Subgroups — #86998

Order 384.

1032 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#5727	C₂	1	1	yes	maximal, characteristic, complemented
3	#5724	C₂	1	1	yes	maximal, characteristic, complemented
4	#5712	C₂	1	2	yes	maximal, complemented
5	#5710	C₂	1	2	yes	maximal, complemented
6	#5705	C₂	1	2	yes	maximal, complemented
7	#5704	C₂	1	2	yes	maximal, complemented
8	#5677	C₂	1	1	yes	maximal, characteristic, complemented
9	#5676	C₂	1	1	yes	maximal, characteristic, complemented
10	#5675	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
12	#5647	C₂	1	2	yes	maximal, complemented
13	#5634	C₂	1	2	yes	maximal, complemented
14	#5584	C₂	1	1	yes	maximal, characteristic, complemented
15	#5582	C₂	1	1	yes	maximal, characteristic, complemented
16	#5580	C₂	1	1	yes	maximal, characteristic, complemented
17	#5578	C₂	1	1	yes	maximal, characteristic, complemented
18	#5576	C₂	1	1	yes	maximal, characteristic, complemented
19	Q₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
20	#5561	C₂	1	1	yes	maximal, characteristic, complemented
21	#5554	C₂	1	1	yes	maximal, characteristic, complemented
22	#5534	C₂	1	2	yes	maximal, complemented
23	#5527	C₂	1	2	yes	maximal, complemented
24	#3561	—	3	1	no	maximal, Sylow
25	C₂×#239	C₂²	1	1	yes	characteristic
26	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic
27	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×#237	C₂²	1	1	yes	characteristic
30	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×#126	C₂²	1	2	yes	complemented
33	C₃×#126	C₂²	1	2	yes	complemented
34	C₃×#124	C₂²	1	1	yes	characteristic
35	C₃×#124	C₂²	1	1	yes	characteristic
36	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
41	C₃×#117	C₂²	1	2	yes	complemented
42	#947	C₂²	1	1	yes	characteristic
43	#947	C₂²	1	1	yes	characteristic, complemented
44	#946	C₂²	1	1	yes	characteristic
45	#946	C₂²	1	1	yes	characteristic
46	#946	C₂²	1	2	yes	complemented
47	#946	C₂²	1	1	yes	characteristic, complemented
48	#944	C₂²	1	1	yes	characteristic, complemented
49	#938	C₂²	1	1	yes	characteristic
50	#936	C₂²	1	1	yes	characteristic
51	#930	C₂²	1	2	yes	—
52	#929	C₂²	1	2	yes	complemented
53	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
54	#924	C₂²	1	2	yes	complemented
55	#898	C₂²	1	2	yes	complemented
56	#898	C₂²	1	1	yes	characteristic, complemented
57	#898	C₂²	1	2	yes	complemented
58	#898	C₂²	1	1	yes	characteristic, complemented
59	#897	C₂²	1	2	yes	—
60	#897	C₂²	1	1	yes	characteristic
61	#897	C₂²	1	2	yes	complemented
62	#897	C₂²	1	2	yes	complemented
63	#897	C₂²	1	1	yes	characteristic, complemented
64	#896	C₂²	1	2	yes	—
65	#896	C₂²	1	2	yes	—
66	#896	C₂²	1	2	yes	complemented
67	#896	C₂²	1	2	yes	complemented
68	#896	C₂²	1	2	yes	complemented
69	#896	C₂²	1	2	yes	complemented
70	#895	C₂²	1	1	yes	characteristic
71	#895	C₂²	1	1	yes	characteristic
72	#895	C₂²	1	2	yes	complemented
73	#894	C₂²	1	1	yes	characteristic
74	#894	C₂²	1	1	yes	characteristic
75	#894	C₂²	1	2	yes	complemented
76	#894	C₂²	1	2	yes	complemented
77	#894	C₂²	1	2	yes	complemented
78	#893	C₂²	1	2	yes	—
79	#892	C₂²	1	2	yes	complemented
80	#890	C₂²	1	1	yes	characteristic, complemented
81	#889	C₂²	1	2	yes	complemented
82	#888	C₂²	1	2	yes	complemented
83	#888	C₂²	1	1	yes	characteristic, complemented
84	#886	C₂²	1	2	yes	—
85	#885	C₂²	1	2	yes	—
86	#885	C₂²	1	2	yes	—
87	#885	C₂²	1	2	yes	complemented
88	#885	C₂²	1	2	yes	complemented
89	#884	C₂²	1	2	yes	—
90	#884	C₂²	1	2	yes	complemented
91	#883	C₂²	1	2	yes	—
92	#883	C₂²	1	2	yes	complemented
93	#883	C₂²	1	2	yes	complemented
94	#882	C₂²	1	2	yes	—
95	#882	C₂²	1	2	yes	—
96	#67⋊C₄	C₂²	1	2	yes	complemented
97	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	#879	C₂²	1	2	yes	complemented
101	#878	C₂²	1	2	yes	complemented
102	#878	C₂²	1	2	yes	complemented
103	#878	C₂²	1	2	yes	complemented
104	#876	C₂²	1	2	yes	complemented
105	#875	C₂²	1	1	yes	characteristic
106	#875	C₂²	1	1	yes	characteristic
107	#875	C₂²	1	2	yes	complemented
108	#875	C₂²	1	2	yes	complemented
109	C₄×D₁₂	C₂²	1	1	yes	characteristic
110	C₄×D₁₂	C₂²	1	1	yes	characteristic
111	C₄×D₁₂	C₂²	1	2	yes	—
112	C₄×D₁₂	C₂²	1	1	yes	characteristic
113	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₁₂	C₂²	1	2	yes	complemented
115	#872	C₂²	1	2	yes	—
116	#872	C₂²	1	1	yes	characteristic, complemented
117	#872	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₃	C₂²	1	1	yes	characteristic
119	#869	C₂²	1	1	yes	characteristic, complemented
120	#869	C₂²	1	2	yes	complemented
121	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂²	1	2	yes	complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#563	—	3	2	no	—
125	#562	—	3	2	no	—
126	#556	—	3	1	no	—
127	#556	D₃	1	1	yes	characteristic, complemented
128	#551	—	3	2	no	—
129	#551	—	3	2	no	—
130	D₄×Q₈	—	3	1	no	—
131	D₄×Q₈	—	3	1	no	—
132	#548	—	3	1	no	—
133	#548	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#543	—	3	2	no	—
137	#542	—	3	2	no	—
138	#542	—	3	1	no	—
139	#542	—	3	1	no	—
140	#542	—	3	2	no	—
141	#538	—	3	2	no	—
142	#536	—	3	1	no	—
143	#536	—	3	1	no	—
144	#533	—	3	1	no	—
145	#529	—	3	1	no	—
146	C₂×#124	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	2	yes	—
153	C₂×#67	C₂³	1	2	yes	—
154	C₂×#67	C₂³	1	2	yes	—
155	C₂×#67	C₂³	1	2	yes	—
156	C₂²×Dic₃	C₂³	1	2	yes	—
157	#239	—	4	2	no	—
158	D₃×Q₈	—	4	2	no	—
159	D₃×Q₈	—	4	2	no	—
160	D₃×Q₈	—	4	2	no	—
161	#237	—	4	2	no	—
162	D₃×D₄	—	4	2	no	—
163	C₂×D₁₂	C₂³	1	1	yes	characteristic
164	C₂×D₁₂	C₂³	1	1	yes	characteristic
165	C₂×D₁₂	C₂³	1	1	yes	characteristic
166	C₂×D₁₂	C₂³	1	2	yes	—
167	C₂×D₁₂	C₂³	1	1	yes	characteristic
168	C₂×D₁₂	C₂³	1	2	yes	—
169	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₃	C₂³	1	2	yes	—
175	C₂×C₄×D₃	C₂³	1	2	yes	—
176	C₂×C₄×D₃	C₂³	1	2	yes	—
177	C₂×C₄×D₃	C₂³	1	2	yes	—
178	C₂×C₄×D₃	C₂³	1	2	yes	—
179	C₂×Dic₆	C₂³	1	1	yes	characteristic
180	C₂×Dic₆	C₂³	1	1	yes	characteristic
181	C₂×Dic₆	C₂³	1	2	yes	—
182	C₂×Dic₆	C₂³	1	2	yes	—
183	C₂×Dic₆	C₂³	1	2	yes	—
184	C₂×Dic₆	C₂³	1	2	yes	—
185	C₃×C₄⋊C₄	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	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₄⋊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	2	yes	—
196	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₄²	C₂³	1	1	yes	characteristic
199	C₃×C₄²	C₂³	1	2	yes	—
200	C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₃×C₄²	C₂³	1	1	yes	characteristic
202	C₃×C₄²	C₂³	1	2	yes	—
203	#217	C₂³	1	2	yes	—
204	#217	C₂³	1	2	yes	—
205	#217	C₂³	1	2	yes	—
206	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
209	(C₂×D₃)⋊C₄	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	1	yes	characteristic
215	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
217	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
219	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
225	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
228	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₃	C₂³	1	2	yes	—
230	C₄⋊Dic₃	C₂³	1	2	yes	—
231	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₃	C₂³	1	2	yes	—
233	C₄⋊Dic₃	C₂³	1	2	yes	—
234	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
236	Dic₃⋊C₄	C₂³	1	2	yes	—
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	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₃⋊C₄	C₂³	1	2	yes	—
247	C₄×Dic₃	C₂³	1	1	yes	characteristic
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	1	no	—
254	C₂²×Q₈	—	3	1	no	—
255	C₂²×Q₈	—	3	1	no	—
256	C₂²×Q₈	—	3	1	no	—
257	C₂²×D₄	—	3	1	no	—
258	C₄⋊Q₈	—	3	1	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	C₄⋊Q₈	—	3	2	no	—
261	C₄⋊Q₈	—	3	1	no	—
262	C₄⋊Q₈	—	3	2	no	—
263	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
264	#126	—	3	1	no	—
265	#126	—	3	1	no	—
266	#126	—	3	2	no	—
267	#126	—	3	2	no	—
268	#126	—	3	2	no	—
269	#126	—	3	2	no	—
270	#126	C₂×D₃	1	2	yes	complemented
271	#126	C₂×D₃	1	2	yes	complemented
272	#125	—	3	1	no	—
273	#125	—	3	2	no	—
274	#124	—	3	1	no	—
275	#124	—	3	1	no	—
276	#124	—	3	1	no	—
277	#124	—	3	2	no	—
278	#124	—	3	2	no	—
279	#124	—	3	2	no	—
280	#124	—	3	2	no	—
281	#124	—	3	1	no	—
282	#124	—	3	1	no	—
283	#124	—	3	2	no	—
284	#124	—	3	2	no	—
285	#124	C₂×D₃	1	1	yes	characteristic
286	#124	C₂×D₃	1	1	yes	characteristic
287	#123	—	3	2	no	—
288	#123	—	3	1	no	—
289	#123	—	3	1	no	—
290	#123	—	3	2	no	—
291	#123	—	3	2	no	—
292	#123	—	3	2	no	—
293	#123	—	3	2	no	—
294	#123	—	3	2	no	—
295	#123	—	3	2	no	—
296	#123	—	3	2	no	—
297	C₂²⋊Q₈	—	3	1	no	—
298	C₂²⋊Q₈	—	3	1	no	—
299	C₂²⋊Q₈	—	3	1	no	—
300	C₂²⋊Q₈	—	3	2	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₂²⋊Q₈	—	3	2	no	—
303	C₂²⋊Q₈	—	3	1	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	C₂²⋊Q₈	—	3	2	no	—
306	C₂²⋊Q₈	—	3	2	no	—
307	C₂²⋊Q₈	—	3	1	no	—
308	C₂²⋊Q₈	—	3	2	no	—
309	C₂²⋊Q₈	—	3	2	no	—
310	C₂²⋊Q₈	—	3	2	no	—
311	C₂²⋊Q₈	—	3	2	no	—
312	C₂²⋊Q₈	—	3	2	no	—
313	C₂²⋊Q₈	—	3	2	no	—
314	C₂²⋊Q₈	—	3	2	no	—
315	C₂²⋊Q₈	—	3	2	no	—
316	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
317	#121	—	3	1	no	—
318	#121	—	3	2	no	—
319	#121	—	3	1	no	—
320	#121	—	3	2	no	—
321	#121	—	3	1	no	—
322	#121	—	3	2	no	—
323	#121	—	3	2	no	—
324	#120	—	3	2	no	—
325	#120	—	3	2	no	—
326	C₄×Q₈	—	3	2	no	—
327	C₄×Q₈	—	3	1	no	—
328	C₄×Q₈	—	3	1	no	—
329	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
330	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
331	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	—	3	2	no	—
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	—	3	1	no	—
336	C₄×D₄	—	3	1	no	—
337	C₄×D₄	—	3	2	no	—
338	C₄×D₄	—	3	1	no	—
339	C₄×D₄	—	3	2	no	—
340	C₄×D₄	C₂×D₃	1	1	yes	characteristic
341	#117	—	3	2	no	—
342	#117	—	3	1	no	—
343	#117	—	3	1	no	—
344	#117	—	3	2	no	—
345	#117	C₂×D₃	1	2	yes	complemented
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	—	3	2	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂³×C₃	C₂⁴	1	2	yes	—
352	C₂²×D₃	—	2	4	no	—
353	C₂²×D₃	—	4	2	no	—
354	C₂²×D₃	—	4	2	no	—
355	C₂²×D₃	C₂⁴	1	2	yes	—
356	C₂²×D₃	C₂⁴	1	1	yes	characteristic
357	C₂²×D₃	C₂⁴	1	1	yes	characteristic
358	C₂²×D₃	C₂⁴	1	1	yes	characteristic
359	C₃×Q₈	—	2	2	no	—
360	C₃×Q₈	—	2	2	no	—
361	C₃×Q₈	—	4	1	no	—
362	C₃×D₄	—	2	2	no	—
363	C₂×C₃×C₄	—	4	2	no	—
364	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
365	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂⁴	1	2	yes	—
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂⁴	1	2	yes	—
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	#67	—	4	2	no	—
375	#67	—	4	2	no	—
376	#67	—	4	2	no	—
377	C₂×Dic₃	—	4	2	no	—
378	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
379	C₂×Dic₃	C₂⁴	1	2	yes	—
380	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₃	C₂⁴	1	2	yes	—
383	C₂×Dic₃	C₂⁴	1	2	yes	—
384	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
386	D₁₂	—	2	2	no	—
387	D₁₂	—	2	2	no	—
388	D₁₂	—	2	2	no	—
389	D₁₂	—	4	2	no	—
390	D₁₂	—	4	1	no	—
391	D₁₂	—	4	2	no	—
392	C₄×D₃	—	2	2	no	—
393	C₄×D₃	—	2	2	no	—
394	C₄×D₃	—	2	2	no	—
395	C₄×D₃	—	2	2	no	—
396	C₄×D₃	—	4	1	no	—
397	C₄×D₃	—	4	2	no	—
398	C₄×D₃	—	4	2	no	—
399	C₄×D₃	—	4	2	no	—
400	C₄×D₃	—	4	2	no	—
401	C₄×D₃	—	4	2	no	—
402	Dic₆	—	2	2	no	—
403	Dic₆	—	2	2	no	—
404	Dic₆	—	4	2	no	—
405	Dic₆	—	4	2	no	—
406	Dic₆	—	4	2	no	—
407	Dic₆	—	4	2	no	—
408	C₂⁴	—	3	2	no	—
409	#41	—	12	2	no	—
410	#41	—	12	2	no	—
411	C₂×Q₈	—	3	1	no	—
412	C₂×Q₈	—	3	1	no	—
413	C₂×Q₈	—	3	2	no	—
414	C₂×Q₈	—	3	2	no	—
415	C₂×Q₈	—	3	2	no	—
416	C₂×Q₈	—	3	2	no	—
417	C₂×Q₈	—	12	2	no	—
418	C₂×Q₈	—	12	2	no	—
419	C₂×Q₈	—	12	2	no	—
420	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
421	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
422	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	1	no	—
427	C₂×D₄	—	3	1	no	—
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	1	no	—
431	C₂×D₄	—	3	2	no	—
432	C₂×D₄	—	12	2	no	—
433	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	1	no	—
437	C₂²×C₄	—	3	1	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	2	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	C₂²×D₃	1	2	yes	—
446	C₄⋊C₄	—	3	1	no	—
447	C₄⋊C₄	—	3	1	no	—
448	C₄⋊C₄	—	3	2	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	—	3	1	no	—
451	C₄⋊C₄	—	3	1	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	1	no	—
454	C₄⋊C₄	—	3	1	no	—
455	C₄⋊C₄	—	3	2	no	—
456	C₄⋊C₄	—	3	2	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	2	no	—
462	C₄⋊C₄	—	3	2	no	—
463	C₄⋊C₄	—	3	2	no	—
464	C₄⋊C₄	—	3	2	no	—
465	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
466	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
467	C₄⋊C₄	C₂²×D₃	1	2	yes	—
468	C₄⋊C₄	C₂²×D₃	1	2	yes	—
469	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
470	C₄⋊C₄	C₂²×D₃	1	2	yes	—
471	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×D₃	1	2	yes	—
473	C₂²⋊C₄	—	3	2	no	—
474	C₂²⋊C₄	—	3	2	no	—
475	C₂²⋊C₄	—	3	2	no	—
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	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	1	no	—
490	C₂²⋊C₄	—	3	1	no	—
491	C₂²⋊C₄	—	3	1	no	—
492	C₂²⋊C₄	—	3	1	no	—
493	C₂²⋊C₄	—	3	2	no	—
494	C₂²⋊C₄	—	3	1	no	—
495	C₂²⋊C₄	—	3	1	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	—	3	2	no	—
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	C₄²	—	3	1	no	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	2	no	—
507	C₄²	—	3	2	no	—
508	C₄²	C₂²×D₃	1	1	yes	characteristic
509	C₄²	C₂²×D₃	1	2	yes	—
510	C₄²	C₂²×D₃	1	1	yes	characteristic
511	C₄²	C₂²×D₃	1	1	yes	characteristic
512	C₄²	C₂²×D₃	1	2	yes	—
513	C₂²×C₃	—	2	2	no	—
514	C₂²×C₃	—	2	2	no	—
515	C₂²×C₃	—	2	2	no	—
516	C₂²×C₃	C₂⁵	1	1	yes	characteristic
517	C₂×D₃	—	2	1	no	—
518	C₂×D₃	—	2	1	no	—
519	C₂×D₃	—	2	1	no	—
520	C₂×D₃	—	2	1	no	—
521	C₂×D₃	—	2	2	no	—
522	C₂×D₃	—	2	1	no	—
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	—	8	4	no	—
529	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
530	C₃×C₄	—	2	2	no	—
531	C₃×C₄	—	2	2	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	2	no	—
536	C₃×C₄	—	2	1	no	—
537	C₃×C₄	—	2	1	no	—
538	C₃×C₄	—	2	1	no	—
539	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
540	Dic₃	—	2	2	no	—
541	Dic₃	—	2	2	no	—
542	Dic₃	—	2	1	no	—
543	Dic₃	—	2	1	no	—
544	Dic₃	—	2	1	no	—
545	Dic₃	—	2	1	no	—
546	Dic₃	—	2	1	no	—
547	Dic₃	—	2	2	no	—
548	C₂³	—	3	1	no	—
549	C₂³	—	3	2	no	—
550	C₂³	—	3	1	no	—
551	C₂³	—	3	1	no	—
552	C₂³	—	6	4	no	—
553	C₂³	—	12	2	no	—
554	C₂³	—	12	2	no	—
555	C₂³	C₂³×D₃	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	6	2	no	—
560	Q₈	—	6	2	no	—
561	Q₈	—	12	2	no	—
562	Q₈	—	12	2	no	—
563	Q₈	—	12	2	no	—
564	Q₈	—	12	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	6	2	no	—
567	D₄	—	6	2	no	—
568	D₄	—	6	2	no	—
569	D₄	—	12	2	no	—
570	D₄	—	12	2	no	—
571	D₄	—	12	1	no	—
572	D₄	—	12	2	no	—
573	D₄	—	12	2	no	—
574	D₄	—	12	2	no	—
575	C₂×C₄	—	3	1	no	—
576	C₂×C₄	—	3	1	no	—
577	C₂×C₄	—	3	2	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	2	no	—
580	C₂×C₄	—	3	2	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	1	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	6	2	no	—
585	C₂×C₄	—	6	2	no	—
586	C₂×C₄	—	6	2	no	—
587	C₂×C₄	—	6	2	no	—
588	C₂×C₄	—	12	2	no	—
589	C₂×C₄	—	12	2	no	—
590	C₂×C₄	—	12	2	no	—
591	C₂×C₄	—	12	2	no	—
592	C₂×C₄	—	12	2	no	—
593	C₂×C₄	—	12	1	no	—
594	C₂×C₄	—	12	2	no	—
595	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₃	1	2	yes	—
600	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
602	C₂×C₄	C₂³×D₃	1	2	yes	—
603	C₂×C₄	C₂³×D₃	1	2	yes	—
604	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
605	C₂×C₃	—	4	2	no	—
606	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
607	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
608	C₂×C₃	#585	1	1	yes	characteristic
609	D₃	—	2	2	no	—
610	D₃	—	4	1	no	—
611	D₃	—	4	1	no	—
612	D₃	—	4	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	3	2	no	—
617	C₂²	—	6	1	no	—
618	C₂²	—	6	1	no	—
619	C₂²	—	6	1	no	—
620	C₂²	—	6	1	no	—
621	C₂²	—	6	2	no	—
622	C₂²	—	6	2	no	—
623	C₂²	—	6	1	no	—
624	C₂²	—	6	1	no	—
625	C₂²	—	6	1	no	—
626	C₂²	—	6	1	no	—
627	C₂²	—	6	2	no	—
628	C₂²	—	24	4	no	—
629	C₂²	C₂⁴×D₃	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	6	1	no	—
640	C₄	—	6	1	no	—
641	C₄	—	6	1	no	—
642	C₄	—	6	2	no	—
643	C₄	—	6	2	no	—
644	C₄	—	6	2	no	—
645	C₄	—	6	1	no	—
646	C₄	—	6	1	no	—
647	C₄	#1009	1	2	yes	—
648	C₃	#3561	1	1	yes	characteristic, complemented, Sylow
649	C₂	—	4	2	no	—
650	C₂	—	6	2	no	—
651	C₂	—	12	2	no	—
652	C₂	—	12	1	no	—
653	C₂	—	12	1	no	—
654	C₂	C₂×#1009	1	1	yes	characteristic
655	C₂	#5964	1	1	yes	characteristic
656	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×#556	C₂
hypercenter	#556	D₃
hypocenter	C₃	#3561
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₃×#556	C₂	semidirect
2. #5727	C₂	semidirect
3. #5724	C₂	semidirect
4. #5712	C₂	semidirect
5. #5710	C₂	semidirect
6. #5705	C₂	semidirect
7. #5704	C₂	semidirect
8. #5677	C₂	semidirect
9. #5676	C₂	semidirect
10. #5675	C₂	semidirect
11. D₃×#124	C₂	semidirect
12. #5647	C₂	semidirect
13. #5634	C₂	semidirect
14. #5584	C₂	semidirect
15. #5582	C₂	semidirect
16. #5580	C₂	semidirect
17. #5578	C₂	semidirect
18. #5576	C₂	semidirect
19. Q₈×D₁₂	C₂	semidirect
20. #5561	C₂	semidirect
21. #5554	C₂	semidirect
22. #5534	C₂	semidirect
23. #5527	C₂	semidirect
27. C₂×D₃×Q₈	C₂²	semidirect
28. C₂×D₃×Q₈	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×#126	C₂²	semidirect
33. C₃×#126	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₄×Q₈	C₂²	semidirect
38. C₃×C₄×Q₈	C₂²	semidirect
39. C₃×C₄×Q₈	C₂²	semidirect
41. C₃×#117	C₂²	semidirect
43. #947	C₂²	semidirect
46. #946	C₂²	semidirect
47. #946	C₂²	semidirect
48. #944	C₂²	semidirect
52. #929	C₂²	semidirect
54. #924	C₂²	semidirect
55. #898	C₂²	semidirect
56. #898	C₂²	semidirect
57. #898	C₂²	semidirect
58. #898	C₂²	semidirect
61. #897	C₂²	semidirect
62. #897	C₂²	semidirect
63. #897	C₂²	semidirect
66. #896	C₂²	semidirect
67. #896	C₂²	semidirect
68. #896	C₂²	semidirect
69. #896	C₂²	semidirect
72. #895	C₂²	semidirect
75. #894	C₂²	semidirect
76. #894	C₂²	semidirect
77. #894	C₂²	semidirect
79. #892	C₂²	semidirect
80. #890	C₂²	semidirect
81. #889	C₂²	semidirect
82. #888	C₂²	semidirect
83. #888	C₂²	semidirect
87. #885	C₂²	semidirect
88. #885	C₂²	semidirect
90. #884	C₂²	semidirect
92. #883	C₂²	semidirect
93. #883	C₂²	semidirect
96. #67⋊C₄	C₂²	semidirect
100. #879	C₂²	semidirect
101. #878	C₂²	semidirect
102. #878	C₂²	semidirect
103. #878	C₂²	semidirect
104. #876	C₂²	semidirect
107. #875	C₂²	semidirect
108. #875	C₂²	semidirect
113. C₄×D₁₂	C₂²	semidirect
114. C₄×D₁₂	C₂²	semidirect
116. #872	C₂²	semidirect
117. #872	C₂²	semidirect
119. #869	C₂²	semidirect
120. #869	C₂²	semidirect
121. C₄×Dic₆	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
127. #556	D₃	semidirect
263. C₄⋊Q₈	C₂×D₃	semidirect
270. #126	C₂×D₃	semidirect
271. #126	C₂×D₃	semidirect
316. C₂²⋊Q₈	C₂×D₃	semidirect
329. C₄×Q₈	C₂×D₃	semidirect
330. C₄×Q₈	C₂×D₃	semidirect
331. C₄×Q₈	C₂×D₃	semidirect
345. #117	C₂×D₃	semidirect
648. C₃	#3561	semidirect

Maximal subgroups

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

subgroup	index
C₃×#556	2
#5727	2
#5724	2
#5712	2
#5710	2
#5705	2
#5704	2
#5677	2
#5676	2
#5675	2
D₃×#124	2
#5647	2
#5634	2
#5584	2
#5582	2
#5580	2
#5578	2
#5576	2
Q₈×D₁₂	2
#5561	2
#5554	2
#5534	2
#5527	2
#3561	3