Subgroups — #86153

Order 384.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 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	#5709	C₂	1	2	yes	maximal, complemented
3	#5705	C₂	1	2	yes	maximal, complemented
4	#5695	C₂	1	1	yes	maximal, characteristic, complemented
5	#5690	C₂	1	1	yes	maximal, characteristic, complemented
6	#5681	C₂	1	1	yes	maximal, characteristic, complemented
7	#5676	C₂	1	1	yes	maximal, characteristic, complemented
8	#5658	C₂	1	2	yes	maximal, complemented
9	#5654	C₂	1	2	yes	maximal, complemented
10	#5635	C₂	1	1	yes	maximal, characteristic, complemented
11	#5630	C₂	1	1	yes	maximal, characteristic, complemented
12	#5618	C₂	1	1	yes	maximal, characteristic, complemented
13	#5609	C₂	1	1	yes	maximal, characteristic, complemented
14	#5580	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#239	C₂	1	1	yes	maximal, characteristic, complemented
16	#5548	C₂	1	1	yes	maximal, characteristic, complemented
17	#5547	C₂	1	2	yes	maximal, complemented
18	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₃×D₄	C₂	1	2	yes	maximal, complemented
20	#5528	C₂	1	2	yes	maximal, complemented
21	#5524	C₂	1	2	yes	maximal, complemented
22	C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
24	#3481	—	3	1	no	maximal, Sylow
25	C₂×#239	C₂²	1	1	yes	characteristic
26	C₂×D₃×D₄	C₂²	1	2	yes	—
27	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	1	yes	characteristic
29	C₂×#235	C₂²	1	2	yes	complemented
30	C₂²×D₁₂	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₃	C₂²	1	2	yes	complemented
32	C₂²×C₄×D₃	C₂²	1	2	yes	complemented
33	C₃×#126	C₂²	1	2	yes	complemented
34	C₃×#125	C₂²	1	1	yes	characteristic, complemented
35	C₃×#124	C₂²	1	1	yes	characteristic, complemented
36	C₃×#123	C₂²	1	2	yes	complemented
37	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×#121	C₂²	1	1	yes	characteristic
39	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₄×D₄	C₂²	1	2	yes	complemented
41	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₃×#117	C₂²	1	2	yes	complemented
43	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
44	#947	C₂²	1	1	yes	characteristic, complemented
45	#946	C₂²	1	1	yes	characteristic, complemented
46	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
47	#940	C₂²	1	1	yes	characteristic
48	#939	C₂²	1	2	yes	complemented
49	#938	C₂²	1	1	yes	characteristic, complemented
50	#937	C₂²	1	2	yes	—
51	D₄×Dic₃	C₂²	1	2	yes	complemented
52	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₄×#67	C₂²	1	1	yes	characteristic
54	C₄×#67	C₂²	1	1	yes	characteristic
55	C₄×#67	C₂²	1	1	yes	characteristic, complemented
56	C₄×#67	C₂²	1	1	yes	characteristic, complemented
57	C₄×#67	C₂²	1	2	yes	complemented
58	C₄×#67	C₂²	1	2	yes	complemented
59	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
60	#926	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
62	#898	C₂²	1	2	yes	complemented
63	#898	C₂²	1	2	yes	complemented
64	#897	C₂²	1	2	yes	complemented
65	#897	C₂²	1	2	yes	complemented
66	#896	C₂²	1	2	yes	complemented
67	#896	C₂²	1	2	yes	complemented
68	#895	C₂²	1	1	yes	characteristic
69	#895	C₂²	1	2	yes	complemented
70	#895	C₂²	1	1	yes	characteristic, complemented
71	#895	C₂²	1	2	yes	complemented
72	#894	C₂²	1	2	yes	complemented
73	#894	C₂²	1	2	yes	complemented
74	#894	C₂²	1	2	yes	complemented
75	#893	C₂²	1	1	yes	characteristic
76	#893	C₂²	1	1	yes	characteristic
77	#893	C₂²	1	2	yes	complemented
78	#893	C₂²	1	2	yes	complemented
79	#892	C₂²	1	2	yes	complemented
80	#892	C₂²	1	1	yes	characteristic, complemented
81	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
82	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
83	#890	C₂²	1	1	yes	characteristic, complemented
84	#889	C₂²	1	2	yes	complemented
85	#888	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	complemented
89	#885	C₂²	1	2	yes	complemented
90	#884	C₂²	1	2	yes	—
91	#884	C₂²	1	2	yes	complemented
92	#884	C₂²	1	2	yes	complemented
93	#883	C₂²	1	2	yes	complemented
94	#883	C₂²	1	2	yes	complemented
95	#882	C₂²	1	2	yes	—
96	#882	C₂²	1	2	yes	complemented
97	#882	C₂²	1	2	yes	complemented
98	#67⋊C₄	C₂²	1	2	yes	—
99	#67⋊C₄	C₂²	1	2	yes	complemented
100	#67⋊C₄	C₂²	1	2	yes	complemented
101	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
102	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
103	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
104	#879	C₂²	1	2	yes	complemented
105	#878	C₂²	1	2	yes	complemented
106	C₄×D₁₂	C₂²	1	1	yes	characteristic
107	C₄×D₁₂	C₂²	1	1	yes	characteristic
108	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
110	C₄×D₁₂	C₂²	1	2	yes	complemented
111	C₄×D₁₂	C₂²	1	2	yes	complemented
112	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₁₂	C₂²	1	2	yes	complemented
115	C₄×D₁₂	C₂²	1	2	yes	complemented
116	#872	C₂²	1	1	yes	characteristic, complemented
117	#872	C₂²	1	1	yes	characteristic, complemented
118	#872	C₂²	1	2	yes	complemented
119	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
121	C₄²×D₃	C₂²	1	2	yes	complemented
122	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#559	—	3	1	no	—
125	#554	—	3	1	no	—
126	#554	—	3	1	no	—
127	#553	—	3	2	no	—
128	#553	—	3	1	no	—
129	#553	—	3	1	no	—
130	#551	—	3	2	no	—
131	#551	—	3	2	no	—
132	#546	—	3	1	no	—
133	#546	—	3	2	no	—
134	#546	—	3	1	no	—
135	D₄²	—	3	1	no	—
136	#532	—	3	1	no	—
137	#529	—	3	1	no	—
138	#529	—	3	2	no	—
139	#529	D₃	1	1	yes	characteristic, complemented
140	#525	—	3	2	no	—
141	#525	—	3	2	no	—
142	C₄×#41	—	3	1	no	—
143	C₄×#41	—	3	1	no	—
144	C₂×C₄×D₄	—	3	2	no	—
145	C₂×C₄×D₄	—	3	1	no	—
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³	1	2	yes	—
156	C₂×#67	C₂³	1	2	yes	—
157	C₂×#67	C₂³	1	2	yes	—
158	C₂×#67	C₂³	1	1	yes	characteristic
159	C₂×#67	C₂³	1	2	yes	—
160	C₂×#67	C₂³	1	2	yes	—
161	C₂×#67	C₂³	1	1	yes	characteristic
162	C₂²×Dic₃	C₂³	1	2	yes	—
163	C₂²×Dic₃	C₂³	1	2	yes	—
164	#239	—	2	4	no	—
165	D₃×D₄	—	2	8	no	—
166	D₃×D₄	—	2	4	no	—
167	#235	—	2	4	no	—
168	#235	—	4	4	no	—
169	C₂×D₁₂	—	2	4	no	—
170	C₂×D₁₂	C₂³	1	2	yes	—
171	C₂×D₁₂	C₂³	1	1	yes	characteristic
172	C₂×D₁₂	C₂³	1	1	yes	characteristic
173	C₂×D₁₂	C₂³	1	2	yes	—
174	C₂×D₁₂	C₂³	1	2	yes	—
175	C₂×D₁₂	C₂³	1	2	yes	—
176	C₂×D₁₂	C₂³	1	1	yes	characteristic
177	C₂×C₄×D₃	—	4	4	no	—
178	C₂×C₄×D₃	—	4	4	no	—
179	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂³	1	2	yes	—
182	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
185	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
186	C₂×C₄×D₃	C₂³	1	2	yes	—
187	C₂×C₄×D₃	C₂³	1	2	yes	—
188	C₂×C₄×D₃	C₂³	1	2	yes	—
189	C₂×C₄×D₃	C₂³	1	2	yes	—
190	C₂×C₄×D₃	C₂³	1	2	yes	—
191	C₂×C₄×D₃	C₂³	1	2	yes	—
192	C₂×C₄×D₃	C₂³	1	2	yes	—
193	C₂×Dic₆	C₂³	1	1	yes	characteristic
194	C₂×Dic₆	C₂³	1	2	yes	—
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃×C₄²	C₂³	1	1	yes	characteristic
207	C₃×C₄²	C₂³	1	1	yes	characteristic
208	C₃×C₄²	C₂³	1	1	yes	characteristic
209	C₃×C₄²	C₂³	1	2	yes	—
210	C₃×C₄²	C₂³	1	1	yes	characteristic
211	#217	C₂³	1	1	yes	characteristic
212	#217	C₂³	1	2	yes	—
213	#217	C₂³	1	2	yes	—
214	#217	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	2	yes	—
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	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
229	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
230	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
231	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₃	C₂³	1	2	yes	—
236	C₄⋊Dic₃	C₂³	1	2	yes	—
237	C₄⋊Dic₃	C₂³	1	2	yes	—
238	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	Dic₃⋊C₄	C₂³	1	2	yes	—
244	Dic₃⋊C₄	C₂³	1	2	yes	—
245	Dic₃⋊C₄	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	1	yes	characteristic
249	C₄×Dic₃	C₂³	1	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₄×Dic₃	C₂³	1	1	yes	characteristic
252	C₄×Dic₃	C₂³	1	2	yes	—
253	C₄×Dic₃	C₂³	1	2	yes	—
254	C₂×#41	—	3	1	no	—
255	C₂×#41	—	3	1	no	—
256	C₂×#41	—	3	2	no	—
257	C₂²×D₄	—	3	2	no	—
258	C₂²×D₄	—	3	1	no	—
259	C₂²×D₄	—	3	1	no	—
260	C₂³×C₄	—	3	2	no	—
261	C₂³×C₄	—	3	2	no	—
262	C₄⋊Q₈	—	3	1	no	—
263	#127	—	3	1	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#126	C₂×D₃	1	2	yes	complemented
268	#125	—	3	2	no	—
269	#125	—	3	1	no	—
270	#125	C₂×D₃	1	1	yes	characteristic, complemented
271	#124	—	3	1	no	—
272	#124	—	3	2	no	—
273	#124	—	3	2	no	—
274	#124	C₂×D₃	1	1	yes	characteristic, complemented
275	#123	—	3	2	no	—
276	#123	—	3	2	no	—
277	#123	—	3	2	no	—
278	#123	—	3	2	no	—
279	#123	—	3	2	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	C₂×D₃	1	2	yes	complemented
283	C₂²⋊Q₈	—	3	1	no	—
284	C₂²⋊Q₈	—	3	2	no	—
285	C₂²⋊Q₈	—	3	2	no	—
286	C₂²⋊Q₈	—	3	2	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	2	no	—
289	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
290	#121	—	3	2	no	—
291	#121	—	3	1	no	—
292	#121	—	3	2	no	—
293	#121	—	3	2	no	—
294	#121	—	3	1	no	—
295	#121	—	3	1	no	—
296	#121	—	3	2	no	—
297	#121	—	3	2	no	—
298	#121	—	3	2	no	—
299	#121	C₂×D₃	1	1	yes	characteristic
300	#120	—	3	2	no	—
301	#120	—	3	2	no	—
302	#120	—	3	2	no	—
303	#120	—	3	2	no	—
304	C₄×Q₈	—	3	1	no	—
305	C₄×Q₈	—	3	1	no	—
306	C₄×Q₈	—	3	1	no	—
307	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
308	C₄×D₄	—	3	2	no	—
309	C₄×D₄	—	3	1	no	—
310	C₄×D₄	—	3	1	no	—
311	C₄×D₄	—	3	2	no	—
312	C₄×D₄	—	3	2	no	—
313	C₄×D₄	—	3	1	no	—
314	C₄×D₄	—	3	1	no	—
315	C₄×D₄	—	3	1	no	—
316	C₄×D₄	—	3	1	no	—
317	C₄×D₄	—	3	2	no	—
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	2	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	1	no	—
327	C₄×D₄	—	3	1	no	—
328	C₄×D₄	—	3	2	no	—
329	C₄×D₄	—	3	1	no	—
330	C₄×D₄	—	3	2	no	—
331	C₄×D₄	—	3	1	no	—
332	C₄×D₄	—	3	1	no	—
333	C₄×D₄	C₂×D₃	1	2	yes	complemented
334	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
335	#117	—	3	1	no	—
336	#117	—	3	2	no	—
337	#117	—	3	1	no	—
338	#117	—	3	1	no	—
339	#117	—	3	1	no	—
340	#117	—	3	2	no	—
341	#117	C₂×D₃	1	2	yes	complemented
342	C₂×C₄⋊C₄	—	3	1	no	—
343	C₂×C₄⋊C₄	—	3	2	no	—
344	C₂×C₄⋊C₄	—	3	1	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₂²⋊C₄	—	3	2	no	—
347	C₂×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₄²	—	3	2	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂×C₄²	—	3	1	no	—
352	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
353	C₂³×C₃	C₂⁴	1	2	yes	—
354	C₂³×C₃	C₂⁴	1	1	yes	characteristic
355	C₂²×D₃	—	2	4	no	—
356	C₂²×D₃	—	2	4	no	—
357	C₂²×D₃	—	2	4	no	—
358	C₂²×D₃	—	2	4	no	—
359	C₂²×D₃	—	4	2	no	—
360	C₂²×D₃	—	4	2	no	—
361	C₂²×D₃	C₂⁴	1	2	yes	—
362	C₂²×D₃	C₂⁴	1	1	yes	characteristic
363	C₂²×D₃	C₂⁴	1	1	yes	characteristic
364	C₂²×D₃	C₂⁴	1	2	yes	—
365	C₃×Q₈	—	2	2	no	—
366	C₃×D₄	—	2	4	no	—
367	C₃×D₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	2	yes	—
374	C₂×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂⁴	1	2	yes	—
378	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	#67	—	2	2	no	—
382	#67	—	2	4	no	—
383	#67	—	2	4	no	—
384	#67	—	4	2	no	—
385	#67	—	4	2	no	—
386	#67	#41	1	4	yes	complemented
387	C₂×Dic₃	—	4	2	no	—
388	C₂×Dic₃	—	4	2	no	—
389	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₃	C₂⁴	1	2	yes	—
395	C₂×Dic₃	C₂⁴	1	2	yes	—
396	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
397	D₁₂	—	2	4	no	—
398	D₁₂	—	2	2	no	—
399	D₁₂	—	2	4	no	—
400	D₁₂	—	2	4	no	—
401	D₁₂	—	2	2	no	—
402	D₁₂	—	4	2	no	—
403	D₁₂	#41	1	4	yes	complemented
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	2	4	no	—
406	C₄×D₃	—	2	2	no	—
407	C₄×D₃	—	2	2	no	—
408	C₄×D₃	—	2	4	no	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	—	2	4	no	—
411	C₄×D₃	—	2	2	no	—
412	C₄×D₃	—	2	2	no	—
413	C₄×D₃	—	2	4	no	—
414	C₄×D₃	—	4	2	no	—
415	C₄×D₃	—	4	2	no	—
416	C₄×D₃	—	4	2	no	—
417	C₄×D₃	—	4	2	no	—
418	Dic₆	—	2	2	no	—
419	Dic₆	—	4	2	no	—
420	C₂⁴	—	3	2	no	—
421	C₂⁴	—	3	2	no	—
422	#41	—	6	4	no	—
423	#41	—	6	4	no	—
424	#41	—	12	4	no	—
425	C₂×Q₈	—	3	1	no	—
426	C₂×Q₈	—	3	2	no	—
427	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	—	3	1	no	—
430	C₂×D₄	—	3	2	no	—
431	C₂×D₄	—	3	2	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	3	1	no	—
435	C₂×D₄	—	3	2	no	—
436	C₂×D₄	—	3	1	no	—
437	C₂×D₄	—	3	2	no	—
438	C₂×D₄	—	3	2	no	—
439	C₂×D₄	—	3	1	no	—
440	C₂×D₄	—	3	2	no	—
441	C₂×D₄	—	6	4	no	—
442	C₂×D₄	—	6	8	no	—
443	C₂×D₄	—	6	4	no	—
444	C₂×D₄	C₂²×D₃	1	2	yes	—
445	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	3	2	no	—
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	2	no	—
451	C₂²×C₄	—	3	1	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	1	no	—
455	C₂²×C₄	—	3	2	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	2	no	—
458	C₂²×C₄	—	3	2	no	—
459	C₂²×C₄	—	3	2	no	—
460	C₂²×C₄	—	3	2	no	—
461	C₂²×C₄	—	3	2	no	—
462	C₂²×C₄	—	12	4	no	—
463	C₂²×C₄	—	12	4	no	—
464	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
465	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
466	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₃	1	2	yes	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	2	no	—
474	C₄⋊C₄	—	3	2	no	—
475	C₄⋊C₄	—	3	1	no	—
476	C₄⋊C₄	—	3	1	no	—
477	C₄⋊C₄	—	3	2	no	—
478	C₄⋊C₄	—	3	1	no	—
479	C₄⋊C₄	—	3	1	no	—
480	C₄⋊C₄	—	3	1	no	—
481	C₄⋊C₄	—	3	2	no	—
482	C₄⋊C₄	—	3	2	no	—
483	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₃	1	2	yes	—
485	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₃	1	2	yes	—
487	C₄⋊C₄	C₂²×D₃	1	2	yes	—
488	C₄⋊C₄	C₂²×D₃	1	2	yes	—
489	C₂²⋊C₄	—	3	1	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	1	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	—	3	2	no	—
498	C₂²⋊C₄	—	3	2	no	—
499	C₂²⋊C₄	—	3	2	no	—
500	C₂²⋊C₄	—	3	2	no	—
501	C₂²⋊C₄	—	3	2	no	—
502	C₂²⋊C₄	—	3	2	no	—
503	C₂²⋊C₄	—	3	1	no	—
504	C₂²⋊C₄	—	3	1	no	—
505	C₂²⋊C₄	—	3	2	no	—
506	C₂²⋊C₄	—	3	1	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₂²⋊C₄	—	3	2	no	—
509	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
511	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
513	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
514	C₄²	—	3	1	no	—
515	C₄²	—	3	2	no	—
516	C₄²	—	3	1	no	—
517	C₄²	—	3	2	no	—
518	C₄²	—	3	1	no	—
519	C₄²	—	3	1	no	—
520	C₄²	—	3	1	no	—
521	C₄²	—	3	1	no	—
522	C₄²	C₂²×D₃	1	1	yes	characteristic
523	C₄²	C₂²×D₃	1	1	yes	characteristic
524	C₄²	C₂²×D₃	1	1	yes	characteristic
525	C₄²	C₂²×D₃	1	2	yes	—
526	C₄²	C₂²×D₃	1	1	yes	characteristic
527	C₂²×C₃	—	2	1	no	—
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	2	2	no	—
531	C₂²×C₃	—	2	2	no	—
532	C₂²×C₃	C₂×#41	1	2	yes	—
533	C₂²×C₃	C₂⁵	1	1	yes	characteristic
534	C₂×D₃	—	2	1	no	—
535	C₂×D₃	—	2	2	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	2	no	—
538	C₂×D₃	—	2	1	no	—
539	C₂×D₃	—	2	1	no	—
540	C₂×D₃	—	2	2	no	—
541	C₂×D₃	—	2	2	no	—
542	C₂×D₃	—	2	2	no	—
543	C₂×D₃	—	2	1	no	—
544	C₂×D₃	—	4	8	no	—
545	C₂×D₃	—	4	8	no	—
546	C₂×D₃	C₂×#41	1	2	yes	—
547	C₂×D₃	C₂×#41	1	4	yes	—
548	C₃×C₄	—	2	1	no	—
549	C₃×C₄	—	2	1	no	—
550	C₃×C₄	—	2	2	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	1	no	—
553	C₃×C₄	—	2	2	no	—
554	C₃×C₄	—	2	1	no	—
555	C₃×C₄	C₂×#41	1	2	yes	—
556	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
557	Dic₃	—	2	1	no	—
558	Dic₃	—	2	1	no	—
559	Dic₃	—	2	1	no	—
560	Dic₃	—	2	1	no	—
561	Dic₃	—	2	2	no	—
562	Dic₃	—	2	2	no	—
563	Dic₃	—	2	1	no	—
564	Dic₃	C₂×#41	1	2	yes	—
565	C₂³	—	3	1	no	—
566	C₂³	—	3	2	no	—
567	C₂³	—	3	2	no	—
568	C₂³	—	3	1	no	—
569	C₂³	—	6	4	no	—
570	C₂³	—	6	4	no	—
571	C₂³	—	6	4	no	—
572	C₂³	—	6	4	no	—
573	C₂³	—	12	2	no	—
574	C₂³	—	12	2	no	—
575	C₂³	C₂³×D₃	1	2	yes	—
576	C₂³	C₂³×D₃	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	6	2	no	—
579	Q₈	—	12	2	no	—
580	D₄	—	2	4	no	—
581	D₄	—	2	2	no	—
582	D₄	—	3	4	no	—
583	D₄	—	3	4	no	—
584	D₄	—	6	4	no	—
585	D₄	—	6	4	no	—
586	D₄	—	6	2	no	—
587	D₄	—	6	4	no	—
588	D₄	—	6	4	no	—
589	D₄	—	6	4	no	—
590	D₄	—	6	2	no	—
591	D₄	—	6	2	no	—
592	D₄	—	12	2	no	—
593	D₄	—	12	2	no	—
594	D₄	—	12	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	3	1	no	—
600	C₂×C₄	—	3	1	no	—
601	C₂×C₄	—	3	1	no	—
602	C₂×C₄	—	3	1	no	—
603	C₂×C₄	—	3	1	no	—
604	C₂×C₄	—	3	2	no	—
605	C₂×C₄	—	3	1	no	—
606	C₂×C₄	—	3	2	no	—
607	C₂×C₄	—	6	4	no	—
608	C₂×C₄	—	6	2	no	—
609	C₂×C₄	—	6	2	no	—
610	C₂×C₄	—	6	4	no	—
611	C₂×C₄	—	6	2	no	—
612	C₂×C₄	—	6	2	no	—
613	C₂×C₄	—	6	2	no	—
614	C₂×C₄	—	6	4	no	—
615	C₂×C₄	—	6	4	no	—
616	C₂×C₄	—	6	2	no	—
617	C₂×C₄	—	12	2	no	—
618	C₂×C₄	—	12	2	no	—
619	C₂×C₄	—	12	2	no	—
620	C₂×C₄	—	12	2	no	—
621	C₂×C₄	—	12	2	no	—
622	C₂×C₄	—	12	2	no	—
623	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₃	1	2	yes	—
625	C₂×C₄	C₂³×D₃	1	2	yes	—
626	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₃	1	2	yes	—
630	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
632	C₂×C₃	—	2	2	no	—
633	C₂×C₃	—	4	2	no	—
634	C₂×C₃	C₂²×#41	1	1	yes	characteristic
635	C₂×C₃	C₂²×#41	1	1	yes	characteristic
636	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
637	D₃	—	2	2	no	—
638	D₃	—	2	4	no	—
639	D₃	—	4	1	no	—
640	D₃	—	4	2	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	3	2	no	—
647	C₂²	—	3	4	no	—
648	C₂²	—	6	2	no	—
649	C₂²	—	6	1	no	—
650	C₂²	—	6	2	no	—
651	C₂²	—	6	1	no	—
652	C₂²	—	6	1	no	—
653	C₂²	—	6	1	no	—
654	C₂²	—	6	2	no	—
655	C₂²	—	6	2	no	—
656	C₂²	—	6	2	no	—
657	C₂²	—	6	1	no	—
658	C₂²	—	12	8	no	—
659	C₂²	—	12	8	no	—
660	C₂²	D₃×#41	1	2	yes	—
661	C₂²	C₂⁴×D₃	1	1	yes	characteristic
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	3	2	no	—
670	C₄	—	6	1	no	—
671	C₄	—	6	1	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	1	no	—
674	C₄	—	6	2	no	—
675	C₄	—	6	2	no	—
676	C₄	—	6	1	no	—
677	C₄	D₃×#41	1	2	yes	—
678	C₄	#1009	1	2	yes	—
679	C₃	#3481	1	1	yes	characteristic, complemented, Sylow
680	C₂	—	2	2	no	—
681	C₂	—	4	2	no	—
682	C₂	—	6	4	no	—
683	C₂	—	6	2	no	—
684	C₂	—	12	2	no	—
685	C₂	—	12	1	no	—
686	C₂	C₂×D₃×#41	1	1	yes	characteristic
687	C₂	C₂×D₃×#41	1	1	yes	characteristic
688	C₂	C₂×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Frattini	C₂²	C₂⁴×D₃
Fitting	C₃×#529	C₂
hypercenter	#529	D₃
hypocenter	C₃	#3481
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₃×#529	C₂	semidirect
2. #5709	C₂	semidirect
3. #5705	C₂	semidirect
4. #5695	C₂	semidirect
5. #5690	C₂	semidirect
6. #5681	C₂	semidirect
7. #5676	C₂	semidirect
8. #5658	C₂	semidirect
9. #5654	C₂	semidirect
10. #5635	C₂	semidirect
11. #5630	C₂	semidirect
12. #5618	C₂	semidirect
13. #5609	C₂	semidirect
14. #5580	C₂	semidirect
15. C₄×#239	C₂	semidirect
16. #5548	C₂	semidirect
17. #5547	C₂	semidirect
18. C₄×D₃×D₄	C₂	semidirect
19. C₄×D₃×D₄	C₂	semidirect
20. #5528	C₂	semidirect
21. #5524	C₂	semidirect
22. C₄×#235	C₂	semidirect
23. C₂×C₄×D₁₂	C₂	semidirect
29. C₂×#235	C₂²	semidirect
31. C₂²×C₄×D₃	C₂²	semidirect
32. C₂²×C₄×D₃	C₂²	semidirect
33. C₃×#126	C₂²	semidirect
34. C₃×#125	C₂²	semidirect
35. C₃×#124	C₂²	semidirect
36. C₃×#123	C₂²	semidirect
37. C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₃×C₄×Q₈	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×C₄×D₄	C₂²	semidirect
42. C₃×#117	C₂²	semidirect
43. C₂×C₃×C₄²	C₂²	semidirect
44. #947	C₂²	semidirect
45. #946	C₂²	semidirect
46. Q₈×Dic₃	C₂²	semidirect
48. #939	C₂²	semidirect
49. #938	C₂²	semidirect
51. D₄×Dic₃	C₂²	semidirect
52. D₄×Dic₃	C₂²	semidirect
55. C₄×#67	C₂²	semidirect
56. C₄×#67	C₂²	semidirect
57. C₄×#67	C₂²	semidirect
58. C₄×#67	C₂²	semidirect
59. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
60. #926	C₂²	semidirect
61. C₂×C₄⋊Dic₃	C₂²	semidirect
62. #898	C₂²	semidirect
63. #898	C₂²	semidirect
64. #897	C₂²	semidirect
65. #897	C₂²	semidirect
66. #896	C₂²	semidirect
67. #896	C₂²	semidirect
69. #895	C₂²	semidirect
70. #895	C₂²	semidirect
71. #895	C₂²	semidirect
72. #894	C₂²	semidirect
73. #894	C₂²	semidirect
74. #894	C₂²	semidirect
77. #893	C₂²	semidirect
78. #893	C₂²	semidirect
79. #892	C₂²	semidirect
80. #892	C₂²	semidirect
81. D₃×C₄⋊C₄	C₂²	semidirect
82. D₃×C₄⋊C₄	C₂²	semidirect
83. #890	C₂²	semidirect
84. #889	C₂²	semidirect
85. #888	C₂²	semidirect
86. #886	C₂²	semidirect
87. #886	C₂²	semidirect
88. #885	C₂²	semidirect
89. #885	C₂²	semidirect
91. #884	C₂²	semidirect
92. #884	C₂²	semidirect
93. #883	C₂²	semidirect
94. #883	C₂²	semidirect
96. #882	C₂²	semidirect
97. #882	C₂²	semidirect
99. #67⋊C₄	C₂²	semidirect
100. #67⋊C₄	C₂²	semidirect
101. D₃×C₂²⋊C₄	C₂²	semidirect
102. D₃×C₂²⋊C₄	C₂²	semidirect
103. D₃×C₂²⋊C₄	C₂²	semidirect
104. #879	C₂²	semidirect
105. #878	C₂²	semidirect
108. C₄×D₁₂	C₂²	semidirect
109. C₄×D₁₂	C₂²	semidirect
110. C₄×D₁₂	C₂²	semidirect
111. C₄×D₁₂	C₂²	semidirect
112. C₄×D₁₂	C₂²	semidirect
113. C₄×D₁₂	C₂²	semidirect
114. C₄×D₁₂	C₂²	semidirect
115. C₄×D₁₂	C₂²	semidirect
116. #872	C₂²	semidirect
117. #872	C₂²	semidirect
118. #872	C₂²	semidirect
119. C₄²×D₃	C₂²	semidirect
120. C₄²×D₃	C₂²	semidirect
121. C₄²×D₃	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
139. #529	D₃	semidirect
267. #126	C₂×D₃	semidirect
270. #125	C₂×D₃	semidirect
274. #124	C₂×D₃	semidirect
282. #123	C₂×D₃	semidirect
289. C₂²⋊Q₈	C₂×D₃	semidirect
307. C₄×Q₈	C₂×D₃	semidirect
333. C₄×D₄	C₂×D₃	semidirect
334. C₄×D₄	C₂×D₃	semidirect
341. #117	C₂×D₃	semidirect
352. C₂×C₄²	C₂×D₃	semidirect
386. #67	#41	semidirect
403. D₁₂	#41	semidirect
679. C₃	#3481	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
#5709	2
#5705	2
#5695	2
#5690	2
#5681	2
#5676	2
#5658	2
#5654	2
#5635	2
#5630	2
#5618	2
#5609	2
#5580	2
C₄×#239	2
#5548	2
#5547	2
C₄×D₃×D₄	2
#5528	2
#5524	2
C₄×#235	2
C₂×C₄×D₁₂	2
#3481	3