Subgroups — D₃×#546 #86661

Order 384.

1900 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
4	#5829	C₂	1	1	yes	maximal, characteristic, complemented
5	#5806	C₂	1	1	yes	maximal, characteristic, complemented
6	#5676	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
8	#5654	C₂	1	2	yes	maximal, complemented
9	D₃×#123	C₂	1	2	yes	maximal, complemented
10	#5630	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#5612	C₂	1	1	yes	maximal, characteristic, complemented
13	#5610	C₂	1	2	yes	maximal, complemented
14	D₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#121	C₂	1	2	yes	maximal, complemented
16	#5591	C₂	1	2	yes	maximal, complemented
17	D₃×#120	C₂	1	2	yes	maximal, complemented
18	#5554	C₂	1	1	yes	maximal, characteristic, complemented
19	#5550	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
22	#5490	C₂	1	2	yes	maximal, complemented
23	C₂×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
24	C₂×#546	—	3	1	no	maximal, Sylow
25	C₂⁴×D₃	C₂²	1	2	yes	—
26	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#67	C₂²	1	2	yes	complemented
29	D₃×#41	—	2	8	no	—
30	C₂×#239	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×#237	C₂²	1	2	yes	complemented
33	C₂×#237	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₃×D₄	—	2	8	no	—
35	C₂×D₃×D₄	C₂²	1	2	yes	—
36	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
37	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
38	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
39	C₂×D₃×D₄	C₂²	1	2	yes	complemented
40	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₃×D₄	C₂²	1	2	yes	complemented
43	C₂×D₃×D₄	C₂²	1	2	yes	complemented
44	C₂×#235	C₂²	1	1	yes	characteristic, complemented
45	C₂×#235	C₂²	1	2	yes	complemented
46	C₂²×D₁₂	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
48	C₂²×C₄×D₃	C₂²	1	2	yes	complemented
49	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄×D₃	C₂²	1	2	yes	complemented
51	C₃×#124	C₂²	1	1	yes	characteristic, complemented
52	C₃×#123	C₂²	1	2	yes	complemented
53	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₃×#121	C₂²	1	2	yes	complemented
55	C₃×#121	C₂²	1	1	yes	characteristic, complemented
56	C₃×#120	C₂²	1	2	yes	complemented
57	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
58	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
60	#953	C₂²	1	2	yes	complemented
61	C₂×#217	C₂²	1	2	yes	complemented
62	#947	C₂²	1	1	yes	characteristic, complemented
63	#946	C₂²	1	1	yes	characteristic, complemented
64	#939	C₂²	1	2	yes	complemented
65	#939	C₂²	1	2	yes	complemented
66	#939	C₂²	1	2	yes	complemented
67	#938	C₂²	1	2	yes	complemented
68	#938	C₂²	1	1	yes	characteristic, complemented
69	#937	C₂²	1	2	yes	complemented
70	#937	C₂²	1	2	yes	complemented
71	#937	C₂²	1	2	yes	complemented
72	#936	C₂²	1	1	yes	characteristic, complemented
73	#935	C₂²	1	2	yes	complemented
74	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
75	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
76	#930	C₂²	1	1	yes	characteristic, complemented
77	#930	C₂²	1	2	yes	complemented
78	#929	C₂²	1	2	yes	complemented
79	C₄×#67	C₂²	1	1	yes	characteristic, complemented
80	C₄×#67	C₂²	1	1	yes	characteristic, complemented
81	C₄×#67	C₂²	1	2	yes	complemented
82	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
83	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
84	#924	C₂²	1	1	yes	characteristic, complemented
85	#897	C₂²	1	1	yes	characteristic, complemented
86	#896	C₂²	1	2	yes	complemented
87	#895	C₂²	1	2	yes	complemented
88	#895	C₂²	1	1	yes	characteristic, complemented
89	#894	C₂²	1	2	yes	complemented
90	#894	C₂²	1	2	yes	complemented
91	#893	C₂²	1	1	yes	characteristic, complemented
92	#893	C₂²	1	1	yes	characteristic, complemented
93	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
95	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	#886	C₂²	1	2	yes	complemented
97	#885	C₂²	1	2	yes	complemented
98	#885	C₂²	1	2	yes	complemented
99	#884	C₂²	1	2	yes	complemented
100	#884	C₂²	1	2	yes	complemented
101	#884	C₂²	1	2	yes	complemented
102	#883	C₂²	1	2	yes	complemented
103	#883	C₂²	1	2	yes	complemented
104	#882	C₂²	1	2	yes	complemented
105	#882	C₂²	1	2	yes	complemented
106	#882	C₂²	1	2	yes	complemented
107	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
109	#67⋊C₄	C₂²	1	2	yes	complemented
110	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
111	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
112	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
115	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
116	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
117	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	#878	C₂²	1	2	yes	complemented
122	#875	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
124	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
125	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
126	C₂²×#41	—	3	1	no	—
127	C₂³×D₄	—	3	1	no	—
128	#546	—	3	1	no	—
129	#546	—	3	1	no	—
130	#546	—	3	1	no	—
131	#546	—	3	2	no	—
132	#546	—	3	1	no	—
133	#546	—	3	2	no	—
134	#546	—	3	1	no	—
135	#546	—	3	2	no	—
136	#546	—	3	1	no	—
137	#546	—	3	1	no	—
138	#546	—	3	2	no	—
139	#546	D₃	1	1	yes	characteristic, direct product factor
140	C₂×#124	—	3	1	no	—
141	C₂×#123	—	3	2	no	—
142	C₂×C₂²⋊Q₈	—	3	1	no	—
143	C₂×#121	—	3	1	no	—
144	C₂×#121	—	3	2	no	—
145	C₂×#120	—	3	2	no	—
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂×C₄×D₄	—	3	1	no	—
148	C₂²×C₂²⋊C₄	—	3	2	no	—
149	C₂⁴×C₃	C₂³	1	2	yes	—
150	C₂³×D₃	—	2	8	no	—
151	C₂³×D₃	—	2	8	no	—
152	C₂³×D₃	—	4	4	no	—
153	C₂³×D₃	C₂³	1	2	yes	—
154	C₂³×D₃	C₂³	1	1	yes	characteristic
155	C₂³×D₃	C₂³	1	2	yes	—
156	C₂³×D₃	C₂³	1	2	yes	—
157	C₂³×D₃	C₂³	1	2	yes	—
158	C₂³×D₃	C₂³	1	2	yes	—
159	C₂³×D₃	C₂³	1	1	yes	characteristic
160	C₃×#41	—	2	4	no	—
161	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic, complemented
162	C₂×C₃×D₄	—	2	4	no	—
163	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
164	C₂×C₃×D₄	C₂³	1	2	yes	—
165	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
166	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
167	C₂×C₃×D₄	C₂³	1	2	yes	complemented
168	C₂×C₃×D₄	C₂³	1	2	yes	complemented
169	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂³	1	2	yes	complemented
171	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic, complemented
172	C₂²×C₃×C₄	C₂³	1	2	yes	complemented
173	C₂×#67	—	2	8	no	—
174	C₂×#67	C₂³	1	1	yes	characteristic
175	C₂×#67	C₂³	1	1	yes	characteristic
176	C₂×#67	C₂³	1	2	yes	—
177	C₂×#67	C₂³	1	2	yes	—
178	C₂×#67	C₂³	1	2	yes	—
179	C₂×#67	C₂³	1	2	yes	—
180	C₂×#67	C₂³	1	2	yes	complemented
181	C₂×#67	C₂³	1	2	yes	complemented
182	C₂×#67	C₂³	1	2	yes	complemented
183	C₂×#67	C₂³	1	2	yes	complemented
184	C₂²×Dic₃	C₂³	1	1	yes	characteristic
185	C₂²×Dic₃	C₂³	1	1	yes	characteristic, complemented
186	C₂²×Dic₃	C₂³	1	2	yes	complemented
187	C₂²×Dic₃	C₂³	1	2	yes	complemented
188	#239	—	2	4	no	—
189	D₃×Q₈	—	2	4	no	—
190	#237	—	2	4	no	—
191	#237	—	2	8	no	—
192	D₃×D₄	—	2	8	no	—
193	D₃×D₄	—	2	8	no	—
194	D₃×D₄	—	2	4	no	—
195	D₃×D₄	—	2	4	no	—
196	D₃×D₄	—	2	8	no	—
197	D₃×D₄	—	2	4	no	—
198	D₃×D₄	—	2	4	no	—
199	D₃×D₄	—	4	4	no	—
200	D₃×D₄	D₄	1	8	yes	complemented
201	#235	—	2	8	no	—
202	#235	—	2	4	no	—
203	C₂×D₁₂	—	2	4	no	—
204	C₂×D₁₂	C₂³	1	1	yes	characteristic
205	C₂×D₁₂	C₂³	1	1	yes	characteristic
206	C₂×D₁₂	C₂³	1	2	yes	—
207	C₂×D₁₂	C₂³	1	1	yes	characteristic
208	C₂×D₁₂	C₂³	1	2	yes	complemented
209	C₂×D₁₂	C₂³	1	2	yes	complemented
210	C₂×C₄×D₃	—	2	8	no	—
211	C₂×C₄×D₃	—	2	4	no	—
212	C₂×C₄×D₃	—	2	4	no	—
213	C₂×C₄×D₃	—	4	4	no	—
214	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₃	C₂³	1	2	yes	—
218	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₃	C₂³	1	2	yes	—
220	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₃	C₂³	1	1	yes	characteristic, complemented
224	C₂×C₄×D₃	C₂³	1	2	yes	complemented
225	C₂×C₄×D₃	C₂³	1	2	yes	complemented
226	C₂×C₄×D₃	C₂³	1	1	yes	characteristic, complemented
227	C₂×C₄×D₃	C₂³	1	2	yes	complemented
228	C₂×C₄×D₃	C₂³	1	2	yes	complemented
229	C₂×Dic₆	C₂³	1	1	yes	characteristic, complemented
230	C₂×Dic₆	C₂³	1	2	yes	complemented
231	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
232	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
233	C₃×C₄⋊C₄	C₂³	1	2	yes	complemented
234	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
237	C₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
238	C₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
239	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
240	C₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
241	C₃×C₄²	C₂³	1	1	yes	characteristic, complemented
242	#217	C₂³	1	2	yes	—
243	#217	C₂³	1	1	yes	characteristic
244	#217	C₂³	1	2	yes	complemented
245	#217	C₂³	1	2	yes	complemented
246	#217	C₂³	1	2	yes	complemented
247	#217	C₂³	1	2	yes	complemented
248	#217	C₂³	1	1	yes	characteristic, complemented
249	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
250	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
251	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
252	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
253	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
254	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
255	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
256	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
257	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
258	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
259	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
260	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
261	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
262	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic, complemented
263	C₄⋊Dic₃	C₂³	1	1	yes	characteristic, complemented
264	C₄⋊Dic₃	C₂³	1	1	yes	characteristic, complemented
265	C₄⋊Dic₃	C₂³	1	2	yes	complemented
266	Dic₃⋊C₄	C₂³	1	2	yes	complemented
267	Dic₃⋊C₄	C₂³	1	2	yes	complemented
268	Dic₃⋊C₄	C₂³	1	1	yes	characteristic, complemented
269	Dic₃⋊C₄	C₂³	1	1	yes	characteristic, complemented
270	Dic₃⋊C₄	C₂³	1	2	yes	complemented
271	C₄×Dic₃	C₂³	1	1	yes	characteristic, complemented
272	C₄×Dic₃	C₂³	1	1	yes	characteristic, complemented
273	C₄×Dic₃	C₂³	1	1	yes	characteristic, complemented
274	C₂⁵	—	3	2	no	—
275	C₂×#41	—	3	1	no	—
276	C₂×#41	—	3	1	no	—
277	C₂×#41	—	3	2	no	—
278	C₂×#41	—	3	1	no	—
279	C₂×#41	—	3	2	no	—
280	C₂×#41	—	6	8	no	—
281	C₂×#41	C₂×D₃	1	1	yes	characteristic, complemented
282	C₂²×Q₈	—	3	1	no	—
283	C₂²×D₄	—	3	1	no	—
284	C₂²×D₄	—	3	2	no	—
285	C₂²×D₄	—	3	1	no	—
286	C₂²×D₄	—	3	2	no	—
287	C₂²×D₄	—	3	1	no	—
288	C₂²×D₄	—	3	2	no	—
289	C₂²×D₄	—	3	1	no	—
290	C₂²×D₄	—	3	1	no	—
291	C₂²×D₄	—	3	2	no	—
292	C₂²×D₄	—	3	2	no	—
293	C₂²×D₄	—	3	1	no	—
294	C₂²×D₄	—	6	8	no	—
295	C₂²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
296	C₂³×C₄	—	3	1	no	—
297	C₂³×C₄	—	3	2	no	—
298	C₂³×C₄	—	3	1	no	—
299	C₂³×C₄	—	3	2	no	—
300	#124	—	3	1	no	—
301	#124	—	3	1	no	—
302	#124	—	3	2	no	—
303	#124	—	3	2	no	—
304	#124	—	3	1	no	—
305	#124	C₂×D₃	1	1	yes	characteristic, complemented
306	#123	—	3	2	no	—
307	#123	—	3	2	no	—
308	#123	—	3	2	no	—
309	#123	—	3	2	no	—
310	#123	—	3	2	no	—
311	#123	—	3	2	no	—
312	#123	—	3	2	no	—
313	#123	C₂×D₃	1	2	yes	complemented
314	C₂²⋊Q₈	—	3	1	no	—
315	C₂²⋊Q₈	—	3	1	no	—
316	C₂²⋊Q₈	—	3	2	no	—
317	C₂²⋊Q₈	—	3	1	no	—
318	C₂²⋊Q₈	—	3	2	no	—
319	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
320	#121	—	3	1	no	—
321	#121	—	3	2	no	—
322	#121	—	3	2	no	—
323	#121	—	3	2	no	—
324	#121	—	3	2	no	—
325	#121	—	3	1	no	—
326	#121	—	3	2	no	—
327	#121	—	3	1	no	—
328	#121	—	3	2	no	—
329	#121	—	3	2	no	—
330	#121	—	3	2	no	—
331	#121	—	3	2	no	—
332	#121	C₂×D₃	1	1	yes	characteristic, complemented
333	#121	C₂×D₃	1	2	yes	complemented
334	#120	—	3	2	no	—
335	#120	—	3	2	no	—
336	#120	—	3	2	no	—
337	#120	—	3	2	no	—
338	#120	—	3	2	no	—
339	#120	—	3	2	no	—
340	#120	—	3	2	no	—
341	#120	C₂×D₃	1	2	yes	complemented
342	C₄×D₄	—	3	1	no	—
343	C₄×D₄	—	3	1	no	—
344	C₄×D₄	—	3	1	no	—
345	C₄×D₄	—	3	2	no	—
346	C₄×D₄	—	3	1	no	—
347	C₄×D₄	—	3	1	no	—
348	C₄×D₄	—	3	1	no	—
349	C₄×D₄	—	3	1	no	—
350	C₄×D₄	—	3	1	no	—
351	C₄×D₄	—	3	2	no	—
352	C₄×D₄	—	3	1	no	—
353	C₄×D₄	—	3	1	no	—
354	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
355	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
356	C₂×C₄⋊C₄	—	3	1	no	—
357	C₂×C₄⋊C₄	—	3	1	no	—
358	C₂×C₄⋊C₄	—	3	2	no	—
359	C₂×C₂²⋊C₄	—	3	2	no	—
360	C₂×C₂²⋊C₄	—	3	2	no	—
361	C₂×C₂²⋊C₄	—	3	2	no	—
362	C₂×C₂²⋊C₄	—	3	1	no	—
363	C₂×C₂²⋊C₄	—	3	2	no	—
364	C₂×C₂²⋊C₄	—	3	2	no	—
365	C₂×C₂²⋊C₄	—	3	2	no	—
366	C₂×C₂²⋊C₄	—	3	2	no	—
367	C₂×C₂²⋊C₄	—	3	2	no	—
368	C₂×C₂²⋊C₄	—	3	2	no	—
369	C₂×C₂²⋊C₄	—	3	2	no	—
370	C₂×C₂²⋊C₄	—	3	2	no	—
371	C₂×C₂²⋊C₄	—	3	1	no	—
372	C₂×C₂²⋊C₄	—	3	2	no	—
373	C₂×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
374	C₂×C₄²	—	3	1	no	—
375	C₂³×C₃	—	2	4	no	—
376	C₂³×C₃	—	2	4	no	—
377	C₂³×C₃	—	4	2	no	—
378	C₂³×C₃	C₂⁴	1	2	yes	—
379	C₂³×C₃	C₂⁴	1	1	yes	characteristic
380	C₂³×C₃	C₂⁴	1	2	yes	—
381	C₂³×C₃	C₂⁴	1	1	yes	characteristic
382	C₂²×D₃	—	2	2	no	—
383	C₂²×D₃	—	2	4	no	—
384	C₂²×D₃	—	2	4	no	—
385	C₂²×D₃	—	2	2	no	—
386	C₂²×D₃	—	2	4	no	—
387	C₂²×D₃	—	2	4	no	—
388	C₂²×D₃	—	2	2	no	—
389	C₂²×D₃	—	2	4	no	—
390	C₂²×D₃	—	2	4	no	—
391	C₂²×D₃	—	2	4	no	—
392	C₂²×D₃	—	2	2	no	—
393	C₂²×D₃	—	2	4	no	—
394	C₂²×D₃	—	2	4	no	—
395	C₂²×D₃	—	2	4	no	—
396	C₂²×D₃	—	2	2	no	—
397	C₂²×D₃	—	2	4	no	—
398	C₂²×D₃	—	4	2	no	—
399	C₂²×D₃	—	4	2	no	—
400	C₂²×D₃	—	4	2	no	—
401	C₂²×D₃	—	4	32	no	—
402	C₂²×D₃	C₂×D₄	1	8	yes	—
403	C₂²×D₃	#41	1	4	yes	complemented
404	C₂²×D₃	C₂⁴	1	2	yes	—
405	C₂²×D₃	C₂⁴	1	1	yes	characteristic
406	C₂²×D₃	C₂⁴	1	2	yes	—
407	C₂²×D₃	C₂⁴	1	1	yes	characteristic
408	C₂²×D₃	C₂⁴	1	1	yes	characteristic
409	C₃×Q₈	—	2	2	no	—
410	C₃×D₄	—	2	4	no	—
411	C₃×D₄	—	2	4	no	—
412	C₃×D₄	—	2	2	no	—
413	C₃×D₄	—	2	2	no	—
414	C₃×D₄	—	4	2	no	—
415	C₃×D₄	C₂×D₄	1	4	yes	complemented
416	C₂×C₃×C₄	—	2	4	no	—
417	C₂×C₃×C₄	—	2	2	no	—
418	C₂×C₃×C₄	—	2	2	no	—
419	C₂×C₃×C₄	—	4	2	no	—
420	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂⁴	1	2	yes	—
424	C₂×C₃×C₄	C₂⁴	1	2	yes	—
425	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
426	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
427	#67	—	2	4	no	—
428	#67	—	2	4	no	—
429	#67	—	2	2	no	—
430	#67	—	2	4	no	—
431	#67	—	2	4	no	—
432	#67	—	2	2	no	—
433	#67	—	2	4	no	—
434	#67	—	4	2	no	—
435	#67	—	4	2	no	—
436	#67	C₂×D₄	1	8	yes	complemented
437	C₂×Dic₃	—	2	4	no	—
438	C₂×Dic₃	—	2	2	no	—
439	C₂×Dic₃	—	2	2	no	—
440	C₂×Dic₃	—	4	2	no	—
441	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
442	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
443	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
444	C₂×Dic₃	C₂⁴	1	2	yes	—
445	C₂×Dic₃	C₂⁴	1	2	yes	—
446	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
447	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
448	D₁₂	—	2	4	no	—
449	D₁₂	—	2	4	no	—
450	D₁₂	—	2	2	no	—
451	D₁₂	—	2	2	no	—
452	D₁₂	—	4	2	no	—
453	D₁₂	C₂×D₄	1	4	yes	complemented
454	C₄×D₃	—	2	2	no	—
455	C₄×D₃	—	2	2	no	—
456	C₄×D₃	—	2	4	no	—
457	C₄×D₃	—	2	4	no	—
458	C₄×D₃	—	2	4	no	—
459	C₄×D₃	—	2	2	no	—
460	C₄×D₃	—	2	2	no	—
461	C₄×D₃	—	2	4	no	—
462	C₄×D₃	—	2	2	no	—
463	C₄×D₃	—	2	2	no	—
464	C₄×D₃	—	2	2	no	—
465	C₄×D₃	—	2	2	no	—
466	C₄×D₃	—	4	2	no	—
467	C₄×D₃	—	4	2	no	—
468	C₄×D₃	C₂×D₄	1	4	yes	—
469	Dic₆	—	2	2	no	—
470	Dic₆	—	2	4	no	—
471	C₂⁴	—	3	1	no	—
472	C₂⁴	—	3	2	no	—
473	C₂⁴	—	3	2	no	—
474	C₂⁴	—	3	1	no	—
475	C₂⁴	—	3	2	no	—
476	C₂⁴	—	3	2	no	—
477	C₂⁴	—	3	2	no	—
478	C₂⁴	—	6	8	no	—
479	C₂⁴	—	6	8	no	—
480	C₂⁴	—	12	4	no	—
481	C₂⁴	C₂²×D₃	1	2	yes	—
482	#41	—	2	4	no	—
483	#41	—	6	8	no	—
484	#41	—	6	4	no	—
485	#41	—	6	8	no	—
486	#41	—	6	4	no	—
487	#41	—	6	4	no	—
488	C₂×Q₈	—	3	2	no	—
489	C₂×Q₈	—	3	1	no	—
490	C₂×Q₈	—	6	4	no	—
491	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic, complemented
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	3	2	no	—
494	C₂×D₄	—	3	8	no	—
495	C₂×D₄	—	3	1	no	—
496	C₂×D₄	—	3	1	no	—
497	C₂×D₄	—	3	2	no	—
498	C₂×D₄	—	3	2	no	—
499	C₂×D₄	—	3	2	no	—
500	C₂×D₄	—	3	2	no	—
501	C₂×D₄	—	3	2	no	—
502	C₂×D₄	—	3	2	no	—
503	C₂×D₄	—	3	2	no	—
504	C₂×D₄	—	3	1	no	—
505	C₂×D₄	—	3	1	no	—
506	C₂×D₄	—	3	2	no	—
507	C₂×D₄	—	3	2	no	—
508	C₂×D₄	—	3	1	no	—
509	C₂×D₄	—	3	2	no	—
510	C₂×D₄	—	6	4	no	—
511	C₂×D₄	—	6	4	no	—
512	C₂×D₄	—	6	8	no	—
513	C₂×D₄	—	6	4	no	—
514	C₂×D₄	—	6	8	no	—
515	C₂×D₄	—	6	8	no	—
516	C₂×D₄	—	6	4	no	—
517	C₂×D₄	—	6	8	no	—
518	C₂×D₄	—	6	4	no	—
519	C₂×D₄	—	12	4	no	—
520	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₃	1	2	yes	—
522	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
523	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
524	C₂×D₄	C₂²×D₃	1	2	yes	complemented
525	C₂×D₄	C₂²×D₃	1	2	yes	complemented
526	C₂²×C₄	—	3	1	no	—
527	C₂²×C₄	—	3	2	no	—
528	C₂²×C₄	—	3	1	no	—
529	C₂²×C₄	—	3	1	no	—
530	C₂²×C₄	—	3	2	no	—
531	C₂²×C₄	—	3	1	no	—
532	C₂²×C₄	—	3	1	no	—
533	C₂²×C₄	—	3	2	no	—
534	C₂²×C₄	—	3	1	no	—
535	C₂²×C₄	—	3	2	no	—
536	C₂²×C₄	—	3	2	no	—
537	C₂²×C₄	—	3	2	no	—
538	C₂²×C₄	—	3	1	no	—
539	C₂²×C₄	—	3	1	no	—
540	C₂²×C₄	—	3	1	no	—
541	C₂²×C₄	—	3	1	no	—
542	C₂²×C₄	—	3	1	no	—
543	C₂²×C₄	—	3	2	no	—
544	C₂²×C₄	—	3	2	no	—
545	C₂²×C₄	—	6	4	no	—
546	C₂²×C₄	—	6	4	no	—
547	C₂²×C₄	—	6	8	no	—
548	C₂²×C₄	—	12	4	no	—
549	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
550	C₂²×C₄	C₂²×D₃	1	2	yes	complemented
551	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic, complemented
552	C₂²×C₄	C₂²×D₃	1	2	yes	complemented
553	C₄⋊C₄	—	3	2	no	—
554	C₄⋊C₄	—	3	1	no	—
555	C₄⋊C₄	—	3	1	no	—
556	C₄⋊C₄	—	3	1	no	—
557	C₄⋊C₄	—	3	1	no	—
558	C₄⋊C₄	—	3	2	no	—
559	C₄⋊C₄	—	3	2	no	—
560	C₄⋊C₄	—	3	2	no	—
561	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic, complemented
562	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic, complemented
563	C₄⋊C₄	C₂²×D₃	1	2	yes	complemented
564	C₂²⋊C₄	—	3	1	no	—
565	C₂²⋊C₄	—	3	2	no	—
566	C₂²⋊C₄	—	3	2	no	—
567	C₂²⋊C₄	—	3	2	no	—
568	C₂²⋊C₄	—	3	2	no	—
569	C₂²⋊C₄	—	3	1	no	—
570	C₂²⋊C₄	—	3	2	no	—
571	C₂²⋊C₄	—	3	1	no	—
572	C₂²⋊C₄	—	3	1	no	—
573	C₂²⋊C₄	—	3	2	no	—
574	C₂²⋊C₄	—	3	2	no	—
575	C₂²⋊C₄	—	3	2	no	—
576	C₂²⋊C₄	—	3	2	no	—
577	C₂²⋊C₄	—	3	2	no	—
578	C₂²⋊C₄	—	3	2	no	—
579	C₂²⋊C₄	—	3	2	no	—
580	C₂²⋊C₄	—	3	2	no	—
581	C₂²⋊C₄	—	3	1	no	—
582	C₂²⋊C₄	—	3	1	no	—
583	C₂²⋊C₄	—	3	2	no	—
584	C₂²⋊C₄	—	3	2	no	—
585	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
586	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
587	C₂²⋊C₄	C₂²×D₃	1	2	yes	complemented
588	C₂²⋊C₄	C₂²×D₃	1	2	yes	complemented
589	C₂²⋊C₄	C₂²×D₃	1	2	yes	complemented
590	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic, complemented
591	C₂²⋊C₄	C₂²×D₃	1	2	yes	complemented
592	C₄²	—	3	1	no	—
593	C₄²	—	3	1	no	—
594	C₄²	—	3	1	no	—
595	C₄²	C₂²×D₃	1	1	yes	characteristic, complemented
596	C₂²×C₃	—	2	1	no	—
597	C₂²×C₃	—	2	2	no	—
598	C₂²×C₃	—	2	2	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	2	1	no	—
601	C₂²×C₃	—	2	2	no	—
602	C₂²×C₃	—	2	1	no	—
603	C₂²×C₃	—	2	2	no	—
604	C₂²×C₃	—	2	1	no	—
605	C₂²×C₃	—	2	2	no	—
606	C₂²×C₃	—	4	8	no	—
607	C₂²×C₃	C₂²×D₄	1	4	yes	—
608	C₂²×C₃	C₂×#41	1	2	yes	complemented
609	C₂²×C₃	C₂⁵	1	1	yes	characteristic
610	C₂×D₃	—	2	1	no	—
611	C₂×D₃	—	2	2	no	—
612	C₂×D₃	—	2	2	no	—
613	C₂×D₃	—	2	1	no	—
614	C₂×D₃	—	2	8	no	—
615	C₂×D₃	—	2	16	no	—
616	C₂×D₃	—	2	1	no	—
617	C₂×D₃	—	2	2	no	—
618	C₂×D₃	—	2	1	no	—
619	C₂×D₃	—	2	2	no	—
620	C₂×D₃	—	2	1	no	—
621	C₂×D₃	—	2	2	no	—
622	C₂×D₃	—	4	8	no	—
623	C₂×D₃	—	4	8	no	—
624	C₂×D₃	—	4	8	no	—
625	C₂×D₃	—	4	4	no	—
626	C₂×D₃	—	4	8	no	—
627	C₂×D₃	C₂²×D₄	1	4	yes	—
628	C₂×D₃	C₂²×D₄	1	2	yes	—
629	C₂×D₃	C₂×#41	1	2	yes	—
630	C₂×D₃	C₂×#41	1	2	yes	complemented
631	C₂×D₃	H(5,𝔽₂)	1	2	yes	—
632	C₃×C₄	—	2	2	no	—
633	C₃×C₄	—	2	1	no	—
634	C₃×C₄	—	2	1	no	—
635	C₃×C₄	—	2	1	no	—
636	C₃×C₄	—	2	1	no	—
637	C₃×C₄	—	2	2	no	—
638	C₃×C₄	C₂²×D₄	1	2	yes	—
639	Dic₃	—	2	2	no	—
640	Dic₃	—	2	1	no	—
641	Dic₃	—	2	1	no	—
642	Dic₃	—	2	1	no	—
643	Dic₃	—	2	1	no	—
644	Dic₃	—	2	2	no	—
645	Dic₃	C₂²×D₄	1	2	yes	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	3	1	no	—
649	C₂³	—	3	8	no	—
650	C₂³	—	3	4	no	—
651	C₂³	—	3	1	no	—
652	C₂³	—	3	2	no	—
653	C₂³	—	3	2	no	—
654	C₂³	—	3	1	no	—
655	C₂³	—	4	2	no	—
656	C₂³	—	6	2	no	—
657	C₂³	—	6	4	no	—
658	C₂³	—	6	4	no	—
659	C₂³	—	6	2	no	—
660	C₂³	—	6	2	no	—
661	C₂³	—	6	4	no	—
662	C₂³	—	6	4	no	—
663	C₂³	—	6	4	no	—
664	C₂³	—	6	2	no	—
665	C₂³	—	6	2	no	—
666	C₂³	—	6	4	no	—
667	C₂³	—	6	4	no	—
668	C₂³	—	6	4	no	—
669	C₂³	—	6	4	no	—
670	C₂³	—	6	4	no	—
671	C₂³	—	6	4	no	—
672	C₂³	—	12	2	no	—
673	C₂³	—	12	2	no	—
674	C₂³	—	12	2	no	—
675	C₂³	—	12	32	no	—
676	C₂³	C₂³×D₃	1	2	yes	—
677	C₂³	C₂³×D₃	1	1	yes	characteristic
678	C₂³	C₂³×D₃	1	2	yes	—
679	C₂³	C₂³×D₃	1	1	yes	characteristic
680	Q₈	—	2	2	no	—
681	Q₈	—	6	4	no	—
682	Q₈	—	6	2	no	—
683	D₄	—	2	4	no	—
684	D₄	—	2	4	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	2	no	—
687	D₄	—	3	8	no	—
688	D₄	—	3	4	no	—
689	D₄	—	4	2	no	—
690	D₄	—	6	4	no	—
691	D₄	—	6	4	no	—
692	D₄	—	6	2	no	—
693	D₄	—	6	4	no	—
694	D₄	—	6	4	no	—
695	D₄	—	6	4	no	—
696	D₄	—	6	2	no	—
697	D₄	—	6	4	no	—
698	D₄	—	6	4	no	—
699	D₄	—	6	2	no	—
700	D₄	—	6	2	no	—
701	D₄	—	12	2	no	—
702	D₄	—	12	2	no	—
703	D₄	—	12	2	no	—
704	D₄	D₃×D₄	1	4	yes	complemented
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	3	1	no	—
709	C₂×C₄	—	3	4	no	—
710	C₂×C₄	—	3	1	no	—
711	C₂×C₄	—	3	1	no	—
712	C₂×C₄	—	3	2	no	—
713	C₂×C₄	—	3	1	no	—
714	C₂×C₄	—	3	2	no	—
715	C₂×C₄	—	3	1	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	6	2	no	—
718	C₂×C₄	—	6	2	no	—
719	C₂×C₄	—	6	2	no	—
720	C₂×C₄	—	6	2	no	—
721	C₂×C₄	—	6	4	no	—
722	C₂×C₄	—	6	4	no	—
723	C₂×C₄	—	6	4	no	—
724	C₂×C₄	—	6	2	no	—
725	C₂×C₄	—	6	4	no	—
726	C₂×C₄	—	6	2	no	—
727	C₂×C₄	—	6	2	no	—
728	C₂×C₄	—	6	2	no	—
729	C₂×C₄	—	6	4	no	—
730	C₂×C₄	—	6	2	no	—
731	C₂×C₄	—	6	2	no	—
732	C₂×C₄	—	12	2	no	—
733	C₂×C₄	—	12	2	no	—
734	C₂×C₄	—	12	2	no	—
735	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
736	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
737	C₂×C₄	C₂³×D₃	1	2	yes	—
738	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
739	C₂×C₄	C₂³×D₃	1	2	yes	—
740	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
741	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
742	C₂×C₃	—	2	2	no	—
743	C₂×C₃	—	2	4	no	—
744	C₂×C₃	—	4	2	no	—
745	C₂×C₃	—	4	1	no	—
746	C₂×C₃	C₂³×D₄	1	1	yes	characteristic
747	C₂×C₃	C₂²×#41	1	1	yes	characteristic
748	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
749	D₃	—	2	2	no	—
750	D₃	—	2	4	no	—
751	D₃	—	4	1	no	—
752	D₃	—	4	2	no	—
753	D₃	#546	1	4	yes	direct product factor
754	C₂²	—	2	1	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	3	2	no	—
765	C₂²	—	3	2	no	—
766	C₂²	—	3	2	no	—
767	C₂²	—	3	4	no	—
768	C₂²	—	3	2	no	—
769	C₂²	—	4	8	no	—
770	C₂²	—	6	8	no	—
771	C₂²	—	6	16	no	—
772	C₂²	—	6	1	no	—
773	C₂²	—	6	2	no	—
774	C₂²	—	6	2	no	—
775	C₂²	—	6	1	no	—
776	C₂²	—	6	1	no	—
777	C₂²	—	6	2	no	—
778	C₂²	—	6	1	no	—
779	C₂²	—	6	2	no	—
780	C₂²	—	6	1	no	—
781	C₂²	—	6	2	no	—
782	C₂²	—	12	8	no	—
783	C₂²	—	12	8	no	—
784	C₂²	—	12	8	no	—
785	C₂²	—	12	4	no	—
786	C₂²	—	12	8	no	—
787	C₂²	C₂×D₃×D₄	1	4	yes	—
788	C₂²	D₃×#41	1	2	yes	complemented
789	C₂²	C₂⁴×D₃	1	1	yes	characteristic
790	C₄	—	2	1	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	2	no	—
796	C₄	—	3	2	no	—
797	C₄	—	6	1	no	—
798	C₄	—	6	1	no	—
799	C₄	—	6	2	no	—
800	C₄	—	6	1	no	—
801	C₄	—	6	1	no	—
802	C₄	—	6	2	no	—
803	C₄	C₂×D₃×D₄	1	2	yes	—
804	C₃	C₂×#546	1	1	yes	characteristic, complemented, Sylow
805	C₂	—	2	2	no	—
806	C₂	—	2	4	no	—
807	C₂	—	3	4	no	—
808	C₂	—	4	2	no	—
809	C₂	—	4	1	no	—
810	C₂	—	6	2	no	—
811	C₂	—	6	4	no	—
812	C₂	—	12	2	no	—
813	C₂	—	12	1	no	—
814	C₂	C₂²×D₃×D₄	1	1	yes	characteristic
815	C₂	C₂×D₃×#41	1	1	yes	characteristic
816	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	C₂×#546
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. C₂×D₃×#41	C₂	semidirect
2. C₂²×D₃×D₄	C₂	semidirect
3. C₃×#546	C₂	semidirect
4. #5829	C₂	semidirect
5. #5806	C₂	semidirect
6. #5676	C₂	semidirect
7. D₃×#124	C₂	semidirect
8. #5654	C₂	semidirect
9. D₃×#123	C₂	semidirect
10. #5630	C₂	semidirect
11. D₃×C₂²⋊Q₈	C₂	semidirect
12. #5612	C₂	semidirect
13. #5610	C₂	semidirect
14. D₃×#121	C₂	semidirect
15. D₃×#121	C₂	semidirect
16. #5591	C₂	semidirect
17. D₃×#120	C₂	semidirect
18. #5554	C₂	semidirect
19. #5550	C₂	semidirect
20. C₄×D₃×D₄	C₂	semidirect
21. C₄×D₃×D₄	C₂	semidirect
22. #5490	C₂	semidirect
23. C₂×D₃×C₂²⋊C₄	C₂	semidirect
26. C₂×C₃×#41	C₂²	semidirect
27. C₂²×C₃×D₄	C₂²	semidirect
28. C₂²×#67	C₂²	semidirect
30. C₂×#239	C₂²	semidirect
31. C₂×D₃×Q₈	C₂²	semidirect
32. C₂×#237	C₂²	semidirect
33. C₂×#237	C₂²	semidirect
39. C₂×D₃×D₄	C₂²	semidirect
40. C₂×D₃×D₄	C₂²	semidirect
41. C₂×D₃×D₄	C₂²	semidirect
42. C₂×D₃×D₄	C₂²	semidirect
43. C₂×D₃×D₄	C₂²	semidirect
44. C₂×#235	C₂²	semidirect
45. C₂×#235	C₂²	semidirect
46. C₂²×D₁₂	C₂²	semidirect
48. C₂²×C₄×D₃	C₂²	semidirect
49. C₂²×C₄×D₃	C₂²	semidirect
50. C₂²×C₄×D₃	C₂²	semidirect
51. C₃×#124	C₂²	semidirect
52. C₃×#123	C₂²	semidirect
53. C₃×C₂²⋊Q₈	C₂²	semidirect
54. C₃×#121	C₂²	semidirect
55. C₃×#121	C₂²	semidirect
56. C₃×#120	C₂²	semidirect
57. C₃×C₄×D₄	C₂²	semidirect
58. C₃×C₄×D₄	C₂²	semidirect
59. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
60. #953	C₂²	semidirect
61. C₂×#217	C₂²	semidirect
62. #947	C₂²	semidirect
63. #946	C₂²	semidirect
64. #939	C₂²	semidirect
65. #939	C₂²	semidirect
66. #939	C₂²	semidirect
67. #938	C₂²	semidirect
68. #938	C₂²	semidirect
69. #937	C₂²	semidirect
70. #937	C₂²	semidirect
71. #937	C₂²	semidirect
72. #936	C₂²	semidirect
73. #935	C₂²	semidirect
74. D₄×Dic₃	C₂²	semidirect
75. D₄×Dic₃	C₂²	semidirect
76. #930	C₂²	semidirect
77. #930	C₂²	semidirect
78. #929	C₂²	semidirect
79. C₄×#67	C₂²	semidirect
80. C₄×#67	C₂²	semidirect
81. C₄×#67	C₂²	semidirect
82. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
83. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
84. #924	C₂²	semidirect
85. #897	C₂²	semidirect
86. #896	C₂²	semidirect
87. #895	C₂²	semidirect
88. #895	C₂²	semidirect
89. #894	C₂²	semidirect
90. #894	C₂²	semidirect
91. #893	C₂²	semidirect
92. #893	C₂²	semidirect
93. D₃×C₄⋊C₄	C₂²	semidirect
94. D₃×C₄⋊C₄	C₂²	semidirect
95. D₃×C₄⋊C₄	C₂²	semidirect
96. #886	C₂²	semidirect
97. #885	C₂²	semidirect
98. #885	C₂²	semidirect
99. #884	C₂²	semidirect
100. #884	C₂²	semidirect
101. #884	C₂²	semidirect
102. #883	C₂²	semidirect
103. #883	C₂²	semidirect
104. #882	C₂²	semidirect
105. #882	C₂²	semidirect
106. #882	C₂²	semidirect
107. #67⋊C₄	C₂²	semidirect
108. #67⋊C₄	C₂²	semidirect
109. #67⋊C₄	C₂²	semidirect
112. D₃×C₂²⋊C₄	C₂²	semidirect
113. D₃×C₂²⋊C₄	C₂²	semidirect
114. D₃×C₂²⋊C₄	C₂²	semidirect
115. D₃×C₂²⋊C₄	C₂²	semidirect
116. D₃×C₂²⋊C₄	C₂²	semidirect
117. D₃×C₂²⋊C₄	C₂²	semidirect
118. D₃×C₂²⋊C₄	C₂²	semidirect
119. D₃×C₂²⋊C₄	C₂²	semidirect
120. D₃×C₂²⋊C₄	C₂²	semidirect
121. #878	C₂²	semidirect
122. #875	C₂²	semidirect
123. C₄×D₁₂	C₂²	semidirect
124. C₄×D₁₂	C₂²	semidirect
125. C₄²×D₃	C₂²	semidirect
139. #546	D₃	direct (N × H)
161. C₂×C₃×Q₈	C₂³	semidirect
167. C₂×C₃×D₄	C₂³	semidirect
168. C₂×C₃×D₄	C₂³	semidirect
170. C₂²×C₃×C₄	C₂³	semidirect
171. C₂²×C₃×C₄	C₂³	semidirect
172. C₂²×C₃×C₄	C₂³	semidirect
180. C₂×#67	C₂³	semidirect
181. C₂×#67	C₂³	semidirect
182. C₂×#67	C₂³	semidirect
183. C₂×#67	C₂³	semidirect
185. C₂²×Dic₃	C₂³	semidirect
186. C₂²×Dic₃	C₂³	semidirect
187. C₂²×Dic₃	C₂³	semidirect
200. D₃×D₄	D₄	semidirect
208. C₂×D₁₂	C₂³	semidirect
209. C₂×D₁₂	C₂³	semidirect
223. C₂×C₄×D₃	C₂³	semidirect
224. C₂×C₄×D₃	C₂³	semidirect
225. C₂×C₄×D₃	C₂³	semidirect
226. C₂×C₄×D₃	C₂³	semidirect
227. C₂×C₄×D₃	C₂³	semidirect
228. C₂×C₄×D₃	C₂³	semidirect
229. C₂×Dic₆	C₂³	semidirect
230. C₂×Dic₆	C₂³	semidirect
231. C₃×C₄⋊C₄	C₂³	semidirect
232. C₃×C₄⋊C₄	C₂³	semidirect
233. C₃×C₄⋊C₄	C₂³	semidirect
236. C₃×C₂²⋊C₄	C₂³	semidirect
237. C₃×C₂²⋊C₄	C₂³	semidirect
238. C₃×C₂²⋊C₄	C₂³	semidirect
239. C₃×C₂²⋊C₄	C₂³	semidirect
240. C₃×C₂²⋊C₄	C₂³	semidirect
241. C₃×C₄²	C₂³	semidirect
244. #217	C₂³	semidirect
245. #217	C₂³	semidirect
246. #217	C₂³	semidirect
247. #217	C₂³	semidirect
248. #217	C₂³	semidirect
253. (C₂×D₃)⋊C₄	C₂³	semidirect
254. (C₂×D₃)⋊C₄	C₂³	semidirect
255. (C₂×D₃)⋊C₄	C₂³	semidirect
256. (C₂×D₃)⋊C₄	C₂³	semidirect
257. (C₂×D₃)⋊C₄	C₂³	semidirect
258. (C₂×D₃)⋊C₄	C₂³	semidirect
259. (C₂×D₃)⋊C₄	C₂³	semidirect
260. (C₂×D₃)⋊C₄	C₂³	semidirect
261. (C₂×D₃)⋊C₄	C₂³	semidirect
262. (C₂×D₃)⋊C₄	C₂³	semidirect
263. C₄⋊Dic₃	C₂³	semidirect
264. C₄⋊Dic₃	C₂³	semidirect
265. C₄⋊Dic₃	C₂³	semidirect
266. Dic₃⋊C₄	C₂³	semidirect
267. Dic₃⋊C₄	C₂³	semidirect
268. Dic₃⋊C₄	C₂³	semidirect
269. Dic₃⋊C₄	C₂³	semidirect
270. Dic₃⋊C₄	C₂³	semidirect
271. C₄×Dic₃	C₂³	semidirect
272. C₄×Dic₃	C₂³	semidirect
273. C₄×Dic₃	C₂³	semidirect
281. C₂×#41	C₂×D₃	semidirect
295. C₂²×D₄	C₂×D₃	semidirect
305. #124	C₂×D₃	semidirect
313. #123	C₂×D₃	semidirect
319. C₂²⋊Q₈	C₂×D₃	semidirect
332. #121	C₂×D₃	semidirect
333. #121	C₂×D₃	semidirect
341. #120	C₂×D₃	semidirect
354. C₄×D₄	C₂×D₃	semidirect
355. C₄×D₄	C₂×D₃	semidirect
373. C₂×C₂²⋊C₄	C₂×D₃	semidirect
403. C₂²×D₃	#41	semidirect
415. C₃×D₄	C₂×D₄	semidirect
436. #67	C₂×D₄	semidirect
453. D₁₂	C₂×D₄	semidirect
491. C₂×Q₈	C₂²×D₃	semidirect
524. C₂×D₄	C₂²×D₃	semidirect
525. C₂×D₄	C₂²×D₃	semidirect
550. C₂²×C₄	C₂²×D₃	semidirect
551. C₂²×C₄	C₂²×D₃	semidirect
552. C₂²×C₄	C₂²×D₃	semidirect
561. C₄⋊C₄	C₂²×D₃	semidirect
562. C₄⋊C₄	C₂²×D₃	semidirect
563. C₄⋊C₄	C₂²×D₃	semidirect
587. C₂²⋊C₄	C₂²×D₃	semidirect
588. C₂²⋊C₄	C₂²×D₃	semidirect
589. C₂²⋊C₄	C₂²×D₃	semidirect
590. C₂²⋊C₄	C₂²×D₃	semidirect
591. C₂²⋊C₄	C₂²×D₃	semidirect
595. C₄²	C₂²×D₃	semidirect
608. C₂²×C₃	C₂×#41	semidirect
630. C₂×D₃	C₂×#41	semidirect
704. D₄	D₃×D₄	semidirect
753. D₃	#546	direct (N × H)
788. C₂²	D₃×#41	semidirect
804. C₃	C₂×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×#41	2
C₂²×D₃×D₄	2
C₃×#546	2
#5829	2
#5806	2
#5676	2
D₃×#124	2
#5654	2
D₃×#123	2
#5630	2
D₃×C₂²⋊Q₈	2
#5612	2
#5610	2
D₃×#121	2
#5591	2
D₃×#120	2
#5554	2
#5550	2
C₄×D₃×D₄	2
#5490	2
C₂×D₃×C₂²⋊C₄	2
C₂×#546	3

Subgroups — D3×#546 #86661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#546 #86661