Subgroups — #86634

Order 384.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 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	#5829	C₂	1	1	yes	maximal, characteristic, complemented
3	#5827	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×#67	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	#5681	C₂	1	1	yes	maximal, characteristic, complemented
8	#5665	C₂	1	2	yes	maximal, complemented
9	#5658	C₂	1	2	yes	maximal, complemented
10	#5642	C₂	1	1	yes	maximal, characteristic, complemented
11	#5624	C₂	1	1	yes	maximal, characteristic, complemented
12	#5619	C₂	1	1	yes	maximal, characteristic, complemented
13	#5618	C₂	1	1	yes	maximal, characteristic, complemented
14	#5618	C₂	1	2	yes	maximal, complemented
15	#5617	C₂	1	2	yes	maximal, complemented
16	#5591	C₂	1	2	yes	maximal, complemented
17	#5586	C₂	1	2	yes	maximal, complemented
18	#5555	C₂	1	1	yes	maximal, characteristic, complemented
19	#5545	C₂	1	1	yes	maximal, characteristic, complemented
20	#5543	C₂	1	1	yes	maximal, characteristic, complemented
21	#5538	C₂	1	1	yes	maximal, characteristic, complemented
22	#5495	C₂	1	2	yes	maximal, complemented
23	C₂×#886	C₂	1	2	yes	maximal, complemented
24	#3513	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
27	C₂²×#67	C₂²	1	2	yes	—
28	C₂³×Dic₃	C₂²	1	2	yes	complemented
29	C₂×#237	C₂²	1	2	yes	complemented
30	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
31	C₃×#124	C₂²	1	1	yes	characteristic, complemented
32	C₃×#123	C₂²	1	2	yes	complemented
33	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×#121	C₂²	1	2	yes	complemented
35	C₃×#121	C₂²	1	1	yes	characteristic, complemented
36	C₃×#120	C₂²	1	2	yes	complemented
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
40	#953	C₂²	1	2	yes	—
41	C₂×#217	C₂²	1	2	yes	complemented
42	#947	C₂²	1	1	yes	characteristic, complemented
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	#940	C₂²	1	1	yes	characteristic
47	#939	C₂²	1	2	yes	—
48	#939	C₂²	1	1	yes	characteristic
49	#939	C₂²	1	2	yes	complemented
50	#939	C₂²	1	2	yes	complemented
51	#939	C₂²	1	2	yes	complemented
52	#938	C₂²	1	1	yes	characteristic
53	#938	C₂²	1	2	yes	complemented
54	#937	C₂²	1	2	yes	—
55	#937	C₂²	1	2	yes	complemented
56	#935	C₂²	1	1	yes	characteristic, complemented
57	D₄×Dic₃	C₂²	1	1	yes	characteristic
58	D₄×Dic₃	C₂²	1	1	yes	characteristic
59	D₄×Dic₃	C₂²	1	1	yes	characteristic
60	D₄×Dic₃	C₂²	1	2	yes	complemented
61	D₄×Dic₃	C₂²	1	2	yes	complemented
62	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
63	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
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	#930	C₂²	1	1	yes	characteristic
68	#930	C₂²	1	1	yes	characteristic, complemented
69	#929	C₂²	1	2	yes	complemented
70	C₄×#67	C₂²	1	1	yes	characteristic
71	C₄×#67	C₂²	1	2	yes	complemented
72	C₄×#67	C₂²	1	1	yes	characteristic, complemented
73	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
74	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
75	#926	C₂²	1	2	yes	complemented
76	#926	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄⋊Dic₃	C₂²	1	2	yes	complemented
79	C₂×C₄⋊Dic₃	C₂²	1	2	yes	complemented
80	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
81	#924	C₂²	1	2	yes	complemented
82	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
83	#898	C₂²	1	2	yes	complemented
84	#898	C₂²	1	1	yes	characteristic, complemented
85	#898	C₂²	1	2	yes	complemented
86	#897	C₂²	1	2	yes	complemented
87	#893	C₂²	1	1	yes	characteristic, complemented
88	#892	C₂²	1	1	yes	characteristic, complemented
89	#892	C₂²	1	2	yes	complemented
90	#890	C₂²	1	2	yes	complemented
91	#890	C₂²	1	1	yes	characteristic, complemented
92	#890	C₂²	1	1	yes	characteristic, complemented
93	#889	C₂²	1	1	yes	characteristic, complemented
94	#886	C₂²	1	2	yes	—
95	#886	C₂²	1	1	yes	characteristic
96	#886	C₂²	1	2	yes	complemented
97	#886	C₂²	1	2	yes	complemented
98	#886	C₂²	1	2	yes	complemented
99	#886	C₂²	1	2	yes	complemented
100	#886	C₂²	1	2	yes	complemented
101	#886	C₂²	1	2	yes	complemented
102	#886	C₂²	1	2	yes	complemented
103	#885	C₂²	1	2	yes	complemented
104	#885	C₂²	1	2	yes	complemented
105	#885	C₂²	1	1	yes	characteristic, complemented
106	#883	C₂²	1	2	yes	complemented
107	#883	C₂²	1	2	yes	complemented
108	#67⋊C₄	C₂²	1	2	yes	complemented
109	#67⋊C₄	C₂²	1	2	yes	complemented
110	#67⋊C₄	C₂²	1	2	yes	complemented
111	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
112	#879	C₂²	1	2	yes	complemented
113	#879	C₂²	1	2	yes	complemented
114	#879	C₂²	1	1	yes	characteristic, complemented
115	#878	C₂²	1	2	yes	complemented
116	#878	C₂²	1	2	yes	complemented
117	#878	C₂²	1	2	yes	complemented
118	#878	C₂²	1	1	yes	characteristic, complemented
119	#877	C₂²	1	2	yes	complemented
120	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
121	#872	C₂²	1	1	yes	characteristic, complemented
122	#869	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#559	—	3	1	no	—
125	#554	—	3	1	no	—
126	#553	—	3	1	no	—
127	#553	—	3	2	no	—
128	#552	—	3	1	no	—
129	#551	—	3	2	no	—
130	#551	—	3	2	no	—
131	#547	—	3	1	no	—
132	#546	—	3	1	no	—
133	#546	—	3	2	no	—
134	#546	D₃	1	1	yes	characteristic, complemented
135	D₄²	—	3	1	no	—
136	#542	—	3	1	no	—
137	#540	—	3	1	no	—
138	#539	—	3	2	no	—
139	#538	—	3	2	no	—
140	#529	—	3	1	no	—
141	#529	—	3	1	no	—
142	#525	—	3	2	no	—
143	C₂×#123	—	3	2	no	—
144	#520	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂⁴×C₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₃×#41	—	2	4	no	—
150	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×D₄	—	2	4	no	—
152	C₂×C₃×D₄	C₂³	1	2	yes	—
153	C₂×C₃×D₄	C₂³	1	2	yes	—
154	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×D₄	C₂³	1	2	yes	—
157	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³	1	2	yes	—
160	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂³	1	2	yes	—
162	C₂×#67	—	4	4	no	—
163	C₂×#67	C₂³	1	2	yes	—
164	C₂×#67	C₂³	1	2	yes	—
165	C₂×#67	C₂³	1	1	yes	characteristic
166	C₂×#67	C₂³	1	2	yes	—
167	C₂×#67	C₂³	1	2	yes	—
168	C₂×#67	C₂³	1	2	yes	—
169	C₂×#67	C₂³	1	1	yes	characteristic
170	C₂×#67	C₂³	1	2	yes	—
171	C₂²×Dic₃	—	4	4	no	—
172	C₂²×Dic₃	C₂³	1	2	yes	—
173	C₂²×Dic₃	C₂³	1	1	yes	characteristic
174	C₂²×Dic₃	C₂³	1	1	yes	characteristic
175	C₂²×Dic₃	C₂³	1	2	yes	—
176	C₂²×Dic₃	C₂³	1	2	yes	—
177	C₂²×Dic₃	C₂³	1	2	yes	—
178	C₂²×Dic₃	C₂³	1	2	yes	—
179	C₂²×Dic₃	C₂³	1	2	yes	—
180	C₂²×Dic₃	C₂³	1	2	yes	—
181	#237	—	4	4	no	—
182	D₃×D₄	—	2	4	no	—
183	C₂×D₁₂	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
185	C₂×C₄×D₃	C₂³	1	2	yes	—
186	C₂×C₄×D₃	C₂³	1	2	yes	—
187	C₂×Dic₆	C₂³	1	1	yes	characteristic
188	C₂×Dic₆	C₂³	1	2	yes	—
189	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₄²	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
207	#217	C₂³	1	1	yes	characteristic
208	#217	C₂³	1	2	yes	—
209	#217	C₂³	1	1	yes	characteristic
210	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
211	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
212	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
220	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
221	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₃	C₂³	1	2	yes	—
224	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₃	C₂³	1	2	yes	—
229	C₄⋊Dic₃	C₂³	1	2	yes	—
230	C₄⋊Dic₃	C₂³	1	2	yes	—
231	C₄⋊Dic₃	C₂³	1	2	yes	—
232	C₄⋊Dic₃	C₂³	1	2	yes	—
233	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₃	C₂³	1	2	yes	—
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	1	yes	characteristic
239	Dic₃⋊C₄	C₂³	1	2	yes	—
240	Dic₃⋊C₄	C₂³	1	2	yes	—
241	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	2	no	—
253	C₂×#41	C₂×D₃	1	1	yes	characteristic
254	C₂²×D₄	—	3	2	no	—
255	C₂²×D₄	—	3	1	no	—
256	C₂²×D₄	C₂×D₃	1	1	yes	characteristic
257	C₂³×C₄	—	3	2	no	—
258	C₄⋊Q₈	—	3	1	no	—
259	#127	—	3	1	no	—
260	#126	—	3	2	no	—
261	#126	—	3	1	no	—
262	#126	—	3	2	no	—
263	#126	—	3	1	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#125	—	3	1	no	—
267	#125	—	3	1	no	—
268	#125	—	3	2	no	—
269	#125	—	3	1	no	—
270	#124	—	3	1	no	—
271	#124	—	3	1	no	—
272	#124	—	3	2	no	—
273	#124	—	3	2	no	—
274	#124	C₂×D₃	1	1	yes	characteristic, complemented
275	#123	—	3	1	no	—
276	#123	—	3	2	no	—
277	#123	—	3	1	no	—
278	#123	—	3	2	no	—
279	#123	—	3	2	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	—	3	2	no	—
283	#123	—	3	2	no	—
284	#123	—	3	2	no	—
285	#123	—	3	2	no	—
286	#123	—	3	2	no	—
287	#123	—	3	2	no	—
288	#123	C₂×D₃	1	2	yes	complemented
289	C₂²⋊Q₈	—	3	1	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	2	no	—
292	C₂²⋊Q₈	—	3	2	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	1	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
297	#121	—	3	2	no	—
298	#121	—	3	2	no	—
299	#121	—	3	1	no	—
300	#121	—	3	2	no	—
301	#121	—	3	2	no	—
302	#121	—	3	2	no	—
303	#121	—	3	1	no	—
304	#121	—	3	1	no	—
305	#121	—	3	1	no	—
306	#121	C₂×D₃	1	2	yes	complemented
307	#121	C₂×D₃	1	1	yes	characteristic, complemented
308	#120	—	3	2	no	—
309	#120	—	3	2	no	—
310	#120	—	3	2	no	—
311	#120	C₂×D₃	1	2	yes	complemented
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	—	3	1	no	—
314	C₄×Q₈	—	3	1	no	—
315	C₄×D₄	—	3	1	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	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	2	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	2	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	1	no	—
327	C₄×D₄	—	3	1	no	—
328	C₄×D₄	—	3	1	no	—
329	C₄×D₄	—	3	2	no	—
330	C₄×D₄	—	3	2	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	3	1	no	—
333	C₄×D₄	C₂×D₃	1	1	yes	characteristic
334	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
335	#117	—	3	1	no	—
336	#117	—	3	2	no	—
337	#117	—	3	1	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	1	no	—
344	C₂×C₄⋊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×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
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	—	2	4	no	—
359	C₂²×D₃	—	4	2	no	—
360	C₂²×D₃	—	4	2	no	—
361	C₂²×D₃	C₂⁴	1	1	yes	characteristic
362	C₂²×D₃	C₂⁴	1	2	yes	—
363	C₃×Q₈	—	2	2	no	—
364	C₃×D₄	—	2	4	no	—
365	C₃×D₄	—	2	4	no	—
366	C₃×D₄	—	2	2	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	4	2	no	—
369	C₃×D₄	#41	1	4	yes	complemented
370	C₂×C₃×C₄	—	2	4	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	4	2	no	—
374	C₂×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	#67	—	2	4	no	—
382	#67	—	2	4	no	—
383	#67	—	2	2	no	—
384	#67	—	4	2	no	—
385	#67	—	4	2	no	—
386	#67	—	4	2	no	—
387	#67	—	4	1	no	—
388	#67	—	4	2	no	—
389	C₂×Dic₃	—	2	4	no	—
390	C₂×Dic₃	—	2	2	no	—
391	C₂×Dic₃	—	4	2	no	—
392	C₂×Dic₃	—	4	2	no	—
393	C₂×Dic₃	—	4	2	no	—
394	C₂×Dic₃	—	4	2	no	—
395	C₂×Dic₃	—	4	2	no	—
396	C₂×Dic₃	—	4	1	no	—
397	C₂×Dic₃	—	4	2	no	—
398	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₃	C₂⁴	1	2	yes	—
405	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₃	C₂⁴	1	2	yes	—
407	C₂×Dic₃	C₂⁴	1	2	yes	—
408	D₁₂	—	2	2	no	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	—	4	2	no	—
411	C₄×D₃	—	4	2	no	—
412	Dic₆	—	4	1	no	—
413	Dic₆	—	4	2	no	—
414	C₂⁴	—	3	2	no	—
415	C₂⁴	C₂²×D₃	1	2	yes	—
416	#41	—	2	4	no	—
417	#41	—	12	4	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	3	2	no	—
420	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	3	2	no	—
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	3	1	no	—
425	C₂×D₄	—	3	1	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	2	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	1	no	—
431	C₂×D₄	—	6	4	no	—
432	C₂×D₄	—	12	4	no	—
433	C₂×D₄	C₂²×D₃	1	2	yes	—
434	C₂×D₄	C₂²×D₃	1	2	yes	—
435	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
436	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
437	C₂×D₄	C₂²×D₃	1	2	yes	—
438	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	2	no	—
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	—	3	2	no	—
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	3	1	no	—
449	C₂²×C₄	—	3	2	no	—
450	C₂²×C₄	—	3	2	no	—
451	C₂²×C₄	—	12	4	no	—
452	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₃	1	2	yes	—
454	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₃	1	2	yes	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	1	no	—
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	—	3	2	no	—
461	C₄⋊C₄	—	3	1	no	—
462	C₄⋊C₄	—	3	2	no	—
463	C₄⋊C₄	—	3	1	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	1	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	1	no	—
471	C₄⋊C₄	—	3	2	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	1	no	—
474	C₄⋊C₄	—	3	1	no	—
475	C₄⋊C₄	—	3	2	no	—
476	C₄⋊C₄	—	3	1	no	—
477	C₄⋊C₄	—	3	1	no	—
478	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₃	1	2	yes	—
480	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	1	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	1	no	—
488	C₂²⋊C₄	—	3	1	no	—
489	C₂²⋊C₄	—	3	1	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	2	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	2	no	—
497	C₂²⋊C₄	—	3	2	no	—
498	C₂²⋊C₄	—	3	2	no	—
499	C₂²⋊C₄	—	3	2	no	—
500	C₂²⋊C₄	—	3	2	no	—
501	C₂²⋊C₄	—	3	1	no	—
502	C₂²⋊C₄	—	3	2	no	—
503	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
505	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
506	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
508	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
510	C₄²	—	3	1	no	—
511	C₄²	—	3	1	no	—
512	C₄²	—	3	1	no	—
513	C₄²	—	3	1	no	—
514	C₄²	—	3	2	no	—
515	C₄²	—	3	2	no	—
516	C₄²	—	3	2	no	—
517	C₄²	—	3	1	no	—
518	C₄²	C₂²×D₃	1	1	yes	characteristic
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	2	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	2	no	—
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	2	no	—
525	C₂²×C₃	—	2	1	no	—
526	C₂²×C₃	—	2	2	no	—
527	C₂²×C₃	—	2	1	no	—
528	C₂²×C₃	—	2	2	no	—
529	C₂²×C₃	—	4	8	no	—
530	C₂²×C₃	C₂×#41	1	4	yes	—
531	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
532	C₂²×C₃	C₂⁵	1	1	yes	characteristic
533	C₂×D₃	—	2	1	no	—
534	C₂×D₃	—	2	2	no	—
535	C₂×D₃	—	2	2	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	2	no	—
538	C₂×D₃	—	2	1	no	—
539	C₂×D₃	—	8	4	no	—
540	C₃×C₄	—	2	1	no	—
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	—	2	2	no	—
543	C₃×C₄	—	2	1	no	—
544	C₃×C₄	—	2	1	no	—
545	C₃×C₄	—	2	2	no	—
546	C₃×C₄	C₂×#41	1	2	yes	—
547	Dic₃	—	2	1	no	—
548	Dic₃	—	2	2	no	—
549	Dic₃	—	2	2	no	—
550	Dic₃	—	2	2	no	—
551	Dic₃	—	2	1	no	—
552	Dic₃	—	2	1	no	—
553	Dic₃	—	2	1	no	—
554	Dic₃	—	2	1	no	—
555	Dic₃	—	2	1	no	—
556	Dic₃	—	2	1	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	3	1	no	—
560	C₂³	—	3	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	6	4	no	—
563	C₂³	—	12	2	no	—
564	C₂³	—	12	2	no	—
565	C₂³	C₂³×D₃	1	2	yes	—
566	C₂³	C₂³×D₃	1	1	yes	characteristic
567	C₂³	C₂³×D₃	1	2	yes	—
568	C₂³	C₂³×D₃	1	1	yes	characteristic
569	Q₈	—	2	2	no	—
570	Q₈	—	12	2	no	—
571	Q₈	—	12	1	no	—
572	D₄	—	2	4	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	6	4	no	—
578	D₄	—	6	2	no	—
579	D₄	—	6	4	no	—
580	D₄	—	6	2	no	—
581	D₄	—	12	2	no	—
582	D₄	—	12	2	no	—
583	D₄	—	12	2	no	—
584	D₄	—	12	1	no	—
585	D₄	—	12	2	no	—
586	D₄	#237	1	4	yes	complemented
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	3	1	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	3	1	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	1	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	3	2	no	—
597	C₂×C₄	—	3	2	no	—
598	C₂×C₄	—	3	1	no	—
599	C₂×C₄	—	3	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	6	2	no	—
602	C₂×C₄	—	6	4	no	—
603	C₂×C₄	—	6	2	no	—
604	C₂×C₄	—	12	2	no	—
605	C₂×C₄	—	12	2	no	—
606	C₂×C₄	—	12	2	no	—
607	C₂×C₄	—	12	2	no	—
608	C₂×C₄	—	12	2	no	—
609	C₂×C₄	—	12	2	no	—
610	C₂×C₄	—	12	2	no	—
611	C₂×C₄	—	12	2	no	—
612	C₂×C₄	—	12	1	no	—
613	C₂×C₄	C₂³×D₃	1	2	yes	—
614	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₃	1	2	yes	—
616	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
620	C₂×C₃	—	2	4	no	—
621	C₂×C₃	—	2	2	no	—
622	C₂×C₃	—	4	1	no	—
623	C₂×C₃	—	4	2	no	—
624	C₂×C₃	C₂²×#41	1	1	yes	characteristic
625	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
626	C₂×C₃	#585	1	1	yes	characteristic
627	D₃	—	4	2	no	—
628	D₃	—	4	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	4	8	no	—
640	C₂²	—	6	1	no	—
641	C₂²	—	6	2	no	—
642	C₂²	—	6	2	no	—
643	C₂²	—	6	1	no	—
644	C₂²	—	6	2	no	—
645	C₂²	—	6	1	no	—
646	C₂²	—	24	4	no	—
647	C₂²	C₂×#237	1	4	yes	—
648	C₂²	#1009	1	2	yes	—
649	C₂²	C₂⁴×D₃	1	1	yes	characteristic
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	6	1	no	—
657	C₄	—	6	1	no	—
658	C₄	—	6	1	no	—
659	C₄	—	6	2	no	—
660	C₄	—	6	2	no	—
661	C₄	—	6	1	no	—
662	C₄	—	6	2	no	—
663	C₄	—	6	1	no	—
664	C₄	—	6	1	no	—
665	C₄	—	6	1	no	—
666	C₄	C₂×#237	1	2	yes	—
667	C₃	#3513	1	1	yes	characteristic, complemented, Sylow
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	12	1	no	—
673	C₂	—	12	2	no	—
674	C₂	C₂²×#237	1	1	yes	characteristic
675	C₂	C₂×#1009	1	1	yes	characteristic
676	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	#3513
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. #5829	C₂	semidirect
3. #5827	C₂	semidirect
4. D₄×#67	C₂	semidirect
5. C₂×D₄×Dic₃	C₂	semidirect
6. #5682	C₂	semidirect
7. #5681	C₂	semidirect
8. #5665	C₂	semidirect
9. #5658	C₂	semidirect
10. #5642	C₂	semidirect
11. #5624	C₂	semidirect
12. #5619	C₂	semidirect
13. #5618	C₂	semidirect
14. #5618	C₂	semidirect
15. #5617	C₂	semidirect
16. #5591	C₂	semidirect
17. #5586	C₂	semidirect
18. #5555	C₂	semidirect
19. #5545	C₂	semidirect
20. #5543	C₂	semidirect
21. #5538	C₂	semidirect
22. #5495	C₂	semidirect
23. C₂×#886	C₂	semidirect
28. C₂³×Dic₃	C₂²	semidirect
29. C₂×#237	C₂²	semidirect
31. C₃×#124	C₂²	semidirect
32. C₃×#123	C₂²	semidirect
33. C₃×C₂²⋊Q₈	C₂²	semidirect
34. C₃×#121	C₂²	semidirect
35. C₃×#121	C₂²	semidirect
36. C₃×#120	C₂²	semidirect
38. C₃×C₄×D₄	C₂²	semidirect
39. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
41. C₂×#217	C₂²	semidirect
42. #947	C₂²	semidirect
43. #946	C₂²	semidirect
44. Q₈×Dic₃	C₂²	semidirect
45. Q₈×Dic₃	C₂²	semidirect
49. #939	C₂²	semidirect
50. #939	C₂²	semidirect
51. #939	C₂²	semidirect
53. #938	C₂²	semidirect
55. #937	C₂²	semidirect
56. #935	C₂²	semidirect
60. D₄×Dic₃	C₂²	semidirect
61. D₄×Dic₃	C₂²	semidirect
62. D₄×Dic₃	C₂²	semidirect
63. D₄×Dic₃	C₂²	semidirect
64. D₄×Dic₃	C₂²	semidirect
65. D₄×Dic₃	C₂²	semidirect
66. D₄×Dic₃	C₂²	semidirect
68. #930	C₂²	semidirect
69. #929	C₂²	semidirect
71. C₄×#67	C₂²	semidirect
72. C₄×#67	C₂²	semidirect
73. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
74. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
75. #926	C₂²	semidirect
76. #926	C₂²	semidirect
77. C₂×C₄⋊Dic₃	C₂²	semidirect
78. C₂×C₄⋊Dic₃	C₂²	semidirect
79. C₂×C₄⋊Dic₃	C₂²	semidirect
80. C₂×C₄⋊Dic₃	C₂²	semidirect
81. #924	C₂²	semidirect
82. C₂×C₄×Dic₃	C₂²	semidirect
83. #898	C₂²	semidirect
84. #898	C₂²	semidirect
85. #898	C₂²	semidirect
86. #897	C₂²	semidirect
87. #893	C₂²	semidirect
88. #892	C₂²	semidirect
89. #892	C₂²	semidirect
90. #890	C₂²	semidirect
91. #890	C₂²	semidirect
92. #890	C₂²	semidirect
93. #889	C₂²	semidirect
96. #886	C₂²	semidirect
97. #886	C₂²	semidirect
98. #886	C₂²	semidirect
99. #886	C₂²	semidirect
100. #886	C₂²	semidirect
101. #886	C₂²	semidirect
102. #886	C₂²	semidirect
103. #885	C₂²	semidirect
104. #885	C₂²	semidirect
105. #885	C₂²	semidirect
106. #883	C₂²	semidirect
107. #883	C₂²	semidirect
108. #67⋊C₄	C₂²	semidirect
109. #67⋊C₄	C₂²	semidirect
110. #67⋊C₄	C₂²	semidirect
111. D₃×C₂²⋊C₄	C₂²	semidirect
112. #879	C₂²	semidirect
113. #879	C₂²	semidirect
114. #879	C₂²	semidirect
115. #878	C₂²	semidirect
116. #878	C₂²	semidirect
117. #878	C₂²	semidirect
118. #878	C₂²	semidirect
119. #877	C₂²	semidirect
120. C₄×D₁₂	C₂²	semidirect
121. #872	C₂²	semidirect
122. #869	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
134. #546	D₃	semidirect
274. #124	C₂×D₃	semidirect
288. #123	C₂×D₃	semidirect
296. C₂²⋊Q₈	C₂×D₃	semidirect
306. #121	C₂×D₃	semidirect
307. #121	C₂×D₃	semidirect
311. #120	C₂×D₃	semidirect
334. C₄×D₄	C₂×D₃	semidirect
349. C₂×C₂²⋊C₄	C₂×D₃	semidirect
369. C₃×D₄	#41	semidirect
586. D₄	#237	semidirect
667. C₃	#3513	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
#5829	2
#5827	2
D₄×#67	2
C₂×D₄×Dic₃	2
#5682	2
#5681	2
#5665	2
#5658	2
#5642	2
#5624	2
#5619	2
#5618	2
#5617	2
#5591	2
#5586	2
#5555	2
#5545	2
#5543	2
#5538	2
#5495	2
C₂×#886	2
#3513	3