Subgroups — D₃×#542 #86549

Order 384.

1132 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#5733	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#5710	C₂	1	2	yes	maximal, complemented
5	D₃×#126	C₂	1	2	yes	maximal, complemented
6	#5682	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×#124	C₂	1	2	yes	maximal, complemented
8	D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
9	#5669	C₂	1	2	yes	maximal, complemented
10	#5662	C₂	1	2	yes	maximal, complemented
11	D₃×#123	C₂	1	2	yes	maximal, complemented
12	#5643	C₂	1	1	yes	maximal, characteristic, complemented
13	#5640	C₂	1	2	yes	maximal, complemented
14	D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	D₃×#121	C₂	1	1	yes	maximal, characteristic
17	#5603	C₂	1	1	yes	maximal, characteristic, complemented
18	#5582	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
20	#5561	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
22	#5534	C₂	1	1	yes	maximal, characteristic, complemented
23	D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#542	—	3	1	no	maximal, Sylow
25	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic
26	C₂×D₃×Q₈	C₂²	1	2	yes	—
27	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂×D₃×D₄	C₂²	1	2	yes	—
29	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₃	C₂²	1	2	yes	—
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×#126	C₂²	1	2	yes	complemented
33	C₃×#124	C₂²	1	2	yes	complemented
34	C₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃×#123	C₂²	1	2	yes	complemented
36	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×#121	C₂²	1	1	yes	characteristic
39	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×#117	C₂²	1	1	yes	characteristic, complemented
42	#947	C₂²	1	2	yes	complemented
43	#947	C₂²	1	1	yes	characteristic, complemented
44	#946	C₂²	1	2	yes	complemented
45	#946	C₂²	1	1	yes	characteristic, complemented
46	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
47	#944	C₂²	1	2	yes	complemented
48	#939	C₂²	1	2	yes	—
49	#938	C₂²	1	1	yes	characteristic
50	#936	C₂²	1	2	yes	complemented
51	#936	C₂²	1	1	yes	characteristic, complemented
52	#935	C₂²	1	2	yes	complemented
53	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
54	#930	C₂²	1	1	yes	characteristic
55	#929	C₂²	1	2	yes	complemented
56	C₄×#67	C₂²	1	2	yes	complemented
57	#926	C₂²	1	1	yes	characteristic, complemented
58	#924	C₂²	1	2	yes	complemented
59	#924	C₂²	1	1	yes	characteristic, complemented
60	#898	C₂²	1	2	yes	complemented
61	#898	C₂²	1	2	yes	complemented
62	#898	C₂²	1	2	yes	complemented
63	#897	C₂²	1	2	yes	complemented
64	#897	C₂²	1	1	yes	characteristic, complemented
65	#896	C₂²	1	2	yes	complemented
66	#896	C₂²	1	2	yes	complemented
67	#896	C₂²	1	2	yes	complemented
68	#895	C₂²	1	1	yes	characteristic
69	#894	C₂²	1	2	yes	complemented
70	#894	C₂²	1	2	yes	complemented
71	#893	C₂²	1	1	yes	characteristic, complemented
72	#892	C₂²	1	1	yes	characteristic, complemented
73	#892	C₂²	1	1	yes	characteristic, complemented
74	D₃×C₄⋊C₄	C₂²	1	2	yes	—
75	D₃×C₄⋊C₄	C₂²	1	2	yes	—
76	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	D₃×C₄⋊C₄	C₂²	1	2	yes	—
78	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	#888	C₂²	1	1	yes	characteristic, complemented
82	#888	C₂²	1	2	yes	complemented
83	#888	C₂²	1	1	yes	characteristic, complemented
84	#887	C₂²	1	2	yes	complemented
85	#887	C₂²	1	1	yes	characteristic, complemented
86	#886	C₂²	1	2	yes	complemented
87	#885	C₂²	1	2	yes	complemented
88	#885	C₂²	1	2	yes	complemented
89	#885	C₂²	1	2	yes	complemented
90	#885	C₂²	1	2	yes	complemented
91	#885	C₂²	1	2	yes	complemented
92	#885	C₂²	1	2	yes	complemented
93	#884	C₂²	1	2	yes	—
94	#883	C₂²	1	2	yes	complemented
95	#883	C₂²	1	2	yes	complemented
96	#67⋊C₄	C₂²	1	2	yes	complemented
97	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
98	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
101	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	#879	C₂²	1	2	yes	complemented
105	#879	C₂²	1	2	yes	complemented
106	#879	C₂²	1	2	yes	complemented
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	1	yes	characteristic, complemented
111	#877	C₂²	1	1	yes	characteristic, complemented
112	#876	C₂²	1	2	yes	complemented
113	#875	C₂²	1	2	yes	complemented
114	#875	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
116	#872	C₂²	1	1	yes	characteristic, complemented
117	#872	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₃	C₂²	1	2	yes	—
119	C₄²×D₃	C₂²	1	1	yes	characteristic
120	C₄²×D₃	C₂²	1	1	yes	characteristic
121	#869	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂²	1	2	yes	complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#542	—	3	1	no	—
125	#542	—	3	2	no	—
126	#542	—	3	2	no	—
127	#542	—	3	1	no	—
128	#542	—	3	2	no	—
129	#542	—	3	2	no	—
130	#542	—	3	1	no	—
131	#542	—	3	1	no	—
132	#542	—	3	1	no	—
133	#542	—	3	1	no	—
134	#542	—	3	1	no	—
135	#542	D₃	1	1	yes	characteristic, direct product factor
136	C₂×C₄⋊Q₈	—	3	1	no	—
137	C₂×#126	—	3	2	no	—
138	C₂×#124	—	3	1	no	—
139	C₂×#124	—	3	2	no	—
140	C₂×#123	—	3	2	no	—
141	C₂×C₂²⋊Q₈	—	3	2	no	—
142	C₂×C₂²⋊Q₈	—	3	1	no	—
143	C₂×#121	—	3	1	no	—
144	C₂×C₄×Q₈	—	3	1	no	—
145	C₂×C₄×D₄	—	3	1	no	—
146	C₂×#117	—	3	1	no	—
147	C₂³×D₃	C₂³	1	1	yes	characteristic
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×Q₈	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×D₄	C₂³	1	2	yes	—
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³	1	2	yes	—
155	C₂×#67	C₂³	1	2	yes	—
156	C₂×#67	C₂³	1	2	yes	—
157	C₂×#67	C₂³	1	2	yes	—
158	C₂²×Dic₃	C₂³	1	1	yes	characteristic
159	C₂²×Dic₃	C₂³	1	2	yes	—
160	D₃×Q₈	—	2	4	no	—
161	D₃×Q₈	—	4	4	no	—
162	D₃×D₄	—	2	4	no	—
163	D₃×D₄	—	4	4	no	—
164	C₂×D₁₂	C₂³	1	1	yes	characteristic
165	C₂×D₁₂	C₂³	1	2	yes	—
166	C₂×C₄×D₃	—	2	4	no	—
167	C₂×C₄×D₃	—	4	4	no	—
168	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₃	C₂³	1	2	yes	—
171	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₃	C₂³	1	2	yes	—
174	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
176	C₂×C₄×D₃	C₂³	1	2	yes	—
177	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×D₃	C₂³	1	2	yes	—
179	C₂×C₄×D₃	C₂³	1	2	yes	—
180	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
181	C₂×Dic₆	C₂³	1	1	yes	characteristic
182	C₂×Dic₆	C₂³	1	2	yes	—
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×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₃×C₄²	C₂³	1	2	yes	—
202	C₃×C₄²	C₂³	1	1	yes	characteristic
203	#217	C₂³	1	1	yes	characteristic
204	#217	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	(C₂×D₃)⋊C₄	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	1	yes	characteristic
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	2	yes	—
224	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₃	C₂³	1	2	yes	—
226	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₃	C₂³	1	2	yes	—
228	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₃	C₂³	1	2	yes	—
230	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
235	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
244	C₄×Dic₃	C₂³	1	2	yes	—
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	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₄×Dic₃	C₂³	1	2	yes	—
252	C₂²×Q₈	—	3	1	no	—
253	C₂²×Q₈	—	3	2	no	—
254	C₂²×D₄	—	3	1	no	—
255	C₂²×D₄	—	3	2	no	—
256	C₂³×C₄	—	3	1	no	—
257	C₂³×C₄	—	3	2	no	—
258	C₄⋊Q₈	—	3	2	no	—
259	C₄⋊Q₈	—	3	2	no	—
260	C₄⋊Q₈	—	3	1	no	—
261	C₄⋊Q₈	—	3	1	no	—
262	C₄⋊Q₈	—	3	1	no	—
263	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
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	2	no	—
270	#126	—	3	2	no	—
271	#126	C₂×D₃	1	2	yes	complemented
272	#124	—	3	1	no	—
273	#124	—	3	2	no	—
274	#124	—	3	1	no	—
275	#124	—	3	2	no	—
276	#124	—	3	2	no	—
277	#124	—	3	2	no	—
278	#124	—	3	2	no	—
279	#124	—	3	2	no	—
280	#124	—	3	2	no	—
281	#124	—	3	2	no	—
282	#124	—	3	1	no	—
283	#124	—	3	2	no	—
284	#124	C₂×D₃	1	1	yes	characteristic, complemented
285	#124	C₂×D₃	1	2	yes	complemented
286	#123	—	3	2	no	—
287	#123	—	3	2	no	—
288	#123	—	3	2	no	—
289	#123	—	3	2	no	—
290	#123	—	3	2	no	—
291	#123	—	3	2	no	—
292	#123	—	3	2	no	—
293	#123	C₂×D₃	1	2	yes	complemented
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	1	no	—
296	C₂²⋊Q₈	—	3	2	no	—
297	C₂²⋊Q₈	—	3	1	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	1	no	—
303	C₂²⋊Q₈	—	3	2	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	C₂²⋊Q₈	—	3	2	no	—
306	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
307	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
308	#121	—	3	1	no	—
309	#121	—	3	2	no	—
310	#121	—	3	1	no	—
311	#121	—	3	1	no	—
312	#121	—	3	2	no	—
313	#121	C₂×D₃	1	1	yes	characteristic
314	C₄×Q₈	—	3	1	no	—
315	C₄×Q₈	—	3	2	no	—
316	C₄×Q₈	—	3	1	no	—
317	C₄×Q₈	—	3	2	no	—
318	C₄×Q₈	—	3	1	no	—
319	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	—	3	2	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	2	no	—
324	C₄×D₄	—	3	1	no	—
325	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
326	#117	—	3	1	no	—
327	#117	—	3	1	no	—
328	#117	—	3	1	no	—
329	#117	—	3	1	no	—
330	#117	—	3	1	no	—
331	#117	—	3	1	no	—
332	#117	—	3	1	no	—
333	#117	C₂×D₃	1	1	yes	characteristic, complemented
334	C₂×C₄⋊C₄	—	3	1	no	—
335	C₂×C₄⋊C₄	—	3	1	no	—
336	C₂×C₄⋊C₄	—	3	1	no	—
337	C₂×C₄⋊C₄	—	3	1	no	—
338	C₂×C₄⋊C₄	—	3	2	no	—
339	C₂×C₄⋊C₄	—	3	2	no	—
340	C₂×C₄⋊C₄	—	3	2	no	—
341	C₂×C₂²⋊C₄	—	3	1	no	—
342	C₂×C₂²⋊C₄	—	3	1	no	—
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	3	2	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₂²⋊C₄	—	3	2	no	—
347	C₂×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₄²	—	3	1	no	—
349	C₂×C₄²	—	3	1	no	—
350	C₂×C₄²	—	3	2	no	—
351	C₂³×C₃	C₂⁴	1	1	yes	characteristic
352	C₂³×C₃	C₂⁴	1	2	yes	—
353	C₂²×D₃	—	2	2	no	—
354	C₂²×D₃	—	2	4	no	—
355	C₂²×D₃	—	2	4	no	—
356	C₂²×D₃	—	2	2	no	—
357	C₂²×D₃	—	2	2	no	—
358	C₂²×D₃	—	2	4	no	—
359	C₂²×D₃	C₂⁴	1	1	yes	characteristic
360	C₂²×D₃	C₂⁴	1	2	yes	—
361	C₂²×D₃	C₂⁴	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂⁴	1	2	yes	—
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
372	C₂×C₃×C₄	C₂⁴	1	2	yes	—
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	#67	—	2	4	no	—
378	#67	—	4	2	no	—
379	#67	—	4	2	no	—
380	C₂×Dic₃	—	2	2	no	—
381	C₂×Dic₃	—	4	2	no	—
382	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₃	C₂⁴	1	2	yes	—
385	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₃	C₂⁴	1	2	yes	—
387	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₃	C₂⁴	1	2	yes	—
390	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
391	D₁₂	—	2	2	no	—
392	D₁₂	—	4	2	no	—
393	C₄×D₃	—	2	2	no	—
394	C₄×D₃	—	2	4	no	—
395	C₄×D₃	—	2	2	no	—
396	C₄×D₃	—	2	4	no	—
397	C₄×D₃	—	2	4	no	—
398	C₄×D₃	—	2	2	no	—
399	C₄×D₃	—	2	2	no	—
400	C₄×D₃	—	2	2	no	—
401	C₄×D₃	—	2	2	no	—
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	4	2	no	—
404	C₄×D₃	—	4	2	no	—
405	C₄×D₃	#41	1	4	yes	—
406	Dic₆	—	2	2	no	—
407	Dic₆	—	2	4	no	—
408	Dic₆	—	4	2	no	—
409	Dic₆	—	4	2	no	—
410	Dic₆	—	4	2	no	—
411	C₂⁴	—	3	1	no	—
412	C₂⁴	—	3	2	no	—
413	C₂×Q₈	—	3	2	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	—	6	4	no	—
419	C₂×Q₈	—	12	4	no	—
420	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
421	C₂×Q₈	C₂²×D₃	1	2	yes	—
422	C₂×D₄	—	3	2	no	—
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	1	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	6	4	no	—
428	C₂×D₄	—	12	4	no	—
429	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
430	C₂×D₄	C₂²×D₃	1	2	yes	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	1	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	2	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	1	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	—	3	2	no	—
446	C₂²×C₄	—	6	4	no	—
447	C₂²×C₄	—	12	4	no	—
448	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×D₃	1	2	yes	—
450	C₄⋊C₄	—	3	1	no	—
451	C₄⋊C₄	—	3	1	no	—
452	C₄⋊C₄	—	3	1	no	—
453	C₄⋊C₄	—	3	1	no	—
454	C₄⋊C₄	—	3	1	no	—
455	C₄⋊C₄	—	3	1	no	—
456	C₄⋊C₄	—	3	2	no	—
457	C₄⋊C₄	—	3	1	no	—
458	C₄⋊C₄	—	3	2	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	2	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	1	yes	characteristic
472	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
473	C₄⋊C₄	C₂²×D₃	1	2	yes	—
474	C₄⋊C₄	C₂²×D₃	1	2	yes	—
475	C₄⋊C₄	C₂²×D₃	1	2	yes	—
476	C₂²⋊C₄	—	3	1	no	—
477	C₂²⋊C₄	—	3	1	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	2	no	—
483	C₂²⋊C₄	—	3	1	no	—
484	C₂²⋊C₄	—	3	1	no	—
485	C₂²⋊C₄	—	3	1	no	—
486	C₂²⋊C₄	—	3	1	no	—
487	C₂²⋊C₄	—	3	2	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	2	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	C₂²×D₃	1	1	yes	characteristic
498	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	2	yes	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	3	1	no	—
508	C₄²	—	3	1	no	—
509	C₄²	—	3	1	no	—
510	C₄²	—	3	2	no	—
511	C₄²	—	3	2	no	—
512	C₄²	—	3	2	no	—
513	C₄²	C₂²×D₃	1	1	yes	characteristic
514	C₄²	C₂²×D₃	1	1	yes	characteristic
515	C₄²	C₂²×D₃	1	2	yes	—
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	—	2	2	no	—
518	C₂²×C₃	—	2	2	no	—
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	2	no	—
522	C₂²×C₃	C₂⁵	1	1	yes	characteristic
523	C₂×D₃	—	2	1	no	—
524	C₂×D₃	—	2	2	no	—
525	C₂×D₃	—	2	2	no	—
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	2	1	no	—
528	C₂×D₃	—	2	2	no	—
529	C₂×D₃	—	4	4	no	—
530	C₂×D₃	—	4	8	no	—
531	C₂×D₃	C₂×#41	1	2	yes	—
532	C₂×D₃	H(5,𝔽₂)	1	2	yes	—
533	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
534	C₃×C₄	—	2	2	no	—
535	C₃×C₄	—	2	1	no	—
536	C₃×C₄	—	2	1	no	—
537	C₃×C₄	—	2	2	no	—
538	C₃×C₄	—	2	2	no	—
539	C₃×C₄	—	2	1	no	—
540	C₃×C₄	—	2	1	no	—
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	C₂×#41	1	2	yes	—
543	Dic₃	—	2	2	no	—
544	Dic₃	—	2	1	no	—
545	Dic₃	—	2	1	no	—
546	Dic₃	—	2	2	no	—
547	Dic₃	—	2	2	no	—
548	Dic₃	—	2	1	no	—
549	Dic₃	—	2	1	no	—
550	Dic₃	—	2	1	no	—
551	Dic₃	C₂×#41	1	2	yes	—
552	C₂³	—	3	1	no	—
553	C₂³	—	3	1	no	—
554	C₂³	—	3	2	no	—
555	C₂³	—	6	2	no	—
556	C₂³	—	6	4	no	—
557	C₂³	—	6	4	no	—
558	C₂³	—	6	2	no	—
559	C₂³	—	6	2	no	—
560	C₂³	—	6	4	no	—
561	C₂³	C₂³×D₃	1	1	yes	characteristic
562	C₂³	C₂³×D₃	1	2	yes	—
563	Q₈	—	2	2	no	—
564	Q₈	—	4	2	no	—
565	Q₈	—	6	4	no	—
566	Q₈	—	6	2	no	—
567	Q₈	—	12	2	no	—
568	Q₈	—	12	2	no	—
569	Q₈	—	12	2	no	—
570	D₄	—	2	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	6	4	no	—
573	D₄	—	6	2	no	—
574	D₄	—	12	2	no	—
575	D₄	—	12	2	no	—
576	D₄	—	12	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	4	no	—
580	C₂×C₄	—	3	1	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	2	no	—
583	C₂×C₄	—	3	1	no	—
584	C₂×C₄	—	3	1	no	—
585	C₂×C₄	—	3	2	no	—
586	C₂×C₄	—	3	1	no	—
587	C₂×C₄	—	3	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	6	2	no	—
590	C₂×C₄	—	6	2	no	—
591	C₂×C₄	—	6	2	no	—
592	C₂×C₄	—	6	4	no	—
593	C₂×C₄	—	6	4	no	—
594	C₂×C₄	—	6	4	no	—
595	C₂×C₄	—	6	2	no	—
596	C₂×C₄	—	6	2	no	—
597	C₂×C₄	—	6	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	C₂³×D₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₃	1	2	yes	—
606	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₃	1	2	yes	—
609	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₃	1	2	yes	—
611	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
612	C₂×C₃	—	4	1	no	—
613	C₂×C₃	—	4	2	no	—
614	C₂×C₃	C₂²×#41	1	1	yes	characteristic
615	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
617	D₃	—	4	1	no	—
618	D₃	—	4	2	no	—
619	D₃	#542	1	4	yes	direct product factor
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	3	2	no	—
627	C₂²	—	3	2	no	—
628	C₂²	—	3	2	no	—
629	C₂²	—	6	1	no	—
630	C₂²	—	6	2	no	—
631	C₂²	—	6	2	no	—
632	C₂²	—	6	1	no	—
633	C₂²	—	6	1	no	—
634	C₂²	—	6	2	no	—
635	C₂²	—	12	4	no	—
636	C₂²	—	12	8	no	—
637	C₂²	C₂⁴×D₃	1	1	yes	characteristic
638	C₄	—	2	1	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	1	no	—
641	C₄	—	2	2	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	1	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	3	2	no	—
647	C₄	—	6	1	no	—
648	C₄	—	6	2	no	—
649	C₄	—	6	1	no	—
650	C₄	—	6	2	no	—
651	C₄	—	6	2	no	—
652	C₄	—	6	1	no	—
653	C₄	—	6	1	no	—
654	C₄	—	6	1	no	—
655	C₄	D₃×#41	1	2	yes	—
656	C₃	C₂×#542	1	1	yes	characteristic, complemented, Sylow
657	C₂	—	3	4	no	—
658	C₂	—	4	1	no	—
659	C₂	—	4	2	no	—
660	C₂	—	12	1	no	—
661	C₂	—	12	2	no	—
662	C₂	C₂×D₃×#41	1	1	yes	characteristic
663	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂	D₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#542	C₂
prime radical	D₃×#121	C₂
hypercenter	#542	D₃
hypocenter	C₃	C₂×#542
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₃×#542	C₂	semidirect
2. #5733	C₂	semidirect
3. D₃×C₄⋊Q₈	C₂	semidirect
4. #5710	C₂	semidirect
5. D₃×#126	C₂	semidirect
6. #5682	C₂	semidirect
7. D₃×#124	C₂	semidirect
8. D₃×#124	C₂	semidirect
9. #5669	C₂	semidirect
10. #5662	C₂	semidirect
11. D₃×#123	C₂	semidirect
12. #5643	C₂	semidirect
13. #5640	C₂	semidirect
14. D₃×C₂²⋊Q₈	C₂	semidirect
15. D₃×C₂²⋊Q₈	C₂	semidirect
17. #5603	C₂	semidirect
18. #5582	C₂	semidirect
19. C₄×D₃×Q₈	C₂	semidirect
20. #5561	C₂	semidirect
21. C₄×D₃×D₄	C₂	semidirect
22. #5534	C₂	semidirect
23. D₃×#117	C₂	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×#126	C₂²	semidirect
33. C₃×#124	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
35. C₃×#123	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₃×C₄×Q₈	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×#117	C₂²	semidirect
42. #947	C₂²	semidirect
43. #947	C₂²	semidirect
44. #946	C₂²	semidirect
45. #946	C₂²	semidirect
46. Q₈×Dic₃	C₂²	semidirect
47. #944	C₂²	semidirect
50. #936	C₂²	semidirect
51. #936	C₂²	semidirect
52. #935	C₂²	semidirect
53. D₄×Dic₃	C₂²	semidirect
55. #929	C₂²	semidirect
56. C₄×#67	C₂²	semidirect
57. #926	C₂²	semidirect
58. #924	C₂²	semidirect
59. #924	C₂²	semidirect
60. #898	C₂²	semidirect
61. #898	C₂²	semidirect
62. #898	C₂²	semidirect
63. #897	C₂²	semidirect
64. #897	C₂²	semidirect
65. #896	C₂²	semidirect
66. #896	C₂²	semidirect
67. #896	C₂²	semidirect
69. #894	C₂²	semidirect
70. #894	C₂²	semidirect
71. #893	C₂²	semidirect
72. #892	C₂²	semidirect
73. #892	C₂²	semidirect
81. #888	C₂²	semidirect
82. #888	C₂²	semidirect
83. #888	C₂²	semidirect
84. #887	C₂²	semidirect
85. #887	C₂²	semidirect
86. #886	C₂²	semidirect
87. #885	C₂²	semidirect
88. #885	C₂²	semidirect
89. #885	C₂²	semidirect
90. #885	C₂²	semidirect
91. #885	C₂²	semidirect
92. #885	C₂²	semidirect
94. #883	C₂²	semidirect
95. #883	C₂²	semidirect
96. #67⋊C₄	C₂²	semidirect
104. #879	C₂²	semidirect
105. #879	C₂²	semidirect
106. #879	C₂²	semidirect
107. #878	C₂²	semidirect
108. #878	C₂²	semidirect
109. #878	C₂²	semidirect
110. #877	C₂²	semidirect
111. #877	C₂²	semidirect
112. #876	C₂²	semidirect
113. #875	C₂²	semidirect
114. #875	C₂²	semidirect
115. C₄×D₁₂	C₂²	semidirect
116. #872	C₂²	semidirect
117. #872	C₂²	semidirect
121. #869	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
135. #542	D₃	direct (N × H)
263. C₄⋊Q₈	C₂×D₃	semidirect
271. #126	C₂×D₃	semidirect
284. #124	C₂×D₃	semidirect
285. #124	C₂×D₃	semidirect
293. #123	C₂×D₃	semidirect
306. C₂²⋊Q₈	C₂×D₃	semidirect
307. C₂²⋊Q₈	C₂×D₃	semidirect
319. C₄×Q₈	C₂×D₃	semidirect
325. C₄×D₄	C₂×D₃	semidirect
333. #117	C₂×D₃	semidirect
619. D₃	#542	direct (N × H)
656. C₃	C₂×#542	semidirect

Maximal subgroups

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

subgroup	index
C₃×#542	2
#5733	2
D₃×C₄⋊Q₈	2
#5710	2
D₃×#126	2
#5682	2
D₃×#124	2
#5669	2
#5662	2
D₃×#123	2
#5643	2
#5640	2
D₃×C₂²⋊Q₈	2
D₃×#121	2
#5603	2
#5582	2
C₄×D₃×Q₈	2
#5561	2
C₄×D₃×D₄	2
#5534	2
D₃×#117	2
C₂×#542	3

Subgroups — D3×#542 #86549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#542 #86549