Subgroups — #6344462

Order 512.

1495 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60295	C₂	1	1	yes	maximal, characteristic
2	#60279	C₂	1	1	yes	maximal, characteristic
3	#60268	C₂	1	1	yes	maximal, characteristic
4	#17841	C₂	1	1	yes	maximal, characteristic, complemented
5	#17841	C₂	1	1	yes	maximal, characteristic, complemented
6	#17839	C₂	1	1	yes	maximal, characteristic, complemented
7	#17839	C₂	1	1	yes	maximal, characteristic, complemented
8	#17837	C₂	1	1	yes	maximal, characteristic, complemented
9	#17836	C₂	1	1	yes	maximal, characteristic, complemented
10	#17835	C₂	1	1	yes	maximal, characteristic, complemented
11	#17834	C₂	1	1	yes	maximal, characteristic, complemented
12	#17833	C₂	1	2	yes	maximal, complemented
13	#17832	C₂	1	2	yes	maximal, complemented
14	#17831	C₂	1	2	yes	maximal, complemented
15	#17830	C₂	1	2	yes	maximal, complemented
16	#17825	C₂	1	2	yes	maximal, complemented
17	#17824	C₂	1	2	yes	maximal, complemented
18	#17820	C₂	1	1	yes	maximal, characteristic, complemented
19	#17817	C₂	1	1	yes	maximal, characteristic, complemented
20	#17812	C₂	1	2	yes	maximal, complemented
21	#17811	C₂	1	2	yes	maximal, complemented
22	#17808	C₂	1	1	yes	maximal, characteristic, complemented
23	#17806	C₂	1	1	yes	maximal, characteristic, complemented
24	#3444	C₂²	1	1	yes	characteristic
25	#2994	—	2	1	no	—
26	#2994	—	2	1	no	—
27	#2993	—	2	2	no	—
28	#2993	C₄	1	2	yes	—
29	#2993	C₄	1	2	yes	—
30	#2992	C₄	1	4	yes	—
31	#2991	C₂²	1	1	yes	characteristic
32	#2991	C₂²	1	1	yes	characteristic
33	#2991	C₂²	1	1	yes	characteristic
34	#2991	C₂²	1	1	yes	characteristic
35	#2990	C₂²	1	1	yes	characteristic
36	#2990	C₂²	1	1	yes	characteristic
37	#2990	C₂²	1	1	yes	characteristic
38	#2990	C₂²	1	1	yes	characteristic
39	#2989	C₂²	1	2	yes	—
40	#2989	C₂²	1	2	yes	—
41	#2989	C₂²	1	2	yes	—
42	#2988	C₂²	1	2	yes	—
43	#2985	—	2	1	no	—
44	#2985	C₄	1	2	yes	—
45	#2981	—	2	1	no	—
46	#2981	C₄	1	2	yes	—
47	#2978	—	2	2	no	—
48	#2976	C₄	1	4	yes	—
49	#2969	—	2	1	no	—
50	#2969	—	2	1	no	—
51	#2967	—	2	2	no	—
52	#2965	C₂²	1	2	yes	—
53	#2965	C₂²	1	2	yes	—
54	#2965	C₂²	1	1	yes	characteristic
55	#2965	C₂²	1	1	yes	characteristic
56	C₈×#41	C₂²	1	1	yes	characteristic
57	C₈×#41	C₂²	1	1	yes	characteristic
58	#2960	—	2	1	no	—
59	#2933	—	2	2	no	—
60	#2931	—	2	1	no	—
61	#2925	C₂²	1	2	yes	—
62	#2925	C₂²	1	2	yes	—
63	#2925	C₂²	1	2	yes	—
64	#2922	C₂²	1	2	yes	—
65	#2922	C₂²	1	2	yes	—
66	#2920	C₂²	1	1	yes	characteristic
67	#2920	C₂²	1	1	yes	characteristic
68	#2920	C₂²	1	1	yes	characteristic
69	C₂×#431	C₂²	1	1	yes	characteristic
70	C₂×#431	C₂²	1	1	yes	characteristic
71	#2906	C₂²	1	2	yes	—
72	C₂×#423	C₂²	1	1	yes	characteristic
73	#1574	C₂²	1	1	yes	characteristic
74	#1574	C₂²	1	1	yes	characteristic
75	#1574	C₂²	1	1	yes	characteristic
76	#1574	C₂²	1	1	yes	characteristic
77	#1574	C₂²	1	1	yes	characteristic
78	#1574	C₂²	1	1	yes	characteristic
79	#1574	C₂²	1	1	yes	characteristic
80	#1574	C₂²	1	1	yes	characteristic
81	#1574	C₂²	1	2	yes	—
82	#1574	C₂²	1	2	yes	—
83	#1574	C₂²	1	1	yes	characteristic
84	#1574	C₂²	1	1	yes	characteristic
85	#1574	C₂²	1	1	yes	characteristic
86	#1574	C₂²	1	1	yes	characteristic
87	#1574	C₂²	1	2	yes	complemented
88	#1574	C₂²	1	2	yes	complemented
89	#1574	C₂²	1	2	yes	complemented
90	#1574	C₂²	1	2	yes	complemented
91	#1573	C₂²	1	1	yes	characteristic
92	#1573	C₂²	1	1	yes	characteristic
93	#1573	C₂²	1	1	yes	characteristic
94	#1573	C₂²	1	1	yes	characteristic
95	#1573	C₂²	1	2	yes	—
96	#1573	C₂²	1	2	yes	—
97	#1573	C₂²	1	2	yes	complemented
98	#1573	C₂²	1	2	yes	complemented
99	#1573	C₂²	1	2	yes	complemented
100	#1573	C₂²	1	2	yes	complemented
101	#1572	C₂²	1	2	yes	—
102	#1572	C₂²	1	2	yes	—
103	#1572	C₂²	1	2	yes	complemented
104	#1572	C₂²	1	2	yes	complemented
105	#1572	C₂²	1	2	yes	complemented
106	#1572	C₂²	1	2	yes	complemented
107	#1571	C₂²	1	2	yes	—
108	#1571	C₂²	1	2	yes	complemented
109	#1571	C₂²	1	2	yes	complemented
110	#1570	C₂²	1	2	yes	—
111	#1570	C₂²	1	2	yes	complemented
112	#1570	C₂²	1	2	yes	complemented
113	#1569	C₂²	1	2	yes	—
114	#1569	C₂²	1	2	yes	—
115	#1569	C₂²	1	2	yes	complemented
116	#1569	C₂²	1	2	yes	complemented
117	#1569	C₂²	1	2	yes	complemented
118	#1569	C₂²	1	2	yes	complemented
119	#1568	C₂²	1	2	yes	complemented
120	#1568	C₂²	1	2	yes	complemented
121	#1567	C₂²	1	1	yes	characteristic
122	#1567	C₂²	1	1	yes	characteristic
123	#1567	C₂²	1	2	yes	complemented
124	#1566	C₂²	1	1	yes	characteristic
125	#1566	C₂²	1	1	yes	characteristic
126	#1566	C₂²	1	2	yes	complemented
127	#1565	C₂²	1	2	yes	—
128	#1565	C₂²	1	2	yes	—
129	#1565	C₂²	1	2	yes	complemented
130	#1565	C₂²	1	2	yes	complemented
131	#1565	C₂²	1	2	yes	complemented
132	#1565	C₂²	1	2	yes	complemented
133	#1564	C₂²	1	1	yes	characteristic
134	#1564	C₂²	1	1	yes	characteristic
135	#1564	C₂²	1	1	yes	characteristic
136	#1564	C₂²	1	1	yes	characteristic
137	#1564	C₂²	1	2	yes	complemented
138	#1564	C₂²	1	2	yes	complemented
139	C₂×#335	C₂²	1	2	yes	complemented
140	C₂×#334	C₂²	1	2	yes	complemented
141	C₂×#131	—	2	2	no	—
142	C₂²×M₁₆	—	2	1	no	—
143	#533	C₂×C₄	1	1	yes	characteristic
144	#533	D₄	1	1	yes	characteristic
145	#533	Q₈	1	1	yes	characteristic
146	#532	C₂×C₄	1	1	yes	characteristic
147	#532	D₄	1	1	yes	characteristic
148	#532	Q₈	1	1	yes	characteristic
149	#529	C₂×C₄	1	2	yes	—
150	#529	C₂×C₄	1	1	yes	characteristic
151	#529	C₂×C₄	1	1	yes	characteristic
152	#529	D₄	1	2	yes	—
153	#529	D₄	1	1	yes	characteristic
154	#529	D₄	1	1	yes	characteristic
155	#529	Q₈	1	2	yes	—
156	#529	Q₈	1	2	yes	—
157	#525	C₂×C₄	1	2	yes	—
158	#525	D₄	1	2	yes	—
159	#525	Q₈	1	1	yes	characteristic
160	#525	Q₈	1	1	yes	characteristic
161	C₄×#41	C₂³	1	2	yes	—
162	C₄×#41	C₂³	1	2	yes	—
163	C₄×#41	C₂³	1	1	yes	characteristic
164	C₄×#41	C₂³	1	1	yes	characteristic
165	C₂²×C₄²	C₂³	1	1	yes	characteristic
166	#446	—	2	2	no	—
167	#446	—	2	1	no	—
168	#446	—	2	1	no	—
169	#446	—	2	2	no	—
170	#446	—	2	2	no	—
171	#446	—	2	1	no	—
172	#446	—	2	1	no	—
173	#446	C₂×C₄	1	4	yes	—
174	#446	C₂×C₄	1	4	yes	—
175	#446	C₂×C₄	1	2	yes	—
176	#446	C₂×C₄	1	2	yes	—
177	C₈×Q₈	—	2	2	no	—
178	C₈×Q₈	—	2	1	no	—
179	C₈×Q₈	—	2	1	no	—
180	C₈×Q₈	—	2	1	no	—
181	C₈×Q₈	—	2	1	no	—
182	C₈×Q₈	C₂×C₄	1	2	yes	—
183	C₈×Q₈	C₂×C₄	1	2	yes	—
184	#436	—	2	2	no	—
185	#436	—	2	1	no	—
186	#436	—	2	1	no	—
187	#436	—	2	2	no	—
188	#436	—	2	2	no	—
189	#436	—	2	2	no	—
190	#436	—	2	2	no	—
191	#436	—	2	2	no	—
192	#436	—	2	2	no	—
193	#436	—	2	1	no	—
194	#436	—	2	1	no	—
195	#436	C₂×C₄	1	4	yes	—
196	#436	C₂×C₄	1	4	yes	—
197	#436	C₂×C₄	1	2	yes	—
198	#436	C₂×C₄	1	2	yes	—
199	#435	—	2	2	no	—
200	#435	—	2	2	no	—
201	#435	—	2	2	no	—
202	#435	—	2	2	no	—
203	#435	—	2	2	no	—
204	#435	—	2	2	no	—
205	#435	—	2	2	no	—
206	#435	—	2	2	no	—
207	#435	—	2	2	no	—
208	#435	—	2	2	no	—
209	#435	C₂×C₄	1	4	yes	—
210	#435	C₂×C₄	1	4	yes	—
211	#435	C₂×C₄	1	4	yes	—
212	#435	C₂×C₄	1	4	yes	—
213	#435	C₂×C₄	1	4	yes	—
214	#435	C₂×C₄	1	4	yes	—
215	C₈×D₄	—	2	2	no	—
216	C₈×D₄	—	2	1	no	—
217	C₈×D₄	—	2	1	no	—
218	C₈×D₄	—	2	2	no	—
219	C₈×D₄	—	2	2	no	—
220	C₈×D₄	—	2	1	no	—
221	C₈×D₄	—	2	1	no	—
222	C₈×D₄	C₂×C₄	1	4	yes	—
223	C₈×D₄	C₂×C₄	1	4	yes	—
224	C₈×D₄	C₂×C₄	1	2	yes	—
225	C₈×D₄	C₂×C₄	1	2	yes	—
226	#433	—	2	2	no	—
227	#433	—	2	2	no	—
228	#433	—	2	2	no	—
229	#433	—	2	2	no	—
230	#433	—	2	2	no	—
231	#433	—	2	2	no	—
232	#433	C₂×C₄	1	4	yes	—
233	#433	C₂×C₄	1	4	yes	—
234	#433	C₂×C₄	1	4	yes	—
235	#433	C₂×C₄	1	4	yes	—
236	#432	—	2	1	no	—
237	#432	—	2	1	no	—
238	#432	C₂×C₄	1	2	yes	—
239	#432	C₂×C₄	1	2	yes	—
240	#432	C₂³	1	2	yes	—
241	#432	C₂³	1	2	yes	—
242	#432	C₂³	1	2	yes	—
243	#432	C₂³	1	2	yes	—
244	#432	C₂³	1	1	yes	characteristic
245	#432	C₂³	1	1	yes	characteristic
246	#432	C₂³	1	2	yes	—
247	#431	—	2	1	no	—
248	#431	—	2	1	no	—
249	#431	—	2	1	no	—
250	#431	—	2	1	no	—
251	#431	C₂×C₄	1	2	yes	—
252	#431	C₂×C₄	1	2	yes	—
253	#431	C₂³	1	1	yes	characteristic
254	#431	C₂³	1	1	yes	characteristic
255	#431	C₂³	1	1	yes	characteristic
256	#431	C₂³	1	1	yes	characteristic
257	#431	C₂³	1	2	yes	—
258	#431	C₂³	1	2	yes	—
259	#431	C₂³	1	2	yes	—
260	#431	C₂³	1	2	yes	—
261	#431	C₂³	1	2	yes	—
262	#431	C₂³	1	1	yes	characteristic
263	#431	C₂³	1	1	yes	characteristic
264	#431	C₂³	1	2	yes	—
265	#431	C₂³	1	2	yes	—
266	#431	C₂³	1	2	yes	—
267	#431	C₂³	1	1	yes	characteristic
268	#431	C₂³	1	1	yes	characteristic
269	#431	C₂³	1	1	yes	characteristic
270	#431	C₂³	1	1	yes	characteristic
271	#431	C₂³	1	2	yes	—
272	#431	C₂³	1	2	yes	—
273	#431	C₂³	1	1	yes	characteristic
274	#431	C₂³	1	1	yes	characteristic
275	#424	—	2	2	no	—
276	#424	—	2	2	no	—
277	#424	—	2	2	no	—
278	#424	C₂×C₄	1	4	yes	—
279	#424	C₂×C₄	1	4	yes	—
280	#423	—	2	1	no	—
281	#423	—	2	1	no	—
282	#423	C₂×C₄	1	2	yes	—
283	#423	C₂³	1	1	yes	characteristic
284	#423	C₂³	1	1	yes	characteristic
285	#423	C₂³	1	1	yes	characteristic
286	#423	C₂³	1	2	yes	—
287	#423	C₂³	1	2	yes	—
288	#423	C₂³	1	1	yes	characteristic
289	#423	C₂³	1	2	yes	—
290	#423	C₂³	1	2	yes	—
291	#423	C₂³	1	2	yes	—
292	#423	C₂³	1	1	yes	characteristic
293	#423	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₈	—	2	1	no	—
295	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
296	C₂×C₄⋊C₈	C₂³	1	2	yes	—
297	C₂×C₄⋊C₈	C₂³	1	2	yes	—
298	C₂×C₄⋊C₈	C₂³	1	2	yes	—
299	C₂×C₄⋊C₈	C₂³	1	2	yes	—
300	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₈	C₂³	1	2	yes	—
303	#408	—	2	2	no	—
304	#408	—	2	2	no	—
305	#408	—	2	2	no	—
306	#408	C₂×C₄	1	4	yes	—
307	#408	C₂×C₄	1	4	yes	—
308	#407	—	2	1	no	—
309	#407	—	2	1	no	—
310	#407	C₂×C₄	1	2	yes	—
311	C₂×C₂²⋊C₈	—	2	1	no	—
312	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
313	#405	—	2	2	no	—
314	#405	—	2	2	no	—
315	#405	—	2	2	no	—
316	C₄×M₁₆	—	2	1	no	—
317	C₄×M₁₆	—	2	1	no	—
318	C₄×M₁₆	C₂³	1	2	yes	—
319	C₄×M₁₆	C₂³	1	2	yes	—
320	C₄×M₁₆	C₂³	1	2	yes	—
321	C₂×C₄×C₈	—	2	1	no	—
322	C₂×C₄×C₈	C₂³	1	2	yes	—
323	C₂×C₄×C₈	C₂³	1	2	yes	—
324	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
325	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
326	#335	C₂³	1	1	yes	characteristic
327	#335	C₂³	1	2	yes	—
328	#335	C₂³	1	2	yes	—
329	#335	C₂³	1	2	yes	—
330	#335	C₂³	1	1	yes	characteristic
331	#335	C₂³	1	1	yes	characteristic
332	#335	C₂³	1	1	yes	characteristic
333	#335	C₂³	1	1	yes	characteristic
334	#335	C₂³	1	1	yes	characteristic
335	#335	C₂³	1	1	yes	characteristic
336	#335	C₂³	1	1	yes	characteristic
337	#335	C₂³	1	2	yes	—
338	#335	C₂³	1	2	yes	—
339	#335	C₂³	1	2	yes	—
340	#335	C₂³	1	2	yes	—
341	#335	C₂³	1	2	yes	—
342	#335	C₂³	1	2	yes	—
343	#335	C₂³	1	2	yes	—
344	#335	C₂³	1	2	yes	—
345	#335	C₂³	1	2	yes	—
346	#334	C₂³	1	1	yes	characteristic
347	#334	C₂³	1	2	yes	—
348	#334	C₂³	1	2	yes	—
349	#334	C₂³	1	2	yes	—
350	#334	C₂³	1	1	yes	characteristic
351	#334	C₂³	1	1	yes	characteristic
352	#334	C₂³	1	1	yes	characteristic
353	#334	C₂³	1	1	yes	characteristic
354	#334	C₂³	1	1	yes	characteristic
355	#334	C₂³	1	1	yes	characteristic
356	#334	C₂³	1	1	yes	characteristic
357	#334	C₂³	1	2	yes	—
358	#334	C₂³	1	2	yes	—
359	#334	C₂³	1	2	yes	—
360	#334	C₂³	1	2	yes	—
361	#334	C₂³	1	2	yes	—
362	#334	C₂³	1	2	yes	—
363	#334	C₂³	1	2	yes	—
364	#334	C₂³	1	2	yes	—
365	#334	C₂³	1	2	yes	—
366	C₂×#41	C₂²×C₄	1	2	yes	—
367	C₂×#41	C₂×D₄	1	2	yes	—
368	C₂×#41	C₂×Q₈	1	1	yes	characteristic
369	C₂×#41	C₂×Q₈	1	1	yes	characteristic
370	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
371	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
372	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
373	#131	—	8	4	no	—
374	C₂×M₁₆	—	2	2	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	2	no	—
378	C₂×M₁₆	—	2	2	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	2	no	—
384	C₂×M₁₆	—	2	2	no	—
385	C₂×M₁₆	—	8	2	no	—
386	C₂×M₁₆	C₂²×C₄	1	4	yes	—
387	C₂×M₁₆	C₂²×C₄	1	4	yes	—
388	C₂×M₁₆	C₂²×C₄	1	4	yes	—
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	2	no	—
392	C₂²×C₈	—	2	2	no	—
393	C₂²×C₈	—	2	2	no	—
394	C₂²×C₈	—	2	2	no	—
395	C₂²×C₈	—	2	2	no	—
396	C₂²×C₈	C₂²×C₄	1	2	yes	—
397	C₂²×C₈	C₂²×C₄	1	2	yes	—
398	C₂²×C₈	C₂²×C₄	1	4	yes	—
399	C₂²×C₈	C₂²×C₄	1	4	yes	—
400	C₄⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
401	C₄⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
402	C₄⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
403	#127	C₄⋊C₄	1	1	yes	characteristic
404	#126	C₄⋊C₄	1	2	yes	—
405	#126	C₄⋊C₄	1	2	yes	—
406	#126	C₄⋊C₄	1	2	yes	—
407	#126	C₄⋊C₄	1	2	yes	—
408	#125	C₄⋊C₄	1	1	yes	characteristic
409	#125	C₄⋊C₄	1	1	yes	characteristic
410	#125	C₄⋊C₄	1	2	yes	—
411	#125	C₄⋊C₄	1	2	yes	—
412	#124	C₄⋊C₄	1	1	yes	characteristic
413	#124	C₄⋊C₄	1	1	yes	characteristic
414	#124	C₄⋊C₄	1	2	yes	—
415	#124	C₄⋊C₄	1	2	yes	—
416	#123	C₄⋊C₄	1	2	yes	—
417	#123	C₄⋊C₄	1	2	yes	—
418	#123	C₄⋊C₄	1	2	yes	—
419	#123	C₄⋊C₄	1	2	yes	—
420	#123	C₄⋊C₄	1	2	yes	—
421	#123	C₄⋊C₄	1	2	yes	—
422	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
423	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
424	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
425	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
426	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
427	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
428	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
429	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
430	#121	C₄⋊C₄	1	2	yes	—
431	#121	C₄⋊C₄	1	2	yes	—
432	#121	C₄⋊C₄	1	2	yes	—
433	#121	C₄⋊C₄	1	2	yes	—
434	#121	C₄⋊C₄	1	1	yes	characteristic
435	#121	C₄⋊C₄	1	1	yes	characteristic
436	#121	C₄⋊C₄	1	1	yes	characteristic
437	#121	C₄⋊C₄	1	1	yes	characteristic
438	#120	C₄⋊C₄	1	2	yes	—
439	#120	C₄⋊C₄	1	2	yes	—
440	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
441	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
442	C₄×Q₈	C₂²×C₄	1	2	yes	—
443	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
444	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
445	C₄×Q₈	C₂×D₄	1	2	yes	—
446	C₄×Q₈	C₂×Q₈	1	2	yes	—
447	C₄×Q₈	C₂×Q₈	1	2	yes	—
448	C₄×D₄	C₂²×C₄	1	2	yes	—
449	C₄×D₄	C₂²×C₄	1	2	yes	—
450	C₄×D₄	C₂²×C₄	1	2	yes	—
451	C₄×D₄	C₂²×C₄	1	2	yes	—
452	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
453	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
454	C₄×D₄	C₂²×C₄	1	2	yes	—
455	C₄×D₄	C₂×D₄	1	2	yes	—
456	C₄×D₄	C₂×D₄	1	2	yes	—
457	C₄×D₄	C₂×D₄	1	2	yes	—
458	C₄×D₄	C₂×D₄	1	2	yes	—
459	C₄×D₄	C₂×D₄	1	1	yes	characteristic
460	C₄×D₄	C₂×D₄	1	1	yes	characteristic
461	C₄×D₄	C₂×D₄	1	2	yes	—
462	C₄×D₄	C₂×Q₈	1	2	yes	—
463	C₄×D₄	C₂×Q₈	1	2	yes	—
464	C₄×D₄	C₂×Q₈	1	2	yes	—
465	C₄×D₄	C₂×Q₈	1	2	yes	—
466	C₄×D₄	C₂×Q₈	1	2	yes	—
467	C₄×D₄	C₂×Q₈	1	2	yes	—
468	#117	C₂²×C₄	1	2	yes	—
469	#117	C₂²×C₄	1	2	yes	—
470	#117	C₂²×C₄	1	2	yes	—
471	#117	C₂×D₄	1	2	yes	—
472	#117	C₂×D₄	1	2	yes	—
473	#117	C₂×D₄	1	2	yes	—
474	#117	C₂×Q₈	1	1	yes	characteristic
475	#117	C₂×Q₈	1	1	yes	characteristic
476	#117	C₂×Q₈	1	2	yes	—
477	#117	C₂×Q₈	1	2	yes	—
478	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
479	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
480	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
481	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
482	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
483	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
484	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
485	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
486	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
487	C₂×C₄²	C₂⁴	1	2	yes	—
488	C₂×C₄²	C₂⁴	1	2	yes	—
489	C₂×C₄²	C₂⁴	1	1	yes	characteristic
490	C₂×C₄²	C₂⁴	1	1	yes	characteristic
491	C₂×C₄²	C₂⁴	1	1	yes	characteristic
492	C₄⋊C₈	—	2	2	no	—
493	C₄⋊C₈	—	2	1	no	—
494	C₄⋊C₈	—	2	1	no	—
495	C₄⋊C₈	—	2	2	no	—
496	C₄⋊C₈	—	2	1	no	—
497	C₄⋊C₈	—	2	2	no	—
498	C₄⋊C₈	—	2	2	no	—
499	C₄⋊C₈	—	2	1	no	—
500	C₄⋊C₈	—	2	2	no	—
501	C₄⋊C₈	—	2	2	no	—
502	C₄⋊C₈	—	2	2	no	—
503	C₄⋊C₈	—	2	2	no	—
504	C₄⋊C₈	—	2	1	no	—
505	C₄⋊C₈	—	2	1	no	—
506	C₄⋊C₈	—	2	1	no	—
507	C₄⋊C₈	—	2	1	no	—
508	C₄⋊C₈	—	2	2	no	—
509	C₄⋊C₈	—	2	2	no	—
510	C₄⋊C₈	C₂²×C₄	1	2	yes	—
511	C₄⋊C₈	C₂²×C₄	1	2	yes	—
512	C₄⋊C₈	C₂²×C₄	1	2	yes	—
513	C₄⋊C₈	C₂²×C₄	1	2	yes	—
514	C₄⋊C₈	C₂²×C₄	1	4	yes	—
515	C₄⋊C₈	C₂²×C₄	1	2	yes	—
516	C₄⋊C₈	C₂²×C₄	1	2	yes	—
517	C₄⋊C₈	C₂²×C₄	1	4	yes	—
518	C₄⋊C₈	C₂²×C₄	1	4	yes	—
519	C₄⋊C₈	C₂²×C₄	1	4	yes	—
520	C₄⋊C₈	C₂²×C₄	1	4	yes	—
521	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
522	C₄⋊C₈	C₂⁴	1	2	yes	—
523	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
524	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
525	C₄⋊C₈	C₂⁴	1	2	yes	—
526	C₄⋊C₈	C₂⁴	1	2	yes	—
527	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
528	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
529	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
530	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
531	C₄⋊C₈	C₂⁴	1	2	yes	—
532	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
533	C₂²⋊C₈	—	2	1	no	—
534	C₂²⋊C₈	—	2	1	no	—
535	C₂²⋊C₈	—	2	1	no	—
536	C₂²⋊C₈	—	2	1	no	—
537	C₂²⋊C₈	—	2	1	no	—
538	C₂²⋊C₈	—	2	1	no	—
539	C₂²⋊C₈	—	2	2	no	—
540	C₂²⋊C₈	—	2	2	no	—
541	C₂²⋊C₈	—	2	1	no	—
542	C₂²⋊C₈	—	2	1	no	—
543	C₂²⋊C₈	—	2	2	no	—
544	C₂²⋊C₈	—	2	2	no	—
545	C₂²⋊C₈	—	2	2	no	—
546	C₂²⋊C₈	—	2	2	no	—
547	C₂²⋊C₈	—	2	2	no	—
548	C₂²⋊C₈	—	2	2	no	—
549	C₂²⋊C₈	—	2	2	no	—
550	C₂²⋊C₈	—	2	2	no	—
551	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
552	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
553	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
554	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
555	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
556	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
557	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
558	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
559	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
560	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
561	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
562	#97	—	2	1	no	—
563	#97	—	2	1	no	—
564	#97	—	2	2	no	—
565	#97	—	2	2	no	—
566	#97	—	2	2	no	—
567	#97	—	2	2	no	—
568	#97	—	2	2	no	—
569	#97	C₂²×C₄	1	4	yes	—
570	#97	C₂²×C₄	1	4	yes	—
571	#97	C₂²×C₄	1	4	yes	—
572	C₄×C₈	—	2	1	no	—
573	C₄×C₈	—	2	1	no	—
574	C₄×C₈	—	2	1	no	—
575	C₄×C₈	—	2	1	no	—
576	C₄×C₈	—	2	2	no	—
577	C₄×C₈	—	2	1	no	—
578	C₄×C₈	—	2	1	no	—
579	C₄×C₈	—	2	2	no	—
580	C₄×C₈	—	2	2	no	—
581	C₄×C₈	—	2	2	no	—
582	C₄×C₈	—	2	2	no	—
583	C₄×C₈	C₂²×C₄	1	2	yes	—
584	C₄×C₈	C₂²×C₄	1	2	yes	—
585	C₄×C₈	C₂²×C₄	1	4	yes	—
586	C₄×C₈	C₂²×C₄	1	4	yes	—
587	C₄×C₈	C₂⁴	1	1	yes	characteristic
588	C₄×C₈	C₂⁴	1	1	yes	characteristic
589	C₄×C₈	C₂⁴	1	2	yes	—
590	C₄×C₈	C₂⁴	1	1	yes	characteristic
591	C₄×C₈	C₂⁴	1	1	yes	characteristic
592	C₄×C₈	C₂⁴	1	2	yes	—
593	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
594	#41	—	4	2	no	—
595	#41	—	4	4	no	—
596	#41	—	4	2	no	—
597	#41	—	4	2	no	—
598	#41	—	4	2	no	—
599	C₂×Q₈	C₂×C₄⋊C₄	1	1	yes	characteristic
600	C₂×Q₈	C₂×C₄⋊C₄	1	1	yes	characteristic
601	C₂×Q₈	C₂×C₄⋊C₄	1	2	yes	—
602	C₂×Q₈	C₂×C₄⋊C₄	1	2	yes	—
603	C₂×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
604	C₂×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
605	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
606	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
607	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
608	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
609	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
610	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
611	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
612	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
613	C₂²×C₄	—	4	1	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	4	1	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
618	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
619	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
620	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
621	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
622	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
623	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
624	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
625	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
626	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
627	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
628	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
629	C₂²×C₄	C₂³×C₄	1	2	yes	—
630	C₂²×C₄	C₂³×C₄	1	2	yes	—
631	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
632	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
633	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
634	C₂²×C₄	C₂²×D₄	1	2	yes	—
635	C₂²×C₄	C₂²×D₄	1	2	yes	—
636	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
637	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
638	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
639	C₂²×C₄	C₂²×Q₈	1	2	yes	—
640	C₂²×C₄	C₂²×Q₈	1	2	yes	—
641	M₁₆	—	4	4	no	—
642	M₁₆	—	4	4	no	—
643	M₁₆	—	4	4	no	—
644	M₁₆	—	4	4	no	—
645	M₁₆	—	8	1	no	—
646	M₁₆	—	8	1	no	—
647	M₁₆	—	8	2	no	—
648	M₁₆	—	8	1	no	—
649	M₁₆	—	8	1	no	—
650	M₁₆	—	8	2	no	—
651	M₁₆	—	8	1	no	—
652	M₁₆	—	8	1	no	—
653	M₁₆	—	8	2	no	—
654	M₁₆	—	8	2	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	2	no	—
660	C₂×C₈	—	2	2	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	—	2	2	no	—
666	C₂×C₈	—	2	2	no	—
667	C₂×C₈	—	4	2	no	—
668	C₂×C₈	—	4	4	no	—
669	C₂×C₈	—	4	4	no	—
670	C₂×C₈	—	4	2	no	—
671	C₂×C₈	—	4	2	no	—
672	C₂×C₈	—	4	2	no	—
673	C₂×C₈	—	8	2	no	—
674	C₂×C₈	—	8	2	no	—
675	C₂×C₈	—	8	2	no	—
676	C₂×C₈	—	8	2	no	—
677	C₂×C₈	—	8	2	no	—
678	C₂×C₈	C₂³×C₄	1	2	yes	—
679	C₂×C₈	C₂³×C₄	1	2	yes	—
680	C₂×C₈	C₂³×C₄	1	2	yes	—
681	C₂×C₈	C₂³×C₄	1	2	yes	—
682	C₂×C₈	C₂³×C₄	1	4	yes	—
683	C₂×C₈	C₂³×C₄	1	4	yes	—
684	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
685	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
686	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
687	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
688	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
689	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
690	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
691	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
692	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
693	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
694	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
695	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
696	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
697	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
698	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
699	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
700	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
701	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
702	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
703	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
704	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
705	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
706	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
707	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
708	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
709	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
710	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
711	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
712	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
713	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
714	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
715	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
716	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
717	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
718	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
719	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
720	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
721	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
722	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
723	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
724	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
725	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
726	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
727	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
728	C₄²	C₂³×C₄	1	1	yes	characteristic
729	C₄²	C₂³×C₄	1	2	yes	—
730	C₄²	C₂³×C₄	1	2	yes	—
731	C₄²	C₂³×C₄	1	1	yes	characteristic
732	C₄²	C₂³×C₄	1	1	yes	characteristic
733	C₄²	C₂²×D₄	1	1	yes	characteristic
734	C₄²	C₂²×D₄	1	1	yes	characteristic
735	C₄²	C₂²×D₄	1	1	yes	characteristic
736	C₄²	C₂²×D₄	1	2	yes	—
737	C₄²	C₂²×D₄	1	2	yes	—
738	C₄²	C₂²×Q₈	1	1	yes	characteristic
739	C₄²	C₂²×Q₈	1	1	yes	characteristic
740	C₄²	C₂²×Q₈	1	1	yes	characteristic
741	C₄²	C₂²×Q₈	1	2	yes	—
742	C₄²	C₂²×Q₈	1	2	yes	—
743	C₄²	C₂⁵	1	1	yes	characteristic
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	C₂²×C₄⋊C₄	1	2	yes	—
748	C₂³	C₂²×C₄⋊C₄	1	2	yes	—
749	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
750	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
751	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	4	2	no	—
755	Q₈	—	4	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	4	2	no	—
759	D₄	—	4	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	2	no	—
765	D₄	—	4	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
796	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
797	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
798	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
799	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
800	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
801	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
802	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
803	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
804	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
805	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
806	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
807	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
808	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
809	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
810	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
811	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
812	C₂×C₄	C₂³×Q₈	1	1	yes	characteristic
813	C₈	—	2	2	no	—
814	C₈	—	2	2	no	—
815	C₈	—	2	4	no	—
816	C₈	—	2	4	no	—
817	C₈	—	2	2	no	—
818	C₈	—	2	2	no	—
819	C₈	—	4	1	no	—
820	C₈	—	4	1	no	—
821	C₈	—	4	2	no	—
822	C₈	—	4	2	no	—
823	C₈	—	4	1	no	—
824	C₈	—	4	2	no	—
825	C₈	—	4	1	no	—
826	C₈	—	4	1	no	—
827	C₈	—	4	1	no	—
828	C₈	—	4	1	no	—
829	C₈	—	4	2	no	—
830	C₈	—	4	1	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	8	2	no	—
847	C₂²	C₂³×C₄⋊C₄	1	1	yes	characteristic
848	C₄	—	2	1	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	#2916	1	2	yes	—
864	C₄	#3573	1	2	yes	—
865	C₄	#3585	1	1	yes	characteristic
866	C₄	#3586	1	1	yes	characteristic
867	C₂	—	4	2	no	—
868	C₂	—	4	2	no	—
869	C₂	—	4	1	no	—
870	C₂	—	4	1	no	—
871	C₂	—	4	1	no	—
872	C₂	#60100	1	1	yes	characteristic
873	C₂	#60109	1	1	yes	characteristic
874	C₂	C₂×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₄²	C₂⁵
socle	C₂²	C₂³×C₄⋊C₄
prime radical	#3444	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ #3444 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #17841	C₂	semidirect
5. #17841	C₂	semidirect
6. #17839	C₂	semidirect
7. #17839	C₂	semidirect
8. #17837	C₂	semidirect
9. #17836	C₂	semidirect
10. #17835	C₂	semidirect
11. #17834	C₂	semidirect
12. #17833	C₂	semidirect
13. #17832	C₂	semidirect
14. #17831	C₂	semidirect
15. #17830	C₂	semidirect
16. #17825	C₂	semidirect
17. #17824	C₂	semidirect
18. #17820	C₂	semidirect
19. #17817	C₂	semidirect
20. #17812	C₂	semidirect
21. #17811	C₂	semidirect
22. #17808	C₂	semidirect
23. #17806	C₂	semidirect
87. #1574	C₂²	semidirect
88. #1574	C₂²	semidirect
89. #1574	C₂²	semidirect
90. #1574	C₂²	semidirect
97. #1573	C₂²	semidirect
98. #1573	C₂²	semidirect
99. #1573	C₂²	semidirect
100. #1573	C₂²	semidirect
103. #1572	C₂²	semidirect
104. #1572	C₂²	semidirect
105. #1572	C₂²	semidirect
106. #1572	C₂²	semidirect
108. #1571	C₂²	semidirect
109. #1571	C₂²	semidirect
111. #1570	C₂²	semidirect
112. #1570	C₂²	semidirect
115. #1569	C₂²	semidirect
116. #1569	C₂²	semidirect
117. #1569	C₂²	semidirect
118. #1569	C₂²	semidirect
119. #1568	C₂²	semidirect
120. #1568	C₂²	semidirect
123. #1567	C₂²	semidirect
126. #1566	C₂²	semidirect
129. #1565	C₂²	semidirect
130. #1565	C₂²	semidirect
131. #1565	C₂²	semidirect
132. #1565	C₂²	semidirect
137. #1564	C₂²	semidirect
138. #1564	C₂²	semidirect
139. C₂×#335	C₂²	semidirect
140. C₂×#334	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#60295	2
#60279	2
#60268	2
#17841	2
#17839	2
#17837	2
#17836	2
#17835	2
#17834	2
#17833	2
#17832	2
#17831	2
#17830	2
#17825	2
#17824	2
#17820	2
#17817	2
#17812	2
#17811	2
#17808	2
#17806	2