Subgroups — #87095

Order 384.

1134 conjugacy classes of subgroups.

The subgroup lattice has 1044 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	#5692	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	#5676	C₂	1	1	yes	maximal, characteristic, complemented
7	#5669	C₂	1	1	yes	maximal, characteristic, complemented
8	#5667	C₂	1	1	yes	maximal, characteristic, complemented
9	#5662	C₂	1	1	yes	maximal, characteristic, complemented
10	#5660	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	#5655	C₂	1	1	yes	maximal, characteristic, complemented
14	#5654	C₂	1	1	yes	maximal, characteristic, complemented
15	#5654	C₂	1	1	yes	maximal, characteristic, complemented
16	#5647	C₂	1	1	yes	maximal, characteristic, complemented
17	#5636	C₂	1	1	yes	maximal, characteristic, complemented
18	#5634	C₂	1	1	yes	maximal, characteristic, complemented
19	#5634	C₂	1	1	yes	maximal, characteristic, complemented
20	#5633	C₂	1	1	yes	maximal, characteristic, complemented
21	#5631	C₂	1	1	yes	maximal, characteristic, complemented
22	#5629	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	#5612	C₂	1	1	yes	maximal, characteristic, complemented
26	#5610	C₂	1	1	yes	maximal, characteristic, complemented
27	#5610	C₂	1	1	yes	maximal, characteristic, complemented
28	#5608	C₂	1	1	yes	maximal, characteristic, complemented
29	#5608	C₂	1	1	yes	maximal, characteristic, complemented
30	D₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
31	#5597	C₂	1	1	yes	maximal, characteristic, complemented
32	#3536	—	3	1	no	maximal, Sylow
33	C₂×#239	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×#237	C₂²	1	1	yes	characteristic, complemented
36	C₂×#237	C₂²	1	1	yes	characteristic, complemented
37	C₂×#237	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
39	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
40	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
41	C₂×#235	C₂²	1	1	yes	characteristic, complemented
42	C₂×#235	C₂²	1	1	yes	characteristic, complemented
43	C₂×#235	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
45	C₃×#125	C₂²	1	1	yes	characteristic, complemented
46	C₃×#124	C₂²	1	1	yes	characteristic, complemented
47	C₃×#124	C₂²	1	1	yes	characteristic, complemented
48	C₃×#123	C₂²	1	1	yes	characteristic, complemented
49	C₃×#123	C₂²	1	1	yes	characteristic, complemented
50	C₃×#123	C₂²	1	1	yes	characteristic, complemented
51	C₃×#123	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₃×#121	C₂²	1	1	yes	characteristic
57	C₃×#121	C₂²	1	1	yes	characteristic, complemented
58	C₃×#121	C₂²	1	1	yes	characteristic, complemented
59	C₃×#121	C₂²	1	1	yes	characteristic, complemented
60	#947	C₂²	1	1	yes	characteristic, complemented
61	#946	C₂²	1	1	yes	characteristic
62	#946	C₂²	1	1	yes	characteristic
63	#946	C₂²	1	1	yes	characteristic, complemented
64	#946	C₂²	1	1	yes	characteristic, complemented
65	#944	C₂²	1	1	yes	characteristic, complemented
66	#939	C₂²	1	1	yes	characteristic
67	#939	C₂²	1	1	yes	characteristic
68	#939	C₂²	1	1	yes	characteristic, complemented
69	#939	C₂²	1	1	yes	characteristic, complemented
70	#939	C₂²	1	1	yes	characteristic, complemented
71	#939	C₂²	1	1	yes	characteristic, complemented
72	#939	C₂²	1	1	yes	characteristic, complemented
73	#938	C₂²	1	1	yes	characteristic
74	#938	C₂²	1	1	yes	characteristic, complemented
75	#938	C₂²	1	1	yes	characteristic, complemented
76	#938	C₂²	1	1	yes	characteristic, complemented
77	#938	C₂²	1	1	yes	characteristic, complemented
78	#937	C₂²	1	1	yes	characteristic
79	#937	C₂²	1	1	yes	characteristic
80	#937	C₂²	1	1	yes	characteristic
81	#936	C₂²	1	1	yes	characteristic, complemented
82	#935	C₂²	1	1	yes	characteristic, complemented
83	#935	C₂²	1	1	yes	characteristic, complemented
84	#930	C₂²	1	1	yes	characteristic
85	#930	C₂²	1	1	yes	characteristic, complemented
86	#929	C₂²	1	1	yes	characteristic, complemented
87	C₄×#67	C₂²	1	1	yes	characteristic
88	C₄×#67	C₂²	1	1	yes	characteristic, complemented
89	C₄×#67	C₂²	1	1	yes	characteristic, complemented
90	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
91	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
92	#924	C₂²	1	1	yes	characteristic, complemented
93	#924	C₂²	1	1	yes	characteristic, complemented
94	#924	C₂²	1	1	yes	characteristic, complemented
95	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	#898	C₂²	1	1	yes	characteristic, complemented
97	#897	C₂²	1	1	yes	characteristic
98	#897	C₂²	1	1	yes	characteristic
99	#897	C₂²	1	1	yes	characteristic, complemented
100	#897	C₂²	1	1	yes	characteristic, complemented
101	#897	C₂²	1	1	yes	characteristic, complemented
102	#896	C₂²	1	1	yes	characteristic
103	#896	C₂²	1	1	yes	characteristic
104	#896	C₂²	1	1	yes	characteristic
105	#896	C₂²	1	1	yes	characteristic
106	#896	C₂²	1	1	yes	characteristic
107	#896	C₂²	1	1	yes	characteristic, complemented
108	#896	C₂²	1	1	yes	characteristic, complemented
109	#896	C₂²	1	1	yes	characteristic, complemented
110	#896	C₂²	1	1	yes	characteristic, complemented
111	#896	C₂²	1	1	yes	characteristic, complemented
112	#896	C₂²	1	1	yes	characteristic, complemented
113	#896	C₂²	1	1	yes	characteristic, complemented
114	#895	C₂²	1	1	yes	characteristic
115	#895	C₂²	1	1	yes	characteristic, complemented
116	#895	C₂²	1	1	yes	characteristic, complemented
117	#894	C₂²	1	1	yes	characteristic, complemented
118	#894	C₂²	1	1	yes	characteristic, complemented
119	#894	C₂²	1	1	yes	characteristic, complemented
120	#894	C₂²	1	1	yes	characteristic, complemented
121	#894	C₂²	1	1	yes	characteristic, complemented
122	#893	C₂²	1	1	yes	characteristic
123	#893	C₂²	1	1	yes	characteristic
124	#893	C₂²	1	1	yes	characteristic, complemented
125	#893	C₂²	1	1	yes	characteristic, complemented
126	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
127	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
128	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
129	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
130	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
131	#890	C₂²	1	1	yes	characteristic, complemented
132	#889	C₂²	1	1	yes	characteristic, complemented
133	#889	C₂²	1	1	yes	characteristic, complemented
134	#888	C₂²	1	1	yes	characteristic, complemented
135	#887	C₂²	1	1	yes	characteristic, complemented
136	#886	C₂²	1	1	yes	characteristic, complemented
137	#885	C₂²	1	1	yes	characteristic, complemented
138	#885	C₂²	1	1	yes	characteristic, complemented
139	#885	C₂²	1	1	yes	characteristic, complemented
140	#885	C₂²	1	1	yes	characteristic, complemented
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, complemented
147	#884	C₂²	1	1	yes	characteristic, complemented
148	#884	C₂²	1	1	yes	characteristic, complemented
149	#884	C₂²	1	1	yes	characteristic, complemented
150	#884	C₂²	1	1	yes	characteristic, complemented
151	#884	C₂²	1	1	yes	characteristic, complemented
152	#884	C₂²	1	1	yes	characteristic, complemented
153	#884	C₂²	1	1	yes	characteristic, complemented
154	#883	C₂²	1	1	yes	characteristic, complemented
155	#883	C₂²	1	1	yes	characteristic, complemented
156	#883	C₂²	1	1	yes	characteristic, complemented
157	#883	C₂²	1	1	yes	characteristic, complemented
158	#883	C₂²	1	1	yes	characteristic, complemented
159	#882	C₂²	1	1	yes	characteristic
160	#882	C₂²	1	1	yes	characteristic
161	#882	C₂²	1	1	yes	characteristic
162	#67⋊C₄	C₂²	1	1	yes	characteristic
163	#67⋊C₄	C₂²	1	1	yes	characteristic
164	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
168	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
169	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
170	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
171	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
172	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
173	#879	C₂²	1	1	yes	characteristic, complemented
174	#879	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	#878	C₂²	1	1	yes	characteristic, complemented
182	#878	C₂²	1	1	yes	characteristic, complemented
183	#877	C₂²	1	1	yes	characteristic, complemented
184	#876	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₁₂	C₂²	1	1	yes	characteristic
186	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
187	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
188	#562	—	3	1	no	—
189	#562	—	3	1	no	—
190	#562	—	3	1	no	—
191	#562	D₃	1	1	yes	characteristic, complemented
192	#554	—	3	1	no	—
193	#554	—	3	1	no	—
194	#548	—	3	1	no	—
195	#548	—	3	1	no	—
196	#547	—	3	1	no	—
197	#547	—	3	1	no	—
198	#546	—	3	1	no	—
199	#546	—	3	1	no	—
200	#546	—	3	1	no	—
201	#546	—	3	1	no	—
202	#546	—	3	1	no	—
203	#546	—	3	1	no	—
204	#543	—	3	1	no	—
205	#543	—	3	1	no	—
206	#542	—	3	1	no	—
207	#542	—	3	1	no	—
208	#539	—	3	1	no	—
209	#539	—	3	1	no	—
210	#538	—	3	1	no	—
211	#538	—	3	1	no	—
212	#537	—	3	1	no	—
213	#537	—	3	1	no	—
214	#537	—	3	1	no	—
215	#537	—	3	1	no	—
216	#525	—	3	1	no	—
217	C₂×C₂²⋊Q₈	—	3	1	no	—
218	C₂×#121	—	3	1	no	—
219	C₂³×D₃	C₂³	1	1	yes	characteristic
220	C₂³×D₃	C₂³	1	1	yes	characteristic
221	C₂³×D₃	C₂³	1	1	yes	characteristic
222	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₃×Q₈	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	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
233	C₂²×C₃×C₄	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	C₂×#67	C₂³	1	1	yes	characteristic
243	C₂×#67	C₂³	1	1	yes	characteristic
244	C₂×#67	C₂³	1	1	yes	characteristic
245	C₂×#67	C₂³	1	1	yes	characteristic
246	C₂×#67	C₂³	1	1	yes	characteristic
247	C₂×#67	C₂³	1	1	yes	characteristic
248	C₂²×Dic₃	C₂³	1	1	yes	characteristic
249	C₂²×Dic₃	C₂³	1	1	yes	characteristic
250	C₂²×Dic₃	C₂³	1	1	yes	characteristic
251	C₂²×Dic₃	C₂³	1	1	yes	characteristic
252	C₂²×Dic₃	C₂³	1	1	yes	characteristic
253	#239	—	4	2	no	—
254	D₃×Q₈	—	4	2	no	—
255	#237	—	4	2	no	—
256	#237	—	4	2	no	—
257	#237	—	4	2	no	—
258	D₃×D₄	—	4	2	no	—
259	D₃×D₄	—	4	2	no	—
260	D₃×D₄	—	4	2	no	—
261	#235	—	4	2	no	—
262	#235	—	4	2	no	—
263	#235	—	4	2	no	—
264	C₂×D₁₂	C₂³	1	1	yes	characteristic
265	C₂×D₁₂	C₂³	1	1	yes	characteristic
266	C₂×D₁₂	C₂³	1	1	yes	characteristic
267	C₂×D₁₂	C₂³	1	1	yes	characteristic
268	C₂×D₁₂	C₂³	1	1	yes	characteristic
269	C₂×D₁₂	C₂³	1	1	yes	characteristic
270	C₂×D₁₂	C₂³	1	1	yes	characteristic
271	C₂×C₄×D₃	—	4	2	no	—
272	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
287	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
288	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
289	C₂×Dic₆	C₂³	1	1	yes	characteristic
290	C₂×Dic₆	C₂³	1	1	yes	characteristic
291	C₂×Dic₆	C₂³	1	1	yes	characteristic
292	C₂×Dic₆	C₂³	1	1	yes	characteristic
293	C₂×Dic₆	C₂³	1	1	yes	characteristic
294	C₂×Dic₆	C₂³	1	1	yes	characteristic
295	C₂×Dic₆	C₂³	1	1	yes	characteristic
296	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
297	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
298	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
299	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
300	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
301	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
302	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
303	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
304	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
305	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
306	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
307	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
308	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
310	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
311	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
312	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
313	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
314	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
315	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
316	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
317	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
318	C₃×C₄²	C₂³	1	1	yes	characteristic
319	#217	C₂³	1	1	yes	characteristic
320	#217	C₂³	1	1	yes	characteristic
321	#217	C₂³	1	1	yes	characteristic
322	#217	C₂³	1	1	yes	characteristic
323	#217	C₂³	1	1	yes	characteristic
324	#217	C₂³	1	1	yes	characteristic
325	#217	C₂³	1	1	yes	characteristic
326	#217	C₂³	1	1	yes	characteristic
327	#217	C₂³	1	1	yes	characteristic
328	#217	C₂³	1	1	yes	characteristic
329	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
330	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
331	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
332	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
333	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
334	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
335	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
336	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
337	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
338	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
339	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
340	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
341	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
342	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
343	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
344	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
345	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
346	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
347	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
348	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
349	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
350	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
351	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
352	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
353	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
354	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
355	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
356	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
357	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
358	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
359	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
360	C₄⋊Dic₃	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	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
370	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
371	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
372	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
373	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
374	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
375	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
376	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
377	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
378	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
379	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
380	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
381	C₄×Dic₃	C₂³	1	1	yes	characteristic
382	C₄×Dic₃	C₂³	1	1	yes	characteristic
383	C₄×Dic₃	C₂³	1	1	yes	characteristic
384	C₄×Dic₃	C₂³	1	1	yes	characteristic
385	C₄×Dic₃	C₂³	1	1	yes	characteristic
386	C₂×#41	—	3	1	no	—
387	C₂×#41	—	3	1	no	—
388	C₂×#41	—	3	1	no	—
389	C₂×#41	—	3	1	no	—
390	C₂×#41	—	3	1	no	—
391	C₂×#41	—	3	1	no	—
392	C₂×#41	—	3	1	no	—
393	C₂²×Q₈	—	3	1	no	—
394	C₂²×D₄	—	3	1	no	—
395	C₂²×D₄	—	3	1	no	—
396	C₂²×D₄	—	3	1	no	—
397	C₂³×C₄	—	3	1	no	—
398	C₄⋊Q₈	—	3	1	no	—
399	C₄⋊Q₈	—	3	1	no	—
400	#126	—	3	1	no	—
401	#126	—	3	1	no	—
402	#126	—	3	1	no	—
403	#126	—	3	1	no	—
404	#125	—	3	1	no	—
405	#125	—	3	1	no	—
406	#125	—	3	1	no	—
407	#125	C₂×D₃	1	1	yes	characteristic, complemented
408	#124	—	3	1	no	—
409	#124	—	3	1	no	—
410	#124	—	3	1	no	—
411	#124	—	3	1	no	—
412	#124	—	3	1	no	—
413	#124	—	3	1	no	—
414	#124	—	3	1	no	—
415	#124	—	3	1	no	—
416	#124	C₂×D₃	1	1	yes	characteristic, complemented
417	#124	C₂×D₃	1	1	yes	characteristic, complemented
418	#123	—	3	1	no	—
419	#123	—	3	1	no	—
420	#123	—	3	1	no	—
421	#123	—	3	1	no	—
422	#123	—	3	1	no	—
423	#123	—	3	1	no	—
424	#123	—	3	1	no	—
425	#123	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic, complemented
433	#123	C₂×D₃	1	1	yes	characteristic, complemented
434	#123	C₂×D₃	1	1	yes	characteristic, complemented
435	#123	C₂×D₃	1	1	yes	characteristic, complemented
436	C₂²⋊Q₈	—	3	1	no	—
437	C₂²⋊Q₈	—	3	1	no	—
438	C₂²⋊Q₈	—	3	1	no	—
439	C₂²⋊Q₈	—	3	1	no	—
440	C₂²⋊Q₈	—	3	1	no	—
441	C₂²⋊Q₈	—	3	1	no	—
442	C₂²⋊Q₈	—	3	1	no	—
443	C₂²⋊Q₈	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic, complemented
469	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
470	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
471	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
472	#121	—	3	1	no	—
473	#121	—	3	1	no	—
474	#121	—	3	1	no	—
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	—	3	1	no	—
491	#121	—	3	1	no	—
492	#121	—	3	1	no	—
493	#121	—	3	1	no	—
494	#121	—	3	1	no	—
495	#121	—	3	1	no	—
496	#121	—	3	1	no	—
497	#121	—	3	1	no	—
498	#121	—	3	1	no	—
499	#121	—	3	1	no	—
500	#121	C₂×D₃	1	1	yes	characteristic
501	#121	C₂×D₃	1	1	yes	characteristic, complemented
502	#121	C₂×D₃	1	1	yes	characteristic, complemented
503	#121	C₂×D₃	1	1	yes	characteristic, complemented
504	#120	—	3	1	no	—
505	#120	—	3	1	no	—
506	#120	—	3	1	no	—
507	#120	—	3	1	no	—
508	#120	—	3	1	no	—
509	#120	—	3	1	no	—
510	C₄×Q₈	—	3	1	no	—
511	C₄×Q₈	—	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	C₄×D₄	—	3	1	no	—
523	C₄×D₄	—	3	1	no	—
524	C₄×D₄	—	3	1	no	—
525	C₄×D₄	—	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	C₂×C₂²⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	—	3	1	no	—
537	C₂×C₂²⋊C₄	—	3	1	no	—
538	C₂×C₂²⋊C₄	—	3	1	no	—
539	C₂×C₂²⋊C₄	—	3	1	no	—
540	C₂×C₂²⋊C₄	—	3	1	no	—
541	C₂³×C₃	C₂⁴	1	1	yes	characteristic
542	C₂³×C₃	C₂⁴	1	1	yes	characteristic
543	C₂³×C₃	C₂⁴	1	1	yes	characteristic
544	C₂³×C₃	C₂⁴	1	1	yes	characteristic
545	C₂²×D₃	—	2	2	no	—
546	C₂²×D₃	—	2	2	no	—
547	C₂²×D₃	—	2	2	no	—
548	C₂²×D₃	—	2	2	no	—
549	C₂²×D₃	—	4	1	no	—
550	C₂²×D₃	—	4	1	no	—
551	C₂²×D₃	—	4	1	no	—
552	C₂²×D₃	—	4	1	no	—
553	C₂²×D₃	—	4	1	no	—
554	C₂²×D₃	C₂⁴	1	1	yes	characteristic
555	C₂²×D₃	C₂⁴	1	1	yes	characteristic
556	C₂²×D₃	C₂⁴	1	1	yes	characteristic
557	C₂²×D₃	C₂⁴	1	1	yes	characteristic
558	C₂²×D₃	C₂⁴	1	1	yes	characteristic
559	C₃×Q₈	—	4	1	no	—
560	C₃×Q₈	—	4	1	no	—
561	C₃×D₄	—	4	1	no	—
562	C₃×D₄	—	4	1	no	—
563	C₃×D₄	—	4	1	no	—
564	C₃×D₄	—	4	1	no	—
565	C₃×D₄	—	4	1	no	—
566	C₃×D₄	—	4	1	no	—
567	C₂×C₃×C₄	—	4	1	no	—
568	C₂×C₃×C₄	—	4	1	no	—
569	C₂×C₃×C₄	—	4	1	no	—
570	C₂×C₃×C₄	—	4	1	no	—
571	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
572	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
573	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
574	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
575	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
576	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
579	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
581	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
582	#67	—	2	2	no	—
583	#67	—	2	2	no	—
584	#67	—	2	2	no	—
585	#67	—	2	2	no	—
586	#67	—	2	2	no	—
587	#67	—	2	2	no	—
588	#67	—	4	1	no	—
589	#67	—	4	1	no	—
590	#67	—	4	1	no	—
591	#67	—	4	1	no	—
592	#67	—	4	1	no	—
593	#67	—	4	1	no	—
594	#67	—	4	1	no	—
595	#67	—	4	1	no	—
596	C₂×Dic₃	—	2	2	no	—
597	C₂×Dic₃	—	2	2	no	—
598	C₂×Dic₃	—	4	1	no	—
599	C₂×Dic₃	—	4	1	no	—
600	C₂×Dic₃	—	4	1	no	—
601	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
602	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
603	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
604	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
605	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
606	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
607	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
608	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
609	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
610	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
611	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
612	D₁₂	—	2	2	no	—
613	D₁₂	—	2	2	no	—
614	D₁₂	—	2	2	no	—
615	D₁₂	—	2	2	no	—
616	D₁₂	—	4	1	no	—
617	D₁₂	—	4	1	no	—
618	D₁₂	—	4	1	no	—
619	C₄×D₃	—	2	2	no	—
620	C₄×D₃	—	2	2	no	—
621	C₄×D₃	—	2	2	no	—
622	C₄×D₃	—	2	2	no	—
623	C₄×D₃	—	2	2	no	—
624	C₄×D₃	—	4	1	no	—
625	C₄×D₃	—	4	1	no	—
626	C₄×D₃	—	4	1	no	—
627	C₄×D₃	—	4	1	no	—
628	C₄×D₃	—	4	1	no	—
629	C₄×D₃	—	4	1	no	—
630	C₄×D₃	—	4	1	no	—
631	C₄×D₃	—	4	1	no	—
632	C₄×D₃	—	4	1	no	—
633	C₄×D₃	—	4	1	no	—
634	C₄×D₃	—	4	1	no	—
635	C₄×D₃	—	4	1	no	—
636	Dic₆	—	2	2	no	—
637	Dic₆	—	2	2	no	—
638	Dic₆	—	4	1	no	—
639	Dic₆	—	4	1	no	—
640	Dic₆	—	4	1	no	—
641	Dic₆	—	4	1	no	—
642	Dic₆	—	4	1	no	—
643	C₂⁴	—	3	1	no	—
644	C₂⁴	—	3	1	no	—
645	C₂⁴	—	3	1	no	—
646	#41	—	12	2	no	—
647	#41	—	12	2	no	—
648	#41	—	12	2	no	—
649	#41	—	12	2	no	—
650	#41	—	12	2	no	—
651	#41	—	12	2	no	—
652	#41	—	12	2	no	—
653	C₂×Q₈	—	3	1	no	—
654	C₂×Q₈	—	3	1	no	—
655	C₂×Q₈	—	3	1	no	—
656	C₂×Q₈	—	3	1	no	—
657	C₂×Q₈	—	3	1	no	—
658	C₂×Q₈	—	3	1	no	—
659	C₂×Q₈	—	3	1	no	—
660	C₂×Q₈	—	12	2	no	—
661	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
662	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
663	C₂×D₄	—	3	1	no	—
664	C₂×D₄	—	3	1	no	—
665	C₂×D₄	—	3	1	no	—
666	C₂×D₄	—	3	1	no	—
667	C₂×D₄	—	3	1	no	—
668	C₂×D₄	—	3	1	no	—
669	C₂×D₄	—	3	1	no	—
670	C₂×D₄	—	3	1	no	—
671	C₂×D₄	—	3	1	no	—
672	C₂×D₄	—	3	1	no	—
673	C₂×D₄	—	3	1	no	—
674	C₂×D₄	—	3	1	no	—
675	C₂×D₄	—	3	1	no	—
676	C₂×D₄	—	3	1	no	—
677	C₂×D₄	—	3	1	no	—
678	C₂×D₄	—	3	1	no	—
679	C₂×D₄	—	3	1	no	—
680	C₂×D₄	—	3	1	no	—
681	C₂×D₄	—	3	1	no	—
682	C₂×D₄	—	3	1	no	—
683	C₂×D₄	—	3	1	no	—
684	C₂×D₄	—	12	2	no	—
685	C₂×D₄	—	12	2	no	—
686	C₂×D₄	—	12	2	no	—
687	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
688	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
689	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
690	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
691	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
692	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
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	—	12	2	no	—
716	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
717	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
718	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
719	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
720	C₄⋊C₄	—	3	1	no	—
721	C₄⋊C₄	—	3	1	no	—
722	C₄⋊C₄	—	3	1	no	—
723	C₄⋊C₄	—	3	1	no	—
724	C₄⋊C₄	—	3	1	no	—
725	C₄⋊C₄	—	3	1	no	—
726	C₄⋊C₄	—	3	1	no	—
727	C₄⋊C₄	—	3	1	no	—
728	C₄⋊C₄	—	3	1	no	—
729	C₄⋊C₄	—	3	1	no	—
730	C₄⋊C₄	—	3	1	no	—
731	C₄⋊C₄	—	3	1	no	—
732	C₄⋊C₄	—	3	1	no	—
733	C₄⋊C₄	—	3	1	no	—
734	C₄⋊C₄	—	3	1	no	—
735	C₄⋊C₄	—	3	1	no	—
736	C₄⋊C₄	—	3	1	no	—
737	C₄⋊C₄	—	3	1	no	—
738	C₄⋊C₄	—	3	1	no	—
739	C₄⋊C₄	—	3	1	no	—
740	C₄⋊C₄	—	3	1	no	—
741	C₄⋊C₄	—	3	1	no	—
742	C₄⋊C₄	—	3	1	no	—
743	C₄⋊C₄	—	3	1	no	—
744	C₄⋊C₄	—	3	1	no	—
745	C₄⋊C₄	—	3	1	no	—
746	C₄⋊C₄	—	3	1	no	—
747	C₄⋊C₄	—	3	1	no	—
748	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
758	C₂²⋊C₄	—	3	1	no	—
759	C₂²⋊C₄	—	3	1	no	—
760	C₂²⋊C₄	—	3	1	no	—
761	C₂²⋊C₄	—	3	1	no	—
762	C₂²⋊C₄	—	3	1	no	—
763	C₂²⋊C₄	—	3	1	no	—
764	C₂²⋊C₄	—	3	1	no	—
765	C₂²⋊C₄	—	3	1	no	—
766	C₂²⋊C₄	—	3	1	no	—
767	C₂²⋊C₄	—	3	1	no	—
768	C₂²⋊C₄	—	3	1	no	—
769	C₂²⋊C₄	—	3	1	no	—
770	C₂²⋊C₄	—	3	1	no	—
771	C₂²⋊C₄	—	3	1	no	—
772	C₂²⋊C₄	—	3	1	no	—
773	C₂²⋊C₄	—	3	1	no	—
774	C₂²⋊C₄	—	3	1	no	—
775	C₂²⋊C₄	—	3	1	no	—
776	C₂²⋊C₄	—	3	1	no	—
777	C₂²⋊C₄	—	3	1	no	—
778	C₂²⋊C₄	—	3	1	no	—
779	C₂²⋊C₄	—	3	1	no	—
780	C₂²⋊C₄	—	3	1	no	—
781	C₂²⋊C₄	—	3	1	no	—
782	C₂²⋊C₄	—	3	1	no	—
783	C₂²⋊C₄	—	3	1	no	—
784	C₂²⋊C₄	—	3	1	no	—
785	C₂²⋊C₄	—	3	1	no	—
786	C₂²⋊C₄	—	3	1	no	—
787	C₂²⋊C₄	—	3	1	no	—
788	C₂²⋊C₄	—	3	1	no	—
789	C₂²⋊C₄	—	3	1	no	—
790	C₂²⋊C₄	—	3	1	no	—
791	C₂²⋊C₄	—	3	1	no	—
792	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
804	C₄²	—	3	1	no	—
805	C₄²	—	3	1	no	—
806	C₄²	—	3	1	no	—
807	C₄²	—	3	1	no	—
808	C₄²	—	3	1	no	—
809	C₄²	C₂²×D₃	1	1	yes	characteristic
810	C₂²×C₃	—	2	1	no	—
811	C₂²×C₃	—	2	1	no	—
812	C₂²×C₃	—	2	1	no	—
813	C₂²×C₃	—	2	1	no	—
814	C₂²×C₃	—	2	1	no	—
815	C₂²×C₃	—	2	1	no	—
816	C₂²×C₃	—	2	1	no	—
817	C₂²×C₃	—	2	1	no	—
818	C₂²×C₃	—	2	1	no	—
819	C₂²×C₃	—	2	1	no	—
820	C₂²×C₃	—	2	1	no	—
821	C₂²×C₃	—	2	1	no	—
822	C₂²×C₃	C₂⁵	1	1	yes	characteristic
823	C₂×D₃	—	2	1	no	—
824	C₂×D₃	—	2	1	no	—
825	C₂×D₃	—	2	1	no	—
826	C₂×D₃	—	2	1	no	—
827	C₂×D₃	—	2	1	no	—
828	C₂×D₃	—	2	1	no	—
829	C₂×D₃	—	2	1	no	—
830	C₂×D₃	—	2	1	no	—
831	C₂×D₃	—	2	1	no	—
832	C₂×D₃	—	2	1	no	—
833	C₂×D₃	—	2	1	no	—
834	C₂×D₃	—	2	1	no	—
835	C₂×D₃	—	2	1	no	—
836	C₂×D₃	—	4	4	no	—
837	C₂×D₃	—	8	2	no	—
838	C₂×D₃	—	8	2	no	—
839	C₂×D₃	H(5,𝔽₂)	1	2	yes	—
840	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
841	C₃×C₄	—	2	1	no	—
842	C₃×C₄	—	2	1	no	—
843	C₃×C₄	—	2	1	no	—
844	C₃×C₄	—	2	1	no	—
845	C₃×C₄	—	2	1	no	—
846	C₃×C₄	—	2	1	no	—
847	C₃×C₄	—	2	1	no	—
848	C₃×C₄	—	2	1	no	—
849	C₃×C₄	—	2	1	no	—
850	C₃×C₄	—	2	1	no	—
851	C₃×C₄	—	2	1	no	—
852	Dic₃	—	2	1	no	—
853	Dic₃	—	2	1	no	—
854	Dic₃	—	2	1	no	—
855	Dic₃	—	2	1	no	—
856	Dic₃	—	2	1	no	—
857	Dic₃	—	2	1	no	—
858	Dic₃	—	2	1	no	—
859	Dic₃	—	2	1	no	—
860	Dic₃	—	2	1	no	—
861	Dic₃	—	2	1	no	—
862	Dic₃	H(5,𝔽₂)	1	2	yes	—
863	C₂³	—	3	1	no	—
864	C₂³	—	3	1	no	—
865	C₂³	—	3	1	no	—
866	C₂³	—	3	1	no	—
867	C₂³	—	3	1	no	—
868	C₂³	—	6	2	no	—
869	C₂³	—	6	2	no	—
870	C₂³	—	6	2	no	—
871	C₂³	—	6	2	no	—
872	C₂³	—	12	1	no	—
873	C₂³	—	12	1	no	—
874	C₂³	—	12	1	no	—
875	C₂³	—	12	1	no	—
876	C₂³	—	12	1	no	—
877	C₂³	C₂³×D₃	1	1	yes	characteristic
878	C₂³	C₂³×D₃	1	1	yes	characteristic
879	C₂³	C₂³×D₃	1	1	yes	characteristic
880	C₂³	C₂³×D₃	1	1	yes	characteristic
881	Q₈	—	4	1	no	—
882	Q₈	—	4	1	no	—
883	Q₈	—	6	2	no	—
884	Q₈	—	6	2	no	—
885	Q₈	—	12	1	no	—
886	Q₈	—	12	1	no	—
887	Q₈	—	12	1	no	—
888	Q₈	—	12	1	no	—
889	Q₈	—	12	1	no	—
890	D₄	—	4	1	no	—
891	D₄	—	4	1	no	—
892	D₄	—	4	1	no	—
893	D₄	—	4	1	no	—
894	D₄	—	4	1	no	—
895	D₄	—	4	1	no	—
896	D₄	—	6	2	no	—
897	D₄	—	6	2	no	—
898	D₄	—	6	2	no	—
899	D₄	—	6	2	no	—
900	D₄	—	6	2	no	—
901	D₄	—	6	2	no	—
902	D₄	—	6	2	no	—
903	D₄	—	6	2	no	—
904	D₄	—	6	2	no	—
905	D₄	—	6	2	no	—
906	D₄	—	12	1	no	—
907	D₄	—	12	1	no	—
908	D₄	—	12	1	no	—
909	D₄	—	12	1	no	—
910	D₄	—	12	1	no	—
911	D₄	—	12	1	no	—
912	D₄	—	12	1	no	—
913	D₄	—	12	1	no	—
914	D₄	—	12	1	no	—
915	D₄	—	12	1	no	—
916	D₄	—	12	1	no	—
917	C₂×C₄	—	3	1	no	—
918	C₂×C₄	—	3	1	no	—
919	C₂×C₄	—	3	1	no	—
920	C₂×C₄	—	3	1	no	—
921	C₂×C₄	—	3	1	no	—
922	C₂×C₄	—	3	1	no	—
923	C₂×C₄	—	3	1	no	—
924	C₂×C₄	—	3	1	no	—
925	C₂×C₄	—	3	1	no	—
926	C₂×C₄	—	3	1	no	—
927	C₂×C₄	—	3	1	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	1	no	—
930	C₂×C₄	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	6	2	no	—
933	C₂×C₄	—	6	2	no	—
934	C₂×C₄	—	6	2	no	—
935	C₂×C₄	—	6	2	no	—
936	C₂×C₄	—	6	2	no	—
937	C₂×C₄	—	6	2	no	—
938	C₂×C₄	—	6	2	no	—
939	C₂×C₄	—	12	1	no	—
940	C₂×C₄	—	12	1	no	—
941	C₂×C₄	—	12	1	no	—
942	C₂×C₄	—	12	1	no	—
943	C₂×C₄	—	12	1	no	—
944	C₂×C₄	—	12	1	no	—
945	C₂×C₄	—	12	1	no	—
946	C₂×C₄	—	12	1	no	—
947	C₂×C₄	—	12	1	no	—
948	C₂×C₄	—	12	1	no	—
949	C₂×C₄	—	12	1	no	—
950	C₂×C₄	—	12	1	no	—
951	C₂×C₄	—	12	1	no	—
952	C₂×C₄	—	12	1	no	—
953	C₂×C₄	—	12	1	no	—
954	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
955	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
956	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
964	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
965	C₂×C₃	—	4	1	no	—
966	C₂×C₃	—	4	1	no	—
967	C₂×C₃	—	4	1	no	—
968	C₂×C₃	—	4	1	no	—
969	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
970	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
971	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
972	D₃	—	2	2	no	—
973	D₃	—	2	2	no	—
974	D₃	—	4	1	no	—
975	D₃	—	4	1	no	—
976	D₃	—	4	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	3	2	no	—
990	C₂²	—	3	2	no	—
991	C₂²	—	6	1	no	—
992	C₂²	—	6	1	no	—
993	C₂²	—	6	1	no	—
994	C₂²	—	6	1	no	—
995	C₂²	—	6	1	no	—
996	C₂²	—	6	1	no	—
997	C₂²	—	6	1	no	—
998	C₂²	—	6	1	no	—
999	C₂²	—	6	1	no	—
1000	C₂²	—	6	1	no	—
1001	C₂²	—	6	1	no	—
1002	C₂²	—	6	1	no	—
1003	C₂²	—	6	1	no	—
1004	C₂²	—	12	4	no	—
1005	C₂²	—	24	2	no	—
1006	C₂²	—	24	2	no	—
1007	C₂²	C₂⁴×D₃	1	1	yes	characteristic
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	3	2	no	—
1020	C₄	—	6	1	no	—
1021	C₄	—	6	1	no	—
1022	C₄	—	6	1	no	—
1023	C₄	—	6	1	no	—
1024	C₄	—	6	1	no	—
1025	C₄	—	6	1	no	—
1026	C₄	—	6	1	no	—
1027	C₄	—	6	1	no	—
1028	C₄	—	6	1	no	—
1029	C₄	—	6	1	no	—
1030	C₃	#3536	1	1	yes	characteristic, complemented, Sylow
1031	C₂	—	4	1	no	—
1032	C₂	—	4	1	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	1	no	—
1035	C₂	—	6	2	no	—
1036	C₂	—	6	2	no	—
1037	C₂	—	12	1	no	—
1038	C₂	—	12	1	no	—
1039	C₂	—	12	1	no	—
1040	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1041	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1042	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	#3536
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. #5692	C₂	semidirect
3. #5690	C₂	semidirect
4. #5678	C₂	semidirect
5. #5677	C₂	semidirect
6. #5676	C₂	semidirect
7. #5669	C₂	semidirect
8. #5667	C₂	semidirect
9. #5662	C₂	semidirect
10. #5660	C₂	semidirect
11. #5657	C₂	semidirect
12. #5656	C₂	semidirect
13. #5655	C₂	semidirect
14. #5654	C₂	semidirect
15. #5654	C₂	semidirect
16. #5647	C₂	semidirect
17. #5636	C₂	semidirect
18. #5634	C₂	semidirect
19. #5634	C₂	semidirect
20. #5633	C₂	semidirect
21. #5631	C₂	semidirect
22. #5629	C₂	semidirect
23. D₃×C₂²⋊Q₈	C₂	semidirect
24. #5621	C₂	semidirect
25. #5612	C₂	semidirect
26. #5610	C₂	semidirect
27. #5610	C₂	semidirect
28. #5608	C₂	semidirect
29. #5608	C₂	semidirect
30. D₃×#121	C₂	semidirect
31. #5597	C₂	semidirect
33. C₂×#239	C₂²	semidirect
34. C₂×D₃×Q₈	C₂²	semidirect
35. C₂×#237	C₂²	semidirect
36. C₂×#237	C₂²	semidirect
37. C₂×#237	C₂²	semidirect
41. C₂×#235	C₂²	semidirect
42. C₂×#235	C₂²	semidirect
43. C₂×#235	C₂²	semidirect
45. C₃×#125	C₂²	semidirect
46. C₃×#124	C₂²	semidirect
47. C₃×#124	C₂²	semidirect
48. C₃×#123	C₂²	semidirect
49. C₃×#123	C₂²	semidirect
50. C₃×#123	C₂²	semidirect
51. C₃×#123	C₂²	semidirect
52. C₃×C₂²⋊Q₈	C₂²	semidirect
53. C₃×C₂²⋊Q₈	C₂²	semidirect
54. C₃×C₂²⋊Q₈	C₂²	semidirect
55. C₃×C₂²⋊Q₈	C₂²	semidirect
57. C₃×#121	C₂²	semidirect
58. C₃×#121	C₂²	semidirect
59. C₃×#121	C₂²	semidirect
60. #947	C₂²	semidirect
63. #946	C₂²	semidirect
64. #946	C₂²	semidirect
65. #944	C₂²	semidirect
68. #939	C₂²	semidirect
69. #939	C₂²	semidirect
70. #939	C₂²	semidirect
71. #939	C₂²	semidirect
72. #939	C₂²	semidirect
74. #938	C₂²	semidirect
75. #938	C₂²	semidirect
76. #938	C₂²	semidirect
77. #938	C₂²	semidirect
81. #936	C₂²	semidirect
82. #935	C₂²	semidirect
83. #935	C₂²	semidirect
85. #930	C₂²	semidirect
86. #929	C₂²	semidirect
88. C₄×#67	C₂²	semidirect
89. C₄×#67	C₂²	semidirect
92. #924	C₂²	semidirect
93. #924	C₂²	semidirect
94. #924	C₂²	semidirect
95. C₂×Dic₃⋊C₄	C₂²	semidirect
96. #898	C₂²	semidirect
99. #897	C₂²	semidirect
100. #897	C₂²	semidirect
101. #897	C₂²	semidirect
107. #896	C₂²	semidirect
108. #896	C₂²	semidirect
109. #896	C₂²	semidirect
110. #896	C₂²	semidirect
111. #896	C₂²	semidirect
112. #896	C₂²	semidirect
113. #896	C₂²	semidirect
115. #895	C₂²	semidirect
116. #895	C₂²	semidirect
117. #894	C₂²	semidirect
118. #894	C₂²	semidirect
119. #894	C₂²	semidirect
120. #894	C₂²	semidirect
121. #894	C₂²	semidirect
124. #893	C₂²	semidirect
125. #893	C₂²	semidirect
127. D₃×C₄⋊C₄	C₂²	semidirect
128. D₃×C₄⋊C₄	C₂²	semidirect
129. D₃×C₄⋊C₄	C₂²	semidirect
130. D₃×C₄⋊C₄	C₂²	semidirect
131. #890	C₂²	semidirect
132. #889	C₂²	semidirect
133. #889	C₂²	semidirect
134. #888	C₂²	semidirect
135. #887	C₂²	semidirect
136. #886	C₂²	semidirect
137. #885	C₂²	semidirect
138. #885	C₂²	semidirect
139. #885	C₂²	semidirect
140. #885	C₂²	semidirect
141. #885	C₂²	semidirect
142. #885	C₂²	semidirect
146. #884	C₂²	semidirect
147. #884	C₂²	semidirect
148. #884	C₂²	semidirect
149. #884	C₂²	semidirect
150. #884	C₂²	semidirect
151. #884	C₂²	semidirect
152. #884	C₂²	semidirect
153. #884	C₂²	semidirect
154. #883	C₂²	semidirect
155. #883	C₂²	semidirect
156. #883	C₂²	semidirect
157. #883	C₂²	semidirect
158. #883	C₂²	semidirect
164. #67⋊C₄	C₂²	semidirect
165. #67⋊C₄	C₂²	semidirect
166. #67⋊C₄	C₂²	semidirect
173. #879	C₂²	semidirect
174. #879	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
181. #878	C₂²	semidirect
182. #878	C₂²	semidirect
183. #877	C₂²	semidirect
184. #876	C₂²	semidirect
186. C₄×D₁₂	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
191. #562	D₃	semidirect
407. #125	C₂×D₃	semidirect
416. #124	C₂×D₃	semidirect
417. #124	C₂×D₃	semidirect
432. #123	C₂×D₃	semidirect
433. #123	C₂×D₃	semidirect
434. #123	C₂×D₃	semidirect
435. #123	C₂×D₃	semidirect
468. C₂²⋊Q₈	C₂×D₃	semidirect
469. C₂²⋊Q₈	C₂×D₃	semidirect
470. C₂²⋊Q₈	C₂×D₃	semidirect
471. C₂²⋊Q₈	C₂×D₃	semidirect
501. #121	C₂×D₃	semidirect
502. #121	C₂×D₃	semidirect
503. #121	C₂×D₃	semidirect
1030. C₃	#3536	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
#5692	2
#5690	2
#5678	2
#5677	2
#5676	2
#5669	2
#5667	2
#5662	2
#5660	2
#5657	2
#5656	2
#5655	2
#5654	2
#5647	2
#5636	2
#5634	2
#5633	2
#5631	2
#5629	2
D₃×C₂²⋊Q₈	2
#5621	2
#5612	2
#5610	2
#5608	2
D₃×#121	2
#5597	2
#3536	3