Subgroups — #61592

Order 256.

1157 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	#3322	C₂	1	2	yes	maximal, complemented
4	#3319	C₂	1	2	yes	maximal, complemented
5	#3314	C₂	1	2	yes	maximal, complemented
6	#3297	C₂	1	2	yes	maximal, complemented
7	#3280	C₂	1	2	yes	maximal, complemented
8	#3273	C₂	1	2	yes	maximal, complemented
9	#3268	C₂	1	2	yes	maximal, complemented
10	#3264	C₂	1	2	yes	maximal, complemented
11	#3213	C₂	1	1	yes	maximal, characteristic, complemented
12	#3211	C₂	1	1	yes	maximal, characteristic, complemented
13	#3194	C₂	1	1	yes	maximal, characteristic, complemented
14	#3193	C₂	1	1	yes	maximal, characteristic, complemented
15	#3190	C₂	1	1	yes	maximal, characteristic, complemented
16	#3186	C₂	1	1	yes	maximal, characteristic, complemented
17	#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	#3100	C₂	1	1	yes	maximal, characteristic, complemented
19	#3006	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×#447	C₂	1	1	yes	maximal, characteristic, complemented
23	#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂³×D₄	C₂²	1	1	yes	characteristic, complemented
26	C₂×AGL(1,ℤ/8)	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×D₈	C₂²	1	2	yes	complemented
30	#555	C₂²	1	1	yes	characteristic, complemented
31	#554	C₂²	1	1	yes	characteristic, complemented
32	#553	—	2	1	no	—
33	#553	C₂²	1	1	yes	characteristic, complemented
34	#553	C₂²	1	1	yes	characteristic, complemented
35	#550	C₂²	1	1	yes	characteristic, complemented
36	#546	—	2	1	no	—
37	#546	—	2	1	no	—
38	#546	—	2	1	no	—
39	#546	—	2	1	no	—
40	#546	—	2	1	no	—
41	#546	—	2	1	no	—
42	#546	C₂²	1	2	yes	—
43	#546	C₂²	1	2	yes	complemented
44	#546	C₂²	1	2	yes	complemented
45	#546	C₂²	1	2	yes	complemented
46	#546	C₂²	1	1	yes	characteristic, complemented
47	#546	C₂²	1	1	yes	characteristic, complemented
48	D₄²	—	2	1	no	—
49	D₄²	C₂²	1	1	yes	characteristic, complemented
50	#540	—	2	1	no	—
51	#538	—	2	1	no	—
52	#538	—	2	1	no	—
53	#532	C₂²	1	1	yes	characteristic, complemented
54	#529	C₂²	1	1	yes	characteristic, complemented
55	C₂×#124	C₂²	1	1	yes	characteristic, complemented
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, complemented
60	C₂×#121	—	2	1	no	—
61	C₂×#121	C₂²	1	1	yes	characteristic
62	C₂×#121	C₂²	1	1	yes	characteristic, complemented
63	C₂×#121	C₂²	1	1	yes	characteristic, complemented
64	C₂×#120	—	2	1	no	—
65	#518	—	2	1	no	—
66	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
67	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
68	C₂²×C₂²⋊C₄	—	2	1	no	—
69	#496	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	#484	C₂²	1	2	yes	complemented
75	#483	C₂²	1	1	yes	characteristic, complemented
76	#482	C₂²	1	2	yes	complemented
77	#480	C₂²	1	1	yes	characteristic, complemented
78	#480	C₂²	1	1	yes	characteristic, complemented
79	#480	C₂²	1	1	yes	characteristic, complemented
80	#480	C₂²	1	2	yes	complemented
81	#478	C₂²	1	2	yes	complemented
82	#474	C₂²	1	2	yes	complemented
83	#469	C₂²	1	2	yes	complemented
84	#468	C₂²	1	2	yes	complemented
85	#468	C₂²	1	2	yes	complemented
86	#468	C₂²	1	2	yes	complemented
87	#467	C₂²	1	2	yes	complemented
88	#466	C₂²	1	2	yes	complemented
89	#466	C₂²	1	2	yes	complemented
90	#465	C₂²	1	2	yes	complemented
91	#464	C₂²	1	2	yes	complemented
92	#463	C₂²	1	2	yes	complemented
93	#463	C₂²	1	2	yes	complemented
94	#463	C₂²	1	2	yes	complemented
95	#463	C₂²	1	2	yes	complemented
96	#459	C₂²	1	2	yes	complemented
97	#452	C₂²	1	2	yes	complemented
98	#452	C₂²	1	2	yes	complemented
99	#451	C₂²	1	1	yes	characteristic, complemented
100	#450	C₂²	1	1	yes	characteristic, complemented
101	#450	C₂²	1	1	yes	characteristic, complemented
102	#450	C₂²	1	2	yes	complemented
103	#450	C₂²	1	2	yes	complemented
104	#449	C₂²	1	2	yes	complemented
105	#449	C₂²	1	2	yes	complemented
106	#449	C₂²	1	2	yes	complemented
107	#449	C₂²	1	2	yes	complemented
108	#448	C₂²	1	1	yes	characteristic, complemented
109	#448	C₂²	1	1	yes	characteristic, complemented
110	#448	C₂²	1	1	yes	characteristic, complemented
111	#447	C₂²	1	1	yes	characteristic
112	#447	C₂²	1	1	yes	characteristic
113	#447	C₂²	1	1	yes	characteristic, complemented
114	#447	C₂²	1	1	yes	characteristic, complemented
115	#447	C₂²	1	1	yes	characteristic, complemented
116	#447	C₂²	1	1	yes	characteristic, complemented
117	#447	C₂²	1	2	yes	complemented
118	#447	C₂²	1	2	yes	complemented
119	#447	C₂²	1	2	yes	complemented
120	#447	C₂²	1	2	yes	complemented
121	#442	C₂²	1	2	yes	complemented
122	#440	C₂²	1	2	yes	complemented
123	C₄×D₈	C₂²	1	2	yes	complemented
124	C₄×D₈	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, complemented
136	#407	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
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×D₄	—	2	1	no	—
150	C₂²×D₄	—	2	1	no	—
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	—	2	1	no	—
157	C₂²×D₄	—	4	4	no	—
158	C₂²×D₄	D₄	1	1	yes	characteristic
159	C₂²×D₄	C₂³	1	1	yes	characteristic
160	C₂²×D₄	C₂³	1	2	yes	—
161	C₂²×D₄	C₂³	1	2	yes	—
162	C₂²×D₄	C₂³	1	1	yes	characteristic
163	C₂²×D₄	C₂³	1	1	yes	characteristic
164	C₂²×D₄	C₂³	1	1	yes	characteristic, complemented
165	C₂³×C₄	—	2	1	no	—
166	C₂³×C₄	—	2	1	no	—
167	C₂³×C₄	C₂³	1	1	yes	characteristic
168	C₂³×C₄	C₂³	1	1	yes	characteristic
169	AGL(1,ℤ/8)	—	4	4	no	—
170	AGL(1,ℤ/8)	—	4	4	no	—
171	#135	—	4	4	no	—
172	C₂×Q₁₆	C₂³	1	2	yes	complemented
173	C₂×SD₁₆	C₂³	1	2	yes	—
174	C₂×SD₁₆	C₂³	1	2	yes	—
175	C₂×SD₁₆	C₂³	1	2	yes	complemented
176	C₂×SD₁₆	C₂³	1	2	yes	complemented
177	C₂×SD₁₆	C₂³	1	2	yes	complemented
178	C₂×D₈	—	4	4	no	—
179	C₂×D₈	C₂³	1	2	yes	—
180	C₂×D₈	C₂³	1	2	yes	—
181	C₂×D₈	C₂³	1	2	yes	—
182	C₂×D₈	C₂³	1	2	yes	—
183	C₂×D₈	C₂³	1	2	yes	—
184	C₂×D₈	C₂³	1	2	yes	—
185	C₂×M₁₆	C₂³	1	2	yes	—
186	C₂×M₁₆	C₂³	1	2	yes	complemented
187	C₂²×C₈	C₂³	1	2	yes	—
188	C₂²×C₈	C₂³	1	2	yes	complemented
189	C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
190	#127	—	2	1	no	—
191	#127	C₂³	1	1	yes	characteristic, complemented
192	#126	—	2	1	no	—
193	#126	—	2	1	no	—
194	#126	—	2	1	no	—
195	#125	—	2	1	no	—
196	#125	C₂³	1	1	yes	characteristic, complemented
197	#124	—	2	1	no	—
198	#124	—	2	1	no	—
199	#124	—	2	1	no	—
200	#124	—	2	1	no	—
201	#124	—	2	1	no	—
202	#124	C₂³	1	2	yes	—
203	#124	C₂³	1	2	yes	—
204	#124	C₂³	1	1	yes	characteristic, complemented
205	#123	—	2	1	no	—
206	#123	—	2	1	no	—
207	#123	—	2	1	no	—
208	#123	—	2	2	no	—
209	#123	—	2	2	no	—
210	#123	—	2	2	no	—
211	#123	—	2	2	no	—
212	#123	—	2	1	no	—
213	#123	—	2	1	no	—
214	#123	—	2	1	no	—
215	#123	—	2	1	no	—
216	C₂²⋊Q₈	—	2	1	no	—
217	C₂²⋊Q₈	—	2	1	no	—
218	C₂²⋊Q₈	—	2	1	no	—
219	C₂²⋊Q₈	—	2	1	no	—
220	C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂²⋊Q₈	C₂³	1	1	yes	characteristic, complemented
225	#121	—	2	1	no	—
226	#121	—	2	1	no	—
227	#121	—	2	1	no	—
228	#121	—	2	1	no	—
229	#121	—	2	1	no	—
230	#121	—	2	1	no	—
231	#121	—	2	1	no	—
232	#121	—	2	1	no	—
233	#121	—	2	1	no	—
234	#121	—	2	1	no	—
235	#121	—	2	1	no	—
236	#121	—	2	2	no	—
237	#121	—	2	2	no	—
238	#121	—	2	2	no	—
239	#121	—	2	2	no	—
240	#121	—	2	1	no	—
241	#121	—	2	1	no	—
242	#121	—	2	1	no	—
243	#121	—	2	1	no	—
244	#121	C₂³	1	1	yes	characteristic
245	#121	C₂³	1	1	yes	characteristic
246	#121	C₂³	1	1	yes	characteristic
247	#121	C₂³	1	1	yes	characteristic
248	#121	C₂³	1	1	yes	characteristic
249	#121	C₂³	1	2	yes	—
250	#121	C₂³	1	2	yes	—
251	#121	C₂³	1	1	yes	characteristic
252	#121	C₂³	1	1	yes	characteristic, complemented
253	#121	C₂³	1	1	yes	characteristic, complemented
254	#121	C₂³	1	1	yes	characteristic, complemented
255	#120	—	2	1	no	—
256	#120	—	2	1	no	—
257	#120	—	2	2	no	—
258	#120	—	2	2	no	—
259	#120	—	2	2	no	—
260	#120	—	2	2	no	—
261	#120	—	2	1	no	—
262	#120	—	2	1	no	—
263	#120	—	2	1	no	—
264	#120	—	2	1	no	—
265	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
266	C₄×D₄	—	2	1	no	—
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	—	2	1	no	—
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	D₄	1	1	yes	characteristic
282	C₄×D₄	C₂³	1	2	yes	—
283	C₄×D₄	C₂³	1	2	yes	—
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
288	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
289	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
290	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
291	#117	—	2	1	no	—
292	#117	—	2	1	no	—
293	#117	C₂³	1	1	yes	characteristic
294	#117	C₂³	1	1	yes	characteristic, complemented
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
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	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	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	#107	C₂³	1	2	yes	complemented
318	#107	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	#102	C₂³	1	2	yes	—
328	#102	C₂³	1	2	yes	—
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	complemented
336	#102	C₂³	1	2	yes	complemented
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	1	yes	characteristic
341	C₂²⋊C₈	C₂³	1	2	yes	—
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	—	2	1	no	—
353	C₂⁴	—	2	1	no	—
354	C₂⁴	—	4	4	no	—
355	C₂⁴	—	4	4	no	—
356	C₂⁴	—	8	2	no	—
357	C₂⁴	C₂×D₄	1	1	yes	characteristic
358	C₂⁴	C₂×D₄	1	1	yes	characteristic
359	#41	—	2	4	no	—
360	#41	—	2	4	no	—
361	#41	—	4	2	no	—
362	#41	—	4	2	no	—
363	#41	—	4	2	no	—
364	#41	—	4	2	no	—
365	#41	—	4	4	no	—
366	#41	—	4	4	no	—
367	#41	—	8	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	C₂⁴	1	2	yes	—
372	C₂×Q₈	C₂⁴	1	1	yes	characteristic
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	8	2	no	—
411	C₂×D₄	—	8	2	no	—
412	C₂×D₄	—	8	2	no	—
413	C₂×D₄	C₂×D₄	1	1	yes	characteristic
414	C₂×D₄	C₂×D₄	1	1	yes	characteristic
415	C₂×D₄	C₂×D₄	1	1	yes	characteristic
416	C₂×D₄	C₂×D₄	1	1	yes	characteristic
417	C₂×D₄	C₂⁴	1	2	yes	—
418	C₂×D₄	C₂⁴	1	1	yes	characteristic
419	C₂×D₄	C₂⁴	1	1	yes	characteristic
420	C₂×D₄	C₂⁴	1	1	yes	characteristic
421	C₂×D₄	C₂⁴	1	2	yes	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	8	2	no	—
439	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴	1	1	yes	characteristic
452	Q₁₆	—	4	2	no	—
453	SD₁₆	—	2	4	no	—
454	SD₁₆	—	4	2	no	—
455	SD₁₆	—	4	2	no	—
456	SD₁₆	—	4	2	no	—
457	SD₁₆	—	4	2	no	—
458	D₈	—	2	4	no	—
459	D₈	—	2	4	no	—
460	D₈	—	2	4	no	—
461	D₈	—	4	2	no	—
462	D₈	—	4	2	no	—
463	D₈	—	4	2	no	—
464	M₁₆	—	4	2	no	—
465	M₁₆	—	4	2	no	—
466	C₂×C₈	—	4	2	no	—
467	C₂×C₈	—	4	2	no	—
468	C₂×C₈	C₂⁴	1	2	yes	—
469	C₂×C₈	C₂⁴	1	2	yes	—
470	C₂×C₈	C₂⁴	1	2	yes	—
471	C₂×C₈	C₂⁴	1	2	yes	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	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	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
485	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
486	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
487	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
488	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
489	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
490	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
491	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
492	C₄⋊C₄	C₂⁴	1	2	yes	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	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	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
526	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
527	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
528	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
529	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	C₂×D₄	1	1	yes	characteristic
534	C₄²	C₂×D₄	1	1	yes	characteristic
535	C₄²	C₂⁴	1	1	yes	characteristic
536	C₄²	C₂⁴	1	1	yes	characteristic
537	C₂³	—	2	4	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	4	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	4	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	4	4	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	8	2	no	—
561	C₂³	—	8	2	no	—
562	C₂³	—	8	1	no	—
563	C₂³	—	8	1	no	—
564	C₂³	—	8	1	no	—
565	C₂³	—	8	1	no	—
566	C₂³	—	8	16	no	—
567	C₂³	C₂²×D₄	1	1	yes	characteristic
568	C₂³	C₂²×D₄	1	1	yes	characteristic
569	C₂³	C₂²×D₄	1	1	yes	characteristic
570	C₂³	C₂²×D₄	1	1	yes	characteristic
571	C₂³	C₂²×D₄	1	1	yes	characteristic
572	Q₈	—	2	2	no	—
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	2	no	—
576	Q₈	—	8	1	no	—
577	D₄	—	2	4	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	1	no	—
588	D₄	—	4	4	no	—
589	D₄	—	4	4	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	4	no	—
593	D₄	—	4	4	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	2	no	—
599	D₄	—	8	1	no	—
600	D₄	—	8	1	no	—
601	D₄	—	8	1	no	—
602	D₄	—	8	2	no	—
603	D₄	—	8	2	no	—
604	D₄	—	8	1	no	—
605	D₄	—	8	1	no	—
606	D₄	—	8	1	no	—
607	D₄	—	8	1	no	—
608	D₄	—	8	1	no	—
609	D₄	—	8	1	no	—
610	D₄	H(5,𝔽₂)	1	4	yes	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	4	no	—
632	C₂×C₄	—	4	4	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	8	2	no	—
637	C₂×C₄	—	8	2	no	—
638	C₂×C₄	—	8	1	no	—
639	C₂×C₄	—	8	1	no	—
640	C₂×C₄	—	8	1	no	—
641	C₂×C₄	—	8	1	no	—
642	C₂×C₄	—	8	1	no	—
643	C₂×C₄	—	8	1	no	—
644	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
649	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
650	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
651	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
652	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
653	C₂×C₄	C₂⁵	1	1	yes	characteristic
654	C₈	—	2	2	no	—
655	C₈	—	2	2	no	—
656	C₈	—	2	2	no	—
657	C₈	—	2	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	4	8	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	8	2	no	—
689	C₂²	—	8	8	no	—
690	C₂²	—	8	4	no	—
691	C₂²	—	8	8	no	—
692	C₂²	—	16	2	no	—
693	C₂²	—	16	2	no	—
694	C₂²	#575	1	2	yes	—
695	C₂²	#576	1	2	yes	—
696	C₂²	C₂³×D₄	1	1	yes	characteristic
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	1	no	—
705	C₄	—	2	1	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
714	C₂	—	2	2	no	—
715	C₂	—	2	2	no	—
716	C₂	—	4	1	no	—
717	C₂	—	4	1	no	—
718	C₂	—	4	1	no	—
719	C₂	—	4	4	no	—
720	C₂	—	8	2	no	—
721	C₂	—	8	1	no	—
722	C₂	—	8	1	no	—
723	C₂	—	8	1	no	—
724	C₂	#3484	1	1	yes	characteristic
725	C₂	C₂×#575	1	1	yes	characteristic
726	C₂	C₂×#576	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. #3519	C₂	semidirect
2. C₂×#546	C₂	semidirect
3. #3322	C₂	semidirect
4. #3319	C₂	semidirect
5. #3314	C₂	semidirect
6. #3297	C₂	semidirect
7. #3280	C₂	semidirect
8. #3273	C₂	semidirect
9. #3268	C₂	semidirect
10. #3264	C₂	semidirect
11. #3213	C₂	semidirect
12. #3211	C₂	semidirect
13. #3194	C₂	semidirect
14. #3193	C₂	semidirect
15. #3190	C₂	semidirect
16. #3186	C₂	semidirect
17. #3114	C₂	semidirect
18. #3100	C₂	semidirect
19. #3006	C₂	semidirect
20. #3003	C₂	semidirect
21. #3002	C₂	semidirect
22. C₂×#447	C₂	semidirect
23. #2974	C₂	semidirect
24. C₂²×#41	C₂²	semidirect
25. C₂³×D₄	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×#135	C₂²	semidirect
29. C₂²×D₈	C₂²	semidirect
30. #555	C₂²	semidirect
31. #554	C₂²	semidirect
33. #553	C₂²	semidirect
34. #553	C₂²	semidirect
35. #550	C₂²	semidirect
43. #546	C₂²	semidirect
44. #546	C₂²	semidirect
45. #546	C₂²	semidirect
46. #546	C₂²	semidirect
47. #546	C₂²	semidirect
49. D₄²	C₂²	semidirect
53. #532	C₂²	semidirect
54. #529	C₂²	semidirect
55. C₂×#124	C₂²	semidirect
57. #525	C₂²	semidirect
59. C₂×C₂²⋊Q₈	C₂²	semidirect
62. C₂×#121	C₂²	semidirect
63. C₂×#121	C₂²	semidirect
67. C₂×C₄×D₄	C₂²	semidirect
69. #496	C₂²	semidirect
70. #495	C₂²	semidirect
71. #489	C₂²	semidirect
72. #488	C₂²	semidirect
73. #485	C₂²	semidirect
74. #484	C₂²	semidirect
75. #483	C₂²	semidirect
76. #482	C₂²	semidirect
77. #480	C₂²	semidirect
78. #480	C₂²	semidirect
79. #480	C₂²	semidirect
80. #480	C₂²	semidirect
81. #478	C₂²	semidirect
82. #474	C₂²	semidirect
83. #469	C₂²	semidirect
84. #468	C₂²	semidirect
85. #468	C₂²	semidirect
86. #468	C₂²	semidirect
87. #467	C₂²	semidirect
88. #466	C₂²	semidirect
89. #466	C₂²	semidirect
90. #465	C₂²	semidirect
91. #464	C₂²	semidirect
92. #463	C₂²	semidirect
93. #463	C₂²	semidirect
94. #463	C₂²	semidirect
95. #463	C₂²	semidirect
96. #459	C₂²	semidirect
97. #452	C₂²	semidirect
98. #452	C₂²	semidirect
99. #451	C₂²	semidirect
100. #450	C₂²	semidirect
101. #450	C₂²	semidirect
102. #450	C₂²	semidirect
103. #450	C₂²	semidirect
104. #449	C₂²	semidirect
105. #449	C₂²	semidirect
106. #449	C₂²	semidirect
107. #449	C₂²	semidirect
108. #448	C₂²	semidirect
109. #448	C₂²	semidirect
110. #448	C₂²	semidirect
113. #447	C₂²	semidirect
114. #447	C₂²	semidirect
115. #447	C₂²	semidirect
116. #447	C₂²	semidirect
117. #447	C₂²	semidirect
118. #447	C₂²	semidirect
119. #447	C₂²	semidirect
120. #447	C₂²	semidirect
121. #442	C₂²	semidirect
122. #440	C₂²	semidirect
123. C₄×D₈	C₂²	semidirect
124. C₄×D₈	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
135. #407	C₂²	semidirect
136. #407	C₂²	semidirect
137. C₂×C₂²⋊C₈	C₂²	semidirect
138. C₂×C₂²⋊C₈	C₂²	semidirect
147. C₂×#41	C₂³	semidirect
164. C₂²×D₄	C₂³	semidirect
172. C₂×Q₁₆	C₂³	semidirect
175. C₂×SD₁₆	C₂³	semidirect
176. C₂×SD₁₆	C₂³	semidirect
177. C₂×SD₁₆	C₂³	semidirect
186. C₂×M₁₆	C₂³	semidirect
188. C₂²×C₈	C₂³	semidirect
189. C₄⋊Q₈	C₂³	semidirect
191. #127	C₂³	semidirect
196. #125	C₂³	semidirect
204. #124	C₂³	semidirect
224. C₂²⋊Q₈	C₂³	semidirect
252. #121	C₂³	semidirect
253. #121	C₂³	semidirect
254. #121	C₂³	semidirect
265. C₄×Q₈	C₂³	semidirect
288. C₄×D₄	C₂³	semidirect
289. C₄×D₄	C₂³	semidirect
290. C₄×D₄	C₂³	semidirect
294. #117	C₂³	semidirect
299. C₂×C₄⋊C₄	C₂³	semidirect
316. #107	C₂³	semidirect
317. #107	C₂³	semidirect
318. #107	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
335. #102	C₂³	semidirect
336. #102	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
#3519	2
C₂×#546	2
#3322	2
#3319	2
#3314	2
#3297	2
#3280	2
#3273	2
#3268	2
#3264	2
#3213	2
#3211	2
#3194	2
#3193	2
#3190	2
#3186	2
#3114	2
#3100	2
#3006	2
#3003	2
#3002	2
C₂×#447	2
#2974	2