Subgroups — #86521

Order 384.

936 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	#5735	C₂	1	1	yes	maximal, characteristic, complemented
3	#5730	C₂	1	1	yes	maximal, characteristic, complemented
4	#5712	C₂	1	1	yes	maximal, characteristic, complemented
5	#5710	C₂	1	1	yes	maximal, characteristic, complemented
6	#5708	C₂	1	1	yes	maximal, characteristic, complemented
7	#5705	C₂	1	1	yes	maximal, characteristic, complemented
8	#5705	C₂	1	1	yes	maximal, characteristic, complemented
9	#5704	C₂	1	1	yes	maximal, characteristic
10	D₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
11	#5701	C₂	1	1	yes	maximal, characteristic, complemented
12	#5699	C₂	1	1	yes	maximal, characteristic, complemented
13	#5696	C₂	1	1	yes	maximal, characteristic, complemented
14	#5696	C₂	1	1	yes	maximal, characteristic, complemented
15	#5694	C₂	1	1	yes	maximal, characteristic, complemented
16	#5693	C₂	1	1	yes	maximal, characteristic, complemented
17	#5692	C₂	1	1	yes	maximal, characteristic, complemented
18	#5692	C₂	1	1	yes	maximal, characteristic, complemented
19	#5691	C₂	1	1	yes	maximal, characteristic, complemented
20	#5690	C₂	1	1	yes	maximal, characteristic, complemented
21	#5689	C₂	1	1	yes	maximal, characteristic, complemented
22	#5646	C₂	1	1	yes	maximal, characteristic, complemented
23	#5638	C₂	1	1	yes	maximal, characteristic, complemented
24	#5637	C₂	1	1	yes	maximal, characteristic, complemented
25	#5634	C₂	1	1	yes	maximal, characteristic, complemented
26	#5584	C₂	1	1	yes	maximal, characteristic, complemented
27	#5582	C₂	1	1	yes	maximal, characteristic, complemented
28	#5581	C₂	1	1	yes	maximal, characteristic, complemented
29	#5578	C₂	1	1	yes	maximal, characteristic, complemented
30	#5533	C₂	1	1	yes	maximal, characteristic, complemented
31	#5527	C₂	1	1	yes	maximal, characteristic, complemented
32	#3564	—	3	1	no	maximal, Sylow
33	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×#126	C₂²	1	1	yes	characteristic
35	C₃×#126	C₂²	1	1	yes	characteristic
36	C₃×#126	C₂²	1	1	yes	characteristic
37	C₃×#126	C₂²	1	1	yes	characteristic
38	C₃×#125	C₂²	1	1	yes	characteristic, complemented
39	C₃×#125	C₂²	1	1	yes	characteristic, complemented
40	C₃×#125	C₂²	1	1	yes	characteristic, complemented
41	C₃×#125	C₂²	1	1	yes	characteristic, complemented
42	C₃×#125	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×#117	C₂²	1	1	yes	characteristic
48	#947	C₂²	1	1	yes	characteristic
49	#946	C₂²	1	1	yes	characteristic
50	#946	C₂²	1	1	yes	characteristic
51	#946	C₂²	1	1	yes	characteristic
52	#946	C₂²	1	1	yes	characteristic, complemented
53	#946	C₂²	1	1	yes	characteristic, complemented
54	#946	C₂²	1	1	yes	characteristic, complemented
55	#944	C₂²	1	1	yes	characteristic, complemented
56	#929	C₂²	1	1	yes	characteristic
57	C₄×#67	C₂²	1	1	yes	characteristic
58	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
59	#924	C₂²	1	1	yes	characteristic
60	#898	C₂²	1	1	yes	characteristic
61	#898	C₂²	1	1	yes	characteristic
62	#898	C₂²	1	1	yes	characteristic
63	#898	C₂²	1	1	yes	characteristic
64	#898	C₂²	1	1	yes	characteristic
65	#898	C₂²	1	1	yes	characteristic
66	#898	C₂²	1	1	yes	characteristic
67	#898	C₂²	1	1	yes	characteristic, complemented
68	#898	C₂²	1	1	yes	characteristic, complemented
69	#898	C₂²	1	1	yes	characteristic, complemented
70	#898	C₂²	1	1	yes	characteristic, complemented
71	#898	C₂²	1	1	yes	characteristic, complemented
72	#897	C₂²	1	1	yes	characteristic
73	#897	C₂²	1	1	yes	characteristic
74	#897	C₂²	1	1	yes	characteristic
75	#897	C₂²	1	1	yes	characteristic
76	#897	C₂²	1	1	yes	characteristic, complemented
77	#897	C₂²	1	1	yes	characteristic, complemented
78	#897	C₂²	1	1	yes	characteristic, complemented
79	#896	C₂²	1	1	yes	characteristic
80	#896	C₂²	1	1	yes	characteristic
81	#896	C₂²	1	1	yes	characteristic
82	#896	C₂²	1	1	yes	characteristic
83	#896	C₂²	1	1	yes	characteristic
84	#896	C₂²	1	1	yes	characteristic
85	#896	C₂²	1	1	yes	characteristic
86	#896	C₂²	1	1	yes	characteristic
87	#896	C₂²	1	1	yes	characteristic, complemented
88	#896	C₂²	1	1	yes	characteristic, complemented
89	#896	C₂²	1	1	yes	characteristic, complemented
90	#896	C₂²	1	1	yes	characteristic, complemented
91	#895	C₂²	1	1	yes	characteristic
92	#895	C₂²	1	1	yes	characteristic
93	#894	C₂²	1	1	yes	characteristic
94	#894	C₂²	1	1	yes	characteristic
95	#894	C₂²	1	1	yes	characteristic
96	#894	C₂²	1	1	yes	characteristic
97	#894	C₂²	1	1	yes	characteristic
98	#894	C₂²	1	1	yes	characteristic
99	#894	C₂²	1	1	yes	characteristic
100	#894	C₂²	1	1	yes	characteristic
101	#894	C₂²	1	1	yes	characteristic
102	#894	C₂²	1	1	yes	characteristic, complemented
103	#894	C₂²	1	1	yes	characteristic, complemented
104	#893	C₂²	1	1	yes	characteristic
105	#893	C₂²	1	1	yes	characteristic
106	#893	C₂²	1	1	yes	characteristic
107	#893	C₂²	1	1	yes	characteristic
108	#893	C₂²	1	1	yes	characteristic, complemented
109	#892	C₂²	1	1	yes	characteristic
110	#892	C₂²	1	1	yes	characteristic
111	#892	C₂²	1	1	yes	characteristic
112	#892	C₂²	1	1	yes	characteristic, complemented
113	#892	C₂²	1	1	yes	characteristic, complemented
114	#892	C₂²	1	1	yes	characteristic, complemented
115	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
116	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
117	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
118	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	#890	C₂²	1	1	yes	characteristic, complemented
121	#890	C₂²	1	1	yes	characteristic, complemented
122	#890	C₂²	1	1	yes	characteristic, complemented
123	#890	C₂²	1	1	yes	characteristic, complemented
124	#889	C₂²	1	1	yes	characteristic, complemented
125	#889	C₂²	1	1	yes	characteristic, complemented
126	#889	C₂²	1	1	yes	characteristic, complemented
127	#889	C₂²	1	1	yes	characteristic, complemented
128	#889	C₂²	1	1	yes	characteristic, complemented
129	#889	C₂²	1	1	yes	characteristic, complemented
130	#889	C₂²	1	1	yes	characteristic, complemented
131	#889	C₂²	1	1	yes	characteristic, complemented
132	#889	C₂²	1	1	yes	characteristic, complemented
133	#888	C₂²	1	1	yes	characteristic, complemented
134	#888	C₂²	1	1	yes	characteristic, complemented
135	#888	C₂²	1	1	yes	characteristic, complemented
136	#888	C₂²	1	1	yes	characteristic, complemented
137	#888	C₂²	1	1	yes	characteristic, complemented
138	#887	C₂²	1	1	yes	characteristic, complemented
139	#887	C₂²	1	1	yes	characteristic, complemented
140	#886	C₂²	1	1	yes	characteristic
141	#885	C₂²	1	1	yes	characteristic
142	#885	C₂²	1	1	yes	characteristic
143	#885	C₂²	1	1	yes	characteristic
144	#884	C₂²	1	1	yes	characteristic
145	#883	C₂²	1	1	yes	characteristic
146	#883	C₂²	1	1	yes	characteristic
147	#883	C₂²	1	1	yes	characteristic
148	#882	C₂²	1	1	yes	characteristic
149	#882	C₂²	1	1	yes	characteristic
150	#67⋊C₄	C₂²	1	1	yes	characteristic
151	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
152	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
153	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
154	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
155	#879	C₂²	1	1	yes	characteristic
156	#879	C₂²	1	1	yes	characteristic
157	#879	C₂²	1	1	yes	characteristic
158	#879	C₂²	1	1	yes	characteristic
159	#879	C₂²	1	1	yes	characteristic
160	#878	C₂²	1	1	yes	characteristic
161	#878	C₂²	1	1	yes	characteristic
162	#878	C₂²	1	1	yes	characteristic
163	#877	C₂²	1	1	yes	characteristic
164	#876	C₂²	1	1	yes	characteristic
165	#876	C₂²	1	1	yes	characteristic
166	#876	C₂²	1	1	yes	characteristic, complemented
167	#876	C₂²	1	1	yes	characteristic, complemented
168	#876	C₂²	1	1	yes	characteristic, complemented
169	#875	C₂²	1	1	yes	characteristic
170	#875	C₂²	1	1	yes	characteristic
171	#875	C₂²	1	1	yes	characteristic, complemented
172	C₄×D₁₂	C₂²	1	1	yes	characteristic
173	C₄×D₁₂	C₂²	1	1	yes	characteristic
174	C₄×D₁₂	C₂²	1	1	yes	characteristic
175	C₄×D₁₂	C₂²	1	1	yes	characteristic
176	#872	C₂²	1	1	yes	characteristic
177	#872	C₂²	1	1	yes	characteristic
178	#872	C₂²	1	1	yes	characteristic
179	#872	C₂²	1	1	yes	characteristic, complemented
180	C₄²×D₃	C₂²	1	1	yes	characteristic
181	#870	C₂²	1	1	yes	characteristic, complemented
182	#869	C₂²	1	1	yes	characteristic, complemented
183	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
187	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
188	#563	—	3	1	no	—
189	#563	—	3	1	no	—
190	#563	—	3	1	no	—
191	#563	—	3	1	no	—
192	#556	—	3	1	no	—
193	#556	—	3	1	no	—
194	#554	—	3	1	no	—
195	#554	—	3	1	no	—
196	#552	—	3	1	no	—
197	#552	—	3	1	no	—
198	#552	—	3	1	no	—
199	#552	—	3	1	no	—
200	#551	—	3	1	no	—
201	#551	—	3	1	no	—
202	#551	—	3	1	no	—
203	#551	—	3	1	no	—
204	#544	—	3	1	no	—
205	#543	—	3	1	no	—
206	#542	—	3	1	no	—
207	#542	—	3	1	no	—
208	#541	—	3	1	no	—
209	#541	—	3	1	no	—
210	#541	—	3	1	no	—
211	#541	D₃	1	1	yes	characteristic, complemented
212	#539	—	3	1	no	—
213	#539	—	3	1	no	—
214	#539	—	3	1	no	—
215	#538	—	3	1	no	—
216	#533	—	3	1	no	—
217	#529	—	3	1	no	—
218	C₂×#126	—	3	1	no	—
219	C₂³×D₃	C₂³	1	1	yes	characteristic
220	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
223	C₂×#67	C₂³	1	1	yes	characteristic
224	C₂×#67	C₂³	1	1	yes	characteristic
225	C₂²×Dic₃	C₂³	1	1	yes	characteristic
226	C₂×D₁₂	C₂³	1	1	yes	characteristic
227	C₂×D₁₂	C₂³	1	1	yes	characteristic
228	C₂×D₁₂	C₂³	1	1	yes	characteristic
229	C₂×D₁₂	C₂³	1	1	yes	characteristic
230	C₂×D₁₂	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
245	C₂×Dic₆	C₂³	1	1	yes	characteristic
246	C₂×Dic₆	C₂³	1	1	yes	characteristic
247	C₂×Dic₆	C₂³	1	1	yes	characteristic
248	C₂×Dic₆	C₂³	1	1	yes	characteristic
249	C₂×Dic₆	C₂³	1	1	yes	characteristic
250	C₂×Dic₆	C₂³	1	1	yes	characteristic
251	C₂×Dic₆	C₂³	1	1	yes	characteristic
252	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₃×C₄²	C₂³	1	1	yes	characteristic
279	C₃×C₄²	C₂³	1	1	yes	characteristic
280	C₃×C₄²	C₂³	1	1	yes	characteristic
281	C₃×C₄²	C₂³	1	1	yes	characteristic
282	C₃×C₄²	C₂³	1	1	yes	characteristic
283	C₃×C₄²	C₂³	1	1	yes	characteristic
284	#217	C₂³	1	1	yes	characteristic
285	#217	C₂³	1	1	yes	characteristic
286	#217	C₂³	1	1	yes	characteristic
287	#217	C₂³	1	1	yes	characteristic
288	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
311	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
312	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
313	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
314	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
315	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
316	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
317	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
318	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
319	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
323	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
324	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
325	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
326	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
327	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
328	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
329	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
330	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
331	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
332	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
333	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
334	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
336	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
338	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
339	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
340	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
341	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
342	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
343	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
344	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
345	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
346	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
347	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
348	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
349	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
350	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
351	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
352	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
353	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
354	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
355	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
356	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
357	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
358	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
359	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
360	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
361	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
362	C₄×Dic₃	C₂³	1	1	yes	characteristic
363	C₄×Dic₃	C₂³	1	1	yes	characteristic
364	C₄×Dic₃	C₂³	1	1	yes	characteristic
365	C₄×Dic₃	C₂³	1	1	yes	characteristic
366	C₄×Dic₃	C₂³	1	1	yes	characteristic
367	C₄×Dic₃	C₂³	1	1	yes	characteristic
368	C₄×Dic₃	C₂³	1	1	yes	characteristic
369	C₄×Dic₃	C₂³	1	1	yes	characteristic
370	C₄×Dic₃	C₂³	1	1	yes	characteristic
371	C₄×Dic₃	C₂³	1	1	yes	characteristic
372	C₄×Dic₃	C₂³	1	1	yes	characteristic
373	C₄×Dic₃	C₂³	1	1	yes	characteristic
374	C₄⋊Q₈	—	3	1	no	—
375	C₄⋊Q₈	—	3	1	no	—
376	C₄⋊Q₈	—	3	1	no	—
377	C₄⋊Q₈	—	3	1	no	—
378	C₄⋊Q₈	—	3	1	no	—
379	C₄⋊Q₈	—	3	1	no	—
380	C₄⋊Q₈	—	3	1	no	—
381	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
382	#126	—	3	1	no	—
383	#126	—	3	1	no	—
384	#126	—	3	1	no	—
385	#126	—	3	1	no	—
386	#126	—	3	1	no	—
387	#126	—	3	1	no	—
388	#126	—	3	1	no	—
389	#126	—	3	1	no	—
390	#126	—	3	1	no	—
391	#126	—	3	1	no	—
392	#126	—	3	1	no	—
393	#126	—	3	1	no	—
394	#126	—	3	1	no	—
395	#126	—	3	1	no	—
396	#126	—	3	1	no	—
397	#126	—	3	1	no	—
398	#126	—	3	1	no	—
399	#126	—	3	1	no	—
400	#126	—	3	1	no	—
401	#126	—	3	1	no	—
402	#126	—	3	1	no	—
403	#126	—	3	1	no	—
404	#126	C₂×D₃	1	1	yes	characteristic
405	#126	C₂×D₃	1	1	yes	characteristic
406	#126	C₂×D₃	1	1	yes	characteristic
407	#126	C₂×D₃	1	1	yes	characteristic
408	#125	—	3	1	no	—
409	#125	—	3	1	no	—
410	#125	—	3	1	no	—
411	#125	—	3	1	no	—
412	#125	—	3	1	no	—
413	#125	—	3	1	no	—
414	#125	—	3	1	no	—
415	#125	—	3	1	no	—
416	#125	—	3	1	no	—
417	#125	—	3	1	no	—
418	#125	—	3	1	no	—
419	#125	—	3	1	no	—
420	#125	—	3	1	no	—
421	#125	—	3	1	no	—
422	#125	C₂×D₃	1	1	yes	characteristic, complemented
423	#125	C₂×D₃	1	1	yes	characteristic, complemented
424	#125	C₂×D₃	1	1	yes	characteristic, complemented
425	#125	C₂×D₃	1	1	yes	characteristic, complemented
426	#125	C₂×D₃	1	1	yes	characteristic, complemented
427	#124	—	3	1	no	—
428	#124	—	3	1	no	—
429	#124	—	3	1	no	—
430	#124	—	3	1	no	—
431	#124	—	3	1	no	—
432	#124	—	3	1	no	—
433	#124	—	3	1	no	—
434	#123	—	3	1	no	—
435	#123	—	3	1	no	—
436	#123	—	3	1	no	—
437	#123	—	3	1	no	—
438	#123	—	3	1	no	—
439	#123	—	3	1	no	—
440	#123	—	3	1	no	—
441	#123	—	3	1	no	—
442	#123	—	3	1	no	—
443	#123	—	3	1	no	—
444	#123	—	3	1	no	—
445	#123	—	3	1	no	—
446	#123	—	3	1	no	—
447	#123	—	3	1	no	—
448	#123	—	3	1	no	—
449	#123	—	3	1	no	—
450	C₂²⋊Q₈	—	3	1	no	—
451	C₂²⋊Q₈	—	3	1	no	—
452	C₂²⋊Q₈	—	3	1	no	—
453	C₂²⋊Q₈	—	3	1	no	—
454	C₂²⋊Q₈	—	3	1	no	—
455	C₂²⋊Q₈	—	3	1	no	—
456	C₂²⋊Q₈	—	3	1	no	—
457	C₂²⋊Q₈	—	3	1	no	—
458	C₂²⋊Q₈	—	3	1	no	—
459	C₂²⋊Q₈	—	3	1	no	—
460	C₂²⋊Q₈	—	3	1	no	—
461	C₂²⋊Q₈	—	3	1	no	—
462	C₂²⋊Q₈	—	3	1	no	—
463	C₂²⋊Q₈	—	3	1	no	—
464	C₂²⋊Q₈	—	3	1	no	—
465	C₂²⋊Q₈	—	3	1	no	—
466	C₂²⋊Q₈	—	3	1	no	—
467	C₂²⋊Q₈	—	3	1	no	—
468	C₂²⋊Q₈	—	3	1	no	—
469	C₂²⋊Q₈	—	3	1	no	—
470	C₂²⋊Q₈	—	3	1	no	—
471	C₂²⋊Q₈	—	3	1	no	—
472	C₂²⋊Q₈	—	3	1	no	—
473	C₂²⋊Q₈	—	3	1	no	—
474	C₂²⋊Q₈	—	3	1	no	—
475	C₂²⋊Q₈	—	3	1	no	—
476	C₂²⋊Q₈	—	3	1	no	—
477	C₂²⋊Q₈	—	3	1	no	—
478	C₂²⋊Q₈	—	3	1	no	—
479	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
480	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
481	#121	—	3	1	no	—
482	#121	—	3	1	no	—
483	#121	—	3	1	no	—
484	#120	—	3	1	no	—
485	#120	—	3	1	no	—
486	C₄×Q₈	—	3	1	no	—
487	C₄×Q₈	—	3	1	no	—
488	C₄×Q₈	—	3	1	no	—
489	C₄×Q₈	—	3	1	no	—
490	C₄×Q₈	—	3	1	no	—
491	C₄×Q₈	—	3	1	no	—
492	C₄×Q₈	—	3	1	no	—
493	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
494	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
495	C₄×D₄	—	3	1	no	—
496	C₄×D₄	—	3	1	no	—
497	C₄×D₄	—	3	1	no	—
498	C₄×D₄	—	3	1	no	—
499	C₄×D₄	—	3	1	no	—
500	C₄×D₄	—	3	1	no	—
501	C₄×D₄	—	3	1	no	—
502	C₄×D₄	—	3	1	no	—
503	C₄×D₄	—	3	1	no	—
504	C₄×D₄	—	3	1	no	—
505	C₄×D₄	—	3	1	no	—
506	#117	—	3	1	no	—
507	#117	—	3	1	no	—
508	#117	—	3	1	no	—
509	#117	—	3	1	no	—
510	#117	—	3	1	no	—
511	#117	—	3	1	no	—
512	#117	—	3	1	no	—
513	#117	—	3	1	no	—
514	#117	—	3	1	no	—
515	#117	—	3	1	no	—
516	#117	—	3	1	no	—
517	#117	C₂×D₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	—	3	1	no	—
519	C₂×C₄⋊C₄	—	3	1	no	—
520	C₂×C₄⋊C₄	—	3	1	no	—
521	C₂×C₄⋊C₄	—	3	1	no	—
522	C₂×C₄⋊C₄	—	3	1	no	—
523	C₂×C₂²⋊C₄	—	3	1	no	—
524	C₂×C₂²⋊C₄	—	3	1	no	—
525	C₂×C₂²⋊C₄	—	3	1	no	—
526	C₂×C₂²⋊C₄	—	3	1	no	—
527	C₂×C₂²⋊C₄	—	3	1	no	—
528	C₂×C₄²	—	3	1	no	—
529	C₂³×C₃	C₂⁴	1	1	yes	characteristic
530	C₂²×D₃	—	2	2	no	—
531	C₂²×D₃	—	4	1	no	—
532	C₂²×D₃	—	4	1	no	—
533	C₂²×D₃	C₂⁴	1	1	yes	characteristic
534	C₂²×D₃	C₂⁴	1	1	yes	characteristic
535	C₂²×D₃	C₂⁴	1	1	yes	characteristic
536	C₂²×D₃	C₂⁴	1	1	yes	characteristic
537	C₃×Q₈	—	4	1	no	—
538	C₃×Q₈	—	4	1	no	—
539	C₂×C₃×C₄	—	4	1	no	—
540	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
542	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
543	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
544	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
545	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
546	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
547	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
548	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
549	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
550	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
551	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
552	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
553	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
554	#67	—	4	1	no	—
555	#67	—	4	1	no	—
556	C₂×Dic₃	—	4	1	no	—
557	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
558	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
559	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
560	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
561	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
562	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
563	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
564	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
565	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
566	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
567	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
568	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
569	D₁₂	—	2	2	no	—
570	D₁₂	—	2	2	no	—
571	D₁₂	—	4	1	no	—
572	D₁₂	—	4	1	no	—
573	D₁₂	—	4	1	no	—
574	C₄×D₃	—	2	2	no	—
575	C₄×D₃	—	2	2	no	—
576	C₄×D₃	—	4	1	no	—
577	C₄×D₃	—	4	1	no	—
578	C₄×D₃	—	4	1	no	—
579	C₄×D₃	—	4	1	no	—
580	C₄×D₃	—	4	1	no	—
581	C₄×D₃	—	4	1	no	—
582	C₄×D₃	—	4	1	no	—
583	C₄×D₃	—	4	1	no	—
584	C₄×D₃	—	4	1	no	—
585	C₄×D₃	—	4	1	no	—
586	C₄×D₃	—	4	1	no	—
587	C₄×D₃	—	4	1	no	—
588	Dic₆	—	4	1	no	—
589	Dic₆	—	4	1	no	—
590	Dic₆	—	4	1	no	—
591	Dic₆	—	4	1	no	—
592	Dic₆	—	4	1	no	—
593	Dic₆	—	4	1	no	—
594	Dic₆	—	4	1	no	—
595	C₂⁴	—	3	1	no	—
596	C₂×Q₈	—	3	1	no	—
597	C₂×Q₈	—	3	1	no	—
598	C₂×Q₈	—	3	1	no	—
599	C₂×Q₈	—	3	1	no	—
600	C₂×Q₈	—	3	1	no	—
601	C₂×Q₈	—	3	1	no	—
602	C₂×Q₈	—	3	1	no	—
603	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
604	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
605	C₂×D₄	—	3	1	no	—
606	C₂×D₄	—	3	1	no	—
607	C₂×D₄	—	3	1	no	—
608	C₂×D₄	—	3	1	no	—
609	C₂×D₄	—	3	1	no	—
610	C₂×D₄	—	3	1	no	—
611	C₂×D₄	—	3	1	no	—
612	C₂²×C₄	—	3	1	no	—
613	C₂²×C₄	—	3	1	no	—
614	C₂²×C₄	—	3	1	no	—
615	C₂²×C₄	—	3	1	no	—
616	C₂²×C₄	—	3	1	no	—
617	C₂²×C₄	—	3	1	no	—
618	C₂²×C₄	—	3	1	no	—
619	C₂²×C₄	—	3	1	no	—
620	C₂²×C₄	—	3	1	no	—
621	C₂²×C₄	—	3	1	no	—
622	C₂²×C₄	—	3	1	no	—
623	C₂²×C₄	—	3	1	no	—
624	C₂²×C₄	—	3	1	no	—
625	C₂²×C₄	—	3	1	no	—
626	C₂²×C₄	—	3	1	no	—
627	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
628	C₄⋊C₄	—	3	1	no	—
629	C₄⋊C₄	—	3	1	no	—
630	C₄⋊C₄	—	3	1	no	—
631	C₄⋊C₄	—	3	1	no	—
632	C₄⋊C₄	—	3	1	no	—
633	C₄⋊C₄	—	3	1	no	—
634	C₄⋊C₄	—	3	1	no	—
635	C₄⋊C₄	—	3	1	no	—
636	C₄⋊C₄	—	3	1	no	—
637	C₄⋊C₄	—	3	1	no	—
638	C₄⋊C₄	—	3	1	no	—
639	C₄⋊C₄	—	3	1	no	—
640	C₄⋊C₄	—	3	1	no	—
641	C₄⋊C₄	—	3	1	no	—
642	C₄⋊C₄	—	3	1	no	—
643	C₄⋊C₄	—	3	1	no	—
644	C₄⋊C₄	—	3	1	no	—
645	C₄⋊C₄	—	3	1	no	—
646	C₄⋊C₄	—	3	1	no	—
647	C₄⋊C₄	—	3	1	no	—
648	C₄⋊C₄	—	3	1	no	—
649	C₄⋊C₄	—	3	1	no	—
650	C₄⋊C₄	—	3	1	no	—
651	C₄⋊C₄	—	3	1	no	—
652	C₄⋊C₄	—	3	1	no	—
653	C₄⋊C₄	—	3	1	no	—
654	C₄⋊C₄	—	3	1	no	—
655	C₄⋊C₄	—	3	1	no	—
656	C₄⋊C₄	—	3	1	no	—
657	C₄⋊C₄	—	3	1	no	—
658	C₄⋊C₄	—	3	1	no	—
659	C₄⋊C₄	—	3	1	no	—
660	C₄⋊C₄	—	3	1	no	—
661	C₄⋊C₄	—	3	1	no	—
662	C₄⋊C₄	—	3	1	no	—
663	C₄⋊C₄	—	3	1	no	—
664	C₄⋊C₄	—	3	1	no	—
665	C₄⋊C₄	—	3	1	no	—
666	C₄⋊C₄	—	3	1	no	—
667	C₄⋊C₄	—	3	1	no	—
668	C₄⋊C₄	—	3	1	no	—
669	C₄⋊C₄	—	3	1	no	—
670	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
671	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
672	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
673	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
674	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
675	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
676	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
677	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
678	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
679	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
680	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
681	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
682	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
683	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
684	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
685	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
686	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
687	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
688	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
689	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
690	C₂²⋊C₄	—	3	1	no	—
691	C₂²⋊C₄	—	3	1	no	—
692	C₂²⋊C₄	—	3	1	no	—
693	C₂²⋊C₄	—	3	1	no	—
694	C₂²⋊C₄	—	3	1	no	—
695	C₂²⋊C₄	—	3	1	no	—
696	C₂²⋊C₄	—	3	1	no	—
697	C₂²⋊C₄	—	3	1	no	—
698	C₂²⋊C₄	—	3	1	no	—
699	C₂²⋊C₄	—	3	1	no	—
700	C₂²⋊C₄	—	3	1	no	—
701	C₂²⋊C₄	—	3	1	no	—
702	C₂²⋊C₄	—	3	1	no	—
703	C₂²⋊C₄	—	3	1	no	—
704	C₂²⋊C₄	—	3	1	no	—
705	C₂²⋊C₄	—	3	1	no	—
706	C₂²⋊C₄	—	3	1	no	—
707	C₂²⋊C₄	—	3	1	no	—
708	C₂²⋊C₄	—	3	1	no	—
709	C₂²⋊C₄	—	3	1	no	—
710	C₂²⋊C₄	—	3	1	no	—
711	C₂²⋊C₄	—	3	1	no	—
712	C₂²⋊C₄	—	3	1	no	—
713	C₂²⋊C₄	—	3	1	no	—
714	C₂²⋊C₄	—	3	1	no	—
715	C₂²⋊C₄	—	3	1	no	—
716	C₂²⋊C₄	—	3	1	no	—
717	C₂²⋊C₄	—	3	1	no	—
718	C₂²⋊C₄	—	3	1	no	—
719	C₂²⋊C₄	—	3	1	no	—
720	C₂²⋊C₄	—	3	1	no	—
721	C₂²⋊C₄	—	3	1	no	—
722	C₂²⋊C₄	—	3	1	no	—
723	C₂²⋊C₄	—	3	1	no	—
724	C₂²⋊C₄	—	3	1	no	—
725	C₂²⋊C₄	—	3	1	no	—
726	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
727	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
728	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
729	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
730	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
731	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
732	C₄²	—	3	1	no	—
733	C₄²	—	3	1	no	—
734	C₄²	—	3	1	no	—
735	C₄²	—	3	1	no	—
736	C₄²	—	3	1	no	—
737	C₄²	—	3	1	no	—
738	C₄²	—	3	1	no	—
739	C₄²	—	3	1	no	—
740	C₄²	—	3	1	no	—
741	C₄²	—	3	1	no	—
742	C₄²	—	3	1	no	—
743	C₄²	—	3	1	no	—
744	C₄²	C₂²×D₃	1	1	yes	characteristic
745	C₄²	C₂²×D₃	1	1	yes	characteristic
746	C₄²	C₂²×D₃	1	1	yes	characteristic
747	C₄²	C₂²×D₃	1	1	yes	characteristic
748	C₄²	C₂²×D₃	1	1	yes	characteristic
749	C₄²	C₂²×D₃	1	1	yes	characteristic
750	C₂²×C₃	—	2	1	no	—
751	C₂²×C₃	—	2	1	no	—
752	C₂²×C₃	—	2	1	no	—
753	C₂²×C₃	C₂⁵	1	1	yes	characteristic
754	C₂×D₃	—	2	1	no	—
755	C₂×D₃	—	2	1	no	—
756	C₂×D₃	—	2	1	no	—
757	C₂×D₃	—	2	1	no	—
758	C₂×D₃	—	2	1	no	—
759	C₂×D₃	—	2	1	no	—
760	C₂×D₃	—	2	1	no	—
761	C₂×D₃	—	2	1	no	—
762	C₂×D₃	—	2	1	no	—
763	C₂×D₃	—	2	1	no	—
764	C₂×D₃	—	2	1	no	—
765	C₂×D₃	—	8	2	no	—
766	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
767	C₃×C₄	—	2	1	no	—
768	C₃×C₄	—	2	1	no	—
769	C₃×C₄	—	2	1	no	—
770	C₃×C₄	—	2	1	no	—
771	C₃×C₄	—	2	1	no	—
772	C₃×C₄	—	2	1	no	—
773	C₃×C₄	—	2	1	no	—
774	C₃×C₄	—	2	1	no	—
775	C₃×C₄	—	2	1	no	—
776	C₃×C₄	—	2	1	no	—
777	C₃×C₄	—	2	1	no	—
778	C₃×C₄	—	2	1	no	—
779	C₃×C₄	—	2	1	no	—
780	C₃×C₄	—	2	1	no	—
781	Dic₃	—	2	1	no	—
782	Dic₃	—	2	1	no	—
783	Dic₃	—	2	1	no	—
784	Dic₃	—	2	1	no	—
785	Dic₃	—	2	1	no	—
786	Dic₃	—	2	1	no	—
787	Dic₃	—	2	1	no	—
788	Dic₃	—	2	1	no	—
789	Dic₃	—	2	1	no	—
790	Dic₃	—	2	1	no	—
791	Dic₃	—	2	1	no	—
792	Dic₃	—	2	1	no	—
793	C₂³	—	3	1	no	—
794	C₂³	—	3	1	no	—
795	C₂³	—	3	1	no	—
796	C₂³	—	3	1	no	—
797	C₂³	—	6	2	no	—
798	C₂³	—	12	1	no	—
799	C₂³	—	12	1	no	—
800	C₂³	C₂³×D₃	1	1	yes	characteristic
801	Q₈	—	4	1	no	—
802	Q₈	—	4	1	no	—
803	Q₈	—	12	1	no	—
804	Q₈	—	12	1	no	—
805	Q₈	—	12	1	no	—
806	Q₈	—	12	1	no	—
807	Q₈	—	12	1	no	—
808	Q₈	—	12	1	no	—
809	Q₈	—	12	1	no	—
810	D₄	—	6	2	no	—
811	D₄	—	6	2	no	—
812	D₄	—	12	1	no	—
813	D₄	—	12	1	no	—
814	D₄	—	12	1	no	—
815	D₄	—	12	1	no	—
816	D₄	—	12	1	no	—
817	C₂×C₄	—	3	1	no	—
818	C₂×C₄	—	3	1	no	—
819	C₂×C₄	—	3	1	no	—
820	C₂×C₄	—	3	1	no	—
821	C₂×C₄	—	3	1	no	—
822	C₂×C₄	—	3	1	no	—
823	C₂×C₄	—	3	1	no	—
824	C₂×C₄	—	3	1	no	—
825	C₂×C₄	—	3	1	no	—
826	C₂×C₄	—	3	1	no	—
827	C₂×C₄	—	3	1	no	—
828	C₂×C₄	—	3	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	6	2	no	—
831	C₂×C₄	—	6	2	no	—
832	C₂×C₄	—	12	1	no	—
833	C₂×C₄	—	12	1	no	—
834	C₂×C₄	—	12	1	no	—
835	C₂×C₄	—	12	1	no	—
836	C₂×C₄	—	12	1	no	—
837	C₂×C₄	—	12	1	no	—
838	C₂×C₄	—	12	1	no	—
839	C₂×C₄	—	12	1	no	—
840	C₂×C₄	—	12	1	no	—
841	C₂×C₄	—	12	1	no	—
842	C₂×C₄	—	12	1	no	—
843	C₂×C₄	—	12	1	no	—
844	C₂×C₄	—	12	1	no	—
845	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
846	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
847	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
848	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
849	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
850	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
851	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
852	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
853	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
854	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
855	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
856	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
857	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
858	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
859	C₂×C₃	—	4	1	no	—
860	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
861	C₂×C₃	#585	1	1	yes	characteristic
862	C₂×C₃	#585	1	1	yes	characteristic
863	D₃	—	2	2	no	—
864	D₃	—	4	1	no	—
865	D₃	—	4	1	no	—
866	D₃	—	4	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	3	2	no	—
871	C₂²	—	6	1	no	—
872	C₂²	—	6	1	no	—
873	C₂²	—	6	1	no	—
874	C₂²	—	6	1	no	—
875	C₂²	—	6	1	no	—
876	C₂²	—	6	1	no	—
877	C₂²	—	6	1	no	—
878	C₂²	—	6	1	no	—
879	C₂²	—	6	1	no	—
880	C₂²	—	6	1	no	—
881	C₂²	—	6	1	no	—
882	C₂²	—	24	2	no	—
883	C₂²	C₂⁴×D₃	1	1	yes	characteristic
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	1	no	—
898	C₄	—	6	1	no	—
899	C₄	—	6	1	no	—
900	C₄	—	6	1	no	—
901	C₄	—	6	1	no	—
902	C₄	—	6	1	no	—
903	C₄	—	6	1	no	—
904	C₄	—	6	1	no	—
905	C₄	—	6	1	no	—
906	C₄	—	6	1	no	—
907	C₄	—	6	1	no	—
908	C₄	—	6	1	no	—
909	C₄	—	6	1	no	—
910	C₃	#3564	1	1	yes	characteristic, complemented, Sylow
911	C₂	—	4	1	no	—
912	C₂	—	6	2	no	—
913	C₂	—	12	1	no	—
914	C₂	—	12	1	no	—
915	C₂	—	12	1	no	—
916	C₂	#5964	1	1	yes	characteristic
917	C₂	D₃×2₋¹⁺⁴	1	1	yes	characteristic
918	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#541	C₂
prime radical	#5704	C₂
hypercenter	#541	D₃
hypocenter	C₃	#3564
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. C₃×#541	C₂	semidirect
2. #5735	C₂	semidirect
3. #5730	C₂	semidirect
4. #5712	C₂	semidirect
5. #5710	C₂	semidirect
6. #5708	C₂	semidirect
7. #5705	C₂	semidirect
8. #5705	C₂	semidirect
10. D₃×#126	C₂	semidirect
11. #5701	C₂	semidirect
12. #5699	C₂	semidirect
13. #5696	C₂	semidirect
14. #5696	C₂	semidirect
15. #5694	C₂	semidirect
16. #5693	C₂	semidirect
17. #5692	C₂	semidirect
18. #5692	C₂	semidirect
19. #5691	C₂	semidirect
20. #5690	C₂	semidirect
21. #5689	C₂	semidirect
22. #5646	C₂	semidirect
23. #5638	C₂	semidirect
24. #5637	C₂	semidirect
25. #5634	C₂	semidirect
26. #5584	C₂	semidirect
27. #5582	C₂	semidirect
28. #5581	C₂	semidirect
29. #5578	C₂	semidirect
30. #5533	C₂	semidirect
31. #5527	C₂	semidirect
33. C₃×C₄⋊Q₈	C₂²	semidirect
38. C₃×#125	C₂²	semidirect
39. C₃×#125	C₂²	semidirect
40. C₃×#125	C₂²	semidirect
41. C₃×#125	C₂²	semidirect
42. C₃×#125	C₂²	semidirect
45. C₃×C₄×Q₈	C₂²	semidirect
46. C₃×C₄×Q₈	C₂²	semidirect
52. #946	C₂²	semidirect
53. #946	C₂²	semidirect
54. #946	C₂²	semidirect
55. #944	C₂²	semidirect
67. #898	C₂²	semidirect
68. #898	C₂²	semidirect
69. #898	C₂²	semidirect
70. #898	C₂²	semidirect
71. #898	C₂²	semidirect
76. #897	C₂²	semidirect
77. #897	C₂²	semidirect
78. #897	C₂²	semidirect
87. #896	C₂²	semidirect
88. #896	C₂²	semidirect
89. #896	C₂²	semidirect
90. #896	C₂²	semidirect
102. #894	C₂²	semidirect
103. #894	C₂²	semidirect
108. #893	C₂²	semidirect
112. #892	C₂²	semidirect
113. #892	C₂²	semidirect
114. #892	C₂²	semidirect
118. D₃×C₄⋊C₄	C₂²	semidirect
119. D₃×C₄⋊C₄	C₂²	semidirect
120. #890	C₂²	semidirect
121. #890	C₂²	semidirect
122. #890	C₂²	semidirect
123. #890	C₂²	semidirect
124. #889	C₂²	semidirect
125. #889	C₂²	semidirect
126. #889	C₂²	semidirect
127. #889	C₂²	semidirect
128. #889	C₂²	semidirect
129. #889	C₂²	semidirect
130. #889	C₂²	semidirect
131. #889	C₂²	semidirect
132. #889	C₂²	semidirect
133. #888	C₂²	semidirect
134. #888	C₂²	semidirect
135. #888	C₂²	semidirect
136. #888	C₂²	semidirect
137. #888	C₂²	semidirect
138. #887	C₂²	semidirect
139. #887	C₂²	semidirect
166. #876	C₂²	semidirect
167. #876	C₂²	semidirect
168. #876	C₂²	semidirect
171. #875	C₂²	semidirect
179. #872	C₂²	semidirect
181. #870	C₂²	semidirect
182. #869	C₂²	semidirect
183. C₄×Dic₆	C₂²	semidirect
184. C₄×Dic₆	C₂²	semidirect
185. C₄×Dic₆	C₂²	semidirect
186. C₄×Dic₆	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
211. #541	D₃	semidirect
381. C₄⋊Q₈	C₂×D₃	semidirect
422. #125	C₂×D₃	semidirect
423. #125	C₂×D₃	semidirect
424. #125	C₂×D₃	semidirect
425. #125	C₂×D₃	semidirect
426. #125	C₂×D₃	semidirect
493. C₄×Q₈	C₂×D₃	semidirect
494. C₄×Q₈	C₂×D₃	semidirect
910. C₃	#3564	semidirect

Maximal subgroups

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

subgroup	index
C₃×#541	2
#5735	2
#5730	2
#5712	2
#5710	2
#5708	2
#5705	2
#5704	2
D₃×#126	2
#5701	2
#5699	2
#5696	2
#5694	2
#5693	2
#5692	2
#5691	2
#5690	2
#5689	2
#5646	2
#5638	2
#5637	2
#5634	2
#5584	2
#5582	2
#5581	2
#5578	2
#5533	2
#5527	2
#3564	3