Subgroups — #86556

Order 384.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 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	#5730	C₂	1	1	yes	maximal, characteristic, complemented
3	#5727	C₂	1	1	yes	maximal, characteristic, complemented
4	#5708	C₂	1	2	yes	maximal, complemented
5	#5705	C₂	1	2	yes	maximal, complemented
6	#5679	C₂	1	2	yes	maximal, complemented
7	#5677	C₂	1	2	yes	maximal, complemented
8	#5676	C₂	1	1	yes	maximal, characteristic, complemented
9	#5671	C₂	1	1	yes	maximal, characteristic, complemented
10	#5660	C₂	1	2	yes	maximal, complemented
11	#5656	C₂	1	2	yes	maximal, complemented
12	#5638	C₂	1	2	yes	maximal, complemented
13	#5635	C₂	1	1	yes	maximal, characteristic, complemented
14	#5631	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	#5612	C₂	1	1	yes	maximal, characteristic, complemented
17	#5611	C₂	1	1	yes	maximal, characteristic, complemented
18	#5578	C₂	1	1	yes	maximal, characteristic, complemented
19	#5574	C₂	1	1	yes	maximal, characteristic, complemented
20	#5561	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
22	#5528	C₂	1	1	yes	maximal, characteristic, complemented
23	#5523	C₂	1	1	yes	maximal, characteristic, complemented
24	#3520	—	3	1	no	maximal, Sylow
25	C₂×#239	C₂²	1	1	yes	characteristic
26	C₂×D₃×Q₈	C₂²	1	2	yes	complemented
27	C₂×#237	C₂²	1	2	yes	complemented
28	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
29	C₂×#235	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₃	C₂²	1	2	yes	—
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×#126	C₂²	1	2	yes	complemented
33	C₃×#124	C₂²	1	1	yes	characteristic
34	C₃×#124	C₂²	1	2	yes	complemented
35	C₃×#123	C₂²	1	2	yes	complemented
36	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₂²⋊Q₈	C₂²	1	2	yes	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	1	yes	characteristic
41	C₃×#117	C₂²	1	1	yes	characteristic, complemented
42	#946	C₂²	1	1	yes	characteristic
43	#946	C₂²	1	2	yes	—
44	#946	C₂²	1	2	yes	complemented
45	#946	C₂²	1	2	yes	complemented
46	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
47	#944	C₂²	1	1	yes	characteristic, complemented
48	#938	C₂²	1	2	yes	—
49	#938	C₂²	1	1	yes	characteristic
50	#937	C₂²	1	2	yes	—
51	#936	C₂²	1	1	yes	characteristic
52	#935	C₂²	1	2	yes	complemented
53	D₄×Dic₃	C₂²	1	1	yes	characteristic
54	#929	C₂²	1	2	yes	complemented
55	C₄×#67	C₂²	1	1	yes	characteristic
56	C₄×#67	C₂²	1	2	yes	—
57	C₄×#67	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
59	#924	C₂²	1	2	yes	complemented
60	#898	C₂²	1	1	yes	characteristic, complemented
61	#897	C₂²	1	2	yes	—
62	#897	C₂²	1	1	yes	characteristic
63	#897	C₂²	1	1	yes	characteristic, complemented
64	#896	C₂²	1	2	yes	—
65	#896	C₂²	1	1	yes	characteristic
66	#896	C₂²	1	2	yes	complemented
67	#896	C₂²	1	2	yes	complemented
68	#894	C₂²	1	1	yes	characteristic
69	#894	C₂²	1	2	yes	complemented
70	#893	C₂²	1	2	yes	—
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	complemented
75	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
77	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
78	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
79	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
80	#890	C₂²	1	2	yes	complemented
81	#889	C₂²	1	2	yes	complemented
82	#889	C₂²	1	2	yes	complemented
83	#889	C₂²	1	1	yes	characteristic, complemented
84	#888	C₂²	1	1	yes	characteristic, complemented
85	#888	C₂²	1	1	yes	characteristic, complemented
86	#885	C₂²	1	1	yes	characteristic, complemented
87	#885	C₂²	1	2	yes	complemented
88	#884	C₂²	1	2	yes	—
89	#884	C₂²	1	1	yes	characteristic
90	#884	C₂²	1	2	yes	complemented
91	#883	C₂²	1	2	yes	—
92	#883	C₂²	1	2	yes	—
93	#883	C₂²	1	1	yes	characteristic
94	#883	C₂²	1	2	yes	complemented
95	#883	C₂²	1	2	yes	complemented
96	#882	C₂²	1	2	yes	—
97	#67⋊C₄	C₂²	1	2	yes	—
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	—
102	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	#879	C₂²	1	2	yes	complemented
105	#879	C₂²	1	1	yes	characteristic, complemented
106	#879	C₂²	1	2	yes	complemented
107	#879	C₂²	1	2	yes	complemented
108	#878	C₂²	1	2	yes	complemented
109	#878	C₂²	1	2	yes	complemented
110	#878	C₂²	1	2	yes	complemented
111	#877	C₂²	1	2	yes	complemented
112	C₄×D₁₂	C₂²	1	1	yes	characteristic
113	C₄×D₁₂	C₂²	1	1	yes	characteristic
114	C₄×D₁₂	C₂²	1	1	yes	characteristic
115	C₄×D₁₂	C₂²	1	2	yes	complemented
116	#872	C₂²	1	2	yes	—
117	#872	C₂²	1	2	yes	complemented
118	#872	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₃	C₂²	1	1	yes	characteristic
120	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂²	1	2	yes	complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#556	—	3	1	no	—
125	#554	—	3	1	no	—
126	#554	—	3	1	no	—
127	#552	—	3	2	no	—
128	#551	—	3	2	no	—
129	#551	—	3	2	no	—
130	D₄×Q₈	—	3	1	no	—
131	#548	—	3	2	no	—
132	#547	—	3	1	no	—
133	#547	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#542	—	3	1	no	—
137	#542	D₃	1	1	yes	characteristic, complemented
138	#539	—	3	2	no	—
139	#539	—	3	2	no	—
140	#533	—	3	1	no	—
141	#529	—	3	1	no	—
142	#525	—	3	2	no	—
143	C₂×C₂²⋊Q₈	—	3	2	no	—
144	#520	—	3	1	no	—
145	#520	—	3	1	no	—
146	C₂×C₄×D₄	—	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	2	yes	—
157	C₂×#67	C₂³	1	1	yes	characteristic
158	C₂×#67	C₂³	1	2	yes	—
159	C₂²×Dic₃	C₂³	1	2	yes	—
160	C₂²×Dic₃	C₂³	1	2	yes	—
161	#239	—	2	4	no	—
162	D₃×Q₈	—	4	4	no	—
163	#237	—	4	4	no	—
164	D₃×D₄	—	2	4	no	—
165	#235	—	2	4	no	—
166	C₂×D₁₂	C₂³	1	1	yes	characteristic
167	C₂×D₁₂	C₂³	1	2	yes	—
168	C₂×D₁₂	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₃	—	4	4	no	—
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	2	yes	—
177	C₂×C₄×D₃	C₂³	1	2	yes	—
178	C₂×C₄×D₃	C₂³	1	2	yes	—
179	C₂×C₄×D₃	C₂³	1	2	yes	—
180	C₂×C₄×D₃	C₂³	1	2	yes	—
181	C₂×C₄×D₃	C₂³	1	2	yes	—
182	C₂×Dic₆	C₂³	1	1	yes	characteristic
183	C₂×Dic₆	C₂³	1	1	yes	characteristic
184	C₂×Dic₆	C₂³	1	2	yes	—
185	C₂×Dic₆	C₂³	1	2	yes	—
186	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₃×C₄²	C₂³	1	1	yes	characteristic
202	C₃×C₄²	C₂³	1	2	yes	—
203	#217	C₂³	1	2	yes	—
204	#217	C₂³	1	1	yes	characteristic
205	#217	C₂³	1	2	yes	—
206	#217	C₂³	1	2	yes	—
207	#217	C₂³	1	2	yes	—
208	#217	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	1	yes	characteristic
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	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	1	yes	characteristic
221	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₃	C₂³	1	2	yes	—
226	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₃	C₂³	1	2	yes	—
228	C₄⋊Dic₃	C₂³	1	2	yes	—
229	C₄⋊Dic₃	C₂³	1	2	yes	—
230	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
231	Dic₃⋊C₄	C₂³	1	2	yes	—
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	2	yes	—
234	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
239	Dic₃⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
245	C₄×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₃	C₂³	1	2	yes	—
247	C₄×Dic₃	C₂³	1	1	yes	characteristic
248	C₄×Dic₃	C₂³	1	1	yes	characteristic
249	C₄×Dic₃	C₂³	1	2	yes	—
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₄×Dic₃	C₂³	1	2	yes	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	2	no	—
254	C₂×#41	—	3	1	no	—
255	C₂²×Q₈	—	3	2	no	—
256	C₂²×D₄	—	3	1	no	—
257	C₂³×C₄	—	3	2	no	—
258	C₄⋊Q₈	—	3	1	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	C₄⋊Q₈	—	3	1	no	—
261	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
262	#126	—	3	1	no	—
263	#126	—	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	1	no	—
269	#125	—	3	2	no	—
270	#125	—	3	2	no	—
271	#125	—	3	2	no	—
272	#124	—	3	1	no	—
273	#124	—	3	1	no	—
274	#124	—	3	2	no	—
275	#124	C₂×D₃	1	1	yes	characteristic
276	#124	C₂×D₃	1	2	yes	complemented
277	#123	—	3	2	no	—
278	#123	—	3	2	no	—
279	#123	—	3	1	no	—
280	#123	—	3	2	no	—
281	#123	—	3	1	no	—
282	#123	—	3	2	no	—
283	#123	—	3	2	no	—
284	#123	—	3	2	no	—
285	#123	—	3	2	no	—
286	#123	C₂×D₃	1	2	yes	complemented
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	—	3	2	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	2	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	—	3	1	no	—
297	C₂²⋊Q₈	—	3	2	no	—
298	C₂²⋊Q₈	—	3	1	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₂²⋊Q₈	—	3	2	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
303	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
304	#121	—	3	2	no	—
305	#121	—	3	1	no	—
306	#121	—	3	1	no	—
307	#121	—	3	2	no	—
308	#121	—	3	2	no	—
309	#121	C₂×D₃	1	1	yes	characteristic
310	#120	—	3	2	no	—
311	#120	—	3	2	no	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	—	3	1	no	—
314	C₄×Q₈	—	3	1	no	—
315	C₄×Q₈	—	3	1	no	—
316	C₄×Q₈	—	3	2	no	—
317	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
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	—	3	2	no	—
324	C₄×D₄	—	3	1	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	2	no	—
327	C₄×D₄	—	3	2	no	—
328	C₄×D₄	—	3	2	no	—
329	C₄×D₄	—	3	2	no	—
330	C₄×D₄	—	3	1	no	—
331	C₄×D₄	—	3	1	no	—
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	—	3	1	no	—
334	C₄×D₄	C₂×D₃	1	1	yes	characteristic
335	#117	—	3	2	no	—
336	#117	—	3	2	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×C₄⋊C₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	1	no	—
343	C₂×C₄⋊C₄	—	3	2	no	—
344	C₂×C₄⋊C₄	—	3	2	no	—
345	C₂×C₄⋊C₄	—	3	1	no	—
346	C₂×C₄⋊C₄	—	3	2	no	—
347	C₂×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂³×C₃	C₂⁴	1	2	yes	—
352	C₂³×C₃	C₂⁴	1	1	yes	characteristic
353	C₂²×D₃	—	2	4	no	—
354	C₂²×D₃	—	2	4	no	—
355	C₂²×D₃	—	4	2	no	—
356	C₂²×D₃	C₂⁴	1	1	yes	characteristic
357	C₂²×D₃	C₂⁴	1	2	yes	—
358	C₂²×D₃	C₂⁴	1	1	yes	characteristic
359	C₃×Q₈	—	2	2	no	—
360	C₃×Q₈	—	4	2	no	—
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	4	2	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	4	2	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	2	yes	—
368	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴	1	2	yes	—
372	C₂×C₃×C₄	C₂⁴	1	2	yes	—
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	#67	—	2	4	no	—
375	#67	—	2	4	no	—
376	#67	—	2	2	no	—
377	#67	—	2	2	no	—
378	#67	—	4	2	no	—
379	C₂×Dic₃	—	2	4	no	—
380	C₂×Dic₃	—	4	2	no	—
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	2	yes	—
386	C₂×Dic₃	C₂⁴	1	2	yes	—
387	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
390	D₁₂	—	2	4	no	—
391	D₁₂	—	2	2	no	—
392	D₁₂	#41	1	4	yes	complemented
393	C₄×D₃	—	2	4	no	—
394	C₄×D₃	—	2	4	no	—
395	C₄×D₃	—	2	2	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	2	no	—
401	C₄×D₃	—	4	2	no	—
402	C₄×D₃	—	4	2	no	—
403	C₄×D₃	—	4	2	no	—
404	C₄×D₃	—	4	2	no	—
405	Dic₆	—	2	2	no	—
406	Dic₆	—	2	4	no	—
407	Dic₆	—	2	2	no	—
408	Dic₆	—	4	2	no	—
409	C₂⁴	—	3	2	no	—
410	#41	—	6	4	no	—
411	#41	—	6	4	no	—
412	#41	—	12	4	no	—
413	C₂×Q₈	—	3	1	no	—
414	C₂×Q₈	—	3	1	no	—
415	C₂×Q₈	—	3	2	no	—
416	C₂×Q₈	—	3	2	no	—
417	C₂×Q₈	—	12	4	no	—
418	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
419	C₂×Q₈	C₂²×D₃	1	2	yes	—
420	C₂×D₄	—	3	1	no	—
421	C₂×D₄	—	3	2	no	—
422	C₂×D₄	—	3	2	no	—
423	C₂×D₄	—	3	1	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	1	no	—
426	C₂×D₄	—	3	1	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	6	4	no	—
429	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
430	C₂×D₄	C₂²×D₃	1	2	yes	—
431	C₂²×C₄	—	3	2	no	—
432	C₂²×C₄	—	3	2	no	—
433	C₂²×C₄	—	3	1	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	2	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	2	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	—	12	4	no	—
446	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
447	C₂²×C₄	C₂²×D₃	1	2	yes	—
448	C₄⋊C₄	—	3	1	no	—
449	C₄⋊C₄	—	3	1	no	—
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	3	1	no	—
453	C₄⋊C₄	—	3	2	no	—
454	C₄⋊C₄	—	3	2	no	—
455	C₄⋊C₄	—	3	1	no	—
456	C₄⋊C₄	—	3	2	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	1	no	—
466	C₄⋊C₄	—	3	1	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	1	no	—
471	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
473	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
474	C₄⋊C₄	C₂²×D₃	1	2	yes	—
475	C₄⋊C₄	C₂²×D₃	1	2	yes	—
476	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₃	1	2	yes	—
478	C₂²⋊C₄	—	3	2	no	—
479	C₂²⋊C₄	—	3	2	no	—
480	C₂²⋊C₄	—	3	2	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	1	no	—
483	C₂²⋊C₄	—	3	1	no	—
484	C₂²⋊C₄	—	3	1	no	—
485	C₂²⋊C₄	—	3	1	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	2	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	2	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	1	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	1	no	—
497	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
502	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
503	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	3	2	no	—
508	C₄²	—	3	2	no	—
509	C₄²	—	3	2	no	—
510	C₄²	—	3	1	no	—
511	C₄²	C₂²×D₃	1	1	yes	characteristic
512	C₄²	C₂²×D₃	1	2	yes	—
513	C₄²	C₂²×D₃	1	1	yes	characteristic
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	—	2	1	no	—
519	C₂²×C₃	—	2	2	no	—
520	C₂²×C₃	C₂⁵	1	1	yes	characteristic
521	C₂×D₃	—	2	1	no	—
522	C₂×D₃	—	2	2	no	—
523	C₂×D₃	—	2	1	no	—
524	C₂×D₃	—	2	2	no	—
525	C₂×D₃	—	2	1	no	—
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	2	1	no	—
528	C₂×D₃	—	4	8	no	—
529	C₂×D₃	C₂×#41	1	4	yes	—
530	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	2	no	—
533	C₃×C₄	—	2	2	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	2	no	—
536	C₃×C₄	—	2	1	no	—
537	C₃×C₄	—	2	1	no	—
538	C₃×C₄	—	2	1	no	—
539	C₃×C₄	C₂×#41	1	2	yes	—
540	Dic₃	—	2	2	no	—
541	Dic₃	—	2	1	no	—
542	Dic₃	—	2	1	no	—
543	Dic₃	—	2	1	no	—
544	Dic₃	—	2	2	no	—
545	Dic₃	—	2	2	no	—
546	Dic₃	—	2	1	no	—
547	Dic₃	—	2	1	no	—
548	Dic₃	H(5,𝔽₂)	1	2	yes	—
549	C₂³	—	3	1	no	—
550	C₂³	—	3	2	no	—
551	C₂³	—	3	1	no	—
552	C₂³	—	6	4	no	—
553	C₂³	—	6	4	no	—
554	C₂³	—	12	2	no	—
555	C₂³	C₂³×D₃	1	2	yes	—
556	C₂³	C₂³×D₃	1	1	yes	characteristic
557	Q₈	—	2	2	no	—
558	Q₈	—	4	2	no	—
559	Q₈	—	6	2	no	—
560	Q₈	—	6	4	no	—
561	Q₈	—	6	2	no	—
562	Q₈	—	12	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	3	4	no	—
565	D₄	—	4	2	no	—
566	D₄	—	6	4	no	—
567	D₄	—	6	2	no	—
568	D₄	—	6	2	no	—
569	D₄	—	6	4	no	—
570	D₄	—	6	4	no	—
571	D₄	—	6	2	no	—
572	D₄	—	12	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	3	1	no	—
575	C₂×C₄	—	3	1	no	—
576	C₂×C₄	—	3	1	no	—
577	C₂×C₄	—	3	2	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	2	no	—
580	C₂×C₄	—	3	1	no	—
581	C₂×C₄	—	3	2	no	—
582	C₂×C₄	—	3	1	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	6	2	no	—
585	C₂×C₄	—	6	4	no	—
586	C₂×C₄	—	6	4	no	—
587	C₂×C₄	—	6	4	no	—
588	C₂×C₄	—	6	2	no	—
589	C₂×C₄	—	6	4	no	—
590	C₂×C₄	—	6	2	no	—
591	C₂×C₄	—	6	2	no	—
592	C₂×C₄	—	12	2	no	—
593	C₂×C₄	—	12	2	no	—
594	C₂×C₄	—	12	2	no	—
595	C₂×C₄	—	12	2	no	—
596	C₂×C₄	—	12	2	no	—
597	C₂×C₄	—	12	2	no	—
598	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₃	1	2	yes	—
601	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
602	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
603	C₂×C₄	C₂³×D₃	1	2	yes	—
604	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₃	1	2	yes	—
606	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
607	C₂×C₃	—	4	2	no	—
608	C₂×C₃	—	4	1	no	—
609	C₂×C₃	C₂²×#41	1	1	yes	characteristic
610	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
612	D₃	—	2	2	no	—
613	D₃	—	2	4	no	—
614	D₃	—	4	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	3	4	no	—
622	C₂²	—	3	2	no	—
623	C₂²	—	6	1	no	—
624	C₂²	—	6	2	no	—
625	C₂²	—	6	1	no	—
626	C₂²	—	6	2	no	—
627	C₂²	—	6	1	no	—
628	C₂²	—	6	1	no	—
629	C₂²	—	6	1	no	—
630	C₂²	—	12	8	no	—
631	C₂²	C₂⁴×D₃	1	1	yes	characteristic
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	3	2	no	—
641	C₄	—	6	1	no	—
642	C₄	—	6	1	no	—
643	C₄	—	6	2	no	—
644	C₄	—	6	2	no	—
645	C₄	—	6	2	no	—
646	C₄	—	6	1	no	—
647	C₄	—	6	1	no	—
648	C₄	—	6	1	no	—
649	C₄	D₃×#41	1	2	yes	—
650	C₃	#3520	1	1	yes	characteristic, complemented, Sylow
651	C₂	—	4	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	6	2	no	—
654	C₂	—	6	4	no	—
655	C₂	—	12	1	no	—
656	C₂	C₂×D₃×#41	1	1	yes	characteristic
657	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
658	C₂	D₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#542	C₂
hypercenter	#542	D₃
hypocenter	C₃	#3520
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. #5730	C₂	semidirect
3. #5727	C₂	semidirect
4. #5708	C₂	semidirect
5. #5705	C₂	semidirect
6. #5679	C₂	semidirect
7. #5677	C₂	semidirect
8. #5676	C₂	semidirect
9. #5671	C₂	semidirect
10. #5660	C₂	semidirect
11. #5656	C₂	semidirect
12. #5638	C₂	semidirect
13. #5635	C₂	semidirect
14. #5631	C₂	semidirect
15. D₃×C₂²⋊Q₈	C₂	semidirect
16. #5612	C₂	semidirect
17. #5611	C₂	semidirect
18. #5578	C₂	semidirect
19. #5574	C₂	semidirect
20. #5561	C₂	semidirect
21. C₄×D₃×D₄	C₂	semidirect
22. #5528	C₂	semidirect
23. #5523	C₂	semidirect
26. C₂×D₃×Q₈	C₂²	semidirect
27. C₂×#237	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×#126	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
35. C₃×#123	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₃×C₄×Q₈	C₂²	semidirect
41. C₃×#117	C₂²	semidirect
44. #946	C₂²	semidirect
45. #946	C₂²	semidirect
46. Q₈×Dic₃	C₂²	semidirect
47. #944	C₂²	semidirect
52. #935	C₂²	semidirect
54. #929	C₂²	semidirect
57. C₄×#67	C₂²	semidirect
58. C₂×C₄⋊Dic₃	C₂²	semidirect
59. #924	C₂²	semidirect
60. #898	C₂²	semidirect
63. #897	C₂²	semidirect
66. #896	C₂²	semidirect
67. #896	C₂²	semidirect
69. #894	C₂²	semidirect
73. #893	C₂²	semidirect
74. #892	C₂²	semidirect
76. D₃×C₄⋊C₄	C₂²	semidirect
77. D₃×C₄⋊C₄	C₂²	semidirect
78. D₃×C₄⋊C₄	C₂²	semidirect
79. D₃×C₄⋊C₄	C₂²	semidirect
80. #890	C₂²	semidirect
81. #889	C₂²	semidirect
82. #889	C₂²	semidirect
83. #889	C₂²	semidirect
84. #888	C₂²	semidirect
85. #888	C₂²	semidirect
86. #885	C₂²	semidirect
87. #885	C₂²	semidirect
90. #884	C₂²	semidirect
94. #883	C₂²	semidirect
95. #883	C₂²	semidirect
99. #67⋊C₄	C₂²	semidirect
100. #67⋊C₄	C₂²	semidirect
104. #879	C₂²	semidirect
105. #879	C₂²	semidirect
106. #879	C₂²	semidirect
107. #879	C₂²	semidirect
108. #878	C₂²	semidirect
109. #878	C₂²	semidirect
110. #878	C₂²	semidirect
111. #877	C₂²	semidirect
115. C₄×D₁₂	C₂²	semidirect
117. #872	C₂²	semidirect
118. #872	C₂²	semidirect
120. C₄×Dic₆	C₂²	semidirect
121. C₄×Dic₆	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
137. #542	D₃	semidirect
261. C₄⋊Q₈	C₂×D₃	semidirect
267. #126	C₂×D₃	semidirect
276. #124	C₂×D₃	semidirect
286. #123	C₂×D₃	semidirect
302. C₂²⋊Q₈	C₂×D₃	semidirect
303. C₂²⋊Q₈	C₂×D₃	semidirect
317. C₄×Q₈	C₂×D₃	semidirect
340. #117	C₂×D₃	semidirect
392. D₁₂	#41	semidirect
650. C₃	#3520	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
#5730	2
#5727	2
#5708	2
#5705	2
#5679	2
#5677	2
#5676	2
#5671	2
#5660	2
#5656	2
#5638	2
#5635	2
#5631	2
D₃×C₂²⋊Q₈	2
#5612	2
#5611	2
#5578	2
#5574	2
#5561	2
C₄×D₃×D₄	2
#5528	2
#5523	2
#3520	3