Subgroups — #87096

Order 384.

1032 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#562	C₂	1	1	yes	maximal, characteristic, complemented
2	#5696	C₂	1	1	yes	maximal, characteristic, complemented
3	#5690	C₂	1	1	yes	maximal, characteristic, complemented
4	#5678	C₂	1	1	yes	maximal, characteristic, complemented
5	#5677	C₂	1	1	yes	maximal, characteristic, complemented
6	#5671	C₂	1	1	yes	maximal, characteristic, complemented
7	#5669	C₂	1	1	yes	maximal, characteristic, complemented
8	#5665	C₂	1	1	yes	maximal, characteristic, complemented
9	#5661	C₂	1	1	yes	maximal, characteristic, complemented
10	#5661	C₂	1	1	yes	maximal, characteristic, complemented
11	#5657	C₂	1	1	yes	maximal, characteristic, complemented
12	#5656	C₂	1	1	yes	maximal, characteristic, complemented
13	#5651	C₂	1	1	yes	maximal, characteristic, complemented
14	#5650	C₂	1	1	yes	maximal, characteristic, complemented
15	#5648	C₂	1	1	yes	maximal, characteristic, complemented
16	#5646	C₂	1	1	yes	maximal, characteristic, complemented
17	#5643	C₂	1	1	yes	maximal, characteristic, complemented
18	#5640	C₂	1	1	yes	maximal, characteristic, complemented
19	#5638	C₂	1	1	yes	maximal, characteristic, complemented
20	#5636	C₂	1	1	yes	maximal, characteristic, complemented
21	#5635	C₂	1	1	yes	maximal, characteristic, complemented
22	#5632	C₂	1	1	yes	maximal, characteristic, complemented
23	D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	#5621	C₂	1	1	yes	maximal, characteristic, complemented
25	#5614	C₂	1	1	yes	maximal, characteristic, complemented
26	#5613	C₂	1	1	yes	maximal, characteristic, complemented
27	#5613	C₂	1	1	yes	maximal, characteristic, complemented
28	#5611	C₂	1	1	yes	maximal, characteristic, complemented
29	#5606	C₂	1	1	yes	maximal, characteristic, complemented
30	#5598	C₂	1	1	yes	maximal, characteristic, complemented
31	#5597	C₂	1	1	yes	maximal, characteristic, complemented
32	#3541	—	3	1	no	maximal, Sylow
33	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic
34	C₂×#237	C₂²	1	1	yes	characteristic
35	C₂×#237	C₂²	1	1	yes	characteristic
36	C₂×#237	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
38	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
39	C₃×#125	C₂²	1	1	yes	characteristic, complemented
40	C₃×#124	C₂²	1	1	yes	characteristic
41	C₃×#124	C₂²	1	1	yes	characteristic, complemented
42	C₃×#123	C₂²	1	1	yes	characteristic
43	C₃×#123	C₂²	1	1	yes	characteristic
44	C₃×#123	C₂²	1	1	yes	characteristic, complemented
45	C₃×#123	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₃×#121	C₂²	1	1	yes	characteristic
51	C₃×#121	C₂²	1	1	yes	characteristic
52	C₃×#121	C₂²	1	1	yes	characteristic
53	C₃×#121	C₂²	1	1	yes	characteristic, complemented
54	#947	C₂²	1	1	yes	characteristic
55	#946	C₂²	1	1	yes	characteristic
56	#946	C₂²	1	1	yes	characteristic
57	#946	C₂²	1	1	yes	characteristic, complemented
58	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
59	#944	C₂²	1	1	yes	characteristic, complemented
60	#944	C₂²	1	1	yes	characteristic, complemented
61	#939	C₂²	1	1	yes	characteristic
62	#939	C₂²	1	1	yes	characteristic
63	#939	C₂²	1	1	yes	characteristic
64	#939	C₂²	1	1	yes	characteristic, complemented
65	#939	C₂²	1	1	yes	characteristic, complemented
66	#938	C₂²	1	1	yes	characteristic
67	#938	C₂²	1	1	yes	characteristic
68	#938	C₂²	1	1	yes	characteristic
69	#938	C₂²	1	1	yes	characteristic
70	#937	C₂²	1	1	yes	characteristic
71	#937	C₂²	1	1	yes	characteristic
72	#937	C₂²	1	1	yes	characteristic
73	#936	C₂²	1	1	yes	characteristic
74	#936	C₂²	1	1	yes	characteristic
75	#935	C₂²	1	1	yes	characteristic
76	#935	C₂²	1	1	yes	characteristic
77	#935	C₂²	1	1	yes	characteristic, complemented
78	#935	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₃	C₂²	1	1	yes	characteristic
80	D₄×Dic₃	C₂²	1	1	yes	characteristic
81	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
82	#930	C₂²	1	1	yes	characteristic
83	#929	C₂²	1	1	yes	characteristic
84	#929	C₂²	1	1	yes	characteristic
85	#929	C₂²	1	1	yes	characteristic
86	C₄×#67	C₂²	1	1	yes	characteristic
87	C₄×#67	C₂²	1	1	yes	characteristic
88	C₄×#67	C₂²	1	1	yes	characteristic
89	C₄×#67	C₂²	1	1	yes	characteristic, complemented
90	C₄×#67	C₂²	1	1	yes	characteristic, complemented
91	#926	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
93	#924	C₂²	1	1	yes	characteristic
94	#924	C₂²	1	1	yes	characteristic
95	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	#898	C₂²	1	1	yes	characteristic
97	#898	C₂²	1	1	yes	characteristic
98	#898	C₂²	1	1	yes	characteristic
99	#898	C₂²	1	1	yes	characteristic, complemented
100	#898	C₂²	1	1	yes	characteristic, complemented
101	#897	C₂²	1	1	yes	characteristic
102	#897	C₂²	1	1	yes	characteristic
103	#897	C₂²	1	1	yes	characteristic
104	#897	C₂²	1	1	yes	characteristic, complemented
105	#896	C₂²	1	1	yes	characteristic
106	#896	C₂²	1	1	yes	characteristic
107	#896	C₂²	1	1	yes	characteristic
108	#896	C₂²	1	1	yes	characteristic
109	#896	C₂²	1	1	yes	characteristic
110	#896	C₂²	1	1	yes	characteristic
111	#896	C₂²	1	1	yes	characteristic, complemented
112	#896	C₂²	1	1	yes	characteristic, complemented
113	#894	C₂²	1	1	yes	characteristic
114	#893	C₂²	1	1	yes	characteristic
115	#893	C₂²	1	1	yes	characteristic
116	#893	C₂²	1	1	yes	characteristic
117	#892	C₂²	1	1	yes	characteristic
118	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	D₃×C₄⋊C₄	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	#888	C₂²	1	1	yes	characteristic, complemented
131	#888	C₂²	1	1	yes	characteristic, complemented
132	#888	C₂²	1	1	yes	characteristic, complemented
133	#888	C₂²	1	1	yes	characteristic, complemented
134	#887	C₂²	1	1	yes	characteristic, complemented
135	#887	C₂²	1	1	yes	characteristic, complemented
136	#886	C₂²	1	1	yes	characteristic
137	#885	C₂²	1	1	yes	characteristic
138	#885	C₂²	1	1	yes	characteristic
139	#885	C₂²	1	1	yes	characteristic
140	#885	C₂²	1	1	yes	characteristic
141	#885	C₂²	1	1	yes	characteristic, complemented
142	#885	C₂²	1	1	yes	characteristic, complemented
143	#884	C₂²	1	1	yes	characteristic
144	#884	C₂²	1	1	yes	characteristic
145	#884	C₂²	1	1	yes	characteristic
146	#884	C₂²	1	1	yes	characteristic
147	#884	C₂²	1	1	yes	characteristic
148	#883	C₂²	1	1	yes	characteristic
149	#883	C₂²	1	1	yes	characteristic
150	#883	C₂²	1	1	yes	characteristic
151	#883	C₂²	1	1	yes	characteristic, complemented
152	#883	C₂²	1	1	yes	characteristic, complemented
153	#882	C₂²	1	1	yes	characteristic
154	#67⋊C₄	C₂²	1	1	yes	characteristic
155	#67⋊C₄	C₂²	1	1	yes	characteristic
156	#67⋊C₄	C₂²	1	1	yes	characteristic
157	#67⋊C₄	C₂²	1	1	yes	characteristic
158	#67⋊C₄	C₂²	1	1	yes	characteristic
159	#67⋊C₄	C₂²	1	1	yes	characteristic
160	#67⋊C₄	C₂²	1	1	yes	characteristic
161	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
162	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
163	#879	C₂²	1	1	yes	characteristic
164	#879	C₂²	1	1	yes	characteristic
165	#879	C₂²	1	1	yes	characteristic
166	#879	C₂²	1	1	yes	characteristic
167	#879	C₂²	1	1	yes	characteristic, complemented
168	#879	C₂²	1	1	yes	characteristic, complemented
169	#879	C₂²	1	1	yes	characteristic, complemented
170	#879	C₂²	1	1	yes	characteristic, complemented
171	#878	C₂²	1	1	yes	characteristic
172	#878	C₂²	1	1	yes	characteristic
173	#878	C₂²	1	1	yes	characteristic, complemented
174	#878	C₂²	1	1	yes	characteristic, complemented
175	#878	C₂²	1	1	yes	characteristic, complemented
176	#878	C₂²	1	1	yes	characteristic, complemented
177	#878	C₂²	1	1	yes	characteristic, complemented
178	#878	C₂²	1	1	yes	characteristic, complemented
179	#878	C₂²	1	1	yes	characteristic, complemented
180	#878	C₂²	1	1	yes	characteristic, complemented
181	#877	C₂²	1	1	yes	characteristic
182	#877	C₂²	1	1	yes	characteristic, complemented
183	#877	C₂²	1	1	yes	characteristic, complemented
184	#876	C₂²	1	1	yes	characteristic
185	C₄×D₁₂	C₂²	1	1	yes	characteristic
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	#562	—	3	1	no	—
191	#562	D₃	1	1	yes	characteristic, complemented
192	#556	—	3	1	no	—
193	#554	—	3	1	no	—
194	#554	—	3	1	no	—
195	#554	—	3	1	no	—
196	#553	—	3	1	no	—
197	#553	—	3	1	no	—
198	#553	—	3	1	no	—
199	#552	—	3	1	no	—
200	D₄×Q₈	—	3	1	no	—
201	#548	—	3	1	no	—
202	#548	—	3	1	no	—
203	#547	—	3	1	no	—
204	#542	—	3	1	no	—
205	#542	—	3	1	no	—
206	#542	—	3	1	no	—
207	#541	—	3	1	no	—
208	#539	—	3	1	no	—
209	#539	—	3	1	no	—
210	#538	—	3	1	no	—
211	#538	—	3	1	no	—
212	#538	—	3	1	no	—
213	#538	—	3	1	no	—
214	#537	—	3	1	no	—
215	#536	—	3	1	no	—
216	#525	—	3	1	no	—
217	#525	—	3	1	no	—
218	C₂×C₂²⋊Q₈	—	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	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
232	C₂×#67	C₂³	1	1	yes	characteristic
233	C₂×#67	C₂³	1	1	yes	characteristic
234	C₂×#67	C₂³	1	1	yes	characteristic
235	C₂×#67	C₂³	1	1	yes	characteristic
236	C₂×#67	C₂³	1	1	yes	characteristic
237	C₂×#67	C₂³	1	1	yes	characteristic
238	C₂×#67	C₂³	1	1	yes	characteristic
239	C₂×#67	C₂³	1	1	yes	characteristic
240	C₂×#67	C₂³	1	1	yes	characteristic
241	C₂×#67	C₂³	1	1	yes	characteristic
242	C₂²×Dic₃	C₂³	1	1	yes	characteristic
243	C₂²×Dic₃	C₂³	1	1	yes	characteristic
244	C₂²×Dic₃	C₂³	1	1	yes	characteristic
245	C₂²×Dic₃	C₂³	1	1	yes	characteristic
246	C₂²×Dic₃	C₂³	1	1	yes	characteristic
247	C₂²×Dic₃	C₂³	1	1	yes	characteristic
248	C₂²×Dic₃	C₂³	1	1	yes	characteristic
249	D₃×Q₈	—	4	2	no	—
250	#237	—	4	2	no	—
251	#237	—	4	2	no	—
252	#237	—	4	2	no	—
253	C₂×D₁₂	C₂³	1	1	yes	characteristic
254	C₂×D₁₂	C₂³	1	1	yes	characteristic
255	C₂×C₄×D₃	—	4	2	no	—
256	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
258	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
259	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
260	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
261	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
262	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
263	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
264	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
265	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
266	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
267	C₂×Dic₆	—	4	2	no	—
268	C₂×Dic₆	C₂³	1	1	yes	characteristic
269	C₂×Dic₆	C₂³	1	1	yes	characteristic
270	C₂×Dic₆	C₂³	1	1	yes	characteristic
271	C₂×Dic₆	C₂³	1	1	yes	characteristic
272	C₂×Dic₆	C₂³	1	1	yes	characteristic
273	C₂×Dic₆	C₂³	1	1	yes	characteristic
274	C₂×Dic₆	C₂³	1	1	yes	characteristic
275	C₂×Dic₆	C₂³	1	1	yes	characteristic
276	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
281	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
282	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
283	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
289	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
290	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
291	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
292	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
293	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
294	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
295	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
296	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
297	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
298	C₃×C₄²	C₂³	1	1	yes	characteristic
299	#217	C₂³	1	1	yes	characteristic
300	#217	C₂³	1	1	yes	characteristic
301	#217	C₂³	1	1	yes	characteristic
302	#217	C₂³	1	1	yes	characteristic
303	#217	C₂³	1	1	yes	characteristic
304	#217	C₂³	1	1	yes	characteristic
305	#217	C₂³	1	1	yes	characteristic
306	#217	C₂³	1	1	yes	characteristic
307	#217	C₂³	1	1	yes	characteristic
308	#217	C₂³	1	1	yes	characteristic
309	#217	C₂³	1	1	yes	characteristic
310	#217	C₂³	1	1	yes	characteristic
311	#217	C₂³	1	1	yes	characteristic
312	#217	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	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
321	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
322	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
323	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
324	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
325	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
326	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
327	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
328	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
329	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
330	(C₂×D₃)⋊C₄	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	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
335	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
336	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
337	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
338	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
339	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
340	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
341	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
342	C₄⋊Dic₃	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	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
365	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
366	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
367	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
368	Dic₃⋊C₄	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×Dic₃	C₂³	1	1	yes	characteristic
375	C₄×Dic₃	C₂³	1	1	yes	characteristic
376	C₄×Dic₃	C₂³	1	1	yes	characteristic
377	C₄×Dic₃	C₂³	1	1	yes	characteristic
378	C₄×Dic₃	C₂³	1	1	yes	characteristic
379	C₄×Dic₃	C₂³	1	1	yes	characteristic
380	C₂×#41	—	3	1	no	—
381	C₂×#41	—	3	1	no	—
382	C₂×#41	—	3	1	no	—
383	C₂²×Q₈	—	3	1	no	—
384	C₂²×Q₈	—	3	1	no	—
385	C₂³×C₄	—	3	1	no	—
386	C₄⋊Q₈	—	3	1	no	—
387	C₄⋊Q₈	—	3	1	no	—
388	C₄⋊Q₈	—	3	1	no	—
389	C₄⋊Q₈	—	3	1	no	—
390	C₄⋊Q₈	—	3	1	no	—
391	C₄⋊Q₈	—	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	—	3	1	no	—
405	#126	—	3	1	no	—
406	#125	—	3	1	no	—
407	#125	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic, complemented
415	#124	—	3	1	no	—
416	#124	—	3	1	no	—
417	#124	—	3	1	no	—
418	#124	—	3	1	no	—
419	#124	—	3	1	no	—
420	#124	—	3	1	no	—
421	#124	—	3	1	no	—
422	#124	—	3	1	no	—
423	#124	—	3	1	no	—
424	#124	C₂×D₃	1	1	yes	characteristic
425	#124	C₂×D₃	1	1	yes	characteristic, complemented
426	#123	—	3	1	no	—
427	#123	—	3	1	no	—
428	#123	—	3	1	no	—
429	#123	—	3	1	no	—
430	#123	—	3	1	no	—
431	#123	—	3	1	no	—
432	#123	—	3	1	no	—
433	#123	—	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	C₂×D₃	1	1	yes	characteristic
441	#123	C₂×D₃	1	1	yes	characteristic
442	#123	C₂×D₃	1	1	yes	characteristic, complemented
443	#123	C₂×D₃	1	1	yes	characteristic, complemented
444	C₂²⋊Q₈	—	3	1	no	—
445	C₂²⋊Q₈	—	3	1	no	—
446	C₂²⋊Q₈	—	3	1	no	—
447	C₂²⋊Q₈	—	3	1	no	—
448	C₂²⋊Q₈	—	3	1	no	—
449	C₂²⋊Q₈	—	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	C₂×D₃	1	1	yes	characteristic
472	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
473	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
474	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
475	#121	—	3	1	no	—
476	#121	—	3	1	no	—
477	#121	—	3	1	no	—
478	#121	—	3	1	no	—
479	#121	—	3	1	no	—
480	#121	—	3	1	no	—
481	#121	—	3	1	no	—
482	#121	—	3	1	no	—
483	#121	—	3	1	no	—
484	#121	—	3	1	no	—
485	#121	—	3	1	no	—
486	#121	—	3	1	no	—
487	#121	—	3	1	no	—
488	#121	—	3	1	no	—
489	#121	—	3	1	no	—
490	#121	C₂×D₃	1	1	yes	characteristic
491	#121	C₂×D₃	1	1	yes	characteristic
492	#121	C₂×D₃	1	1	yes	characteristic
493	#121	C₂×D₃	1	1	yes	characteristic, complemented
494	#120	—	3	1	no	—
495	#120	—	3	1	no	—
496	#120	—	3	1	no	—
497	#120	—	3	1	no	—
498	C₄×Q₈	—	3	1	no	—
499	C₄×Q₈	—	3	1	no	—
500	C₄×Q₈	—	3	1	no	—
501	C₄×Q₈	—	3	1	no	—
502	C₄×Q₈	—	3	1	no	—
503	C₄×D₄	—	3	1	no	—
504	C₄×D₄	—	3	1	no	—
505	C₄×D₄	—	3	1	no	—
506	C₄×D₄	—	3	1	no	—
507	C₄×D₄	—	3	1	no	—
508	C₄×D₄	—	3	1	no	—
509	C₄×D₄	—	3	1	no	—
510	C₄×D₄	—	3	1	no	—
511	C₄×D₄	—	3	1	no	—
512	C₄×D₄	—	3	1	no	—
513	C₄×D₄	—	3	1	no	—
514	C₄×D₄	—	3	1	no	—
515	C₄×D₄	—	3	1	no	—
516	C₄×D₄	—	3	1	no	—
517	C₄×D₄	—	3	1	no	—
518	C₄×D₄	—	3	1	no	—
519	C₄×D₄	—	3	1	no	—
520	C₄×D₄	—	3	1	no	—
521	C₄×D₄	—	3	1	no	—
522	#117	—	3	1	no	—
523	#117	—	3	1	no	—
524	#117	—	3	1	no	—
525	#117	—	3	1	no	—
526	#117	—	3	1	no	—
527	C₂×C₄⋊C₄	—	3	1	no	—
528	C₂×C₄⋊C₄	—	3	1	no	—
529	C₂×C₄⋊C₄	—	3	1	no	—
530	C₂×C₄⋊C₄	—	3	1	no	—
531	C₂×C₄⋊C₄	—	3	1	no	—
532	C₂×C₄⋊C₄	—	3	1	no	—
533	C₂×C₂²⋊C₄	—	3	1	no	—
534	C₂×C₂²⋊C₄	—	3	1	no	—
535	C₂³×C₃	C₂⁴	1	1	yes	characteristic
536	C₂³×C₃	C₂⁴	1	1	yes	characteristic
537	C₂³×C₃	C₂⁴	1	1	yes	characteristic
538	C₂³×C₃	C₂⁴	1	1	yes	characteristic
539	C₂²×D₃	—	2	2	no	—
540	C₂²×D₃	—	4	1	no	—
541	C₂²×D₃	—	4	1	no	—
542	C₂²×D₃	C₂⁴	1	1	yes	characteristic
543	C₂²×D₃	C₂⁴	1	1	yes	characteristic
544	C₂²×D₃	C₂⁴	1	1	yes	characteristic
545	C₃×Q₈	—	4	1	no	—
546	C₃×Q₈	—	4	1	no	—
547	C₃×D₄	—	4	1	no	—
548	C₃×D₄	—	4	1	no	—
549	C₃×D₄	—	4	1	no	—
550	C₃×D₄	—	4	1	no	—
551	C₃×D₄	—	4	1	no	—
552	C₃×D₄	—	4	1	no	—
553	C₂×C₃×C₄	—	4	1	no	—
554	C₂×C₃×C₄	—	4	1	no	—
555	C₂×C₃×C₄	—	4	1	no	—
556	C₂×C₃×C₄	—	4	1	no	—
557	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
558	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
559	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
560	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
561	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
563	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
564	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
565	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
566	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
567	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
568	#67	—	2	2	no	—
569	#67	—	2	2	no	—
570	#67	—	2	2	no	—
571	#67	—	2	2	no	—
572	#67	—	4	1	no	—
573	#67	—	4	1	no	—
574	#67	—	4	1	no	—
575	#67	—	4	1	no	—
576	#67	—	4	1	no	—
577	#67	—	4	1	no	—
578	C₂×Dic₃	—	2	2	no	—
579	C₂×Dic₃	—	2	2	no	—
580	C₂×Dic₃	—	2	2	no	—
581	C₂×Dic₃	—	4	1	no	—
582	C₂×Dic₃	—	4	1	no	—
583	C₂×Dic₃	—	4	1	no	—
584	C₂×Dic₃	—	4	1	no	—
585	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
586	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
587	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
588	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
589	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
590	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
591	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
592	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
593	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
594	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
595	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
596	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
597	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
598	D₁₂	—	2	2	no	—
599	D₁₂	—	4	1	no	—
600	C₄×D₃	—	2	2	no	—
601	C₄×D₃	—	2	2	no	—
602	C₄×D₃	—	4	1	no	—
603	C₄×D₃	—	4	1	no	—
604	C₄×D₃	—	4	1	no	—
605	C₄×D₃	—	4	1	no	—
606	C₄×D₃	—	4	1	no	—
607	C₄×D₃	—	4	1	no	—
608	C₄×D₃	—	4	1	no	—
609	C₄×D₃	—	4	1	no	—
610	C₄×D₃	—	4	1	no	—
611	Dic₆	—	2	2	no	—
612	Dic₆	—	2	2	no	—
613	Dic₆	—	2	2	no	—
614	Dic₆	—	4	1	no	—
615	Dic₆	—	4	1	no	—
616	Dic₆	—	4	1	no	—
617	Dic₆	—	4	1	no	—
618	Dic₆	—	4	1	no	—
619	C₂⁴	—	3	1	no	—
620	#41	—	12	2	no	—
621	#41	—	12	2	no	—
622	#41	—	12	2	no	—
623	C₂×Q₈	—	3	1	no	—
624	C₂×Q₈	—	3	1	no	—
625	C₂×Q₈	—	3	1	no	—
626	C₂×Q₈	—	3	1	no	—
627	C₂×Q₈	—	3	1	no	—
628	C₂×Q₈	—	3	1	no	—
629	C₂×Q₈	—	3	1	no	—
630	C₂×Q₈	—	3	1	no	—
631	C₂×Q₈	—	12	2	no	—
632	C₂×Q₈	—	12	2	no	—
633	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
634	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
635	C₂×D₄	—	3	1	no	—
636	C₂×D₄	—	3	1	no	—
637	C₂×D₄	—	3	1	no	—
638	C₂×D₄	—	3	1	no	—
639	C₂×D₄	—	3	1	no	—
640	C₂×D₄	—	3	1	no	—
641	C₂×D₄	—	3	1	no	—
642	C₂×D₄	—	3	1	no	—
643	C₂×D₄	—	3	1	no	—
644	C₂×D₄	—	3	1	no	—
645	C₂×D₄	—	3	1	no	—
646	C₂×D₄	—	3	1	no	—
647	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
648	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
649	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
650	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
651	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
652	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
653	C₂²×C₄	—	3	1	no	—
654	C₂²×C₄	—	3	1	no	—
655	C₂²×C₄	—	3	1	no	—
656	C₂²×C₄	—	3	1	no	—
657	C₂²×C₄	—	3	1	no	—
658	C₂²×C₄	—	3	1	no	—
659	C₂²×C₄	—	3	1	no	—
660	C₂²×C₄	—	3	1	no	—
661	C₂²×C₄	—	3	1	no	—
662	C₂²×C₄	—	3	1	no	—
663	C₂²×C₄	—	3	1	no	—
664	C₂²×C₄	—	3	1	no	—
665	C₂²×C₄	—	3	1	no	—
666	C₂²×C₄	—	3	1	no	—
667	C₂²×C₄	—	3	1	no	—
668	C₂²×C₄	—	3	1	no	—
669	C₂²×C₄	—	3	1	no	—
670	C₂²×C₄	—	3	1	no	—
671	C₂²×C₄	—	12	2	no	—
672	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
673	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
674	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
675	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
676	C₄⋊C₄	—	3	1	no	—
677	C₄⋊C₄	—	3	1	no	—
678	C₄⋊C₄	—	3	1	no	—
679	C₄⋊C₄	—	3	1	no	—
680	C₄⋊C₄	—	3	1	no	—
681	C₄⋊C₄	—	3	1	no	—
682	C₄⋊C₄	—	3	1	no	—
683	C₄⋊C₄	—	3	1	no	—
684	C₄⋊C₄	—	3	1	no	—
685	C₄⋊C₄	—	3	1	no	—
686	C₄⋊C₄	—	3	1	no	—
687	C₄⋊C₄	—	3	1	no	—
688	C₄⋊C₄	—	3	1	no	—
689	C₄⋊C₄	—	3	1	no	—
690	C₄⋊C₄	—	3	1	no	—
691	C₄⋊C₄	—	3	1	no	—
692	C₄⋊C₄	—	3	1	no	—
693	C₄⋊C₄	—	3	1	no	—
694	C₄⋊C₄	—	3	1	no	—
695	C₄⋊C₄	—	3	1	no	—
696	C₄⋊C₄	—	3	1	no	—
697	C₄⋊C₄	—	3	1	no	—
698	C₄⋊C₄	—	3	1	no	—
699	C₄⋊C₄	—	3	1	no	—
700	C₄⋊C₄	—	3	1	no	—
701	C₄⋊C₄	—	3	1	no	—
702	C₄⋊C₄	—	3	1	no	—
703	C₄⋊C₄	—	3	1	no	—
704	C₄⋊C₄	—	3	1	no	—
705	C₄⋊C₄	—	3	1	no	—
706	C₄⋊C₄	—	3	1	no	—
707	C₄⋊C₄	—	3	1	no	—
708	C₄⋊C₄	—	3	1	no	—
709	C₄⋊C₄	—	3	1	no	—
710	C₄⋊C₄	—	3	1	no	—
711	C₄⋊C₄	—	3	1	no	—
712	C₄⋊C₄	—	3	1	no	—
713	C₄⋊C₄	—	3	1	no	—
714	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
715	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
716	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
717	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
718	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
719	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
721	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
722	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
724	C₂²⋊C₄	—	3	1	no	—
725	C₂²⋊C₄	—	3	1	no	—
726	C₂²⋊C₄	—	3	1	no	—
727	C₂²⋊C₄	—	3	1	no	—
728	C₂²⋊C₄	—	3	1	no	—
729	C₂²⋊C₄	—	3	1	no	—
730	C₂²⋊C₄	—	3	1	no	—
731	C₂²⋊C₄	—	3	1	no	—
732	C₂²⋊C₄	—	3	1	no	—
733	C₂²⋊C₄	—	3	1	no	—
734	C₂²⋊C₄	—	3	1	no	—
735	C₂²⋊C₄	—	3	1	no	—
736	C₂²⋊C₄	—	3	1	no	—
737	C₂²⋊C₄	—	3	1	no	—
738	C₂²⋊C₄	—	3	1	no	—
739	C₂²⋊C₄	—	3	1	no	—
740	C₂²⋊C₄	—	3	1	no	—
741	C₂²⋊C₄	—	3	1	no	—
742	C₂²⋊C₄	—	3	1	no	—
743	C₂²⋊C₄	—	3	1	no	—
744	C₂²⋊C₄	—	3	1	no	—
745	C₂²⋊C₄	—	3	1	no	—
746	C₂²⋊C₄	—	3	1	no	—
747	C₂²⋊C₄	—	3	1	no	—
748	C₂²⋊C₄	—	3	1	no	—
749	C₂²⋊C₄	—	3	1	no	—
750	C₂²⋊C₄	—	3	1	no	—
751	C₂²⋊C₄	—	3	1	no	—
752	C₂²⋊C₄	—	3	1	no	—
753	C₂²⋊C₄	—	3	1	no	—
754	C₂²⋊C₄	—	3	1	no	—
755	C₂²⋊C₄	—	3	1	no	—
756	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
757	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
758	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
759	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
760	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
761	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
762	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
763	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
764	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
765	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
766	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
767	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
768	C₄²	—	3	1	no	—
769	C₄²	—	3	1	no	—
770	C₄²	—	3	1	no	—
771	C₄²	—	3	1	no	—
772	C₄²	—	3	1	no	—
773	C₄²	—	3	1	no	—
774	C₄²	—	3	1	no	—
775	C₄²	—	3	1	no	—
776	C₄²	—	3	1	no	—
777	C₄²	—	3	1	no	—
778	C₄²	—	3	1	no	—
779	C₄²	C₂²×D₃	1	1	yes	characteristic
780	C₂²×C₃	—	2	1	no	—
781	C₂²×C₃	—	2	1	no	—
782	C₂²×C₃	—	2	1	no	—
783	C₂²×C₃	—	2	1	no	—
784	C₂²×C₃	—	2	1	no	—
785	C₂²×C₃	—	2	1	no	—
786	C₂²×C₃	—	2	1	no	—
787	C₂²×C₃	—	2	1	no	—
788	C₂²×C₃	—	2	1	no	—
789	C₂²×C₃	—	2	1	no	—
790	C₂²×C₃	—	2	1	no	—
791	C₂²×C₃	—	2	1	no	—
792	C₂²×C₃	C₂⁵	1	1	yes	characteristic
793	C₂×D₃	—	2	1	no	—
794	C₂×D₃	—	2	1	no	—
795	C₂×D₃	—	2	1	no	—
796	C₂×D₃	—	2	1	no	—
797	C₂×D₃	—	2	1	no	—
798	C₂×D₃	—	2	1	no	—
799	C₂×D₃	—	2	1	no	—
800	C₂×D₃	—	2	1	no	—
801	C₂×D₃	—	4	4	no	—
802	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
803	C₃×C₄	—	2	1	no	—
804	C₃×C₄	—	2	1	no	—
805	C₃×C₄	—	2	1	no	—
806	C₃×C₄	—	2	1	no	—
807	C₃×C₄	—	2	1	no	—
808	C₃×C₄	—	2	1	no	—
809	C₃×C₄	—	2	1	no	—
810	C₃×C₄	—	2	1	no	—
811	C₃×C₄	—	2	1	no	—
812	C₃×C₄	—	2	1	no	—
813	C₃×C₄	—	2	1	no	—
814	Dic₃	—	2	1	no	—
815	Dic₃	—	2	1	no	—
816	Dic₃	—	2	1	no	—
817	Dic₃	—	2	1	no	—
818	Dic₃	—	2	1	no	—
819	Dic₃	—	2	1	no	—
820	Dic₃	—	2	1	no	—
821	Dic₃	—	2	1	no	—
822	Dic₃	—	2	1	no	—
823	Dic₃	—	2	1	no	—
824	Dic₃	—	2	1	no	—
825	Dic₃	—	2	1	no	—
826	Dic₃	H(5,𝔽₂)	1	2	yes	—
827	C₂³	—	3	1	no	—
828	C₂³	—	3	1	no	—
829	C₂³	—	3	1	no	—
830	C₂³	—	6	2	no	—
831	C₂³	—	12	1	no	—
832	C₂³	—	12	1	no	—
833	C₂³	C₂³×D₃	1	1	yes	characteristic
834	C₂³	C₂³×D₃	1	1	yes	characteristic
835	C₂³	C₂³×D₃	1	1	yes	characteristic
836	C₂³	C₂³×D₃	1	1	yes	characteristic
837	Q₈	—	4	1	no	—
838	Q₈	—	4	1	no	—
839	Q₈	—	6	2	no	—
840	Q₈	—	6	2	no	—
841	Q₈	—	6	2	no	—
842	Q₈	—	12	1	no	—
843	Q₈	—	12	1	no	—
844	Q₈	—	12	1	no	—
845	Q₈	—	12	1	no	—
846	Q₈	—	12	1	no	—
847	D₄	—	4	1	no	—
848	D₄	—	4	1	no	—
849	D₄	—	4	1	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	D₄	—	4	1	no	—
853	D₄	—	6	2	no	—
854	D₄	—	6	2	no	—
855	D₄	—	6	2	no	—
856	D₄	—	6	2	no	—
857	D₄	—	6	2	no	—
858	D₄	—	12	1	no	—
859	D₄	—	12	1	no	—
860	D₄	—	12	1	no	—
861	D₄	—	12	1	no	—
862	D₄	—	12	1	no	—
863	D₄	—	12	1	no	—
864	D₄	—	12	1	no	—
865	C₂×C₄	—	3	1	no	—
866	C₂×C₄	—	3	1	no	—
867	C₂×C₄	—	3	1	no	—
868	C₂×C₄	—	3	1	no	—
869	C₂×C₄	—	3	1	no	—
870	C₂×C₄	—	3	1	no	—
871	C₂×C₄	—	3	1	no	—
872	C₂×C₄	—	3	1	no	—
873	C₂×C₄	—	3	1	no	—
874	C₂×C₄	—	3	1	no	—
875	C₂×C₄	—	3	1	no	—
876	C₂×C₄	—	3	1	no	—
877	C₂×C₄	—	3	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	6	2	no	—
883	C₂×C₄	—	6	2	no	—
884	C₂×C₄	—	6	2	no	—
885	C₂×C₄	—	6	2	no	—
886	C₂×C₄	—	6	2	no	—
887	C₂×C₄	—	12	1	no	—
888	C₂×C₄	—	12	1	no	—
889	C₂×C₄	—	12	1	no	—
890	C₂×C₄	—	12	1	no	—
891	C₂×C₄	—	12	1	no	—
892	C₂×C₄	—	12	1	no	—
893	C₂×C₄	—	12	1	no	—
894	C₂×C₄	—	12	1	no	—
895	C₂×C₄	—	12	1	no	—
896	C₂×C₄	—	12	1	no	—
897	C₂×C₄	—	12	1	no	—
898	C₂×C₄	—	12	1	no	—
899	C₂×C₄	—	12	1	no	—
900	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
908	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
909	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
910	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
911	C₂×C₃	—	4	1	no	—
912	C₂×C₃	—	4	1	no	—
913	C₂×C₃	—	4	1	no	—
914	C₂×C₃	—	4	1	no	—
915	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
916	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
917	C₂×C₃	#585	1	1	yes	characteristic
918	D₃	—	2	2	no	—
919	D₃	—	4	1	no	—
920	D₃	—	4	1	no	—
921	C₂²	—	2	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	3	2	no	—
934	C₂²	—	6	1	no	—
935	C₂²	—	6	1	no	—
936	C₂²	—	6	1	no	—
937	C₂²	—	6	1	no	—
938	C₂²	—	6	1	no	—
939	C₂²	—	6	1	no	—
940	C₂²	—	6	1	no	—
941	C₂²	—	6	1	no	—
942	C₂²	—	12	4	no	—
943	C₂²	C₂⁴×D₃	1	1	yes	characteristic
944	C₄	—	2	1	no	—
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	3	2	no	—
956	C₄	—	6	1	no	—
957	C₄	—	6	1	no	—
958	C₄	—	6	1	no	—
959	C₄	—	6	1	no	—
960	C₄	—	6	1	no	—
961	C₄	—	6	1	no	—
962	C₄	—	6	1	no	—
963	C₄	—	6	1	no	—
964	C₄	—	6	1	no	—
965	C₄	—	6	1	no	—
966	C₄	—	6	1	no	—
967	C₄	—	6	1	no	—
968	C₃	#3541	1	1	yes	characteristic, complemented, Sylow
969	C₂	—	4	1	no	—
970	C₂	—	4	1	no	—
971	C₂	—	4	1	no	—
972	C₂	—	4	1	no	—
973	C₂	—	6	2	no	—
974	C₂	—	12	1	no	—
975	C₂	—	12	1	no	—
976	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
977	C₂	#5966	1	1	yes	characteristic
978	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×#562	C₂
hypercenter	#562	D₃
hypocenter	C₃	#3541
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. C₃×#562	C₂	semidirect
2. #5696	C₂	semidirect
3. #5690	C₂	semidirect
4. #5678	C₂	semidirect
5. #5677	C₂	semidirect
6. #5671	C₂	semidirect
7. #5669	C₂	semidirect
8. #5665	C₂	semidirect
9. #5661	C₂	semidirect
10. #5661	C₂	semidirect
11. #5657	C₂	semidirect
12. #5656	C₂	semidirect
13. #5651	C₂	semidirect
14. #5650	C₂	semidirect
15. #5648	C₂	semidirect
16. #5646	C₂	semidirect
17. #5643	C₂	semidirect
18. #5640	C₂	semidirect
19. #5638	C₂	semidirect
20. #5636	C₂	semidirect
21. #5635	C₂	semidirect
22. #5632	C₂	semidirect
23. D₃×C₂²⋊Q₈	C₂	semidirect
24. #5621	C₂	semidirect
25. #5614	C₂	semidirect
26. #5613	C₂	semidirect
27. #5613	C₂	semidirect
28. #5611	C₂	semidirect
29. #5606	C₂	semidirect
30. #5598	C₂	semidirect
31. #5597	C₂	semidirect
36. C₂×#237	C₂²	semidirect
38. C₂²×Dic₆	C₂²	semidirect
39. C₃×#125	C₂²	semidirect
41. C₃×#124	C₂²	semidirect
44. C₃×#123	C₂²	semidirect
45. C₃×#123	C₂²	semidirect
47. C₃×C₂²⋊Q₈	C₂²	semidirect
48. C₃×C₂²⋊Q₈	C₂²	semidirect
49. C₃×C₂²⋊Q₈	C₂²	semidirect
53. C₃×#121	C₂²	semidirect
57. #946	C₂²	semidirect
58. Q₈×Dic₃	C₂²	semidirect
59. #944	C₂²	semidirect
60. #944	C₂²	semidirect
64. #939	C₂²	semidirect
65. #939	C₂²	semidirect
77. #935	C₂²	semidirect
78. #935	C₂²	semidirect
81. D₄×Dic₃	C₂²	semidirect
89. C₄×#67	C₂²	semidirect
90. C₄×#67	C₂²	semidirect
91. #926	C₂²	semidirect
92. C₂×C₄⋊Dic₃	C₂²	semidirect
95. C₂×Dic₃⋊C₄	C₂²	semidirect
99. #898	C₂²	semidirect
100. #898	C₂²	semidirect
104. #897	C₂²	semidirect
111. #896	C₂²	semidirect
112. #896	C₂²	semidirect
121. D₃×C₄⋊C₄	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. #888	C₂²	semidirect
131. #888	C₂²	semidirect
132. #888	C₂²	semidirect
133. #888	C₂²	semidirect
134. #887	C₂²	semidirect
135. #887	C₂²	semidirect
141. #885	C₂²	semidirect
142. #885	C₂²	semidirect
151. #883	C₂²	semidirect
152. #883	C₂²	semidirect
167. #879	C₂²	semidirect
168. #879	C₂²	semidirect
169. #879	C₂²	semidirect
170. #879	C₂²	semidirect
173. #878	C₂²	semidirect
174. #878	C₂²	semidirect
175. #878	C₂²	semidirect
176. #878	C₂²	semidirect
177. #878	C₂²	semidirect
178. #878	C₂²	semidirect
179. #878	C₂²	semidirect
180. #878	C₂²	semidirect
182. #877	C₂²	semidirect
183. #877	C₂²	semidirect
186. C₄×Dic₆	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
191. #562	D₃	semidirect
414. #125	C₂×D₃	semidirect
425. #124	C₂×D₃	semidirect
442. #123	C₂×D₃	semidirect
443. #123	C₂×D₃	semidirect
472. C₂²⋊Q₈	C₂×D₃	semidirect
473. C₂²⋊Q₈	C₂×D₃	semidirect
474. C₂²⋊Q₈	C₂×D₃	semidirect
493. #121	C₂×D₃	semidirect
968. C₃	#3541	semidirect

Maximal subgroups

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

subgroup	index
C₃×#562	2
#5696	2
#5690	2
#5678	2
#5677	2
#5671	2
#5669	2
#5665	2
#5661	2
#5657	2
#5656	2
#5651	2
#5650	2
#5648	2
#5646	2
#5643	2
#5640	2
#5638	2
#5636	2
#5635	2
#5632	2
D₃×C₂²⋊Q₈	2
#5621	2
#5614	2
#5613	2
#5611	2
#5606	2
#5598	2
#5597	2
#3541	3