Subgroups — #61141

Order 256.

1069 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	#3321	C₂	1	1	yes	maximal, characteristic, complemented
4	#3320	C₂	1	1	yes	maximal, characteristic, complemented
5	#3319	C₂	1	1	yes	maximal, characteristic, complemented
6	#3318	C₂	1	1	yes	maximal, characteristic, complemented
7	#3317	C₂	1	1	yes	maximal, characteristic, complemented
8	#3316	C₂	1	1	yes	maximal, characteristic, complemented
9	#3315	C₂	1	1	yes	maximal, characteristic, complemented
10	#3314	C₂	1	1	yes	maximal, characteristic, complemented
11	#3313	C₂	1	1	yes	maximal, characteristic, complemented
12	#3312	C₂	1	1	yes	maximal, characteristic, complemented
13	#3311	C₂	1	1	yes	maximal, characteristic, complemented
14	#3310	C₂	1	1	yes	maximal, characteristic, complemented
15	#3309	C₂	1	1	yes	maximal, characteristic, complemented
16	#3308	C₂	1	1	yes	maximal, characteristic, complemented
17	#3307	C₂	1	1	yes	maximal, characteristic, complemented
18	#3306	C₂	1	1	yes	maximal, characteristic, complemented
19	#3135	C₂	1	1	yes	maximal, characteristic, complemented
20	#3091	C₂	1	1	yes	maximal, characteristic, complemented
21	#3091	C₂	1	1	yes	maximal, characteristic, complemented
22	#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	#3054	C₂	1	1	yes	maximal, characteristic, complemented
24	#3050	C₂	1	1	yes	maximal, characteristic, complemented
25	#3035	C₂	1	1	yes	maximal, characteristic, complemented
26	#3002	C₂	1	1	yes	maximal, characteristic, complemented
27	#3002	C₂	1	1	yes	maximal, characteristic, complemented
28	#2943	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#435	C₂	1	1	yes	maximal, characteristic, complemented
30	#2896	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#416	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#41	C₂²	1	1	yes	characteristic
33	C₂²×#41	C₂²	1	1	yes	characteristic
34	C₂×#135	C₂²	1	1	yes	characteristic
35	C₂×#135	C₂²	1	1	yes	characteristic, complemented
36	C₂×#135	C₂²	1	1	yes	characteristic, complemented
37	C₂²×M₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₈	C₂²	1	1	yes	characteristic, complemented
39	#556	C₂²	1	1	yes	characteristic, complemented
40	#555	C₂²	1	1	yes	characteristic, complemented
41	#554	C₂²	1	1	yes	characteristic, complemented
42	#553	C₂²	1	1	yes	characteristic
43	#553	C₂²	1	1	yes	characteristic, complemented
44	#552	—	2	1	no	—
45	#552	C₂²	1	1	yes	characteristic
46	#552	C₂²	1	1	yes	characteristic, complemented
47	#551	—	2	1	no	—
48	#551	—	2	1	no	—
49	#550	C₂²	1	1	yes	characteristic
50	D₄×Q₈	C₂²	1	1	yes	characteristic
51	#548	C₂²	1	1	yes	characteristic
52	#548	C₂²	1	1	yes	characteristic
53	#547	—	2	1	no	—
54	#547	C₂²	1	1	yes	characteristic
55	#547	C₂²	1	1	yes	characteristic, complemented
56	#546	—	2	1	no	—
57	#546	—	2	1	no	—
58	#546	—	2	1	no	—
59	#546	C₂²	1	1	yes	characteristic
60	#546	C₂²	1	1	yes	characteristic
61	D₄²	—	2	1	no	—
62	D₄²	C₂²	1	1	yes	characteristic
63	#533	C₂²	1	1	yes	characteristic, complemented
64	#532	—	2	1	no	—
65	#532	C₂²	1	1	yes	characteristic
66	#529	—	2	1	no	—
67	#529	—	2	1	no	—
68	#529	—	2	1	no	—
69	#525	—	2	1	no	—
70	#525	—	2	1	no	—
71	#525	C₂²	1	1	yes	characteristic
72	#525	C₂²	1	1	yes	characteristic
73	#525	C₂²	1	1	yes	characteristic, complemented
74	#525	C₂²	1	1	yes	characteristic, complemented
75	C₄×#41	—	2	1	no	—
76	C₄×#41	C₂²	1	1	yes	characteristic
77	C₄×#41	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄×D₄	—	2	1	no	—
79	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
80	C₂×#117	C₂²	1	1	yes	characteristic, complemented
81	C₂×#117	C₂²	1	1	yes	characteristic, complemented
82	#491	C₂²	1	1	yes	characteristic, complemented
83	#491	C₂²	1	1	yes	characteristic, complemented
84	#490	C₂²	1	1	yes	characteristic, complemented
85	#490	C₂²	1	1	yes	characteristic, complemented
86	#489	C₂²	1	1	yes	characteristic, complemented
87	#489	C₂²	1	1	yes	characteristic, complemented
88	#489	C₂²	1	1	yes	characteristic, complemented
89	#489	C₂²	1	1	yes	characteristic, complemented
90	#485	C₂²	1	1	yes	characteristic, complemented
91	#485	C₂²	1	1	yes	characteristic, complemented
92	#485	C₂²	1	1	yes	characteristic, complemented
93	#485	C₂²	1	1	yes	characteristic, complemented
94	#484	C₂²	1	1	yes	characteristic, complemented
95	#484	C₂²	1	1	yes	characteristic, complemented
96	#483	C₂²	1	1	yes	characteristic, complemented
97	#483	C₂²	1	1	yes	characteristic, complemented
98	#482	C₂²	1	1	yes	characteristic, complemented
99	#482	C₂²	1	1	yes	characteristic, complemented
100	#482	C₂²	1	1	yes	characteristic, complemented
101	#482	C₂²	1	1	yes	characteristic, complemented
102	#481	C₂²	1	1	yes	characteristic, complemented
103	#481	C₂²	1	1	yes	characteristic, complemented
104	#480	C₂²	1	1	yes	characteristic, complemented
105	#480	C₂²	1	1	yes	characteristic, complemented
106	#479	C₂²	1	1	yes	characteristic, complemented
107	#479	C₂²	1	1	yes	characteristic, complemented
108	#478	C₂²	1	1	yes	characteristic, complemented
109	#478	C₂²	1	1	yes	characteristic, complemented
110	#477	C₂²	1	1	yes	characteristic, complemented
111	#476	C₂²	1	1	yes	characteristic, complemented
112	#475	C₂²	1	1	yes	characteristic, complemented
113	#474	C₂²	1	1	yes	characteristic, complemented
114	#470	C₂²	1	1	yes	characteristic, complemented
115	#470	C₂²	1	1	yes	characteristic, complemented
116	#469	C₂²	1	1	yes	characteristic, complemented
117	#469	C₂²	1	1	yes	characteristic, complemented
118	#468	C₂²	1	1	yes	characteristic, complemented
119	#468	C₂²	1	1	yes	characteristic, complemented
120	#468	C₂²	1	1	yes	characteristic, complemented
121	#468	C₂²	1	1	yes	characteristic, complemented
122	#467	C₂²	1	1	yes	characteristic, complemented
123	#467	C₂²	1	1	yes	characteristic, complemented
124	#466	C₂²	1	1	yes	characteristic, complemented
125	#466	C₂²	1	1	yes	characteristic, complemented
126	#465	C₂²	1	1	yes	characteristic, complemented
127	#465	C₂²	1	1	yes	characteristic, complemented
128	#465	C₂²	1	1	yes	characteristic, complemented
129	#465	C₂²	1	1	yes	characteristic, complemented
130	#464	C₂²	1	1	yes	characteristic, complemented
131	#464	C₂²	1	1	yes	characteristic, complemented
132	#463	C₂²	1	1	yes	characteristic, complemented
133	#463	C₂²	1	1	yes	characteristic, complemented
134	#462	C₂²	1	1	yes	characteristic, complemented
135	#461	C₂²	1	1	yes	characteristic, complemented
136	#460	C₂²	1	1	yes	characteristic, complemented
137	#459	C₂²	1	1	yes	characteristic, complemented
138	#452	C₂²	1	1	yes	characteristic, complemented
139	#452	C₂²	1	1	yes	characteristic, complemented
140	#452	C₂²	1	1	yes	characteristic, complemented
141	#452	C₂²	1	1	yes	characteristic, complemented
142	#451	C₂²	1	1	yes	characteristic, complemented
143	#451	C₂²	1	1	yes	characteristic, complemented
144	#450	C₂²	1	1	yes	characteristic, complemented
145	#450	C₂²	1	1	yes	characteristic, complemented
146	#449	C₂²	1	1	yes	characteristic, complemented
147	#449	C₂²	1	1	yes	characteristic, complemented
148	#449	C₂²	1	1	yes	characteristic, complemented
149	#449	C₂²	1	1	yes	characteristic, complemented
150	#448	C₂²	1	1	yes	characteristic, complemented
151	#448	C₂²	1	1	yes	characteristic, complemented
152	#447	C₂²	1	1	yes	characteristic, complemented
153	#447	C₂²	1	1	yes	characteristic, complemented
154	#442	C₂²	1	1	yes	characteristic, complemented
155	#442	C₂²	1	1	yes	characteristic, complemented
156	#441	C₂²	1	1	yes	characteristic, complemented
157	#441	C₂²	1	1	yes	characteristic, complemented
158	#440	C₂²	1	1	yes	characteristic, complemented
159	#440	C₂²	1	1	yes	characteristic, complemented
160	#440	C₂²	1	1	yes	characteristic, complemented
161	#440	C₂²	1	1	yes	characteristic, complemented
162	#435	C₂²	1	1	yes	characteristic
163	#435	C₂²	1	1	yes	characteristic
164	#435	C₂²	1	1	yes	characteristic, complemented
165	#435	C₂²	1	1	yes	characteristic, complemented
166	#435	C₂²	1	1	yes	characteristic, complemented
167	#435	C₂²	1	1	yes	characteristic, complemented
168	#435	C₂²	1	1	yes	characteristic, complemented
169	#435	C₂²	1	1	yes	characteristic, complemented
170	#427	C₂²	1	1	yes	characteristic, complemented
171	#427	C₂²	1	1	yes	characteristic, complemented
172	#427	C₂²	1	1	yes	characteristic, complemented
173	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
174	#419	C₂²	1	1	yes	characteristic, complemented
175	#419	C₂²	1	1	yes	characteristic, complemented
176	#418	C₂²	1	1	yes	characteristic, complemented
177	#418	C₂²	1	1	yes	characteristic, complemented
178	#417	C₂²	1	1	yes	characteristic, complemented
179	#417	C₂²	1	1	yes	characteristic, complemented
180	#417	C₂²	1	1	yes	characteristic, complemented
181	#417	C₂²	1	1	yes	characteristic, complemented
182	#416	C₂²	1	1	yes	characteristic
183	#416	C₂²	1	1	yes	characteristic
184	#416	C₂²	1	1	yes	characteristic
185	#416	C₂²	1	1	yes	characteristic, complemented
186	#416	C₂²	1	1	yes	characteristic, complemented
187	#416	C₂²	1	1	yes	characteristic, complemented
188	#416	C₂²	1	1	yes	characteristic, complemented
189	#416	C₂²	1	1	yes	characteristic, complemented
190	#416	C₂²	1	1	yes	characteristic, complemented
191	#416	C₂²	1	1	yes	characteristic, complemented
192	#416	C₂²	1	1	yes	characteristic, complemented
193	#416	C₂²	1	1	yes	characteristic, complemented
194	#416	C₂²	1	1	yes	characteristic, complemented
195	#416	C₂²	1	1	yes	characteristic, complemented
196	C₂×#103	C₂²	1	1	yes	characteristic, complemented
197	C₂×#103	C₂²	1	1	yes	characteristic, complemented
198	C₂×#102	C₂²	1	1	yes	characteristic, complemented
199	C₂×#102	C₂²	1	1	yes	characteristic, complemented
200	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
201	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
202	C₂×#97	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41	—	2	1	no	—
204	C₂×#41	—	2	1	no	—
205	C₂×#41	—	2	1	no	—
206	C₂×#41	—	2	1	no	—
207	C₂×#41	—	2	1	no	—
208	C₂×#41	—	2	4	no	—
209	C₂×#41	—	2	4	no	—
210	C₂×#41	—	4	2	no	—
211	C₂×#41	—	4	2	no	—
212	C₂×#41	C₂³	1	1	yes	characteristic
213	C₂×#41	C₂³	1	1	yes	characteristic
214	C₂×#41	C₂³	1	1	yes	characteristic
215	C₂×#41	C₂³	1	1	yes	characteristic
216	C₂×#41	C₂³	1	1	yes	characteristic
217	C₂×#41	C₂³	1	1	yes	characteristic
218	C₂×#41	C₂³	1	1	yes	characteristic
219	C₂×#41	C₂³	1	1	yes	characteristic
220	C₂²×Q₈	C₂³	1	1	yes	characteristic
221	C₂²×Q₈	C₂³	1	1	yes	characteristic
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	D₄	1	1	yes	characteristic
226	C₂²×D₄	C₂³	1	1	yes	characteristic
227	C₂²×D₄	C₂³	1	1	yes	characteristic
228	C₂³×C₄	—	2	1	no	—
229	C₂³×C₄	—	2	1	no	—
230	C₂³×C₄	C₂³	1	1	yes	characteristic
231	C₂³×C₄	C₂³	1	1	yes	characteristic
232	#135	—	2	4	no	—
233	#135	—	4	2	no	—
234	#135	—	4	2	no	—
235	C₂×Q₁₆	C₂³	1	1	yes	characteristic
236	C₂×Q₁₆	C₂³	1	1	yes	characteristic
237	C₂×Q₁₆	C₂³	1	1	yes	characteristic
238	C₂×SD₁₆	C₂³	1	1	yes	characteristic
239	C₂×SD₁₆	C₂³	1	1	yes	characteristic
240	C₂×SD₁₆	C₂³	1	1	yes	characteristic
241	C₂×SD₁₆	C₂³	1	1	yes	characteristic
242	C₂×SD₁₆	C₂³	1	1	yes	characteristic
243	C₂×SD₁₆	C₂³	1	1	yes	characteristic
244	C₂×D₈	C₂³	1	1	yes	characteristic
245	C₂×D₈	C₂³	1	1	yes	characteristic
246	C₂×D₈	C₂³	1	1	yes	characteristic
247	C₂×M₁₆	—	4	2	no	—
248	C₂×M₁₆	C₂³	1	1	yes	characteristic
249	C₂×M₁₆	C₂³	1	1	yes	characteristic
250	C₂×M₁₆	C₂³	1	1	yes	characteristic
251	C₂×M₁₆	C₂³	1	1	yes	characteristic
252	C₂²×C₈	—	4	2	no	—
253	C₂²×C₈	C₂³	1	1	yes	characteristic
254	C₂²×C₈	C₂³	1	1	yes	characteristic
255	C₂²×C₈	C₂³	1	1	yes	characteristic
256	C₂²×C₈	C₂³	1	1	yes	characteristic
257	C₂²×C₈	C₂³	1	1	yes	characteristic
258	C₂²×C₈	C₂³	1	1	yes	characteristic
259	C₂²×C₈	C₂³	1	1	yes	characteristic
260	C₂²×C₈	C₂³	1	1	yes	characteristic
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	C₂³	1	1	yes	characteristic
263	C₄⋊Q₈	C₂³	1	1	yes	characteristic
264	C₄⋊Q₈	C₂³	1	1	yes	characteristic
265	#127	—	2	1	no	—
266	#127	C₂³	1	1	yes	characteristic
267	#126	—	2	1	no	—
268	#126	—	2	1	no	—
269	#126	—	2	1	no	—
270	#126	—	2	1	no	—
271	#126	—	2	1	no	—
272	#126	—	2	1	no	—
273	#125	—	2	1	no	—
274	#125	—	2	1	no	—
275	#125	—	2	1	no	—
276	#125	C₂³	1	1	yes	characteristic
277	#125	C₂³	1	1	yes	characteristic
278	#124	—	2	1	no	—
279	#124	—	2	1	no	—
280	#124	—	2	1	no	—
281	#124	—	2	1	no	—
282	#124	—	2	1	no	—
283	#124	C₂³	1	1	yes	characteristic
284	#124	C₂³	1	1	yes	characteristic
285	#123	—	2	1	no	—
286	#123	—	2	1	no	—
287	#123	—	2	1	no	—
288	#123	—	2	1	no	—
289	#123	—	2	1	no	—
290	#123	—	2	1	no	—
291	#123	—	2	1	no	—
292	#123	—	2	1	no	—
293	#123	—	2	1	no	—
294	#123	—	2	1	no	—
295	#123	—	2	1	no	—
296	#123	—	2	1	no	—
297	#123	—	2	1	no	—
298	#123	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₂²⋊Q₈	—	2	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
309	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
310	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
311	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
312	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
313	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
314	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
315	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
316	#121	—	2	1	no	—
317	#121	—	2	1	no	—
318	#121	—	2	1	no	—
319	#121	—	2	1	no	—
320	#121	—	2	1	no	—
321	#121	—	2	1	no	—
322	#121	—	2	1	no	—
323	#121	—	2	1	no	—
324	#121	—	2	1	no	—
325	#121	—	2	1	no	—
326	#121	—	2	1	no	—
327	#121	—	2	1	no	—
328	#121	—	2	1	no	—
329	#121	C₂³	1	1	yes	characteristic
330	#121	C₂³	1	1	yes	characteristic
331	#121	C₂³	1	1	yes	characteristic
332	#121	C₂³	1	1	yes	characteristic
333	#121	C₂³	1	1	yes	characteristic
334	#121	C₂³	1	1	yes	characteristic
335	#121	C₂³	1	1	yes	characteristic
336	#121	C₂³	1	1	yes	characteristic
337	#120	—	2	1	no	—
338	#120	—	2	1	no	—
339	#120	—	2	1	no	—
340	#120	—	2	1	no	—
341	#120	—	2	1	no	—
342	#120	—	2	1	no	—
343	#120	—	2	1	no	—
344	#120	—	2	1	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	C₂³	1	1	yes	characteristic
349	C₄×Q₈	C₂³	1	1	yes	characteristic
350	C₄×Q₈	C₂³	1	1	yes	characteristic
351	C₄×Q₈	C₂³	1	1	yes	characteristic
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	D₄	1	1	yes	characteristic
374	C₄×D₄	D₄	1	1	yes	characteristic
375	C₄×D₄	D₄	1	1	yes	characteristic
376	C₄×D₄	D₄	1	1	yes	characteristic
377	C₄×D₄	C₂³	1	1	yes	characteristic
378	C₄×D₄	C₂³	1	1	yes	characteristic
379	C₄×D₄	C₂³	1	1	yes	characteristic
380	C₄×D₄	C₂³	1	1	yes	characteristic
381	C₄×D₄	C₂³	1	1	yes	characteristic
382	C₄×D₄	C₂³	1	1	yes	characteristic
383	C₄×D₄	C₂³	1	1	yes	characteristic
384	C₄×D₄	C₂³	1	1	yes	characteristic
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	—	2	1	no	—
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	—	2	1	no	—
391	#117	—	2	1	no	—
392	#117	—	2	1	no	—
393	#117	—	2	1	no	—
394	#117	C₂³	1	1	yes	characteristic
395	#117	C₂³	1	1	yes	characteristic
396	#117	C₂³	1	1	yes	characteristic
397	#117	C₂³	1	1	yes	characteristic
398	#117	C₂³	1	1	yes	characteristic
399	#117	C₂³	1	1	yes	characteristic
400	#117	C₂³	1	1	yes	characteristic
401	#117	C₂³	1	1	yes	characteristic
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	C₂³	1	1	yes	characteristic
419	#107	C₂³	1	1	yes	characteristic
420	#107	C₂³	1	1	yes	characteristic
421	#107	C₂³	1	1	yes	characteristic
422	#107	C₂³	1	1	yes	characteristic
423	#107	C₂³	1	1	yes	characteristic
424	#107	C₂³	1	1	yes	characteristic
425	#106	C₂³	1	1	yes	characteristic
426	#106	C₂³	1	1	yes	characteristic
427	#106	C₂³	1	1	yes	characteristic
428	#106	C₂³	1	1	yes	characteristic
429	#106	C₂³	1	1	yes	characteristic
430	#106	C₂³	1	1	yes	characteristic
431	C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₄⋊C₈	C₂³	1	1	yes	characteristic
433	C₄⋊C₈	C₂³	1	1	yes	characteristic
434	C₄⋊C₈	C₂³	1	1	yes	characteristic
435	#103	C₂³	1	1	yes	characteristic
436	#103	C₂³	1	1	yes	characteristic
437	#103	C₂³	1	1	yes	characteristic
438	#103	C₂³	1	1	yes	characteristic
439	#103	C₂³	1	1	yes	characteristic
440	#103	C₂³	1	1	yes	characteristic
441	#103	C₂³	1	1	yes	characteristic
442	#103	C₂³	1	1	yes	characteristic
443	#103	C₂³	1	1	yes	characteristic
444	#103	C₂³	1	1	yes	characteristic
445	#103	C₂³	1	1	yes	characteristic
446	#103	C₂³	1	1	yes	characteristic
447	#103	C₂³	1	1	yes	characteristic
448	#103	C₂³	1	1	yes	characteristic
449	#103	C₂³	1	1	yes	characteristic
450	#103	C₂³	1	1	yes	characteristic
451	#103	C₂³	1	1	yes	characteristic
452	#103	C₂³	1	1	yes	characteristic
453	#103	C₂³	1	1	yes	characteristic
454	#103	C₂³	1	1	yes	characteristic
455	#102	C₂³	1	1	yes	characteristic
456	#102	C₂³	1	1	yes	characteristic
457	#102	C₂³	1	1	yes	characteristic
458	#102	C₂³	1	1	yes	characteristic
459	#102	C₂³	1	1	yes	characteristic
460	#102	C₂³	1	1	yes	characteristic
461	#102	C₂³	1	1	yes	characteristic
462	#102	C₂³	1	1	yes	characteristic
463	#102	C₂³	1	1	yes	characteristic
464	#102	C₂³	1	1	yes	characteristic
465	#102	C₂³	1	1	yes	characteristic
466	#102	C₂³	1	1	yes	characteristic
467	#102	C₂³	1	1	yes	characteristic
468	#102	C₂³	1	1	yes	characteristic
469	#102	C₂³	1	1	yes	characteristic
470	#102	C₂³	1	1	yes	characteristic
471	#102	C₂³	1	1	yes	characteristic
472	#102	C₂³	1	1	yes	characteristic
473	#102	C₂³	1	1	yes	characteristic
474	#102	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈	C₂³	1	1	yes	characteristic
478	C₂²⋊C₈	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈	C₂³	1	1	yes	characteristic
480	C₂²⋊C₈	C₂³	1	1	yes	characteristic
481	C₂²⋊C₈	C₂³	1	1	yes	characteristic
482	C₂²⋊C₈	C₂³	1	1	yes	characteristic
483	#97	C₂³	1	1	yes	characteristic
484	#97	C₂³	1	1	yes	characteristic
485	#97	C₂³	1	1	yes	characteristic
486	#97	C₂³	1	1	yes	characteristic
487	C₂⁴	—	2	1	no	—
488	C₂⁴	—	2	1	no	—
489	C₂⁴	C₂×D₄	1	1	yes	characteristic
490	C₂⁴	C₂×D₄	1	1	yes	characteristic
491	#41	—	2	2	no	—
492	#41	—	2	2	no	—
493	#41	—	2	2	no	—
494	#41	—	2	2	no	—
495	#41	—	2	2	no	—
496	#41	—	2	2	no	—
497	#41	—	2	2	no	—
498	#41	—	2	2	no	—
499	#41	—	2	2	no	—
500	#41	—	2	2	no	—
501	#41	—	2	2	no	—
502	#41	—	4	4	no	—
503	#41	—	4	4	no	—
504	#41	—	4	1	no	—
505	#41	—	4	1	no	—
506	#41	—	4	1	no	—
507	#41	—	4	1	no	—
508	#41	—	4	4	no	—
509	#41	—	4	4	no	—
510	#41	—	4	4	no	—
511	#41	#41	1	4	yes	complemented
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	2	2	no	—
518	C₂×Q₈	—	4	1	no	—
519	C₂×Q₈	—	4	1	no	—
520	C₂×Q₈	C₂⁴	1	1	yes	characteristic
521	C₂×Q₈	C₂⁴	1	1	yes	characteristic
522	C₂×Q₈	C₂⁴	1	1	yes	characteristic
523	C₂×Q₈	C₂⁴	1	1	yes	characteristic
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	4	1	no	—
547	C₂×D₄	—	4	1	no	—
548	C₂×D₄	—	4	2	no	—
549	C₂×D₄	—	4	4	no	—
550	C₂×D₄	—	4	4	no	—
551	C₂×D₄	—	4	4	no	—
552	C₂×D₄	C₂×D₄	1	1	yes	characteristic
553	C₂×D₄	C₂×D₄	1	1	yes	characteristic
554	C₂×D₄	C₂×D₄	1	1	yes	characteristic
555	C₂×D₄	C₂×D₄	1	1	yes	characteristic
556	C₂×D₄	C₂⁴	1	1	yes	characteristic
557	C₂×D₄	C₂⁴	1	1	yes	characteristic
558	C₂×D₄	C₂⁴	1	1	yes	characteristic
559	C₂×D₄	C₂⁴	1	1	yes	characteristic
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	4	4	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴	1	1	yes	characteristic
597	Q₁₆	—	2	2	no	—
598	Q₁₆	—	4	1	no	—
599	Q₁₆	—	4	1	no	—
600	SD₁₆	—	2	2	no	—
601	SD₁₆	—	2	2	no	—
602	SD₁₆	—	4	1	no	—
603	SD₁₆	—	4	1	no	—
604	SD₁₆	—	4	1	no	—
605	SD₁₆	—	4	1	no	—
606	D₈	—	2	2	no	—
607	D₈	—	4	1	no	—
608	D₈	—	4	1	no	—
609	M₁₆	—	4	1	no	—
610	M₁₆	—	4	1	no	—
611	M₁₆	—	4	1	no	—
612	M₁₆	—	4	1	no	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	—	2	2	no	—
617	C₂×C₈	—	4	1	no	—
618	C₂×C₈	—	4	1	no	—
619	C₂×C₈	—	4	1	no	—
620	C₂×C₈	—	4	1	no	—
621	C₂×C₈	C₂⁴	1	1	yes	characteristic
622	C₂×C₈	C₂⁴	1	1	yes	characteristic
623	C₂×C₈	C₂⁴	1	1	yes	characteristic
624	C₂×C₈	C₂⁴	1	1	yes	characteristic
625	C₂×C₈	C₂⁴	1	1	yes	characteristic
626	C₂×C₈	C₂⁴	1	1	yes	characteristic
627	C₂×C₈	C₂⁴	1	1	yes	characteristic
628	C₂×C₈	C₂⁴	1	1	yes	characteristic
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
657	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
658	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
659	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
660	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
661	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
662	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
663	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
664	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
665	C₂²⋊C₄	—	2	1	no	—
666	C₂²⋊C₄	—	2	1	no	—
667	C₂²⋊C₄	—	2	1	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	1	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	1	no	—
679	C₂²⋊C₄	—	2	1	no	—
680	C₂²⋊C₄	—	2	1	no	—
681	C₂²⋊C₄	—	2	1	no	—
682	C₂²⋊C₄	—	2	1	no	—
683	C₂²⋊C₄	—	2	1	no	—
684	C₂²⋊C₄	—	2	1	no	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	1	no	—
689	C₂²⋊C₄	—	2	1	no	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	2	1	no	—
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
698	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
699	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
700	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
701	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
702	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
703	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
704	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
705	C₄²	—	2	1	no	—
706	C₄²	—	2	1	no	—
707	C₄²	—	2	1	no	—
708	C₄²	—	2	1	no	—
709	C₄²	—	2	1	no	—
710	C₄²	—	2	1	no	—
711	C₄²	—	2	1	no	—
712	C₄²	—	2	1	no	—
713	C₄²	—	2	1	no	—
714	C₄²	—	2	1	no	—
715	C₄²	—	2	1	no	—
716	C₄²	—	2	1	no	—
717	C₄²	C₂×D₄	1	1	yes	characteristic
718	C₄²	C₂×D₄	1	1	yes	characteristic
719	C₄²	C₂⁴	1	1	yes	characteristic
720	C₄²	C₂⁴	1	1	yes	characteristic
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	4	1	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	8	1	no	—
736	C₂³	—	8	1	no	—
737	C₂³	C₂²×D₄	1	1	yes	characteristic
738	C₂³	C₂²×D₄	1	1	yes	characteristic
739	C₂³	C₂²×D₄	1	1	yes	characteristic
740	C₂³	C₂²×D₄	1	1	yes	characteristic
741	C₂³	C₂²×D₄	1	1	yes	characteristic
742	Q₈	—	2	1	no	—
743	Q₈	—	2	1	no	—
744	Q₈	—	2	1	no	—
745	Q₈	—	2	1	no	—
746	Q₈	—	2	1	no	—
747	Q₈	—	2	1	no	—
748	Q₈	—	2	1	no	—
749	Q₈	—	4	2	no	—
750	Q₈	—	4	2	no	—
751	Q₈	—	4	2	no	—
752	Q₈	—	8	1	no	—
753	Q₈	C₂×#41	1	2	yes	—
754	D₄	—	2	4	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	1	no	—
758	D₄	—	2	1	no	—
759	D₄	—	2	1	no	—
760	D₄	—	2	1	no	—
761	D₄	—	2	1	no	—
762	D₄	—	2	1	no	—
763	D₄	—	2	1	no	—
764	D₄	—	4	1	no	—
765	D₄	—	4	1	no	—
766	D₄	—	4	2	no	—
767	D₄	—	4	2	no	—
768	D₄	—	4	2	no	—
769	D₄	—	4	2	no	—
770	D₄	—	4	2	no	—
771	D₄	—	4	2	no	—
772	D₄	—	4	2	no	—
773	D₄	—	4	2	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	2	no	—
778	D₄	—	4	2	no	—
779	D₄	—	4	2	no	—
780	D₄	—	8	1	no	—
781	D₄	—	8	1	no	—
782	D₄	—	8	1	no	—
783	D₄	—	8	1	no	—
784	D₄	—	8	1	no	—
785	D₄	C₂×#41	1	2	yes	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	8	1	no	—
829	C₂×C₄	—	8	1	no	—
830	C₂×C₄	—	8	1	no	—
831	C₂×C₄	—	8	1	no	—
832	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
841	C₂×C₄	C₂×#41	1	2	yes	—
842	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
843	C₂×C₄	C₂⁵	1	1	yes	characteristic
844	C₈	—	2	1	no	—
845	C₈	—	2	1	no	—
846	C₈	—	2	1	no	—
847	C₈	—	2	1	no	—
848	C₈	—	2	1	no	—
849	C₈	—	2	1	no	—
850	C₈	—	2	1	no	—
851	C₈	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	4	4	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	8	2	no	—
879	C₂²	—	8	4	no	—
880	C₂²	—	8	4	no	—
881	C₂²	#546	1	2	yes	—
882	C₂²	#575	1	2	yes	—
883	C₂²	C₂³×D₄	1	1	yes	characteristic
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	1	no	—
904	C₄	#546	1	2	yes	—
905	C₄	C₂²×#41	1	1	yes	characteristic
906	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
907	C₂	—	2	2	no	—
908	C₂	—	2	2	no	—
909	C₂	—	4	1	no	—
910	C₂	—	4	1	no	—
911	C₂	—	4	1	no	—
912	C₂	—	4	2	no	—
913	C₂	—	8	1	no	—
914	C₂	—	8	1	no	—
915	C₂	—	8	1	no	—
916	C₂	C₂×#546	1	1	yes	characteristic
917	C₂	C₂×#575	1	1	yes	characteristic
918	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
socle	C₂²	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3475	C₂	semidirect
2. D₄×#41	C₂	semidirect
3. #3321	C₂	semidirect
4. #3320	C₂	semidirect
5. #3319	C₂	semidirect
6. #3318	C₂	semidirect
7. #3317	C₂	semidirect
8. #3316	C₂	semidirect
9. #3315	C₂	semidirect
10. #3314	C₂	semidirect
11. #3313	C₂	semidirect
12. #3312	C₂	semidirect
13. #3311	C₂	semidirect
14. #3310	C₂	semidirect
15. #3309	C₂	semidirect
16. #3308	C₂	semidirect
17. #3307	C₂	semidirect
18. #3306	C₂	semidirect
19. #3135	C₂	semidirect
20. #3091	C₂	semidirect
21. #3091	C₂	semidirect
22. #3076	C₂	semidirect
23. #3054	C₂	semidirect
24. #3050	C₂	semidirect
25. #3035	C₂	semidirect
26. #3002	C₂	semidirect
27. #3002	C₂	semidirect
28. #2943	C₂	semidirect
29. C₂×#435	C₂	semidirect
30. #2896	C₂	semidirect
31. C₂×#416	C₂	semidirect
35. C₂×#135	C₂²	semidirect
36. C₂×#135	C₂²	semidirect
37. C₂²×M₁₆	C₂²	semidirect
38. C₂³×C₈	C₂²	semidirect
39. #556	C₂²	semidirect
40. #555	C₂²	semidirect
41. #554	C₂²	semidirect
43. #553	C₂²	semidirect
46. #552	C₂²	semidirect
55. #547	C₂²	semidirect
63. #533	C₂²	semidirect
73. #525	C₂²	semidirect
74. #525	C₂²	semidirect
77. C₄×#41	C₂²	semidirect
80. C₂×#117	C₂²	semidirect
81. C₂×#117	C₂²	semidirect
82. #491	C₂²	semidirect
83. #491	C₂²	semidirect
84. #490	C₂²	semidirect
85. #490	C₂²	semidirect
86. #489	C₂²	semidirect
87. #489	C₂²	semidirect
88. #489	C₂²	semidirect
89. #489	C₂²	semidirect
90. #485	C₂²	semidirect
91. #485	C₂²	semidirect
92. #485	C₂²	semidirect
93. #485	C₂²	semidirect
94. #484	C₂²	semidirect
95. #484	C₂²	semidirect
96. #483	C₂²	semidirect
97. #483	C₂²	semidirect
98. #482	C₂²	semidirect
99. #482	C₂²	semidirect
100. #482	C₂²	semidirect
101. #482	C₂²	semidirect
102. #481	C₂²	semidirect
103. #481	C₂²	semidirect
104. #480	C₂²	semidirect
105. #480	C₂²	semidirect
106. #479	C₂²	semidirect
107. #479	C₂²	semidirect
108. #478	C₂²	semidirect
109. #478	C₂²	semidirect
110. #477	C₂²	semidirect
111. #476	C₂²	semidirect
112. #475	C₂²	semidirect
113. #474	C₂²	semidirect
114. #470	C₂²	semidirect
115. #470	C₂²	semidirect
116. #469	C₂²	semidirect
117. #469	C₂²	semidirect
118. #468	C₂²	semidirect
119. #468	C₂²	semidirect
120. #468	C₂²	semidirect
121. #468	C₂²	semidirect
122. #467	C₂²	semidirect
123. #467	C₂²	semidirect
124. #466	C₂²	semidirect
125. #466	C₂²	semidirect
126. #465	C₂²	semidirect
127. #465	C₂²	semidirect
128. #465	C₂²	semidirect
129. #465	C₂²	semidirect
130. #464	C₂²	semidirect
131. #464	C₂²	semidirect
132. #463	C₂²	semidirect
133. #463	C₂²	semidirect
134. #462	C₂²	semidirect
135. #461	C₂²	semidirect
136. #460	C₂²	semidirect
137. #459	C₂²	semidirect
138. #452	C₂²	semidirect
139. #452	C₂²	semidirect
140. #452	C₂²	semidirect
141. #452	C₂²	semidirect
142. #451	C₂²	semidirect
143. #451	C₂²	semidirect
144. #450	C₂²	semidirect
145. #450	C₂²	semidirect
146. #449	C₂²	semidirect
147. #449	C₂²	semidirect
148. #449	C₂²	semidirect
149. #449	C₂²	semidirect
150. #448	C₂²	semidirect
151. #448	C₂²	semidirect
152. #447	C₂²	semidirect
153. #447	C₂²	semidirect
154. #442	C₂²	semidirect
155. #442	C₂²	semidirect
156. #441	C₂²	semidirect
157. #441	C₂²	semidirect
158. #440	C₂²	semidirect
159. #440	C₂²	semidirect
160. #440	C₂²	semidirect
161. #440	C₂²	semidirect
164. #435	C₂²	semidirect
165. #435	C₂²	semidirect
166. #435	C₂²	semidirect
167. #435	C₂²	semidirect
168. #435	C₂²	semidirect
169. #435	C₂²	semidirect
170. #427	C₂²	semidirect
171. #427	C₂²	semidirect
172. #427	C₂²	semidirect
173. C₂×C₄⋊C₈	C₂²	semidirect
174. #419	C₂²	semidirect
175. #419	C₂²	semidirect
176. #418	C₂²	semidirect
177. #418	C₂²	semidirect
178. #417	C₂²	semidirect
179. #417	C₂²	semidirect
180. #417	C₂²	semidirect
181. #417	C₂²	semidirect
185. #416	C₂²	semidirect
186. #416	C₂²	semidirect
187. #416	C₂²	semidirect
188. #416	C₂²	semidirect
189. #416	C₂²	semidirect
190. #416	C₂²	semidirect
191. #416	C₂²	semidirect
192. #416	C₂²	semidirect
193. #416	C₂²	semidirect
194. #416	C₂²	semidirect
195. #416	C₂²	semidirect
196. C₂×#103	C₂²	semidirect
197. C₂×#103	C₂²	semidirect
198. C₂×#102	C₂²	semidirect
199. C₂×#102	C₂²	semidirect
200. C₂×C₂²⋊C₈	C₂²	semidirect
201. C₂×C₂²⋊C₈	C₂²	semidirect
202. C₂×#97	C₂²	semidirect
511. #41	#41	semidirect

Maximal subgroups

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

subgroup	index
#3475	2
D₄×#41	2
#3321	2
#3320	2
#3319	2
#3318	2
#3317	2
#3316	2
#3315	2
#3314	2
#3313	2
#3312	2
#3311	2
#3310	2
#3309	2
#3308	2
#3307	2
#3306	2
#3135	2
#3091	2
#3076	2
#3054	2
#3050	2
#3035	2
#3002	2
#2943	2
C₂×#435	2
#2896	2
C₂×#416	2