Subgroups — C₂×#3521 #62780

Order 256.

3657 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3521	C₂	1	32	yes	maximal, direct product factor
2	C₂×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#554	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#553	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#553	C₂	1	2	yes	maximal, complemented
7	C₂×#552	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#552	C₂	1	2	yes	maximal, complemented
9	C₂×#551	C₂	1	2	yes	maximal, complemented
10	C₂×#551	C₂	1	2	yes	maximal, complemented
11	C₂×#547	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#546	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#542	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#541	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#539	C₂	1	2	yes	maximal, complemented
17	C₂×#538	C₂	1	2	yes	maximal, complemented
18	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#529	C₂	1	2	yes	maximal, complemented
20	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#126	C₂	1	2	yes	maximal, complemented
22	C₂×#520	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#518	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#41	C₂²	1	1	yes	characteristic
26	C₂²×#41	C₂²	1	1	yes	characteristic
27	C₂³×D₄	C₂²	1	1	yes	characteristic
28	#556	C₂²	1	16	yes	complemented
29	#556	C₂²	1	16	yes	complemented
30	#554	C₂²	1	16	yes	complemented
31	#553	C₂²	1	16	yes	complemented
32	#553	C₂²	1	32	yes	complemented
33	#552	C₂²	1	16	yes	complemented
34	#552	C₂²	1	32	yes	complemented
35	#551	C₂²	1	32	yes	complemented
36	#551	C₂²	1	32	yes	complemented
37	#547	C₂²	1	16	yes	complemented
38	#546	C₂²	1	16	yes	complemented
39	#546	C₂²	1	16	yes	complemented
40	#542	C₂²	1	16	yes	complemented
41	#541	C₂²	1	16	yes	complemented
42	#539	C₂²	1	32	yes	complemented
43	#538	C₂²	1	32	yes	complemented
44	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	#529	C₂²	1	16	yes	complemented
47	#529	C₂²	1	32	yes	complemented
48	#529	C₂²	1	16	yes	complemented
49	C₂×#126	C₂²	1	1	yes	characteristic
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	2	yes	—
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×#126	C₂²	1	1	yes	characteristic, complemented
59	C₂×#126	C₂²	1	2	yes	complemented
60	C₂×#126	C₂²	1	2	yes	complemented
61	C₂×#126	C₂²	1	32	yes	complemented
62	C₂×#125	C₂²	1	2	yes	complemented
63	C₂×#125	C₂²	1	1	yes	characteristic, complemented
64	C₂×#125	C₂²	1	1	yes	characteristic, complemented
65	C₂×#125	C₂²	1	2	yes	complemented
66	C₂×#125	C₂²	1	2	yes	complemented
67	C₂×#125	C₂²	1	1	yes	characteristic, complemented
68	C₂×#124	C₂²	1	1	yes	characteristic
69	C₂×#124	C₂²	1	1	yes	characteristic
70	C₂×#124	C₂²	1	2	yes	—
71	C₂×#124	C₂²	1	1	yes	characteristic
72	C₂×#124	C₂²	1	2	yes	complemented
73	C₂×#123	C₂²	1	2	yes	—
74	C₂×#123	C₂²	1	1	yes	characteristic
75	C₂×#123	C₂²	1	2	yes	—
76	C₂×#123	C₂²	1	2	yes	—
77	C₂×#123	C₂²	1	2	yes	complemented
78	C₂×#123	C₂²	1	2	yes	complemented
79	C₂×#123	C₂²	1	1	yes	characteristic, complemented
80	C₂×#123	C₂²	1	2	yes	complemented
81	C₂×#123	C₂²	1	2	yes	complemented
82	C₂×#123	C₂²	1	2	yes	complemented
83	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
84	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
85	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
88	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
89	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
90	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
91	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
93	C₂×#121	C₂²	1	1	yes	characteristic
94	C₂×#121	C₂²	1	1	yes	characteristic
95	C₂×#121	C₂²	1	2	yes	—
96	C₂×#121	C₂²	1	2	yes	—
97	C₂×#121	C₂²	1	1	yes	characteristic
98	C₂×#121	C₂²	1	2	yes	complemented
99	C₂×#121	C₂²	1	2	yes	complemented
100	C₂×#120	C₂²	1	2	yes	—
101	C₂×#120	C₂²	1	2	yes	—
102	#520	C₂²	1	16	yes	complemented
103	#518	C₂²	1	16	yes	complemented
104	C₄×#41	C₂²	1	16	yes	complemented
105	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
110	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
112	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
113	C₂×C₄×D₄	C₂²	1	2	yes	—
114	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
115	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
116	C₂×C₄×D₄	C₂²	1	2	yes	—
117	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
118	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
119	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
120	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
121	C₂×C₄×D₄	C₂²	1	2	yes	complemented
122	C₂×C₄×D₄	C₂²	1	2	yes	complemented
123	C₂×C₄×D₄	C₂²	1	2	yes	complemented
124	C₂×C₄×D₄	C₂²	1	2	yes	complemented
125	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₄×D₄	C₂²	1	2	yes	complemented
127	C₂×C₄×D₄	C₂²	1	2	yes	complemented
128	C₂×#117	C₂²	1	1	yes	characteristic
129	C₂×#117	C₂²	1	1	yes	characteristic
130	C₂×#117	C₂²	1	2	yes	complemented
131	C₂×#117	C₂²	1	1	yes	characteristic, complemented
132	C₂×#117	C₂²	1	1	yes	characteristic, complemented
133	C₂×#117	C₂²	1	2	yes	complemented
134	C₂×#117	C₂²	1	2	yes	complemented
135	C₂×#117	C₂²	1	2	yes	complemented
136	C₂×#117	C₂²	1	2	yes	complemented
137	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
138	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
139	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
140	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
141	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
142	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
143	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
144	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
145	C₂²×C₄²	C₂²	1	2	yes	complemented
146	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
147	C₂⁵	C₂³	1	2	yes	—
148	C₂×#41	—	2	8	no	—
149	C₂×#41	—	2	8	no	—
150	C₂×#41	C₂³	1	8	yes	—
151	C₂×#41	C₂³	1	8	yes	—
152	C₂²×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×Q₈	C₂³	1	1	yes	characteristic
154	C₂²×Q₈	C₂³	1	1	yes	characteristic
155	C₂²×Q₈	C₂³	1	2	yes	—
156	C₂²×D₄	—	2	8	no	—
157	C₂²×D₄	C₂³	1	2	yes	—
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	8	yes	—
162	C₂²×D₄	C₂³	1	1	yes	characteristic
163	C₂²×D₄	C₂³	1	1	yes	characteristic
164	C₂²×D₄	C₂³	1	2	yes	—
165	C₂²×D₄	C₂³	1	2	yes	—
166	C₂²×D₄	C₂³	1	1	yes	characteristic
167	C₂²×D₄	C₂³	1	1	yes	characteristic
168	C₂³×C₄	C₂³	1	2	yes	—
169	C₂³×C₄	C₂³	1	2	yes	—
170	C₂³×C₄	C₂³	1	1	yes	characteristic
171	C₂³×C₄	C₂³	1	1	yes	characteristic
172	C₂³×C₄	C₂³	1	1	yes	characteristic
173	C₂³×C₄	C₂³	1	2	yes	—
174	C₂³×C₄	C₂³	1	2	yes	—
175	C₂³×C₄	C₂³	1	2	yes	—
176	C₂³×C₄	C₂³	1	2	yes	—
177	C₂³×C₄	C₂³	1	2	yes	—
178	C₂³×C₄	C₂³	1	2	yes	—
179	C₂³×C₄	C₂³	1	2	yes	—
180	C₂³×C₄	C₂³	1	1	yes	characteristic
181	C₂³×C₄	C₂³	1	1	yes	characteristic
182	C₄⋊Q₈	C₂³	1	8	yes	complemented
183	C₄⋊Q₈	C₂³	1	8	yes	complemented
184	#126	C₂³	1	8	yes	—
185	#126	C₂³	1	16	yes	—
186	#126	C₂³	1	16	yes	—
187	#126	C₂³	1	16	yes	—
188	#126	C₂³	1	16	yes	—
189	#126	C₂³	1	16	yes	complemented
190	#126	C₂³	1	16	yes	complemented
191	#126	C₂³	1	16	yes	complemented
192	#126	C₂³	1	16	yes	complemented
193	#126	C₂³	1	8	yes	complemented
194	#126	C₂³	1	16	yes	complemented
195	#126	C₂³	1	16	yes	complemented
196	#125	C₂³	1	16	yes	complemented
197	#125	C₂³	1	8	yes	complemented
198	#125	C₂³	1	8	yes	complemented
199	#125	C₂³	1	16	yes	complemented
200	#125	C₂³	1	16	yes	complemented
201	#125	C₂³	1	8	yes	complemented
202	#124	C₂³	1	8	yes	—
203	#124	C₂³	1	8	yes	—
204	#124	C₂³	1	16	yes	—
205	#124	C₂³	1	8	yes	—
206	#124	C₂³	1	16	yes	complemented
207	#123	C₂³	1	16	yes	—
208	#123	C₂³	1	8	yes	—
209	#123	C₂³	1	16	yes	—
210	#123	C₂³	1	16	yes	—
211	#123	C₂³	1	16	yes	complemented
212	#123	C₂³	1	16	yes	complemented
213	#123	C₂³	1	8	yes	complemented
214	#123	C₂³	1	16	yes	complemented
215	#123	C₂³	1	16	yes	complemented
216	#123	C₂³	1	16	yes	complemented
217	C₂²⋊Q₈	C₂³	1	8	yes	—
218	C₂²⋊Q₈	C₂³	1	8	yes	—
219	C₂²⋊Q₈	C₂³	1	8	yes	complemented
220	C₂²⋊Q₈	C₂³	1	8	yes	complemented
221	C₂²⋊Q₈	C₂³	1	16	yes	complemented
222	C₂²⋊Q₈	C₂³	1	16	yes	complemented
223	C₂²⋊Q₈	C₂³	1	16	yes	complemented
224	C₂²⋊Q₈	C₂³	1	16	yes	complemented
225	C₂²⋊Q₈	C₂³	1	8	yes	complemented
226	C₂²⋊Q₈	C₂³	1	16	yes	complemented
227	#121	C₂³	1	8	yes	—
228	#121	C₂³	1	8	yes	—
229	#121	C₂³	1	16	yes	—
230	#121	C₂³	1	16	yes	—
231	#121	C₂³	1	8	yes	—
232	#121	C₂³	1	16	yes	complemented
233	#121	C₂³	1	16	yes	complemented
234	#120	C₂³	1	16	yes	—
235	#120	C₂³	1	16	yes	—
236	C₄×Q₈	C₂³	1	8	yes	complemented
237	C₄×Q₈	C₂³	1	8	yes	complemented
238	C₄×Q₈	C₂³	1	8	yes	complemented
239	C₄×Q₈	C₂³	1	8	yes	complemented
240	C₄×Q₈	C₂³	1	16	yes	complemented
241	C₄×Q₈	C₂³	1	8	yes	complemented
242	C₄×D₄	C₂³	1	8	yes	—
243	C₄×D₄	C₂³	1	8	yes	—
244	C₄×D₄	C₂³	1	16	yes	—
245	C₄×D₄	C₂³	1	8	yes	—
246	C₄×D₄	C₂³	1	8	yes	—
247	C₄×D₄	C₂³	1	16	yes	—
248	C₄×D₄	C₂³	1	8	yes	—
249	C₄×D₄	C₂³	1	8	yes	—
250	C₄×D₄	C₂³	1	8	yes	—
251	C₄×D₄	C₂³	1	8	yes	—
252	C₄×D₄	C₂³	1	16	yes	complemented
253	C₄×D₄	C₂³	1	16	yes	complemented
254	C₄×D₄	C₂³	1	16	yes	complemented
255	C₄×D₄	C₂³	1	16	yes	complemented
256	C₄×D₄	C₂³	1	8	yes	complemented
257	C₄×D₄	C₂³	1	16	yes	complemented
258	C₄×D₄	C₂³	1	16	yes	complemented
259	#117	C₂³	1	8	yes	—
260	#117	C₂³	1	8	yes	—
261	#117	C₂³	1	16	yes	complemented
262	#117	C₂³	1	8	yes	complemented
263	#117	C₂³	1	8	yes	complemented
264	#117	C₂³	1	16	yes	complemented
265	#117	C₂³	1	16	yes	complemented
266	#117	C₂³	1	16	yes	complemented
267	#117	C₂³	1	16	yes	complemented
268	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
299	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
300	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
301	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
302	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
308	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
309	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
311	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
312	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
313	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
314	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
315	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
318	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
320	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
321	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
323	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
326	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
330	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
334	C₂×C₄²	C₂³	1	1	yes	characteristic
335	C₂×C₄²	C₂³	1	2	yes	—
336	C₂×C₄²	C₂³	1	1	yes	characteristic
337	C₂×C₄²	C₂³	1	1	yes	characteristic
338	C₂×C₄²	C₂³	1	2	yes	—
339	C₂×C₄²	C₂³	1	2	yes	—
340	C₂×C₄²	C₂³	1	2	yes	—
341	C₂×C₄²	C₂³	1	2	yes	—
342	C₂×C₄²	C₂³	1	1	yes	characteristic
343	C₂×C₄²	C₂³	1	1	yes	characteristic
344	C₂×C₄²	C₂³	1	2	yes	—
345	C₂×C₄²	C₂³	1	1	yes	characteristic
346	C₂×C₄²	C₂³	1	16	yes	complemented
347	C₂×C₄²	C₂³	1	8	yes	complemented
348	C₂⁴	—	2	8	no	—
349	C₂⁴	—	4	4	no	—
350	C₂⁴	—	4	4	no	—
351	C₂⁴	C₂⁴	1	1	yes	characteristic
352	C₂⁴	C₂⁴	1	2	yes	—
353	C₂⁴	C₂⁴	1	1	yes	characteristic
354	C₂⁴	C₂⁴	1	1	yes	characteristic
355	C₂⁴	C₂⁴	1	2	yes	—
356	C₂⁴	C₂⁴	1	8	yes	—
357	#41	—	2	32	no	—
358	#41	—	2	32	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×Q₈	—	4	4	no	—
363	C₂×Q₈	C₂⁴	1	4	yes	—
364	C₂×Q₈	C₂⁴	1	4	yes	—
365	C₂×Q₈	C₂⁴	1	4	yes	—
366	C₂×Q₈	C₂⁴	1	8	yes	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	32	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	#41	1	8	yes	—
378	C₂×D₄	C₂⁴	1	8	yes	—
379	C₂×D₄	C₂⁴	1	4	yes	—
380	C₂×D₄	C₂⁴	1	8	yes	—
381	C₂×D₄	C₂⁴	1	8	yes	—
382	C₂×D₄	C₂⁴	1	4	yes	—
383	C₂×D₄	C₂⁴	1	4	yes	—
384	C₂×D₄	C₂⁴	1	8	yes	—
385	C₂×D₄	C₂⁴	1	8	yes	—
386	C₂×D₄	C₂⁴	1	4	yes	—
387	C₂×D₄	C₂⁴	1	4	yes	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	4	4	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	C₂⁴	1	8	yes	—
403	C₂²×C₄	C₂⁴	1	4	yes	—
404	C₂²×C₄	C₂⁴	1	8	yes	—
405	C₂²×C₄	C₂⁴	1	4	yes	—
406	C₂²×C₄	C₂⁴	1	4	yes	—
407	C₂²×C₄	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴	1	2	yes	—
411	C₂²×C₄	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴	1	2	yes	—
414	C₂²×C₄	C₂⁴	1	2	yes	—
415	C₂²×C₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴	1	2	yes	—
417	C₂²×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴	1	2	yes	—
419	C₂²×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴	1	2	yes	—
423	C₂²×C₄	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴	1	8	yes	—
425	C₂²×C₄	C₂⁴	1	8	yes	—
426	C₂²×C₄	C₂⁴	1	4	yes	—
427	C₂²×C₄	C₂⁴	1	4	yes	—
428	C₂²×C₄	C₂⁴	1	8	yes	—
429	C₂²×C₄	C₂⁴	1	8	yes	—
430	C₂²×C₄	C₂⁴	1	8	yes	—
431	C₂²×C₄	C₂⁴	1	8	yes	—
432	C₂²×C₄	C₂⁴	1	8	yes	—
433	C₂²×C₄	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄	C₂⁴	1	4	yes	—
435	C₄⋊C₄	C₂⁴	1	8	yes	—
436	C₄⋊C₄	C₂⁴	1	4	yes	—
437	C₄⋊C₄	C₂⁴	1	4	yes	—
438	C₄⋊C₄	C₂⁴	1	4	yes	—
439	C₄⋊C₄	C₂⁴	1	8	yes	—
440	C₄⋊C₄	C₂⁴	1	8	yes	—
441	C₄⋊C₄	C₂⁴	1	4	yes	—
442	C₄⋊C₄	C₂⁴	1	8	yes	—
443	C₄⋊C₄	C₂⁴	1	8	yes	—
444	C₄⋊C₄	C₂⁴	1	8	yes	—
445	C₄⋊C₄	C₂⁴	1	8	yes	—
446	C₄⋊C₄	C₂⁴	1	8	yes	—
447	C₄⋊C₄	C₂⁴	1	8	yes	—
448	C₄⋊C₄	C₂⁴	1	4	yes	—
449	C₄⋊C₄	C₂⁴	1	4	yes	—
450	C₄⋊C₄	C₂⁴	1	4	yes	—
451	C₄⋊C₄	C₂⁴	1	4	yes	—
452	C₄⋊C₄	C₂⁴	1	4	yes	—
453	C₄⋊C₄	C₂⁴	1	4	yes	—
454	C₄⋊C₄	C₂⁴	1	8	yes	—
455	C₄⋊C₄	C₂⁴	1	8	yes	—
456	C₄⋊C₄	C₂⁴	1	8	yes	—
457	C₄⋊C₄	C₂⁴	1	8	yes	—
458	C₄⋊C₄	C₂⁴	1	8	yes	—
459	C₄⋊C₄	C₂⁴	1	4	yes	—
460	C₄⋊C₄	C₂⁴	1	4	yes	—
461	C₄⋊C₄	C₂⁴	1	8	yes	—
462	C₄⋊C₄	C₂⁴	1	8	yes	—
463	C₄⋊C₄	C₂⁴	1	4	yes	—
464	C₂²⋊C₄	C₂⁴	1	4	yes	—
465	C₂²⋊C₄	C₂⁴	1	8	yes	—
466	C₂²⋊C₄	C₂⁴	1	4	yes	—
467	C₂²⋊C₄	C₂⁴	1	4	yes	—
468	C₂²⋊C₄	C₂⁴	1	4	yes	—
469	C₂²⋊C₄	C₂⁴	1	8	yes	—
470	C₂²⋊C₄	C₂⁴	1	8	yes	—
471	C₂²⋊C₄	C₂⁴	1	8	yes	—
472	C₂²⋊C₄	C₂⁴	1	8	yes	—
473	C₂²⋊C₄	C₂⁴	1	8	yes	—
474	C₂²⋊C₄	C₂⁴	1	8	yes	—
475	C₂²⋊C₄	C₂⁴	1	8	yes	—
476	C₂²⋊C₄	C₂⁴	1	8	yes	—
477	C₂²⋊C₄	C₂⁴	1	8	yes	—
478	C₂²⋊C₄	C₂⁴	1	8	yes	—
479	C₂²⋊C₄	C₂⁴	1	4	yes	—
480	C₂²⋊C₄	C₂⁴	1	8	yes	—
481	C₂²⋊C₄	C₂⁴	1	8	yes	—
482	C₂²⋊C₄	C₂⁴	1	4	yes	—
483	C₂²⋊C₄	C₂⁴	1	8	yes	—
484	C₂²⋊C₄	C₂⁴	1	4	yes	—
485	C₂²⋊C₄	C₂⁴	1	8	yes	—
486	C₂²⋊C₄	C₂⁴	1	8	yes	—
487	C₂²⋊C₄	C₂⁴	1	8	yes	—
488	C₂²⋊C₄	C₂⁴	1	4	yes	—
489	C₂²⋊C₄	C₂⁴	1	4	yes	—
490	C₂²⋊C₄	C₂⁴	1	8	yes	—
491	C₂²⋊C₄	C₂⁴	1	4	yes	—
492	C₄²	C₂⁴	1	4	yes	—
493	C₄²	C₂⁴	1	4	yes	—
494	C₄²	C₂⁴	1	4	yes	—
495	C₄²	C₂⁴	1	8	yes	—
496	C₄²	C₂⁴	1	8	yes	—
497	C₄²	C₂⁴	1	4	yes	—
498	C₄²	C₂⁴	1	8	yes	—
499	C₄²	C₂⁴	1	8	yes	—
500	C₄²	C₂⁴	1	4	yes	—
501	C₄²	C₂⁴	1	8	yes	—
502	C₄²	C₂⁴	1	8	yes	—
503	C₄²	C₂⁴	1	4	yes	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	4	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	4	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	16	no	—
519	C₂³	—	4	8	no	—
520	C₂³	—	4	8	no	—
521	C₂³	—	8	16	no	—
522	C₂³	C₂×#41	1	8	yes	—
523	C₂³	C₂⁵	1	2	yes	—
524	C₂³	C₂⁵	1	4	yes	—
525	C₂³	C₂⁵	1	2	yes	—
526	C₂³	C₂⁵	1	2	yes	—
527	C₂³	C₂⁵	1	4	yes	—
528	C₂³	C₂⁵	1	1	yes	characteristic
529	Q₈	—	2	8	no	—
530	Q₈	—	2	8	no	—
531	Q₈	—	4	4	no	—
532	Q₈	—	4	8	no	—
533	D₄	—	2	16	no	—
534	D₄	—	2	16	no	—
535	D₄	—	2	16	no	—
536	D₄	—	2	8	no	—
537	D₄	—	4	8	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	8	no	—
541	D₄	—	4	4	no	—
542	D₄	C₂×#41	1	16	yes	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	16	no	—
549	C₂×C₄	—	2	16	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	8	no	—
565	C₂×C₄	—	4	8	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	8	no	—
568	C₂×C₄	—	4	8	no	—
569	C₂×C₄	—	4	8	no	—
570	C₂×C₄	—	4	8	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	4	8	no	—
574	C₂×C₄	C₂×#41	1	4	yes	—
575	C₂×C₄	C₂⁵	1	2	yes	—
576	C₂×C₄	C₂⁵	1	2	yes	—
577	C₂×C₄	C₂⁵	1	2	yes	—
578	C₂×C₄	C₂⁵	1	2	yes	—
579	C₂×C₄	C₂⁵	1	4	yes	—
580	C₂×C₄	C₂⁵	1	2	yes	—
581	C₂×C₄	C₂⁵	1	4	yes	—
582	C₂×C₄	C₂⁵	1	4	yes	—
583	C₂×C₄	C₂⁵	1	2	yes	—
584	C₂×C₄	C₂⁵	1	4	yes	—
585	C₂×C₄	C₂⁵	1	2	yes	—
586	C₂×C₄	C₂⁵	1	4	yes	—
587	C₂×C₄	C₂⁵	1	2	yes	—
588	C₂×C₄	C₂⁵	1	2	yes	—
589	C₂×C₄	C₂⁵	1	2	yes	—
590	C₂×C₄	C₂⁵	1	4	yes	—
591	C₂×C₄	C₂⁵	1	2	yes	—
592	C₂×C₄	C₂⁵	1	2	yes	—
593	C₂²	—	2	4	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	16	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	8	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	8	16	no	—
613	C₂²	C₂²×#41	1	8	yes	—
614	C₂²	C₂²×#41	1	2	yes	—
615	C₂²	#585	1	2	yes	—
616	C₂²	#585	1	2	yes	—
617	C₂²	C₂⁶	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	4	no	—
622	C₄	—	2	4	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	4	no	—
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	2	2	no	—
631	C₄	—	2	4	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	4	no	—
634	C₄	—	2	2	no	—
635	C₄	C₂²×#41	1	4	yes	—
636	C₂	—	2	8	no	—
637	C₂	—	4	2	no	—
638	C₂	—	4	2	no	—
639	C₂	—	4	4	no	—
640	C₂	—	4	2	no	—
641	C₂	#3521	1	4	yes	direct product factor
642	C₂	C₂³×#41	1	1	yes	characteristic
643	C₂	C₂×#585	1	1	yes	characteristic
644	C₂	C₂×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶
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. #3521	C₂	direct (N × H)
2. C₂×#556	C₂	semidirect
3. C₂×#556	C₂	semidirect
4. C₂×#554	C₂	semidirect
5. C₂×#553	C₂	semidirect
6. C₂×#553	C₂	semidirect
7. C₂×#552	C₂	semidirect
8. C₂×#552	C₂	semidirect
9. C₂×#551	C₂	semidirect
10. C₂×#551	C₂	semidirect
11. C₂×#547	C₂	semidirect
12. C₂×#546	C₂	semidirect
13. C₂×#546	C₂	semidirect
14. C₂×#542	C₂	semidirect
15. C₂×#541	C₂	semidirect
16. C₂×#539	C₂	semidirect
17. C₂×#538	C₂	semidirect
18. C₂×#529	C₂	semidirect
19. C₂×#529	C₂	semidirect
20. C₂×#529	C₂	semidirect
21. C₂²×#126	C₂	semidirect
22. C₂×#520	C₂	semidirect
23. C₂×#518	C₂	semidirect
24. C₂×C₄×#41	C₂	semidirect
28. #556	C₂²	semidirect
29. #556	C₂²	semidirect
30. #554	C₂²	semidirect
31. #553	C₂²	semidirect
32. #553	C₂²	semidirect
33. #552	C₂²	semidirect
34. #552	C₂²	semidirect
35. #551	C₂²	semidirect
36. #551	C₂²	semidirect
37. #547	C₂²	semidirect
38. #546	C₂²	semidirect
39. #546	C₂²	semidirect
40. #542	C₂²	semidirect
41. #541	C₂²	semidirect
42. #539	C₂²	semidirect
43. #538	C₂²	semidirect
44. C₂×C₄⋊Q₈	C₂²	semidirect
45. C₂×C₄⋊Q₈	C₂²	semidirect
46. #529	C₂²	semidirect
47. #529	C₂²	semidirect
48. #529	C₂²	semidirect
54. C₂×#126	C₂²	semidirect
55. C₂×#126	C₂²	semidirect
56. C₂×#126	C₂²	semidirect
57. C₂×#126	C₂²	semidirect
58. C₂×#126	C₂²	semidirect
59. C₂×#126	C₂²	semidirect
60. C₂×#126	C₂²	semidirect
61. C₂×#126	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
72. C₂×#124	C₂²	semidirect
77. C₂×#123	C₂²	semidirect
78. C₂×#123	C₂²	semidirect
79. C₂×#123	C₂²	semidirect
80. C₂×#123	C₂²	semidirect
81. C₂×#123	C₂²	semidirect
82. C₂×#123	C₂²	semidirect
85. C₂×C₂²⋊Q₈	C₂²	semidirect
86. C₂×C₂²⋊Q₈	C₂²	semidirect
87. C₂×C₂²⋊Q₈	C₂²	semidirect
88. C₂×C₂²⋊Q₈	C₂²	semidirect
89. C₂×C₂²⋊Q₈	C₂²	semidirect
90. C₂×C₂²⋊Q₈	C₂²	semidirect
91. C₂×C₂²⋊Q₈	C₂²	semidirect
92. C₂×C₂²⋊Q₈	C₂²	semidirect
98. C₂×#121	C₂²	semidirect
99. C₂×#121	C₂²	semidirect
102. #520	C₂²	semidirect
103. #518	C₂²	semidirect
104. C₄×#41	C₂²	semidirect
105. C₂×C₄×Q₈	C₂²	semidirect
106. C₂×C₄×Q₈	C₂²	semidirect
107. C₂×C₄×Q₈	C₂²	semidirect
108. C₂×C₄×Q₈	C₂²	semidirect
109. C₂×C₄×Q₈	C₂²	semidirect
110. C₂×C₄×Q₈	C₂²	semidirect
121. C₂×C₄×D₄	C₂²	semidirect
122. C₂×C₄×D₄	C₂²	semidirect
123. C₂×C₄×D₄	C₂²	semidirect
124. C₂×C₄×D₄	C₂²	semidirect
125. C₂×C₄×D₄	C₂²	semidirect
126. C₂×C₄×D₄	C₂²	semidirect
127. C₂×C₄×D₄	C₂²	semidirect
130. C₂×#117	C₂²	semidirect
131. C₂×#117	C₂²	semidirect
132. C₂×#117	C₂²	semidirect
133. C₂×#117	C₂²	semidirect
134. C₂×#117	C₂²	semidirect
135. C₂×#117	C₂²	semidirect
136. C₂×#117	C₂²	semidirect
137. C₂²×C₄⋊C₄	C₂²	semidirect
138. C₂²×C₄⋊C₄	C₂²	semidirect
139. C₂²×C₄⋊C₄	C₂²	semidirect
140. C₂²×C₄⋊C₄	C₂²	semidirect
145. C₂²×C₄²	C₂²	semidirect
146. C₂²×C₄²	C₂²	semidirect
182. C₄⋊Q₈	C₂³	semidirect
183. C₄⋊Q₈	C₂³	semidirect
189. #126	C₂³	semidirect
190. #126	C₂³	semidirect
191. #126	C₂³	semidirect
192. #126	C₂³	semidirect
193. #126	C₂³	semidirect
194. #126	C₂³	semidirect
195. #126	C₂³	semidirect
196. #125	C₂³	semidirect
197. #125	C₂³	semidirect
198. #125	C₂³	semidirect
199. #125	C₂³	semidirect
200. #125	C₂³	semidirect
201. #125	C₂³	semidirect
206. #124	C₂³	semidirect
211. #123	C₂³	semidirect
212. #123	C₂³	semidirect
213. #123	C₂³	semidirect
214. #123	C₂³	semidirect
215. #123	C₂³	semidirect
216. #123	C₂³	semidirect
219. C₂²⋊Q₈	C₂³	semidirect
220. C₂²⋊Q₈	C₂³	semidirect
221. C₂²⋊Q₈	C₂³	semidirect
222. C₂²⋊Q₈	C₂³	semidirect
223. C₂²⋊Q₈	C₂³	semidirect
224. C₂²⋊Q₈	C₂³	semidirect
225. C₂²⋊Q₈	C₂³	semidirect
226. C₂²⋊Q₈	C₂³	semidirect
232. #121	C₂³	semidirect
233. #121	C₂³	semidirect
236. C₄×Q₈	C₂³	semidirect
237. C₄×Q₈	C₂³	semidirect
238. C₄×Q₈	C₂³	semidirect
239. C₄×Q₈	C₂³	semidirect
240. C₄×Q₈	C₂³	semidirect
241. C₄×Q₈	C₂³	semidirect
252. C₄×D₄	C₂³	semidirect
253. C₄×D₄	C₂³	semidirect
254. C₄×D₄	C₂³	semidirect
255. C₄×D₄	C₂³	semidirect
256. C₄×D₄	C₂³	semidirect
257. C₄×D₄	C₂³	semidirect
258. C₄×D₄	C₂³	semidirect
261. #117	C₂³	semidirect
262. #117	C₂³	semidirect
263. #117	C₂³	semidirect
264. #117	C₂³	semidirect
265. #117	C₂³	semidirect
266. #117	C₂³	semidirect
267. #117	C₂³	semidirect
298. C₂×C₄⋊C₄	C₂³	semidirect
299. C₂×C₄⋊C₄	C₂³	semidirect
300. C₂×C₄⋊C₄	C₂³	semidirect
301. C₂×C₄⋊C₄	C₂³	semidirect
346. C₂×C₄²	C₂³	semidirect
347. C₂×C₄²	C₂³	semidirect
641. C₂	#3521	direct (N × H)

Maximal subgroups

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

subgroup	index
#3521	2
C₂×#556	2
C₂×#554	2
C₂×#553	2
C₂×#552	2
C₂×#551	2
C₂×#547	2
C₂×#546	2
C₂×#542	2
C₂×#541	2
C₂×#539	2
C₂×#538	2
C₂×#529	2
C₂²×#126	2
C₂×#520	2
C₂×#518	2
C₂×C₄×#41	2

Subgroups — C2×#3521 #62780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3521 #62780