Subgroups — #86627

Order 384.

1132 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	Dic₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	#5824	C₂	1	1	yes	maximal, characteristic, complemented
4	#5806	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#5680	C₂	1	1	yes	maximal, characteristic, complemented
7	#5671	C₂	1	1	yes	maximal, characteristic, complemented
8	#5650	C₂	1	2	yes	maximal, complemented
9	#5649	C₂	1	2	yes	maximal, complemented
10	#5642	C₂	1	1	yes	maximal, characteristic, complemented
11	#5622	C₂	1	1	yes	maximal, characteristic, complemented
12	#5616	C₂	1	1	yes	maximal, characteristic, complemented
13	#5601	C₂	1	2	yes	maximal, complemented
14	#5600	C₂	1	2	yes	maximal, complemented
15	#5600	C₂	1	1	yes	maximal, characteristic, complemented
16	#5587	C₂	1	2	yes	maximal, complemented
17	#5586	C₂	1	2	yes	maximal, complemented
18	#5541	C₂	1	1	yes	maximal, characteristic, complemented
19	#5539	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
22	#5495	C₂	1	2	yes	maximal, complemented
23	C₂×#877	C₂	1	2	yes	maximal, complemented
24	#3475	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
27	C₂³×Dic₃	C₂²	1	2	yes	—
28	C₂×#237	C₂²	1	1	yes	characteristic
29	C₂×#237	C₂²	1	1	yes	characteristic
30	C₃×#124	C₂²	1	1	yes	characteristic
31	C₃×#123	C₂²	1	2	yes	—
32	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃×#121	C₂²	1	2	yes	—
34	C₃×#121	C₂²	1	1	yes	characteristic
35	C₃×#120	C₂²	1	2	yes	—
36	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
39	#953	C₂²	1	2	yes	—
40	C₂×#217	C₂²	1	2	yes	—
41	C₂×#217	C₂²	1	2	yes	—
42	#946	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	#944	C₂²	1	1	yes	characteristic, complemented
46	#939	C₂²	1	2	yes	—
47	#939	C₂²	1	2	yes	complemented
48	#939	C₂²	1	2	yes	complemented
49	#938	C₂²	1	1	yes	characteristic
50	#936	C₂²	1	1	yes	characteristic
51	#936	C₂²	1	2	yes	complemented
52	#935	C₂²	1	2	yes	—
53	#935	C₂²	1	2	yes	—
54	#935	C₂²	1	2	yes	complemented
55	#935	C₂²	1	2	yes	complemented
56	D₄×Dic₃	C₂²	1	2	yes	—
57	D₄×Dic₃	C₂²	1	2	yes	—
58	D₄×Dic₃	C₂²	1	1	yes	characteristic
59	D₄×Dic₃	C₂²	1	1	yes	characteristic
60	D₄×Dic₃	C₂²	1	1	yes	characteristic
61	D₄×Dic₃	C₂²	1	1	yes	characteristic
62	D₄×Dic₃	C₂²	1	1	yes	characteristic
63	D₄×Dic₃	C₂²	1	1	yes	characteristic
64	D₄×Dic₃	C₂²	1	2	yes	complemented
65	D₄×Dic₃	C₂²	1	2	yes	complemented
66	D₄×Dic₃	C₂²	1	2	yes	complemented
67	#929	C₂²	1	2	yes	complemented
68	C₄×#67	C₂²	1	1	yes	characteristic
69	C₄×#67	C₂²	1	2	yes	complemented
70	C₄×#67	C₂²	1	1	yes	characteristic, complemented
71	#926	C₂²	1	2	yes	complemented
72	#926	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
74	#924	C₂²	1	1	yes	characteristic
75	#924	C₂²	1	2	yes	complemented
76	#924	C₂²	1	1	yes	characteristic, complemented
77	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
78	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
79	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic
80	C₂×C₄×Dic₃	C₂²	1	2	yes	complemented
81	C₂×C₄×Dic₃	C₂²	1	2	yes	complemented
82	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
83	#898	C₂²	1	2	yes	complemented
84	#892	C₂²	1	1	yes	characteristic, complemented
85	#892	C₂²	1	1	yes	characteristic, complemented
86	#890	C₂²	1	2	yes	complemented
87	#890	C₂²	1	1	yes	characteristic, complemented
88	#889	C₂²	1	2	yes	complemented
89	#889	C₂²	1	2	yes	complemented
90	#888	C₂²	1	1	yes	characteristic, complemented
91	#887	C₂²	1	2	yes	complemented
92	#887	C₂²	1	1	yes	characteristic, complemented
93	#887	C₂²	1	1	yes	characteristic, complemented
94	#886	C₂²	1	2	yes	—
95	#885	C₂²	1	2	yes	complemented
96	#883	C₂²	1	2	yes	complemented
97	#67⋊C₄	C₂²	1	1	yes	characteristic
98	#67⋊C₄	C₂²	1	2	yes	complemented
99	#67⋊C₄	C₂²	1	2	yes	complemented
100	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	#879	C₂²	1	2	yes	complemented
102	#879	C₂²	1	2	yes	complemented
103	#879	C₂²	1	2	yes	complemented
104	#879	C₂²	1	2	yes	complemented
105	#879	C₂²	1	2	yes	complemented
106	#878	C₂²	1	2	yes	—
107	#878	C₂²	1	2	yes	complemented
108	#878	C₂²	1	2	yes	complemented
109	#878	C₂²	1	2	yes	complemented
110	#877	C₂²	1	2	yes	—
111	#877	C₂²	1	1	yes	characteristic
112	#877	C₂²	1	2	yes	—
113	#877	C₂²	1	2	yes	—
114	#877	C₂²	1	2	yes	complemented
115	#877	C₂²	1	2	yes	complemented
116	#877	C₂²	1	2	yes	complemented
117	#877	C₂²	1	2	yes	complemented
118	#877	C₂²	1	2	yes	complemented
119	#877	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
121	#870	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	#555	—	3	1	no	—
126	#554	—	3	1	no	—
127	#553	—	3	2	no	—
128	#552	—	3	2	no	—
129	#552	—	3	1	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	D₃	1	1	yes	characteristic, complemented
136	#533	—	3	1	no	—
137	#529	—	3	1	no	—
138	#529	—	3	2	no	—
139	#529	—	3	2	no	—
140	#529	—	3	1	no	—
141	#525	—	3	2	no	—
142	C₄×#41	—	3	1	no	—
143	C₄×#41	—	3	1	no	—
144	C₄×#41	—	3	1	no	—
145	C₂×C₄×D₄	—	3	1	no	—
146	C₂×#117	—	3	2	no	—
147	C₂⁴×C₃	C₂³	1	2	yes	—
148	C₃×#41	—	2	4	no	—
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	—	2	4	no	—
151	C₂×C₃×D₄	C₂³	1	2	yes	—
152	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×D₄	C₂³	1	2	yes	—
155	C₂×C₃×D₄	C₂³	1	2	yes	—
156	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³	1	2	yes	—
159	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³	1	2	yes	—
161	C₂×#67	C₂³	1	1	yes	characteristic
162	C₂×#67	C₂³	1	2	yes	—
163	C₂×#67	C₂³	1	1	yes	characteristic
164	C₂×#67	C₂³	1	2	yes	—
165	C₂²×Dic₃	—	2	8	no	—
166	C₂²×Dic₃	C₂³	1	2	yes	—
167	C₂²×Dic₃	C₂³	1	2	yes	—
168	C₂²×Dic₃	C₂³	1	2	yes	—
169	C₂²×Dic₃	C₂³	1	2	yes	—
170	C₂²×Dic₃	C₂³	1	1	yes	characteristic
171	C₂²×Dic₃	C₂³	1	2	yes	—
172	C₂²×Dic₃	C₂³	1	2	yes	—
173	C₂²×Dic₃	C₂³	1	1	yes	characteristic
174	C₂²×Dic₃	C₂³	1	2	yes	—
175	C₂²×Dic₃	C₂³	1	1	yes	characteristic
176	C₂²×Dic₃	C₂³	1	1	yes	characteristic
177	#237	—	2	4	no	—
178	#237	—	2	4	no	—
179	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×Dic₆	C₂³	1	1	yes	characteristic
183	C₂×Dic₆	C₂³	1	1	yes	characteristic
184	C₂×Dic₆	C₂³	1	2	yes	—
185	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄²	C₂³	1	1	yes	characteristic
196	#217	C₂³	1	1	yes	characteristic
197	#217	C₂³	1	2	yes	—
198	#217	C₂³	1	2	yes	—
199	#217	C₂³	1	2	yes	—
200	#217	C₂³	1	2	yes	—
201	#217	C₂³	1	1	yes	characteristic
202	#217	C₂³	1	2	yes	—
203	#217	C₂³	1	2	yes	—
204	#217	C₂³	1	2	yes	—
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	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
210	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₃	C₂³	1	2	yes	—
218	C₄⋊Dic₃	C₂³	1	2	yes	—
219	C₄⋊Dic₃	C₂³	1	2	yes	—
220	C₄⋊Dic₃	C₂³	1	2	yes	—
221	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
222	Dic₃⋊C₄	C₂³	1	2	yes	—
223	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
224	Dic₃⋊C₄	C₂³	1	2	yes	—
225	Dic₃⋊C₄	C₂³	1	2	yes	—
226	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
227	Dic₃⋊C₄	C₂³	1	2	yes	—
228	Dic₃⋊C₄	C₂³	1	2	yes	—
229	Dic₃⋊C₄	C₂³	1	2	yes	—
230	Dic₃⋊C₄	C₂³	1	2	yes	—
231	Dic₃⋊C₄	C₂³	1	2	yes	—
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₃⋊C₄	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	2	yes	—
236	C₄×Dic₃	C₂³	1	2	yes	—
237	C₄×Dic₃	C₂³	1	1	yes	characteristic
238	C₄×Dic₃	C₂³	1	1	yes	characteristic
239	C₄×Dic₃	C₂³	1	1	yes	characteristic
240	C₄×Dic₃	C₂³	1	1	yes	characteristic
241	C₄×Dic₃	C₂³	1	1	yes	characteristic
242	C₄×Dic₃	C₂³	1	2	yes	—
243	C₄×Dic₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
249	C₄×Dic₃	C₂³	1	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₂×#41	—	3	1	no	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	C₂×D₃	1	1	yes	characteristic
254	C₂²×D₄	C₂×D₃	1	1	yes	characteristic
255	C₂³×C₄	—	3	2	no	—
256	C₄⋊Q₈	—	3	1	no	—
257	C₄⋊Q₈	—	3	1	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	#125	—	3	2	no	—
265	#125	—	3	2	no	—
266	#125	—	3	1	no	—
267	#125	—	3	2	no	—
268	#125	—	3	1	no	—
269	#124	—	3	1	no	—
270	#124	—	3	2	no	—
271	#124	—	3	2	no	—
272	#124	C₂×D₃	1	1	yes	characteristic
273	#123	—	3	2	no	—
274	#123	—	3	2	no	—
275	#123	—	3	2	no	—
276	#123	—	3	2	no	—
277	#123	—	3	2	no	—
278	#123	—	3	2	no	—
279	#123	—	3	2	no	—
280	#123	C₂×D₃	1	2	yes	—
281	C₂²⋊Q₈	—	3	1	no	—
282	C₂²⋊Q₈	—	3	1	no	—
283	C₂²⋊Q₈	—	3	2	no	—
284	C₂²⋊Q₈	—	3	1	no	—
285	C₂²⋊Q₈	—	3	2	no	—
286	C₂²⋊Q₈	—	3	2	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	2	no	—
289	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
290	#121	—	3	2	no	—
291	#121	—	3	2	no	—
292	#121	—	3	2	no	—
293	#121	—	3	1	no	—
294	#121	C₂×D₃	1	2	yes	—
295	#121	C₂×D₃	1	1	yes	characteristic
296	#120	—	3	2	no	—
297	#120	C₂×D₃	1	2	yes	—
298	C₄×Q₈	—	3	1	no	—
299	C₄×Q₈	—	3	1	no	—
300	C₄×Q₈	—	3	1	no	—
301	C₄×Q₈	—	3	1	no	—
302	C₄×Q₈	—	3	2	no	—
303	C₄×Q₈	—	3	1	no	—
304	C₄×Q₈	—	3	1	no	—
305	C₄×D₄	—	3	1	no	—
306	C₄×D₄	—	3	1	no	—
307	C₄×D₄	—	3	2	no	—
308	C₄×D₄	—	3	1	no	—
309	C₄×D₄	—	3	2	no	—
310	C₄×D₄	—	3	1	no	—
311	C₄×D₄	—	3	2	no	—
312	C₄×D₄	—	3	1	no	—
313	C₄×D₄	—	3	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	1	no	—
317	C₄×D₄	—	3	1	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	2	no	—
323	C₄×D₄	C₂×D₃	1	1	yes	characteristic
324	C₄×D₄	C₂×D₃	1	1	yes	characteristic
325	#117	—	3	2	no	—
326	#117	—	3	1	no	—
327	#117	—	3	1	no	—
328	#117	—	3	1	no	—
329	#117	—	3	1	no	—
330	#117	—	3	2	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	—	3	2	no	—
337	#117	—	3	1	no	—
338	#117	—	3	2	no	—
339	C₂×C₄⋊C₄	—	3	2	no	—
340	C₂×C₄⋊C₄	—	3	2	no	—
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	C₂×D₃	1	2	yes	—
345	C₂×C₄²	—	3	2	no	—
346	C₂×C₄²	—	3	2	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂×C₄²	—	3	1	no	—
349	C₂×C₄²	—	3	1	no	—
350	C₂³×C₃	—	2	4	no	—
351	C₂³×C₃	—	2	4	no	—
352	C₂³×C₃	—	4	2	no	—
353	C₂³×C₃	C₂⁴	1	2	yes	—
354	C₂³×C₃	C₂⁴	1	1	yes	characteristic
355	C₂³×C₃	C₂⁴	1	1	yes	characteristic
356	C₂³×C₃	C₂⁴	1	2	yes	—
357	C₂²×D₃	C₂⁴	1	1	yes	characteristic
358	C₃×Q₈	—	2	2	no	—
359	C₃×D₄	—	2	2	no	—
360	C₃×D₄	—	2	4	no	—
361	C₃×D₄	—	2	4	no	—
362	C₃×D₄	—	2	2	no	—
363	C₃×D₄	—	4	2	no	—
364	C₃×D₄	#41	1	4	yes	complemented
365	C₂×C₃×C₄	—	2	4	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	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	1	yes	characteristic
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	#67	—	2	4	no	—
377	#67	—	2	2	no	—
378	#67	—	2	2	no	—
379	#67	—	4	2	no	—
380	C₂×Dic₃	—	2	4	no	—
381	C₂×Dic₃	—	2	4	no	—
382	C₂×Dic₃	—	2	2	no	—
383	C₂×Dic₃	—	2	4	no	—
384	C₂×Dic₃	—	2	4	no	—
385	C₂×Dic₃	—	2	4	no	—
386	C₂×Dic₃	—	2	4	no	—
387	C₂×Dic₃	—	4	1	no	—
388	C₂×Dic₃	—	4	2	no	—
389	C₂×Dic₃	—	4	1	no	—
390	C₂×Dic₃	#41	1	4	yes	complemented
391	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₃	C₂⁴	1	2	yes	—
395	C₂×Dic₃	C₂⁴	1	2	yes	—
396	C₂×Dic₃	C₂⁴	1	2	yes	—
397	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₃	C₂⁴	1	2	yes	—
400	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	2	2	no	—
404	C₄×D₃	—	4	1	no	—
405	Dic₆	—	2	2	no	—
406	Dic₆	—	2	2	no	—
407	Dic₆	—	4	2	no	—
408	C₂⁴	C₂²×D₃	1	2	yes	—
409	#41	—	2	4	no	—
410	#41	—	6	4	no	—
411	#41	—	6	4	no	—
412	C₂×Q₈	—	3	1	no	—
413	C₂×Q₈	—	3	1	no	—
414	C₂×Q₈	—	3	2	no	—
415	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	3	1	no	—
418	C₂×D₄	—	3	2	no	—
419	C₂×D₄	—	3	1	no	—
420	C₂×D₄	—	3	2	no	—
421	C₂×D₄	C₂²×D₃	1	2	yes	—
422	C₂×D₄	C₂²×D₃	1	2	yes	—
423	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
424	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
425	C₂×D₄	C₂²×D₃	1	2	yes	—
426	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
427	C₂²×C₄	—	3	1	no	—
428	C₂²×C₄	—	3	2	no	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	—	3	1	no	—
431	C₂²×C₄	—	3	2	no	—
432	C₂²×C₄	—	3	2	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	1	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	6	8	no	—
442	C₂²×C₄	C₂²×D₃	1	2	yes	—
443	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
444	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
445	C₂²×C₄	C₂²×D₃	1	2	yes	—
446	C₄⋊C₄	—	3	1	no	—
447	C₄⋊C₄	—	3	1	no	—
448	C₄⋊C₄	—	3	1	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	—	3	2	no	—
455	C₄⋊C₄	—	3	1	no	—
456	C₄⋊C₄	—	3	2	no	—
457	C₄⋊C₄	—	3	1	no	—
458	C₄⋊C₄	—	3	1	no	—
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	—	3	2	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₄⋊C₄	—	3	2	no	—
463	C₄⋊C₄	—	3	2	no	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	2	no	—
466	C₄⋊C₄	—	3	2	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
470	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
471	C₄⋊C₄	C₂²×D₃	1	2	yes	—
472	C₂²⋊C₄	—	3	1	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	—	3	1	no	—
483	C₂²⋊C₄	—	3	2	no	—
484	C₂²⋊C₄	—	3	2	no	—
485	C₂²⋊C₄	—	3	1	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	1	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
490	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
491	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
494	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
495	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
496	C₄²	—	3	1	no	—
497	C₄²	—	3	1	no	—
498	C₄²	—	3	1	no	—
499	C₄²	—	3	2	no	—
500	C₄²	—	3	2	no	—
501	C₄²	—	3	1	no	—
502	C₄²	—	3	2	no	—
503	C₄²	—	3	2	no	—
504	C₄²	—	3	2	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	3	2	no	—
508	C₄²	—	3	1	no	—
509	C₄²	—	3	1	no	—
510	C₄²	—	3	1	no	—
511	C₄²	C₂²×D₃	1	1	yes	characteristic
512	C₂²×C₃	—	2	2	no	—
513	C₂²×C₃	—	2	1	no	—
514	C₂²×C₃	—	2	2	no	—
515	C₂²×C₃	—	2	1	no	—
516	C₂²×C₃	—	2	2	no	—
517	C₂²×C₃	—	2	1	no	—
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	2	2	no	—
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	2	no	—
522	C₂²×C₃	—	4	8	no	—
523	C₂²×C₃	C₂×#41	1	4	yes	—
524	C₂²×C₃	C₂×#41	1	2	yes	—
525	C₂²×C₃	C₂⁵	1	1	yes	characteristic
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	2	1	no	—
528	C₂×D₃	—	2	1	no	—
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	2	no	—
533	C₃×C₄	—	2	2	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	C₂×#41	1	2	yes	—
536	Dic₃	—	2	2	no	—
537	Dic₃	—	2	1	no	—
538	Dic₃	—	2	1	no	—
539	Dic₃	—	2	2	no	—
540	Dic₃	—	2	2	no	—
541	Dic₃	—	2	1	no	—
542	Dic₃	—	2	2	no	—
543	Dic₃	—	2	1	no	—
544	Dic₃	—	2	1	no	—
545	Dic₃	C₂×#41	1	2	yes	—
546	Dic₃	C₂×#41	1	2	yes	—
547	C₂³	—	2	4	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	3	1	no	—
550	C₂³	—	4	2	no	—
551	C₂³	C₂³×D₃	1	2	yes	—
552	C₂³	C₂³×D₃	1	1	yes	characteristic
553	C₂³	C₂³×D₃	1	2	yes	—
554	C₂³	C₂³×D₃	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	6	2	no	—
557	Q₈	—	6	2	no	—
558	Q₈	—	12	2	no	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	6	2	no	—
565	D₄	—	6	4	no	—
566	D₄	—	6	2	no	—
567	D₄	—	12	2	no	—
568	D₄	#237	1	4	yes	complemented
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	3	4	no	—
573	C₂×C₄	—	3	1	no	—
574	C₂×C₄	—	3	1	no	—
575	C₂×C₄	—	3	1	no	—
576	C₂×C₄	—	3	2	no	—
577	C₂×C₄	—	3	1	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	1	no	—
580	C₂×C₄	—	3	2	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	2	no	—
583	C₂×C₄	—	3	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	6	2	no	—
586	C₂×C₄	—	6	4	no	—
587	C₂×C₄	—	6	4	no	—
588	C₂×C₄	—	6	4	no	—
589	C₂×C₄	—	6	4	no	—
590	C₂×C₄	—	6	2	no	—
591	C₂×C₄	—	6	4	no	—
592	C₂×C₄	—	6	4	no	—
593	C₂×C₄	—	6	2	no	—
594	C₂×C₄	—	12	1	no	—
595	C₂×C₄	—	12	1	no	—
596	C₂×C₄	—	12	2	no	—
597	C₂×C₄	—	12	1	no	—
598	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₃	1	2	yes	—
601	C₂×C₄	C₂³×D₃	1	2	yes	—
602	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
603	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
605	C₂×C₃	—	2	2	no	—
606	C₂×C₃	—	2	4	no	—
607	C₂×C₃	—	4	1	no	—
608	C₂×C₃	—	4	2	no	—
609	C₂×C₃	C₂²×#41	1	1	yes	characteristic
610	C₂×C₃	C₂²×#41	1	1	yes	characteristic
611	C₂×C₃	#585	1	1	yes	characteristic
612	D₃	—	4	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	4	8	no	—
624	C₂²	—	6	1	no	—
625	C₂²	—	6	1	no	—
626	C₂²	—	6	1	no	—
627	C₂²	C₂×#237	1	4	yes	—
628	C₂²	D₃×#41	1	2	yes	—
629	C₂²	C₂⁴×D₃	1	1	yes	characteristic
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	3	2	no	—
637	C₄	—	3	2	no	—
638	C₄	—	6	1	no	—
639	C₄	—	6	2	no	—
640	C₄	—	6	2	no	—
641	C₄	—	6	2	no	—
642	C₄	—	6	1	no	—
643	C₄	—	6	1	no	—
644	C₄	—	6	1	no	—
645	C₄	—	6	2	no	—
646	C₄	—	6	1	no	—
647	C₄	C₂×#237	1	2	yes	—
648	C₃	#3475	1	1	yes	characteristic, complemented, Sylow
649	C₂	—	2	2	no	—
650	C₂	—	2	4	no	—
651	C₂	—	4	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	12	1	no	—
654	C₂	C₂²×#237	1	1	yes	characteristic
655	C₂	C₂×D₃×#41	1	1	yes	characteristic
656	C₂	#5966	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#546	C₂
hypercenter	#546	D₃
hypocenter	C₃	#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₃×#546	C₂	semidirect
2. Dic₃×#41	C₂	semidirect
3. #5824	C₂	semidirect
4. #5806	C₂	semidirect
5. C₂×D₄×Dic₃	C₂	semidirect
6. #5680	C₂	semidirect
7. #5671	C₂	semidirect
8. #5650	C₂	semidirect
9. #5649	C₂	semidirect
10. #5642	C₂	semidirect
11. #5622	C₂	semidirect
12. #5616	C₂	semidirect
13. #5601	C₂	semidirect
14. #5600	C₂	semidirect
15. #5600	C₂	semidirect
16. #5587	C₂	semidirect
17. #5586	C₂	semidirect
18. #5541	C₂	semidirect
19. #5539	C₂	semidirect
20. C₄×#237	C₂	semidirect
21. C₄×#237	C₂	semidirect
22. #5495	C₂	semidirect
23. C₂×#877	C₂	semidirect
42. #946	C₂²	semidirect
43. Q₈×Dic₃	C₂²	semidirect
44. Q₈×Dic₃	C₂²	semidirect
45. #944	C₂²	semidirect
47. #939	C₂²	semidirect
48. #939	C₂²	semidirect
51. #936	C₂²	semidirect
54. #935	C₂²	semidirect
55. #935	C₂²	semidirect
64. D₄×Dic₃	C₂²	semidirect
65. D₄×Dic₃	C₂²	semidirect
66. D₄×Dic₃	C₂²	semidirect
67. #929	C₂²	semidirect
69. C₄×#67	C₂²	semidirect
70. C₄×#67	C₂²	semidirect
71. #926	C₂²	semidirect
72. #926	C₂²	semidirect
75. #924	C₂²	semidirect
76. #924	C₂²	semidirect
77. C₂×Dic₃⋊C₄	C₂²	semidirect
78. C₂×Dic₃⋊C₄	C₂²	semidirect
80. C₂×C₄×Dic₃	C₂²	semidirect
81. C₂×C₄×Dic₃	C₂²	semidirect
82. C₂×C₄×Dic₃	C₂²	semidirect
83. #898	C₂²	semidirect
84. #892	C₂²	semidirect
85. #892	C₂²	semidirect
86. #890	C₂²	semidirect
87. #890	C₂²	semidirect
88. #889	C₂²	semidirect
89. #889	C₂²	semidirect
90. #888	C₂²	semidirect
91. #887	C₂²	semidirect
92. #887	C₂²	semidirect
93. #887	C₂²	semidirect
95. #885	C₂²	semidirect
96. #883	C₂²	semidirect
98. #67⋊C₄	C₂²	semidirect
99. #67⋊C₄	C₂²	semidirect
100. #67⋊C₄	C₂²	semidirect
101. #879	C₂²	semidirect
102. #879	C₂²	semidirect
103. #879	C₂²	semidirect
104. #879	C₂²	semidirect
105. #879	C₂²	semidirect
107. #878	C₂²	semidirect
108. #878	C₂²	semidirect
109. #878	C₂²	semidirect
114. #877	C₂²	semidirect
115. #877	C₂²	semidirect
116. #877	C₂²	semidirect
117. #877	C₂²	semidirect
118. #877	C₂²	semidirect
119. #877	C₂²	semidirect
120. C₄²×D₃	C₂²	semidirect
121. #870	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
135. #546	D₃	semidirect
364. C₃×D₄	#41	semidirect
390. C₂×Dic₃	#41	semidirect
568. D₄	#237	semidirect
648. C₃	#3475	semidirect

Maximal subgroups

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

subgroup	index
C₃×#546	2
Dic₃×#41	2
#5824	2
#5806	2
C₂×D₄×Dic₃	2
#5680	2
#5671	2
#5650	2
#5649	2
#5642	2
#5622	2
#5616	2
#5601	2
#5600	2
#5587	2
#5586	2
#5541	2
#5539	2
C₄×#237	2
#5495	2
C₂×#877	2
#3475	3