Subgroups — #7624902

Order 512.

1269 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62271	C₂	1	1	yes	maximal, characteristic, complemented
2	#62267	C₂	1	1	yes	maximal, characteristic
3	#33919	C₂	1	1	yes	maximal, characteristic, complemented
4	#33916	C₂	1	1	yes	maximal, characteristic, complemented
5	#33911	C₂	1	1	yes	maximal, characteristic, complemented
6	#33904	C₂	1	1	yes	maximal, characteristic, complemented
7	#33895	C₂	1	1	yes	maximal, characteristic, complemented
8	#33894	C₂	1	1	yes	maximal, characteristic, complemented
9	#33887	C₂	1	1	yes	maximal, characteristic, complemented
10	#33882	C₂	1	1	yes	maximal, characteristic, complemented
11	#33879	C₂	1	1	yes	maximal, characteristic, complemented
12	#33879	C₂	1	1	yes	maximal, characteristic, complemented
13	#33867	C₂	1	1	yes	maximal, characteristic, complemented
14	#33866	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
16	#33842	C₂	1	1	yes	maximal, characteristic, complemented
17	#33836	C₂	1	1	yes	maximal, characteristic, complemented
18	#33836	C₂	1	1	yes	maximal, characteristic, complemented
19	#33827	C₂	1	1	yes	maximal, characteristic, complemented
20	#33824	C₂	1	1	yes	maximal, characteristic, complemented
21	#33768	C₂	1	1	yes	maximal, characteristic, complemented
22	#33767	C₂	1	1	yes	maximal, characteristic, complemented
23	#33756	C₂	1	1	yes	maximal, characteristic, complemented
24	#33755	C₂	1	1	yes	maximal, characteristic, complemented
25	#33745	C₂	1	1	yes	maximal, characteristic, complemented
26	#33741	C₂	1	1	yes	maximal, characteristic, complemented
27	#33613	C₂	1	1	yes	maximal, characteristic, complemented
28	#33608	C₂	1	1	yes	maximal, characteristic, complemented
29	#33606	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#2219	C₂	1	1	yes	maximal, characteristic, complemented
31	#33436	C₂	1	1	yes	maximal, characteristic, complemented
32	#3541	—	2	1	no	—
33	#3538	—	2	1	no	—
34	C₂×#510	C₂²	1	1	yes	characteristic
35	C₂×#510	C₂²	1	1	yes	characteristic, complemented
36	C₂²×Q₃₂	C₂²	1	1	yes	characteristic
37	C₂²×Q₃₂	C₂²	1	1	yes	characteristic, complemented
38	C₂×#504	C₂²	1	1	yes	characteristic
39	C₂²×M₃₂	C₂²	1	1	yes	characteristic
40	#3342	C₂²	1	1	yes	characteristic
41	#3339	C₂²	1	1	yes	characteristic
42	#3338	C₂²	1	1	yes	characteristic
43	#3336	C₂²	1	1	yes	characteristic
44	#3336	C₂²	1	1	yes	characteristic
45	#3336	C₂²	1	1	yes	characteristic
46	#3336	C₂²	1	1	yes	characteristic
47	#3336	C₂²	1	1	yes	characteristic
48	#3320	—	2	1	no	—
49	#3316	—	2	1	no	—
50	#3315	—	2	1	no	—
51	#3313	—	2	1	no	—
52	#3312	—	2	1	no	—
53	#3312	—	2	1	no	—
54	#3312	—	2	1	no	—
55	#3312	—	2	1	no	—
56	D₄×Q₁₆	C₂²	1	1	yes	characteristic
57	D₄×Q₁₆	C₂²	1	1	yes	characteristic
58	D₄×Q₁₆	C₂²	1	1	yes	characteristic
59	D₄×Q₁₆	C₂²	1	1	yes	characteristic
60	D₄×Q₁₆	C₂²	1	1	yes	characteristic
61	#3285	C₂²	1	1	yes	characteristic
62	#3285	C₂²	1	1	yes	characteristic
63	#3283	C₂²	1	1	yes	characteristic
64	#3261	—	2	1	no	—
65	#3258	—	2	1	no	—
66	#3202	—	2	1	no	—
67	#3201	—	2	1	no	—
68	#3196	—	2	1	no	—
69	#3195	—	2	1	no	—
70	#3177	C₂²	1	1	yes	characteristic
71	#3177	C₂²	1	1	yes	characteristic
72	#3177	C₂²	1	1	yes	characteristic
73	#3175	C₂²	1	1	yes	characteristic
74	#3061	C₂²	1	1	yes	characteristic
75	#3059	C₂²	1	1	yes	characteristic
76	#3059	C₂²	1	1	yes	characteristic
77	#3059	C₂²	1	1	yes	characteristic
78	#3050	C₂²	1	1	yes	characteristic
79	C₂×#467	C₂²	1	1	yes	characteristic
80	C₂×#467	C₂²	1	1	yes	characteristic
81	C₂×#467	C₂²	1	1	yes	characteristic
82	#2929	C₂²	1	1	yes	characteristic
83	#2255	C₂²	1	1	yes	characteristic, complemented
84	#2253	C₂²	1	1	yes	characteristic, complemented
85	#2251	C₂²	1	1	yes	characteristic, complemented
86	#2247	C₂²	1	1	yes	characteristic, complemented
87	#2245	C₂²	1	1	yes	characteristic, complemented
88	#2245	C₂²	1	1	yes	characteristic, complemented
89	#2242	C₂²	1	1	yes	characteristic, complemented
90	#2241	C₂²	1	1	yes	characteristic, complemented
91	#2237	C₂²	1	1	yes	characteristic
92	#2237	C₂²	1	1	yes	characteristic
93	#2237	C₂²	1	1	yes	characteristic, complemented
94	#2237	C₂²	1	1	yes	characteristic, complemented
95	#2237	C₂²	1	1	yes	characteristic, complemented
96	#2237	C₂²	1	1	yes	characteristic, complemented
97	#2237	C₂²	1	1	yes	characteristic, complemented
98	#2236	C₂²	1	1	yes	characteristic
99	#2236	C₂²	1	1	yes	characteristic
100	#2236	C₂²	1	1	yes	characteristic
101	#2236	C₂²	1	1	yes	characteristic
102	#2236	C₂²	1	1	yes	characteristic, complemented
103	#2235	C₂²	1	1	yes	characteristic
104	#2235	C₂²	1	1	yes	characteristic, complemented
105	#2234	C₂²	1	1	yes	characteristic, complemented
106	#2232	C₂²	1	1	yes	characteristic
107	#2229	C₂²	1	1	yes	characteristic, complemented
108	#2229	C₂²	1	1	yes	characteristic, complemented
109	#2229	C₂²	1	1	yes	characteristic, complemented
110	#2229	C₂²	1	1	yes	characteristic, complemented
111	#2229	C₂²	1	1	yes	characteristic, complemented
112	#2228	C₂²	1	1	yes	characteristic, complemented
113	#2227	C₂²	1	1	yes	characteristic, complemented
114	#2225	C₂²	1	1	yes	characteristic, complemented
115	#2220	C₂²	1	1	yes	characteristic
116	#2220	C₂²	1	1	yes	characteristic
117	#2220	C₂²	1	1	yes	characteristic, complemented
118	#2219	C₂²	1	1	yes	characteristic
119	#2219	C₂²	1	1	yes	characteristic
120	#2219	C₂²	1	1	yes	characteristic
121	#2219	C₂²	1	1	yes	characteristic
122	#2219	C₂²	1	1	yes	characteristic
123	#2219	C₂²	1	1	yes	characteristic
124	#2219	C₂²	1	1	yes	characteristic
125	#2219	C₂²	1	1	yes	characteristic
126	#2219	C₂²	1	1	yes	characteristic
127	#2219	C₂²	1	1	yes	characteristic
128	#2219	C₂²	1	1	yes	characteristic, complemented
129	#2219	C₂²	1	1	yes	characteristic, complemented
130	#2219	C₂²	1	1	yes	characteristic, complemented
131	#2217	C₂²	1	1	yes	characteristic
132	#2217	C₂²	1	1	yes	characteristic
133	#2217	C₂²	1	1	yes	characteristic
134	#2217	C₂²	1	1	yes	characteristic
135	#2217	C₂²	1	1	yes	characteristic, complemented
136	#2216	C₂²	1	1	yes	characteristic
137	#2216	C₂²	1	1	yes	characteristic
138	#2216	C₂²	1	1	yes	characteristic
139	#2216	C₂²	1	1	yes	characteristic
140	#2216	C₂²	1	1	yes	characteristic
141	#2216	C₂²	1	1	yes	characteristic
142	#2216	C₂²	1	1	yes	characteristic
143	#2216	C₂²	1	1	yes	characteristic
144	#2216	C₂²	1	1	yes	characteristic, complemented
145	#2216	C₂²	1	1	yes	characteristic, complemented
146	#2216	C₂²	1	1	yes	characteristic, complemented
147	#2211	C₂²	1	1	yes	characteristic, complemented
148	#2211	C₂²	1	1	yes	characteristic, complemented
149	#2209	C₂²	1	1	yes	characteristic, complemented
150	#2209	C₂²	1	1	yes	characteristic, complemented
151	#2209	C₂²	1	1	yes	characteristic, complemented
152	#2209	C₂²	1	1	yes	characteristic, complemented
153	#2209	C₂²	1	1	yes	characteristic, complemented
154	#2208	C₂²	1	1	yes	characteristic, complemented
155	#2189	C₂²	1	1	yes	characteristic
156	#2189	C₂²	1	1	yes	characteristic
157	#2189	C₂²	1	1	yes	characteristic, complemented
158	#2189	C₂²	1	1	yes	characteristic, complemented
159	#2188	C₂²	1	1	yes	characteristic
160	#2188	C₂²	1	1	yes	characteristic
161	#2188	C₂²	1	1	yes	characteristic
162	#2188	C₂²	1	1	yes	characteristic
163	#2188	C₂²	1	1	yes	characteristic
164	#2188	C₂²	1	1	yes	characteristic, complemented
165	#2188	C₂²	1	1	yes	characteristic, complemented
166	#2188	C₂²	1	1	yes	characteristic, complemented
167	#2188	C₂²	1	1	yes	characteristic, complemented
168	#2188	C₂²	1	1	yes	characteristic, complemented
169	#2185	C₂²	1	1	yes	characteristic
170	#2185	C₂²	1	1	yes	characteristic, complemented
171	#2176	C₂²	1	1	yes	characteristic, complemented
172	#2176	C₂²	1	1	yes	characteristic, complemented
173	#2176	C₂²	1	1	yes	characteristic, complemented
174	#2175	C₂²	1	1	yes	characteristic, complemented
175	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
176	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
177	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
178	C₄×SD₃₂	C₂²	1	1	yes	characteristic, complemented
179	#2169	C₂²	1	1	yes	characteristic
180	#2169	C₂²	1	1	yes	characteristic
181	#2168	C₂²	1	1	yes	characteristic
182	#2168	C₂²	1	1	yes	characteristic
183	#2168	C₂²	1	1	yes	characteristic
184	#2168	C₂²	1	1	yes	characteristic
185	D₄×C₁₆	C₂²	1	1	yes	characteristic
186	D₄×C₁₆	C₂²	1	1	yes	characteristic
187	#2159	C₂²	1	1	yes	characteristic
188	#2159	C₂²	1	1	yes	characteristic, complemented
189	#2158	C₂²	1	1	yes	characteristic, complemented
190	C₂×#367	C₂²	1	1	yes	characteristic
191	#2151	C₂²	1	1	yes	characteristic
192	#2141	C₂²	1	1	yes	characteristic
193	#2141	C₂²	1	1	yes	characteristic, complemented
194	#2141	C₂²	1	1	yes	characteristic, complemented
195	#2139	C₂²	1	1	yes	characteristic
196	#2138	C₂²	1	1	yes	characteristic, complemented
197	C₂×#358	C₂²	1	1	yes	characteristic
198	C₂×#358	C₂²	1	1	yes	characteristic
199	C₂×#358	C₂²	1	1	yes	characteristic, complemented
200	#2113	C₂²	1	1	yes	characteristic
201	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
202	#2108	C₂²	1	1	yes	characteristic
203	C₂×#135	C₂³	1	1	yes	characteristic
204	C₂×#135	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
206	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
207	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
208	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
209	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
210	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
211	C₂×#131	C₂³	1	1	yes	characteristic
212	C₂³×C₈	C₂³	1	1	yes	characteristic
213	#563	—	4	1	no	—
214	#563	—	4	1	no	—
215	#563	—	4	1	no	—
216	#562	—	4	1	no	—
217	#556	—	2	1	no	—
218	#554	—	2	1	no	—
219	#554	—	4	1	no	—
220	#553	—	2	1	no	—
221	#553	—	4	1	no	—
222	#552	—	2	1	no	—
223	#552	—	2	1	no	—
224	#552	—	2	1	no	—
225	#552	—	2	1	no	—
226	#552	—	2	1	no	—
227	#551	—	4	1	no	—
228	#551	—	4	1	no	—
229	D₄×Q₈	—	2	1	no	—
230	D₄×Q₈	—	2	1	no	—
231	D₄×Q₈	—	2	1	no	—
232	D₄×Q₈	—	2	1	no	—
233	D₄×Q₈	—	2	1	no	—
234	#548	—	2	1	no	—
235	#548	—	2	1	no	—
236	#547	—	2	1	no	—
237	#544	—	4	1	no	—
238	#544	—	4	1	no	—
239	#542	—	2	1	no	—
240	#542	—	4	1	no	—
241	#541	—	2	1	no	—
242	#541	—	2	1	no	—
243	#541	—	2	1	no	—
244	#539	—	4	1	no	—
245	#539	—	4	1	no	—
246	#539	—	4	1	no	—
247	#538	—	4	1	no	—
248	#538	—	4	1	no	—
249	#537	—	2	1	no	—
250	#536	—	2	1	no	—
251	#536	—	2	1	no	—
252	#536	—	2	1	no	—
253	#525	—	2	1	no	—
254	#525	D₄	1	1	yes	characteristic
255	C₂×C₂²⋊Q₈	—	2	1	no	—
256	C₂×C₂²⋊Q₈	—	2	1	no	—
257	C₂×C₂²⋊Q₈	—	2	1	no	—
258	#510	—	4	2	no	—
259	#510	—	4	2	no	—
260	C₂×Q₃₂	—	4	2	no	—
261	C₂×Q₃₂	—	4	2	no	—
262	C₂×Q₃₂	C₂³	1	1	yes	characteristic
263	C₂×Q₃₂	C₂³	1	1	yes	characteristic
264	C₂×Q₃₂	C₂³	1	1	yes	characteristic
265	C₂×Q₃₂	C₂³	1	1	yes	characteristic
266	C₂×Q₃₂	C₂³	1	1	yes	characteristic
267	C₂×Q₃₂	C₂³	1	1	yes	characteristic
268	C₂×Q₃₂	C₂³	1	1	yes	characteristic
269	C₂×Q₃₂	C₂³	1	1	yes	characteristic
270	C₂×Q₃₂	C₂³	1	1	yes	characteristic
271	C₂×Q₃₂	C₂³	1	1	yes	characteristic
272	C₂×Q₃₂	C₂³	1	1	yes	characteristic
273	C₂×Q₃₂	C₂³	1	1	yes	characteristic
274	C₂×SD₃₂	C₂³	1	1	yes	characteristic
275	C₂×SD₃₂	C₂³	1	1	yes	characteristic
276	C₂×SD₃₂	C₂³	1	1	yes	characteristic
277	C₂×SD₃₂	C₂³	1	1	yes	characteristic
278	#504	—	4	2	no	—
279	C₂×M₃₂	—	4	2	no	—
280	C₂×M₃₂	C₂³	1	1	yes	characteristic
281	C₂×M₃₂	C₂³	1	1	yes	characteristic
282	C₂×M₃₂	C₂³	1	1	yes	characteristic
283	C₂×M₃₂	C₂³	1	1	yes	characteristic
284	C₂×M₃₂	C₂³	1	1	yes	characteristic
285	C₂×M₃₂	C₂³	1	1	yes	characteristic
286	C₂²×C₁₆	C₂³	1	1	yes	characteristic
287	C₂²×C₁₆	C₂³	1	1	yes	characteristic
288	C₂²×C₁₆	C₂³	1	1	yes	characteristic
289	C₂²×C₁₆	C₂³	1	1	yes	characteristic
290	C₂²×C₁₆	C₂³	1	1	yes	characteristic
291	C₂²×C₁₆	C₂³	1	1	yes	characteristic
292	#500	C₂³	1	1	yes	characteristic
293	#499	C₂³	1	1	yes	characteristic
294	#499	C₂³	1	1	yes	characteristic
295	#499	C₂³	1	1	yes	characteristic
296	#495	C₂³	1	1	yes	characteristic
297	#494	C₂³	1	1	yes	characteristic
298	#494	C₂³	1	1	yes	characteristic
299	#494	C₂³	1	1	yes	characteristic
300	#491	—	2	1	no	—
301	#491	—	2	1	no	—
302	#491	—	2	1	no	—
303	#489	—	2	1	no	—
304	#485	—	2	1	no	—
305	#485	—	2	1	no	—
306	#485	—	2	1	no	—
307	#485	—	2	1	no	—
308	#485	—	2	1	no	—
309	#485	—	2	1	no	—
310	#485	—	2	1	no	—
311	#484	—	2	1	no	—
312	#484	—	2	1	no	—
313	#483	—	2	1	no	—
314	#483	—	2	1	no	—
315	#483	—	2	1	no	—
316	#483	—	2	1	no	—
317	#483	—	2	1	no	—
318	#482	—	2	1	no	—
319	#481	—	2	1	no	—
320	#479	—	2	1	no	—
321	#479	—	2	1	no	—
322	#479	—	2	1	no	—
323	#479	—	2	1	no	—
324	#479	—	2	1	no	—
325	#478	—	2	1	no	—
326	#477	—	2	1	no	—
327	#475	—	2	1	no	—
328	#470	—	2	1	no	—
329	#470	—	2	1	no	—
330	#470	—	2	1	no	—
331	#470	—	2	1	no	—
332	#470	—	2	1	no	—
333	#470	—	2	1	no	—
334	#470	—	2	1	no	—
335	#470	—	2	1	no	—
336	#470	—	2	1	no	—
337	#468	—	2	1	no	—
338	#468	—	2	1	no	—
339	#468	—	2	1	no	—
340	#467	—	2	1	no	—
341	#467	—	2	1	no	—
342	#467	—	2	1	no	—
343	#467	—	2	1	no	—
344	#467	—	2	1	no	—
345	#467	—	2	1	no	—
346	#467	C₂³	1	1	yes	characteristic
347	#467	C₂³	1	1	yes	characteristic
348	#467	C₂³	1	1	yes	characteristic
349	#467	C₂³	1	1	yes	characteristic
350	#467	C₂³	1	1	yes	characteristic
351	#467	C₂³	1	1	yes	characteristic
352	#467	C₂³	1	1	yes	characteristic
353	#467	C₂³	1	1	yes	characteristic
354	#467	C₂³	1	1	yes	characteristic
355	#467	C₂³	1	1	yes	characteristic
356	#467	C₂³	1	1	yes	characteristic
357	#467	C₂³	1	1	yes	characteristic
358	#467	C₂³	1	1	yes	characteristic
359	#467	C₂³	1	1	yes	characteristic
360	#467	C₂³	1	1	yes	characteristic
361	#467	C₂³	1	1	yes	characteristic
362	#467	C₂³	1	1	yes	characteristic
363	#467	C₂³	1	1	yes	characteristic
364	#467	C₂³	1	1	yes	characteristic
365	#467	C₂³	1	1	yes	characteristic
366	#467	C₂³	1	1	yes	characteristic
367	#466	C₂³	1	1	yes	characteristic
368	#466	C₂³	1	1	yes	characteristic
369	#466	C₂³	1	1	yes	characteristic
370	#465	—	2	1	no	—
371	#465	—	2	1	no	—
372	#464	—	2	1	no	—
373	#464	—	2	1	no	—
374	#462	—	2	1	no	—
375	#462	—	2	1	no	—
376	#462	—	2	1	no	—
377	#462	—	2	1	no	—
378	#462	—	2	1	no	—
379	#461	—	2	1	no	—
380	#452	—	2	1	no	—
381	#452	—	2	1	no	—
382	#452	—	2	1	no	—
383	#452	—	2	1	no	—
384	#451	—	2	1	no	—
385	#451	—	2	1	no	—
386	#451	—	2	1	no	—
387	#451	—	2	1	no	—
388	#451	—	2	1	no	—
389	#451	—	2	1	no	—
390	#451	—	2	1	no	—
391	#451	—	2	1	no	—
392	#451	—	2	1	no	—
393	#451	—	2	1	no	—
394	#448	—	2	1	no	—
395	#448	—	2	1	no	—
396	#441	—	2	1	no	—
397	#441	—	2	1	no	—
398	#441	—	2	1	no	—
399	#440	—	2	1	no	—
400	C₄×Q₁₆	C₂³	1	1	yes	characteristic
401	C₄×Q₁₆	C₂³	1	1	yes	characteristic
402	C₄×Q₁₆	C₂³	1	1	yes	characteristic
403	C₄×Q₁₆	C₂³	1	1	yes	characteristic
404	C₄×Q₁₆	C₂³	1	1	yes	characteristic
405	C₄×Q₁₆	C₂³	1	1	yes	characteristic
406	C₄×Q₁₆	C₂³	1	1	yes	characteristic
407	C₄×D₈	C₂³	1	1	yes	characteristic
408	#435	D₄	1	1	yes	characteristic
409	#435	D₄	1	1	yes	characteristic
410	#435	D₄	1	1	yes	characteristic
411	#435	D₄	1	1	yes	characteristic
412	C₈×D₄	C₂³	1	1	yes	characteristic
413	C₈×D₄	C₂³	1	1	yes	characteristic
414	C₈×D₄	C₂³	1	1	yes	characteristic
415	C₈×D₄	C₂³	1	1	yes	characteristic
416	#427	C₂³	1	1	yes	characteristic
417	#427	C₂³	1	1	yes	characteristic
418	#427	C₂³	1	1	yes	characteristic
419	#427	C₂³	1	1	yes	characteristic
420	C₂×#107	C₂³	1	1	yes	characteristic
421	C₂×#107	C₂³	1	1	yes	characteristic
422	C₂×#107	C₂³	1	1	yes	characteristic
423	C₂×#107	C₂³	1	1	yes	characteristic
424	#424	D₄	1	1	yes	characteristic
425	#419	—	2	1	no	—
426	#419	—	2	1	no	—
427	#419	—	2	1	no	—
428	#417	—	2	1	no	—
429	#416	—	2	1	no	—
430	C₂×#103	—	2	1	no	—
431	C₂×#103	—	2	1	no	—
432	C₂×#103	—	2	1	no	—
433	#408	D₄	1	1	yes	characteristic
434	#407	D₄	1	1	yes	characteristic
435	#405	C₂³	1	1	yes	characteristic
436	#367	C₂³	1	1	yes	characteristic
437	#367	C₂³	1	1	yes	characteristic
438	#367	C₂³	1	1	yes	characteristic
439	#367	C₂³	1	1	yes	characteristic
440	#367	C₂³	1	1	yes	characteristic
441	#367	C₂³	1	1	yes	characteristic
442	#367	C₂³	1	1	yes	characteristic
443	#367	C₂³	1	1	yes	characteristic
444	#366	C₂³	1	1	yes	characteristic
445	#366	C₂³	1	1	yes	characteristic
446	#366	C₂³	1	1	yes	characteristic
447	#366	C₂³	1	1	yes	characteristic
448	#366	C₂³	1	1	yes	characteristic
449	#366	C₂³	1	1	yes	characteristic
450	#366	C₂³	1	1	yes	characteristic
451	#366	C₂³	1	1	yes	characteristic
452	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
453	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
454	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
455	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
456	#358	C₂³	1	1	yes	characteristic
457	#358	C₂³	1	1	yes	characteristic
458	#358	C₂³	1	1	yes	characteristic
459	#358	C₂³	1	1	yes	characteristic
460	#358	C₂³	1	1	yes	characteristic
461	#358	C₂³	1	1	yes	characteristic
462	#358	C₂³	1	1	yes	characteristic
463	#358	C₂³	1	1	yes	characteristic
464	#358	C₂³	1	1	yes	characteristic
465	#358	C₂³	1	1	yes	characteristic
466	#358	C₂³	1	1	yes	characteristic
467	#358	C₂³	1	1	yes	characteristic
468	#358	C₂³	1	1	yes	characteristic
469	#358	C₂³	1	1	yes	characteristic
470	#358	C₂³	1	1	yes	characteristic
471	#358	C₂³	1	1	yes	characteristic
472	#358	C₂³	1	1	yes	characteristic
473	#358	C₂³	1	1	yes	characteristic
474	#358	C₂³	1	1	yes	characteristic
475	#358	C₂³	1	1	yes	characteristic
476	#358	C₂³	1	1	yes	characteristic
477	#358	C₂³	1	1	yes	characteristic
478	#358	C₂³	1	1	yes	characteristic
479	#358	C₂³	1	1	yes	characteristic
480	#358	C₂³	1	1	yes	characteristic
481	#358	C₂³	1	1	yes	characteristic
482	#358	C₂³	1	1	yes	characteristic
483	#358	C₂³	1	1	yes	characteristic
484	#357	C₂³	1	1	yes	characteristic
485	#357	C₂³	1	1	yes	characteristic
486	#357	C₂³	1	1	yes	characteristic
487	#357	C₂³	1	1	yes	characteristic
488	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
489	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
490	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
491	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
492	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
493	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
494	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
495	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
496	#346	C₂³	1	1	yes	characteristic
497	#346	C₂³	1	1	yes	characteristic
498	C₄×C₁₆	C₂³	1	1	yes	characteristic
499	C₄×C₁₆	C₂³	1	1	yes	characteristic
500	C₂×#41	—	2	1	no	—
501	C₂×#41	—	2	1	no	—
502	C₂×#41	C₂×D₄	1	1	yes	characteristic
503	C₂²×Q₈	—	2	1	no	—
504	C₂²×Q₈	—	2	1	no	—
505	C₂²×Q₈	—	2	1	no	—
506	C₂²×Q₈	—	2	1	no	—
507	C₂²×Q₈	—	2	1	no	—
508	C₂²×Q₈	—	2	1	no	—
509	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
510	#135	—	4	1	no	—
511	#135	—	4	1	no	—
512	#135	—	4	1	no	—
513	#135	—	4	1	no	—
514	C₂×Q₁₆	—	2	1	no	—
515	C₂×Q₁₆	—	2	1	no	—
516	C₂×Q₁₆	—	2	1	no	—
517	C₂×Q₁₆	—	2	1	no	—
518	C₂×Q₁₆	—	2	1	no	—
519	C₂×Q₁₆	—	2	1	no	—
520	C₂×Q₁₆	—	2	1	no	—
521	C₂×Q₁₆	—	2	1	no	—
522	C₂×Q₁₆	—	2	1	no	—
523	C₂×Q₁₆	—	4	1	no	—
524	C₂×Q₁₆	—	4	1	no	—
525	C₂×Q₁₆	—	4	1	no	—
526	C₂×Q₁₆	—	4	1	no	—
527	C₂×Q₁₆	—	4	1	no	—
528	C₂×Q₁₆	—	4	1	no	—
529	C₂×Q₁₆	—	4	1	no	—
530	C₂×Q₁₆	—	4	1	no	—
531	C₂×Q₁₆	—	4	1	no	—
532	C₂×Q₁₆	—	4	1	no	—
533	C₂×Q₁₆	—	4	1	no	—
534	C₂×Q₁₆	—	4	1	no	—
535	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
536	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
537	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
538	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
539	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
540	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
541	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
542	C₂×SD₁₆	—	2	1	no	—
543	C₂×SD₁₆	—	2	1	no	—
544	C₂×SD₁₆	—	2	1	no	—
545	C₂×D₈	C₂⁴	1	1	yes	characteristic
546	#131	—	4	1	no	—
547	#131	—	4	1	no	—
548	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
549	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
550	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
551	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
552	C₂²×C₈	—	4	1	no	—
553	C₂²×C₈	—	4	1	no	—
554	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
555	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
556	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
557	C₂²×C₈	C₂⁴	1	1	yes	characteristic
558	C₂²×C₈	C₂⁴	1	1	yes	characteristic
559	C₂²×C₈	C₂⁴	1	1	yes	characteristic
560	C₂²×C₈	C₂⁴	1	1	yes	characteristic
561	C₂²×C₈	C₂⁴	1	1	yes	characteristic
562	C₄⋊Q₈	—	2	1	no	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	—	4	1	no	—
567	C₄⋊Q₈	—	4	1	no	—
568	C₄⋊Q₈	—	4	1	no	—
569	C₄⋊Q₈	—	4	1	no	—
570	C₄⋊Q₈	—	4	1	no	—
571	C₄⋊Q₈	—	4	1	no	—
572	C₄⋊Q₈	—	4	1	no	—
573	C₄⋊Q₈	—	4	1	no	—
574	#126	—	4	1	no	—
575	#126	—	4	1	no	—
576	#126	—	4	1	no	—
577	#126	—	4	1	no	—
578	#126	—	4	1	no	—
579	#126	—	4	1	no	—
580	#126	—	4	1	no	—
581	#126	—	4	1	no	—
582	#126	—	4	1	no	—
583	#126	—	4	1	no	—
584	#126	—	4	1	no	—
585	#126	—	4	1	no	—
586	#126	—	4	1	no	—
587	#126	—	4	1	no	—
588	#126	—	4	1	no	—
589	#125	—	2	1	no	—
590	#125	—	2	1	no	—
591	#125	—	2	1	no	—
592	#125	—	4	1	no	—
593	#125	—	4	1	no	—
594	#125	—	4	1	no	—
595	#125	—	4	1	no	—
596	#125	—	4	1	no	—
597	#125	—	4	1	no	—
598	#125	—	4	1	no	—
599	#125	—	4	1	no	—
600	#125	—	4	1	no	—
601	#125	—	4	1	no	—
602	#125	—	4	1	no	—
603	#125	—	4	1	no	—
604	#124	—	2	1	no	—
605	#124	—	4	1	no	—
606	#124	—	4	1	no	—
607	#124	—	4	1	no	—
608	#124	—	4	1	no	—
609	#124	—	4	1	no	—
610	#124	—	4	1	no	—
611	#124	—	4	1	no	—
612	#123	—	4	1	no	—
613	#123	—	4	1	no	—
614	#123	—	4	1	no	—
615	#123	—	4	1	no	—
616	#123	—	4	1	no	—
617	#123	—	4	1	no	—
618	#123	—	4	1	no	—
619	#123	—	4	1	no	—
620	#123	—	4	1	no	—
621	#123	—	4	1	no	—
622	#123	—	4	1	no	—
623	#123	—	4	1	no	—
624	#123	—	4	1	no	—
625	#123	—	4	1	no	—
626	#123	—	4	1	no	—
627	#123	—	4	1	no	—
628	#123	D₈	1	1	yes	characteristic
629	#123	D₈	1	1	yes	characteristic
630	C₂²⋊Q₈	—	2	1	no	—
631	C₂²⋊Q₈	—	2	1	no	—
632	C₂²⋊Q₈	—	2	1	no	—
633	C₂²⋊Q₈	—	2	1	no	—
634	C₂²⋊Q₈	—	2	1	no	—
635	C₂²⋊Q₈	—	2	1	no	—
636	C₂²⋊Q₈	—	2	1	no	—
637	C₂²⋊Q₈	—	2	1	no	—
638	C₂²⋊Q₈	—	2	1	no	—
639	C₂²⋊Q₈	—	2	1	no	—
640	C₂²⋊Q₈	—	2	1	no	—
641	C₂²⋊Q₈	—	2	1	no	—
642	C₂²⋊Q₈	—	2	1	no	—
643	C₂²⋊Q₈	—	2	1	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	—	2	1	no	—
646	C₂²⋊Q₈	—	2	1	no	—
647	C₂²⋊Q₈	—	2	1	no	—
648	C₂²⋊Q₈	—	2	1	no	—
649	C₂²⋊Q₈	—	2	1	no	—
650	C₂²⋊Q₈	—	2	1	no	—
651	C₂²⋊Q₈	—	4	1	no	—
652	C₂²⋊Q₈	—	4	1	no	—
653	C₂²⋊Q₈	—	4	1	no	—
654	C₂²⋊Q₈	—	4	1	no	—
655	C₂²⋊Q₈	—	4	1	no	—
656	C₂²⋊Q₈	—	4	1	no	—
657	C₂²⋊Q₈	—	4	1	no	—
658	C₂²⋊Q₈	—	4	1	no	—
659	C₂²⋊Q₈	—	4	1	no	—
660	C₂²⋊Q₈	—	4	1	no	—
661	C₂²⋊Q₈	—	4	1	no	—
662	C₂²⋊Q₈	—	4	1	no	—
663	C₂²⋊Q₈	—	4	1	no	—
664	C₂²⋊Q₈	—	4	1	no	—
665	C₂²⋊Q₈	—	4	1	no	—
666	C₂²⋊Q₈	—	4	1	no	—
667	C₂²⋊Q₈	—	4	1	no	—
668	C₂²⋊Q₈	—	4	1	no	—
669	C₂²⋊Q₈	—	4	1	no	—
670	C₂²⋊Q₈	—	4	1	no	—
671	C₂²⋊Q₈	—	4	1	no	—
672	C₂²⋊Q₈	—	4	1	no	—
673	C₂²⋊Q₈	D₈	1	1	yes	characteristic
674	C₂²⋊Q₈	D₈	1	1	yes	characteristic
675	#121	—	2	1	no	—
676	#121	—	2	1	no	—
677	#121	—	2	1	no	—
678	#121	—	4	1	no	—
679	#121	—	4	1	no	—
680	#121	—	4	1	no	—
681	#121	—	4	1	no	—
682	#121	—	4	1	no	—
683	#121	—	4	1	no	—
684	#121	—	4	1	no	—
685	#121	D₈	1	1	yes	characteristic
686	#121	D₈	1	1	yes	characteristic
687	#120	—	4	1	no	—
688	#120	D₈	1	1	yes	characteristic
689	#120	D₈	1	1	yes	characteristic
690	C₄×Q₈	—	2	1	no	—
691	C₄×Q₈	—	2	1	no	—
692	C₄×Q₈	—	2	1	no	—
693	C₄×Q₈	—	2	1	no	—
694	C₄×Q₈	—	2	1	no	—
695	C₄×Q₈	—	2	1	no	—
696	C₄×Q₈	—	2	1	no	—
697	C₄×Q₈	—	4	1	no	—
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	—	4	1	no	—
700	C₄×D₄	—	4	1	no	—
701	C₄×D₄	—	4	1	no	—
702	C₄×D₄	—	4	1	no	—
703	C₄×D₄	—	4	1	no	—
704	C₄×D₄	—	4	1	no	—
705	C₄×D₄	—	4	1	no	—
706	C₄×D₄	—	4	1	no	—
707	C₄×D₄	—	4	1	no	—
708	C₄×D₄	—	4	1	no	—
709	C₄×D₄	—	4	1	no	—
710	C₄×D₄	C₂×D₄	1	1	yes	characteristic
711	C₄×D₄	C₂×D₄	1	1	yes	characteristic
712	C₄×D₄	C₂×D₄	1	1	yes	characteristic
713	C₄×D₄	C₂×D₄	1	1	yes	characteristic
714	#117	—	2	1	no	—
715	#117	—	2	1	no	—
716	#117	—	2	1	no	—
717	#117	—	2	1	no	—
718	#117	—	4	1	no	—
719	#117	—	4	1	no	—
720	#117	—	4	1	no	—
721	#117	—	4	1	no	—
722	#117	—	4	1	no	—
723	#117	C₂×D₄	1	1	yes	characteristic
724	C₂×C₄⋊C₄	—	2	1	no	—
725	C₂×C₄⋊C₄	—	2	1	no	—
726	C₂×C₄⋊C₄	—	2	1	no	—
727	C₂×C₄⋊C₄	—	2	1	no	—
728	C₂×C₄⋊C₄	—	4	1	no	—
729	C₂×C₄⋊C₄	—	4	1	no	—
730	C₂×C₄⋊C₄	—	4	1	no	—
731	C₂×C₄⋊C₄	—	4	1	no	—
732	C₂×C₂²⋊C₄	—	4	1	no	—
733	C₂×C₂²⋊C₄	—	4	1	no	—
734	C₂×C₂²⋊C₄	—	4	1	no	—
735	Q₃₂	—	2	2	no	—
736	Q₃₂	—	2	2	no	—
737	Q₃₂	—	2	2	no	—
738	Q₃₂	—	4	1	no	—
739	Q₃₂	—	4	1	no	—
740	Q₃₂	—	4	1	no	—
741	Q₃₂	—	4	1	no	—
742	Q₃₂	—	4	1	no	—
743	Q₃₂	—	4	1	no	—
744	Q₃₂	—	4	1	no	—
745	Q₃₂	—	4	1	no	—
746	Q₃₂	—	4	1	no	—
747	SD₃₂	—	2	2	no	—
748	SD₃₂	—	4	1	no	—
749	SD₃₂	—	4	1	no	—
750	SD₃₂	—	4	1	no	—
751	M₃₂	—	2	2	no	—
752	M₃₂	—	2	2	no	—
753	M₃₂	—	2	2	no	—
754	M₃₂	—	4	1	no	—
755	M₃₂	—	4	1	no	—
756	M₃₂	—	4	1	no	—
757	C₂×C₁₆	—	2	2	no	—
758	C₂×C₁₆	—	2	2	no	—
759	C₂×C₁₆	—	4	1	no	—
760	C₂×C₁₆	—	4	1	no	—
761	C₂×C₁₆	—	4	1	no	—
762	C₂×C₁₆	—	4	1	no	—
763	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
764	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
765	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
766	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
767	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
768	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
769	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
770	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
771	#107	—	2	1	no	—
772	#107	—	2	1	no	—
773	#107	—	2	1	no	—
774	#107	—	2	1	no	—
775	#107	—	2	1	no	—
776	#107	C₂⁴	1	1	yes	characteristic
777	#107	C₂⁴	1	1	yes	characteristic
778	#107	C₂⁴	1	1	yes	characteristic
779	#107	C₂⁴	1	1	yes	characteristic
780	#107	C₂⁴	1	1	yes	characteristic
781	#107	C₂⁴	1	1	yes	characteristic
782	#107	C₂⁴	1	1	yes	characteristic
783	#107	C₂⁴	1	1	yes	characteristic
784	#106	—	2	1	no	—
785	#106	—	2	1	no	—
786	#106	—	2	1	no	—
787	#106	—	2	1	no	—
788	#106	—	2	1	no	—
789	#106	—	2	1	no	—
790	#106	—	2	1	no	—
791	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
792	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
793	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
794	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
795	#103	—	2	1	no	—
796	#103	—	2	1	no	—
797	#103	—	2	1	no	—
798	#103	—	2	1	no	—
799	#103	—	2	1	no	—
800	#103	—	2	1	no	—
801	#103	—	2	1	no	—
802	#103	—	2	1	no	—
803	#103	—	2	1	no	—
804	#103	—	2	1	no	—
805	#103	—	2	1	no	—
806	#103	—	2	1	no	—
807	#103	—	2	1	no	—
808	#103	—	2	1	no	—
809	#103	—	2	1	no	—
810	#103	—	2	1	no	—
811	#103	—	2	1	no	—
812	#103	—	2	1	no	—
813	#103	—	2	1	no	—
814	#103	—	2	1	no	—
815	#103	—	2	1	no	—
816	#103	—	2	1	no	—
817	#103	—	2	1	no	—
818	#103	—	2	1	no	—
819	#103	—	2	1	no	—
820	#103	—	2	1	no	—
821	#103	—	2	1	no	—
822	#103	—	2	1	no	—
823	#102	—	2	1	no	—
824	#102	—	2	1	no	—
825	#102	—	2	1	no	—
826	#102	—	2	1	no	—
827	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
828	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
829	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
830	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
831	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
832	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
833	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
834	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
835	#97	C₂×D₄	1	1	yes	characteristic
836	#97	C₂×D₄	1	1	yes	characteristic
837	C₄×C₈	C₂⁴	1	1	yes	characteristic
838	C₄×C₈	C₂⁴	1	1	yes	characteristic
839	C₂⁴	C₂×D₈	1	1	yes	characteristic
840	#41	—	4	1	no	—
841	#41	—	4	1	no	—
842	#41	—	8	1	no	—
843	#41	—	8	1	no	—
844	#41	—	8	1	no	—
845	#41	—	8	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	1	no	—
850	C₂×Q₈	—	2	1	no	—
851	C₂×Q₈	—	2	1	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	4	1	no	—
854	C₂×Q₈	—	4	1	no	—
855	C₂×Q₈	—	4	1	no	—
856	C₂×Q₈	—	4	1	no	—
857	C₂×Q₈	—	4	1	no	—
858	C₂×Q₈	—	4	1	no	—
859	C₂×Q₈	—	4	1	no	—
860	C₂×Q₈	—	8	1	no	—
861	C₂×Q₈	—	8	1	no	—
862	C₂×Q₈	—	8	1	no	—
863	C₂×Q₈	—	8	1	no	—
864	C₂×Q₈	—	8	1	no	—
865	C₂×Q₈	—	8	1	no	—
866	C₂×Q₈	—	8	1	no	—
867	C₂×Q₈	—	8	1	no	—
868	C₂×Q₈	—	8	1	no	—
869	C₂×Q₈	—	8	1	no	—
870	C₂×Q₈	—	8	1	no	—
871	C₂×Q₈	—	8	1	no	—
872	C₂×Q₈	C₂×D₈	1	1	yes	characteristic
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	—	4	1	no	—
875	C₂×D₄	—	4	1	no	—
876	C₂×D₄	—	4	1	no	—
877	C₂×D₄	—	4	1	no	—
878	C₂×D₄	—	4	1	no	—
879	C₂×D₄	C₂×D₈	1	1	yes	characteristic
880	C₂×D₄	C₂×D₈	1	1	yes	characteristic
881	C₂×D₄	C₂×D₈	1	1	yes	characteristic
882	C₂×D₄	C₂×D₈	1	1	yes	characteristic
883	C₂×D₄	C₂×D₈	1	1	yes	characteristic
884	C₂×D₄	C₂×D₈	1	1	yes	characteristic
885	C₂×D₄	C₂×D₈	1	1	yes	characteristic
886	C₂²×C₄	—	4	1	no	—
887	C₂²×C₄	—	4	1	no	—
888	C₂²×C₄	—	4	1	no	—
889	C₂²×C₄	—	4	1	no	—
890	C₂²×C₄	—	4	1	no	—
891	C₂²×C₄	—	4	1	no	—
892	C₂²×C₄	—	4	1	no	—
893	C₂²×C₄	—	4	1	no	—
894	C₂²×C₄	—	4	1	no	—
895	C₂²×C₄	—	4	1	no	—
896	C₂²×C₄	—	4	1	no	—
897	C₂²×C₄	—	4	1	no	—
898	C₂²×C₄	—	4	1	no	—
899	C₂²×C₄	—	4	1	no	—
900	C₂²×C₄	—	4	1	no	—
901	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
902	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
903	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
904	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
905	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
906	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
907	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
908	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
909	Q₁₆	—	2	1	no	—
910	Q₁₆	—	2	1	no	—
911	Q₁₆	—	2	1	no	—
912	Q₁₆	—	2	1	no	—
913	Q₁₆	—	2	1	no	—
914	Q₁₆	—	2	1	no	—
915	Q₁₆	—	2	1	no	—
916	Q₁₆	—	2	1	no	—
917	Q₁₆	—	2	1	no	—
918	Q₁₆	—	2	1	no	—
919	Q₁₆	—	2	1	no	—
920	Q₁₆	—	2	1	no	—
921	Q₁₆	—	2	1	no	—
922	Q₁₆	—	2	1	no	—
923	Q₁₆	—	8	1	no	—
924	Q₁₆	—	8	1	no	—
925	Q₁₆	—	8	1	no	—
926	Q₁₆	—	8	1	no	—
927	Q₁₆	—	8	1	no	—
928	Q₁₆	—	8	1	no	—
929	Q₁₆	—	8	1	no	—
930	Q₁₆	—	8	1	no	—
931	Q₁₆	—	8	1	no	—
932	SD₁₆	—	8	1	no	—
933	SD₁₆	—	8	1	no	—
934	SD₁₆	—	8	1	no	—
935	D₈	—	2	1	no	—
936	D₈	—	2	1	no	—
937	M₁₆	—	4	1	no	—
938	M₁₆	—	4	1	no	—
939	M₁₆	—	4	1	no	—
940	M₁₆	—	4	1	no	—
941	C₂×C₈	—	2	1	no	—
942	C₂×C₈	—	2	1	no	—
943	C₂×C₈	—	2	1	no	—
944	C₂×C₈	—	2	1	no	—
945	C₂×C₈	—	2	1	no	—
946	C₂×C₈	—	2	1	no	—
947	C₂×C₈	—	2	1	no	—
948	C₂×C₈	—	2	1	no	—
949	C₂×C₈	—	2	1	no	—
950	C₂×C₈	—	2	1	no	—
951	C₂×C₈	—	4	1	no	—
952	C₂×C₈	—	4	1	no	—
953	C₂×C₈	—	4	1	no	—
954	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
955	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
956	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
957	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
958	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
959	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
960	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
961	C₂×C₈	C₂⁵	1	1	yes	characteristic
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	4	1	no	—
971	C₄⋊C₄	—	4	1	no	—
972	C₄⋊C₄	—	4	1	no	—
973	C₄⋊C₄	—	4	1	no	—
974	C₄⋊C₄	—	4	1	no	—
975	C₄⋊C₄	—	4	1	no	—
976	C₄⋊C₄	—	4	1	no	—
977	C₄⋊C₄	—	4	1	no	—
978	C₄⋊C₄	—	4	1	no	—
979	C₄⋊C₄	—	4	1	no	—
980	C₄⋊C₄	—	4	1	no	—
981	C₄⋊C₄	—	4	1	no	—
982	C₄⋊C₄	—	4	1	no	—
983	C₄⋊C₄	—	4	1	no	—
984	C₄⋊C₄	—	4	1	no	—
985	C₄⋊C₄	—	4	1	no	—
986	C₄⋊C₄	—	4	1	no	—
987	C₄⋊C₄	—	4	1	no	—
988	C₄⋊C₄	—	4	1	no	—
989	C₄⋊C₄	—	4	1	no	—
990	C₄⋊C₄	—	4	1	no	—
991	C₄⋊C₄	—	4	1	no	—
992	C₄⋊C₄	—	4	1	no	—
993	C₄⋊C₄	—	4	1	no	—
994	C₄⋊C₄	—	4	1	no	—
995	C₄⋊C₄	—	4	1	no	—
996	C₄⋊C₄	—	4	1	no	—
997	C₄⋊C₄	—	4	1	no	—
998	C₄⋊C₄	—	4	1	no	—
999	C₄⋊C₄	—	4	1	no	—
1000	C₄⋊C₄	—	4	1	no	—
1001	C₄⋊C₄	—	4	1	no	—
1002	C₄⋊C₄	—	4	1	no	—
1003	C₄⋊C₄	—	4	1	no	—
1004	C₄⋊C₄	—	4	1	no	—
1005	C₄⋊C₄	—	4	1	no	—
1006	C₄⋊C₄	—	4	1	no	—
1007	C₄⋊C₄	—	4	1	no	—
1008	C₄⋊C₄	—	4	1	no	—
1009	C₄⋊C₄	—	4	1	no	—
1010	C₄⋊C₄	—	4	1	no	—
1011	C₄⋊C₄	—	4	1	no	—
1012	C₄⋊C₄	—	4	1	no	—
1013	C₄⋊C₄	—	4	1	no	—
1014	C₄⋊C₄	—	4	1	no	—
1015	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1016	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1017	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1018	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1019	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1020	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1021	C₂²⋊C₄	—	4	1	no	—
1022	C₂²⋊C₄	—	4	1	no	—
1023	C₂²⋊C₄	—	4	1	no	—
1024	C₂²⋊C₄	—	4	1	no	—
1025	C₂²⋊C₄	—	4	1	no	—
1026	C₂²⋊C₄	—	4	1	no	—
1027	C₂²⋊C₄	—	4	1	no	—
1028	C₂²⋊C₄	—	4	1	no	—
1029	C₂²⋊C₄	—	4	1	no	—
1030	C₂²⋊C₄	—	4	1	no	—
1031	C₂²⋊C₄	—	4	1	no	—
1032	C₂²⋊C₄	—	4	1	no	—
1033	C₂²⋊C₄	—	4	1	no	—
1034	C₂²⋊C₄	—	4	1	no	—
1035	C₂²⋊C₄	—	4	1	no	—
1036	C₂²⋊C₄	—	4	1	no	—
1037	C₂²⋊C₄	—	4	1	no	—
1038	C₂²⋊C₄	—	4	1	no	—
1039	C₂²⋊C₄	—	4	1	no	—
1040	C₂²⋊C₄	—	4	1	no	—
1041	C₂²⋊C₄	—	4	1	no	—
1042	C₂²⋊C₄	—	4	1	no	—
1043	C₂²⋊C₄	—	4	1	no	—
1044	C₂²⋊C₄	—	4	1	no	—
1045	C₂²⋊C₄	—	4	1	no	—
1046	C₂²⋊C₄	—	4	1	no	—
1047	C₂²⋊C₄	—	4	1	no	—
1048	C₂²⋊C₄	—	4	1	no	—
1049	C₂²⋊C₄	—	4	1	no	—
1050	C₂²⋊C₄	—	4	1	no	—
1051	C₂²⋊C₄	—	4	1	no	—
1052	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1053	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1054	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1055	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1056	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1057	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1058	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1059	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1060	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1061	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1062	C₄²	—	4	1	no	—
1063	C₄²	—	4	1	no	—
1064	C₄²	—	4	1	no	—
1065	C₄²	—	4	1	no	—
1066	C₄²	—	4	1	no	—
1067	C₄²	—	4	1	no	—
1068	C₄²	—	4	1	no	—
1069	C₄²	—	4	1	no	—
1070	C₄²	—	4	1	no	—
1071	C₄²	—	4	1	no	—
1072	C₄²	—	4	1	no	—
1073	C₄²	C₂²×D₄	1	1	yes	characteristic
1074	C₄²	C₂²×D₄	1	1	yes	characteristic
1075	C₁₆	—	2	1	no	—
1076	C₁₆	—	2	1	no	—
1077	C₁₆	—	2	1	no	—
1078	C₁₆	—	2	1	no	—
1079	C₁₆	—	2	1	no	—
1080	C₁₆	—	2	1	no	—
1081	C₁₆	—	2	1	no	—
1082	C₁₆	H(5,𝔽₂)	1	2	yes	—
1083	C₂³	—	2	2	no	—
1084	C₂³	—	4	1	no	—
1085	C₂³	—	4	1	no	—
1086	C₂³	—	4	1	no	—
1087	C₂³	C₂²×D₈	1	1	yes	characteristic
1088	C₂³	C₂²×D₈	1	1	yes	characteristic
1089	C₂³	C₂²×D₈	1	1	yes	characteristic
1090	C₂³	C₂²×D₈	1	1	yes	characteristic
1091	C₂³	C₂²×D₈	1	1	yes	characteristic
1092	Q₈	—	4	1	no	—
1093	Q₈	—	4	1	no	—
1094	Q₈	—	4	1	no	—
1095	Q₈	—	4	1	no	—
1096	Q₈	—	4	1	no	—
1097	Q₈	—	4	1	no	—
1098	Q₈	—	4	1	no	—
1099	Q₈	—	4	1	no	—
1100	Q₈	—	4	1	no	—
1101	Q₈	—	4	1	no	—
1102	Q₈	—	4	1	no	—
1103	Q₈	—	4	1	no	—
1104	Q₈	—	4	1	no	—
1105	Q₈	—	4	1	no	—
1106	Q₈	—	4	1	no	—
1107	Q₈	—	16	1	no	—
1108	Q₈	—	16	1	no	—
1109	Q₈	—	16	1	no	—
1110	Q₈	—	16	1	no	—
1111	Q₈	—	16	1	no	—
1112	Q₈	—	16	1	no	—
1113	Q₈	—	16	1	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	4	1	no	—
1117	D₄	—	4	1	no	—
1118	D₄	—	4	1	no	—
1119	D₄	—	4	1	no	—
1120	D₄	—	4	1	no	—
1121	D₄	—	4	1	no	—
1122	D₄	—	4	1	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	16	1	no	—
1125	D₄	—	16	1	no	—
1126	D₄	—	16	1	no	—
1127	D₄	—	16	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	4	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	1	no	—
1141	C₂×C₄	—	4	1	no	—
1142	C₂×C₄	—	4	1	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	8	2	no	—
1157	C₂×C₄	—	8	2	no	—
1158	C₂×C₄	—	16	1	no	—
1159	C₂×C₄	—	16	1	no	—
1160	C₂×C₄	—	16	1	no	—
1161	C₂×C₄	—	16	1	no	—
1162	C₂×C₄	—	16	1	no	—
1163	C₂×C₄	—	16	1	no	—
1164	C₂×C₄	—	16	1	no	—
1165	C₂×C₄	—	16	1	no	—
1166	C₂×C₄	—	16	1	no	—
1167	C₂×C₄	—	16	1	no	—
1168	C₂×C₄	—	16	1	no	—
1169	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1170	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1171	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1172	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1173	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1174	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1175	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1177	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1178	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1179	C₈	—	2	1	no	—
1180	C₈	—	2	1	no	—
1181	C₈	—	2	1	no	—
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	2	1	no	—
1186	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1187	C₈	#585	1	1	yes	characteristic
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	1	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	8	2	no	—
1203	C₂²	—	8	1	no	—
1204	C₂²	—	8	1	no	—
1205	C₂²	—	8	1	no	—
1206	C₂²	#3417	1	2	yes	—
1207	C₂²	C₂³×D₈	1	1	yes	characteristic
1208	C₄	—	2	1	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	1	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	2	1	no	—
1214	C₄	—	2	1	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	1	no	—
1217	C₄	—	8	1	no	—
1218	C₄	—	8	1	no	—
1219	C₄	—	8	1	no	—
1220	C₄	—	8	1	no	—
1221	C₄	—	8	1	no	—
1222	C₄	—	8	1	no	—
1223	C₄	—	8	1	no	—
1224	C₄	—	8	1	no	—
1225	C₄	—	8	1	no	—
1226	C₄	—	8	1	no	—
1227	C₄	—	8	1	no	—
1228	C₄	—	8	1	no	—
1229	C₄	—	8	1	no	—
1230	C₄	—	8	1	no	—
1231	C₄	—	8	1	no	—
1232	C₄	#3496	1	1	yes	characteristic
1233	C₄	#3584	1	1	yes	characteristic
1234	C₂	—	2	2	no	—
1235	C₂	—	4	1	no	—
1236	C₂	—	4	1	no	—
1237	C₂	—	4	1	no	—
1238	C₂	—	4	1	no	—
1239	C₂	—	16	1	no	—
1240	C₂	#62245	1	1	yes	characteristic
1241	C₂	C₂×#3417	1	1	yes	characteristic
1242	C₂	#62637	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁵
prime radical	#62267	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #525 ◁ #2929 ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #62271	C₂	semidirect
3. #33919	C₂	semidirect
4. #33916	C₂	semidirect
5. #33911	C₂	semidirect
6. #33904	C₂	semidirect
7. #33895	C₂	semidirect
8. #33894	C₂	semidirect
9. #33887	C₂	semidirect
10. #33882	C₂	semidirect
11. #33879	C₂	semidirect
12. #33879	C₂	semidirect
13. #33867	C₂	semidirect
14. #33866	C₂	semidirect
15. D₄×Q₃₂	C₂	semidirect
16. #33842	C₂	semidirect
17. #33836	C₂	semidirect
18. #33836	C₂	semidirect
19. #33827	C₂	semidirect
20. #33824	C₂	semidirect
21. #33768	C₂	semidirect
22. #33767	C₂	semidirect
23. #33756	C₂	semidirect
24. #33755	C₂	semidirect
25. #33745	C₂	semidirect
26. #33741	C₂	semidirect
27. #33613	C₂	semidirect
28. #33608	C₂	semidirect
29. #33606	C₂	semidirect
30. C₂×#2219	C₂	semidirect
31. #33436	C₂	semidirect
35. C₂×#510	C₂²	semidirect
37. C₂²×Q₃₂	C₂²	semidirect
83. #2255	C₂²	semidirect
84. #2253	C₂²	semidirect
85. #2251	C₂²	semidirect
86. #2247	C₂²	semidirect
87. #2245	C₂²	semidirect
88. #2245	C₂²	semidirect
89. #2242	C₂²	semidirect
90. #2241	C₂²	semidirect
93. #2237	C₂²	semidirect
94. #2237	C₂²	semidirect
95. #2237	C₂²	semidirect
96. #2237	C₂²	semidirect
97. #2237	C₂²	semidirect
102. #2236	C₂²	semidirect
104. #2235	C₂²	semidirect
105. #2234	C₂²	semidirect
107. #2229	C₂²	semidirect
108. #2229	C₂²	semidirect
109. #2229	C₂²	semidirect
110. #2229	C₂²	semidirect
111. #2229	C₂²	semidirect
112. #2228	C₂²	semidirect
113. #2227	C₂²	semidirect
114. #2225	C₂²	semidirect
117. #2220	C₂²	semidirect
128. #2219	C₂²	semidirect
129. #2219	C₂²	semidirect
130. #2219	C₂²	semidirect
135. #2217	C₂²	semidirect
144. #2216	C₂²	semidirect
145. #2216	C₂²	semidirect
146. #2216	C₂²	semidirect
147. #2211	C₂²	semidirect
148. #2211	C₂²	semidirect
149. #2209	C₂²	semidirect
150. #2209	C₂²	semidirect
151. #2209	C₂²	semidirect
152. #2209	C₂²	semidirect
153. #2209	C₂²	semidirect
154. #2208	C₂²	semidirect
157. #2189	C₂²	semidirect
158. #2189	C₂²	semidirect
164. #2188	C₂²	semidirect
165. #2188	C₂²	semidirect
166. #2188	C₂²	semidirect
167. #2188	C₂²	semidirect
168. #2188	C₂²	semidirect
170. #2185	C₂²	semidirect
171. #2176	C₂²	semidirect
172. #2176	C₂²	semidirect
173. #2176	C₂²	semidirect
174. #2175	C₂²	semidirect
175. C₄×Q₃₂	C₂²	semidirect
176. C₄×Q₃₂	C₂²	semidirect
177. C₄×Q₃₂	C₂²	semidirect
178. C₄×SD₃₂	C₂²	semidirect
188. #2159	C₂²	semidirect
189. #2158	C₂²	semidirect
193. #2141	C₂²	semidirect
194. #2141	C₂²	semidirect
196. #2138	C₂²	semidirect
199. C₂×#358	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#62271	2
#62267	2
#33919	2
#33916	2
#33911	2
#33904	2
#33895	2
#33894	2
#33887	2
#33882	2
#33879	2
#33867	2
#33866	2
D₄×Q₃₂	2
#33842	2
#33836	2
#33827	2
#33824	2
#33768	2
#33767	2
#33756	2
#33755	2
#33745	2
#33741	2
#33613	2
#33608	2
#33606	2
C₂×#2219	2
#33436	2