Subgroups — #61536

Order 256.

925 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3521	C₂	1	1	yes	maximal, characteristic, complemented
2	#3513	C₂	1	1	yes	maximal, characteristic, complemented
3	#3401	C₂	1	1	yes	maximal, characteristic, complemented
4	#3389	C₂	1	1	yes	maximal, characteristic, complemented
5	#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	#3349	C₂	1	1	yes	maximal, characteristic, complemented
8	#3345	C₂	1	1	yes	maximal, characteristic, complemented
9	#3337	C₂	1	1	yes	maximal, characteristic, complemented
10	#3330	C₂	1	1	yes	maximal, characteristic, complemented
11	#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	#3323	C₂	1	1	yes	maximal, characteristic, complemented
13	#3323	C₂	1	1	yes	maximal, characteristic, complemented
14	#3322	C₂	1	1	yes	maximal, characteristic, complemented
15	#3322	C₂	1	1	yes	maximal, characteristic, complemented
16	#3280	C₂	1	1	yes	maximal, characteristic, complemented
17	#3267	C₂	1	1	yes	maximal, characteristic, complemented
18	#3264	C₂	1	1	yes	maximal, characteristic, complemented
19	#3183	C₂	1	1	yes	maximal, characteristic, complemented
20	#3179	C₂	1	1	yes	maximal, characteristic, complemented
21	#3178	C₂	1	1	yes	maximal, characteristic, complemented
22	#3124	C₂	1	1	yes	maximal, characteristic, complemented
23	#3123	C₂	1	1	yes	maximal, characteristic, complemented
24	#3119	C₂	1	1	yes	maximal, characteristic, complemented
25	#3118	C₂	1	1	yes	maximal, characteristic, complemented
26	#3105	C₂	1	1	yes	maximal, characteristic, complemented
27	#3102	C₂	1	1	yes	maximal, characteristic, complemented
28	#2969	C₂	1	1	yes	maximal, characteristic, complemented
29	#2952	C₂	1	1	yes	maximal, characteristic, complemented
30	#2948	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
33	C₂×#135	C₂²	1	1	yes	characteristic
34	C₂²×D₈	C₂²	1	1	yes	characteristic
35	#559	C₂²	1	1	yes	characteristic, complemented
36	#556	C₂²	1	1	yes	characteristic
37	#556	C₂²	1	1	yes	characteristic, complemented
38	#554	C₂²	1	1	yes	characteristic, complemented
39	#554	C₂²	1	1	yes	characteristic, complemented
40	#553	—	2	1	no	—
41	#553	—	2	1	no	—
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	#551	—	2	1	no	—
50	#551	—	2	1	no	—
51	#547	C₂²	1	1	yes	characteristic, complemented
52	#547	C₂²	1	1	yes	characteristic, complemented
53	#546	—	2	1	no	—
54	#546	C₂²	1	1	yes	characteristic
55	#546	C₂²	1	1	yes	characteristic
56	#546	C₂²	1	1	yes	characteristic, complemented
57	#546	C₂²	1	1	yes	characteristic, complemented
58	D₄²	C₂²	1	1	yes	characteristic
59	#542	C₂²	1	1	yes	characteristic
60	#542	C₂²	1	1	yes	characteristic, complemented
61	#541	C₂²	1	1	yes	characteristic, complemented
62	#540	C₂²	1	1	yes	characteristic, complemented
63	#539	—	2	1	no	—
64	#539	—	2	1	no	—
65	#538	—	2	1	no	—
66	#538	—	2	1	no	—
67	#529	—	2	1	no	—
68	#529	C₂²	1	1	yes	characteristic
69	#529	C₂²	1	1	yes	characteristic, complemented
70	#529	C₂²	1	1	yes	characteristic, complemented
71	C₂×#126	—	2	1	no	—
72	#525	—	2	1	no	—
73	C₂×#123	—	2	1	no	—
74	#520	C₂²	1	1	yes	characteristic, complemented
75	#520	C₂²	1	1	yes	characteristic, complemented
76	#518	C₂²	1	1	yes	characteristic
77	#518	C₂²	1	1	yes	characteristic, complemented
78	C₄×#41	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
80	#501	C₂²	1	1	yes	characteristic, complemented
81	#501	C₂²	1	1	yes	characteristic, complemented
82	#499	C₂²	1	1	yes	characteristic, complemented
83	#497	C₂²	1	1	yes	characteristic, complemented
84	#496	C₂²	1	1	yes	characteristic
85	#495	C₂²	1	1	yes	characteristic, complemented
86	#488	C₂²	1	1	yes	characteristic, complemented
87	#488	C₂²	1	1	yes	characteristic, complemented
88	#488	C₂²	1	1	yes	characteristic, complemented
89	#488	C₂²	1	1	yes	characteristic, complemented
90	#487	C₂²	1	1	yes	characteristic, complemented
91	#486	C₂²	1	1	yes	characteristic, complemented
92	#485	C₂²	1	1	yes	characteristic, complemented
93	#485	C₂²	1	1	yes	characteristic, complemented
94	#485	C₂²	1	1	yes	characteristic, complemented
95	#485	C₂²	1	1	yes	characteristic, complemented
96	#484	C₂²	1	1	yes	characteristic, complemented
97	#484	C₂²	1	1	yes	characteristic, complemented
98	#482	C₂²	1	1	yes	characteristic
99	#482	C₂²	1	1	yes	characteristic, complemented
100	#481	C₂²	1	1	yes	characteristic, complemented
101	#481	C₂²	1	1	yes	characteristic, complemented
102	#480	C₂²	1	1	yes	characteristic, complemented
103	#480	C₂²	1	1	yes	characteristic, complemented
104	#479	C₂²	1	1	yes	characteristic, complemented
105	#479	C₂²	1	1	yes	characteristic, complemented
106	#478	C₂²	1	1	yes	characteristic, complemented
107	#478	C₂²	1	1	yes	characteristic, complemented
108	#478	C₂²	1	1	yes	characteristic, complemented
109	#478	C₂²	1	1	yes	characteristic, complemented
110	#478	C₂²	1	1	yes	characteristic, complemented
111	#478	C₂²	1	1	yes	characteristic, complemented
112	#477	C₂²	1	1	yes	characteristic, complemented
113	#476	C₂²	1	1	yes	characteristic, complemented
114	#474	C₂²	1	1	yes	characteristic, complemented
115	#474	C₂²	1	1	yes	characteristic, complemented
116	#470	C₂²	1	1	yes	characteristic, complemented
117	#470	C₂²	1	1	yes	characteristic, complemented
118	#469	C₂²	1	1	yes	characteristic
119	#469	C₂²	1	1	yes	characteristic, complemented
120	#468	C₂²	1	1	yes	characteristic
121	#468	C₂²	1	1	yes	characteristic, complemented
122	#468	C₂²	1	1	yes	characteristic, complemented
123	#468	C₂²	1	1	yes	characteristic, complemented
124	#467	C₂²	1	1	yes	characteristic, complemented
125	#466	C₂²	1	1	yes	characteristic, complemented
126	#465	C₂²	1	1	yes	characteristic
127	#465	C₂²	1	1	yes	characteristic, complemented
128	#464	C₂²	1	1	yes	characteristic, complemented
129	#464	C₂²	1	1	yes	characteristic, complemented
130	#463	C₂²	1	1	yes	characteristic
131	#463	C₂²	1	1	yes	characteristic
132	#463	C₂²	1	1	yes	characteristic, complemented
133	#463	C₂²	1	1	yes	characteristic, complemented
134	#463	C₂²	1	1	yes	characteristic, complemented
135	#463	C₂²	1	1	yes	characteristic, complemented
136	#461	C₂²	1	1	yes	characteristic, complemented
137	#461	C₂²	1	1	yes	characteristic, complemented
138	#460	C₂²	1	1	yes	characteristic, complemented
139	#459	C₂²	1	1	yes	characteristic
140	#452	C₂²	1	1	yes	characteristic, complemented
141	#452	C₂²	1	1	yes	characteristic, complemented
142	#450	C₂²	1	1	yes	characteristic
143	#450	C₂²	1	1	yes	characteristic
144	#450	C₂²	1	1	yes	characteristic, complemented
145	#450	C₂²	1	1	yes	characteristic, complemented
146	#449	C₂²	1	1	yes	characteristic
147	#449	C₂²	1	1	yes	characteristic
148	#449	C₂²	1	1	yes	characteristic, complemented
149	#449	C₂²	1	1	yes	characteristic, complemented
150	#447	C₂²	1	1	yes	characteristic
151	#447	C₂²	1	1	yes	characteristic
152	#446	C₂²	1	1	yes	characteristic, complemented
153	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
154	#442	C₂²	1	1	yes	characteristic
155	#442	C₂²	1	1	yes	characteristic
156	#442	C₂²	1	1	yes	characteristic
157	#442	C₂²	1	1	yes	characteristic, complemented
158	#442	C₂²	1	1	yes	characteristic, complemented
159	#442	C₂²	1	1	yes	characteristic, complemented
160	#441	C₂²	1	1	yes	characteristic, complemented
161	#441	C₂²	1	1	yes	characteristic, complemented
162	#440	C₂²	1	1	yes	characteristic, complemented
163	#440	C₂²	1	1	yes	characteristic, complemented
164	#440	C₂²	1	1	yes	characteristic, complemented
165	#440	C₂²	1	1	yes	characteristic, complemented
166	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
167	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
168	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
169	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
170	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
171	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
172	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
173	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
174	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
175	C₄×D₈	C₂²	1	1	yes	characteristic
176	C₄×D₈	C₂²	1	1	yes	characteristic
177	C₄×D₈	C₂²	1	1	yes	characteristic
178	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
182	#436	C₂²	1	1	yes	characteristic
183	#436	C₂²	1	1	yes	characteristic, complemented
184	#436	C₂²	1	1	yes	characteristic, complemented
185	#435	C₂²	1	1	yes	characteristic
186	#435	C₂²	1	1	yes	characteristic, complemented
187	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
188	#433	C₂²	1	1	yes	characteristic, complemented
189	#433	C₂²	1	1	yes	characteristic, complemented
190	#431	C₂²	1	1	yes	characteristic, complemented
191	#428	C₂²	1	1	yes	characteristic, complemented
192	#427	C₂²	1	1	yes	characteristic, complemented
193	C₂×#106	C₂²	1	1	yes	characteristic, complemented
194	#418	C₂²	1	1	yes	characteristic
195	#418	C₂²	1	1	yes	characteristic, complemented
196	#418	C₂²	1	1	yes	characteristic, complemented
197	#417	C₂²	1	1	yes	characteristic, complemented
198	#417	C₂²	1	1	yes	characteristic, complemented
199	#417	C₂²	1	1	yes	characteristic, complemented
200	#405	C₂²	1	1	yes	characteristic, complemented
201	#405	C₂²	1	1	yes	characteristic, complemented
202	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41	—	2	1	no	—
204	C₂×#41	C₂³	1	1	yes	characteristic
205	C₂×#41	C₂³	1	1	yes	characteristic
206	C₂×#41	C₂³	1	1	yes	characteristic
207	C₂²×D₄	—	2	1	no	—
208	C₂²×D₄	C₂³	1	1	yes	characteristic
209	C₂²×D₄	C₂³	1	1	yes	characteristic
210	C₂²×D₄	C₂³	1	1	yes	characteristic
211	C₂³×C₄	—	2	1	no	—
212	AGL(1,ℤ/8)	—	2	4	no	—
213	#135	—	2	4	no	—
214	C₂×Q₁₆	C₂³	1	1	yes	characteristic
215	C₂×Q₁₆	C₂³	1	1	yes	characteristic
216	C₂×SD₁₆	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆	C₂³	1	1	yes	characteristic
218	C₂×SD₁₆	C₂³	1	1	yes	characteristic
219	C₂×SD₁₆	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆	C₂³	1	1	yes	characteristic
222	C₂×SD₁₆	C₂³	1	1	yes	characteristic
223	C₂×SD₁₆	C₂³	1	1	yes	characteristic
224	C₂×D₈	—	2	4	no	—
225	C₂×D₈	C₂³	1	1	yes	characteristic
226	C₂×D₈	C₂³	1	1	yes	characteristic
227	C₂×D₈	C₂³	1	1	yes	characteristic
228	C₂×D₈	C₂³	1	1	yes	characteristic
229	C₂×D₈	C₂³	1	1	yes	characteristic
230	C₂×D₈	C₂³	1	1	yes	characteristic
231	C₂×M₁₆	C₂³	1	1	yes	characteristic
232	C₂×M₁₆	C₂³	1	1	yes	characteristic
233	C₂×M₁₆	C₂³	1	1	yes	characteristic
234	C₂×M₁₆	C₂³	1	1	yes	characteristic
235	C₂²×C₈	C₂³	1	1	yes	characteristic
236	C₂²×C₈	C₂³	1	1	yes	characteristic
237	C₄⋊Q₈	C₂³	1	1	yes	characteristic
238	C₄⋊Q₈	C₂³	1	1	yes	characteristic
239	C₄⋊Q₈	C₂³	1	1	yes	characteristic
240	#127	C₂³	1	1	yes	characteristic
241	#126	—	2	1	no	—
242	#126	—	2	1	no	—
243	#126	—	2	1	no	—
244	#126	—	2	1	no	—
245	#126	—	2	1	no	—
246	#126	—	2	1	no	—
247	#126	—	2	1	no	—
248	#126	—	2	1	no	—
249	#126	—	2	1	no	—
250	#126	—	2	1	no	—
251	#126	—	2	1	no	—
252	#126	—	2	1	no	—
253	#126	—	2	1	no	—
254	#126	—	2	1	no	—
255	#126	D₄	1	1	yes	characteristic
256	#126	D₄	1	1	yes	characteristic
257	#125	—	2	1	no	—
258	#125	—	2	1	no	—
259	#125	—	2	1	no	—
260	#125	—	2	1	no	—
261	#125	D₄	1	1	yes	characteristic
262	#125	C₂³	1	1	yes	characteristic
263	#125	C₂³	1	1	yes	characteristic
264	#125	C₂³	1	1	yes	characteristic
265	#125	C₂³	1	1	yes	characteristic
266	#124	—	2	1	no	—
267	#124	—	2	1	no	—
268	#124	—	2	1	no	—
269	#124	—	2	1	no	—
270	#124	D₄	1	1	yes	characteristic
271	#124	C₂³	1	1	yes	characteristic
272	#124	C₂³	1	1	yes	characteristic
273	#124	C₂³	1	1	yes	characteristic
274	#124	C₂³	1	1	yes	characteristic
275	#123	—	2	1	no	—
276	#123	—	2	1	no	—
277	#123	—	2	1	no	—
278	#123	—	2	1	no	—
279	#123	—	2	1	no	—
280	#123	—	2	1	no	—
281	#123	—	2	1	no	—
282	#123	—	2	1	no	—
283	#123	—	2	1	no	—
284	#123	—	2	1	no	—
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	D₄	1	1	yes	characteristic
296	#123	D₄	1	1	yes	characteristic
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	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	D₄	1	1	yes	characteristic
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	#121	—	2	1	no	—
315	#121	—	2	1	no	—
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	D₄	1	1	yes	characteristic
325	#121	C₂³	1	1	yes	characteristic
326	#121	C₂³	1	1	yes	characteristic
327	#121	C₂³	1	1	yes	characteristic
328	#121	C₂³	1	1	yes	characteristic
329	#121	C₂³	1	1	yes	characteristic
330	#121	C₂³	1	1	yes	characteristic
331	#120	—	2	1	no	—
332	#120	—	2	1	no	—
333	#120	—	2	1	no	—
334	#120	—	2	1	no	—
335	#120	—	2	1	no	—
336	#120	—	2	1	no	—
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	C₂³	1	1	yes	characteristic
339	C₄×Q₈	C₂³	1	1	yes	characteristic
340	C₄×Q₈	C₂³	1	1	yes	characteristic
341	C₄×Q₈	C₂³	1	1	yes	characteristic
342	C₄×Q₈	C₂³	1	1	yes	characteristic
343	C₄×Q₈	C₂³	1	1	yes	characteristic
344	C₄×Q₈	C₂³	1	1	yes	characteristic
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
363	C₄×D₄	C₂³	1	1	yes	characteristic
364	C₄×D₄	C₂³	1	1	yes	characteristic
365	C₄×D₄	C₂³	1	1	yes	characteristic
366	C₄×D₄	C₂³	1	1	yes	characteristic
367	C₄×D₄	C₂³	1	1	yes	characteristic
368	C₄×D₄	C₂³	1	1	yes	characteristic
369	C₄×D₄	C₂³	1	1	yes	characteristic
370	C₄×D₄	C₂³	1	1	yes	characteristic
371	C₄×D₄	C₂³	1	1	yes	characteristic
372	C₄×D₄	C₂³	1	1	yes	characteristic
373	C₄×D₄	C₂³	1	1	yes	characteristic
374	C₄×D₄	C₂³	1	1	yes	characteristic
375	C₄×D₄	C₂³	1	1	yes	characteristic
376	C₄×D₄	C₂³	1	1	yes	characteristic
377	C₄×D₄	C₂³	1	1	yes	characteristic
378	C₄×D₄	C₂³	1	1	yes	characteristic
379	#117	—	2	1	no	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	C₂³	1	1	yes	characteristic
388	#117	C₂³	1	1	yes	characteristic
389	#117	C₂³	1	1	yes	characteristic
390	#117	C₂³	1	1	yes	characteristic
391	#117	C₂³	1	1	yes	characteristic
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	C₂³	1	1	yes	characteristic
411	#107	C₂³	1	1	yes	characteristic
412	#107	C₂³	1	1	yes	characteristic
413	#107	C₂³	1	1	yes	characteristic
414	#107	C₂³	1	1	yes	characteristic
415	#107	C₂³	1	1	yes	characteristic
416	#107	C₂³	1	1	yes	characteristic
417	#107	C₂³	1	1	yes	characteristic
418	#107	C₂³	1	1	yes	characteristic
419	#106	C₂³	1	1	yes	characteristic
420	#106	C₂³	1	1	yes	characteristic
421	#106	C₂³	1	1	yes	characteristic
422	#106	C₂³	1	1	yes	characteristic
423	#106	C₂³	1	1	yes	characteristic
424	#106	C₂³	1	1	yes	characteristic
425	#106	C₂³	1	1	yes	characteristic
426	#106	C₂³	1	1	yes	characteristic
427	C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₄⋊C₈	C₂³	1	1	yes	characteristic
433	#103	C₂³	1	1	yes	characteristic
434	#103	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	#102	C₂³	1	1	yes	characteristic
446	#102	C₂³	1	1	yes	characteristic
447	#102	C₂³	1	1	yes	characteristic
448	#102	C₂³	1	1	yes	characteristic
449	#102	C₂³	1	1	yes	characteristic
450	#102	C₂³	1	1	yes	characteristic
451	#102	C₂³	1	1	yes	characteristic
452	#102	C₂³	1	1	yes	characteristic
453	#102	C₂³	1	1	yes	characteristic
454	#102	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	C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	#97	C₂³	1	1	yes	characteristic
472	#97	C₂³	1	1	yes	characteristic
473	#97	C₂³	1	1	yes	characteristic
474	#97	C₂³	1	1	yes	characteristic
475	C₄×C₈	C₂³	1	1	yes	characteristic
476	C₄×C₈	C₂³	1	1	yes	characteristic
477	C₄×C₈	C₂³	1	1	yes	characteristic
478	C₄×C₈	C₂³	1	1	yes	characteristic
479	C₄×C₈	C₂³	1	1	yes	characteristic
480	C₄×C₈	C₂³	1	1	yes	characteristic
481	C₂⁴	—	2	1	no	—
482	C₂⁴	—	2	1	no	—
483	C₂⁴	—	2	1	no	—
484	#41	—	2	2	no	—
485	#41	—	2	2	no	—
486	#41	—	2	2	no	—
487	#41	—	4	1	no	—
488	#41	—	4	1	no	—
489	#41	—	4	1	no	—
490	#41	—	8	2	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
494	C₂×Q₈	C₂⁴	1	1	yes	characteristic
495	C₂×Q₈	C₂⁴	1	1	yes	characteristic
496	C₂×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	4	1	no	—
515	C₂×D₄	—	4	1	no	—
516	C₂×D₄	—	4	1	no	—
517	C₂×D₄	—	8	2	no	—
518	C₂×D₄	C₂×D₄	1	1	yes	characteristic
519	C₂×D₄	C₂×D₄	1	1	yes	characteristic
520	C₂×D₄	C₂×D₄	1	1	yes	characteristic
521	C₂×D₄	C₂⁴	1	1	yes	characteristic
522	C₂×D₄	C₂⁴	1	1	yes	characteristic
523	C₂×D₄	C₂⁴	1	1	yes	characteristic
524	C₂×D₄	C₂⁴	1	1	yes	characteristic
525	C₂×D₄	C₂⁴	1	1	yes	characteristic
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	8	2	no	—
547	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴	1	1	yes	characteristic
552	Q₁₆	—	2	2	no	—
553	Q₁₆	—	4	1	no	—
554	SD₁₆	—	2	2	no	—
555	SD₁₆	—	2	2	no	—
556	SD₁₆	—	2	2	no	—
557	SD₁₆	—	2	2	no	—
558	SD₁₆	—	4	1	no	—
559	SD₁₆	—	4	1	no	—
560	SD₁₆	—	4	1	no	—
561	SD₁₆	—	4	1	no	—
562	D₈	—	2	2	no	—
563	D₈	—	2	2	no	—
564	D₈	—	2	2	no	—
565	D₈	—	2	2	no	—
566	D₈	—	4	1	no	—
567	D₈	#41	1	4	yes	complemented
568	M₁₆	—	2	2	no	—
569	M₁₆	—	4	1	no	—
570	M₁₆	—	4	1	no	—
571	M₁₆	—	4	1	no	—
572	C₂×C₈	—	2	2	no	—
573	C₂×C₈	—	2	2	no	—
574	C₂×C₈	C₂⁴	1	1	yes	characteristic
575	C₂×C₈	C₂⁴	1	1	yes	characteristic
576	C₂×C₈	C₂⁴	1	1	yes	characteristic
577	C₂×C₈	C₂⁴	1	1	yes	characteristic
578	C₂×C₈	C₂⁴	1	1	yes	characteristic
579	C₂×C₈	C₂⁴	1	1	yes	characteristic
580	C₂×C₈	C₂⁴	1	1	yes	characteristic
581	C₂×C₈	C₂⁴	1	1	yes	characteristic
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
610	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
611	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
612	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
613	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
614	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
615	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
616	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
617	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
618	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
619	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
620	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
621	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
622	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
623	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
624	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
625	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
626	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	—	2	1	no	—
663	C₂²⋊C₄	—	2	1	no	—
664	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
665	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
666	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
667	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
668	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
669	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
670	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
671	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
672	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
673	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
674	C₄²	—	2	1	no	—
675	C₄²	—	2	1	no	—
676	C₄²	—	2	1	no	—
677	C₄²	—	2	1	no	—
678	C₄²	—	2	1	no	—
679	C₄²	—	2	1	no	—
680	C₄²	—	2	1	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	C₂×D₄	1	1	yes	characteristic
684	C₄²	C₂×D₄	1	1	yes	characteristic
685	C₄²	C₂⁴	1	1	yes	characteristic
686	C₄²	C₂⁴	1	1	yes	characteristic
687	C₄²	C₂⁴	1	1	yes	characteristic
688	C₄²	C₂⁴	1	1	yes	characteristic
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	—	4	2	no	—
698	C₂³	—	8	1	no	—
699	C₂³	—	8	1	no	—
700	C₂³	—	8	1	no	—
701	C₂³	—	8	1	no	—
702	C₂³	—	8	1	no	—
703	C₂³	C₂²×D₄	1	1	yes	characteristic
704	C₂³	C₂²×D₄	1	1	yes	characteristic
705	C₂³	C₂²×D₄	1	1	yes	characteristic
706	Q₈	—	2	1	no	—
707	Q₈	—	2	1	no	—
708	Q₈	—	2	1	no	—
709	Q₈	—	2	1	no	—
710	Q₈	—	2	1	no	—
711	Q₈	—	2	1	no	—
712	Q₈	—	4	1	no	—
713	Q₈	—	8	1	no	—
714	Q₈	—	8	1	no	—
715	D₄	—	2	1	no	—
716	D₄	—	2	1	no	—
717	D₄	—	2	1	no	—
718	D₄	—	2	1	no	—
719	D₄	—	2	1	no	—
720	D₄	—	2	1	no	—
721	D₄	—	2	1	no	—
722	D₄	—	2	1	no	—
723	D₄	—	4	1	no	—
724	D₄	—	4	1	no	—
725	D₄	—	4	1	no	—
726	D₄	—	4	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	2	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	1	no	—
734	D₄	—	8	1	no	—
735	D₄	—	8	1	no	—
736	D₄	—	8	1	no	—
737	D₄	—	8	1	no	—
738	D₄	—	8	1	no	—
739	D₄	—	8	1	no	—
740	D₄	C₂×#41	1	2	yes	—
741	D₄	C₂×#41	1	2	yes	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	8	1	no	—
766	C₂×C₄	—	8	1	no	—
767	C₂×C₄	—	8	1	no	—
768	C₂×C₄	—	8	1	no	—
769	C₂×C₄	—	8	1	no	—
770	C₂×C₄	—	8	1	no	—
771	C₂×C₄	—	8	1	no	—
772	C₂×C₄	—	8	1	no	—
773	C₂×C₄	—	8	1	no	—
774	C₂×C₄	—	8	1	no	—
775	C₂×C₄	—	8	1	no	—
776	C₂×C₄	—	8	1	no	—
777	C₂×C₄	—	8	1	no	—
778	C₂×C₄	—	8	1	no	—
779	C₂×C₄	—	8	1	no	—
780	C₂×C₄	—	8	1	no	—
781	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
787	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
790	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
792	C₂×C₄	C₂⁵	1	1	yes	characteristic
793	C₈	—	2	1	no	—
794	C₈	—	2	1	no	—
795	C₈	—	2	1	no	—
796	C₈	—	2	1	no	—
797	C₈	—	2	1	no	—
798	C₈	—	2	1	no	—
799	C₈	—	2	1	no	—
800	C₈	C₂×#41	1	2	yes	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	8	4	no	—
826	C₂²	—	16	2	no	—
827	C₂²	—	16	2	no	—
828	C₂²	C₂³×D₄	1	1	yes	characteristic
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	2	1	no	—
837	C₄	—	2	1	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	1	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	C₂²×#41	1	1	yes	characteristic
852	C₄	#585	1	1	yes	characteristic
853	C₂	—	4	1	no	—
854	C₂	—	4	1	no	—
855	C₂	—	4	1	no	—
856	C₂	—	4	2	no	—
857	C₂	—	4	2	no	—
858	C₂	—	8	1	no	—
859	C₂	—	8	1	no	—
860	C₂	—	8	1	no	—
861	C₂	D₄×#41	1	1	yes	characteristic
862	C₂	#3584	1	1	yes	characteristic
863	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3521	C₂	semidirect
2. #3513	C₂	semidirect
3. #3401	C₂	semidirect
4. #3389	C₂	semidirect
5. #3361	C₂	semidirect
6. #3360	C₂	semidirect
7. #3349	C₂	semidirect
8. #3345	C₂	semidirect
9. #3337	C₂	semidirect
10. #3330	C₂	semidirect
11. #3324	C₂	semidirect
12. #3323	C₂	semidirect
13. #3323	C₂	semidirect
14. #3322	C₂	semidirect
15. #3322	C₂	semidirect
16. #3280	C₂	semidirect
17. #3267	C₂	semidirect
18. #3264	C₂	semidirect
19. #3183	C₂	semidirect
20. #3179	C₂	semidirect
21. #3178	C₂	semidirect
22. #3124	C₂	semidirect
23. #3123	C₂	semidirect
24. #3119	C₂	semidirect
25. #3118	C₂	semidirect
26. #3105	C₂	semidirect
27. #3102	C₂	semidirect
28. #2969	C₂	semidirect
29. #2952	C₂	semidirect
30. #2948	C₂	semidirect
31. C₄×AGL(1,ℤ/8)	C₂	semidirect
35. #559	C₂²	semidirect
37. #556	C₂²	semidirect
38. #554	C₂²	semidirect
39. #554	C₂²	semidirect
43. #553	C₂²	semidirect
46. #552	C₂²	semidirect
51. #547	C₂²	semidirect
52. #547	C₂²	semidirect
56. #546	C₂²	semidirect
57. #546	C₂²	semidirect
60. #542	C₂²	semidirect
61. #541	C₂²	semidirect
62. #540	C₂²	semidirect
69. #529	C₂²	semidirect
70. #529	C₂²	semidirect
74. #520	C₂²	semidirect
75. #520	C₂²	semidirect
77. #518	C₂²	semidirect
78. C₄×#41	C₂²	semidirect
79. C₂×C₄×D₄	C₂²	semidirect
80. #501	C₂²	semidirect
81. #501	C₂²	semidirect
82. #499	C₂²	semidirect
83. #497	C₂²	semidirect
85. #495	C₂²	semidirect
86. #488	C₂²	semidirect
87. #488	C₂²	semidirect
88. #488	C₂²	semidirect
89. #488	C₂²	semidirect
90. #487	C₂²	semidirect
91. #486	C₂²	semidirect
92. #485	C₂²	semidirect
93. #485	C₂²	semidirect
94. #485	C₂²	semidirect
95. #485	C₂²	semidirect
96. #484	C₂²	semidirect
97. #484	C₂²	semidirect
99. #482	C₂²	semidirect
100. #481	C₂²	semidirect
101. #481	C₂²	semidirect
102. #480	C₂²	semidirect
103. #480	C₂²	semidirect
104. #479	C₂²	semidirect
105. #479	C₂²	semidirect
106. #478	C₂²	semidirect
107. #478	C₂²	semidirect
108. #478	C₂²	semidirect
109. #478	C₂²	semidirect
110. #478	C₂²	semidirect
111. #478	C₂²	semidirect
112. #477	C₂²	semidirect
113. #476	C₂²	semidirect
114. #474	C₂²	semidirect
115. #474	C₂²	semidirect
116. #470	C₂²	semidirect
117. #470	C₂²	semidirect
119. #469	C₂²	semidirect
121. #468	C₂²	semidirect
122. #468	C₂²	semidirect
123. #468	C₂²	semidirect
124. #467	C₂²	semidirect
125. #466	C₂²	semidirect
127. #465	C₂²	semidirect
128. #464	C₂²	semidirect
129. #464	C₂²	semidirect
132. #463	C₂²	semidirect
133. #463	C₂²	semidirect
134. #463	C₂²	semidirect
135. #463	C₂²	semidirect
136. #461	C₂²	semidirect
137. #461	C₂²	semidirect
138. #460	C₂²	semidirect
140. #452	C₂²	semidirect
141. #452	C₂²	semidirect
144. #450	C₂²	semidirect
145. #450	C₂²	semidirect
148. #449	C₂²	semidirect
149. #449	C₂²	semidirect
152. #446	C₂²	semidirect
153. C₈×Q₈	C₂²	semidirect
157. #442	C₂²	semidirect
158. #442	C₂²	semidirect
159. #442	C₂²	semidirect
160. #441	C₂²	semidirect
161. #441	C₂²	semidirect
162. #440	C₂²	semidirect
163. #440	C₂²	semidirect
164. #440	C₂²	semidirect
165. #440	C₂²	semidirect
166. C₄×Q₁₆	C₂²	semidirect
167. C₄×SD₁₆	C₂²	semidirect
168. C₄×SD₁₆	C₂²	semidirect
169. C₄×SD₁₆	C₂²	semidirect
170. C₄×SD₁₆	C₂²	semidirect
171. C₄×SD₁₆	C₂²	semidirect
172. C₄×SD₁₆	C₂²	semidirect
173. C₄×SD₁₆	C₂²	semidirect
174. C₄×SD₁₆	C₂²	semidirect
178. C₄×D₈	C₂²	semidirect
179. C₄×D₈	C₂²	semidirect
180. C₄×D₈	C₂²	semidirect
181. C₄×D₈	C₂²	semidirect
183. #436	C₂²	semidirect
184. #436	C₂²	semidirect
186. #435	C₂²	semidirect
187. C₈×D₄	C₂²	semidirect
188. #433	C₂²	semidirect
189. #433	C₂²	semidirect
190. #431	C₂²	semidirect
191. #428	C₂²	semidirect
192. #427	C₂²	semidirect
193. C₂×#106	C₂²	semidirect
195. #418	C₂²	semidirect
196. #418	C₂²	semidirect
197. #417	C₂²	semidirect
198. #417	C₂²	semidirect
199. #417	C₂²	semidirect
200. #405	C₂²	semidirect
201. #405	C₂²	semidirect
202. C₄×M₁₆	C₂²	semidirect
567. D₈	#41	semidirect

Maximal subgroups

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

subgroup	index
#3521	2
#3513	2
#3401	2
#3389	2
#3361	2
#3360	2
#3349	2
#3345	2
#3337	2
#3330	2
#3324	2
#3323	2
#3322	2
#3280	2
#3267	2
#3264	2
#3183	2
#3179	2
#3178	2
#3124	2
#3123	2
#3119	2
#3118	2
#3105	2
#3102	2
#2969	2
#2952	2
#2948	2
C₄×AGL(1,ℤ/8)	2