Subgroups — #86641

Order 384.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 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	#5827	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	#5682	C₂	1	1	yes	maximal, characteristic, complemented
7	#5671	C₂	1	1	yes	maximal, characteristic, complemented
8	#5665	C₂	1	2	yes	maximal, complemented
9	#5650	C₂	1	2	yes	maximal, complemented
10	#5635	C₂	1	1	yes	maximal, characteristic, complemented
11	#5622	C₂	1	1	yes	maximal, characteristic, complemented
12	#5611	C₂	1	1	yes	maximal, characteristic, complemented
13	#5603	C₂	1	1	yes	maximal, characteristic, complemented
14	#5602	C₂	1	2	yes	maximal, complemented
15	#5598	C₂	1	2	yes	maximal, complemented
16	#5587	C₂	1	2	yes	maximal, complemented
17	#5586	C₂	1	2	yes	maximal, complemented
18	#5546	C₂	1	1	yes	maximal, characteristic, complemented
19	#5543	C₂	1	1	yes	maximal, characteristic, complemented
20	#5538	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
22	#5495	C₂	1	2	yes	maximal, complemented
23	C₂×#878	C₂	1	2	yes	maximal, complemented
24	#3520	—	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	2	yes	complemented
30	C₂²×Dic₆	C₂²	1	2	yes	complemented
31	C₃×#124	C₂²	1	1	yes	characteristic
32	C₃×#123	C₂²	1	2	yes	—
33	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×#121	C₂²	1	2	yes	—
35	C₃×#121	C₂²	1	1	yes	characteristic
36	C₃×#120	C₂²	1	2	yes	—
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
40	#953	C₂²	1	2	yes	—
41	C₂×#217	C₂²	1	2	yes	—
42	C₂×#217	C₂²	1	2	yes	—
43	#946	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
46	#944	C₂²	1	1	yes	characteristic, complemented
47	#939	C₂²	1	2	yes	—
48	#939	C₂²	1	1	yes	characteristic
49	#939	C₂²	1	2	yes	complemented
50	#938	C₂²	1	1	yes	characteristic
51	#936	C₂²	1	1	yes	characteristic
52	#936	C₂²	1	2	yes	complemented
53	#935	C₂²	1	2	yes	—
54	#935	C₂²	1	1	yes	characteristic
55	#935	C₂²	1	2	yes	complemented
56	#935	C₂²	1	2	yes	complemented
57	#935	C₂²	1	2	yes	complemented
58	D₄×Dic₃	C₂²	1	2	yes	—
59	D₄×Dic₃	C₂²	1	2	yes	—
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	1	yes	characteristic
65	D₄×Dic₃	C₂²	1	2	yes	—
66	D₄×Dic₃	C₂²	1	2	yes	complemented
67	D₄×Dic₃	C₂²	1	2	yes	complemented
68	#929	C₂²	1	2	yes	complemented
69	C₄×#67	C₂²	1	1	yes	characteristic
70	C₄×#67	C₂²	1	2	yes	complemented
71	C₄×#67	C₂²	1	1	yes	characteristic, complemented
72	#926	C₂²	1	2	yes	complemented
73	#926	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
75	C₂×C₄⋊Dic₃	C₂²	1	2	yes	complemented
76	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
77	#924	C₂²	1	1	yes	characteristic
78	#924	C₂²	1	2	yes	complemented
79	#924	C₂²	1	1	yes	characteristic, complemented
80	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
81	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
82	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic
83	#898	C₂²	1	1	yes	characteristic, complemented
84	#897	C₂²	1	2	yes	complemented
85	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
86	#890	C₂²	1	2	yes	complemented
87	#889	C₂²	1	2	yes	complemented
88	#889	C₂²	1	1	yes	characteristic, complemented
89	#889	C₂²	1	2	yes	complemented
90	#888	C₂²	1	1	yes	characteristic, complemented
91	#888	C₂²	1	1	yes	characteristic, complemented
92	#887	C₂²	1	2	yes	complemented
93	#887	C₂²	1	1	yes	characteristic, complemented
94	#886	C₂²	1	1	yes	characteristic
95	#886	C₂²	1	2	yes	complemented
96	#885	C₂²	1	2	yes	complemented
97	#885	C₂²	1	1	yes	characteristic, complemented
98	#883	C₂²	1	2	yes	complemented
99	#67⋊C₄	C₂²	1	2	yes	—
100	#67⋊C₄	C₂²	1	2	yes	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	1	yes	characteristic, complemented
106	#878	C₂²	1	2	yes	—
107	#878	C₂²	1	1	yes	characteristic
108	#878	C₂²	1	2	yes	—
109	#878	C₂²	1	2	yes	—
110	#878	C₂²	1	2	yes	complemented
111	#878	C₂²	1	2	yes	complemented
112	#878	C₂²	1	2	yes	complemented
113	#878	C₂²	1	2	yes	complemented
114	#878	C₂²	1	2	yes	complemented
115	#878	C₂²	1	2	yes	complemented
116	#878	C₂²	1	2	yes	complemented
117	#877	C₂²	1	2	yes	—
118	#877	C₂²	1	2	yes	complemented
119	#877	C₂²	1	2	yes	complemented
120	#872	C₂²	1	1	yes	characteristic, complemented
121	#869	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	#554	—	3	1	no	—
126	#554	—	3	1	no	—
127	#552	—	3	2	no	—
128	#551	—	3	2	no	—
129	#551	—	3	2	no	—
130	D₄×Q₈	—	3	1	no	—
131	#548	—	3	2	no	—
132	#547	—	3	1	no	—
133	#547	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	D₃	1	1	yes	characteristic, complemented
136	#542	—	3	1	no	—
137	#542	—	3	1	no	—
138	#539	—	3	2	no	—
139	#539	—	3	2	no	—
140	#533	—	3	1	no	—
141	#529	—	3	1	no	—
142	#525	—	3	2	no	—
143	C₂×C₂²⋊Q₈	—	3	2	no	—
144	#520	—	3	1	no	—
145	#520	—	3	1	no	—
146	C₂×C₄×D₄	—	3	1	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	1	yes	characteristic
152	C₂×C₃×D₄	C₂³	1	2	yes	—
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	—	4	4	no	—
166	C₂²×Dic₃	C₂³	1	1	yes	characteristic
167	C₂²×Dic₃	C₂³	1	2	yes	—
168	C₂²×Dic₃	C₂³	1	2	yes	—
169	C₂²×Dic₃	C₂³	1	1	yes	characteristic
170	C₂²×Dic₃	C₂³	1	2	yes	—
171	C₂²×Dic₃	C₂³	1	2	yes	—
172	C₂²×Dic₃	C₂³	1	2	yes	—
173	C₂²×Dic₃	C₂³	1	2	yes	—
174	C₂²×Dic₃	C₂³	1	2	yes	—
175	C₂²×Dic₃	C₂³	1	2	yes	—
176	#237	—	2	4	no	—
177	#237	—	4	4	no	—
178	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
179	C₂×C₄×D₃	C₂³	1	2	yes	—
180	C₂×Dic₆	—	4	4	no	—
181	C₂×Dic₆	C₂³	1	1	yes	characteristic
182	C₂×Dic₆	C₂³	1	1	yes	characteristic
183	C₂×Dic₆	C₂³	1	2	yes	—
184	C₂×Dic₆	C₂³	1	2	yes	—
185	C₂×Dic₆	C₂³	1	2	yes	—
186	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃×C₄⋊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	1	yes	characteristic
193	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₄²	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	1	yes	characteristic
201	#217	C₂³	1	2	yes	—
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	1	yes	characteristic
209	#217	C₂³	1	1	yes	characteristic
210	#217	C₂³	1	1	yes	characteristic
211	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
212	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₃	C₂³	1	2	yes	—
219	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₃	C₂³	1	2	yes	—
223	C₄⋊Dic₃	C₂³	1	2	yes	—
224	C₄⋊Dic₃	C₂³	1	2	yes	—
225	C₄⋊Dic₃	C₂³	1	2	yes	—
226	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
228	Dic₃⋊C₄	C₂³	1	2	yes	—
229	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
230	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
231	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
243	C₄×Dic₃	C₂³	1	2	yes	—
244	C₄×Dic₃	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	2	yes	—
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₄×Dic₃	C₂³	1	2	yes	—
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₄×Dic₃	C₂³	1	1	yes	characteristic
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	2	no	—
254	C₂×#41	C₂×D₃	1	1	yes	characteristic
255	C₂²×Q₈	—	3	2	no	—
256	C₂²×D₄	C₂×D₃	1	1	yes	characteristic
257	C₂³×C₄	—	3	2	no	—
258	C₄⋊Q₈	—	3	1	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	C₄⋊Q₈	—	3	1	no	—
261	C₄⋊Q₈	—	3	1	no	—
262	#126	—	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	#125	—	3	1	no	—
269	#125	—	3	2	no	—
270	#125	—	3	2	no	—
271	#125	—	3	2	no	—
272	#124	—	3	1	no	—
273	#124	—	3	2	no	—
274	#124	—	3	1	no	—
275	#124	—	3	2	no	—
276	#124	C₂×D₃	1	1	yes	characteristic
277	#123	—	3	2	no	—
278	#123	—	3	1	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	1	no	—
285	#123	—	3	2	no	—
286	#123	C₂×D₃	1	2	yes	—
287	C₂²⋊Q₈	—	3	1	no	—
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	—	3	2	no	—
290	C₂²⋊Q₈	—	3	1	no	—
291	C₂²⋊Q₈	—	3	2	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	—	3	2	no	—
297	C₂²⋊Q₈	—	3	2	no	—
298	C₂²⋊Q₈	—	3	2	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₂²⋊Q₈	—	3	2	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₂²⋊Q₈	—	3	2	no	—
303	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
304	#121	—	3	1	no	—
305	#121	—	3	2	no	—
306	#121	—	3	2	no	—
307	#121	—	3	1	no	—
308	#121	C₂×D₃	1	2	yes	—
309	#121	C₂×D₃	1	1	yes	characteristic
310	#120	—	3	2	no	—
311	#120	C₂×D₃	1	2	yes	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	—	3	1	no	—
314	C₄×Q₈	—	3	1	no	—
315	C₄×Q₈	—	3	2	no	—
316	C₄×Q₈	—	3	1	no	—
317	C₄×Q₈	—	3	1	no	—
318	C₄×D₄	—	3	1	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	2	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	1	no	—
326	C₄×D₄	—	3	2	no	—
327	C₄×D₄	—	3	2	no	—
328	C₄×D₄	—	3	2	no	—
329	C₄×D₄	—	3	1	no	—
330	C₄×D₄	—	3	1	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	C₂×D₃	1	1	yes	characteristic
334	C₄×D₄	C₂×D₃	1	1	yes	characteristic
335	#117	—	3	1	no	—
336	#117	—	3	2	no	—
337	#117	—	3	2	no	—
338	#117	—	3	2	no	—
339	#117	—	3	2	no	—
340	#117	—	3	1	no	—
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	2	no	—
343	C₂×C₄⋊C₄	—	3	2	no	—
344	C₂×C₄⋊C₄	—	3	1	no	—
345	C₂×C₄⋊C₄	—	3	2	no	—
346	C₂×C₄⋊C₄	—	3	1	no	—
347	C₂×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	C₂×D₃	1	2	yes	—
350	C₂×C₄²	—	3	1	no	—
351	C₂³×C₃	—	2	4	no	—
352	C₂³×C₃	—	2	4	no	—
353	C₂³×C₃	—	4	2	no	—
354	C₂³×C₃	C₂⁴	1	2	yes	—
355	C₂³×C₃	C₂⁴	1	1	yes	characteristic
356	C₂³×C₃	C₂⁴	1	2	yes	—
357	C₂³×C₃	C₂⁴	1	1	yes	characteristic
358	C₂²×D₃	C₂⁴	1	1	yes	characteristic
359	C₃×Q₈	—	2	2	no	—
360	C₃×D₄	—	2	4	no	—
361	C₃×D₄	—	2	4	no	—
362	C₃×D₄	—	2	2	no	—
363	C₃×D₄	—	2	2	no	—
364	C₃×D₄	—	4	2	no	—
365	C₃×D₄	#41	1	4	yes	complemented
366	C₂×C₃×C₄	—	2	4	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	4	2	no	—
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	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	#67	—	2	4	no	—
378	#67	—	2	2	no	—
379	#67	—	2	2	no	—
380	#67	—	4	2	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	2	no	—
386	C₂×Dic₃	—	4	2	no	—
387	C₂×Dic₃	—	4	2	no	—
388	C₂×Dic₃	—	4	2	no	—
389	C₂×Dic₃	—	4	2	no	—
390	C₂×Dic₃	—	4	2	no	—
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	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₃	C₂⁴	1	2	yes	—
397	C₂×Dic₃	C₂⁴	1	2	yes	—
398	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₃	C₂⁴	1	2	yes	—
401	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	4	2	no	—
404	Dic₆	—	2	2	no	—
405	Dic₆	—	2	2	no	—
406	Dic₆	—	2	4	no	—
407	Dic₆	—	4	2	no	—
408	Dic₆	—	4	2	no	—
409	C₂⁴	C₂²×D₃	1	2	yes	—
410	#41	—	2	4	no	—
411	#41	—	6	4	no	—
412	#41	—	12	4	no	—
413	C₂×Q₈	—	3	1	no	—
414	C₂×Q₈	—	3	1	no	—
415	C₂×Q₈	—	3	2	no	—
416	C₂×Q₈	—	3	2	no	—
417	C₂×Q₈	—	3	2	no	—
418	C₂×Q₈	—	12	4	no	—
419	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	3	1	no	—
422	C₂×D₄	—	3	2	no	—
423	C₂×D₄	—	3	1	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
426	C₂×D₄	C₂²×D₃	1	2	yes	—
427	C₂×D₄	C₂²×D₃	1	2	yes	—
428	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₃	1	2	yes	—
430	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	—	3	2	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	2	no	—
438	C₂²×C₄	—	3	2	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	2	no	—
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	12	4	no	—
444	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
445	C₂²×C₄	C₂²×D₃	1	2	yes	—
446	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
447	C₂²×C₄	C₂²×D₃	1	2	yes	—
448	C₄⋊C₄	—	3	1	no	—
449	C₄⋊C₄	—	3	1	no	—
450	C₄⋊C₄	—	3	1	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	1	no	—
454	C₄⋊C₄	—	3	2	no	—
455	C₄⋊C₄	—	3	2	no	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	1	no	—
458	C₄⋊C₄	—	3	2	no	—
459	C₄⋊C₄	—	3	2	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	1	no	—
466	C₄⋊C₄	—	3	1	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	2	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	1	no	—
474	C₄⋊C₄	—	3	1	no	—
475	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₃	1	2	yes	—
478	C₂²⋊C₄	—	3	1	no	—
479	C₂²⋊C₄	—	3	2	no	—
480	C₂²⋊C₄	—	3	2	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	2	no	—
483	C₂²⋊C₄	—	3	2	no	—
484	C₂²⋊C₄	—	3	2	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	1	no	—
488	C₂²⋊C₄	—	3	1	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	1	no	—
492	C₂²⋊C₄	—	3	1	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	1	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	1	no	—
497	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
498	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
503	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	3	1	no	—
508	C₄²	—	3	2	no	—
509	C₄²	—	3	2	no	—
510	C₄²	—	3	2	no	—
511	C₄²	—	3	2	no	—
512	C₄²	—	3	1	no	—
513	C₄²	C₂²×D₃	1	1	yes	characteristic
514	C₂²×C₃	—	2	1	no	—
515	C₂²×C₃	—	2	2	no	—
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	—	2	2	no	—
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	2	2	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	—	4	8	no	—
525	C₂²×C₃	C₂×#41	1	4	yes	—
526	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
527	C₂²×C₃	C₂⁵	1	1	yes	characteristic
528	C₂×D₃	—	2	1	no	—
529	C₂×D₃	—	2	1	no	—
530	C₂×D₃	—	2	1	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	2	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	2	no	—
536	C₃×C₄	—	2	1	no	—
537	C₃×C₄	C₂×#41	1	2	yes	—
538	Dic₃	—	2	2	no	—
539	Dic₃	—	2	1	no	—
540	Dic₃	—	2	1	no	—
541	Dic₃	—	2	2	no	—
542	Dic₃	—	2	2	no	—
543	Dic₃	—	2	2	no	—
544	Dic₃	—	2	1	no	—
545	Dic₃	—	2	1	no	—
546	Dic₃	—	2	1	no	—
547	Dic₃	—	2	1	no	—
548	Dic₃	H(5,𝔽₂)	1	2	yes	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	3	1	no	—
552	C₂³	—	4	2	no	—
553	C₂³	C₂³×D₃	1	2	yes	—
554	C₂³	C₂³×D₃	1	1	yes	characteristic
555	C₂³	C₂³×D₃	1	2	yes	—
556	C₂³	C₂³×D₃	1	1	yes	characteristic
557	Q₈	—	2	2	no	—
558	Q₈	—	6	2	no	—
559	Q₈	—	6	4	no	—
560	Q₈	—	6	2	no	—
561	Q₈	—	12	2	no	—
562	Q₈	—	12	2	no	—
563	D₄	—	2	4	no	—
564	D₄	—	2	4	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	2	no	—
567	D₄	—	4	2	no	—
568	D₄	—	6	2	no	—
569	D₄	—	6	4	no	—
570	D₄	—	6	2	no	—
571	D₄	—	12	2	no	—
572	D₄	#237	1	4	yes	complemented
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	3	1	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	1	no	—
584	C₂×C₄	—	3	2	no	—
585	C₂×C₄	—	3	1	no	—
586	C₂×C₄	—	3	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	6	2	no	—
589	C₂×C₄	—	6	4	no	—
590	C₂×C₄	—	6	4	no	—
591	C₂×C₄	—	6	4	no	—
592	C₂×C₄	—	6	2	no	—
593	C₂×C₄	—	6	2	no	—
594	C₂×C₄	—	12	2	no	—
595	C₂×C₄	—	12	2	no	—
596	C₂×C₄	—	12	2	no	—
597	C₂×C₄	—	12	2	no	—
598	C₂×C₄	—	12	2	no	—
599	C₂×C₄	—	12	2	no	—
600	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₃	1	2	yes	—
602	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
603	C₂×C₄	C₂³×D₃	1	2	yes	—
604	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
607	C₂×C₃	—	2	2	no	—
608	C₂×C₃	—	2	4	no	—
609	C₂×C₃	—	4	1	no	—
610	C₂×C₃	—	4	2	no	—
611	C₂×C₃	C₂²×#41	1	1	yes	characteristic
612	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
613	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
614	D₃	—	4	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	4	8	no	—
626	C₂²	—	6	1	no	—
627	C₂²	—	6	1	no	—
628	C₂²	—	6	1	no	—
629	C₂²	C₂×#237	1	4	yes	—
630	C₂²	#1010	1	2	yes	—
631	C₂²	C₂⁴×D₃	1	1	yes	characteristic
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	3	2	no	—
639	C₄	—	6	1	no	—
640	C₄	—	6	2	no	—
641	C₄	—	6	1	no	—
642	C₄	—	6	1	no	—
643	C₄	—	6	1	no	—
644	C₄	—	6	1	no	—
645	C₄	—	6	2	no	—
646	C₄	—	6	2	no	—
647	C₄	—	6	2	no	—
648	C₄	—	6	1	no	—
649	C₄	C₂×#237	1	2	yes	—
650	C₃	#3520	1	1	yes	characteristic, complemented, Sylow
651	C₂	—	2	2	no	—
652	C₂	—	2	4	no	—
653	C₂	—	4	2	no	—
654	C₂	—	4	1	no	—
655	C₂	—	12	1	no	—
656	C₂	C₂²×#237	1	1	yes	characteristic
657	C₂	C₂×#1010	1	1	yes	characteristic
658	C₂	D₃×H(5,𝔽₂)	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	#3520
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. #5827	C₂	semidirect
3. #5824	C₂	semidirect
4. #5806	C₂	semidirect
5. C₂×D₄×Dic₃	C₂	semidirect
6. #5682	C₂	semidirect
7. #5671	C₂	semidirect
8. #5665	C₂	semidirect
9. #5650	C₂	semidirect
10. #5635	C₂	semidirect
11. #5622	C₂	semidirect
12. #5611	C₂	semidirect
13. #5603	C₂	semidirect
14. #5602	C₂	semidirect
15. #5598	C₂	semidirect
16. #5587	C₂	semidirect
17. #5586	C₂	semidirect
18. #5546	C₂	semidirect
19. #5543	C₂	semidirect
20. #5538	C₂	semidirect
21. D₄×Dic₆	C₂	semidirect
22. #5495	C₂	semidirect
23. C₂×#878	C₂	semidirect
29. C₂×#237	C₂²	semidirect
30. C₂²×Dic₆	C₂²	semidirect
43. #946	C₂²	semidirect
44. Q₈×Dic₃	C₂²	semidirect
45. Q₈×Dic₃	C₂²	semidirect
46. #944	C₂²	semidirect
49. #939	C₂²	semidirect
52. #936	C₂²	semidirect
55. #935	C₂²	semidirect
56. #935	C₂²	semidirect
57. #935	C₂²	semidirect
66. D₄×Dic₃	C₂²	semidirect
67. D₄×Dic₃	C₂²	semidirect
68. #929	C₂²	semidirect
70. C₄×#67	C₂²	semidirect
71. C₄×#67	C₂²	semidirect
72. #926	C₂²	semidirect
73. #926	C₂²	semidirect
75. C₂×C₄⋊Dic₃	C₂²	semidirect
76. C₂×C₄⋊Dic₃	C₂²	semidirect
78. #924	C₂²	semidirect
79. #924	C₂²	semidirect
80. C₂×Dic₃⋊C₄	C₂²	semidirect
81. C₂×Dic₃⋊C₄	C₂²	semidirect
83. #898	C₂²	semidirect
84. #897	C₂²	semidirect
85. D₃×C₄⋊C₄	C₂²	semidirect
86. #890	C₂²	semidirect
87. #889	C₂²	semidirect
88. #889	C₂²	semidirect
89. #889	C₂²	semidirect
90. #888	C₂²	semidirect
91. #888	C₂²	semidirect
92. #887	C₂²	semidirect
93. #887	C₂²	semidirect
95. #886	C₂²	semidirect
96. #885	C₂²	semidirect
97. #885	C₂²	semidirect
98. #883	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
110. #878	C₂²	semidirect
111. #878	C₂²	semidirect
112. #878	C₂²	semidirect
113. #878	C₂²	semidirect
114. #878	C₂²	semidirect
115. #878	C₂²	semidirect
116. #878	C₂²	semidirect
118. #877	C₂²	semidirect
119. #877	C₂²	semidirect
120. #872	C₂²	semidirect
121. #869	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
135. #546	D₃	semidirect
365. C₃×D₄	#41	semidirect
572. D₄	#237	semidirect
650. C₃	#3520	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
#5827	2
#5824	2
#5806	2
C₂×D₄×Dic₃	2
#5682	2
#5671	2
#5665	2
#5650	2
#5635	2
#5622	2
#5611	2
#5603	2
#5602	2
#5598	2
#5587	2
#5586	2
#5546	2
#5543	2
#5538	2
D₄×Dic₆	2
#5495	2
C₂×#878	2
#3520	3