Subgroups — #62835

Order 256.

3574 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3561	C₂	1	4	yes	maximal, complemented
2	#3559	C₂	1	4	yes	maximal, complemented
3	#3554	C₂	1	4	yes	maximal, complemented
4	#3550	C₂	1	2	yes	maximal, complemented
5	#3548	C₂	1	2	yes	maximal, complemented
6	#3547	C₂	1	4	yes	maximal, complemented
7	#3536	C₂	1	4	yes	maximal, complemented
8	#3522	C₂	1	4	yes	maximal, complemented
9	#3520	C₂	1	4	yes	maximal, complemented
10	#3511	C₂	1	2	yes	maximal, complemented
11	#3511	C₂	1	4	yes	maximal, complemented
12	#3508	C₂	1	2	yes	maximal, complemented
13	#3507	C₂	1	2	yes	maximal, complemented
14	#3506	C₂	1	2	yes	maximal, complemented
15	#3503	C₂	1	2	yes	maximal, complemented
16	#3501	C₂	1	2	yes	maximal, complemented
17	#3499	C₂	1	2	yes	maximal, complemented
18	#3497	C₂	1	2	yes	maximal, complemented
19	#3494	C₂	1	4	yes	maximal, complemented
20	#3489	C₂	1	4	yes	maximal, complemented
21	#3444	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#533	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#532	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴	C₂²	1	4	yes	complemented
25	C₂²×#41	C₂²	1	2	yes	—
26	#563	C₂²	1	8	yes	complemented
27	#562	C₂²	1	16	yes	complemented
28	#562	C₂²	1	8	yes	complemented
29	#559	C₂²	1	8	yes	complemented
30	#559	C₂²	1	4	yes	complemented
31	#559	C₂²	1	4	yes	complemented
32	Q₈²	C₂²	1	4	yes	complemented
33	#557	C₂²	1	4	yes	complemented
34	#556	C₂²	1	4	yes	complemented
35	#556	C₂²	1	8	yes	complemented
36	#556	C₂²	1	4	yes	complemented
37	#555	C₂²	1	8	yes	complemented
38	#555	C₂²	1	4	yes	complemented
39	#554	C₂²	1	8	yes	—
40	#554	C₂²	1	4	yes	complemented
41	#554	C₂²	1	4	yes	complemented
42	#554	C₂²	1	8	yes	complemented
43	#554	C₂²	1	8	yes	complemented
44	#554	C₂²	1	4	yes	complemented
45	#553	C₂²	1	8	yes	complemented
46	#553	C₂²	1	8	yes	complemented
47	#553	C₂²	1	8	yes	complemented
48	#552	C₂²	1	8	yes	complemented
49	#551	C₂²	1	16	yes	—
50	#550	C₂²	1	4	yes	complemented
51	#550	C₂²	1	4	yes	complemented
52	#550	C₂²	1	4	yes	complemented
53	D₄×Q₈	C₂²	1	8	yes	—
54	D₄×Q₈	C₂²	1	4	yes	complemented
55	D₄×Q₈	C₂²	1	4	yes	complemented
56	D₄×Q₈	C₂²	1	4	yes	complemented
57	D₄×Q₈	C₂²	1	4	yes	complemented
58	#548	C₂²	1	8	yes	complemented
59	#548	C₂²	1	8	yes	complemented
60	#548	C₂²	1	8	yes	complemented
61	#548	C₂²	1	8	yes	complemented
62	#547	C₂²	1	8	yes	complemented
63	#547	C₂²	1	16	yes	complemented
64	#547	C₂²	1	8	yes	complemented
65	#547	C₂²	1	4	yes	complemented
66	#547	C₂²	1	4	yes	complemented
67	#547	C₂²	1	8	yes	complemented
68	#547	C₂²	1	4	yes	complemented
69	#546	C₂²	1	16	yes	—
70	#546	C₂²	1	8	yes	—
71	#546	C₂²	1	8	yes	—
72	#544	C₂²	1	4	yes	—
73	#544	C₂²	1	8	yes	complemented
74	#543	C₂²	1	8	yes	—
75	#542	C₂²	1	8	yes	complemented
76	#542	C₂²	1	8	yes	complemented
77	#542	C₂²	1	8	yes	complemented
78	#542	C₂²	1	8	yes	complemented
79	#542	C₂²	1	16	yes	complemented
80	#540	C₂²	1	8	yes	complemented
81	#540	C₂²	1	8	yes	complemented
82	#539	C₂²	1	8	yes	complemented
83	#539	C₂²	1	16	yes	complemented
84	#538	C₂²	1	8	yes	—
85	#537	C₂²	1	4	yes	complemented
86	#537	C₂²	1	8	yes	complemented
87	#537	C₂²	1	8	yes	complemented
88	#537	C₂²	1	8	yes	complemented
89	#536	C₂²	1	4	yes	complemented
90	#536	C₂²	1	8	yes	complemented
91	#536	C₂²	1	8	yes	complemented
92	#535	C₂²	1	4	yes	—
93	#533	C₂²	1	2	yes	—
94	#533	C₂²	1	2	yes	—
95	#533	C₂²	1	2	yes	—
96	#533	C₂²	1	2	yes	—
97	#533	C₂²	1	1	yes	characteristic
98	#533	C₂²	1	2	yes	complemented
99	#533	C₂²	1	2	yes	complemented
100	#533	C₂²	1	2	yes	complemented
101	#533	C₂²	1	2	yes	complemented
102	#533	C₂²	1	1	yes	characteristic, complemented
103	#533	C₂²	1	1	yes	characteristic, complemented
104	#533	C₂²	1	4	yes	complemented
105	#532	C₂²	1	2	yes	—
106	#532	C₂²	1	2	yes	—
107	#532	C₂²	1	2	yes	—
108	#532	C₂²	1	2	yes	—
109	#532	C₂²	1	2	yes	—
110	#532	C₂²	1	2	yes	—
111	#532	C₂²	1	2	yes	—
112	#532	C₂²	1	2	yes	—
113	#532	C₂²	1	1	yes	characteristic
114	#532	C₂²	1	1	yes	characteristic, complemented
115	#532	C₂²	1	1	yes	characteristic, complemented
116	#532	C₂²	1	8	yes	complemented
117	#532	C₂²	1	4	yes	complemented
118	#532	C₂²	1	4	yes	complemented
119	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
120	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊Q₈	C₂²	1	4	yes	complemented
123	C₂×#127	C₂²	1	1	yes	characteristic
124	#529	C₂²	1	2	yes	—
125	#529	C₂²	1	2	yes	—
126	#529	C₂²	1	2	yes	complemented
127	#529	C₂²	1	2	yes	complemented
128	#529	C₂²	1	2	yes	complemented
129	#529	C₂²	1	2	yes	complemented
130	#529	C₂²	1	8	yes	complemented
131	C₂×#125	C₂²	1	2	yes	complemented
132	C₂×#124	C₂²	1	2	yes	—
133	#525	C₂²	1	2	yes	—
134	#525	C₂²	1	2	yes	—
135	#525	C₂²	1	2	yes	—
136	#525	C₂²	1	8	yes	—
137	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
138	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
139	C₂×C₂²⋊Q₈	C₂²	1	8	yes	—
140	C₂×#121	C₂²	1	2	yes	—
141	C₂×#121	C₂²	1	2	yes	—
142	#520	C₂²	1	4	yes	—
143	#520	C₂²	1	4	yes	complemented
144	#520	C₂²	1	8	yes	complemented
145	#518	C₂²	1	4	yes	—
146	C₄×#41	C₂²	1	2	yes	—
147	C₄×#41	C₂²	1	2	yes	complemented
148	C₄×#41	C₂²	1	2	yes	complemented
149	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
150	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
151	C₂×C₄×D₄	C₂²	1	2	yes	—
152	C₂×C₄×D₄	C₂²	1	2	yes	—
153	C₂×#117	C₂²	1	2	yes	—
154	C₂²×C₄²	C₂²	1	1	yes	characteristic
155	2₋¹⁺⁴	—	4	16	no	—
156	C₂×#41	—	4	8	no	—
157	C₂×#41	C₂³	1	2	yes	—
158	C₂×#41	C₂³	1	2	yes	—
159	C₂×#41	C₂³	1	4	yes	—
160	C₂×#41	C₂³	1	2	yes	—
161	C₂×#41	C₂³	1	8	yes	—
162	C₂×#41	C₂³	1	8	yes	—
163	C₂×#41	C₂³	1	4	yes	—
164	C₂×#41	C₂³	1	4	yes	—
165	C₂×#41	C₂³	1	4	yes	—
166	C₂×#41	C₂³	1	8	yes	—
167	C₂×#41	C₂³	1	16	yes	—
168	C₂²×Q₈	C₂³	1	2	yes	—
169	C₂²×Q₈	C₂³	1	2	yes	—
170	C₂²×Q₈	C₂³	1	8	yes	—
171	C₂²×Q₈	C₂³	1	2	yes	—
172	C₂²×Q₈	C₂³	1	8	yes	—
173	C₂²×D₄	C₂³	1	2	yes	—
174	C₂²×D₄	C₂³	1	2	yes	—
175	C₂²×D₄	C₂³	1	4	yes	—
176	C₂²×D₄	C₂³	1	2	yes	—
177	C₂³×C₄	C₂³	1	1	yes	characteristic
178	C₂³×C₄	C₂³	1	1	yes	characteristic
179	C₂³×C₄	C₂³	1	4	yes	—
180	C₂³×C₄	C₂³	1	1	yes	characteristic
181	C₄⋊Q₈	C₂³	1	2	yes	—
182	C₄⋊Q₈	C₂³	1	2	yes	—
183	C₄⋊Q₈	C₂³	1	2	yes	—
184	C₄⋊Q₈	C₂³	1	2	yes	—
185	C₄⋊Q₈	C₂³	1	2	yes	—
186	C₄⋊Q₈	C₂³	1	2	yes	—
187	C₄⋊Q₈	C₂³	1	2	yes	—
188	C₄⋊Q₈	C₂³	1	2	yes	—
189	C₄⋊Q₈	C₂³	1	2	yes	—
190	C₄⋊Q₈	C₂³	1	2	yes	—
191	C₄⋊Q₈	C₂³	1	2	yes	—
192	C₄⋊Q₈	C₂³	1	2	yes	—
193	C₄⋊Q₈	C₂³	1	8	yes	—
194	C₄⋊Q₈	C₂³	1	8	yes	—
195	C₄⋊Q₈	C₂³	1	8	yes	—
196	C₄⋊Q₈	C₂³	1	1	yes	characteristic
197	C₄⋊Q₈	C₂³	1	1	yes	characteristic
198	C₄⋊Q₈	C₂³	1	1	yes	characteristic
199	C₄⋊Q₈	C₂³	1	8	yes	—
200	C₄⋊Q₈	C₂³	1	16	yes	—
201	#127	C₂³	1	2	yes	—
202	#127	C₂³	1	2	yes	—
203	#127	C₂³	1	2	yes	—
204	#127	C₂³	1	2	yes	—
205	#127	C₂³	1	1	yes	characteristic
206	#127	C₂³	1	8	yes	—
207	#126	C₂³	1	4	yes	—
208	#126	C₂³	1	4	yes	—
209	#126	C₂³	1	16	yes	—
210	#126	C₂³	1	16	yes	—
211	#126	C₂³	1	16	yes	—
212	#125	C₂³	1	4	yes	—
213	#125	C₂³	1	4	yes	—
214	#125	C₂³	1	4	yes	—
215	#125	C₂³	1	4	yes	—
216	#125	C₂³	1	2	yes	—
217	#125	C₂³	1	2	yes	—
218	#125	C₂³	1	2	yes	—
219	#125	C₂³	1	8	yes	—
220	#125	C₂³	1	8	yes	—
221	#125	C₂³	1	16	yes	—
222	#124	C₂³	1	4	yes	—
223	#124	C₂³	1	4	yes	—
224	#124	C₂³	1	4	yes	—
225	#124	C₂³	1	4	yes	—
226	#124	C₂³	1	2	yes	—
227	#124	C₂³	1	2	yes	—
228	#124	C₂³	1	2	yes	—
229	#124	C₂³	1	8	yes	—
230	#124	C₂³	1	8	yes	—
231	#124	C₂³	1	8	yes	—
232	#124	C₂³	1	16	yes	—
233	#124	C₂³	1	16	yes	—
234	#124	C₂³	1	16	yes	—
235	#123	C₂³	1	4	yes	—
236	#123	C₂³	1	4	yes	—
237	#123	C₂³	1	4	yes	—
238	#123	C₂³	1	16	yes	—
239	#123	C₂³	1	16	yes	—
240	#123	C₂³	1	16	yes	—
241	#123	C₂³	1	16	yes	—
242	#123	C₂³	1	16	yes	—
243	#123	C₂³	1	16	yes	—
244	#123	C₂³	1	16	yes	—
245	#123	C₂³	1	16	yes	—
246	C₂²⋊Q₈	C₂³	1	2	yes	—
247	C₂²⋊Q₈	C₂³	1	4	yes	—
248	C₂²⋊Q₈	C₂³	1	4	yes	—
249	C₂²⋊Q₈	C₂³	1	4	yes	—
250	C₂²⋊Q₈	C₂³	1	4	yes	—
251	C₂²⋊Q₈	C₂³	1	4	yes	—
252	C₂²⋊Q₈	C₂³	1	4	yes	—
253	C₂²⋊Q₈	C₂³	1	4	yes	—
254	C₂²⋊Q₈	C₂³	1	4	yes	—
255	C₂²⋊Q₈	C₂³	1	8	yes	—
256	C₂²⋊Q₈	C₂³	1	8	yes	—
257	C₂²⋊Q₈	C₂³	1	16	yes	—
258	C₂²⋊Q₈	C₂³	1	16	yes	—
259	C₂²⋊Q₈	C₂³	1	2	yes	—
260	C₂²⋊Q₈	C₂³	1	2	yes	—
261	C₂²⋊Q₈	C₂³	1	2	yes	—
262	C₂²⋊Q₈	C₂³	1	2	yes	—
263	C₂²⋊Q₈	C₂³	1	2	yes	—
264	C₂²⋊Q₈	C₂³	1	8	yes	—
265	C₂²⋊Q₈	C₂³	1	8	yes	—
266	C₂²⋊Q₈	C₂³	1	8	yes	—
267	C₂²⋊Q₈	C₂³	1	16	yes	—
268	C₂²⋊Q₈	C₂³	1	16	yes	—
269	C₂²⋊Q₈	C₂³	1	16	yes	—
270	C₂²⋊Q₈	C₂³	1	16	yes	—
271	C₂²⋊Q₈	C₂³	1	16	yes	—
272	C₂²⋊Q₈	C₂³	1	16	yes	—
273	C₂²⋊Q₈	C₂³	1	16	yes	—
274	#121	C₂³	1	4	yes	—
275	#121	C₂³	1	4	yes	—
276	#121	C₂³	1	4	yes	—
277	#121	C₂³	1	4	yes	—
278	#121	C₂³	1	4	yes	—
279	#121	C₂³	1	4	yes	—
280	#121	C₂³	1	4	yes	—
281	#121	C₂³	1	4	yes	—
282	#121	C₂³	1	2	yes	—
283	#121	C₂³	1	2	yes	—
284	#121	C₂³	1	2	yes	—
285	#121	C₂³	1	2	yes	—
286	#121	C₂³	1	2	yes	—
287	#121	C₂³	1	2	yes	—
288	#121	C₂³	1	8	yes	—
289	#121	C₂³	1	8	yes	—
290	#121	C₂³	1	8	yes	—
291	#121	C₂³	1	16	yes	—
292	#121	C₂³	1	8	yes	—
293	#121	C₂³	1	8	yes	—
294	#121	C₂³	1	16	yes	—
295	#121	C₂³	1	16	yes	—
296	#121	C₂³	1	16	yes	—
297	#121	C₂³	1	16	yes	—
298	#121	C₂³	1	16	yes	—
299	#120	C₂³	1	4	yes	—
300	#120	C₂³	1	16	yes	—
301	C₄×Q₈	C₂³	1	4	yes	—
302	C₄×Q₈	C₂³	1	4	yes	—
303	C₄×Q₈	C₂³	1	4	yes	—
304	C₄×Q₈	C₂³	1	4	yes	—
305	C₄×Q₈	C₂³	1	4	yes	—
306	C₄×Q₈	C₂³	1	4	yes	—
307	C₄×Q₈	C₂³	1	4	yes	—
308	C₄×Q₈	C₂³	1	4	yes	—
309	C₄×Q₈	C₂³	1	2	yes	—
310	C₄×Q₈	C₂³	1	2	yes	—
311	C₄×Q₈	C₂³	1	2	yes	—
312	C₄×Q₈	C₂³	1	2	yes	—
313	C₄×Q₈	C₂³	1	2	yes	—
314	C₄×Q₈	C₂³	1	2	yes	—
315	C₄×Q₈	C₂³	1	8	yes	—
316	C₄×Q₈	C₂³	1	8	yes	—
317	C₄×Q₈	C₂³	1	8	yes	—
318	C₄×D₄	C₂³	1	4	yes	—
319	C₄×D₄	C₂³	1	4	yes	—
320	C₄×D₄	C₂³	1	4	yes	—
321	C₄×D₄	C₂³	1	4	yes	—
322	C₄×D₄	C₂³	1	4	yes	—
323	C₄×D₄	C₂³	1	4	yes	—
324	C₄×D₄	C₂³	1	4	yes	—
325	C₄×D₄	C₂³	1	4	yes	—
326	C₄×D₄	C₂³	1	4	yes	—
327	C₄×D₄	C₂³	1	4	yes	—
328	C₄×D₄	C₂³	1	2	yes	—
329	C₄×D₄	C₂³	1	2	yes	—
330	C₄×D₄	C₂³	1	4	yes	—
331	C₄×D₄	C₂³	1	4	yes	—
332	C₄×D₄	C₂³	1	4	yes	—
333	C₄×D₄	C₂³	1	4	yes	—
334	C₄×D₄	C₂³	1	2	yes	—
335	C₄×D₄	C₂³	1	2	yes	—
336	C₄×D₄	C₂³	1	2	yes	—
337	C₄×D₄	C₂³	1	2	yes	—
338	C₄×D₄	C₂³	1	8	yes	—
339	C₄×D₄	C₂³	1	8	yes	—
340	C₄×D₄	C₂³	1	8	yes	—
341	C₄×D₄	C₂³	1	8	yes	—
342	C₄×D₄	C₂³	1	16	yes	—
343	C₄×D₄	C₂³	1	8	yes	—
344	C₄×D₄	C₂³	1	16	yes	—
345	C₄×D₄	C₂³	1	16	yes	—
346	C₄×D₄	C₂³	1	8	yes	—
347	C₄×D₄	C₂³	1	8	yes	—
348	C₄×D₄	C₂³	1	16	yes	—
349	#117	C₂³	1	4	yes	—
350	#117	C₂³	1	4	yes	—
351	#117	C₂³	1	4	yes	—
352	#117	C₂³	1	4	yes	—
353	#117	C₂³	1	2	yes	—
354	#117	C₂³	1	4	yes	—
355	#117	C₂³	1	2	yes	—
356	#117	C₂³	1	4	yes	—
357	#117	C₂³	1	2	yes	—
358	#117	C₂³	1	4	yes	—
359	#117	C₂³	1	8	yes	—
360	#117	C₂³	1	8	yes	—
361	#117	C₂³	1	16	yes	—
362	C₂×C₄⋊C₄	C₂³	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³	1	8	yes	—
371	C₂×C₄⋊C₄	C₂³	1	8	yes	—
372	C₂×C₄⋊C₄	C₂³	1	16	yes	—
373	C₂×C₄⋊C₄	C₂³	1	8	yes	—
374	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
376	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
378	C₂×C₄²	C₂³	1	4	yes	—
379	C₂×C₄²	C₂³	1	1	yes	characteristic
380	C₂×C₄²	C₂³	1	1	yes	characteristic
381	C₂×C₄²	C₂³	1	1	yes	characteristic
382	C₂×C₄²	C₂³	1	1	yes	characteristic
383	C₂×C₄²	C₂³	1	1	yes	characteristic
384	C₂×C₄²	C₂³	1	4	yes	—
385	C₂×C₄²	C₂³	1	1	yes	characteristic
386	C₂×C₄²	C₂³	1	1	yes	characteristic
387	C₂×C₄²	C₂³	1	1	yes	characteristic
388	C₂×C₄²	C₂³	1	1	yes	characteristic
389	C₂×C₄²	C₂³	1	1	yes	characteristic
390	C₂×C₄²	C₂³	1	1	yes	characteristic
391	C₂×C₄²	C₂³	1	1	yes	characteristic
392	C₂⁴	C₂⁴	1	1	yes	characteristic
393	C₂⁴	C₂⁴	1	4	yes	—
394	#41	—	2	16	no	—
395	#41	—	2	8	no	—
396	#41	—	2	8	no	—
397	#41	—	4	8	no	—
398	#41	—	4	4	no	—
399	#41	—	4	8	no	—
400	#41	—	4	32	no	—
401	#41	—	4	8	no	—
402	#41	—	4	16	no	—
403	#41	—	4	16	no	—
404	#41	—	4	16	no	—
405	C₂×Q₈	—	2	8	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	—	4	16	no	—
409	C₂×Q₈	—	4	16	no	—
410	C₂×Q₈	C₂⁴	1	2	yes	—
411	C₂×Q₈	C₂⁴	1	4	yes	—
412	C₂×Q₈	C₂⁴	1	2	yes	—
413	C₂×Q₈	C₂⁴	1	4	yes	—
414	C₂×Q₈	C₂⁴	1	4	yes	—
415	C₂×Q₈	C₂⁴	1	4	yes	—
416	C₂×Q₈	C₂⁴	1	2	yes	—
417	C₂×Q₈	C₂⁴	1	4	yes	—
418	C₂×Q₈	C₂⁴	1	16	yes	—
419	C₂×Q₈	C₂⁴	1	4	yes	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	4	4	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	—	4	8	no	—
424	C₂×D₄	C₂⁴	1	4	yes	—
425	C₂×D₄	C₂⁴	1	4	yes	—
426	C₂×D₄	C₂⁴	1	4	yes	—
427	C₂×D₄	C₂⁴	1	2	yes	—
428	C₂×D₄	C₂⁴	1	4	yes	—
429	C₂×D₄	C₂⁴	1	4	yes	—
430	C₂×D₄	C₂⁴	1	8	yes	—
431	C₂×D₄	C₂⁴	1	2	yes	—
432	C₂×D₄	C₂⁴	1	4	yes	—
433	C₂×D₄	C₂⁴	1	4	yes	—
434	C₂×D₄	C₂⁴	1	16	yes	—
435	C₂×D₄	C₂⁴	1	2	yes	—
436	C₂×D₄	C₂⁴	1	4	yes	—
437	C₂×D₄	C₂⁴	1	16	yes	—
438	C₂×D₄	C₂⁴	1	8	yes	—
439	C₂×D₄	C₂⁴	1	4	yes	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	8	no	—
444	C₂²×C₄	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴	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	C₂²×C₄	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴	1	4	yes	—
458	C₂²×C₄	C₂⁴	1	4	yes	—
459	C₂²×C₄	C₂⁴	1	4	yes	—
460	C₂²×C₄	C₂⁴	1	4	yes	—
461	C₂²×C₄	C₂⁴	1	8	yes	—
462	C₂²×C₄	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴	1	4	yes	—
466	C₂²×C₄	C₂⁴	1	4	yes	—
467	C₂²×C₄	C₂⁴	1	16	yes	—
468	C₂²×C₄	C₂⁴	1	16	yes	—
469	C₂²×C₄	C₂⁴	1	8	yes	—
470	C₂²×C₄	C₂⁴	1	16	yes	—
471	C₂²×C₄	C₂⁴	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴	1	1	yes	characteristic
473	C₄⋊C₄	C₂⁴	1	2	yes	—
474	C₄⋊C₄	C₂⁴	1	4	yes	—
475	C₄⋊C₄	C₂⁴	1	4	yes	—
476	C₄⋊C₄	C₂⁴	1	4	yes	—
477	C₄⋊C₄	C₂⁴	1	4	yes	—
478	C₄⋊C₄	C₂⁴	1	4	yes	—
479	C₄⋊C₄	C₂⁴	1	4	yes	—
480	C₄⋊C₄	C₂⁴	1	8	yes	—
481	C₄⋊C₄	C₂⁴	1	16	yes	—
482	C₄⋊C₄	C₂⁴	1	4	yes	—
483	C₄⋊C₄	C₂⁴	1	4	yes	—
484	C₄⋊C₄	C₂⁴	1	4	yes	—
485	C₄⋊C₄	C₂⁴	1	4	yes	—
486	C₄⋊C₄	C₂⁴	1	4	yes	—
487	C₄⋊C₄	C₂⁴	1	4	yes	—
488	C₄⋊C₄	C₂⁴	1	16	yes	—
489	C₄⋊C₄	C₂⁴	1	16	yes	—
490	C₄⋊C₄	C₂⁴	1	16	yes	—
491	C₄⋊C₄	C₂⁴	1	8	yes	—
492	C₄⋊C₄	C₂⁴	1	8	yes	—
493	C₄⋊C₄	C₂⁴	1	8	yes	—
494	C₄⋊C₄	C₂⁴	1	4	yes	—
495	C₄⋊C₄	C₂⁴	1	2	yes	—
496	C₄⋊C₄	C₂⁴	1	4	yes	—
497	C₄⋊C₄	C₂⁴	1	2	yes	—
498	C₄⋊C₄	C₂⁴	1	2	yes	—
499	C₄⋊C₄	C₂⁴	1	2	yes	—
500	C₄⋊C₄	C₂⁴	1	2	yes	—
501	C₄⋊C₄	C₂⁴	1	4	yes	—
502	C₄⋊C₄	C₂⁴	1	4	yes	—
503	C₄⋊C₄	C₂⁴	1	4	yes	—
504	C₄⋊C₄	C₂⁴	1	4	yes	—
505	C₂²⋊C₄	C₂⁴	1	4	yes	—
506	C₂²⋊C₄	C₂⁴	1	8	yes	—
507	C₂²⋊C₄	C₂⁴	1	8	yes	—
508	C₂²⋊C₄	C₂⁴	1	8	yes	—
509	C₂²⋊C₄	C₂⁴	1	8	yes	—
510	C₂²⋊C₄	C₂⁴	1	16	yes	—
511	C₂²⋊C₄	C₂⁴	1	16	yes	—
512	C₂²⋊C₄	C₂⁴	1	8	yes	—
513	C₂²⋊C₄	C₂⁴	1	8	yes	—
514	C₂²⋊C₄	C₂⁴	1	4	yes	—
515	C₂²⋊C₄	C₂⁴	1	4	yes	—
516	C₂²⋊C₄	C₂⁴	1	4	yes	—
517	C₂²⋊C₄	C₂⁴	1	16	yes	—
518	C₂²⋊C₄	C₂⁴	1	16	yes	—
519	C₂²⋊C₄	C₂⁴	1	4	yes	—
520	C₂²⋊C₄	C₂⁴	1	4	yes	—
521	C₂²⋊C₄	C₂⁴	1	4	yes	—
522	C₂²⋊C₄	C₂⁴	1	16	yes	—
523	C₂²⋊C₄	C₂⁴	1	4	yes	—
524	C₂²⋊C₄	C₂⁴	1	4	yes	—
525	C₄²	C₂⁴	1	1	yes	characteristic
526	C₄²	C₂⁴	1	1	yes	characteristic
527	C₄²	C₂⁴	1	1	yes	characteristic
528	C₄²	C₂⁴	1	1	yes	characteristic
529	C₄²	C₂⁴	1	1	yes	characteristic
530	C₄²	C₂⁴	1	1	yes	characteristic
531	C₄²	C₂⁴	1	1	yes	characteristic
532	C₄²	C₂⁴	1	1	yes	characteristic
533	C₄²	C₂⁴	1	1	yes	characteristic
534	C₄²	C₂⁴	1	1	yes	characteristic
535	C₄²	C₂⁴	1	1	yes	characteristic
536	C₄²	C₂⁴	1	1	yes	characteristic
537	C₄²	C₂⁴	1	1	yes	characteristic
538	C₄²	C₂⁴	1	1	yes	characteristic
539	C₄²	C₂⁴	1	1	yes	characteristic
540	C₄²	C₂⁴	1	1	yes	characteristic
541	C₄²	C₂⁴	1	8	yes	—
542	C₄²	C₂⁴	1	4	yes	—
543	C₄²	C₂⁴	1	4	yes	—
544	C₄²	C₂⁴	1	4	yes	—
545	C₄²	C₂⁴	1	8	yes	—
546	C₄²	C₂⁴	1	16	yes	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	8	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	4	no	—
552	C₂³	—	4	4	no	—
553	C₂³	C₂⁵	1	1	yes	characteristic
554	C₂³	C₂⁵	1	8	yes	—
555	C₂³	C₂⁵	1	4	yes	—
556	C₂³	C₂⁵	1	1	yes	characteristic
557	C₂³	C₂⁵	1	1	yes	characteristic
558	Q₈	—	2	8	no	—
559	Q₈	—	2	8	no	—
560	Q₈	—	2	4	no	—
561	Q₈	—	2	8	no	—
562	Q₈	—	2	4	no	—
563	Q₈	—	2	8	no	—
564	Q₈	—	4	16	no	—
565	Q₈	—	4	4	no	—
566	Q₈	—	4	4	no	—
567	Q₈	—	4	2	no	—
568	D₄	—	2	16	no	—
569	D₄	—	2	8	no	—
570	D₄	—	2	8	no	—
571	D₄	—	2	8	no	—
572	D₄	—	2	4	no	—
573	D₄	—	2	8	no	—
574	D₄	—	2	8	no	—
575	D₄	—	2	4	no	—
576	D₄	—	2	8	no	—
577	D₄	—	4	4	no	—
578	D₄	—	4	4	no	—
579	D₄	—	4	8	no	—
580	D₄	—	4	4	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	16	no	—
583	D₄	—	4	16	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	8	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	16	no	—
592	C₂×C₄	—	2	8	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	8	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	8	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	4	8	no	—
607	C₂×C₄	—	4	4	no	—
608	C₂×C₄	—	4	16	no	—
609	C₂×C₄	—	4	16	no	—
610	C₂×C₄	—	4	16	no	—
611	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
612	C₂×C₄	2₋¹⁺⁴	1	4	yes	complemented
613	C₂×C₄	C₂⁵	1	1	yes	characteristic
614	C₂×C₄	C₂⁵	1	4	yes	—
615	C₂×C₄	C₂⁵	1	1	yes	characteristic
616	C₂×C₄	C₂⁵	1	1	yes	characteristic
617	C₂×C₄	C₂⁵	1	1	yes	characteristic
618	C₂×C₄	C₂⁵	1	8	yes	—
619	C₂×C₄	C₂⁵	1	1	yes	characteristic
620	C₂×C₄	C₂⁵	1	1	yes	characteristic
621	C₂×C₄	C₂⁵	1	1	yes	characteristic
622	C₂×C₄	C₂⁵	1	4	yes	—
623	C₂×C₄	C₂⁵	1	4	yes	—
624	C₂×C₄	C₂⁵	1	8	yes	—
625	C₂×C₄	C₂⁵	1	8	yes	—
626	C₂×C₄	C₂⁵	1	1	yes	characteristic
627	C₂×C₄	C₂⁵	1	1	yes	characteristic
628	C₂×C₄	C₂⁵	1	1	yes	characteristic
629	C₂×C₄	C₂⁵	1	1	yes	characteristic
630	C₂×C₄	C₂⁵	1	1	yes	characteristic
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	8	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	8	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	2	8	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	8	8	no	—
646	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
647	C₂²	C₂×2₋¹⁺⁴	1	2	yes	—
648	C₂²	C₂⁶	1	1	yes	characteristic
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	8	no	—
652	C₄	—	2	4	no	—
653	C₄	—	2	8	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	8	no	—
662	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
663	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
664	C₄	C₂×2₋¹⁺⁴	1	2	yes	—
665	C₄	C₂×2₋¹⁺⁴	1	2	yes	—
666	C₄	#585	1	2	yes	—
667	C₂	—	2	2	no	—
668	C₂	—	2	2	no	—
669	C₂	—	4	4	no	—
670	C₂	—	4	1	no	—
671	C₂	—	4	8	no	—
672	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
674	C₂	C₂×#585	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3561	C₂	semidirect
2. #3559	C₂	semidirect
3. #3554	C₂	semidirect
4. #3550	C₂	semidirect
5. #3548	C₂	semidirect
6. #3547	C₂	semidirect
7. #3536	C₂	semidirect
8. #3522	C₂	semidirect
9. #3520	C₂	semidirect
10. #3511	C₂	semidirect
11. #3511	C₂	semidirect
12. #3508	C₂	semidirect
13. #3507	C₂	semidirect
14. #3506	C₂	semidirect
15. #3503	C₂	semidirect
16. #3501	C₂	semidirect
17. #3499	C₂	semidirect
18. #3497	C₂	semidirect
19. #3494	C₂	semidirect
20. #3489	C₂	semidirect
21. #3444	C₂	semidirect
22. C₂×#533	C₂	semidirect
23. C₂×#532	C₂	semidirect
24. C₂×2₋¹⁺⁴	C₂²	semidirect
26. #563	C₂²	semidirect
27. #562	C₂²	semidirect
28. #562	C₂²	semidirect
29. #559	C₂²	semidirect
30. #559	C₂²	semidirect
31. #559	C₂²	semidirect
32. Q₈²	C₂²	semidirect
33. #557	C₂²	semidirect
34. #556	C₂²	semidirect
35. #556	C₂²	semidirect
36. #556	C₂²	semidirect
37. #555	C₂²	semidirect
38. #555	C₂²	semidirect
40. #554	C₂²	semidirect
41. #554	C₂²	semidirect
42. #554	C₂²	semidirect
43. #554	C₂²	semidirect
44. #554	C₂²	semidirect
45. #553	C₂²	semidirect
46. #553	C₂²	semidirect
47. #553	C₂²	semidirect
48. #552	C₂²	semidirect
50. #550	C₂²	semidirect
51. #550	C₂²	semidirect
52. #550	C₂²	semidirect
54. D₄×Q₈	C₂²	semidirect
55. D₄×Q₈	C₂²	semidirect
56. D₄×Q₈	C₂²	semidirect
57. D₄×Q₈	C₂²	semidirect
58. #548	C₂²	semidirect
59. #548	C₂²	semidirect
60. #548	C₂²	semidirect
61. #548	C₂²	semidirect
62. #547	C₂²	semidirect
63. #547	C₂²	semidirect
64. #547	C₂²	semidirect
65. #547	C₂²	semidirect
66. #547	C₂²	semidirect
67. #547	C₂²	semidirect
68. #547	C₂²	semidirect
73. #544	C₂²	semidirect
75. #542	C₂²	semidirect
76. #542	C₂²	semidirect
77. #542	C₂²	semidirect
78. #542	C₂²	semidirect
79. #542	C₂²	semidirect
80. #540	C₂²	semidirect
81. #540	C₂²	semidirect
82. #539	C₂²	semidirect
83. #539	C₂²	semidirect
85. #537	C₂²	semidirect
86. #537	C₂²	semidirect
87. #537	C₂²	semidirect
88. #537	C₂²	semidirect
89. #536	C₂²	semidirect
90. #536	C₂²	semidirect
91. #536	C₂²	semidirect
98. #533	C₂²	semidirect
99. #533	C₂²	semidirect
100. #533	C₂²	semidirect
101. #533	C₂²	semidirect
102. #533	C₂²	semidirect
103. #533	C₂²	semidirect
104. #533	C₂²	semidirect
114. #532	C₂²	semidirect
115. #532	C₂²	semidirect
116. #532	C₂²	semidirect
117. #532	C₂²	semidirect
118. #532	C₂²	semidirect
120. C₂×C₄⋊Q₈	C₂²	semidirect
121. C₂×C₄⋊Q₈	C₂²	semidirect
122. C₂×C₄⋊Q₈	C₂²	semidirect
126. #529	C₂²	semidirect
127. #529	C₂²	semidirect
128. #529	C₂²	semidirect
129. #529	C₂²	semidirect
130. #529	C₂²	semidirect
131. C₂×#125	C₂²	semidirect
143. #520	C₂²	semidirect
144. #520	C₂²	semidirect
147. C₄×#41	C₂²	semidirect
148. C₄×#41	C₂²	semidirect
149. C₂×C₄×Q₈	C₂²	semidirect
150. C₂×C₄×Q₈	C₂²	semidirect
612. C₂×C₄	2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
#3561	2
#3559	2
#3554	2
#3550	2
#3548	2
#3547	2
#3536	2
#3522	2
#3520	2
#3511	2
#3508	2
#3507	2
#3506	2
#3503	2
#3501	2
#3499	2
#3497	2
#3494	2
#3489	2
#3444	2
C₂×#533	2
C₂×#532	2