Subgroups — #86552

Order 384.

1040 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#5733	C₂	1	1	yes	maximal, characteristic, complemented
3	#5728	C₂	1	1	yes	maximal, characteristic, complemented
4	#5705	C₂	1	2	yes	maximal, complemented
5	#5702	C₂	1	2	yes	maximal, complemented
6	#5682	C₂	1	1	yes	maximal, characteristic, complemented
7	#5681	C₂	1	2	yes	maximal, complemented
8	#5679	C₂	1	2	yes	maximal, complemented
9	D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
10	#5664	C₂	1	2	yes	maximal, complemented
11	#5658	C₂	1	2	yes	maximal, complemented
12	#5641	C₂	1	2	yes	maximal, complemented
13	#5637	C₂	1	2	yes	maximal, complemented
14	#5628	C₂	1	1	yes	maximal, characteristic, complemented
15	#5624	C₂	1	1	yes	maximal, characteristic, complemented
16	#5607	C₂	1	1	yes	maximal, characteristic
17	#5600	C₂	1	1	yes	maximal, characteristic, complemented
18	#5580	C₂	1	1	yes	maximal, characteristic, complemented
19	#5572	C₂	1	1	yes	maximal, characteristic, complemented
20	#5557	C₂	1	1	yes	maximal, characteristic, complemented
21	#5545	C₂	1	1	yes	maximal, characteristic, complemented
22	#5534	C₂	1	1	yes	maximal, characteristic, complemented
23	#5522	C₂	1	1	yes	maximal, characteristic, complemented
24	#3510	—	3	1	no	maximal, Sylow
25	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic
26	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×#235	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×#124	C₂²	1	1	yes	characteristic
31	C₃×#124	C₂²	1	2	yes	complemented
32	C₃×#123	C₂²	1	2	yes	complemented
33	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×#121	C₂²	1	1	yes	characteristic
36	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃×#117	C₂²	1	1	yes	characteristic, complemented
39	#947	C₂²	1	1	yes	characteristic
40	#947	C₂²	1	2	yes	complemented
41	#946	C₂²	1	2	yes	—
42	#946	C₂²	1	2	yes	complemented
43	#946	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₃	C₂²	1	2	yes	complemented
45	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
46	#940	C₂²	1	2	yes	—
47	#938	C₂²	1	1	yes	characteristic
48	#937	C₂²	1	2	yes	—
49	#936	C₂²	1	1	yes	characteristic
50	#935	C₂²	1	2	yes	complemented
51	D₄×Dic₃	C₂²	1	1	yes	characteristic
52	D₄×Dic₃	C₂²	1	2	yes	complemented
53	#930	C₂²	1	1	yes	characteristic
54	C₄×#67	C₂²	1	2	yes	—
55	C₄×#67	C₂²	1	2	yes	complemented
56	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
57	#926	C₂²	1	2	yes	complemented
58	#924	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
60	#898	C₂²	1	2	yes	complemented
61	#898	C₂²	1	2	yes	complemented
62	#898	C₂²	1	2	yes	complemented
63	#898	C₂²	1	2	yes	complemented
64	#897	C₂²	1	2	yes	—
65	#897	C₂²	1	1	yes	characteristic, complemented
66	#896	C₂²	1	2	yes	complemented
67	#895	C₂²	1	1	yes	characteristic
68	#894	C₂²	1	2	yes	—
69	#894	C₂²	1	2	yes	complemented
70	#894	C₂²	1	2	yes	complemented
71	#893	C₂²	1	1	yes	characteristic
72	#893	C₂²	1	1	yes	characteristic
73	#893	C₂²	1	1	yes	characteristic
74	#892	C₂²	1	2	yes	—
75	#892	C₂²	1	1	yes	characteristic
76	#892	C₂²	1	1	yes	characteristic
77	#892	C₂²	1	2	yes	complemented
78	#890	C₂²	1	1	yes	characteristic, complemented
79	#890	C₂²	1	1	yes	characteristic, complemented
80	#888	C₂²	1	2	yes	complemented
81	#887	C₂²	1	1	yes	characteristic, complemented
82	#887	C₂²	1	2	yes	complemented
83	#887	C₂²	1	2	yes	complemented
84	#887	C₂²	1	1	yes	characteristic, complemented
85	#887	C₂²	1	1	yes	characteristic, complemented
86	#886	C₂²	1	2	yes	complemented
87	#886	C₂²	1	2	yes	complemented
88	#885	C₂²	1	2	yes	—
89	#885	C₂²	1	2	yes	—
90	#885	C₂²	1	2	yes	—
91	#885	C₂²	1	2	yes	complemented
92	#885	C₂²	1	2	yes	complemented
93	#885	C₂²	1	2	yes	complemented
94	#883	C₂²	1	2	yes	—
95	#883	C₂²	1	2	yes	complemented
96	#883	C₂²	1	2	yes	complemented
97	#882	C₂²	1	2	yes	—
98	#67⋊C₄	C₂²	1	1	yes	characteristic
99	#67⋊C₄	C₂²	1	1	yes	characteristic
100	#67⋊C₄	C₂²	1	2	yes	—
101	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
102	#67⋊C₄	C₂²	1	2	yes	complemented
103	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
104	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
106	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
107	#879	C₂²	1	2	yes	complemented
108	#879	C₂²	1	2	yes	complemented
109	#879	C₂²	1	2	yes	complemented
110	#878	C₂²	1	2	yes	complemented
111	#877	C₂²	1	2	yes	complemented
112	#875	C₂²	1	1	yes	characteristic
113	C₄×D₁₂	C₂²	1	1	yes	characteristic
114	C₄×D₁₂	C₂²	1	2	yes	complemented
115	#872	C₂²	1	2	yes	—
116	#872	C₂²	1	1	yes	characteristic
117	#872	C₂²	1	2	yes	complemented
118	#872	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₃	C₂²	1	1	yes	characteristic
120	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
121	#869	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂²	1	2	yes	complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#559	—	3	2	no	—
125	#559	—	3	2	no	—
126	#556	—	3	2	no	—
127	#556	—	3	2	no	—
128	#551	—	3	2	no	—
129	#551	—	3	2	no	—
130	#551	—	3	2	no	—
131	#551	—	3	2	no	—
132	#542	—	3	1	no	—
133	#542	—	3	1	no	—
134	#542	—	3	1	no	—
135	#542	D₃	1	1	yes	characteristic, complemented
136	#536	—	3	1	no	—
137	#535	—	3	1	no	—
138	#533	—	3	1	no	—
139	#529	—	3	1	no	—
140	#529	—	3	1	no	—
141	#529	—	3	1	no	—
142	#529	—	3	1	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	2	yes	—
150	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×D₄	C₂³	1	2	yes	—
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	2	yes	—
154	C₂×#67	C₂³	1	1	yes	characteristic
155	C₂×#67	C₂³	1	2	yes	—
156	C₂×#67	C₂³	1	1	yes	characteristic
157	C₂×#67	C₂³	1	2	yes	—
158	C₂×#67	C₂³	1	2	yes	—
159	C₂²×Dic₃	C₂³	1	2	yes	—
160	C₂²×Dic₃	C₂³	1	1	yes	characteristic
161	C₂²×Dic₃	C₂³	1	1	yes	characteristic
162	D₃×Q₈	—	2	4	no	—
163	D₃×D₄	—	2	4	no	—
164	#235	—	2	4	no	—
165	C₂×D₁₂	C₂³	1	1	yes	characteristic
166	C₂×D₁₂	C₂³	1	1	yes	characteristic
167	C₂×D₁₂	C₂³	1	2	yes	—
168	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₃	C₂³	1	2	yes	—
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	1	yes	characteristic
177	C₂×Dic₆	C₂³	1	1	yes	characteristic
178	C₂×Dic₆	C₂³	1	2	yes	—
179	C₂×Dic₆	C₂³	1	1	yes	characteristic
180	C₂×Dic₆	C₂³	1	2	yes	—
181	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄²	C₂³	1	1	yes	characteristic
196	C₃×C₄²	C₂³	1	2	yes	—
197	C₃×C₄²	C₂³	1	1	yes	characteristic
198	#217	C₂³	1	2	yes	—
199	#217	C₂³	1	2	yes	—
200	#217	C₂³	1	2	yes	—
201	#217	C₂³	1	2	yes	—
202	#217	C₂³	1	2	yes	—
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	1	yes	characteristic
208	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
221	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₃	C₂³	1	2	yes	—
223	C₄⋊Dic₃	C₂³	1	2	yes	—
224	C₄⋊Dic₃	C₂³	1	2	yes	—
225	C₄⋊Dic₃	C₂³	1	2	yes	—
226	Dic₃⋊C₄	C₂³	1	2	yes	—
227	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
228	Dic₃⋊C₄	C₂³	1	2	yes	—
229	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
230	Dic₃⋊C₄	C₂³	1	2	yes	—
231	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₃⋊C₄	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	2	yes	—
236	C₄×Dic₃	C₂³	1	2	yes	—
237	C₄×Dic₃	C₂³	1	2	yes	—
238	C₄×Dic₃	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	1	yes	characteristic
243	C₄×Dic₃	C₂³	1	1	yes	characteristic
244	C₄×Dic₃	C₂³	1	1	yes	characteristic
245	C₄×Dic₃	C₂³	1	2	yes	—
246	C₄×Dic₃	C₂³	1	1	yes	characteristic
247	C₄×Dic₃	C₂³	1	1	yes	characteristic
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	2	no	—
253	C₄⋊Q₈	—	3	1	no	—
254	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
255	#127	—	3	2	no	—
256	#126	—	3	2	no	—
257	#126	—	3	2	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	C₂×D₃	1	2	yes	complemented
264	#125	—	3	1	no	—
265	#125	—	3	1	no	—
266	#124	—	3	1	no	—
267	#124	—	3	2	no	—
268	#124	—	3	1	no	—
269	#124	—	3	2	no	—
270	#124	—	3	2	no	—
271	#124	—	3	2	no	—
272	#124	—	3	2	no	—
273	#124	—	3	2	no	—
274	#124	—	3	2	no	—
275	#124	—	3	1	no	—
276	#124	C₂×D₃	1	1	yes	characteristic
277	#124	C₂×D₃	1	2	yes	complemented
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	C₂×D₃	1	2	yes	complemented
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	—	3	2	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
297	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
298	#121	—	3	1	no	—
299	#121	—	3	1	no	—
300	#121	—	3	1	no	—
301	#121	C₂×D₃	1	1	yes	characteristic
302	#120	—	3	2	no	—
303	#120	—	3	2	no	—
304	C₄×Q₈	—	3	1	no	—
305	C₄×Q₈	—	3	2	no	—
306	C₄×Q₈	—	3	1	no	—
307	C₄×Q₈	—	3	1	no	—
308	C₄×Q₈	—	3	1	no	—
309	C₄×Q₈	—	3	2	no	—
310	C₄×Q₈	—	3	2	no	—
311	C₄×Q₈	—	3	1	no	—
312	C₄×Q₈	—	3	2	no	—
313	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
314	C₄×D₄	—	3	1	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	—	3	1	no	—
319	C₄×D₄	—	3	1	no	—
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	—	3	1	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	1	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	2	no	—
327	C₄×D₄	—	3	1	no	—
328	C₄×D₄	—	3	2	no	—
329	C₄×D₄	C₂×D₃	1	1	yes	characteristic
330	#117	—	3	2	no	—
331	#117	—	3	1	no	—
332	#117	—	3	1	no	—
333	#117	—	3	2	no	—
334	#117	—	3	2	no	—
335	#117	—	3	2	no	—
336	#117	—	3	1	no	—
337	#117	—	3	1	no	—
338	#117	—	3	2	no	—
339	#117	—	3	2	no	—
340	#117	C₂×D₃	1	1	yes	characteristic, complemented
341	C₂×C₂²⋊C₄	—	3	2	no	—
342	C₂×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	3	2	no	—
345	C₂×C₄²	—	3	1	no	—
346	C₂×C₄²	—	3	1	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂³×C₃	C₂⁴	1	2	yes	—
349	C₂³×C₃	C₂⁴	1	1	yes	characteristic
350	C₂²×D₃	—	2	4	no	—
351	C₂²×D₃	—	4	2	no	—
352	C₂²×D₃	—	4	2	no	—
353	C₂²×D₃	C₂⁴	1	2	yes	—
354	C₂²×D₃	C₂⁴	1	1	yes	characteristic
355	C₂²×D₃	C₂⁴	1	1	yes	characteristic
356	C₃×Q₈	—	2	2	no	—
357	C₃×Q₈	—	4	2	no	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	4	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	4	2	no	—
362	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂⁴	1	2	yes	—
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	2	yes	—
368	C₂×C₃×C₄	C₂⁴	1	2	yes	—
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	#67	—	2	2	no	—
372	#67	—	2	2	no	—
373	#67	—	2	4	no	—
374	#67	—	4	2	no	—
375	#67	—	4	2	no	—
376	C₂×Dic₃	—	4	2	no	—
377	C₂×Dic₃	—	4	1	no	—
378	C₂×Dic₃	—	4	1	no	—
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	C₂×Dic₃	C₂⁴	1	2	yes	—
384	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₃	C₂⁴	1	2	yes	—
386	C₂×Dic₃	C₂⁴	1	2	yes	—
387	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
388	D₁₂	—	2	2	no	—
389	D₁₂	—	2	2	no	—
390	D₁₂	—	4	2	no	—
391	C₄×D₃	—	2	4	no	—
392	C₄×D₃	—	2	2	no	—
393	C₄×D₃	—	4	2	no	—
394	C₄×D₃	—	4	1	no	—
395	C₄×D₃	—	4	1	no	—
396	C₄×D₃	—	4	1	no	—
397	C₄×D₃	—	4	2	no	—
398	C₄×D₃	—	4	1	no	—
399	C₄×D₃	#41	1	4	yes	—
400	Dic₆	—	2	2	no	—
401	Dic₆	—	2	2	no	—
402	Dic₆	—	2	4	no	—
403	Dic₆	—	4	2	no	—
404	C₂⁴	—	3	2	no	—
405	#41	—	6	4	no	—
406	C₂×Q₈	—	3	1	no	—
407	C₂×Q₈	—	3	2	no	—
408	C₂×Q₈	—	3	1	no	—
409	C₂×Q₈	—	3	2	no	—
410	C₂×Q₈	—	6	4	no	—
411	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
412	C₂×Q₈	C₂²×D₃	1	2	yes	—
413	C₂×D₄	—	3	1	no	—
414	C₂×D₄	—	3	2	no	—
415	C₂×D₄	—	3	1	no	—
416	C₂×D₄	—	3	2	no	—
417	C₂×D₄	—	3	2	no	—
418	C₂×D₄	—	3	1	no	—
419	C₂×D₄	—	3	1	no	—
420	C₂×D₄	—	3	2	no	—
421	C₂×D₄	—	6	4	no	—
422	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
423	C₂×D₄	C₂²×D₃	1	2	yes	—
424	C₂²×C₄	—	3	1	no	—
425	C₂²×C₄	—	3	1	no	—
426	C₂²×C₄	—	3	1	no	—
427	C₂²×C₄	—	3	2	no	—
428	C₂²×C₄	—	3	1	no	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	—	3	1	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	1	no	—
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	—	3	2	no	—
436	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₃	1	2	yes	—
438	C₄⋊C₄	—	3	2	no	—
439	C₄⋊C₄	—	3	2	no	—
440	C₄⋊C₄	—	3	1	no	—
441	C₄⋊C₄	—	3	1	no	—
442	C₄⋊C₄	—	3	1	no	—
443	C₄⋊C₄	—	3	1	no	—
444	C₄⋊C₄	—	3	1	no	—
445	C₄⋊C₄	—	3	1	no	—
446	C₄⋊C₄	—	3	2	no	—
447	C₄⋊C₄	—	3	2	no	—
448	C₄⋊C₄	—	3	2	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	2	no	—
454	C₄⋊C₄	—	3	2	no	—
455	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
456	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
457	C₄⋊C₄	C₂²×D₃	1	2	yes	—
458	C₄⋊C₄	C₂²×D₃	1	2	yes	—
459	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
460	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂²×D₃	1	2	yes	—
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	2	no	—
467	C₂²⋊C₄	—	3	1	no	—
468	C₂²⋊C₄	—	3	1	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	2	no	—
475	C₂²⋊C₄	—	3	2	no	—
476	C₂²⋊C₄	—	3	2	no	—
477	C₂²⋊C₄	—	3	1	no	—
478	C₂²⋊C₄	—	3	1	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	C₂²×D₃	1	2	yes	—
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	1	yes	characteristic
488	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
489	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
490	C₄²	—	3	1	no	—
491	C₄²	—	3	1	no	—
492	C₄²	—	3	1	no	—
493	C₄²	—	3	1	no	—
494	C₄²	—	3	1	no	—
495	C₄²	—	3	1	no	—
496	C₄²	—	3	1	no	—
497	C₄²	—	3	1	no	—
498	C₄²	—	3	2	no	—
499	C₄²	—	3	2	no	—
500	C₄²	—	3	2	no	—
501	C₄²	—	3	2	no	—
502	C₄²	—	3	2	no	—
503	C₄²	C₂²×D₃	1	1	yes	characteristic
504	C₄²	C₂²×D₃	1	1	yes	characteristic
505	C₄²	C₂²×D₃	1	2	yes	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	2	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	C₂⁵	1	1	yes	characteristic
513	C₂×D₃	—	2	1	no	—
514	C₂×D₃	—	2	1	no	—
515	C₂×D₃	—	2	1	no	—
516	C₂×D₃	—	2	2	no	—
517	C₂×D₃	—	2	1	no	—
518	C₂×D₃	—	2	2	no	—
519	C₂×D₃	—	2	1	no	—
520	C₂×D₃	—	2	2	no	—
521	C₂×D₃	—	8	4	no	—
522	C₂×D₃	C₂×#41	1	2	yes	—
523	C₃×C₄	—	2	2	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	—	2	2	no	—
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	2	no	—
531	C₃×C₄	C₂×#41	1	2	yes	—
532	Dic₃	—	2	2	no	—
533	Dic₃	—	2	1	no	—
534	Dic₃	—	2	2	no	—
535	Dic₃	—	2	2	no	—
536	Dic₃	—	2	1	no	—
537	Dic₃	—	2	1	no	—
538	Dic₃	—	2	1	no	—
539	Dic₃	—	2	1	no	—
540	Dic₃	C₂×#41	1	2	yes	—
541	C₂³	—	3	1	no	—
542	C₂³	—	3	2	no	—
543	C₂³	—	3	1	no	—
544	C₂³	—	6	4	no	—
545	C₂³	—	12	2	no	—
546	C₂³	—	12	2	no	—
547	C₂³	C₂³×D₃	1	2	yes	—
548	C₂³	C₂³×D₃	1	1	yes	characteristic
549	Q₈	—	2	2	no	—
550	Q₈	—	4	2	no	—
551	Q₈	—	6	4	no	—
552	Q₈	—	6	2	no	—
553	Q₈	—	6	2	no	—
554	Q₈	—	12	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	4	2	no	—
557	D₄	—	6	2	no	—
558	D₄	—	6	4	no	—
559	D₄	—	6	2	no	—
560	D₄	—	6	2	no	—
561	D₄	—	6	2	no	—
562	D₄	—	12	2	no	—
563	D₄	—	12	2	no	—
564	D₄	—	12	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	3	1	no	—
567	C₂×C₄	—	3	4	no	—
568	C₂×C₄	—	3	1	no	—
569	C₂×C₄	—	3	1	no	—
570	C₂×C₄	—	3	1	no	—
571	C₂×C₄	—	3	1	no	—
572	C₂×C₄	—	3	2	no	—
573	C₂×C₄	—	3	2	no	—
574	C₂×C₄	—	3	1	no	—
575	C₂×C₄	—	3	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	6	4	no	—
578	C₂×C₄	—	6	2	no	—
579	C₂×C₄	—	12	1	no	—
580	C₂×C₄	—	12	2	no	—
581	C₂×C₄	—	12	1	no	—
582	C₂×C₄	—	12	1	no	—
583	C₂×C₄	—	12	2	no	—
584	C₂×C₄	—	12	1	no	—
585	C₂×C₄	—	12	1	no	—
586	C₂×C₄	—	12	1	no	—
587	C₂×C₄	—	12	2	no	—
588	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₃	1	2	yes	—
590	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₃	1	2	yes	—
594	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₃	1	2	yes	—
596	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
597	C₂×C₃	—	4	2	no	—
598	C₂×C₃	—	4	1	no	—
599	C₂×C₃	C₂²×#41	1	1	yes	characteristic
600	C₂×C₃	#585	1	1	yes	characteristic
601	C₂×C₃	#585	1	1	yes	characteristic
602	D₃	—	2	2	no	—
603	D₃	—	4	1	no	—
604	D₃	—	4	2	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	3	2	no	—
612	C₂²	—	6	1	no	—
613	C₂²	—	6	1	no	—
614	C₂²	—	6	1	no	—
615	C₂²	—	6	2	no	—
616	C₂²	—	6	1	no	—
617	C₂²	—	6	2	no	—
618	C₂²	—	6	1	no	—
619	C₂²	—	6	2	no	—
620	C₂²	—	24	4	no	—
621	C₂²	C₂⁴×D₃	1	1	yes	characteristic
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	3	2	no	—
631	C₄	—	6	1	no	—
632	C₄	—	6	2	no	—
633	C₄	—	6	1	no	—
634	C₄	—	6	1	no	—
635	C₄	—	6	1	no	—
636	C₄	—	6	1	no	—
637	C₄	—	6	2	no	—
638	C₄	—	6	2	no	—
639	C₄	D₃×#41	1	2	yes	—
640	C₃	#3510	1	1	yes	characteristic, complemented, Sylow
641	C₂	—	4	2	no	—
642	C₂	—	4	1	no	—
643	C₂	—	6	2	no	—
644	C₂	—	12	2	no	—
645	C₂	—	12	1	no	—
646	C₂	C₂×D₃×#41	1	1	yes	characteristic
647	C₂	#5966	1	1	yes	characteristic
648	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#542	C₂
prime radical	#5607	C₂
hypercenter	#542	D₃
hypocenter	C₃	#3510
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₃×#542	C₂	semidirect
2. #5733	C₂	semidirect
3. #5728	C₂	semidirect
4. #5705	C₂	semidirect
5. #5702	C₂	semidirect
6. #5682	C₂	semidirect
7. #5681	C₂	semidirect
8. #5679	C₂	semidirect
9. D₃×#124	C₂	semidirect
10. #5664	C₂	semidirect
11. #5658	C₂	semidirect
12. #5641	C₂	semidirect
13. #5637	C₂	semidirect
14. #5628	C₂	semidirect
15. #5624	C₂	semidirect
17. #5600	C₂	semidirect
18. #5580	C₂	semidirect
19. #5572	C₂	semidirect
20. #5557	C₂	semidirect
21. #5545	C₂	semidirect
22. #5534	C₂	semidirect
23. #5522	C₂	semidirect
28. C₃×C₄⋊Q₈	C₂²	semidirect
29. C₃×#126	C₂²	semidirect
31. C₃×#124	C₂²	semidirect
32. C₃×#123	C₂²	semidirect
33. C₃×C₂²⋊Q₈	C₂²	semidirect
34. C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×Q₈	C₂²	semidirect
38. C₃×#117	C₂²	semidirect
40. #947	C₂²	semidirect
42. #946	C₂²	semidirect
43. #946	C₂²	semidirect
44. Q₈×Dic₃	C₂²	semidirect
45. Q₈×Dic₃	C₂²	semidirect
50. #935	C₂²	semidirect
52. D₄×Dic₃	C₂²	semidirect
55. C₄×#67	C₂²	semidirect
57. #926	C₂²	semidirect
58. #924	C₂²	semidirect
59. C₂×C₄×Dic₃	C₂²	semidirect
60. #898	C₂²	semidirect
61. #898	C₂²	semidirect
62. #898	C₂²	semidirect
63. #898	C₂²	semidirect
65. #897	C₂²	semidirect
66. #896	C₂²	semidirect
69. #894	C₂²	semidirect
70. #894	C₂²	semidirect
77. #892	C₂²	semidirect
78. #890	C₂²	semidirect
79. #890	C₂²	semidirect
80. #888	C₂²	semidirect
81. #887	C₂²	semidirect
82. #887	C₂²	semidirect
83. #887	C₂²	semidirect
84. #887	C₂²	semidirect
85. #887	C₂²	semidirect
86. #886	C₂²	semidirect
87. #886	C₂²	semidirect
91. #885	C₂²	semidirect
92. #885	C₂²	semidirect
93. #885	C₂²	semidirect
95. #883	C₂²	semidirect
96. #883	C₂²	semidirect
101. #67⋊C₄	C₂²	semidirect
102. #67⋊C₄	C₂²	semidirect
103. #67⋊C₄	C₂²	semidirect
107. #879	C₂²	semidirect
108. #879	C₂²	semidirect
109. #879	C₂²	semidirect
110. #878	C₂²	semidirect
111. #877	C₂²	semidirect
114. C₄×D₁₂	C₂²	semidirect
117. #872	C₂²	semidirect
118. #872	C₂²	semidirect
120. C₄²×D₃	C₂²	semidirect
121. #869	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
135. #542	D₃	semidirect
254. C₄⋊Q₈	C₂×D₃	semidirect
263. #126	C₂×D₃	semidirect
277. #124	C₂×D₃	semidirect
287. #123	C₂×D₃	semidirect
296. C₂²⋊Q₈	C₂×D₃	semidirect
297. C₂²⋊Q₈	C₂×D₃	semidirect
313. C₄×Q₈	C₂×D₃	semidirect
340. #117	C₂×D₃	semidirect
640. 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×#542	2
#5733	2
#5728	2
#5705	2
#5702	2
#5682	2
#5681	2
#5679	2
D₃×#124	2
#5664	2
#5658	2
#5641	2
#5637	2
#5628	2
#5624	2
#5607	2
#5600	2
#5580	2
#5572	2
#5557	2
#5545	2
#5534	2
#5522	2
#3510	3