Subgroups — #86151

Order 384.

1132 conjugacy classes of subgroups.

The subgroup lattice has 658 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	#5708	C₂	1	2	yes	maximal, complemented
3	#5705	C₂	1	2	yes	maximal, complemented
4	#5694	C₂	1	1	yes	maximal, characteristic, complemented
5	#5690	C₂	1	1	yes	maximal, characteristic, complemented
6	#5676	C₂	1	1	yes	maximal, characteristic, complemented
7	#5671	C₂	1	1	yes	maximal, characteristic, complemented
8	#5661	C₂	1	2	yes	maximal, complemented
9	#5659	C₂	1	2	yes	maximal, complemented
10	#5639	C₂	1	1	yes	maximal, characteristic, complemented
11	#5631	C₂	1	1	yes	maximal, characteristic, complemented
12	#5616	C₂	1	1	yes	maximal, characteristic, complemented
13	#5612	C₂	1	1	yes	maximal, characteristic, complemented
14	#5578	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#239	C₂	1	1	yes	maximal, characteristic, complemented
16	#5557	C₂	1	2	yes	maximal, complemented
17	#5557	C₂	1	1	yes	maximal, characteristic, complemented
18	#5547	C₂	1	2	yes	maximal, complemented
19	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
20	#5528	C₂	1	2	yes	maximal, complemented
21	D₃×#117	C₂	1	2	yes	maximal, complemented
22	C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
24	#3475	—	3	1	no	maximal, Sylow
25	C₂×#239	C₂²	1	1	yes	characteristic
26	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×#235	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₃	C₂²	1	2	yes	—
30	C₃×#126	C₂²	1	2	yes	complemented
31	C₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₃×#124	C₂²	1	1	yes	characteristic
33	C₃×#123	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×C₄×D₄	C₂²	1	2	yes	complemented
39	C₃×#117	C₂²	1	2	yes	complemented
40	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
41	#946	C₂²	1	1	yes	characteristic
42	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
43	#944	C₂²	1	1	yes	characteristic, complemented
44	#939	C₂²	1	2	yes	complemented
45	#938	C₂²	1	2	yes	—
46	#938	C₂²	1	1	yes	characteristic
47	#937	C₂²	1	2	yes	—
48	#936	C₂²	1	1	yes	characteristic
49	#936	C₂²	1	2	yes	complemented
50	D₄×Dic₃	C₂²	1	1	yes	characteristic
51	C₄×#67	C₂²	1	1	yes	characteristic
52	C₄×#67	C₂²	1	1	yes	characteristic
53	C₄×#67	C₂²	1	2	yes	—
54	C₄×#67	C₂²	1	2	yes	complemented
55	C₄×#67	C₂²	1	1	yes	characteristic, complemented
56	C₄×#67	C₂²	1	2	yes	complemented
57	C₄×#67	C₂²	1	1	yes	characteristic, complemented
58	C₄×#67	C₂²	1	2	yes	complemented
59	#926	C₂²	1	1	yes	characteristic, complemented
60	#926	C₂²	1	1	yes	characteristic, complemented
61	#926	C₂²	1	2	yes	complemented
62	#898	C₂²	1	2	yes	complemented
63	#897	C₂²	1	1	yes	characteristic
64	#897	C₂²	1	2	yes	complemented
65	#897	C₂²	1	1	yes	characteristic, complemented
66	#896	C₂²	1	2	yes	—
67	#896	C₂²	1	2	yes	complemented
68	#896	C₂²	1	2	yes	complemented
69	#894	C₂²	1	2	yes	—
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	2	yes	complemented
74	#892	C₂²	1	2	yes	—
75	#892	C₂²	1	2	yes	—
76	#892	C₂²	1	2	yes	complemented
77	#892	C₂²	1	1	yes	characteristic, complemented
78	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
80	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
81	#890	C₂²	1	1	yes	characteristic, complemented
82	#890	C₂²	1	2	yes	complemented
83	#889	C₂²	1	2	yes	complemented
84	#889	C₂²	1	2	yes	complemented
85	#888	C₂²	1	1	yes	characteristic, complemented
86	#885	C₂²	1	2	yes	complemented
87	#884	C₂²	1	2	yes	—
88	#884	C₂²	1	2	yes	complemented
89	#883	C₂²	1	2	yes	—
90	#883	C₂²	1	2	yes	—
91	#883	C₂²	1	2	yes	—
92	#883	C₂²	1	2	yes	complemented
93	#883	C₂²	1	2	yes	complemented
94	#882	C₂²	1	2	yes	—
95	#67⋊C₄	C₂²	1	2	yes	—
96	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
97	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	#879	C₂²	1	2	yes	complemented
100	#879	C₂²	1	2	yes	complemented
101	#879	C₂²	1	2	yes	complemented
102	#879	C₂²	1	2	yes	complemented
103	#878	C₂²	1	2	yes	complemented
104	#877	C₂²	1	2	yes	complemented
105	#877	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
109	C₄×D₁₂	C₂²	1	1	yes	characteristic
110	C₄×D₁₂	C₂²	1	2	yes	complemented
111	#872	C₂²	1	1	yes	characteristic
112	#872	C₂²	1	2	yes	—
113	#872	C₂²	1	2	yes	complemented
114	#872	C₂²	1	1	yes	characteristic, complemented
115	C₄²×D₃	C₂²	1	1	yes	characteristic
116	C₄²×D₃	C₂²	1	2	yes	complemented
117	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	2	yes	complemented
124	#556	—	3	1	no	—
125	#555	—	3	1	no	—
126	#554	—	3	1	no	—
127	#553	—	3	2	no	—
128	#552	—	3	2	no	—
129	#552	—	3	1	no	—
130	#552	—	3	1	no	—
131	#551	—	3	2	no	—
132	#551	—	3	2	no	—
133	#547	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#533	—	3	1	no	—
137	#529	—	3	1	no	—
138	#529	—	3	2	no	—
139	#529	—	3	2	no	—
140	#529	D₃	1	1	yes	characteristic, complemented
141	#525	—	3	2	no	—
142	C₄×#41	—	3	1	no	—
143	C₄×#41	—	3	1	no	—
144	C₄×#41	—	3	1	no	—
145	C₂×C₄×D₄	—	3	1	no	—
146	C₂×#117	—	3	2	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	2	yes	—
151	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	2	yes	—
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	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	1	yes	characteristic
159	C₂×#67	C₂³	1	2	yes	—
160	C₂²×Dic₃	C₂³	1	2	yes	—
161	#239	—	2	4	no	—
162	D₃×D₄	—	2	4	no	—
163	#235	—	2	4	no	—
164	#235	—	2	4	no	—
165	C₂×D₁₂	C₂³	1	1	yes	characteristic
166	C₂×D₁₂	C₂³	1	2	yes	—
167	C₂×D₁₂	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₃	—	2	8	no	—
169	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₃	C₂³	1	2	yes	—
171	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₃	C₂³	1	2	yes	—
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	2	yes	—
177	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×D₃	C₂³	1	2	yes	—
179	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂³	1	2	yes	—
181	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×Dic₆	C₂³	1	1	yes	characteristic
183	C₂×Dic₆	C₂³	1	1	yes	characteristic
184	C₂×Dic₆	C₂³	1	2	yes	—
185	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₄²	C₂³	1	1	yes	characteristic
197	C₃×C₄²	C₂³	1	1	yes	characteristic
198	C₃×C₄²	C₂³	1	2	yes	—
199	C₃×C₄²	C₂³	1	1	yes	characteristic
200	C₃×C₄²	C₂³	1	1	yes	characteristic
201	#217	C₂³	1	2	yes	—
202	#217	C₂³	1	2	yes	—
203	#217	C₂³	1	2	yes	—
204	#217	C₂³	1	2	yes	—
205	#217	C₂³	1	1	yes	characteristic
206	#217	C₂³	1	2	yes	—
207	#217	C₂³	1	1	yes	characteristic
208	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
209	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
215	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₃	C₂³	1	2	yes	—
225	C₄⋊Dic₃	C₂³	1	2	yes	—
226	C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₄⋊Dic₃	C₂³	1	2	yes	—
228	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	2	yes	—
238	Dic₃⋊C₄	C₂³	1	2	yes	—
239	Dic₃⋊C₄	C₂³	1	2	yes	—
240	C₄×Dic₃	C₂³	1	1	yes	characteristic
241	C₄×Dic₃	C₂³	1	2	yes	—
242	C₄×Dic₃	C₂³	1	1	yes	characteristic
243	C₄×Dic₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₄×Dic₃	C₂³	1	2	yes	—
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₂×#41	—	3	1	no	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	1	no	—
254	C₂²×D₄	—	3	1	no	—
255	C₂³×C₄	—	3	2	no	—
256	C₄⋊Q₈	—	3	1	no	—
257	C₄⋊Q₈	—	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	C₂×D₃	1	2	yes	complemented
264	#125	—	3	2	no	—
265	#125	—	3	2	no	—
266	#125	—	3	1	no	—
267	#125	—	3	2	no	—
268	#125	C₂×D₃	1	1	yes	characteristic, complemented
269	#124	—	3	1	no	—
270	#124	—	3	2	no	—
271	#124	—	3	2	no	—
272	#124	C₂×D₃	1	1	yes	characteristic
273	#123	—	3	2	no	—
274	#123	—	3	2	no	—
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	C₂×D₃	1	2	yes	complemented
281	C₂²⋊Q₈	—	3	1	no	—
282	C₂²⋊Q₈	—	3	2	no	—
283	C₂²⋊Q₈	—	3	1	no	—
284	C₂²⋊Q₈	—	3	2	no	—
285	C₂²⋊Q₈	—	3	2	no	—
286	C₂²⋊Q₈	—	3	1	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	2	no	—
292	#121	—	3	1	no	—
293	#121	—	3	2	no	—
294	#121	—	3	2	no	—
295	#121	C₂×D₃	1	1	yes	characteristic
296	#120	—	3	2	no	—
297	#120	—	3	2	no	—
298	C₄×Q₈	—	3	1	no	—
299	C₄×Q₈	—	3	1	no	—
300	C₄×Q₈	—	3	1	no	—
301	C₄×Q₈	—	3	1	no	—
302	C₄×Q₈	—	3	1	no	—
303	C₄×Q₈	—	3	2	no	—
304	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
305	C₄×D₄	—	3	1	no	—
306	C₄×D₄	—	3	2	no	—
307	C₄×D₄	—	3	2	no	—
308	C₄×D₄	—	3	1	no	—
309	C₄×D₄	—	3	1	no	—
310	C₄×D₄	—	3	1	no	—
311	C₄×D₄	—	3	2	no	—
312	C₄×D₄	—	3	1	no	—
313	C₄×D₄	—	3	2	no	—
314	C₄×D₄	—	3	1	no	—
315	C₄×D₄	—	3	1	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	—	3	1	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	—	3	1	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	C₂×D₃	1	1	yes	characteristic
324	C₄×D₄	C₂×D₃	1	2	yes	complemented
325	#117	—	3	2	no	—
326	#117	—	3	1	no	—
327	#117	—	3	1	no	—
328	#117	—	3	2	no	—
329	#117	—	3	2	no	—
330	#117	—	3	2	no	—
331	#117	—	3	1	no	—
332	#117	—	3	2	no	—
333	#117	—	3	2	no	—
334	#117	—	3	1	no	—
335	#117	—	3	2	no	—
336	#117	—	3	1	no	—
337	#117	—	3	2	no	—
338	#117	C₂×D₃	1	2	yes	complemented
339	C₂×C₄⋊C₄	—	3	2	no	—
340	C₂×C₄⋊C₄	—	3	2	no	—
341	C₂×C₄⋊C₄	—	3	1	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	2	no	—
346	C₂×C₄²	—	3	2	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂×C₄²	—	3	1	no	—
349	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
350	C₂³×C₃	C₂⁴	1	2	yes	—
351	C₂³×C₃	C₂⁴	1	1	yes	characteristic
352	C₂²×D₃	—	2	4	no	—
353	C₂²×D₃	—	2	4	no	—
354	C₂²×D₃	—	4	2	no	—
355	C₂²×D₃	C₂⁴	1	1	yes	characteristic
356	C₂²×D₃	C₂⁴	1	1	yes	characteristic
357	C₂²×D₃	C₂⁴	1	2	yes	—
358	C₃×Q₈	—	2	2	no	—
359	C₃×D₄	—	2	2	no	—
360	C₃×D₄	—	4	2	no	—
361	C₂×C₃×C₄	—	2	4	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	4	1	no	—
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	2	yes	—
369	C₂×C₃×C₄	C₂⁴	1	2	yes	—
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴	1	2	yes	—
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	#67	—	2	2	no	—
375	#67	—	2	4	no	—
376	#67	—	2	4	no	—
377	#67	—	2	2	no	—
378	#67	—	4	2	no	—
379	C₂×Dic₃	—	2	4	no	—
380	C₂×Dic₃	C₂⁴	1	2	yes	—
381	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₃	C₂⁴	1	2	yes	—
385	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₃	C₂⁴	1	2	yes	—
387	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
389	D₁₂	—	2	2	no	—
390	D₁₂	—	2	4	no	—
391	D₁₂	#41	1	4	yes	complemented
392	C₄×D₃	—	2	4	no	—
393	C₄×D₃	—	2	4	no	—
394	C₄×D₃	—	2	4	no	—
395	C₄×D₃	—	2	4	no	—
396	C₄×D₃	—	2	2	no	—
397	C₄×D₃	—	2	2	no	—
398	C₄×D₃	—	2	2	no	—
399	C₄×D₃	—	2	4	no	—
400	C₄×D₃	—	4	1	no	—
401	C₄×D₃	—	4	2	no	—
402	C₄×D₃	—	4	2	no	—
403	C₄×D₃	—	4	1	no	—
404	C₄×D₃	#41	1	4	yes	complemented
405	Dic₆	—	2	2	no	—
406	Dic₆	—	2	2	no	—
407	Dic₆	—	4	2	no	—
408	C₂⁴	—	3	2	no	—
409	#41	—	6	4	no	—
410	#41	—	6	4	no	—
411	#41	—	6	4	no	—
412	C₂×Q₈	—	3	1	no	—
413	C₂×Q₈	—	3	1	no	—
414	C₂×Q₈	—	3	2	no	—
415	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
416	C₂×D₄	—	3	1	no	—
417	C₂×D₄	—	3	2	no	—
418	C₂×D₄	—	3	1	no	—
419	C₂×D₄	—	3	2	no	—
420	C₂×D₄	—	3	2	no	—
421	C₂×D₄	—	3	1	no	—
422	C₂×D₄	—	3	1	no	—
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	6	4	no	—
425	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
426	C₂×D₄	C₂²×D₃	1	2	yes	—
427	C₂²×C₄	—	3	1	no	—
428	C₂²×C₄	—	3	2	no	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	—	3	2	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	—	3	2	no	—
436	C₂²×C₄	—	3	1	no	—
437	C₂²×C₄	—	3	1	no	—
438	C₂²×C₄	—	3	2	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	6	8	no	—
442	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
443	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
444	C₂²×C₄	C₂²×D₃	1	2	yes	—
445	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
446	C₄⋊C₄	—	3	1	no	—
447	C₄⋊C₄	—	3	1	no	—
448	C₄⋊C₄	—	3	1	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	1	no	—
455	C₄⋊C₄	—	3	1	no	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	2	no	—
459	C₄⋊C₄	—	3	2	no	—
460	C₄⋊C₄	—	3	1	no	—
461	C₄⋊C₄	—	3	1	no	—
462	C₄⋊C₄	—	3	2	no	—
463	C₄⋊C₄	—	3	2	no	—
464	C₄⋊C₄	—	3	2	no	—
465	C₄⋊C₄	—	3	2	no	—
466	C₄⋊C₄	C₂²×D₃	1	2	yes	—
467	C₄⋊C₄	C₂²×D₃	1	2	yes	—
468	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
470	C₄⋊C₄	C₂²×D₃	1	2	yes	—
471	C₄⋊C₄	C₂²×D₃	1	2	yes	—
472	C₂²⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	—	3	2	no	—
474	C₂²⋊C₄	—	3	2	no	—
475	C₂²⋊C₄	—	3	1	no	—
476	C₂²⋊C₄	—	3	2	no	—
477	C₂²⋊C₄	—	3	1	no	—
478	C₂²⋊C₄	—	3	2	no	—
479	C₂²⋊C₄	—	3	1	no	—
480	C₂²⋊C₄	—	3	1	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	2	no	—
483	C₂²⋊C₄	—	3	2	no	—
484	C₂²⋊C₄	—	3	2	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	1	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	1	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
494	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
495	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
496	C₄²	—	3	2	no	—
497	C₄²	—	3	2	no	—
498	C₄²	—	3	2	no	—
499	C₄²	—	3	2	no	—
500	C₄²	—	3	1	no	—
501	C₄²	—	3	1	no	—
502	C₄²	—	3	1	no	—
503	C₄²	—	3	1	no	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	2	no	—
507	C₄²	C₂²×D₃	1	1	yes	characteristic
508	C₄²	C₂²×D₃	1	1	yes	characteristic
509	C₄²	C₂²×D₃	1	1	yes	characteristic
510	C₄²	C₂²×D₃	1	1	yes	characteristic
511	C₄²	C₂²×D₃	1	2	yes	—
512	C₂²×C₃	—	2	2	no	—
513	C₂²×C₃	—	2	1	no	—
514	C₂²×C₃	—	2	1	no	—
515	C₂²×C₃	—	2	2	no	—
516	C₂²×C₃	—	2	2	no	—
517	C₂²×C₃	—	2	1	no	—
518	C₂²×C₃	C₂⁵	1	1	yes	characteristic
519	C₂×D₃	—	2	2	no	—
520	C₂×D₃	—	2	1	no	—
521	C₂×D₃	—	2	2	no	—
522	C₂×D₃	—	2	1	no	—
523	C₂×D₃	—	2	1	no	—
524	C₂×D₃	—	2	1	no	—
525	C₂×D₃	—	2	1	no	—
526	C₂×D₃	—	4	8	no	—
527	C₂×D₃	C₂×#41	1	2	yes	—
528	C₂×D₃	C₂×#41	1	4	yes	—
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	2	2	no	—
532	C₃×C₄	—	2	2	no	—
533	C₃×C₄	—	2	2	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	1	no	—
536	C₃×C₄	C₂×#41	1	2	yes	—
537	C₃×C₄	C₂×#41	1	2	yes	—
538	Dic₃	—	2	2	no	—
539	Dic₃	—	2	1	no	—
540	Dic₃	—	2	1	no	—
541	Dic₃	—	2	2	no	—
542	Dic₃	—	2	1	no	—
543	Dic₃	—	2	1	no	—
544	Dic₃	—	2	2	no	—
545	Dic₃	—	2	1	no	—
546	Dic₃	C₂×#41	1	2	yes	—
547	C₂³	—	3	1	no	—
548	C₂³	—	3	2	no	—
549	C₂³	—	3	1	no	—
550	C₂³	—	6	4	no	—
551	C₂³	—	6	4	no	—
552	C₂³	—	12	2	no	—
553	C₂³	C₂³×D₃	1	2	yes	—
554	C₂³	C₂³×D₃	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	6	2	no	—
557	Q₈	—	6	2	no	—
558	Q₈	—	12	2	no	—
559	D₄	—	2	2	no	—
560	D₄	—	3	4	no	—
561	D₄	—	4	2	no	—
562	D₄	—	6	2	no	—
563	D₄	—	6	4	no	—
564	D₄	—	6	2	no	—
565	D₄	—	6	4	no	—
566	D₄	—	6	2	no	—
567	D₄	—	6	4	no	—
568	D₄	—	12	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	3	1	no	—
573	C₂×C₄	—	3	4	no	—
574	C₂×C₄	—	3	2	no	—
575	C₂×C₄	—	3	1	no	—
576	C₂×C₄	—	3	1	no	—
577	C₂×C₄	—	3	1	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	2	no	—
580	C₂×C₄	—	3	2	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	6	4	no	—
584	C₂×C₄	—	6	4	no	—
585	C₂×C₄	—	6	4	no	—
586	C₂×C₄	—	6	4	no	—
587	C₂×C₄	—	6	4	no	—
588	C₂×C₄	—	6	4	no	—
589	C₂×C₄	—	6	2	no	—
590	C₂×C₄	—	6	2	no	—
591	C₂×C₄	—	6	2	no	—
592	C₂×C₄	—	12	1	no	—
593	C₂×C₄	—	12	2	no	—
594	C₂×C₄	—	12	1	no	—
595	C₂×C₄	—	12	2	no	—
596	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₃	1	2	yes	—
600	C₂×C₄	C₂³×D₃	1	2	yes	—
601	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
602	C₂×C₄	C₂³×D₃	1	2	yes	—
603	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
605	C₂×C₃	—	4	2	no	—
606	C₂×C₃	—	4	1	no	—
607	C₂×C₃	C₂²×#41	1	1	yes	characteristic
608	C₂×C₃	C₂²×#41	1	1	yes	characteristic
609	C₂×C₃	#585	1	1	yes	characteristic
610	D₃	—	2	2	no	—
611	D₃	—	2	4	no	—
612	D₃	—	4	1	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	3	2	no	—
620	C₂²	—	3	4	no	—
621	C₂²	—	6	2	no	—
622	C₂²	—	6	1	no	—
623	C₂²	—	6	2	no	—
624	C₂²	—	6	1	no	—
625	C₂²	—	6	1	no	—
626	C₂²	—	6	1	no	—
627	C₂²	—	6	1	no	—
628	C₂²	—	12	8	no	—
629	C₂²	C₂⁴×D₃	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	3	2	no	—
638	C₄	—	6	2	no	—
639	C₄	—	6	1	no	—
640	C₄	—	6	1	no	—
641	C₄	—	6	1	no	—
642	C₄	—	6	2	no	—
643	C₄	—	6	1	no	—
644	C₄	—	6	2	no	—
645	C₄	—	6	1	no	—
646	C₄	D₃×#41	1	2	yes	—
647	C₄	D₃×#41	1	2	yes	—
648	C₃	#3475	1	1	yes	characteristic, complemented, Sylow
649	C₂	—	4	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	6	2	no	—
652	C₂	—	6	4	no	—
653	C₂	—	12	1	no	—
654	C₂	C₂×D₃×#41	1	1	yes	characteristic
655	C₂	C₂×D₃×#41	1	1	yes	characteristic
656	C₂	#5964	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	#3475
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. #5708	C₂	semidirect
3. #5705	C₂	semidirect
4. #5694	C₂	semidirect
5. #5690	C₂	semidirect
6. #5676	C₂	semidirect
7. #5671	C₂	semidirect
8. #5661	C₂	semidirect
9. #5659	C₂	semidirect
10. #5639	C₂	semidirect
11. #5631	C₂	semidirect
12. #5616	C₂	semidirect
13. #5612	C₂	semidirect
14. #5578	C₂	semidirect
15. C₄×#239	C₂	semidirect
16. #5557	C₂	semidirect
17. #5557	C₂	semidirect
18. #5547	C₂	semidirect
19. C₄×D₃×D₄	C₂	semidirect
20. #5528	C₂	semidirect
21. D₃×#117	C₂	semidirect
22. C₄×#235	C₂	semidirect
23. C₄×#235	C₂	semidirect
30. C₃×#126	C₂²	semidirect
31. C₃×#125	C₂²	semidirect
33. C₃×#123	C₂²	semidirect
34. C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×Q₈	C₂²	semidirect
38. C₃×C₄×D₄	C₂²	semidirect
39. C₃×#117	C₂²	semidirect
40. C₂×C₃×C₄²	C₂²	semidirect
42. Q₈×Dic₃	C₂²	semidirect
43. #944	C₂²	semidirect
44. #939	C₂²	semidirect
49. #936	C₂²	semidirect
54. C₄×#67	C₂²	semidirect
55. C₄×#67	C₂²	semidirect
56. C₄×#67	C₂²	semidirect
57. C₄×#67	C₂²	semidirect
58. C₄×#67	C₂²	semidirect
59. #926	C₂²	semidirect
60. #926	C₂²	semidirect
61. #926	C₂²	semidirect
62. #898	C₂²	semidirect
64. #897	C₂²	semidirect
65. #897	C₂²	semidirect
67. #896	C₂²	semidirect
68. #896	C₂²	semidirect
70. #894	C₂²	semidirect
73. #893	C₂²	semidirect
76. #892	C₂²	semidirect
77. #892	C₂²	semidirect
79. D₃×C₄⋊C₄	C₂²	semidirect
80. D₃×C₄⋊C₄	C₂²	semidirect
81. #890	C₂²	semidirect
82. #890	C₂²	semidirect
83. #889	C₂²	semidirect
84. #889	C₂²	semidirect
85. #888	C₂²	semidirect
86. #885	C₂²	semidirect
88. #884	C₂²	semidirect
92. #883	C₂²	semidirect
93. #883	C₂²	semidirect
99. #879	C₂²	semidirect
100. #879	C₂²	semidirect
101. #879	C₂²	semidirect
102. #879	C₂²	semidirect
103. #878	C₂²	semidirect
104. #877	C₂²	semidirect
105. #877	C₂²	semidirect
110. C₄×D₁₂	C₂²	semidirect
113. #872	C₂²	semidirect
114. #872	C₂²	semidirect
116. C₄²×D₃	C₂²	semidirect
117. C₄²×D₃	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
140. #529	D₃	semidirect
263. #126	C₂×D₃	semidirect
268. #125	C₂×D₃	semidirect
280. #123	C₂×D₃	semidirect
289. C₂²⋊Q₈	C₂×D₃	semidirect
304. C₄×Q₈	C₂×D₃	semidirect
324. C₄×D₄	C₂×D₃	semidirect
338. #117	C₂×D₃	semidirect
349. C₂×C₄²	C₂×D₃	semidirect
391. D₁₂	#41	semidirect
404. C₄×D₃	#41	semidirect
648. C₃	#3475	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
#5708	2
#5705	2
#5694	2
#5690	2
#5676	2
#5671	2
#5661	2
#5659	2
#5639	2
#5631	2
#5616	2
#5612	2
#5578	2
C₄×#239	2
#5557	2
#5547	2
C₄×D₃×D₄	2
#5528	2
D₃×#117	2
C₄×#235	2
#3475	3