Subgroups — #86984

Order 384.

1040 conjugacy classes of subgroups.

The subgroup lattice has 640 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	#5732	C₂	1	1	yes	maximal, characteristic, complemented
3	#5724	C₂	1	1	yes	maximal, characteristic, complemented
4	#5710	C₂	1	2	yes	maximal, complemented
5	#5706	C₂	1	2	yes	maximal, complemented
6	#5705	C₂	1	2	yes	maximal, complemented
7	#5705	C₂	1	2	yes	maximal, complemented
8	#5681	C₂	1	1	yes	maximal, characteristic, complemented
9	#5674	C₂	1	1	yes	maximal, characteristic
10	D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
11	#5671	C₂	1	1	yes	maximal, characteristic, complemented
12	#5640	C₂	1	2	yes	maximal, complemented
13	#5637	C₂	1	2	yes	maximal, complemented
14	#5585	C₂	1	1	yes	maximal, characteristic, complemented
15	#5585	C₂	1	1	yes	maximal, characteristic, complemented
16	#5578	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#239	C₂	1	1	yes	maximal, characteristic, complemented
18	#5572	C₂	1	1	yes	maximal, characteristic, complemented
19	#5568	C₂	1	1	yes	maximal, characteristic, complemented
20	#5559	C₂	1	1	yes	maximal, characteristic, complemented
21	#5545	C₂	1	1	yes	maximal, characteristic, complemented
22	#5528	C₂	1	2	yes	maximal, complemented
23	#5527	C₂	1	2	yes	maximal, complemented
24	#3510	—	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×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#126	C₂²	1	2	yes	complemented
30	C₃×#126	C₂²	1	2	yes	complemented
31	C₃×#124	C₂²	1	1	yes	characteristic
32	C₃×#124	C₂²	1	1	yes	characteristic
33	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃×#117	C₂²	1	2	yes	complemented
39	#947	C₂²	1	1	yes	characteristic
40	#947	C₂²	1	1	yes	characteristic
41	#947	C₂²	1	2	yes	complemented
42	#947	C₂²	1	1	yes	characteristic, complemented
43	#946	C₂²	1	1	yes	characteristic
44	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
46	#944	C₂²	1	1	yes	characteristic, complemented
47	#944	C₂²	1	1	yes	characteristic, complemented
48	#940	C₂²	1	1	yes	characteristic
49	#936	C₂²	1	1	yes	characteristic
50	D₄×Dic₃	C₂²	1	1	yes	characteristic
51	#929	C₂²	1	2	yes	complemented
52	C₄×#67	C₂²	1	2	yes	—
53	C₄×#67	C₂²	1	2	yes	complemented
54	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
55	#898	C₂²	1	2	yes	complemented
56	#898	C₂²	1	2	yes	complemented
57	#898	C₂²	1	2	yes	complemented
58	#897	C₂²	1	1	yes	characteristic
59	#897	C₂²	1	2	yes	complemented
60	#896	C₂²	1	1	yes	characteristic
61	#896	C₂²	1	1	yes	characteristic
62	#896	C₂²	1	2	yes	complemented
63	#896	C₂²	1	2	yes	complemented
64	#896	C₂²	1	2	yes	complemented
65	#894	C₂²	1	2	yes	—
66	#894	C₂²	1	2	yes	—
67	#894	C₂²	1	2	yes	complemented
68	#894	C₂²	1	2	yes	complemented
69	#894	C₂²	1	2	yes	complemented
70	#894	C₂²	1	2	yes	complemented
71	#893	C₂²	1	2	yes	—
72	#893	C₂²	1	1	yes	characteristic
73	#893	C₂²	1	2	yes	complemented
74	#893	C₂²	1	1	yes	characteristic, complemented
75	#892	C₂²	1	2	yes	—
76	#892	C₂²	1	1	yes	characteristic
77	#892	C₂²	1	2	yes	complemented
78	#892	C₂²	1	2	yes	complemented
79	#889	C₂²	1	1	yes	characteristic, complemented
80	#889	C₂²	1	1	yes	characteristic, complemented
81	#888	C₂²	1	1	yes	characteristic, complemented
82	#887	C₂²	1	2	yes	complemented
83	#887	C₂²	1	1	yes	characteristic, complemented
84	#886	C₂²	1	2	yes	complemented
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	—
91	#883	C₂²	1	2	yes	complemented
92	#883	C₂²	1	2	yes	complemented
93	#882	C₂²	1	2	yes	—
94	#882	C₂²	1	2	yes	—
95	#67⋊C₄	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	#879	C₂²	1	2	yes	complemented
102	#878	C₂²	1	2	yes	complemented
103	#877	C₂²	1	2	yes	complemented
104	#876	C₂²	1	2	yes	complemented
105	#875	C₂²	1	1	yes	characteristic
106	#875	C₂²	1	2	yes	complemented
107	#875	C₂²	1	1	yes	characteristic, complemented
108	#874	C₂²	1	1	yes	characteristic
109	C₄×D₁₂	C₂²	1	2	yes	—
110	C₄×D₁₂	C₂²	1	1	yes	characteristic
111	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₁₂	C₂²	1	2	yes	complemented
113	#872	C₂²	1	1	yes	characteristic
114	#872	C₂²	1	2	yes	—
115	#872	C₂²	1	1	yes	characteristic
116	#872	C₂²	1	2	yes	complemented
117	C₄²×D₃	C₂²	1	1	yes	characteristic
118	C₄²×D₃	C₂²	1	2	yes	complemented
119	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₆	C₂²	1	1	yes	characteristic, 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	#559	—	3	1	no	—
125	#559	—	3	1	no	—
126	#559	—	3	1	no	—
127	#559	—	3	1	no	—
128	#556	—	3	1	no	—
129	#556	—	3	1	no	—
130	#556	—	3	1	no	—
131	#556	D₃	1	1	yes	characteristic, complemented
132	#551	—	3	2	no	—
133	#551	—	3	2	no	—
134	#551	—	3	2	no	—
135	#551	—	3	2	no	—
136	#542	—	3	2	no	—
137	#542	—	3	2	no	—
138	#536	—	3	1	no	—
139	#535	—	3	1	no	—
140	#533	—	3	1	no	—
141	#529	—	3	2	no	—
142	#529	—	3	2	no	—
143	C₂×#124	—	3	1	no	—
144	#519	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₄×#41	—	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	—	2	4	no	—
158	D₃×Q₈	—	2	4	no	—
159	D₃×D₄	—	2	4	no	—
160	C₂×D₁₂	C₂³	1	1	yes	characteristic
161	C₂×D₁₂	C₂³	1	2	yes	—
162	C₂×D₁₂	C₂³	1	1	yes	characteristic
163	C₂×D₁₂	C₂³	1	2	yes	—
164	C₂×D₁₂	C₂³	1	2	yes	—
165	C₂×C₄×D₃	C₂³	1	2	yes	—
166	C₂×C₄×D₃	C₂³	1	2	yes	—
167	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₃	C₂³	1	2	yes	—
170	C₂×C₄×D₃	C₂³	1	2	yes	—
171	C₂×C₄×D₃	C₂³	1	2	yes	—
172	C₂×C₄×D₃	C₂³	1	2	yes	—
173	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
174	C₂×Dic₆	C₂³	1	1	yes	characteristic
175	C₂×Dic₆	C₂³	1	2	yes	—
176	C₂×Dic₆	C₂³	1	1	yes	characteristic
177	C₂×Dic₆	C₂³	1	1	yes	characteristic
178	C₂×Dic₆	C₂³	1	1	yes	characteristic
179	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₄²	C₂³	1	1	yes	characteristic
193	C₃×C₄²	C₂³	1	1	yes	characteristic
194	C₃×C₄²	C₂³	1	1	yes	characteristic
195	C₃×C₄²	C₂³	1	2	yes	—
196	C₃×C₄²	C₂³	1	2	yes	—
197	#217	C₂³	1	2	yes	—
198	#217	C₂³	1	2	yes	—
199	#217	C₂³	1	2	yes	—
200	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
201	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
204	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
205	(C₂×D₃)⋊C₄	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	2	yes	—
209	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₃	C₂³	1	2	yes	—
223	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₃	C₂³	1	2	yes	—
225	Dic₃⋊C₄	C₂³	1	2	yes	—
226	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
227	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
228	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
229	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
230	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
231	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
238	Dic₃⋊C₄	C₂³	1	2	yes	—
239	C₄×Dic₃	C₂³	1	1	yes	characteristic
240	C₄×Dic₃	C₂³	1	1	yes	characteristic
241	C₄×Dic₃	C₂³	1	1	yes	characteristic
242	C₄×Dic₃	C₂³	1	2	yes	—
243	C₄×Dic₃	C₂³	1	2	yes	—
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	2	yes	—
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₂×#41	—	3	1	no	—
250	C₂²×Q₈	—	3	1	no	—
251	C₂²×D₄	—	3	1	no	—
252	C₄⋊Q₈	—	3	1	no	—
253	C₄⋊Q₈	—	3	1	no	—
254	C₄⋊Q₈	—	3	1	no	—
255	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
256	#127	—	3	1	no	—
257	#127	—	3	1	no	—
258	#126	—	3	2	no	—
259	#126	—	3	2	no	—
260	#126	—	3	2	no	—
261	#126	—	3	2	no	—
262	#126	—	3	2	no	—
263	#126	—	3	2	no	—
264	#126	C₂×D₃	1	2	yes	complemented
265	#126	C₂×D₃	1	2	yes	complemented
266	#125	—	3	1	no	—
267	#125	—	3	1	no	—
268	#124	—	3	1	no	—
269	#124	—	3	1	no	—
270	#124	—	3	1	no	—
271	#124	—	3	2	no	—
272	#124	—	3	1	no	—
273	#124	—	3	2	no	—
274	#124	—	3	2	no	—
275	#124	—	3	2	no	—
276	#124	—	3	2	no	—
277	#124	—	3	1	no	—
278	#124	—	3	1	no	—
279	#124	—	3	2	no	—
280	#124	C₂×D₃	1	1	yes	characteristic
281	#124	C₂×D₃	1	1	yes	characteristic
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	—	3	2	no	—
289	#123	—	3	2	no	—
290	#123	—	3	2	no	—
291	#123	—	3	2	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	1	no	—
296	C₂²⋊Q₈	—	3	1	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	C₂×D₃	1	2	yes	complemented
302	#121	—	3	2	no	—
303	#121	—	3	2	no	—
304	#120	—	3	2	no	—
305	#120	—	3	2	no	—
306	C₄×Q₈	—	3	1	no	—
307	C₄×Q₈	—	3	1	no	—
308	C₄×Q₈	—	3	2	no	—
309	C₄×Q₈	—	3	1	no	—
310	C₄×Q₈	—	3	2	no	—
311	C₄×Q₈	—	3	1	no	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	—	3	1	no	—
314	C₄×Q₈	—	3	1	no	—
315	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
316	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
317	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
318	C₄×D₄	—	3	1	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	2	no	—
321	C₄×D₄	—	3	2	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	2	no	—
327	C₄×D₄	—	3	2	no	—
328	C₄×D₄	—	3	1	no	—
329	C₄×D₄	—	3	1	no	—
330	C₄×D₄	—	3	2	no	—
331	C₄×D₄	C₂×D₃	1	1	yes	characteristic
332	#117	—	3	1	no	—
333	#117	—	3	2	no	—
334	#117	—	3	2	no	—
335	#117	—	3	2	no	—
336	#117	—	3	2	no	—
337	#117	—	3	1	no	—
338	#117	—	3	1	no	—
339	#117	—	3	2	no	—
340	#117	—	3	2	no	—
341	#117	C₂×D₃	1	2	yes	complemented
342	C₂×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	3	2	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₄²	—	3	1	no	—
347	C₂×C₄²	—	3	2	no	—
348	C₂³×C₃	C₂⁴	1	2	yes	—
349	C₂²×D₃	—	2	4	no	—
350	C₂²×D₃	—	4	2	no	—
351	C₂²×D₃	—	4	2	no	—
352	C₂²×D₃	C₂⁴	1	2	yes	—
353	C₂²×D₃	C₂⁴	1	2	yes	—
354	C₂²×D₃	C₂⁴	1	1	yes	characteristic
355	C₃×Q₈	—	2	2	no	—
356	C₃×Q₈	—	2	2	no	—
357	C₃×Q₈	—	4	1	no	—
358	C₃×D₄	—	2	2	no	—
359	C₂×C₃×C₄	—	4	2	no	—
360	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
361	C₂×C₃×C₄	C₂⁴	1	2	yes	—
362	C₂×C₃×C₄	C₂⁴	1	2	yes	—
363	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂⁴	1	2	yes	—
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	1	yes	characteristic
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	#67	—	2	4	no	—
371	#67	—	4	2	no	—
372	#67	—	4	2	no	—
373	C₂×Dic₃	—	4	2	no	—
374	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
375	C₂×Dic₃	C₂⁴	1	2	yes	—
376	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
377	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
378	C₂×Dic₃	C₂⁴	1	2	yes	—
379	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
380	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
383	D₁₂	—	2	4	no	—
384	D₁₂	—	2	2	no	—
385	D₁₂	—	2	2	no	—
386	D₁₂	—	4	2	no	—
387	D₁₂	—	4	2	no	—
388	C₄×D₃	—	2	4	no	—
389	C₄×D₃	—	2	4	no	—
390	C₄×D₃	—	4	1	no	—
391	C₄×D₃	—	4	2	no	—
392	C₄×D₃	—	4	1	no	—
393	C₄×D₃	—	4	2	no	—
394	C₄×D₃	—	4	2	no	—
395	C₄×D₃	—	4	2	no	—
396	C₄×D₃	#41	1	4	yes	—
397	Dic₆	—	2	2	no	—
398	Dic₆	—	2	4	no	—
399	Dic₆	—	4	1	no	—
400	Dic₆	—	4	1	no	—
401	Dic₆	—	4	1	no	—
402	C₂⁴	—	3	2	no	—
403	#41	—	6	4	no	—
404	C₂×Q₈	—	3	2	no	—
405	C₂×Q₈	—	3	1	no	—
406	C₂×Q₈	—	3	1	no	—
407	C₂×Q₈	—	3	1	no	—
408	C₂×Q₈	—	3	1	no	—
409	C₂×Q₈	—	6	4	no	—
410	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
411	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
412	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
413	C₂×D₄	—	3	2	no	—
414	C₂×D₄	—	3	2	no	—
415	C₂×D₄	—	3	2	no	—
416	C₂×D₄	—	3	2	no	—
417	C₂×D₄	—	3	1	no	—
418	C₂×D₄	—	3	1	no	—
419	C₂×D₄	—	3	2	no	—
420	C₂×D₄	—	3	2	no	—
421	C₂×D₄	—	6	4	no	—
422	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
423	C₂²×C₄	—	3	1	no	—
424	C₂²×C₄	—	3	2	no	—
425	C₂²×C₄	—	3	2	no	—
426	C₂²×C₄	—	3	2	no	—
427	C₂²×C₄	—	3	1	no	—
428	C₂²×C₄	—	3	1	no	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	—	3	2	no	—
431	C₂²×C₄	—	3	2	no	—
432	C₂²×C₄	—	3	2	no	—
433	C₂²×C₄	C₂²×D₃	1	2	yes	—
434	C₄⋊C₄	—	3	1	no	—
435	C₄⋊C₄	—	3	1	no	—
436	C₄⋊C₄	—	3	1	no	—
437	C₄⋊C₄	—	3	1	no	—
438	C₄⋊C₄	—	3	1	no	—
439	C₄⋊C₄	—	3	1	no	—
440	C₄⋊C₄	—	3	2	no	—
441	C₄⋊C₄	—	3	1	no	—
442	C₄⋊C₄	—	3	1	no	—
443	C₄⋊C₄	—	3	2	no	—
444	C₄⋊C₄	—	3	2	no	—
445	C₄⋊C₄	—	3	2	no	—
446	C₄⋊C₄	—	3	2	no	—
447	C₄⋊C₄	—	3	2	no	—
448	C₄⋊C₄	—	3	1	no	—
449	C₄⋊C₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
455	C₄⋊C₄	C₂²×D₃	1	2	yes	—
456	C₄⋊C₄	C₂²×D₃	1	2	yes	—
457	C₄⋊C₄	C₂²×D₃	1	2	yes	—
458	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
459	C₄⋊C₄	C₂²×D₃	1	2	yes	—
460	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
462	C₂²⋊C₄	—	3	2	no	—
463	C₂²⋊C₄	—	3	2	no	—
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	3	2	no	—
466	C₂²⋊C₄	—	3	1	no	—
467	C₂²⋊C₄	—	3	1	no	—
468	C₂²⋊C₄	—	3	2	no	—
469	C₂²⋊C₄	—	3	2	no	—
470	C₂²⋊C₄	—	3	2	no	—
471	C₂²⋊C₄	—	3	2	no	—
472	C₂²⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	—	3	2	no	—
474	C₂²⋊C₄	—	3	1	no	—
475	C₂²⋊C₄	—	3	1	no	—
476	C₂²⋊C₄	—	3	2	no	—
477	C₂²⋊C₄	—	3	2	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	C₂²×D₃	1	2	yes	—
485	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
487	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
489	C₄²	—	3	1	no	—
490	C₄²	—	3	2	no	—
491	C₄²	—	3	2	no	—
492	C₄²	—	3	1	no	—
493	C₄²	—	3	1	no	—
494	C₄²	—	3	2	no	—
495	C₄²	—	3	2	no	—
496	C₄²	—	3	2	no	—
497	C₄²	—	3	1	no	—
498	C₄²	—	3	1	no	—
499	C₄²	C₂²×D₃	1	2	yes	—
500	C₄²	C₂²×D₃	1	1	yes	characteristic
501	C₄²	C₂²×D₃	1	2	yes	—
502	C₄²	C₂²×D₃	1	1	yes	characteristic
503	C₄²	C₂²×D₃	1	1	yes	characteristic
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	C₂⁵	1	1	yes	characteristic
508	C₂×D₃	—	2	1	no	—
509	C₂×D₃	—	2	1	no	—
510	C₂×D₃	—	2	2	no	—
511	C₂×D₃	—	2	2	no	—
512	C₂×D₃	—	2	2	no	—
513	C₂×D₃	—	2	2	no	—
514	C₂×D₃	—	2	2	no	—
515	C₂×D₃	—	2	2	no	—
516	C₂×D₃	—	8	4	no	—
517	C₂×D₃	C₂×#41	1	2	yes	—
518	C₃×C₄	—	2	2	no	—
519	C₃×C₄	—	2	2	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	2	1	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	2	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	C₂×#41	1	2	yes	—
528	Dic₃	—	2	2	no	—
529	Dic₃	—	2	1	no	—
530	Dic₃	—	2	1	no	—
531	Dic₃	—	2	1	no	—
532	Dic₃	—	2	1	no	—
533	Dic₃	—	2	1	no	—
534	Dic₃	—	2	1	no	—
535	Dic₃	—	2	2	no	—
536	Dic₃	C₂×#41	1	2	yes	—
537	C₂³	—	3	1	no	—
538	C₂³	—	3	2	no	—
539	C₂³	—	3	2	no	—
540	C₂³	—	6	4	no	—
541	C₂³	—	12	2	no	—
542	C₂³	—	12	2	no	—
543	C₂³	C₂³×D₃	1	2	yes	—
544	Q₈	—	2	2	no	—
545	Q₈	—	2	2	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	6	4	no	—
548	Q₈	—	6	2	no	—
549	Q₈	—	12	1	no	—
550	Q₈	—	12	1	no	—
551	Q₈	—	12	1	no	—
552	D₄	—	2	2	no	—
553	D₄	—	6	4	no	—
554	D₄	—	6	4	no	—
555	D₄	—	6	2	no	—
556	D₄	—	6	2	no	—
557	D₄	—	12	2	no	—
558	D₄	—	12	2	no	—
559	D₄	—	12	2	no	—
560	D₄	—	12	2	no	—
561	C₂×C₄	—	3	1	no	—
562	C₂×C₄	—	3	4	no	—
563	C₂×C₄	—	3	1	no	—
564	C₂×C₄	—	3	2	no	—
565	C₂×C₄	—	3	1	no	—
566	C₂×C₄	—	3	1	no	—
567	C₂×C₄	—	3	2	no	—
568	C₂×C₄	—	3	1	no	—
569	C₂×C₄	—	3	1	no	—
570	C₂×C₄	—	3	1	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	6	4	no	—
573	C₂×C₄	—	6	4	no	—
574	C₂×C₄	—	12	2	no	—
575	C₂×C₄	—	12	2	no	—
576	C₂×C₄	—	12	1	no	—
577	C₂×C₄	—	12	2	no	—
578	C₂×C₄	—	12	1	no	—
579	C₂×C₄	—	12	2	no	—
580	C₂×C₄	—	12	2	no	—
581	C₂×C₄	C₂³×D₃	1	2	yes	—
582	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₃	1	2	yes	—
585	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₃	1	2	yes	—
587	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
591	C₂×C₃	—	4	2	no	—
592	C₂×C₃	C₂²×#41	1	1	yes	characteristic
593	C₂×C₃	#585	1	1	yes	characteristic
594	C₂×C₃	#585	1	1	yes	characteristic
595	D₃	—	2	2	no	—
596	D₃	—	4	2	no	—
597	D₃	—	4	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	3	2	no	—
602	C₂²	—	6	1	no	—
603	C₂²	—	6	1	no	—
604	C₂²	—	6	2	no	—
605	C₂²	—	6	2	no	—
606	C₂²	—	6	2	no	—
607	C₂²	—	6	2	no	—
608	C₂²	—	6	2	no	—
609	C₂²	—	6	2	no	—
610	C₂²	—	24	4	no	—
611	C₂²	C₂⁴×D₃	1	1	yes	characteristic
612	C₄	—	2	2	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	3	2	no	—
622	C₄	—	6	2	no	—
623	C₄	—	6	1	no	—
624	C₄	—	6	1	no	—
625	C₄	—	6	1	no	—
626	C₄	—	6	2	no	—
627	C₄	—	6	1	no	—
628	C₄	—	6	1	no	—
629	C₄	—	6	1	no	—
630	C₄	D₃×#41	1	2	yes	—
631	C₃	#3510	1	1	yes	characteristic, complemented, Sylow
632	C₂	—	4	2	no	—
633	C₂	—	6	2	no	—
634	C₂	—	12	2	no	—
635	C₂	—	12	2	no	—
636	C₂	C₂×D₃×#41	1	1	yes	characteristic
637	C₂	#5964	1	1	yes	characteristic
638	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#556	C₂
prime radical	#5674	C₂
hypercenter	#556	D₃
hypocenter	C₃	#3510
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. #5732	C₂	semidirect
3. #5724	C₂	semidirect
4. #5710	C₂	semidirect
5. #5706	C₂	semidirect
6. #5705	C₂	semidirect
7. #5705	C₂	semidirect
8. #5681	C₂	semidirect
10. D₃×#124	C₂	semidirect
11. #5671	C₂	semidirect
12. #5640	C₂	semidirect
13. #5637	C₂	semidirect
14. #5585	C₂	semidirect
15. #5585	C₂	semidirect
16. #5578	C₂	semidirect
17. C₄×#239	C₂	semidirect
18. #5572	C₂	semidirect
19. #5568	C₂	semidirect
20. #5559	C₂	semidirect
21. #5545	C₂	semidirect
22. #5528	C₂	semidirect
23. #5527	C₂	semidirect
28. C₃×C₄⋊Q₈	C₂²	semidirect
29. C₃×#126	C₂²	semidirect
30. C₃×#126	C₂²	semidirect
33. C₃×C₂²⋊Q₈	C₂²	semidirect
34. C₃×C₄×Q₈	C₂²	semidirect
35. C₃×C₄×Q₈	C₂²	semidirect
36. C₃×C₄×Q₈	C₂²	semidirect
38. C₃×#117	C₂²	semidirect
41. #947	C₂²	semidirect
42. #947	C₂²	semidirect
44. Q₈×Dic₃	C₂²	semidirect
45. Q₈×Dic₃	C₂²	semidirect
46. #944	C₂²	semidirect
47. #944	C₂²	semidirect
51. #929	C₂²	semidirect
53. C₄×#67	C₂²	semidirect
55. #898	C₂²	semidirect
56. #898	C₂²	semidirect
57. #898	C₂²	semidirect
59. #897	C₂²	semidirect
62. #896	C₂²	semidirect
63. #896	C₂²	semidirect
64. #896	C₂²	semidirect
67. #894	C₂²	semidirect
68. #894	C₂²	semidirect
69. #894	C₂²	semidirect
70. #894	C₂²	semidirect
73. #893	C₂²	semidirect
74. #893	C₂²	semidirect
77. #892	C₂²	semidirect
78. #892	C₂²	semidirect
79. #889	C₂²	semidirect
80. #889	C₂²	semidirect
81. #888	C₂²	semidirect
82. #887	C₂²	semidirect
83. #887	C₂²	semidirect
84. #886	C₂²	semidirect
87. #885	C₂²	semidirect
88. #885	C₂²	semidirect
91. #883	C₂²	semidirect
92. #883	C₂²	semidirect
96. #67⋊C₄	C₂²	semidirect
100. #879	C₂²	semidirect
101. #879	C₂²	semidirect
102. #878	C₂²	semidirect
103. #877	C₂²	semidirect
104. #876	C₂²	semidirect
106. #875	C₂²	semidirect
107. #875	C₂²	semidirect
111. C₄×D₁₂	C₂²	semidirect
112. C₄×D₁₂	C₂²	semidirect
116. #872	C₂²	semidirect
118. C₄²×D₃	C₂²	semidirect
119. C₄×Dic₆	C₂²	semidirect
120. C₄×Dic₆	C₂²	semidirect
121. C₄×Dic₆	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
131. #556	D₃	semidirect
255. C₄⋊Q₈	C₂×D₃	semidirect
264. #126	C₂×D₃	semidirect
265. #126	C₂×D₃	semidirect
301. C₂²⋊Q₈	C₂×D₃	semidirect
315. C₄×Q₈	C₂×D₃	semidirect
316. C₄×Q₈	C₂×D₃	semidirect
317. C₄×Q₈	C₂×D₃	semidirect
341. #117	C₂×D₃	semidirect
631. C₃	#3510	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
#5732	2
#5724	2
#5710	2
#5706	2
#5705	2
#5681	2
#5674	2
D₃×#124	2
#5671	2
#5640	2
#5637	2
#5585	2
#5578	2
C₄×#239	2
#5572	2
#5568	2
#5559	2
#5545	2
#5528	2
#5527	2
#3510	3