Subgroups — C₂×#3564 #62734

Order 256.

3299 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3564	C₂	1	32	yes	maximal, direct product factor
2	C₂×#563	C₂	1	2	yes	maximal, complemented
3	C₂×#563	C₂	1	2	yes	maximal, complemented
4	C₂×#556	C₂	1	2	yes	maximal, complemented
5	C₂×#554	C₂	1	2	yes	maximal, complemented
6	C₂×#552	C₂	1	2	yes	maximal, complemented
7	C₂×#552	C₂	1	2	yes	maximal, complemented
8	C₂×#551	C₂	1	2	yes	maximal, complemented
9	C₂×#551	C₂	1	2	yes	maximal, complemented
10	C₂×#544	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#542	C₂	1	2	yes	maximal, complemented
13	C₂×#541	C₂	1	2	yes	maximal, complemented
14	C₂×#541	C₂	1	2	yes	maximal, complemented
15	C₂×#539	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#539	C₂	1	2	yes	maximal, complemented
17	C₂×#538	C₂	1	1	yes	maximal, characteristic
18	C₂×#533	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#126	C₂	1	1	yes	maximal, characteristic, complemented
21	#563	C₂²	1	32	yes	complemented
22	#563	C₂²	1	32	yes	complemented
23	#556	C₂²	1	32	yes	complemented
24	#554	C₂²	1	32	yes	complemented
25	#552	C₂²	1	32	yes	complemented
26	#552	C₂²	1	32	yes	complemented
27	#551	C₂²	1	32	yes	complemented
28	#551	C₂²	1	32	yes	complemented
29	#544	C₂²	1	16	yes	complemented
30	#543	C₂²	1	16	yes	complemented
31	#542	C₂²	1	32	yes	complemented
32	#541	C₂²	1	32	yes	complemented
33	#541	C₂²	1	32	yes	complemented
34	#539	C₂²	1	16	yes	complemented
35	#539	C₂²	1	32	yes	complemented
36	#538	C₂²	1	16	yes	—
37	#533	C₂²	1	16	yes	complemented
38	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
41	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
43	#529	C₂²	1	16	yes	complemented
44	C₂×#126	C₂²	1	2	yes	—
45	C₂×#126	C₂²	1	2	yes	—
46	C₂×#126	C₂²	1	2	yes	—
47	C₂×#126	C₂²	1	2	yes	—
48	C₂×#126	C₂²	1	2	yes	—
49	C₂×#126	C₂²	1	2	yes	—
50	C₂×#126	C₂²	1	2	yes	—
51	C₂×#126	C₂²	1	2	yes	—
52	C₂×#126	C₂²	1	2	yes	—
53	C₂×#126	C₂²	1	16	yes	complemented
54	C₂×#126	C₂²	1	2	yes	complemented
55	C₂×#126	C₂²	1	2	yes	complemented
56	C₂×#126	C₂²	1	2	yes	complemented
57	C₂×#126	C₂²	1	2	yes	complemented
58	C₂×#125	C₂²	1	1	yes	characteristic, complemented
59	C₂×#125	C₂²	1	2	yes	complemented
60	C₂×#125	C₂²	1	2	yes	complemented
61	C₂×#125	C₂²	1	2	yes	complemented
62	C₂×#125	C₂²	1	2	yes	complemented
63	C₂×#125	C₂²	1	2	yes	complemented
64	C₂×#125	C₂²	1	2	yes	complemented
65	C₂×#125	C₂²	1	2	yes	complemented
66	C₂×#125	C₂²	1	2	yes	complemented
67	C₂×#125	C₂²	1	2	yes	complemented
68	C₂×#124	C₂²	1	2	yes	—
69	C₂×#124	C₂²	1	2	yes	—
70	C₂×#124	C₂²	1	2	yes	—
71	C₂×#124	C₂²	1	1	yes	characteristic, complemented
72	C₂×#123	C₂²	1	2	yes	—
73	C₂×#123	C₂²	1	2	yes	—
74	C₂×#123	C₂²	1	2	yes	—
75	C₂×#123	C₂²	1	2	yes	—
76	C₂×#123	C₂²	1	2	yes	—
77	C₂×#123	C₂²	1	2	yes	—
78	C₂×#123	C₂²	1	2	yes	—
79	C₂×#123	C₂²	1	2	yes	complemented
80	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
81	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
82	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
83	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
84	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
85	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
86	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
87	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
88	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
89	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
90	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
91	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
92	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
93	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
95	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
96	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
97	C₂×#121	C₂²	1	1	yes	characteristic
98	C₂×#121	C₂²	1	2	yes	—
99	C₂×#120	C₂²	1	2	yes	—
100	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
102	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
105	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄	C₂²	1	2	yes	—
107	C₂×C₄×D₄	C₂²	1	2	yes	—
108	C₂×C₄×D₄	C₂²	1	2	yes	—
109	C₂×C₄×D₄	C₂²	1	2	yes	—
110	C₂×C₄×D₄	C₂²	1	2	yes	—
111	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
112	C₂×#117	C₂²	1	2	yes	—
113	C₂×#117	C₂²	1	2	yes	—
114	C₂×#117	C₂²	1	2	yes	—
115	C₂×#117	C₂²	1	2	yes	—
116	C₂×#117	C₂²	1	2	yes	complemented
117	C₂×#117	C₂²	1	2	yes	complemented
118	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
122	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
123	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
126	C₂²×C₄²	C₂²	1	1	yes	characteristic
127	C₂⁵	C₂³	1	1	yes	characteristic
128	C₂²×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×Q₈	C₂³	1	2	yes	—
130	C₂²×Q₈	C₂³	1	1	yes	characteristic
131	C₂²×Q₈	C₂³	1	2	yes	—
132	C₂²×Q₈	C₂³	1	2	yes	—
133	C₂²×Q₈	C₂³	1	1	yes	characteristic
134	C₂²×D₄	C₂³	1	2	yes	—
135	C₂²×D₄	C₂³	1	2	yes	—
136	C₂²×D₄	C₂³	1	2	yes	—
137	C₂²×D₄	C₂³	1	1	yes	characteristic
138	C₂³×C₄	C₂³	1	1	yes	characteristic
139	C₂³×C₄	C₂³	1	1	yes	characteristic
140	C₂³×C₄	C₂³	1	1	yes	characteristic
141	C₂³×C₄	C₂³	1	1	yes	characteristic
142	C₂³×C₄	C₂³	1	1	yes	characteristic
143	C₂³×C₄	C₂³	1	1	yes	characteristic
144	C₂³×C₄	C₂³	1	2	yes	—
145	C₂³×C₄	C₂³	1	2	yes	—
146	C₂³×C₄	C₂³	1	2	yes	—
147	C₂³×C₄	C₂³	1	2	yes	—
148	C₂³×C₄	C₂³	1	2	yes	—
149	C₄⋊Q₈	C₂³	1	8	yes	complemented
150	C₄⋊Q₈	C₂³	1	8	yes	complemented
151	C₄⋊Q₈	C₂³	1	16	yes	complemented
152	C₄⋊Q₈	C₂³	1	16	yes	complemented
153	C₄⋊Q₈	C₂³	1	16	yes	complemented
154	#126	C₂³	1	16	yes	—
155	#126	C₂³	1	16	yes	—
156	#126	C₂³	1	16	yes	—
157	#126	C₂³	1	16	yes	—
158	#126	C₂³	1	16	yes	—
159	#126	C₂³	1	16	yes	—
160	#126	C₂³	1	16	yes	—
161	#126	C₂³	1	16	yes	—
162	#126	C₂³	1	16	yes	—
163	#126	C₂³	1	16	yes	complemented
164	#126	C₂³	1	16	yes	complemented
165	#126	C₂³	1	16	yes	complemented
166	#126	C₂³	1	16	yes	complemented
167	#125	C₂³	1	8	yes	complemented
168	#125	C₂³	1	16	yes	complemented
169	#125	C₂³	1	16	yes	complemented
170	#125	C₂³	1	16	yes	complemented
171	#125	C₂³	1	16	yes	complemented
172	#125	C₂³	1	16	yes	complemented
173	#125	C₂³	1	16	yes	complemented
174	#125	C₂³	1	16	yes	complemented
175	#125	C₂³	1	16	yes	complemented
176	#125	C₂³	1	16	yes	complemented
177	#124	C₂³	1	16	yes	—
178	#124	C₂³	1	16	yes	—
179	#124	C₂³	1	16	yes	—
180	#124	C₂³	1	8	yes	complemented
181	#123	C₂³	1	16	yes	—
182	#123	C₂³	1	16	yes	—
183	#123	C₂³	1	16	yes	—
184	#123	C₂³	1	16	yes	—
185	#123	C₂³	1	16	yes	—
186	#123	C₂³	1	16	yes	—
187	#123	C₂³	1	16	yes	—
188	#123	C₂³	1	16	yes	complemented
189	C₂²⋊Q₈	C₂³	1	8	yes	—
190	C₂²⋊Q₈	C₂³	1	8	yes	—
191	C₂²⋊Q₈	C₂³	1	8	yes	—
192	C₂²⋊Q₈	C₂³	1	16	yes	—
193	C₂²⋊Q₈	C₂³	1	16	yes	—
194	C₂²⋊Q₈	C₂³	1	16	yes	—
195	C₂²⋊Q₈	C₂³	1	16	yes	—
196	C₂²⋊Q₈	C₂³	1	16	yes	—
197	C₂²⋊Q₈	C₂³	1	16	yes	—
198	C₂²⋊Q₈	C₂³	1	16	yes	—
199	C₂²⋊Q₈	C₂³	1	16	yes	—
200	C₂²⋊Q₈	C₂³	1	16	yes	—
201	C₂²⋊Q₈	C₂³	1	16	yes	complemented
202	C₂²⋊Q₈	C₂³	1	16	yes	complemented
203	C₂²⋊Q₈	C₂³	1	16	yes	complemented
204	C₂²⋊Q₈	C₂³	1	16	yes	complemented
205	C₂²⋊Q₈	C₂³	1	16	yes	complemented
206	#121	C₂³	1	8	yes	—
207	#121	C₂³	1	16	yes	—
208	#120	C₂³	1	16	yes	—
209	C₄×Q₈	C₂³	1	8	yes	complemented
210	C₄×Q₈	C₂³	1	16	yes	complemented
211	C₄×Q₈	C₂³	1	8	yes	complemented
212	C₄×Q₈	C₂³	1	8	yes	complemented
213	C₄×Q₈	C₂³	1	16	yes	complemented
214	C₄×Q₈	C₂³	1	16	yes	complemented
215	C₄×D₄	C₂³	1	16	yes	—
216	C₄×D₄	C₂³	1	16	yes	—
217	C₄×D₄	C₂³	1	16	yes	—
218	C₄×D₄	C₂³	1	16	yes	—
219	C₄×D₄	C₂³	1	16	yes	—
220	C₄×D₄	C₂³	1	8	yes	complemented
221	#117	C₂³	1	16	yes	—
222	#117	C₂³	1	16	yes	—
223	#117	C₂³	1	16	yes	—
224	#117	C₂³	1	16	yes	—
225	#117	C₂³	1	16	yes	complemented
226	#117	C₂³	1	16	yes	complemented
227	C₂×C₄⋊C₄	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄	C₂³	1	8	yes	—
234	C₂×C₄⋊C₄	C₂³	1	8	yes	—
235	C₂×C₄⋊C₄	C₂³	1	8	yes	—
236	C₂×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄	C₂³	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
264	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
274	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
275	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
276	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
277	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
278	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
288	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
289	C₂×C₄²	C₂³	1	2	yes	—
290	C₂×C₄²	C₂³	1	2	yes	—
291	C₂×C₄²	C₂³	1	2	yes	—
292	C₂×C₄²	C₂³	1	2	yes	—
293	C₂×C₄²	C₂³	1	2	yes	—
294	C₂×C₄²	C₂³	1	2	yes	—
295	C₂×C₄²	C₂³	1	1	yes	characteristic
296	C₂×C₄²	C₂³	1	2	yes	—
297	C₂×C₄²	C₂³	1	1	yes	characteristic
298	C₂×C₄²	C₂³	1	1	yes	characteristic
299	C₂×C₄²	C₂³	1	1	yes	characteristic
300	C₂×C₄²	C₂³	1	8	yes	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	4	2	no	—
303	C₂⁴	—	4	2	no	—
304	C₂⁴	C₂⁴	1	2	yes	—
305	C₂⁴	C₂⁴	1	2	yes	—
306	C₂⁴	C₂⁴	1	1	yes	characteristic
307	C₂⁴	C₂⁴	1	4	yes	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	—	4	4	no	—
310	C₂×Q₈	—	4	4	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	—	4	4	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	C₂⁴	1	4	yes	—
315	C₂×Q₈	C₂⁴	1	8	yes	—
316	C₂×Q₈	C₂⁴	1	4	yes	—
317	C₂×Q₈	C₂⁴	1	8	yes	—
318	C₂×Q₈	C₂⁴	1	8	yes	—
319	C₂×Q₈	C₂⁴	1	4	yes	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	C₂⁴	1	8	yes	—
325	C₂×D₄	C₂⁴	1	8	yes	—
326	C₂×D₄	C₂⁴	1	8	yes	—
327	C₂×D₄	C₂⁴	1	4	yes	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	C₂⁴	1	4	yes	—
340	C₂²×C₄	C₂⁴	1	4	yes	—
341	C₂²×C₄	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴	1	2	yes	—
344	C₂²×C₄	C₂⁴	1	2	yes	—
345	C₂²×C₄	C₂⁴	1	2	yes	—
346	C₂²×C₄	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄	C₂⁴	1	2	yes	—
348	C₂²×C₄	C₂⁴	1	2	yes	—
349	C₂²×C₄	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴	1	2	yes	—
352	C₂²×C₄	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴	1	2	yes	—
354	C₂²×C₄	C₂⁴	1	2	yes	—
355	C₂²×C₄	C₂⁴	1	2	yes	—
356	C₂²×C₄	C₂⁴	1	2	yes	—
357	C₂²×C₄	C₂⁴	1	4	yes	—
358	C₂²×C₄	C₂⁴	1	4	yes	—
359	C₂²×C₄	C₂⁴	1	4	yes	—
360	C₂²×C₄	C₂⁴	1	4	yes	—
361	C₂²×C₄	C₂⁴	1	8	yes	—
362	C₂²×C₄	C₂⁴	1	8	yes	—
363	C₂²×C₄	C₂⁴	1	8	yes	—
364	C₂²×C₄	C₂⁴	1	8	yes	—
365	C₂²×C₄	C₂⁴	1	8	yes	—
366	C₄⋊C₄	C₂⁴	1	8	yes	—
367	C₄⋊C₄	C₂⁴	1	8	yes	—
368	C₄⋊C₄	C₂⁴	1	8	yes	—
369	C₄⋊C₄	C₂⁴	1	8	yes	—
370	C₄⋊C₄	C₂⁴	1	8	yes	—
371	C₄⋊C₄	C₂⁴	1	8	yes	—
372	C₄⋊C₄	C₂⁴	1	8	yes	—
373	C₄⋊C₄	C₂⁴	1	8	yes	—
374	C₄⋊C₄	C₂⁴	1	8	yes	—
375	C₄⋊C₄	C₂⁴	1	8	yes	—
376	C₄⋊C₄	C₂⁴	1	8	yes	—
377	C₄⋊C₄	C₂⁴	1	8	yes	—
378	C₄⋊C₄	C₂⁴	1	8	yes	—
379	C₄⋊C₄	C₂⁴	1	8	yes	—
380	C₄⋊C₄	C₂⁴	1	8	yes	—
381	C₄⋊C₄	C₂⁴	1	8	yes	—
382	C₄⋊C₄	C₂⁴	1	8	yes	—
383	C₄⋊C₄	C₂⁴	1	8	yes	—
384	C₄⋊C₄	C₂⁴	1	8	yes	—
385	C₄⋊C₄	C₂⁴	1	8	yes	—
386	C₄⋊C₄	C₂⁴	1	8	yes	—
387	C₄⋊C₄	C₂⁴	1	8	yes	—
388	C₄⋊C₄	C₂⁴	1	8	yes	—
389	C₄⋊C₄	C₂⁴	1	4	yes	—
390	C₄⋊C₄	C₂⁴	1	8	yes	—
391	C₄⋊C₄	C₂⁴	1	4	yes	—
392	C₄⋊C₄	C₂⁴	1	8	yes	—
393	C₄⋊C₄	C₂⁴	1	8	yes	—
394	C₄⋊C₄	C₂⁴	1	4	yes	—
395	C₄⋊C₄	C₂⁴	1	8	yes	—
396	C₄⋊C₄	C₂⁴	1	4	yes	—
397	C₄⋊C₄	C₂⁴	1	8	yes	—
398	C₄⋊C₄	C₂⁴	1	8	yes	—
399	C₂²⋊C₄	C₂⁴	1	8	yes	—
400	C₂²⋊C₄	C₂⁴	1	8	yes	—
401	C₂²⋊C₄	C₂⁴	1	8	yes	—
402	C₂²⋊C₄	C₂⁴	1	8	yes	—
403	C₂²⋊C₄	C₂⁴	1	8	yes	—
404	C₂²⋊C₄	C₂⁴	1	8	yes	—
405	C₂²⋊C₄	C₂⁴	1	8	yes	—
406	C₂²⋊C₄	C₂⁴	1	8	yes	—
407	C₂²⋊C₄	C₂⁴	1	8	yes	—
408	C₂²⋊C₄	C₂⁴	1	8	yes	—
409	C₂²⋊C₄	C₂⁴	1	8	yes	—
410	C₂²⋊C₄	C₂⁴	1	8	yes	—
411	C₂²⋊C₄	C₂⁴	1	8	yes	—
412	C₂²⋊C₄	C₂⁴	1	8	yes	—
413	C₂²⋊C₄	C₂⁴	1	8	yes	—
414	C₂²⋊C₄	C₂⁴	1	8	yes	—
415	C₂²⋊C₄	C₂⁴	1	8	yes	—
416	C₂²⋊C₄	C₂⁴	1	8	yes	—
417	C₂²⋊C₄	C₂⁴	1	8	yes	—
418	C₂²⋊C₄	C₂⁴	1	8	yes	—
419	C₂²⋊C₄	C₂⁴	1	8	yes	—
420	C₄²	C₂⁴	1	4	yes	—
421	C₄²	C₂⁴	1	4	yes	—
422	C₄²	C₂⁴	1	4	yes	—
423	C₄²	C₂⁴	1	4	yes	—
424	C₄²	C₂⁴	1	8	yes	—
425	C₄²	C₂⁴	1	8	yes	—
426	C₄²	C₂⁴	1	8	yes	—
427	C₄²	C₂⁴	1	8	yes	—
428	C₄²	C₂⁴	1	8	yes	—
429	C₄²	C₂⁴	1	8	yes	—
430	C₄²	C₂⁴	1	8	yes	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	8	8	no	—
443	C₂³	2₋¹⁺⁴	1	4	yes	—
444	C₂³	C₂⁵	1	4	yes	—
445	C₂³	C₂⁵	1	4	yes	—
446	C₂³	C₂⁵	1	2	yes	—
447	C₂³	C₂⁵	1	1	yes	characteristic
448	Q₈	—	4	4	no	—
449	Q₈	—	4	8	no	—
450	Q₈	—	4	8	no	—
451	Q₈	—	4	4	no	—
452	Q₈	—	4	8	no	—
453	Q₈	—	4	4	no	—
454	D₄	—	2	16	no	—
455	D₄	—	4	8	no	—
456	D₄	—	4	4	no	—
457	D₄	—	4	8	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	8	no	—
481	C₂×C₄	—	4	8	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	4	8	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	C₂⁵	1	2	yes	—
486	C₂×C₄	C₂⁵	1	2	yes	—
487	C₂×C₄	C₂⁵	1	4	yes	—
488	C₂×C₄	C₂⁵	1	4	yes	—
489	C₂×C₄	C₂⁵	1	2	yes	—
490	C₂×C₄	C₂⁵	1	4	yes	—
491	C₂×C₄	C₂⁵	1	2	yes	—
492	C₂×C₄	C₂⁵	1	2	yes	—
493	C₂×C₄	C₂⁵	1	4	yes	—
494	C₂×C₄	C₂⁵	1	4	yes	—
495	C₂×C₄	C₂⁵	1	2	yes	—
496	C₂×C₄	C₂⁵	1	4	yes	—
497	C₂×C₄	C₂⁵	1	4	yes	—
498	C₂×C₄	C₂⁵	1	4	yes	—
499	C₂×C₄	C₂⁵	1	4	yes	—
500	C₂×C₄	C₂⁵	1	4	yes	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	8	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	4	8	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	8	8	no	—
513	C₂²	C₂×2₋¹⁺⁴	1	4	yes	—
514	C₂²	C₂×2₋¹⁺⁴	1	2	yes	—
515	C₂²	#585	1	2	yes	—
516	C₂²	#585	1	2	yes	—
517	C₂²	C₂⁶	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	4	no	—
521	C₄	—	2	4	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	4	no	—
524	C₄	—	2	4	no	—
525	C₄	—	2	4	no	—
526	C₄	—	2	4	no	—
527	C₄	—	2	4	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	4	no	—
534	C₂	—	2	4	no	—
535	C₂	—	4	4	no	—
536	C₂	—	4	4	no	—
537	C₂	#3564	1	4	yes	direct product factor
538	C₂	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
539	C₂	C₂×#585	1	1	yes	characteristic
540	C₂	C₂×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶
prime radical	C₂×#538	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3564	C₂	direct (N × H)
2. C₂×#563	C₂	semidirect
3. C₂×#563	C₂	semidirect
4. C₂×#556	C₂	semidirect
5. C₂×#554	C₂	semidirect
6. C₂×#552	C₂	semidirect
7. C₂×#552	C₂	semidirect
8. C₂×#551	C₂	semidirect
9. C₂×#551	C₂	semidirect
10. C₂×#544	C₂	semidirect
11. C₂×#543	C₂	semidirect
12. C₂×#542	C₂	semidirect
13. C₂×#541	C₂	semidirect
14. C₂×#541	C₂	semidirect
15. C₂×#539	C₂	semidirect
16. C₂×#539	C₂	semidirect
18. C₂×#533	C₂	semidirect
19. C₂×#529	C₂	semidirect
20. C₂²×#126	C₂	semidirect
21. #563	C₂²	semidirect
22. #563	C₂²	semidirect
23. #556	C₂²	semidirect
24. #554	C₂²	semidirect
25. #552	C₂²	semidirect
26. #552	C₂²	semidirect
27. #551	C₂²	semidirect
28. #551	C₂²	semidirect
29. #544	C₂²	semidirect
30. #543	C₂²	semidirect
31. #542	C₂²	semidirect
32. #541	C₂²	semidirect
33. #541	C₂²	semidirect
34. #539	C₂²	semidirect
35. #539	C₂²	semidirect
37. #533	C₂²	semidirect
38. C₂×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₄⋊Q₈	C₂²	semidirect
40. C₂×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₄⋊Q₈	C₂²	semidirect
43. #529	C₂²	semidirect
53. C₂×#126	C₂²	semidirect
54. C₂×#126	C₂²	semidirect
55. C₂×#126	C₂²	semidirect
56. C₂×#126	C₂²	semidirect
57. C₂×#126	C₂²	semidirect
58. C₂×#125	C₂²	semidirect
59. C₂×#125	C₂²	semidirect
60. C₂×#125	C₂²	semidirect
61. C₂×#125	C₂²	semidirect
62. C₂×#125	C₂²	semidirect
63. C₂×#125	C₂²	semidirect
64. C₂×#125	C₂²	semidirect
65. C₂×#125	C₂²	semidirect
66. C₂×#125	C₂²	semidirect
67. C₂×#125	C₂²	semidirect
71. C₂×#124	C₂²	semidirect
79. C₂×#123	C₂²	semidirect
92. C₂×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₂²⋊Q₈	C₂²	semidirect
94. C₂×C₂²⋊Q₈	C₂²	semidirect
95. C₂×C₂²⋊Q₈	C₂²	semidirect
96. C₂×C₂²⋊Q₈	C₂²	semidirect
100. C₂×C₄×Q₈	C₂²	semidirect
101. C₂×C₄×Q₈	C₂²	semidirect
102. C₂×C₄×Q₈	C₂²	semidirect
103. C₂×C₄×Q₈	C₂²	semidirect
104. C₂×C₄×Q₈	C₂²	semidirect
105. C₂×C₄×Q₈	C₂²	semidirect
111. C₂×C₄×D₄	C₂²	semidirect
116. C₂×#117	C₂²	semidirect
117. C₂×#117	C₂²	semidirect
121. C₂²×C₄⋊C₄	C₂²	semidirect
149. C₄⋊Q₈	C₂³	semidirect
150. C₄⋊Q₈	C₂³	semidirect
151. C₄⋊Q₈	C₂³	semidirect
152. C₄⋊Q₈	C₂³	semidirect
153. C₄⋊Q₈	C₂³	semidirect
163. #126	C₂³	semidirect
164. #126	C₂³	semidirect
165. #126	C₂³	semidirect
166. #126	C₂³	semidirect
167. #125	C₂³	semidirect
168. #125	C₂³	semidirect
169. #125	C₂³	semidirect
170. #125	C₂³	semidirect
171. #125	C₂³	semidirect
172. #125	C₂³	semidirect
173. #125	C₂³	semidirect
174. #125	C₂³	semidirect
175. #125	C₂³	semidirect
176. #125	C₂³	semidirect
180. #124	C₂³	semidirect
188. #123	C₂³	semidirect
201. C₂²⋊Q₈	C₂³	semidirect
202. C₂²⋊Q₈	C₂³	semidirect
203. C₂²⋊Q₈	C₂³	semidirect
204. C₂²⋊Q₈	C₂³	semidirect
205. C₂²⋊Q₈	C₂³	semidirect
209. C₄×Q₈	C₂³	semidirect
210. C₄×Q₈	C₂³	semidirect
211. C₄×Q₈	C₂³	semidirect
212. C₄×Q₈	C₂³	semidirect
213. C₄×Q₈	C₂³	semidirect
214. C₄×Q₈	C₂³	semidirect
220. C₄×D₄	C₂³	semidirect
225. #117	C₂³	semidirect
226. #117	C₂³	semidirect
263. C₂×C₄⋊C₄	C₂³	semidirect
537. C₂	#3564	direct (N × H)

Maximal subgroups

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

subgroup	index
#3564	2
C₂×#563	2
C₂×#556	2
C₂×#554	2
C₂×#552	2
C₂×#551	2
C₂×#544	2
C₂×#543	2
C₂×#542	2
C₂×#541	2
C₂×#539	2
C₂×#538	2
C₂×#533	2
C₂×#529	2
C₂²×#126	2

Subgroups — C2×#3564 #62734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3564 #62734