Subgroups — #86163

Order 384.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#5705	C₂	1	4	yes	maximal, complemented
3	#5691	C₂	1	2	yes	maximal, complemented
4	D₃×#124	C₂	1	2	yes	maximal, complemented
5	#5657	C₂	1	4	yes	maximal, complemented
6	#5633	C₂	1	2	yes	maximal, complemented
7	#5612	C₂	1	2	yes	maximal, complemented
8	#5585	C₂	1	1	yes	maximal, characteristic, complemented
9	Q₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#5563	C₂	1	2	yes	maximal, complemented
11	#5550	C₂	1	2	yes	maximal, complemented
12	D₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
13	#5542	C₂	1	1	yes	maximal, characteristic, complemented
14	#5534	C₂	1	2	yes	maximal, complemented
15	#5521	C₂	1	2	yes	maximal, complemented
16	#5477	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
18	#3514	—	3	1	no	maximal, Sylow
19	C₂×D₃×Q₈	C₂²	1	2	yes	complemented
20	C₂×D₃×D₄	C₂²	1	2	yes	—
21	C₂×#235	C₂²	1	1	yes	characteristic
22	C₂×#235	C₂²	1	2	yes	complemented
23	C₂²×D₁₂	C₂²	1	2	yes	—
24	C₃×#126	C₂²	1	2	yes	complemented
25	C₃×#125	C₂²	1	1	yes	characteristic, complemented
26	C₃×#124	C₂²	1	1	yes	characteristic
27	C₃×#123	C₂²	1	2	yes	complemented
28	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#121	C₂²	1	1	yes	characteristic
30	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₃×C₄×D₄	C₂²	1	2	yes	complemented
33	C₃×#117	C₂²	1	2	yes	complemented
34	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
35	#947	C₂²	1	2	yes	complemented
36	#938	C₂²	1	4	yes	complemented
37	#937	C₂²	1	4	yes	complemented
38	#936	C₂²	1	2	yes	—
39	#930	C₂²	1	2	yes	—
40	#930	C₂²	1	2	yes	complemented
41	#930	C₂²	1	2	yes	complemented
42	C₄×#67	C₂²	1	2	yes	complemented
43	C₄×#67	C₂²	1	2	yes	complemented
44	#926	C₂²	1	1	yes	characteristic, complemented
45	#926	C₂²	1	2	yes	complemented
46	#924	C₂²	1	2	yes	complemented
47	#898	C₂²	1	4	yes	complemented
48	#897	C₂²	1	4	yes	complemented
49	#897	C₂²	1	2	yes	complemented
50	#896	C₂²	1	4	yes	complemented
51	#895	C₂²	1	2	yes	—
52	#894	C₂²	1	4	yes	complemented
53	#894	C₂²	1	4	yes	complemented
54	#893	C₂²	1	4	yes	complemented
55	#893	C₂²	1	4	yes	complemented
56	#893	C₂²	1	2	yes	complemented
57	#892	C₂²	1	4	yes	complemented
58	#887	C₂²	1	2	yes	complemented
59	#885	C₂²	1	4	yes	complemented
60	#885	C₂²	1	4	yes	complemented
61	#885	C₂²	1	4	yes	complemented
62	#884	C₂²	1	4	yes	complemented
63	#883	C₂²	1	4	yes	complemented
64	#882	C₂²	1	4	yes	—
65	D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
66	D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
67	D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
68	#879	C₂²	1	4	yes	complemented
69	#875	C₂²	1	2	yes	complemented
70	#875	C₂²	1	2	yes	complemented
71	#874	C₂²	1	1	yes	characteristic
72	C₄×D₁₂	C₂²	1	1	yes	characteristic
73	C₄×D₁₂	C₂²	1	1	yes	characteristic
74	C₄×D₁₂	C₂²	1	2	yes	—
75	C₄×D₁₂	C₂²	1	2	yes	complemented
76	C₄×D₁₂	C₂²	1	2	yes	complemented
77	C₄×D₁₂	C₂²	1	2	yes	complemented
78	#872	C₂²	1	2	yes	complemented
79	C₄²×D₃	C₂²	1	2	yes	complemented
80	#869	C₂²	1	1	yes	characteristic, complemented
81	#869	C₂²	1	2	yes	complemented
82	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
84	#559	—	3	1	no	—
85	#556	—	3	1	no	—
86	#555	—	3	2	no	—
87	#551	—	3	4	no	—
88	D₄×Q₈	—	3	1	no	—
89	#548	—	3	2	no	—
90	#546	—	3	2	no	—
91	#546	—	3	2	no	—
92	D₄²	—	3	1	no	—
93	#542	—	3	2	no	—
94	#538	—	3	4	no	—
95	#532	—	3	1	no	—
96	#529	—	3	2	no	—
97	#529	D₃	1	1	yes	characteristic, complemented
98	C₂×#124	—	3	2	no	—
99	#518	—	3	2	no	—
100	C₄×#41	—	3	1	no	—
101	C₂³×D₃	C₂³	1	4	yes	—
102	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
104	C₂×C₃×D₄	C₂³	1	2	yes	—
105	C₂²×C₃×C₄	C₂³	1	2	yes	—
106	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
107	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
108	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
109	C₂×#67	C₂³	1	2	yes	—
110	C₂×#67	C₂³	1	4	yes	—
111	C₂×#67	C₂³	1	4	yes	—
112	D₃×Q₈	—	4	4	no	—
113	D₃×D₄	—	4	4	no	—
114	#235	—	2	4	no	—
115	#235	—	4	4	no	—
116	C₂×D₁₂	—	2	8	no	—
117	C₂×D₁₂	C₂³	1	2	yes	—
118	C₂×D₁₂	C₂³	1	2	yes	—
119	C₂×D₁₂	C₂³	1	4	yes	—
120	C₂×D₁₂	C₂³	1	2	yes	—
121	C₂×D₁₂	C₂³	1	1	yes	characteristic
122	C₂×C₄×D₃	C₂³	1	2	yes	—
123	C₂×C₄×D₃	C₂³	1	2	yes	—
124	C₂×C₄×D₃	C₂³	1	2	yes	—
125	C₂×C₄×D₃	C₂³	1	4	yes	—
126	C₂×C₄×D₃	C₂³	1	4	yes	—
127	C₂×C₄×D₃	C₂³	1	4	yes	—
128	C₂×Dic₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₆	C₂³	1	2	yes	—
130	C₂×Dic₆	C₂³	1	4	yes	—
131	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₃×C₄²	C₂³	1	1	yes	characteristic
143	C₃×C₄²	C₂³	1	1	yes	characteristic
144	C₃×C₄²	C₂³	1	2	yes	—
145	C₃×C₄²	C₂³	1	1	yes	characteristic
146	C₃×C₄²	C₂³	1	1	yes	characteristic
147	#217	C₂³	1	4	yes	—
148	#217	C₂³	1	4	yes	—
149	#217	C₂³	1	2	yes	—
150	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
151	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
152	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
153	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
154	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
155	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
156	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
157	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
158	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
159	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₃	C₂³	1	2	yes	—
162	C₄⋊Dic₃	C₂³	1	2	yes	—
163	C₄⋊Dic₃	C₂³	1	4	yes	—
164	Dic₃⋊C₄	C₂³	1	2	yes	—
165	Dic₃⋊C₄	C₂³	1	2	yes	—
166	Dic₃⋊C₄	C₂³	1	4	yes	—
167	C₄×Dic₃	C₂³	1	2	yes	—
168	C₄×Dic₃	C₂³	1	2	yes	—
169	C₄×Dic₃	C₂³	1	2	yes	—
170	C₄×Dic₃	C₂³	1	4	yes	—
171	C₂×#41	—	3	1	no	—
172	C₂×#41	—	3	2	no	—
173	C₂²×Q₈	—	3	2	no	—
174	C₂²×D₄	—	3	2	no	—
175	C₂²×D₄	—	3	2	no	—
176	C₄⋊Q₈	—	3	1	no	—
177	C₄⋊Q₈	—	3	2	no	—
178	#127	—	3	1	no	—
179	#126	—	3	4	no	—
180	#126	—	3	4	no	—
181	#126	C₂×D₃	1	2	yes	complemented
182	#125	C₂×D₃	1	1	yes	characteristic, complemented
183	#124	—	3	2	no	—
184	#124	—	3	2	no	—
185	#124	—	3	4	no	—
186	#124	—	3	4	no	—
187	#124	—	3	4	no	—
188	#124	—	3	2	no	—
189	#124	—	3	2	no	—
190	#124	C₂×D₃	1	1	yes	characteristic
191	#123	—	3	4	no	—
192	#123	—	3	4	no	—
193	#123	—	3	4	no	—
194	#123	C₂×D₃	1	2	yes	complemented
195	C₂²⋊Q₈	—	3	2	no	—
196	C₂²⋊Q₈	—	3	2	no	—
197	C₂²⋊Q₈	—	3	4	no	—
198	C₂²⋊Q₈	—	3	4	no	—
199	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
200	#121	—	3	4	no	—
201	#121	—	3	2	no	—
202	#121	—	3	2	no	—
203	#121	—	3	2	no	—
204	#121	—	3	2	no	—
205	#121	—	3	4	no	—
206	#121	C₂×D₃	1	1	yes	characteristic
207	#120	—	3	4	no	—
208	#120	—	3	4	no	—
209	C₄×Q₈	—	3	2	no	—
210	C₄×Q₈	—	3	1	no	—
211	C₄×Q₈	—	3	1	no	—
212	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
213	C₄×D₄	—	3	2	no	—
214	C₄×D₄	—	3	2	no	—
215	C₄×D₄	—	3	4	no	—
216	C₄×D₄	—	3	4	no	—
217	C₄×D₄	—	3	2	no	—
218	C₄×D₄	—	3	1	no	—
219	C₄×D₄	—	3	1	no	—
220	C₄×D₄	—	3	2	no	—
221	C₄×D₄	—	3	2	no	—
222	C₄×D₄	—	3	2	no	—
223	C₄×D₄	—	3	2	no	—
224	C₄×D₄	C₂×D₃	1	1	yes	characteristic
225	C₄×D₄	C₂×D₃	1	2	yes	complemented
226	#117	—	3	1	no	—
227	#117	—	3	2	no	—
228	#117	—	3	4	no	—
229	#117	—	3	2	no	—
230	#117	C₂×D₃	1	2	yes	complemented
231	C₂×C₂²⋊C₄	—	3	4	no	—
232	C₂×C₂²⋊C₄	—	3	4	no	—
233	C₂×C₂²⋊C₄	—	3	4	no	—
234	C₂×C₄²	—	3	2	no	—
235	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
236	C₂³×C₃	C₂⁴	1	2	yes	—
237	C₂³×C₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₃	—	2	8	no	—
239	C₂²×D₃	—	4	4	no	—
240	C₂²×D₃	—	4	4	no	—
241	C₂²×D₃	C₂⁴	1	4	yes	—
242	C₂²×D₃	C₂⁴	1	2	yes	—
243	C₃×Q₈	—	2	2	no	—
244	C₃×D₄	—	2	2	no	—
245	C₃×D₄	—	4	2	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	4	1	no	—
250	C₂×C₃×C₄	C₂⁴	1	2	yes	—
251	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂⁴	1	2	yes	—
256	C₂×C₃×C₄	C₂⁴	1	2	yes	—
257	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
259	#67	—	2	4	no	—
260	#67	—	4	4	no	—
261	#67	—	4	4	no	—
262	C₂×Dic₃	C₂⁴	1	2	yes	—
263	C₂×Dic₃	C₂⁴	1	2	yes	—
264	C₂×Dic₃	C₂⁴	1	2	yes	—
265	C₂×Dic₃	C₂⁴	1	4	yes	—
266	D₁₂	—	2	8	no	—
267	D₁₂	—	2	4	no	—
268	D₁₂	—	2	4	no	—
269	D₁₂	—	4	2	no	—
270	D₁₂	#41	1	4	yes	complemented
271	C₄×D₃	—	2	4	no	—
272	C₄×D₃	—	2	4	no	—
273	C₄×D₃	—	4	2	no	—
274	C₄×D₃	—	4	4	no	—
275	C₄×D₃	—	4	4	no	—
276	C₄×D₃	—	4	4	no	—
277	Dic₆	—	2	2	no	—
278	Dic₆	—	2	4	no	—
279	Dic₆	—	4	4	no	—
280	C₂⁴	—	3	4	no	—
281	#41	—	6	4	no	—
282	#41	—	12	4	no	—
283	C₂×Q₈	—	3	1	no	—
284	C₂×Q₈	—	3	2	no	—
285	C₂×Q₈	—	3	4	no	—
286	C₂×Q₈	—	12	4	no	—
287	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
288	C₂×D₄	—	3	2	no	—
289	C₂×D₄	—	3	4	no	—
290	C₂×D₄	—	3	4	no	—
291	C₂×D₄	—	3	1	no	—
292	C₂×D₄	—	3	4	no	—
293	C₂×D₄	—	3	2	no	—
294	C₂×D₄	—	3	2	no	—
295	C₂×D₄	—	3	2	no	—
296	C₂×D₄	—	6	8	no	—
297	C₂×D₄	—	12	4	no	—
298	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
299	C₂×D₄	C₂²×D₃	1	2	yes	—
300	C₂²×C₄	—	3	2	no	—
301	C₂²×C₄	—	3	2	no	—
302	C₂²×C₄	—	3	2	no	—
303	C₂²×C₄	—	3	4	no	—
304	C₂²×C₄	—	3	4	no	—
305	C₂²×C₄	—	3	4	no	—
306	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
307	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
308	C₂²×C₄	C₂²×D₃	1	2	yes	—
309	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
310	C₄⋊C₄	—	3	1	no	—
311	C₄⋊C₄	—	3	2	no	—
312	C₄⋊C₄	—	3	1	no	—
313	C₄⋊C₄	—	3	2	no	—
314	C₄⋊C₄	—	3	2	no	—
315	C₄⋊C₄	—	3	4	no	—
316	C₄⋊C₄	—	3	2	no	—
317	C₄⋊C₄	—	3	4	no	—
318	C₄⋊C₄	C₂²×D₃	1	2	yes	—
319	C₄⋊C₄	C₂²×D₃	1	2	yes	—
320	C₄⋊C₄	C₂²×D₃	1	2	yes	—
321	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
322	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
323	C₄⋊C₄	C₂²×D₃	1	2	yes	—
324	C₂²⋊C₄	—	3	4	no	—
325	C₂²⋊C₄	—	3	4	no	—
326	C₂²⋊C₄	—	3	2	no	—
327	C₂²⋊C₄	—	3	2	no	—
328	C₂²⋊C₄	—	3	4	no	—
329	C₂²⋊C₄	—	3	4	no	—
330	C₂²⋊C₄	—	3	4	no	—
331	C₂²⋊C₄	—	3	4	no	—
332	C₂²⋊C₄	—	3	4	no	—
333	C₂²⋊C₄	—	3	2	no	—
334	C₂²⋊C₄	—	3	4	no	—
335	C₂²⋊C₄	—	3	4	no	—
336	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
337	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
338	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
339	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
340	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
341	C₄²	—	3	2	no	—
342	C₄²	—	3	2	no	—
343	C₄²	—	3	2	no	—
344	C₄²	—	3	4	no	—
345	C₄²	C₂²×D₃	1	1	yes	characteristic
346	C₄²	C₂²×D₃	1	1	yes	characteristic
347	C₄²	C₂²×D₃	1	1	yes	characteristic
348	C₄²	C₂²×D₃	1	1	yes	characteristic
349	C₄²	C₂²×D₃	1	2	yes	—
350	C₂²×C₃	—	2	1	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	2	1	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	1	no	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	C₂⁵	1	1	yes	characteristic
357	C₂×D₃	—	2	2	no	—
358	C₂×D₃	—	2	2	no	—
359	C₂×D₃	—	2	4	no	—
360	C₂×D₃	—	2	4	no	—
361	C₂×D₃	—	2	4	no	—
362	C₂×D₃	—	8	8	no	—
363	C₂×D₃	C₂×#41	1	4	yes	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	2	no	—
370	C₃×C₄	—	2	1	no	—
371	C₃×C₄	C₂×#41	1	2	yes	—
372	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
373	Dic₃	—	2	2	no	—
374	Dic₃	—	2	4	no	—
375	Dic₃	—	2	2	no	—
376	Dic₃	—	2	2	no	—
377	C₂³	—	3	2	no	—
378	C₂³	—	3	4	no	—
379	C₂³	—	6	8	no	—
380	C₂³	—	12	4	no	—
381	C₂³	—	12	4	no	—
382	C₂³	C₂³×D₃	1	2	yes	—
383	C₂³	C₂³×D₃	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	6	2	no	—
386	Q₈	—	6	4	no	—
387	Q₈	—	12	4	no	—
388	D₄	—	2	2	no	—
389	D₄	—	3	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	6	8	no	—
392	D₄	—	6	4	no	—
393	D₄	—	6	4	no	—
394	D₄	—	6	4	no	—
395	D₄	—	12	2	no	—
396	D₄	—	12	4	no	—
397	D₄	—	12	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	3	2	no	—
402	C₂×C₄	—	3	2	no	—
403	C₂×C₄	—	3	2	no	—
404	C₂×C₄	—	3	4	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	6	4	no	—
407	C₂×C₄	—	6	4	no	—
408	C₂×C₄	—	12	4	no	—
409	C₂×C₄	—	12	4	no	—
410	C₂×C₄	—	12	2	no	—
411	C₂×C₄	—	12	4	no	—
412	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
413	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
414	C₂×C₄	C₂³×D₃	1	2	yes	—
415	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
417	C₂×C₄	C₂³×D₃	1	2	yes	—
418	C₂×C₄	C₂³×D₃	1	2	yes	—
419	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
421	C₂×C₃	—	4	2	no	—
422	C₂×C₃	—	4	1	no	—
423	C₂×C₃	C₂²×#41	1	1	yes	characteristic
424	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂×C₃	#585	1	1	yes	characteristic
426	D₃	—	2	4	no	—
427	D₃	—	4	4	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	3	4	no	—
435	C₂²	—	6	2	no	—
436	C₂²	—	6	2	no	—
437	C₂²	—	6	4	no	—
438	C₂²	—	6	4	no	—
439	C₂²	—	6	4	no	—
440	C₂²	—	24	8	no	—
441	C₂²	C₂⁴×D₃	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	6	2	no	—
450	C₄	—	6	2	no	—
451	C₄	—	6	4	no	—
452	C₄	—	6	2	no	—
453	C₄	D₃×#41	1	2	yes	—
454	C₄	#1009	1	2	yes	—
455	C₃	#3514	1	1	yes	characteristic, complemented, Sylow
456	C₂	—	4	2	no	—
457	C₂	—	4	1	no	—
458	C₂	—	6	4	no	—
459	C₂	—	12	4	no	—
460	C₂	C₂×D₃×#41	1	1	yes	characteristic
461	C₂	C₂×#1009	1	1	yes	characteristic
462	C₂	#5964	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#529	C₂
hypercenter	#529	D₃
hypocenter	C₃	#3514
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₃×#529	C₂	semidirect
2. #5705	C₂	semidirect
3. #5691	C₂	semidirect
4. D₃×#124	C₂	semidirect
5. #5657	C₂	semidirect
6. #5633	C₂	semidirect
7. #5612	C₂	semidirect
8. #5585	C₂	semidirect
9. Q₈×D₁₂	C₂	semidirect
10. #5563	C₂	semidirect
11. #5550	C₂	semidirect
12. D₄×D₁₂	C₂	semidirect
13. #5542	C₂	semidirect
14. #5534	C₂	semidirect
15. #5521	C₂	semidirect
16. #5477	C₂	semidirect
17. C₄×#235	C₂	semidirect
19. C₂×D₃×Q₈	C₂²	semidirect
22. C₂×#235	C₂²	semidirect
24. C₃×#126	C₂²	semidirect
25. C₃×#125	C₂²	semidirect
27. C₃×#123	C₂²	semidirect
28. C₃×C₂²⋊Q₈	C₂²	semidirect
30. C₃×C₄×Q₈	C₂²	semidirect
32. C₃×C₄×D₄	C₂²	semidirect
33. C₃×#117	C₂²	semidirect
34. C₂×C₃×C₄²	C₂²	semidirect
35. #947	C₂²	semidirect
36. #938	C₂²	semidirect
37. #937	C₂²	semidirect
40. #930	C₂²	semidirect
41. #930	C₂²	semidirect
42. C₄×#67	C₂²	semidirect
43. C₄×#67	C₂²	semidirect
44. #926	C₂²	semidirect
45. #926	C₂²	semidirect
46. #924	C₂²	semidirect
47. #898	C₂²	semidirect
48. #897	C₂²	semidirect
49. #897	C₂²	semidirect
50. #896	C₂²	semidirect
52. #894	C₂²	semidirect
53. #894	C₂²	semidirect
54. #893	C₂²	semidirect
55. #893	C₂²	semidirect
56. #893	C₂²	semidirect
57. #892	C₂²	semidirect
58. #887	C₂²	semidirect
59. #885	C₂²	semidirect
60. #885	C₂²	semidirect
61. #885	C₂²	semidirect
62. #884	C₂²	semidirect
63. #883	C₂²	semidirect
65. D₃×C₂²⋊C₄	C₂²	semidirect
66. D₃×C₂²⋊C₄	C₂²	semidirect
67. D₃×C₂²⋊C₄	C₂²	semidirect
68. #879	C₂²	semidirect
69. #875	C₂²	semidirect
70. #875	C₂²	semidirect
75. C₄×D₁₂	C₂²	semidirect
76. C₄×D₁₂	C₂²	semidirect
77. C₄×D₁₂	C₂²	semidirect
78. #872	C₂²	semidirect
79. C₄²×D₃	C₂²	semidirect
80. #869	C₂²	semidirect
81. #869	C₂²	semidirect
82. C₄×Dic₆	C₂²	semidirect
83. C₄×Dic₆	C₂²	semidirect
97. #529	D₃	semidirect
181. #126	C₂×D₃	semidirect
182. #125	C₂×D₃	semidirect
194. #123	C₂×D₃	semidirect
199. C₂²⋊Q₈	C₂×D₃	semidirect
212. C₄×Q₈	C₂×D₃	semidirect
225. C₄×D₄	C₂×D₃	semidirect
230. #117	C₂×D₃	semidirect
235. C₂×C₄²	C₂×D₃	semidirect
270. D₁₂	#41	semidirect
455. C₃	#3514	semidirect

Maximal subgroups

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

subgroup	index
C₃×#529	2
#5705	2
#5691	2
D₃×#124	2
#5657	2
#5633	2
#5612	2
#5585	2
Q₈×D₁₂	2
#5563	2
#5550	2
D₄×D₁₂	2
#5542	2
#5534	2
#5521	2
#5477	2
C₄×#235	2
#3514	3