Subgroups — #86245

Order 384.

1232 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	#5834	C₂	1	2	yes	maximal, complemented
3	#5829	C₂	1	2	yes	maximal, complemented
4	#5728	C₂	1	1	yes	maximal, characteristic, complemented
5	#5725	C₂	1	1	yes	maximal, characteristic, complemented
6	#5716	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
8	#5681	C₂	1	2	yes	maximal, complemented
9	#5676	C₂	1	2	yes	maximal, complemented
10	#5619	C₂	1	2	yes	maximal, complemented
11	#5612	C₂	1	2	yes	maximal, complemented
12	#5607	C₂	1	2	yes	maximal, complemented
13	#5599	C₂	1	2	yes	maximal, complemented
14	#5562	C₂	1	2	yes	maximal, complemented
15	#5559	C₂	1	2	yes	maximal, complemented
16	#5554	C₂	1	2	yes	maximal, complemented
17	#5545	C₂	1	2	yes	maximal, complemented
18	#5477	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
20	#3508	—	3	1	no	maximal, Sylow
21	C₂×C₃×#41	C₂²	1	2	yes	complemented
22	C₂×#239	C₂²	1	2	yes	complemented
23	C₂×#237	C₂²	1	2	yes	complemented
24	C₂×D₃×D₄	C₂²	1	2	yes	—
25	C₂×D₃×D₄	C₂²	1	2	yes	—
26	C₂×D₃×D₄	C₂²	1	2	yes	—
27	C₂×#235	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	2	yes	complemented
29	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃×#127	C₂²	1	1	yes	characteristic
31	C₃×#124	C₂²	1	2	yes	complemented
32	C₃×#121	C₂²	1	2	yes	complemented
33	C₃×#121	C₂²	1	2	yes	complemented
34	C₃×C₄×D₄	C₂²	1	2	yes	complemented
35	C₃×C₄×D₄	C₂²	1	2	yes	complemented
36	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
37	#947	C₂²	1	2	yes	complemented
38	#946	C₂²	1	2	yes	—
39	Q₈×Dic₃	C₂²	1	2	yes	complemented
40	#940	C₂²	1	2	yes	—
41	#940	C₂²	1	2	yes	—
42	#940	C₂²	1	2	yes	—
43	#940	C₂²	1	4	yes	complemented
44	#939	C₂²	1	4	yes	complemented
45	#938	C₂²	1	2	yes	complemented
46	#938	C₂²	1	2	yes	complemented
47	#938	C₂²	1	4	yes	complemented
48	#937	C₂²	1	4	yes	—
49	#936	C₂²	1	2	yes	complemented
50	D₄×Dic₃	C₂²	1	2	yes	complemented
51	D₄×Dic₃	C₂²	1	2	yes	complemented
52	#930	C₂²	1	2	yes	complemented
53	#930	C₂²	1	2	yes	complemented
54	#930	C₂²	1	4	yes	complemented
55	#929	C₂²	1	4	yes	complemented
56	C₄×#67	C₂²	1	1	yes	characteristic
57	C₄×#67	C₂²	1	1	yes	characteristic
58	C₄×#67	C₂²	1	1	yes	characteristic, complemented
59	C₄×#67	C₂²	1	1	yes	characteristic, complemented
60	C₄×#67	C₂²	1	4	yes	complemented
61	C₂×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
62	#926	C₂²	1	1	yes	characteristic, complemented
63	#897	C₂²	1	2	yes	—
64	#895	C₂²	1	2	yes	complemented
65	#895	C₂²	1	2	yes	complemented
66	#893	C₂²	1	2	yes	complemented
67	#893	C₂²	1	2	yes	complemented
68	#892	C₂²	1	2	yes	—
69	#890	C₂²	1	2	yes	complemented
70	#887	C₂²	1	2	yes	complemented
71	#886	C₂²	1	4	yes	complemented
72	#885	C₂²	1	4	yes	complemented
73	#884	C₂²	1	4	yes	complemented
74	#883	C₂²	1	4	yes	complemented
75	#883	C₂²	1	4	yes	complemented
76	#882	C₂²	1	4	yes	—
77	#67⋊C₄	C₂²	1	4	yes	complemented
78	D₃×C₂²⋊C₄	C₂²	1	4	yes	—
79	#875	C₂²	1	2	yes	complemented
80	#874	C₂²	1	1	yes	characteristic
81	C₄×D₁₂	C₂²	1	1	yes	characteristic
82	C₄×D₁₂	C₂²	1	1	yes	characteristic
83	C₄×D₁₂	C₂²	1	2	yes	complemented
84	C₄×D₁₂	C₂²	1	2	yes	complemented
85	#872	C₂²	1	1	yes	characteristic
86	#872	C₂²	1	1	yes	characteristic, complemented
87	C₄²×D₃	C₂²	1	1	yes	characteristic
88	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
89	#869	C₂²	1	1	yes	characteristic, complemented
90	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
91	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
92	#559	—	3	2	no	—
93	#559	—	3	2	no	—
94	#550	—	3	2	no	—
95	#550	—	3	2	no	—
96	#546	—	3	2	no	—
97	#546	—	3	2	no	—
98	#546	—	3	2	no	—
99	#546	—	3	2	no	—
100	#540	—	3	2	no	—
101	#540	—	3	2	no	—
102	#535	—	3	2	no	—
103	#533	—	3	1	no	—
104	#532	—	3	1	no	—
105	#532	—	3	1	no	—
106	#532	—	3	1	no	—
107	#532	D₃	1	1	yes	characteristic, complemented
108	C₂×#127	—	3	1	no	—
109	#518	—	3	2	no	—
110	C₄×#41	—	3	1	no	—
111	C₂³×D₃	C₂³	1	4	yes	—
112	C₃×#41	—	4	4	no	—
113	C₂×C₃×Q₈	C₂³	1	2	yes	—
114	C₂×C₃×D₄	C₂³	1	2	yes	—
115	C₂×C₃×D₄	C₂³	1	2	yes	—
116	C₂×C₃×D₄	C₂³	1	2	yes	—
117	C₂×C₃×D₄	C₂³	1	4	yes	—
118	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
119	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
120	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
121	C₂²×C₃×C₄	C₂³	1	4	yes	—
122	C₂×#67	C₂³	1	4	yes	—
123	C₂×#67	C₂³	1	1	yes	characteristic
124	C₂×#67	C₂³	1	1	yes	characteristic
125	C₂×#67	C₂³	1	4	yes	—
126	C₂×#67	C₂³	1	4	yes	—
127	C₂×#67	C₂³	1	4	yes	—
128	C₂×#67	C₂³	1	4	yes	—
129	C₂²×Dic₃	C₂³	1	4	yes	—
130	#239	—	4	4	no	—
131	#237	—	4	4	no	—
132	D₃×D₄	—	2	8	no	—
133	D₃×D₄	—	4	4	no	—
134	D₃×D₄	—	4	4	no	—
135	#235	—	2	4	no	—
136	#235	—	4	4	no	—
137	C₂×D₁₂	C₂³	1	1	yes	characteristic
138	C₂×D₁₂	C₂³	1	2	yes	—
139	C₂×D₁₂	C₂³	1	2	yes	—
140	C₂×D₁₂	C₂³	1	2	yes	—
141	C₂×D₁₂	C₂³	1	4	yes	—
142	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₃	C₂³	1	4	yes	—
148	C₂×C₄×D₃	C₂³	1	4	yes	—
149	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
150	C₂×Dic₆	C₂³	1	1	yes	characteristic
151	C₂×Dic₆	C₂³	1	2	yes	—
152	C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₃×C₄²	C₂³	1	1	yes	characteristic
157	C₃×C₄²	C₂³	1	1	yes	characteristic
158	C₃×C₄²	C₂³	1	1	yes	characteristic
159	C₃×C₄²	C₂³	1	1	yes	characteristic
160	#217	C₂³	1	4	yes	—
161	#217	C₂³	1	4	yes	—
162	#217	C₂³	1	1	yes	characteristic
163	#217	C₂³	1	1	yes	characteristic
164	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
165	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
166	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
167	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
168	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
169	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
170	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
171	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
172	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
173	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
174	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₃	C₂³	1	2	yes	—
176	C₄⋊Dic₃	C₂³	1	2	yes	—
177	C₄⋊Dic₃	C₂³	1	4	yes	—
178	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
179	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
180	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
181	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
182	Dic₃⋊C₄	C₂³	1	4	yes	—
183	C₄×Dic₃	C₂³	1	1	yes	characteristic
184	C₄×Dic₃	C₂³	1	1	yes	characteristic
185	C₄×Dic₃	C₂³	1	1	yes	characteristic
186	C₄×Dic₃	C₂³	1	1	yes	characteristic
187	C₄×Dic₃	C₂³	1	1	yes	characteristic
188	C₄×Dic₃	C₂³	1	1	yes	characteristic
189	C₄×Dic₃	C₂³	1	4	yes	—
190	C₂×#41	—	3	2	no	—
191	C₂×#41	—	3	2	no	—
192	C₂×#41	—	3	1	no	—
193	C₂×#41	—	3	2	no	—
194	C₂×#41	C₂×D₃	1	2	yes	complemented
195	C₂²×D₄	—	3	2	no	—
196	C₂²×D₄	—	3	2	no	—
197	C₂²×D₄	—	3	2	no	—
198	C₄⋊Q₈	—	3	1	no	—
199	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
200	#127	—	3	2	no	—
201	#127	—	3	2	no	—
202	#127	—	3	2	no	—
203	#127	—	3	4	no	—
204	#127	—	3	1	no	—
205	#127	C₂×D₃	1	1	yes	characteristic
206	#125	—	3	2	no	—
207	#124	—	3	2	no	—
208	#124	—	3	2	no	—
209	#124	—	3	4	no	—
210	#124	—	3	2	no	—
211	#124	C₂×D₃	1	2	yes	complemented
212	#123	—	3	4	no	—
213	#123	—	3	4	no	—
214	#123	—	3	4	no	—
215	#123	—	3	4	no	—
216	C₂²⋊Q₈	—	3	2	no	—
217	C₂²⋊Q₈	—	3	2	no	—
218	#121	—	3	2	no	—
219	#121	—	3	2	no	—
220	#121	—	3	4	no	—
221	#121	—	3	4	no	—
222	#121	—	3	2	no	—
223	#121	—	3	2	no	—
224	#121	—	3	4	no	—
225	#121	—	3	2	no	—
226	#121	—	3	2	no	—
227	#121	—	3	4	no	—
228	#121	C₂×D₃	1	2	yes	complemented
229	#121	C₂×D₃	1	2	yes	complemented
230	#120	—	3	4	no	—
231	#120	—	3	4	no	—
232	C₄×Q₈	—	3	2	no	—
233	C₄×Q₈	—	3	2	no	—
234	C₄×Q₈	—	3	1	no	—
235	C₄×Q₈	—	3	1	no	—
236	C₄×D₄	—	3	2	no	—
237	C₄×D₄	—	3	2	no	—
238	C₄×D₄	—	3	1	no	—
239	C₄×D₄	—	3	1	no	—
240	C₄×D₄	—	3	1	no	—
241	C₄×D₄	—	3	1	no	—
242	C₄×D₄	—	3	4	no	—
243	C₄×D₄	—	3	2	no	—
244	C₄×D₄	—	3	2	no	—
245	C₄×D₄	—	3	4	no	—
246	C₄×D₄	—	3	1	no	—
247	C₄×D₄	—	3	1	no	—
248	C₄×D₄	—	3	2	no	—
249	C₄×D₄	—	3	2	no	—
250	C₄×D₄	C₂×D₃	1	2	yes	complemented
251	C₄×D₄	C₂×D₃	1	2	yes	complemented
252	#117	—	3	1	no	—
253	#117	—	3	2	no	—
254	#117	—	3	1	no	—
255	#117	—	3	1	no	—
256	C₂×C₂²⋊C₄	—	3	4	no	—
257	C₂×C₂²⋊C₄	—	3	4	no	—
258	C₂×C₄²	—	3	1	no	—
259	C₂×C₄²	—	3	1	no	—
260	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
261	C₂³×C₃	C₂⁴	1	4	yes	—
262	C₂³×C₃	C₂⁴	1	1	yes	characteristic
263	C₂²×D₃	—	2	8	no	—
264	C₂²×D₃	—	4	4	no	—
265	C₂²×D₃	—	4	4	no	—
266	C₂²×D₃	C₂⁴	1	4	yes	—
267	C₂²×D₃	C₂⁴	1	1	yes	characteristic
268	C₂²×D₃	C₂⁴	1	1	yes	characteristic
269	C₃×Q₈	—	2	4	no	—
270	C₃×D₄	—	2	4	no	—
271	C₃×D₄	—	2	4	no	—
272	C₃×D₄	—	2	4	no	—
273	C₃×D₄	—	4	4	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	4	4	no	—
278	C₂×C₃×C₄	C₂⁴	1	4	yes	—
279	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
285	#67	—	2	2	no	—
286	#67	—	2	2	no	—
287	#67	—	2	8	no	—
288	#67	—	4	4	no	—
289	#67	—	4	4	no	—
290	#67	—	4	4	no	—
291	#67	—	4	4	no	—
292	C₂×Dic₃	—	4	4	no	—
293	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
294	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
297	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₃	C₂⁴	1	4	yes	—
299	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
300	D₁₂	—	2	2	no	—
301	D₁₂	—	2	4	no	—
302	D₁₂	—	2	4	no	—
303	D₁₂	—	2	4	no	—
304	D₁₂	—	4	4	no	—
305	C₄×D₃	—	2	2	no	—
306	C₄×D₃	—	2	2	no	—
307	C₄×D₃	—	2	2	no	—
308	C₄×D₃	—	2	2	no	—
309	C₄×D₃	—	2	2	no	—
310	C₄×D₃	—	4	4	no	—
311	C₄×D₃	—	4	4	no	—
312	C₄×D₃	#41	1	4	yes	complemented
313	Dic₆	—	2	4	no	—
314	Dic₆	—	2	2	no	—
315	C₂⁴	—	3	4	no	—
316	#41	—	4	4	no	—
317	#41	—	6	4	no	—
318	#41	—	12	4	no	—
319	#41	—	12	4	no	—
320	#41	—	12	4	no	—
321	C₂×Q₈	—	3	1	no	—
322	C₂×Q₈	—	3	2	no	—
323	C₂×Q₈	C₂²×D₃	1	2	yes	—
324	C₂×D₄	—	3	1	no	—
325	C₂×D₄	—	3	4	no	—
326	C₂×D₄	—	3	1	no	—
327	C₂×D₄	—	3	4	no	—
328	C₂×D₄	—	3	4	no	—
329	C₂×D₄	—	3	4	no	—
330	C₂×D₄	—	3	4	no	—
331	C₂×D₄	—	3	1	no	—
332	C₂×D₄	—	3	2	no	—
333	C₂×D₄	—	3	2	no	—
334	C₂×D₄	—	3	2	no	—
335	C₂×D₄	—	3	4	no	—
336	C₂×D₄	—	6	8	no	—
337	C₂×D₄	—	12	4	no	—
338	C₂×D₄	—	12	4	no	—
339	C₂×D₄	C₂²×D₃	1	2	yes	—
340	C₂×D₄	C₂²×D₃	1	2	yes	—
341	C₂×D₄	C₂²×D₃	1	2	yes	—
342	C₂×D₄	C₂²×D₃	1	4	yes	—
343	C₂²×C₄	—	3	1	no	—
344	C₂²×C₄	—	3	4	no	—
345	C₂²×C₄	—	3	1	no	—
346	C₂²×C₄	—	3	1	no	—
347	C₂²×C₄	—	3	1	no	—
348	C₂²×C₄	—	3	1	no	—
349	C₂²×C₄	—	3	1	no	—
350	C₂²×C₄	—	3	4	no	—
351	C₂²×C₄	—	3	4	no	—
352	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
353	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
354	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
355	C₂²×C₄	C₂²×D₃	1	4	yes	—
356	C₄⋊C₄	—	3	1	no	—
357	C₄⋊C₄	—	3	1	no	—
358	C₄⋊C₄	—	3	2	no	—
359	C₄⋊C₄	—	3	1	no	—
360	C₄⋊C₄	—	3	1	no	—
361	C₄⋊C₄	—	3	1	no	—
362	C₄⋊C₄	—	3	1	no	—
363	C₄⋊C₄	—	3	2	no	—
364	C₄⋊C₄	—	3	4	no	—
365	C₄⋊C₄	—	3	4	no	—
366	C₄⋊C₄	C₂²×D₃	1	2	yes	—
367	C₄⋊C₄	C₂²×D₃	1	2	yes	—
368	C₂²⋊C₄	—	3	4	no	—
369	C₂²⋊C₄	—	3	1	no	—
370	C₂²⋊C₄	—	3	1	no	—
371	C₂²⋊C₄	—	3	4	no	—
372	C₂²⋊C₄	—	3	1	no	—
373	C₂²⋊C₄	—	3	1	no	—
374	C₂²⋊C₄	—	3	4	no	—
375	C₂²⋊C₄	—	3	4	no	—
376	C₂²⋊C₄	—	3	4	no	—
377	C₂²⋊C₄	—	3	1	no	—
378	C₂²⋊C₄	—	3	1	no	—
379	C₂²⋊C₄	—	3	4	no	—
380	C₂²⋊C₄	—	3	4	no	—
381	C₂²⋊C₄	C₂²×D₃	1	4	yes	—
382	C₂²⋊C₄	C₂²×D₃	1	4	yes	—
383	C₄²	—	3	1	no	—
384	C₄²	—	3	1	no	—
385	C₄²	—	3	1	no	—
386	C₄²	—	3	1	no	—
387	C₄²	—	3	1	no	—
388	C₄²	—	3	1	no	—
389	C₄²	—	3	4	no	—
390	C₄²	C₂²×D₃	1	1	yes	characteristic
391	C₄²	C₂²×D₃	1	1	yes	characteristic
392	C₄²	C₂²×D₃	1	1	yes	characteristic
393	C₄²	C₂²×D₃	1	1	yes	characteristic
394	C₂²×C₃	—	2	1	no	—
395	C₂²×C₃	—	2	4	no	—
396	C₂²×C₃	—	2	4	no	—
397	C₂²×C₃	—	2	1	no	—
398	C₂²×C₃	—	2	4	no	—
399	C₂²×C₃	—	2	1	no	—
400	C₂²×C₃	C₂⁵	1	1	yes	characteristic
401	C₂×D₃	—	2	1	no	—
402	C₂×D₃	—	2	1	no	—
403	C₂×D₃	—	2	1	no	—
404	C₂×D₃	—	2	4	no	—
405	C₂×D₃	—	2	1	no	—
406	C₂×D₃	—	2	1	no	—
407	C₂×D₃	—	2	4	no	—
408	C₂×D₃	—	2	4	no	—
409	C₂×D₃	—	8	8	no	—
410	C₂×D₃	C₂×#41	1	2	yes	—
411	C₃×C₄	—	2	1	no	—
412	C₃×C₄	—	2	1	no	—
413	C₃×C₄	—	2	4	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	C₂×#41	1	2	yes	—
416	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
417	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
418	Dic₃	—	2	1	no	—
419	Dic₃	—	2	4	no	—
420	Dic₃	—	2	1	no	—
421	Dic₃	—	2	1	no	—
422	Dic₃	—	2	1	no	—
423	Dic₃	—	2	1	no	—
424	Dic₃	C₂×#41	1	2	yes	—
425	C₂³	—	3	1	no	—
426	C₂³	—	3	4	no	—
427	C₂³	—	3	1	no	—
428	C₂³	—	6	8	no	—
429	C₂³	—	12	4	no	—
430	C₂³	—	12	4	no	—
431	C₂³	C₂³×D₃	1	4	yes	—
432	C₂³	C₂³×D₃	1	1	yes	characteristic
433	Q₈	—	2	4	no	—
434	Q₈	—	6	2	no	—
435	Q₈	—	6	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	4	no	—
439	D₄	—	4	4	no	—
440	D₄	—	6	2	no	—
441	D₄	—	6	8	no	—
442	D₄	—	6	2	no	—
443	D₄	—	6	2	no	—
444	D₄	—	6	4	no	—
445	D₄	—	6	4	no	—
446	D₄	—	6	4	no	—
447	D₄	—	12	4	no	—
448	D₄	—	12	4	no	—
449	D₄	—	12	4	no	—
450	D₄	—	12	4	no	—
451	D₄	—	12	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	3	1	no	—
456	C₂×C₄	—	3	4	no	—
457	C₂×C₄	—	3	1	no	—
458	C₂×C₄	—	3	1	no	—
459	C₂×C₄	—	3	1	no	—
460	C₂×C₄	—	3	1	no	—
461	C₂×C₄	—	3	1	no	—
462	C₂×C₄	—	3	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	6	2	no	—
465	C₂×C₄	—	6	2	no	—
466	C₂×C₄	—	6	2	no	—
467	C₂×C₄	—	6	2	no	—
468	C₂×C₄	—	6	2	no	—
469	C₂×C₄	—	12	4	no	—
470	C₂×C₄	—	12	4	no	—
471	C₂×C₄	—	12	4	no	—
472	C₂×C₄	C₂³×D₃	1	4	yes	—
473	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
474	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
475	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
476	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
477	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
478	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
479	C₂×C₃	—	4	4	no	—
480	C₂×C₃	—	4	1	no	—
481	C₂×C₃	C₂²×#41	1	1	yes	characteristic
482	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
484	D₃	—	2	2	no	—
485	D₃	—	4	1	no	—
486	D₃	—	4	4	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	3	2	no	—
494	C₂²	—	6	1	no	—
495	C₂²	—	6	1	no	—
496	C₂²	—	6	1	no	—
497	C₂²	—	6	4	no	—
498	C₂²	—	6	1	no	—
499	C₂²	—	6	4	no	—
500	C₂²	—	6	1	no	—
501	C₂²	—	6	4	no	—
502	C₂²	—	24	8	no	—
503	C₂²	C₂⁴×D₃	1	1	yes	characteristic
504	C₄	—	2	1	no	—
505	C₄	—	2	4	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	3	2	no	—
509	C₄	—	6	1	no	—
510	C₄	—	6	1	no	—
511	C₄	—	6	1	no	—
512	C₄	—	6	1	no	—
513	C₄	—	6	1	no	—
514	C₄	—	6	4	no	—
515	C₄	#1004	1	2	yes	—
516	C₄	D₃×#41	1	2	yes	—
517	C₄	#1009	1	2	yes	—
518	C₃	#3508	1	1	yes	characteristic, complemented, Sylow
519	C₂	—	4	4	no	—
520	C₂	—	4	1	no	—
521	C₂	—	6	2	no	—
522	C₂	—	12	4	no	—
523	C₂	—	12	1	no	—
524	C₂	C₂×#1004	1	1	yes	characteristic
525	C₂	C₂×D₃×#41	1	1	yes	characteristic
526	C₂	C₂×#1009	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#532	C₂
hypercenter	#532	D₃
hypocenter	C₃	#3508
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₃×#532	C₂	semidirect
2. #5834	C₂	semidirect
3. #5829	C₂	semidirect
4. #5728	C₂	semidirect
5. #5725	C₂	semidirect
6. #5716	C₂	semidirect
7. D₃×#127	C₂	semidirect
8. #5681	C₂	semidirect
9. #5676	C₂	semidirect
10. #5619	C₂	semidirect
11. #5612	C₂	semidirect
12. #5607	C₂	semidirect
13. #5599	C₂	semidirect
14. #5562	C₂	semidirect
15. #5559	C₂	semidirect
16. #5554	C₂	semidirect
17. #5545	C₂	semidirect
18. #5477	C₂	semidirect
19. C₄×#235	C₂	semidirect
21. C₂×C₃×#41	C₂²	semidirect
22. C₂×#239	C₂²	semidirect
23. C₂×#237	C₂²	semidirect
28. C₂×#235	C₂²	semidirect
29. C₃×C₄⋊Q₈	C₂²	semidirect
31. C₃×#124	C₂²	semidirect
32. C₃×#121	C₂²	semidirect
33. C₃×#121	C₂²	semidirect
34. C₃×C₄×D₄	C₂²	semidirect
35. C₃×C₄×D₄	C₂²	semidirect
36. C₂×C₃×C₄²	C₂²	semidirect
37. #947	C₂²	semidirect
39. Q₈×Dic₃	C₂²	semidirect
43. #940	C₂²	semidirect
44. #939	C₂²	semidirect
45. #938	C₂²	semidirect
46. #938	C₂²	semidirect
47. #938	C₂²	semidirect
49. #936	C₂²	semidirect
50. D₄×Dic₃	C₂²	semidirect
51. D₄×Dic₃	C₂²	semidirect
52. #930	C₂²	semidirect
53. #930	C₂²	semidirect
54. #930	C₂²	semidirect
55. #929	C₂²	semidirect
58. C₄×#67	C₂²	semidirect
59. C₄×#67	C₂²	semidirect
60. C₄×#67	C₂²	semidirect
62. #926	C₂²	semidirect
64. #895	C₂²	semidirect
65. #895	C₂²	semidirect
66. #893	C₂²	semidirect
67. #893	C₂²	semidirect
69. #890	C₂²	semidirect
70. #887	C₂²	semidirect
71. #886	C₂²	semidirect
72. #885	C₂²	semidirect
73. #884	C₂²	semidirect
74. #883	C₂²	semidirect
75. #883	C₂²	semidirect
77. #67⋊C₄	C₂²	semidirect
79. #875	C₂²	semidirect
83. C₄×D₁₂	C₂²	semidirect
84. C₄×D₁₂	C₂²	semidirect
86. #872	C₂²	semidirect
88. C₄²×D₃	C₂²	semidirect
89. #869	C₂²	semidirect
90. C₄×Dic₆	C₂²	semidirect
91. C₄×Dic₆	C₂²	semidirect
107. #532	D₃	semidirect
194. C₂×#41	C₂×D₃	semidirect
199. C₄⋊Q₈	C₂×D₃	semidirect
211. #124	C₂×D₃	semidirect
228. #121	C₂×D₃	semidirect
229. #121	C₂×D₃	semidirect
250. C₄×D₄	C₂×D₃	semidirect
251. C₄×D₄	C₂×D₃	semidirect
260. C₂×C₄²	C₂×D₃	semidirect
312. C₄×D₃	#41	semidirect
518. C₃	#3508	semidirect

Maximal subgroups

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

subgroup	index
C₃×#532	2
#5834	2
#5829	2
#5728	2
#5725	2
#5716	2
D₃×#127	2
#5681	2
#5676	2
#5619	2
#5612	2
#5607	2
#5599	2
#5562	2
#5559	2
#5554	2
#5545	2
#5477	2
C₄×#235	2
#3508	3