C₂²	1	2	yes	complemented
71	#894	C₂²	1	2	yes	—
72	#894	C₂²	1	2	yes	—
73	#893	C₂²	1	2	yes	—
74	#893	C₂²	1	2	yes	—
75	#892	C₂²	1	2	yes	complemented
76	#892	C₂²	1	2	yes	complemented
77	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
78	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
79	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
80	#889	C₂²	1	2	yes	complemented
81	#889	C₂²	1	2	yes	complemented
82	#889	C₂²	1	2	yes	complemented
83	#887	C₂²	1	2	yes	complemented
84	#885	C₂²	1	2	yes	complemented
85	#884	C₂²	1	2	yes	—
86	#884	C₂²	1	2	yes	—
87	#883	C₂²	1	2	yes	complemented
88	#883	C₂²	1	2	yes	complemented
89	#883	C₂²	1	2	yes	complemented
90	#883	C₂²	1	2	yes	complemented
91	#67⋊C₄	C₂²	1	2	yes	complemented
92	#67⋊C₄	C₂²	1	2	yes	complemented
93	#67⋊C₄	C₂²	1	2	yes	complemented
94	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
95	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
96	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
97	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	#879	C₂²	1	2	yes	—
99	#879	C₂²	1	2	yes	—
100	#879	C₂²	1	2	yes	—
101	#879	C₂²	1	2	yes	—
102	#879	C₂²	1	2	yes	complemented
103	#877	C₂²	1	2	yes	complemented
104	#876	C₂²	1	2	yes	complemented
105	#875	C₂²	1	1	yes	characteristic
106	#875	C₂²	1	1	yes	characteristic
107	C₄×D₁₂	C₂²	1	1	yes	characteristic
108	C₄×D₁₂	C₂²	1	1	yes	characteristic
109	C₄×D₁₂	C₂²	1	1	yes	characteristic
110	C₄×D₁₂	C₂²	1	1	yes	characteristic
111	C₄×D₁₂	C₂²	1	1	yes	characteristic
112	C₄×D₁₂	C₂²	1	1	yes	characteristic
113	#872	C₂²	1	2	yes	complemented
114	#872	C₂²	1	2	yes	complemented
115	C₄²×D₃	C₂²	1	2	yes	complemented
116	#870	C₂²	1	1	yes	characteristic, complemented
117	#870	C₂²	1	1	yes	characteristic, complemented
118	#869	C₂²	1	1	yes	characteristic, complemented
119	#869	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#556	—	3	1	no	—
125	#556	—	3	1	no	—
126	#554	—	3	1	no	—
127	#553	—	3	2	no	—
128	#553	—	3	1	no	—
129	#552	—	3	2	no	—
130	#552	—	3	1	no	—
131	#551	—	3	2	no	—
132	#551	—	3	2	no	—
133	#547	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#542	—	3	1	no	—
137	#541	—	3	1	no	—
138	#539	—	3	2	no	—
139	#538	—	3	2	no	—
140	#529	—	3	2	no	—
141	#529	—	3	1	no	—
142	#529	D₃	1	1	yes	characteristic, complemented
143	C₂×#126	—	3	2	no	—
144	#520	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₄×#41	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂×#67	C₂³	1	2	yes	—
158	C₂×#67	C₂³	1	2	yes	—
159	C₂×#67	C₂³	1	2	yes	—
160	C₂×#67	C₂³	1	2	yes	—
161	C₂²×Dic₃	C₂³	1	2	yes	—
162	#235	—	2	4	no	—
163	#235	—	2	4	no	—
164	C₂×D₁₂	—	2	4	no	—
165	C₂×D₁₂	C₂³	1	1	yes	characteristic
166	C₂×D₁₂	C₂³	1	2	yes	—
167	C₂×D₁₂	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₃	C₂³	1	2	yes	—
169	C₂×C₄×D₃	C₂³	1	2	yes	—
170	C₂×C₄×D₃	C₂³	1	2	yes	—
171	C₂×C₄×D₃	C₂³	1	2	yes	—
172	C₂×C₄×D₃	C₂³	1	2	yes	—
173	C₂×C₄×D₃	C₂³	1	2	yes	—
174	C₂×C₄×D₃	C₂³	1	2	yes	—
175	C₂×C₄×D₃	C₂³	1	2	yes	—
176	C₂×Dic₆	C₂³	1	1	yes	characteristic
177	C₂×Dic₆	C₂³	1	1	yes	characteristic
178	C₂×Dic₆	C₂³	1	2	yes	—
179	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₄²	C₂³	1	1	yes	characteristic
200	C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₃×C₄²	C₂³	1	1	yes	characteristic
202	C₃×C₄²	C₂³	1	1	yes	characteristic
203	C₃×C₄²	C₂³	1	1	yes	characteristic
204	C₃×C₄²	C₂³	1	1	yes	characteristic
205	#217	C₂³	1	2	yes	—
206	#217	C₂³	1	2	yes	—
207	#217	C₂³	1	2	yes	—
208	#217	C₂³	1	2	yes	—
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	2	yes	—
211	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₃	C₂³	1	2	yes	—
228	C₄⋊Dic₃	C₂³	1	2	yes	—
229	C₄⋊Dic₃	C₂³	1	2	yes	—
230	C₄⋊Dic₃	C₂³	1	2	yes	—
231	Dic₃⋊C₄	C₂³	1	2	yes	—
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	2	yes	—
234	Dic₃⋊C₄	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	2	yes	—
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	2	yes	—
238	Dic₃⋊C₄	C₂³	1	2	yes	—
239	Dic₃⋊C₄	C₂³	1	2	yes	—
240	Dic₃⋊C₄	C₂³	1	2	yes	—
241	Dic₃⋊C₄	C₂³	1	2	yes	—
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	C₄×Dic₃	C₂³	1	2	yes	—
244	C₄×Dic₃	C₂³	1	2	yes	—
245	C₄×Dic₃	C₂³	1	2	yes	—
246	C₄×Dic₃	C₂³	1	2	yes	—
247	C₄×Dic₃	C₂³	1	2	yes	—
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₂×#41	—	3	1	no	—
250	C₂×#41	—	3	1	no	—
251	C₂²×D₄	—	3	1	no	—
252	C₄⋊Q₈	—	3	1	no	—
253	C₄⋊Q₈	—	3	1	no	—
254	#126	—	3	2	no	—
255	#126	—	3	2	no	—
256	#126	—	3	2	no	—
257	#126	—	3	2	no	—
258	#126	—	3	2	no	—
259	#126	—	3	2	no	—
260	#126	—	3	2	no	—
261	#126	—	3	2	no	—
262	#126	—	3	2	no	—
263	#126	—	3	2	no	—
264	#126	C₂×D₃	1	1	yes	characteristic
265	#126	C₂×D₃	1	1	yes	characteristic, complemented
266	#125	—	3	2	no	—
267	#125	—	3	2	no	—
268	#125	—	3	2	no	—
269	#125	—	3	1	no	—
270	#125	—	3	1	no	—
271	#125	C₂×D₃	1	1	yes	characteristic, complemented
272	#124	—	3	2	no	—
273	#124	—	3	2	no	—
274	#124	—	3	1	no	—
275	#124	—	3	1	no	—
276	#124	C₂×D₃	1	1	yes	characteristic
277	#123	—	3	2	no	—
278	#123	—	3	2	no	—
279	#123	—	3	2	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	—	3	2	no	—
283	#123	—	3	2	no	—
284	#123	—	3	2	no	—
285	#123	C₂×D₃	1	1	yes	characteristic
286	#123	C₂×D₃	1	1	yes	characteristic, complemented
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	2	no	—
289	C₂²⋊Q₈	—	3	1	no	—
290	C₂²⋊Q₈	—	3	1	no	—
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
297	#121	—	3	2	no	—
298	#121	—	3	2	no	—
299	#121	—	3	1	no	—
300	#121	—	3	1	no	—
301	#121	—	3	2	no	—
302	#121	—	3	2	no	—
303	#121	C₂×D₃	1	1	yes	characteristic
304	#120	—	3	2	no	—
305	#120	—	3	2	no	—
306	C₄×Q₈	—	3	2	no	—
307	C₄×Q₈	—	3	1	no	—
308	C₄×Q₈	—	3	1	no	—
309	C₄×Q₈	—	3	1	no	—
310	C₄×Q₈	—	3	1	no	—
311	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
312	C₄×D₄	—	3	2	no	—
313	C₄×D₄	—	3	2	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	—	3	2	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	—	3	1	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	1	no	—
325	C₄×D₄	—	3	1	no	—
326	C₄×D₄	C₂×D₃	1	1	yes	characteristic
327	C₄×D₄	C₂×D₃	1	1	yes	characteristic
328	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
329	#117	—	3	1	no	—
330	#117	—	3	1	no	—
331	#117	—	3	2	no	—
332	#117	—	3	2	no	—
333	#117	—	3	2	no	—
334	#117	—	3	2	no	—
335	#117	—	3	2	no	—
336	#117	C₂×D₃	1	1	yes	characteristic
337	#117	C₂×D₃	1	1	yes	characteristic, complemented
338	C₂×C₄⋊C₄	—	3	1	no	—
339	C₂×C₄⋊C₄	—	3	2	no	—
340	C₂×C₄⋊C₄	—	3	2	no	—
341	C₂×C₄⋊C₄	—	3	2	no	—
342	C₂×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	3	2	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₄²	—	3	2	no	—
347	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
348	C₂³×C₃	C₂⁴	1	1	yes	characteristic
349	C₂³×C₃	C₂⁴	1	1	yes	characteristic
350	C₂³×C₃	C₂⁴	1	1	yes	characteristic
351	C₂²×D₃	—	2	4	no	—
352	C₂²×D₃	—	4	2	no	—
353	C₂²×D₃	—	4	2	no	—
354	C₂²×D₃	C₂⁴	1	2	yes	—
355	C₂²×D₃	C₂⁴	1	2	yes	—
356	C₃×Q₈	—	4	1	no	—
357	C₃×D₄	—	4	1	no	—
358	C₃×D₄	—	4	1	no	—
359	C₃×D₄	—	4	1	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	4	1	no	—
364	C₂×C₃×C₄	—	4	1	no	—
365	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	#67	—	2	4	no	—
378	#67	—	2	4	no	—
379	#67	—	4	2	no	—
380	#67	—	4	2	no	—
381	C₂×Dic₃	—	4	2	no	—
382	C₂×Dic₃	C₂⁴	1	2	yes	—
383	C₂×Dic₃	C₂⁴	1	2	yes	—
384	C₂×Dic₃	C₂⁴	1	2	yes	—
385	C₂×Dic₃	C₂⁴	1	2	yes	—
386	C₂×Dic₃	C₂⁴	1	2	yes	—
387	C₂×Dic₃	C₂⁴	1	2	yes	—
388	D₁₂	—	2	4	no	—
389	D₁₂	—	2	2	no	—
390	D₁₂	#41	1	4	yes	—
391	C₄×D₃	—	2	4	no	—
392	C₄×D₃	—	2	4	no	—
393	C₄×D₃	—	4	2	no	—
394	C₄×D₃	—	4	2	no	—
395	C₄×D₃	—	4	2	no	—
396	C₄×D₃	—	4	2	no	—
397	C₄×D₃	—	4	2	no	—
398	C₄×D₃	—	4	2	no	—
399	Dic₆	—	2	2	no	—
400	Dic₆	—	2	2	no	—
401	Dic₆	—	4	2	no	—
402	C₂⁴	—	3	2	no	—
403	#41	—	6	4	no	—
404	#41	—	6	4	no	—
405	C₂×Q₈	—	3	1	no	—
406	C₂×Q₈	—	3	1	no	—
407	C₂×Q₈	—	3	2	no	—
408	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
409	C₂×D₄	—	3	2	no	—
410	C₂×D₄	—	3	2	no	—
411	C₂×D₄	—	3	2	no	—
412	C₂×D₄	—	3	2	no	—
413	C₂×D₄	—	3	1	no	—
414	C₂×D₄	—	3	2	no	—
415	C₂×D₄	—	3	1	no	—
416	C₂×D₄	—	6	4	no	—
417	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
418	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
419	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
420	C₂²×C₄	—	3	2	no	—
421	C₂²×C₄	—	3	2	no	—
422	C₂²×C₄	—	3	2	no	—
423	C₂²×C₄	—	3	2	no	—
424	C₂²×C₄	—	3	2	no	—
425	C₂²×C₄	—	3	2	no	—
426	C₂²×C₄	—	3	2	no	—
427	C₂²×C₄	—	3	2	no	—
428	C₂²×C₄	—	3	2	no	—
429	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
432	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
433	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
434	C₄⋊C₄	—	3	2	no	—
435	C₄⋊C₄	—	3	1	no	—
436	C₄⋊C₄	—	3	2	no	—
437	C₄⋊C₄	—	3	2	no	—
438	C₄⋊C₄	—	3	1	no	—
439	C₄⋊C₄	—	3	2	no	—
440	C₄⋊C₄	—	3	2	no	—
441	C₄⋊C₄	—	3	2	no	—
442	C₄⋊C₄	—	3	2	no	—
443	C₄⋊C₄	—	3	2	no	—
444	C₄⋊C₄	—	3	2	no	—
445	C₄⋊C₄	—	3	1	no	—
446	C₄⋊C₄	—	3	1	no	—
447	C₄⋊C₄	—	3	2	no	—
448	C₄⋊C₄	—	3	2	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	2	no	—
454	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
455	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
456	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
457	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
458	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
459	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
460	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
462	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
463	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	3	2	no	—
466	C₂²⋊C₄	—	3	2	no	—
467	C₂²⋊C₄	—	3	2	no	—
468	C₂²⋊C₄	—	3	2	no	—
469	C₂²⋊C₄	—	3	2	no	—
470	C₂²⋊C₄	—	3	2	no	—
471	C₂²⋊C₄	—	3	2	no	—
472	C₂²⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	—	3	2	no	—
474	C₂²⋊C₄	—	3	2	no	—
475	C₂²⋊C₄	—	3	2	no	—
476	C₂²⋊C₄	—	3	2	no	—
477	C₂²⋊C₄	—	3	2	no	—
478	C₂²⋊C₄	—	3	2	no	—
479	C₂²⋊C₄	—	3	2	no	—
480	C₂²⋊C₄	—	3	2	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
483	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
484	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
485	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
486	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
487	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
488	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
489	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
490	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
491	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
492	C₄²	—	3	2	no	—
493	C₄²	—	3	2	no	—
494	C₄²	—	3	2	no	—
495	C₄²	—	3	2	no	—
496	C₄²	—	3	2	no	—
497	C₄²	—	3	2	no	—
498	C₄²	C₂²×D₃	1	1	yes	characteristic
499	C₄²	C₂²×D₃	1	1	yes	characteristic
500	C₄²	C₂²×D₃	1	1	yes	characteristic
501	C₄²	C₂²×D₃	1	1	yes	characteristic
502	C₄²	C₂²×D₃	1	1	yes	characteristic
503	C₄²	C₂²×D₃	1	1	yes	characteristic
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	1	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	1	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	C₂⁵	1	1	yes	characteristic
514	C₂×D₃	—	2	2	no	—
515	C₂×D₃	—	2	2	no	—
516	C₂×D₃	—	2	2	no	—
517	C₂×D₃	—	2	2	no	—
518	C₂×D₃	—	2	2	no	—
519	C₂×D₃	—	8	4	no	—
520	C₂×D₃	C₂×#41	1	4	yes	—
521	C₃×C₄	—	2	1	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	—	2	1	no	—
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	C₂×#41	1	2	yes	—
533	Dic₃	—	2	2	no	—
534	Dic₃	—	2	2	no	—
535	Dic₃	—	2	2	no	—
536	Dic₃	—	2	2	no	—
537	Dic₃	—	2	2	no	—
538	Dic₃	—	2	2	no	—
539	C₂³	—	3	2	no	—
540	C₂³	—	3	2	no	—
541	C₂³	—	6	4	no	—
542	C₂³	—	12	2	no	—
543	C₂³	—	12	2	no	—
544	C₂³	C₂³×D₃	1	1	yes	characteristic
545	C₂³	C₂³×D₃	1	1	yes	characteristic
546	C₂³	C₂³×D₃	1	1	yes	characteristic
547	Q₈	—	4	1	no	—
548	Q₈	—	6	2	no	—
549	Q₈	—	6	2	no	—
550	Q₈	—	12	2	no	—
551	D₄	—	3	4	no	—
552	D₄	—	4	1	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	6	4	no	—
556	D₄	—	6	4	no	—
557	D₄	—	6	4	no	—
558	D₄	—	6	2	no	—
559	D₄	—	12	2	no	—
560	D₄	—	12	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	3	2	no	—
565	C₂×C₄	—	3	2	no	—
566	C₂×C₄	—	3	2	no	—
567	C₂×C₄	—	3	2	no	—
568	C₂×C₄	—	3	2	no	—
569	C₂×C₄	—	3	2	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	6	4	no	—
573	C₂×C₄	—	6	4	no	—
574	C₂×C₄	—	12	2	no	—
575	C₂×C₄	—	12	2	no	—
576	C₂×C₄	—	12	2	no	—
577	C₂×C₄	—	12	2	no	—
578	C₂×C₄	—	12	2	no	—
579	C₂×C₄	—	12	2	no	—
580	C₂×C₄	—	12	2	no	—
581	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
582	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
593	C₂×C₃	—	4	1	no	—
594	C₂×C₃	—	4	1	no	—
595	C₂×C₃	—	4	1	no	—
596	C₂×C₃	C₂²×#41	1	1	yes	characteristic
597	C₂×C₃	#585	1	1	yes	characteristic
598	C₂×C₃	#585	1	1	yes	characteristic
599	D₃	—	2	4	no	—
600	D₃	—	4	2	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	3	4	no	—
611	C₂²	—	6	2	no	—
612	C₂²	—	6	2	no	—
613	C₂²	—	6	2	no	—
614	C₂²	—	6	2	no	—
615	C₂²	—	6	2	no	—
616	C₂²	—	24	4	no	—
617	C₂²	C₂⁴×D₃	1	1	yes	characteristic
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	6	2	no	—
630	C₄	—	6	2	no	—
631	C₄	—	6	2	no	—
632	C₄	—	6	2	no	—
633	C₄	—	6	2	no	—
634	C₄	—	6	2	no	—
635	C₄	D₃×#41	1	2	yes	—
636	C₃	#3521	1	1	yes	characteristic, complemented, Sylow
637	C₂	—	4	1	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	1	no	—
640	C₂	—	6	4	no	—
641	C₂	—	12	2	no	—
642	C₂	C₂×D₃×#41	1	1	yes	characteristic
643	C₂	#5964	1	1	yes	characteristic
644	C₂	#5964	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#529	C₂
hypercenter	#529	D₃
hypocenter	C₃	#3521
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₃×#529	C₂	semidirect
2. #5706	C₂	semidirect
3. D₃×#126	C₂	semidirect
4. #5693	C₂	semidirect
5. #5679	C₂	semidirect
6. #5661	C₂	semidirect
7. #5659	C₂	semidirect
8. #5638	C₂	semidirect
9. #5613	C₂	semidirect
10. #5584	C₂	semidirect
11. #5579	C₂	semidirect
12. #5565	C₂	semidirect
13. #5551	C₂	semidirect
14. #5550	C₂	semidirect
15. #5550	C₂	semidirect
16. #5542	C₂	semidirect
17. #5541	C₂	semidirect
18. #5534	C₂	semidirect
19. #5523	C₂	semidirect
20. #5521	C₂	semidirect
21. #5518	C₂	semidirect
22. #5479	C₂	semidirect
23. C₄×#235	C₂	semidirect
29. C₃×#126	C₂²	semidirect
30. C₃×#125	C₂²	semidirect
33. C₃×#123	C₂²	semidirect
34. C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×Q₈	C₂²	semidirect
39. C₃×C₄×D₄	C₂²	semidirect
41. C₃×#117	C₂²	semidirect
42. C₂×C₃×C₄²	C₂²	semidirect
43. #946	C₂²	semidirect
44. #946	C₂²	semidirect
45. #939	C₂²	semidirect
46. #938	C₂²	semidirect
53. #929	C₂²	semidirect
54. C₄×#67	C₂²	semidirect
55. C₄×#67	C₂²	semidirect
56. C₄×#67	C₂²	semidirect
58. #926	C₂²	semidirect
59. C₂×C₄⋊Dic₃	C₂²	semidirect
62. #924	C₂²	semidirect
63. #924	C₂²	semidirect
64. #898	C₂²	semidirect
65. #898	C₂²	semidirect
66. #898	C₂²	semidirect
67. #898	C₂²	semidirect
68. #896	C₂²	semidirect
69. #896	C₂²	semidirect
70. #896	C₂²	semidirect
75. #892	C₂²	semidirect
76. #892	C₂²	semidirect
77. D₃×C₄⋊C₄	C₂²	semidirect
78. D₃×C₄⋊C₄	C₂²	semidirect
79. D₃×C₄⋊C₄	C₂²	semidirect
80. #889	C₂²	semidirect
81. #889	C₂²	semidirect
82. #889	C₂²	semidirect
83. #887	C₂²	semidirect
84. #885	C₂²	semidirect
87. #883	C₂²	semidirect
88. #883	C₂²	semidirect
89. #883	C₂²	semidirect
90. #883	C₂²	semidirect
91. #67⋊C₄	C₂²	semidirect
92. #67⋊C₄	C₂²	semidirect
93. #67⋊C₄	C₂²	semidirect
102. #879	C₂²	semidirect
103. #877	C₂²	semidirect
104. #876	C₂²	semidirect
113. #872	C₂²	semidirect
114. #872	C₂²	semidirect
115. C₄²×D₃	C₂²	semidirect
116. #870	C₂²	semidirect
117. #870	C₂²	semidirect
118. #869	C₂²	semidirect
119. #869	C₂²	semidirect
120. C₄×Dic₆	C₂²	semidirect
121. C₄×Dic₆	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
142. #529	D₃	semidirect
265. #126	C₂×D₃	semidirect
271. #125	C₂×D₃	semidirect
286. #123	C₂×D₃	semidirect
296. C₂²⋊Q₈	C₂×D₃	semidirect
311. C₄×Q₈	C₂×D₃	semidirect
328. C₄×D₄	C₂×D₃	semidirect
337. #117	C₂×D₃	semidirect
347. C₂×C₄²	C₂×D₃	semidirect
636. C₃	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₃×#529	2
#5706	2
D₃×#126	2
#5693	2
#5679	2
#5661	2
#5659	2
#5638	2
#5613	2
#5584	2
#5579	2
#5565	2
#5551	2
#5550	2
#5542	2
#5541	2
#5534	2
#5523	2
#5521	2
#5518	2
#5479	2
C₄×#235	2
#3521	3