Subgroups — #61601

Order 256.

1125 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	#3323	C₂	1	2	yes	maximal, complemented
4	#3311	C₂	1	2	yes	maximal, complemented
5	#3306	C₂	1	2	yes	maximal, complemented
6	#3296	C₂	1	2	yes	maximal, complemented
7	#3282	C₂	1	2	yes	maximal, complemented
8	#3275	C₂	1	2	yes	maximal, complemented
9	#3267	C₂	1	2	yes	maximal, complemented
10	#3266	C₂	1	2	yes	maximal, complemented
11	#3215	C₂	1	1	yes	maximal, characteristic, complemented
12	#3211	C₂	1	1	yes	maximal, characteristic, complemented
13	#3195	C₂	1	1	yes	maximal, characteristic, complemented
14	#3194	C₂	1	1	yes	maximal, characteristic, complemented
15	#3190	C₂	1	1	yes	maximal, characteristic, complemented
16	#3187	C₂	1	1	yes	maximal, characteristic, complemented
17	#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	#3101	C₂	1	1	yes	maximal, characteristic, complemented
19	#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	#3003	C₂	1	1	yes	maximal, characteristic, complemented
21	#3002	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#450	C₂	1	1	yes	maximal, characteristic, complemented
23	#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41	C₂²	1	1	yes	characteristic
25	C₂³×D₄	C₂²	1	1	yes	characteristic
26	C₂×#137	C₂²	1	2	yes	complemented
27	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
28	C₂×#135	C₂²	1	2	yes	complemented
29	C₂²×SD₁₆	C₂²	1	2	yes	complemented
30	#556	C₂²	1	1	yes	characteristic, complemented
31	#554	—	2	1	no	—
32	#552	C₂²	1	1	yes	characteristic, complemented
33	#552	C₂²	1	1	yes	characteristic, complemented
34	#551	—	2	1	no	—
35	#551	—	2	1	no	—
36	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
37	#548	C₂²	1	1	yes	characteristic, complemented
38	#548	C₂²	1	1	yes	characteristic, complemented
39	#547	C₂²	1	1	yes	characteristic, complemented
40	#547	C₂²	1	1	yes	characteristic, complemented
41	#546	—	2	1	no	—
42	#546	—	2	1	no	—
43	#546	—	2	1	no	—
44	#546	—	2	1	no	—
45	#546	—	2	1	no	—
46	#546	C₂²	1	2	yes	—
47	#546	C₂²	1	2	yes	—
48	#546	C₂²	1	2	yes	—
49	#546	C₂²	1	2	yes	—
50	#542	—	2	1	no	—
51	#539	—	2	1	no	—
52	#539	—	2	1	no	—
53	#533	C₂²	1	1	yes	characteristic, complemented
54	#529	C₂²	1	1	yes	characteristic, complemented
55	C₂×#124	C₂²	1	1	yes	characteristic
56	#525	C₂²	1	1	yes	characteristic
57	#525	C₂²	1	1	yes	characteristic, complemented
58	C₂×#123	—	2	1	no	—
59	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
60	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
61	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
62	C₂×#121	—	2	1	no	—
63	C₂×#121	C₂²	1	1	yes	characteristic
64	C₂×#120	—	2	1	no	—
65	#520	—	2	1	no	—
66	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
67	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
68	C₂²×C₂²⋊C₄	—	2	1	no	—
69	#497	C₂²	1	2	yes	complemented
70	#495	C₂²	1	2	yes	complemented
71	#489	C₂²	1	2	yes	complemented
72	#488	C₂²	1	2	yes	complemented
73	#485	C₂²	1	2	yes	complemented
74	#483	C₂²	1	1	yes	characteristic, complemented
75	#483	C₂²	1	1	yes	characteristic, complemented
76	#483	C₂²	1	1	yes	characteristic, complemented
77	#483	C₂²	1	2	yes	complemented
78	#482	C₂²	1	2	yes	complemented
79	#481	C₂²	1	2	yes	complemented
80	#480	C₂²	1	1	yes	characteristic, complemented
81	#478	C₂²	1	2	yes	complemented
82	#476	C₂²	1	2	yes	complemented
83	#470	C₂²	1	2	yes	complemented
84	#470	C₂²	1	2	yes	complemented
85	#469	C₂²	1	2	yes	complemented
86	#468	C₂²	1	2	yes	complemented
87	#467	C₂²	1	2	yes	complemented
88	#465	C₂²	1	2	yes	complemented
89	#465	C₂²	1	2	yes	complemented
90	#465	C₂²	1	2	yes	complemented
91	#464	C₂²	1	2	yes	complemented
92	#464	C₂²	1	2	yes	complemented
93	#464	C₂²	1	2	yes	complemented
94	#463	C₂²	1	2	yes	complemented
95	#463	C₂²	1	2	yes	complemented
96	#461	C₂²	1	2	yes	complemented
97	#452	C₂²	1	2	yes	complemented
98	#452	C₂²	1	2	yes	complemented
99	#452	C₂²	1	2	yes	complemented
100	#452	C₂²	1	2	yes	complemented
101	#451	C₂²	1	1	yes	characteristic, complemented
102	#451	C₂²	1	1	yes	characteristic, complemented
103	#451	C₂²	1	1	yes	characteristic, complemented
104	#451	C₂²	1	2	yes	complemented
105	#450	C₂²	1	1	yes	characteristic
106	#450	C₂²	1	1	yes	characteristic
107	#450	C₂²	1	1	yes	characteristic
108	#450	C₂²	1	1	yes	characteristic
109	#450	C₂²	1	1	yes	characteristic
110	#450	C₂²	1	1	yes	characteristic
111	#450	C₂²	1	2	yes	complemented
112	#450	C₂²	1	2	yes	complemented
113	#450	C₂²	1	2	yes	complemented
114	#449	C₂²	1	2	yes	complemented
115	#449	C₂²	1	2	yes	complemented
116	#448	C₂²	1	1	yes	characteristic, complemented
117	#448	C₂²	1	2	yes	complemented
118	#447	C₂²	1	1	yes	characteristic
119	#447	C₂²	1	1	yes	characteristic
120	#447	C₂²	1	2	yes	complemented
121	#442	C₂²	1	2	yes	complemented
122	#440	C₂²	1	2	yes	complemented
123	C₄×SD₁₆	C₂²	1	2	yes	complemented
124	C₄×SD₁₆	C₂²	1	2	yes	complemented
125	#436	C₂²	1	2	yes	complemented
126	#435	C₂²	1	2	yes	complemented
127	#435	C₂²	1	2	yes	complemented
128	C₈×D₄	C₂²	1	2	yes	complemented
129	#432	C₂²	1	1	yes	characteristic, complemented
130	#431	C₂²	1	1	yes	characteristic, complemented
131	#418	C₂²	1	2	yes	complemented
132	#417	C₂²	1	2	yes	complemented
133	#416	C₂²	1	2	yes	complemented
134	C₂×#102	C₂²	1	2	yes	complemented
135	#407	C₂²	1	1	yes	characteristic
136	#407	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
139	C₂⁵	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	—	2	1	no	—
142	C₂×#41	—	2	1	no	—
143	C₂×#41	—	4	4	no	—
144	C₂×#41	C₂³	1	2	yes	—
145	C₂×#41	C₂³	1	2	yes	—
146	C₂×#41	C₂³	1	1	yes	characteristic
147	C₂×#41	C₂³	1	1	yes	characteristic, complemented
148	C₂²×Q₈	C₂³	1	1	yes	characteristic
149	C₂²×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×Q₈	C₂³	1	1	yes	characteristic, complemented
151	C₂²×D₄	—	2	1	no	—
152	C₂²×D₄	—	2	1	no	—
153	C₂²×D₄	—	2	1	no	—
154	C₂²×D₄	—	2	1	no	—
155	C₂²×D₄	—	2	1	no	—
156	C₂²×D₄	—	4	4	no	—
157	C₂²×D₄	D₄	1	1	yes	characteristic
158	C₂²×D₄	C₂³	1	1	yes	characteristic
159	C₂²×D₄	C₂³	1	2	yes	—
160	C₂²×D₄	C₂³	1	2	yes	—
161	C₂²×D₄	C₂³	1	1	yes	characteristic
162	C₂³×C₄	—	2	1	no	—
163	C₂³×C₄	—	2	1	no	—
164	C₂³×C₄	C₂³	1	1	yes	characteristic
165	C₂³×C₄	C₂³	1	1	yes	characteristic
166	#137	—	4	4	no	—
167	AGL(1,ℤ/8)	—	4	4	no	—
168	#135	—	4	4	no	—
169	C₂×Q₁₆	C₂³	1	2	yes	complemented
170	C₂×Q₁₆	C₂³	1	2	yes	complemented
171	C₂×Q₁₆	C₂³	1	2	yes	complemented
172	C₂×SD₁₆	—	4	4	no	—
173	C₂×SD₁₆	C₂³	1	2	yes	—
174	C₂×SD₁₆	C₂³	1	2	yes	—
175	C₂×SD₁₆	C₂³	1	2	yes	—
176	C₂×SD₁₆	C₂³	1	2	yes	—
177	C₂×SD₁₆	C₂³	1	2	yes	—
178	C₂×SD₁₆	C₂³	1	2	yes	—
179	C₂×SD₁₆	C₂³	1	2	yes	complemented
180	C₂×D₈	C₂³	1	2	yes	—
181	C₂×D₈	C₂³	1	2	yes	—
182	C₂×M₁₆	C₂³	1	2	yes	—
183	C₂×M₁₆	C₂³	1	2	yes	complemented
184	C₂²×C₈	C₂³	1	2	yes	—
185	C₂²×C₈	C₂³	1	2	yes	complemented
186	C₄⋊Q₈	—	2	1	no	—
187	C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
188	C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
189	#126	—	2	1	no	—
190	#126	—	2	1	no	—
191	#126	—	2	1	no	—
192	#126	—	2	1	no	—
193	#126	—	2	1	no	—
194	#125	—	2	1	no	—
195	#125	—	2	1	no	—
196	#125	—	2	1	no	—
197	#125	C₂³	1	1	yes	characteristic, complemented
198	#124	—	2	1	no	—
199	#124	—	2	1	no	—
200	#124	—	2	1	no	—
201	#124	—	2	1	no	—
202	#124	—	2	1	no	—
203	#124	C₂³	1	2	yes	—
204	#124	C₂³	1	2	yes	—
205	#124	C₂³	1	1	yes	characteristic, complemented
206	#123	—	2	1	no	—
207	#123	—	2	1	no	—
208	#123	—	2	1	no	—
209	#123	—	2	1	no	—
210	#123	—	2	1	no	—
211	#123	—	2	2	no	—
212	#123	—	2	2	no	—
213	#123	—	2	2	no	—
214	#123	—	2	2	no	—
215	#123	—	2	1	no	—
216	#123	—	2	1	no	—
217	#123	—	2	1	no	—
218	#123	—	2	1	no	—
219	C₂²⋊Q₈	—	2	1	no	—
220	C₂²⋊Q₈	—	2	1	no	—
221	C₂²⋊Q₈	—	2	1	no	—
222	C₂²⋊Q₈	—	2	1	no	—
223	C₂²⋊Q₈	—	2	1	no	—
224	C₂²⋊Q₈	—	2	1	no	—
225	C₂²⋊Q₈	—	2	1	no	—
226	C₂²⋊Q₈	—	2	1	no	—
227	C₂²⋊Q₈	—	2	1	no	—
228	C₂²⋊Q₈	—	2	1	no	—
229	C₂²⋊Q₈	—	2	1	no	—
230	C₂²⋊Q₈	—	2	1	no	—
231	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
232	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
233	C₂²⋊Q₈	C₂³	1	2	yes	—
234	C₂²⋊Q₈	C₂³	1	2	yes	—
235	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
236	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
237	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
238	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
239	C₂²⋊Q₈	C₂³	1	1	yes	characteristic, complemented
240	C₂²⋊Q₈	C₂³	1	1	yes	characteristic, complemented
241	C₂²⋊Q₈	C₂³	1	1	yes	characteristic, complemented
242	#121	—	2	1	no	—
243	#121	—	2	1	no	—
244	#121	—	2	1	no	—
245	#121	—	2	1	no	—
246	#121	—	2	1	no	—
247	#121	—	2	2	no	—
248	#121	—	2	2	no	—
249	#121	—	2	2	no	—
250	#121	—	2	2	no	—
251	#121	C₂³	1	2	yes	—
252	#121	C₂³	1	2	yes	—
253	#121	C₂³	1	1	yes	characteristic
254	#121	C₂³	1	1	yes	characteristic
255	#121	C₂³	1	1	yes	characteristic, complemented
256	#120	—	2	1	no	—
257	#120	—	2	1	no	—
258	#120	—	2	2	no	—
259	#120	—	2	2	no	—
260	#120	—	2	2	no	—
261	#120	—	2	2	no	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
265	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
266	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	D₄	1	1	yes	characteristic
278	C₄×D₄	D₄	1	1	yes	characteristic
279	C₄×D₄	D₄	1	1	yes	characteristic
280	C₄×D₄	D₄	1	1	yes	characteristic
281	C₄×D₄	C₂³	1	2	yes	—
282	C₄×D₄	C₂³	1	2	yes	—
283	C₄×D₄	C₂³	1	1	yes	characteristic
284	C₄×D₄	C₂³	1	1	yes	characteristic
285	C₄×D₄	C₂³	1	1	yes	characteristic
286	C₄×D₄	C₂³	1	1	yes	characteristic
287	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
288	#117	—	2	1	no	—
289	#117	—	2	1	no	—
290	#117	—	2	1	no	—
291	#117	—	2	1	no	—
292	#117	C₂³	1	1	yes	characteristic
293	#117	C₂³	1	1	yes	characteristic, complemented
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
315	C₂×C₄²	C₂³	1	1	yes	characteristic
316	#107	C₂³	1	2	yes	complemented
317	#106	C₂³	1	2	yes	complemented
318	#106	C₂³	1	2	yes	complemented
319	#106	C₂³	1	2	yes	complemented
320	C₄⋊C₈	C₂³	1	2	yes	complemented
321	C₄⋊C₈	C₂³	1	2	yes	complemented
322	#103	C₂³	1	2	yes	complemented
323	#103	C₂³	1	2	yes	complemented
324	#103	C₂³	1	2	yes	complemented
325	#103	C₂³	1	2	yes	complemented
326	#103	C₂³	1	2	yes	complemented
327	#103	C₂³	1	2	yes	complemented
328	#103	C₂³	1	2	yes	complemented
329	#102	C₂³	1	2	yes	—
330	#102	C₂³	1	2	yes	—
331	#102	C₂³	1	2	yes	—
332	#102	C₂³	1	2	yes	—
333	#102	C₂³	1	2	yes	—
334	#102	C₂³	1	2	yes	—
335	#102	C₂³	1	2	yes	—
336	#102	C₂³	1	2	yes	—
337	#102	C₂³	1	2	yes	complemented
338	C₂²⋊C₈	C₂³	1	1	yes	characteristic
339	C₂²⋊C₈	C₂³	1	1	yes	characteristic
340	C₂²⋊C₈	C₂³	1	2	yes	—
341	C₂²⋊C₈	C₂³	1	1	yes	characteristic
342	C₂²⋊C₈	C₂³	1	1	yes	characteristic
343	C₂²⋊C₈	C₂³	1	2	yes	—
344	C₂²⋊C₈	C₂³	1	2	yes	complemented
345	C₂²⋊C₈	C₂³	1	2	yes	complemented
346	#97	C₂³	1	2	yes	complemented
347	C₄×C₈	C₂³	1	2	yes	complemented
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	2	1	no	—
350	C₂⁴	—	2	2	no	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	4	4	no	—
353	C₂⁴	—	4	4	no	—
354	C₂⁴	—	8	2	no	—
355	C₂⁴	C₂×D₄	1	1	yes	characteristic
356	C₂⁴	C₂×D₄	1	1	yes	characteristic
357	#41	—	2	4	no	—
358	#41	—	2	4	no	—
359	#41	—	4	2	no	—
360	#41	—	4	2	no	—
361	#41	—	4	2	no	—
362	#41	—	4	2	no	—
363	#41	—	4	4	no	—
364	#41	—	4	4	no	—
365	#41	—	4	4	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	—	4	2	no	—
372	C₂×Q₈	—	4	2	no	—
373	C₂×Q₈	C₂⁴	1	2	yes	—
374	C₂×Q₈	C₂⁴	1	1	yes	characteristic
375	C₂×Q₈	C₂⁴	1	1	yes	characteristic
376	C₂×Q₈	C₂⁴	1	1	yes	characteristic
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	8	2	no	—
402	C₂×D₄	C₂×D₄	1	1	yes	characteristic
403	C₂×D₄	C₂×D₄	1	1	yes	characteristic
404	C₂×D₄	C₂×D₄	1	1	yes	characteristic
405	C₂×D₄	C₂×D₄	1	1	yes	characteristic
406	C₂×D₄	C₂⁴	1	2	yes	—
407	C₂×D₄	C₂⁴	1	1	yes	characteristic
408	C₂×D₄	C₂⁴	1	2	yes	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	—	8	2	no	—
426	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴	1	1	yes	characteristic
439	Q₁₆	—	4	2	no	—
440	Q₁₆	—	4	2	no	—
441	Q₁₆	—	4	2	no	—
442	SD₁₆	—	2	4	no	—
443	SD₁₆	—	2	4	no	—
444	SD₁₆	—	2	4	no	—
445	SD₁₆	—	4	2	no	—
446	SD₁₆	—	4	2	no	—
447	SD₁₆	—	4	2	no	—
448	SD₁₆	—	4	2	no	—
449	D₈	—	2	4	no	—
450	D₈	—	4	2	no	—
451	M₁₆	—	4	2	no	—
452	M₁₆	—	4	2	no	—
453	C₂×C₈	—	4	2	no	—
454	C₂×C₈	—	4	2	no	—
455	C₂×C₈	C₂⁴	1	2	yes	—
456	C₂×C₈	C₂⁴	1	2	yes	—
457	C₂×C₈	C₂⁴	1	2	yes	—
458	C₂×C₈	C₂⁴	1	2	yes	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
483	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
484	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
485	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
486	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
487	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
488	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
489	C₄⋊C₄	C₂⁴	1	2	yes	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
518	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
519	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
520	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
521	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
522	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
523	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
524	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	C₂×D₄	1	1	yes	characteristic
531	C₄²	C₂×D₄	1	1	yes	characteristic
532	C₄²	C₂⁴	1	1	yes	characteristic
533	C₄²	C₂⁴	1	1	yes	characteristic
534	C₂³	—	2	4	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	4	no	—
545	C₂³	—	4	4	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	2	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	4	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	8	2	no	—
554	C₂³	—	8	2	no	—
555	C₂³	—	8	16	no	—
556	C₂³	C₂²×D₄	1	1	yes	characteristic
557	C₂³	C₂²×D₄	1	1	yes	characteristic
558	C₂³	C₂²×D₄	1	1	yes	characteristic
559	C₂³	C₂²×D₄	1	1	yes	characteristic
560	C₂³	C₂²×D₄	1	1	yes	characteristic
561	Q₈	—	2	2	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	4	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	8	1	no	—
569	Q₈	—	8	1	no	—
570	D₄	—	2	4	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	4	no	—
580	D₄	—	4	4	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	4	no	—
583	D₄	—	4	4	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	8	2	no	—
588	D₄	—	8	2	no	—
589	D₄	—	8	1	no	—
590	D₄	—	8	1	no	—
591	D₄	H(5,𝔽₂)	1	4	yes	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	8	2	no	—
622	C₂×C₄	—	8	2	no	—
623	C₂×C₄	—	8	1	no	—
624	C₂×C₄	—	8	1	no	—
625	C₂×C₄	—	8	1	no	—
626	C₂×C₄	—	8	1	no	—
627	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
629	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
630	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
631	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
632	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
633	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
635	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
636	C₂×C₄	C₂⁵	1	1	yes	characteristic
637	C₈	—	2	2	no	—
638	C₈	—	2	2	no	—
639	C₈	—	2	2	no	—
640	C₈	—	2	2	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	4	4	no	—
656	C₂²	—	4	8	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	8	2	no	—
666	C₂²	—	8	8	no	—
667	C₂²	—	8	4	no	—
668	C₂²	—	8	8	no	—
669	C₂²	#575	1	2	yes	—
670	C₂²	#577	1	2	yes	—
671	C₂²	C₂³×D₄	1	1	yes	characteristic
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	1	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	1	no	—
690	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
691	C₂	—	2	2	no	—
692	C₂	—	2	2	no	—
693	C₂	—	4	1	no	—
694	C₂	—	4	1	no	—
695	C₂	—	4	1	no	—
696	C₂	—	4	4	no	—
697	C₂	—	8	1	no	—
698	C₂	—	8	2	no	—
699	C₂	#3484	1	1	yes	characteristic
700	C₂	C₂×#575	1	1	yes	characteristic
701	C₂	C₂×#577	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 ◁ 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. #3520	C₂	semidirect
2. C₂×#546	C₂	semidirect
3. #3323	C₂	semidirect
4. #3311	C₂	semidirect
5. #3306	C₂	semidirect
6. #3296	C₂	semidirect
7. #3282	C₂	semidirect
8. #3275	C₂	semidirect
9. #3267	C₂	semidirect
10. #3266	C₂	semidirect
11. #3215	C₂	semidirect
12. #3211	C₂	semidirect
13. #3195	C₂	semidirect
14. #3194	C₂	semidirect
15. #3190	C₂	semidirect
16. #3187	C₂	semidirect
17. #3114	C₂	semidirect
18. #3101	C₂	semidirect
19. #3007	C₂	semidirect
20. #3003	C₂	semidirect
21. #3002	C₂	semidirect
22. C₂×#450	C₂	semidirect
23. #2974	C₂	semidirect
26. C₂×#137	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×#135	C₂²	semidirect
29. C₂²×SD₁₆	C₂²	semidirect
30. #556	C₂²	semidirect
32. #552	C₂²	semidirect
33. #552	C₂²	semidirect
36. D₄×Q₈	C₂²	semidirect
37. #548	C₂²	semidirect
38. #548	C₂²	semidirect
39. #547	C₂²	semidirect
40. #547	C₂²	semidirect
53. #533	C₂²	semidirect
54. #529	C₂²	semidirect
57. #525	C₂²	semidirect
61. C₂×C₂²⋊Q₈	C₂²	semidirect
69. #497	C₂²	semidirect
70. #495	C₂²	semidirect
71. #489	C₂²	semidirect
72. #488	C₂²	semidirect
73. #485	C₂²	semidirect
74. #483	C₂²	semidirect
75. #483	C₂²	semidirect
76. #483	C₂²	semidirect
77. #483	C₂²	semidirect
78. #482	C₂²	semidirect
79. #481	C₂²	semidirect
80. #480	C₂²	semidirect
81. #478	C₂²	semidirect
82. #476	C₂²	semidirect
83. #470	C₂²	semidirect
84. #470	C₂²	semidirect
85. #469	C₂²	semidirect
86. #468	C₂²	semidirect
87. #467	C₂²	semidirect
88. #465	C₂²	semidirect
89. #465	C₂²	semidirect
90. #465	C₂²	semidirect
91. #464	C₂²	semidirect
92. #464	C₂²	semidirect
93. #464	C₂²	semidirect
94. #463	C₂²	semidirect
95. #463	C₂²	semidirect
96. #461	C₂²	semidirect
97. #452	C₂²	semidirect
98. #452	C₂²	semidirect
99. #452	C₂²	semidirect
100. #452	C₂²	semidirect
101. #451	C₂²	semidirect
102. #451	C₂²	semidirect
103. #451	C₂²	semidirect
104. #451	C₂²	semidirect
111. #450	C₂²	semidirect
112. #450	C₂²	semidirect
113. #450	C₂²	semidirect
114. #449	C₂²	semidirect
115. #449	C₂²	semidirect
116. #448	C₂²	semidirect
117. #448	C₂²	semidirect
120. #447	C₂²	semidirect
121. #442	C₂²	semidirect
122. #440	C₂²	semidirect
123. C₄×SD₁₆	C₂²	semidirect
124. C₄×SD₁₆	C₂²	semidirect
125. #436	C₂²	semidirect
126. #435	C₂²	semidirect
127. #435	C₂²	semidirect
128. C₈×D₄	C₂²	semidirect
129. #432	C₂²	semidirect
130. #431	C₂²	semidirect
131. #418	C₂²	semidirect
132. #417	C₂²	semidirect
133. #416	C₂²	semidirect
134. C₂×#102	C₂²	semidirect
136. #407	C₂²	semidirect
138. C₂×C₂²⋊C₈	C₂²	semidirect
147. C₂×#41	C₂³	semidirect
150. C₂²×Q₈	C₂³	semidirect
169. C₂×Q₁₆	C₂³	semidirect
170. C₂×Q₁₆	C₂³	semidirect
171. C₂×Q₁₆	C₂³	semidirect
179. C₂×SD₁₆	C₂³	semidirect
183. C₂×M₁₆	C₂³	semidirect
185. C₂²×C₈	C₂³	semidirect
187. C₄⋊Q₈	C₂³	semidirect
188. C₄⋊Q₈	C₂³	semidirect
197. #125	C₂³	semidirect
205. #124	C₂³	semidirect
239. C₂²⋊Q₈	C₂³	semidirect
240. C₂²⋊Q₈	C₂³	semidirect
241. C₂²⋊Q₈	C₂³	semidirect
255. #121	C₂³	semidirect
264. C₄×Q₈	C₂³	semidirect
265. C₄×Q₈	C₂³	semidirect
266. C₄×Q₈	C₂³	semidirect
287. C₄×D₄	C₂³	semidirect
293. #117	C₂³	semidirect
301. C₂×C₄⋊C₄	C₂³	semidirect
316. #107	C₂³	semidirect
317. #106	C₂³	semidirect
318. #106	C₂³	semidirect
319. #106	C₂³	semidirect
320. C₄⋊C₈	C₂³	semidirect
321. C₄⋊C₈	C₂³	semidirect
322. #103	C₂³	semidirect
323. #103	C₂³	semidirect
324. #103	C₂³	semidirect
325. #103	C₂³	semidirect
326. #103	C₂³	semidirect
327. #103	C₂³	semidirect
328. #103	C₂³	semidirect
337. #102	C₂³	semidirect
344. C₂²⋊C₈	C₂³	semidirect
345. C₂²⋊C₈	C₂³	semidirect
346. #97	C₂³	semidirect
347. C₄×C₈	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#3520	2
C₂×#546	2
#3323	2
#3311	2
#3306	2
#3296	2
#3282	2
#3275	2
#3267	2
#3266	2
#3215	2
#3211	2
#3195	2
#3194	2
#3190	2
#3187	2
#3114	2
#3101	2
#3007	2
#3003	2
#3002	2
C₂×#450	2
#2974	2