Subgroups — #62606

Order 256.

833 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3565	C₂	1	1	yes	maximal, characteristic, complemented
2	#3554	C₂	1	1	yes	maximal, characteristic, complemented
3	#3374	C₂	1	1	yes	maximal, characteristic, complemented
4	#3372	C₂	1	1	yes	maximal, characteristic, complemented
5	#3371	C₂	1	1	yes	maximal, characteristic, complemented
6	#3370	C₂	1	1	yes	maximal, characteristic, complemented
7	#3321	C₂	1	1	yes	maximal, characteristic, complemented
8	#3320	C₂	1	1	yes	maximal, characteristic, complemented
9	#3317	C₂	1	1	yes	maximal, characteristic, complemented
10	#3315	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	#3309	C₂	1	1	yes	maximal, characteristic, complemented
14	#3307	C₂	1	1	yes	maximal, characteristic, complemented
15	#3303	C₂	1	1	yes	maximal, characteristic, complemented
16	#3302	C₂	1	1	yes	maximal, characteristic, complemented
17	#3301	C₂	1	1	yes	maximal, characteristic, complemented
18	#3300	C₂	1	1	yes	maximal, characteristic, complemented
19	#3244	C₂	1	1	yes	maximal, characteristic, complemented
20	#3243	C₂	1	1	yes	maximal, characteristic, complemented
21	#3231	C₂	1	1	yes	maximal, characteristic, complemented
22	#3225	C₂	1	1	yes	maximal, characteristic, complemented
23	#3225	C₂	1	1	yes	maximal, characteristic, complemented
24	#3212	C₂	1	1	yes	maximal, characteristic, complemented
25	#3181	C₂	1	1	yes	maximal, characteristic, complemented
26	#3175	C₂	1	1	yes	maximal, characteristic, complemented
27	#3173	C₂	1	1	yes	maximal, characteristic, complemented
28	#3137	C₂	1	1	yes	maximal, characteristic, complemented
29	#3137	C₂	1	1	yes	maximal, characteristic, complemented
30	#3135	C₂	1	1	yes	maximal, characteristic, complemented
31	#2968	C₂	1	1	yes	maximal, characteristic, complemented
32	#563	—	2	1	no	—
33	#562	—	2	1	no	—
34	#562	—	2	1	no	—
35	#562	—	2	1	no	—
36	#559	—	2	1	no	—
37	#559	C₂²	1	1	yes	characteristic
38	#557	C₂²	1	1	yes	characteristic
39	#557	C₂²	1	1	yes	characteristic
40	#556	—	2	1	no	—
41	#556	C₂²	1	1	yes	characteristic
42	#555	C₂²	1	1	yes	characteristic
43	#554	—	2	1	no	—
44	#554	C₂²	1	1	yes	characteristic
45	#553	C₂²	1	1	yes	characteristic
46	#553	C₂²	1	1	yes	characteristic
47	#552	—	2	1	no	—
48	#552	C₂²	1	1	yes	characteristic
49	#552	C₂²	1	1	yes	characteristic
50	#550	C₂²	1	1	yes	characteristic
51	D₄×Q₈	C₂²	1	1	yes	characteristic
52	#548	C₂²	1	1	yes	characteristic
53	#548	C₂²	1	1	yes	characteristic
54	#547	C₂²	1	1	yes	characteristic
55	#547	C₂²	1	1	yes	characteristic
56	#544	C₂²	1	1	yes	characteristic
57	#544	C₂²	1	1	yes	characteristic
58	#542	—	2	1	no	—
59	#542	—	2	1	no	—
60	#542	—	2	1	no	—
61	#542	C₂²	1	1	yes	characteristic
62	#542	C₂²	1	1	yes	characteristic
63	#542	C₂²	1	1	yes	characteristic
64	#542	C₂²	1	1	yes	characteristic
65	#541	—	2	1	no	—
66	#540	—	2	1	no	—
67	#539	—	2	1	no	—
68	#539	—	2	1	no	—
69	#539	—	2	1	no	—
70	#536	C₂²	1	1	yes	characteristic
71	#536	C₂²	1	1	yes	characteristic
72	#533	C₂²	1	1	yes	characteristic
73	#533	C₂²	1	1	yes	characteristic
74	#532	C₂²	1	1	yes	characteristic
75	#529	C₂²	1	1	yes	characteristic
76	#529	C₂²	1	1	yes	characteristic
77	#501	C₂²	1	1	yes	characteristic
78	#500	C₂²	1	1	yes	characteristic
79	#498	C₂²	1	1	yes	characteristic
80	#497	C₂²	1	1	yes	characteristic
81	#495	C₂²	1	1	yes	characteristic
82	#495	C₂²	1	1	yes	characteristic
83	#491	C₂²	1	1	yes	characteristic
84	#491	C₂²	1	1	yes	characteristic
85	#491	C₂²	1	1	yes	characteristic
86	#491	C₂²	1	1	yes	characteristic
87	#491	C₂²	1	1	yes	characteristic
88	#490	C₂²	1	1	yes	characteristic
89	#490	C₂²	1	1	yes	characteristic
90	#489	C₂²	1	1	yes	characteristic
91	#489	C₂²	1	1	yes	characteristic
92	#489	C₂²	1	1	yes	characteristic
93	#489	C₂²	1	1	yes	characteristic
94	#489	C₂²	1	1	yes	characteristic
95	#489	C₂²	1	1	yes	characteristic
96	#489	C₂²	1	1	yes	characteristic
97	#488	C₂²	1	1	yes	characteristic
98	#488	C₂²	1	1	yes	characteristic
99	#488	C₂²	1	1	yes	characteristic
100	#488	C₂²	1	1	yes	characteristic
101	#487	C₂²	1	1	yes	characteristic
102	#487	C₂²	1	1	yes	characteristic
103	#487	C₂²	1	1	yes	characteristic
104	#487	C₂²	1	1	yes	characteristic
105	#485	C₂²	1	1	yes	characteristic
106	#485	C₂²	1	1	yes	characteristic
107	#485	C₂²	1	1	yes	characteristic
108	#485	C₂²	1	1	yes	characteristic
109	#485	C₂²	1	1	yes	characteristic
110	#485	C₂²	1	1	yes	characteristic
111	#484	C₂²	1	1	yes	characteristic
112	#483	C₂²	1	1	yes	characteristic
113	#482	C₂²	1	1	yes	characteristic
114	#482	C₂²	1	1	yes	characteristic
115	#481	C₂²	1	1	yes	characteristic
116	#480	C₂²	1	1	yes	characteristic
117	#479	C₂²	1	1	yes	characteristic
118	#479	C₂²	1	1	yes	characteristic
119	#479	C₂²	1	1	yes	characteristic
120	#479	C₂²	1	1	yes	characteristic
121	#479	C₂²	1	1	yes	characteristic
122	#479	C₂²	1	1	yes	characteristic
123	#478	C₂²	1	1	yes	characteristic
124	#478	C₂²	1	1	yes	characteristic
125	#477	C₂²	1	1	yes	characteristic
126	#476	C₂²	1	1	yes	characteristic
127	#475	C₂²	1	1	yes	characteristic
128	#474	C₂²	1	1	yes	characteristic
129	#470	C₂²	1	1	yes	characteristic
130	#469	C₂²	1	1	yes	characteristic
131	#468	C₂²	1	1	yes	characteristic
132	#468	C₂²	1	1	yes	characteristic
133	#467	C₂²	1	1	yes	characteristic
134	#467	C₂²	1	1	yes	characteristic
135	#467	C₂²	1	1	yes	characteristic
136	#466	C₂²	1	1	yes	characteristic
137	#465	C₂²	1	1	yes	characteristic
138	#465	C₂²	1	1	yes	characteristic
139	#465	C₂²	1	1	yes	characteristic
140	#465	C₂²	1	1	yes	characteristic
141	#464	C₂²	1	1	yes	characteristic
142	#464	C₂²	1	1	yes	characteristic
143	#463	C₂²	1	1	yes	characteristic
144	#463	C₂²	1	1	yes	characteristic
145	#462	C₂²	1	1	yes	characteristic
146	#462	C₂²	1	1	yes	characteristic
147	#462	C₂²	1	1	yes	characteristic
148	#461	C₂²	1	1	yes	characteristic
149	#461	C₂²	1	1	yes	characteristic
150	#461	C₂²	1	1	yes	characteristic
151	#460	C₂²	1	1	yes	characteristic
152	#459	C₂²	1	1	yes	characteristic
153	#452	C₂²	1	1	yes	characteristic
154	#452	C₂²	1	1	yes	characteristic
155	#452	C₂²	1	1	yes	characteristic
156	#452	C₂²	1	1	yes	characteristic
157	#451	C₂²	1	1	yes	characteristic
158	#451	C₂²	1	1	yes	characteristic
159	#449	C₂²	1	1	yes	characteristic
160	#449	C₂²	1	1	yes	characteristic
161	#449	C₂²	1	1	yes	characteristic
162	#449	C₂²	1	1	yes	characteristic
163	#448	C₂²	1	1	yes	characteristic
164	#448	C₂²	1	1	yes	characteristic
165	#446	C₂²	1	1	yes	characteristic
166	#446	C₂²	1	1	yes	characteristic
167	#442	C₂²	1	1	yes	characteristic
168	#441	C₂²	1	1	yes	characteristic
169	#441	C₂²	1	1	yes	characteristic
170	#441	C₂²	1	1	yes	characteristic
171	#440	C₂²	1	1	yes	characteristic
172	#440	C₂²	1	1	yes	characteristic
173	#440	C₂²	1	1	yes	characteristic
174	#440	C₂²	1	1	yes	characteristic
175	C₄×Q₁₆	C₂²	1	1	yes	characteristic
176	C₄×SD₁₆	C₂²	1	1	yes	characteristic
177	C₄×SD₁₆	C₂²	1	1	yes	characteristic
178	C₄×D₈	C₂²	1	1	yes	characteristic
179	#435	C₂²	1	1	yes	characteristic
180	#435	C₂²	1	1	yes	characteristic
181	#435	C₂²	1	1	yes	characteristic
182	#435	C₂²	1	1	yes	characteristic
183	C₈×D₄	C₂²	1	1	yes	characteristic
184	C₈×D₄	C₂²	1	1	yes	characteristic
185	#433	C₂²	1	1	yes	characteristic
186	#433	C₂²	1	1	yes	characteristic
187	#431	C₂²	1	1	yes	characteristic
188	#419	C₂²	1	1	yes	characteristic
189	#419	C₂²	1	1	yes	characteristic
190	#417	C₂²	1	1	yes	characteristic
191	#417	C₂²	1	1	yes	characteristic
192	#416	C₂²	1	1	yes	characteristic
193	#416	C₂²	1	1	yes	characteristic
194	#416	C₂²	1	1	yes	characteristic
195	#416	C₂²	1	1	yes	characteristic
196	#416	C₂²	1	1	yes	characteristic
197	#416	C₂²	1	1	yes	characteristic
198	C₂×#103	C₂²	1	1	yes	characteristic
199	C₂×#103	C₂²	1	1	yes	characteristic
200	#405	C₂²	1	1	yes	characteristic
201	#405	C₂²	1	1	yes	characteristic
202	C₂×#97	C₂²	1	1	yes	characteristic
203	C₂×#41	C₂³	1	1	yes	characteristic
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×Q₈	C₂³	1	1	yes	characteristic
208	C₂²×Q₈	C₂³	1	1	yes	characteristic
209	C₂×Q₁₆	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆	C₂³	1	1	yes	characteristic
211	C₂×Q₁₆	C₂³	1	1	yes	characteristic
212	C₂×Q₁₆	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆	C₂³	1	1	yes	characteristic
215	C₂×SD₁₆	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×D₈	C₂³	1	1	yes	characteristic
220	C₂×D₈	C₂³	1	1	yes	characteristic
221	C₂×M₁₆	C₂³	1	1	yes	characteristic
222	C₂×M₁₆	C₂³	1	1	yes	characteristic
223	C₂²×C₈	C₂³	1	1	yes	characteristic
224	C₂²×C₈	C₂³	1	1	yes	characteristic
225	C₂²×C₈	C₂³	1	1	yes	characteristic
226	C₂²×C₈	C₂³	1	1	yes	characteristic
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	C₂³	1	1	yes	characteristic
232	C₄⋊Q₈	C₂³	1	1	yes	characteristic
233	C₄⋊Q₈	C₂³	1	1	yes	characteristic
234	C₄⋊Q₈	C₂³	1	1	yes	characteristic
235	C₄⋊Q₈	C₂³	1	1	yes	characteristic
236	C₄⋊Q₈	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	—	2	1	no	—
241	#127	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
254	#126	D₄	1	1	yes	characteristic
255	#125	—	2	1	no	—
256	#125	—	2	1	no	—
257	#125	—	2	1	no	—
258	#125	—	2	1	no	—
259	#125	—	2	1	no	—
260	#125	—	2	1	no	—
261	#125	—	2	1	no	—
262	#125	—	2	1	no	—
263	#125	—	2	1	no	—
264	#125	—	2	1	no	—
265	#125	D₄	1	1	yes	characteristic
266	#125	C₂³	1	1	yes	characteristic
267	#125	C₂³	1	1	yes	characteristic
268	#125	C₂³	1	1	yes	characteristic
269	#125	C₂³	1	1	yes	characteristic
270	#125	C₂³	1	1	yes	characteristic
271	#124	—	2	1	no	—
272	#124	—	2	1	no	—
273	#124	—	2	1	no	—
274	#124	—	2	1	no	—
275	#124	—	2	1	no	—
276	#124	—	2	1	no	—
277	#124	—	2	1	no	—
278	#124	—	2	1	no	—
279	#124	—	2	1	no	—
280	#124	—	2	1	no	—
281	#124	D₄	1	1	yes	characteristic
282	#124	C₂³	1	1	yes	characteristic
283	#124	C₂³	1	1	yes	characteristic
284	#124	C₂³	1	1	yes	characteristic
285	#124	C₂³	1	1	yes	characteristic
286	#124	C₂³	1	1	yes	characteristic
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	#123	—	2	1	no	—
300	#123	—	2	1	no	—
301	#123	—	2	1	no	—
302	#123	—	2	1	no	—
303	#123	—	2	1	no	—
304	#123	—	2	1	no	—
305	#123	—	2	1	no	—
306	#123	D₄	1	1	yes	characteristic
307	#123	D₄	1	1	yes	characteristic
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	—	2	1	no	—
310	C₂²⋊Q₈	—	2	1	no	—
311	C₂²⋊Q₈	—	2	1	no	—
312	C₂²⋊Q₈	—	2	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₂²⋊Q₈	—	2	1	no	—
316	C₂²⋊Q₈	—	2	1	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	2	1	no	—
325	C₂²⋊Q₈	—	2	1	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	D₄	1	1	yes	characteristic
331	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
332	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
333	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
334	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
335	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
336	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
337	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
338	#121	—	2	1	no	—
339	#121	—	2	1	no	—
340	#121	—	2	1	no	—
341	#121	—	2	1	no	—
342	#121	—	2	1	no	—
343	#121	—	2	1	no	—
344	#121	—	2	1	no	—
345	#121	—	2	1	no	—
346	#121	—	2	1	no	—
347	#121	—	2	1	no	—
348	#121	—	2	1	no	—
349	#121	D₄	1	1	yes	characteristic
350	#121	C₂³	1	1	yes	characteristic
351	#121	C₂³	1	1	yes	characteristic
352	#121	C₂³	1	1	yes	characteristic
353	#121	C₂³	1	1	yes	characteristic
354	#121	C₂³	1	1	yes	characteristic
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	C₂³	1	1	yes	characteristic
362	C₄×Q₈	C₂³	1	1	yes	characteristic
363	C₄×Q₈	C₂³	1	1	yes	characteristic
364	C₄×Q₈	C₂³	1	1	yes	characteristic
365	C₄×Q₈	C₂³	1	1	yes	characteristic
366	C₄×Q₈	C₂³	1	1	yes	characteristic
367	C₄×Q₈	C₂³	1	1	yes	characteristic
368	C₄×Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
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	C₄×D₄	C₂³	1	1	yes	characteristic
386	C₄×D₄	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
393	#117	C₂³	1	1	yes	characteristic
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	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
403	C₂×C₄²	C₂³	1	1	yes	characteristic
404	#107	C₂³	1	1	yes	characteristic
405	#107	C₂³	1	1	yes	characteristic
406	#107	C₂³	1	1	yes	characteristic
407	#107	C₂³	1	1	yes	characteristic
408	#107	C₂³	1	1	yes	characteristic
409	#107	C₂³	1	1	yes	characteristic
410	#106	C₂³	1	1	yes	characteristic
411	#106	C₂³	1	1	yes	characteristic
412	#106	C₂³	1	1	yes	characteristic
413	#106	C₂³	1	1	yes	characteristic
414	#106	C₂³	1	1	yes	characteristic
415	#106	C₂³	1	1	yes	characteristic
416	C₄⋊C₈	C₂³	1	1	yes	characteristic
417	C₄⋊C₈	C₂³	1	1	yes	characteristic
418	C₄⋊C₈	C₂³	1	1	yes	characteristic
419	C₄⋊C₈	C₂³	1	1	yes	characteristic
420	C₄⋊C₈	C₂³	1	1	yes	characteristic
421	C₄⋊C₈	C₂³	1	1	yes	characteristic
422	#103	C₂³	1	1	yes	characteristic
423	#103	C₂³	1	1	yes	characteristic
424	#103	C₂³	1	1	yes	characteristic
425	#103	C₂³	1	1	yes	characteristic
426	#103	C₂³	1	1	yes	characteristic
427	#103	C₂³	1	1	yes	characteristic
428	#103	C₂³	1	1	yes	characteristic
429	#103	C₂³	1	1	yes	characteristic
430	#103	C₂³	1	1	yes	characteristic
431	#103	C₂³	1	1	yes	characteristic
432	#103	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	#103	C₂³	1	1	yes	characteristic
446	#103	C₂³	1	1	yes	characteristic
447	#103	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	C₂²⋊C₈	C₂³	1	1	yes	characteristic
463	C₂²⋊C₈	C₂³	1	1	yes	characteristic
464	C₂²⋊C₈	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	#97	C₂³	1	1	yes	characteristic
469	#97	C₂³	1	1	yes	characteristic
470	#97	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	C₄×C₈	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	#41	—	4	1	no	—
479	#41	—	4	1	no	—
480	#41	—	4	1	no	—
481	#41	—	4	1	no	—
482	#41	—	4	1	no	—
483	#41	—	4	1	no	—
484	#41	—	4	1	no	—
485	#41	—	4	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	4	1	no	—
494	C₂×Q₈	—	4	1	no	—
495	C₂×Q₈	—	4	1	no	—
496	C₂×Q₈	—	4	1	no	—
497	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
498	C₂×Q₈	C₂⁴	1	1	yes	characteristic
499	C₂×Q₈	C₂⁴	1	1	yes	characteristic
500	C₂×Q₈	C₂⁴	1	1	yes	characteristic
501	C₂×Q₈	C₂⁴	1	1	yes	characteristic
502	C₂×Q₈	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
515	C₂×D₄	C₂×D₄	1	1	yes	characteristic
516	C₂×D₄	C₂×D₄	1	1	yes	characteristic
517	C₂×D₄	C₂⁴	1	1	yes	characteristic
518	C₂×D₄	C₂⁴	1	1	yes	characteristic
519	C₂×D₄	C₂⁴	1	1	yes	characteristic
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴	1	1	yes	characteristic
538	Q₁₆	—	4	1	no	—
539	Q₁₆	—	4	1	no	—
540	Q₁₆	—	4	1	no	—
541	Q₁₆	—	4	1	no	—
542	SD₁₆	—	4	1	no	—
543	SD₁₆	—	4	1	no	—
544	SD₁₆	—	4	1	no	—
545	SD₁₆	—	4	1	no	—
546	SD₁₆	—	4	1	no	—
547	SD₁₆	—	4	1	no	—
548	D₈	—	4	1	no	—
549	D₈	—	4	1	no	—
550	M₁₆	—	4	1	no	—
551	M₁₆	—	4	1	no	—
552	C₂×C₈	—	4	1	no	—
553	C₂×C₈	—	4	1	no	—
554	C₂×C₈	—	4	1	no	—
555	C₂×C₈	—	4	1	no	—
556	C₂×C₈	C₂⁴	1	1	yes	characteristic
557	C₂×C₈	C₂⁴	1	1	yes	characteristic
558	C₂×C₈	C₂⁴	1	1	yes	characteristic
559	C₂×C₈	C₂⁴	1	1	yes	characteristic
560	C₂×C₈	C₂⁴	1	1	yes	characteristic
561	C₂×C₈	C₂⁴	1	1	yes	characteristic
562	C₂×C₈	C₂⁴	1	1	yes	characteristic
563	C₂×C₈	C₂⁴	1	1	yes	characteristic
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
605	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
607	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
608	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
614	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
615	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
617	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
618	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
619	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
620	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
653	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
657	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
658	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
660	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
661	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
662	C₄²	—	2	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	2	1	no	—
666	C₄²	—	2	1	no	—
667	C₄²	—	2	1	no	—
668	C₄²	—	2	1	no	—
669	C₄²	—	2	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	2	1	no	—
673	C₄²	C₂×D₄	1	1	yes	characteristic
674	C₄²	C₂×D₄	1	1	yes	characteristic
675	C₄²	C₂⁴	1	1	yes	characteristic
676	C₄²	C₂⁴	1	1	yes	characteristic
677	C₄²	C₂⁴	1	1	yes	characteristic
678	C₄²	C₂⁴	1	1	yes	characteristic
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	C₂²×D₄	1	1	yes	characteristic
683	C₂³	C₂²×D₄	1	1	yes	characteristic
684	C₂³	C₂²×D₄	1	1	yes	characteristic
685	Q₈	—	2	1	no	—
686	Q₈	—	2	1	no	—
687	Q₈	—	2	1	no	—
688	Q₈	—	2	1	no	—
689	Q₈	—	2	1	no	—
690	Q₈	—	2	1	no	—
691	Q₈	—	2	1	no	—
692	Q₈	—	2	1	no	—
693	Q₈	—	2	1	no	—
694	Q₈	—	2	1	no	—
695	Q₈	—	4	1	no	—
696	Q₈	—	8	1	no	—
697	Q₈	—	8	1	no	—
698	Q₈	—	8	1	no	—
699	Q₈	—	8	1	no	—
700	Q₈	—	8	1	no	—
701	Q₈	—	8	1	no	—
702	Q₈	—	8	1	no	—
703	D₄	—	2	1	no	—
704	D₄	—	2	1	no	—
705	D₄	—	2	1	no	—
706	D₄	—	2	1	no	—
707	D₄	—	2	1	no	—
708	D₄	—	2	1	no	—
709	D₄	—	4	1	no	—
710	D₄	—	4	1	no	—
711	D₄	—	4	1	no	—
712	D₄	—	4	2	no	—
713	D₄	—	8	1	no	—
714	D₄	—	8	1	no	—
715	D₄	—	8	1	no	—
716	D₄	—	8	1	no	—
717	D₄	—	8	1	no	—
718	D₄	—	8	1	no	—
719	D₄	—	8	1	no	—
720	D₄	—	8	1	no	—
721	D₄	—	8	1	no	—
722	D₄	—	8	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	8	1	no	—
745	C₂×C₄	—	8	1	no	—
746	C₂×C₄	—	8	1	no	—
747	C₂×C₄	—	8	1	no	—
748	C₂×C₄	—	8	1	no	—
749	C₂×C₄	—	8	1	no	—
750	C₂×C₄	—	8	1	no	—
751	C₂×C₄	—	8	1	no	—
752	C₂×C₄	—	8	1	no	—
753	C₂×C₄	—	8	1	no	—
754	C₂×C₄	—	8	1	no	—
755	C₂×C₄	—	8	1	no	—
756	C₂×C₄	—	8	1	no	—
757	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
763	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
767	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
768	C₂×C₄	C₂⁵	1	1	yes	characteristic
769	C₈	—	2	1	no	—
770	C₈	—	2	1	no	—
771	C₈	—	2	1	no	—
772	C₈	—	2	1	no	—
773	C₈	—	2	1	no	—
774	C₈	—	2	1	no	—
775	C₈	—	2	1	no	—
776	C₈	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	C₂³×D₄	1	1	yes	characteristic
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	1	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	1	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	#585	1	1	yes	characteristic
821	C₄	#585	1	1	yes	characteristic
822	C₂	—	4	1	no	—
823	C₂	—	4	1	no	—
824	C₂	—	4	1	no	—
825	C₂	—	8	1	no	—
826	C₂	—	8	1	no	—
827	C₂	—	8	1	no	—
828	C₂	#3500	1	1	yes	characteristic
829	C₂	#3584	1	1	yes	characteristic
830	C₂	#3586	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. #3565	C₂	semidirect
2. #3554	C₂	semidirect
3. #3374	C₂	semidirect
4. #3372	C₂	semidirect
5. #3371	C₂	semidirect
6. #3370	C₂	semidirect
7. #3321	C₂	semidirect
8. #3320	C₂	semidirect
9. #3317	C₂	semidirect
10. #3315	C₂	semidirect
11. #3313	C₂	semidirect
12. #3312	C₂	semidirect
13. #3309	C₂	semidirect
14. #3307	C₂	semidirect
15. #3303	C₂	semidirect
16. #3302	C₂	semidirect
17. #3301	C₂	semidirect
18. #3300	C₂	semidirect
19. #3244	C₂	semidirect
20. #3243	C₂	semidirect
21. #3231	C₂	semidirect
22. #3225	C₂	semidirect
23. #3225	C₂	semidirect
24. #3212	C₂	semidirect
25. #3181	C₂	semidirect
26. #3175	C₂	semidirect
27. #3173	C₂	semidirect
28. #3137	C₂	semidirect
29. #3137	C₂	semidirect
30. #3135	C₂	semidirect
31. #2968	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3565	2
#3554	2
#3374	2
#3372	2
#3371	2
#3370	2
#3321	2
#3320	2
#3317	2
#3315	2
#3313	2
#3312	2
#3309	2
#3307	2
#3303	2
#3302	2
#3301	2
#3300	2
#3244	2
#3243	2
#3231	2
#3225	2
#3212	2
#3181	2
#3175	2
#3173	2
#3137	2
#3135	2
#2968	2