Subgroups — C₂×#20243408 #26215815

Order 12032.

1618 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13093951	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243408	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688882	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
9	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
10	#15689147	—	2	2	no	—
11	#15689147	C₂²	1	4	yes	complemented
12	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
13	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
14	C₂×#13093951	—	2	8	no	—
15	C₂×#13093951	C₂²	1	8	yes	—
16	C₄×C₄⋊Dic₄₇	—	2	2	no	—
17	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
18	C₂×C₄₇⋊#95	—	2	1	no	—
19	#15688882	C₂²	1	8	yes	complemented
20	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
21	C₄×#41×C₄₇	—	2	2	no	—
22	C₄×#41×C₄₇	—	2	2	no	—
23	C₄×#41×C₄₇	C₄	1	4	yes	complemented
24	C₄×#41×C₄₇	C₂²	1	4	yes	—
25	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
26	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₄₇	—	2	1	no	—
28	C₂×C₄×D₄×C₄₇	—	2	1	no	—
29	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic, complemented
31	C₂×#117×C₄₇	—	2	1	no	—
32	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₄₇	—	2	1	no	—
34	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₂³×Dic₄₇	—	2	2	no	—
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	4	no	—
38	C₂×#10625329	—	2	4	no	—
39	C₂×#10625329	C₂³	1	4	yes	—
40	C₂²×C₄₇⋊C₈	—	2	2	no	—
41	C₂×C₄⋊Dic₄₇	—	2	8	no	—
42	C₂×C₄⋊Dic₄₇	—	2	4	no	—
43	C₂×C₄×Dic₄₇	—	2	4	no	—
44	C₂×C₄×Dic₄₇	—	2	4	no	—
45	C₂×C₄×Dic₄₇	—	2	2	no	—
46	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
47	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
48	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
49	#13093951	—	2	16	no	—
50	C₄₇⋊#95	—	2	4	no	—
51	C₂×#41×C₄₇	—	2	1	no	—
52	C₂×#41×C₄₇	—	2	1	no	—
53	C₂×#41×C₄₇	—	2	2	no	—
54	C₂×#41×C₄₇	—	2	2	no	—
55	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×#41×C₄₇	D₄	1	4	yes	—
57	C₂×#41×C₄₇	Q₈	1	4	yes	—
58	C₂×#41×C₄₇	C₂³	1	2	yes	—
59	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₄₇	—	2	1	no	—
61	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	—	2	1	no	—
63	C₂³×C₄×C₄₇	—	2	1	no	—
64	C₂³×C₄×C₄₇	—	2	1	no	—
65	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₄×Q₈×C₄₇	—	2	2	no	—
69	C₄×Q₈×C₄₇	—	2	2	no	—
70	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
71	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
72	C₄×D₄×C₄₇	—	2	4	no	—
73	C₄×D₄×C₄₇	—	2	4	no	—
74	C₄×D₄×C₄₇	—	2	4	no	—
75	C₄×D₄×C₄₇	—	2	4	no	—
76	C₄×D₄×C₄₇	—	2	2	no	—
77	C₄×D₄×C₄₇	—	2	2	no	—
78	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
79	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
80	#117×C₄₇	—	2	1	no	—
81	#117×C₄₇	—	2	1	no	—
82	#117×C₄₇	—	2	4	no	—
83	#117×C₄₇	—	2	4	no	—
84	#117×C₄₇	C₂×C₄	1	2	yes	—
85	#117×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
93	C₂×C₄²×C₄₇	—	2	1	no	—
94	C₂×C₄²×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	—	2	1	no	—
96	C₂×C₄²×C₄₇	—	2	4	no	—
97	C₂×C₄²×C₄₇	—	2	4	no	—
98	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
101	C₂×C₄²×C₄₇	D₄	1	2	yes	—
102	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₇	D₄	1	2	yes	—
105	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
106	C₂⁴×C₄₇	—	2	1	no	—
107	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
108	#41×C₄₇	—	2	4	no	—
109	#41×C₄₇	—	2	4	no	—
110	#41×C₄₇	—	2	4	no	—
111	#41×C₄₇	—	2	4	no	—
112	#41×C₄₇	—	2	4	no	—
113	#41×C₄₇	—	2	2	no	—
114	#41×C₄₇	—	2	2	no	—
115	#41×C₄₇	C₄⋊C₄	1	8	yes	complemented
116	#41×C₄₇	C₂×D₄	1	4	yes	—
117	#41×C₄₇	C₂×Q₈	1	4	yes	—
118	C₂×Q₈×C₄₇	—	2	1	no	—
119	C₂×Q₈×C₄₇	—	2	2	no	—
120	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	complemented
121	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂×D₄×C₄₇	—	2	2	no	—
123	C₂×D₄×C₄₇	—	2	4	no	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	1	no	—
127	C₂×D₄×C₄₇	—	2	2	no	—
128	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	complemented
129	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	4	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	4	no	—
134	C₂²×C₄×C₄₇	—	2	4	no	—
135	C₂²×C₄×C₄₇	—	2	2	no	—
136	C₂²×C₄×C₄₇	—	2	1	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	4	no	—
139	C₂²×C₄×C₄₇	—	2	4	no	—
140	C₂²×C₄×C₄₇	—	4	2	no	—
141	C₂²×C₄×C₄₇	—	4	4	no	—
142	C₂²×C₄×C₄₇	—	4	4	no	—
143	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
147	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
148	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
158	C₂²×C₄×C₄₇	#41	1	2	yes	—
159	C₂²×C₄×C₄₇	#41	1	2	yes	—
160	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
161	C₂²×Dic₄₇	—	2	8	no	—
162	C₂²×Dic₄₇	—	2	4	no	—
163	C₂²×Dic₄₇	—	4	4	no	—
164	C₂²×Dic₄₇	—	4	4	no	—
165	C₄⋊C₄×C₄₇	—	2	4	no	—
166	C₄⋊C₄×C₄₇	—	2	4	no	—
167	C₄⋊C₄×C₄₇	—	2	1	no	—
168	C₄⋊C₄×C₄₇	—	2	1	no	—
169	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
170	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
171	C₂²⋊C₄×C₄₇	—	2	2	no	—
172	C₂²⋊C₄×C₄₇	—	2	2	no	—
173	C₂²⋊C₄×C₄₇	—	2	4	no	—
174	C₂²⋊C₄×C₄₇	—	2	4	no	—
175	C₄²×C₄₇	—	2	2	no	—
176	C₄²×C₄₇	—	2	4	no	—
177	C₄²×C₄₇	—	2	4	no	—
178	C₄²×C₄₇	—	2	2	no	—
179	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
180	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
181	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
182	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
183	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
184	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
185	C₄²×C₄₇	C₂×D₄	1	2	yes	—
186	C₄²×C₄₇	C₂×D₄	1	2	yes	—
187	C₄⋊Dic₄₇	—	2	16	no	—
188	C₄×Dic₄₇	—	2	4	no	—
189	C₄×Dic₄₇	—	2	4	no	—
190	C₄×Dic₄₇	—	4	4	no	—
191	#10625329	—	2	4	no	—
192	#10625329	—	2	4	no	—
193	#10625329	—	4	4	no	—
194	C₂×C₄₇⋊C₈	—	2	4	no	—
195	C₂×C₄₇⋊C₈	—	4	4	no	—
196	C₂³×C₄₇	—	2	2	no	—
197	C₂³×C₄₇	—	2	2	no	—
198	C₂³×C₄₇	—	2	2	no	—
199	C₂³×C₄₇	—	2	4	no	—
200	C₂³×C₄₇	—	4	2	no	—
201	C₂³×C₄₇	—	4	2	no	—
202	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×C₄₇	#121	1	2	yes	—
205	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
206	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₄₇	—	2	2	no	—
208	Q₈×C₄₇	—	2	4	no	—
209	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	complemented
210	D₄×C₄₇	—	2	4	no	—
211	D₄×C₄₇	—	2	4	no	—
212	D₄×C₄₇	—	2	8	no	—
213	D₄×C₄₇	—	2	2	no	—
214	D₄×C₄₇	—	2	4	no	—
215	D₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	complemented
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	4	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	4	no	—
222	C₂×C₄×C₄₇	—	2	4	no	—
223	C₂×C₄×C₄₇	—	2	8	no	—
224	C₂×C₄×C₄₇	—	2	4	no	—
225	C₂×C₄×C₄₇	—	2	4	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	4	2	no	—
229	C₂×C₄×C₄₇	—	4	2	no	—
230	C₂×C₄×C₄₇	—	4	8	no	—
231	C₂×C₄×C₄₇	—	4	2	no	—
232	C₂×C₄×C₄₇	—	4	2	no	—
233	C₂×C₄×C₄₇	—	4	8	no	—
234	C₂×C₄×C₄₇	#104	1	4	yes	complemented
235	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
236	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
237	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
241	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
242	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
243	C₂×C₄×C₄₇	#117	1	2	yes	—
244	C₂×C₄×C₄₇	#117	1	2	yes	—
245	C₂×C₄×C₄₇	#121	1	2	yes	—
246	C₂×C₄×C₄₇	#121	1	2	yes	—
247	C₂×C₄×C₄₇	#121	1	2	yes	—
248	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
249	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
250	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
251	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
257	C₂×Dic₄₇	—	2	8	no	—
258	C₂×Dic₄₇	—	4	16	no	—
259	C₂×Dic₄₇	—	4	4	no	—
260	C₂×Dic₄₇	—	4	4	no	—
261	C₄₇⋊C₈	—	4	4	no	—
262	C₂×#1806	—	47	1	no	maximal, Sylow
263	C₂²×C₄₇	—	2	4	no	—
264	C₂²×C₄₇	—	2	4	no	—
265	C₂²×C₄₇	—	2	1	no	—
266	C₂²×C₄₇	—	2	1	no	—
267	C₂²×C₄₇	—	2	1	no	—
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	—	2	4	no	—
270	C₂²×C₄₇	—	4	8	no	—
271	C₂²×C₄₇	—	4	2	no	—
272	C₂²×C₄₇	—	4	2	no	—
273	C₂²×C₄₇	#380	1	2	yes	—
274	C₂²×C₄₇	#380	1	2	yes	—
275	C₂²×C₄₇	C₂×#104	1	2	yes	—
276	C₂²×C₄₇	#421	1	2	yes	—
277	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
278	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
279	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
280	C₄×C₄₇	—	2	2	no	—
281	C₄×C₄₇	—	2	2	no	—
282	C₄×C₄₇	—	2	2	no	—
283	C₄×C₄₇	—	2	4	no	—
284	C₄×C₄₇	—	4	2	no	—
285	C₄×C₄₇	—	4	2	no	—
286	C₄×C₄₇	#380	1	2	yes	—
287	C₄×C₄₇	#380	1	2	yes	—
288	C₄×C₄₇	C₂×#104	1	4	yes	complemented
289	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
290	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
291	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
292	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
293	Dic₄₇	—	4	8	no	—
294	C₂×C₄×#41	D₄₇	1	1	yes	characteristic
295	C₂×#423	—	47	1	no	—
296	C₂²×#104	—	47	2	no	—
297	C₂×C₄×C₄⋊C₄	—	47	1	no	—
298	#1806	—	47	8	no	—
299	C₂×#339	—	47	2	no	—
300	C₂×C₄₇	—	2	1	no	—
301	C₂×C₄₇	—	2	1	no	—
302	C₂×C₄₇	—	2	2	no	—
303	C₂×C₄₇	—	4	4	no	—
304	C₂×C₄₇	#1806	1	4	yes	complemented
305	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
306	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
307	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
308	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
309	C₂²×M₁₆	—	47	2	no	—
310	C₄×#41	—	2	2	no	—
311	C₄×#41	—	2	2	no	—
312	C₄×#41	Dic₄₇	1	4	yes	complemented
313	C₄×#41	C₂×D₄₇	1	4	yes	—
314	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
315	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
316	C₂×C₄×D₄	—	2	1	no	—
317	C₂×C₄×D₄	—	2	1	no	—
318	C₂×C₄×D₄	Dic₄₇	1	1	yes	characteristic, complemented
319	C₂×C₄×D₄	Dic₄₇	1	1	yes	characteristic, complemented
320	C₂×#117	—	2	1	no	—
321	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	—	94	1	no	—
323	C₂²×C₄²	—	2	1	no	—
324	C₂²×C₄²	—	47	2	no	—
325	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
326	#423	—	47	4	no	—
327	#423	—	94	2	no	—
328	C₂×C₄⋊C₈	—	94	1	no	—
329	C₂×C₄⋊C₈	—	94	1	no	—
330	C₂×#104	—	47	8	no	—
331	C₂×#104	—	94	8	no	—
332	C₄×C₄⋊C₄	—	47	4	no	—
333	C₄×C₄⋊C₄	—	94	2	no	—
334	C₂×#95	—	94	1	no	—
335	#339	—	47	8	no	—
336	C₄₇	C₂×#1806	1	1	yes	characteristic, complemented, Sylow
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	Dic₉₄	1	4	yes	—
342	C₂×#41	D₁₈₈	1	4	yes	—
343	C₂×#41	C₂×Dic₄₇	1	2	yes	—
344	C₂×#41	C₂²×D₄₇	1	2	yes	—
345	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	—	94	2	no	—
352	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
355	C₂×M₁₆	—	47	4	no	—
356	C₂×M₁₆	—	94	2	no	—
357	C₂×M₁₆	—	94	4	no	—
358	C₂×M₁₆	—	94	4	no	—
359	C₂²×C₈	—	94	2	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
363	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
364	C₄×D₄	—	2	4	no	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	—	2	4	no	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
371	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	4	no	—
375	#117	—	2	4	no	—
376	#117	C₂×Dic₄₇	1	2	yes	—
377	#117	C₂²×D₄₇	1	2	yes	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	94	8	no	—
381	C₂×C₄⋊C₄	—	94	4	no	—
382	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	—	2	4	no	—
391	C₂×C₄²	—	2	4	no	—
392	C₂×C₄²	—	47	4	no	—
393	C₂×C₄²	—	94	4	no	—
394	C₂×C₄²	—	94	4	no	—
395	C₂×C₄²	—	94	2	no	—
396	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
397	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
398	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
399	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
400	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
401	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
402	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
403	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
404	C₄⋊C₈	—	94	4	no	—
405	C₄⋊C₈	—	94	4	no	—
406	#104	—	94	16	no	—
407	#95	—	94	4	no	—
408	C₂⁴	—	2	1	no	—
409	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
410	#41	—	2	4	no	—
411	#41	—	2	4	no	—
412	#41	—	2	4	no	—
413	#41	—	2	4	no	—
414	#41	—	2	4	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	C₄⋊Dic₄₇	1	8	yes	complemented
418	#41	C₂×Dic₉₄	1	4	yes	—
419	#41	C₂×D₁₈₈	1	4	yes	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	C₄⋊Dic₄₇	1	4	yes	complemented
423	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	complemented
431	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	94	8	no	—
446	C₂²×C₄	—	94	4	no	—
447	C₂²×C₄	—	188	4	no	—
448	C₂²×C₄	—	188	4	no	—
449	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
450	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
451	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
452	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
453	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
454	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
456	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
457	C₂²×C₄	#10625350	1	2	yes	—
458	C₂²×C₄	#10625350	1	2	yes	—
459	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
462	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
463	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
466	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
467	M₁₆	—	94	4	no	—
468	M₁₆	—	94	4	no	—
469	M₁₆	—	188	4	no	—
470	C₂×C₈	—	94	4	no	—
471	C₂×C₈	—	188	4	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	94	16	no	—
477	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
478	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	4	no	—
485	C₄²	—	2	4	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	94	4	no	—
488	C₄²	—	94	4	no	—
489	C₄²	—	188	4	no	—
490	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
491	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
492	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
493	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
494	C₄²	C₂²×Dic₄₇	1	2	yes	—
495	C₄²	C₂²×Dic₄₇	1	2	yes	—
496	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
497	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
505	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
506	C₂³	#13093998	1	2	yes	—
507	C₂³	#13094003	1	2	yes	—
508	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
509	Q₈	—	2	4	no	—
510	Q₈	—	2	2	no	—
511	Q₈	C₂×C₄⋊Dic₄₇	1	4	yes	complemented
512	D₄	—	2	8	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	4	no	—
516	D₄	—	2	2	no	—
517	D₄	C₂×C₄⋊Dic₄₇	1	4	yes	complemented
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	8	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	8	no	—
536	C₂×C₄	—	94	8	no	—
537	C₂×C₄	—	188	4	no	—
538	C₂×C₄	—	188	16	no	—
539	C₂×C₄	—	188	4	no	—
540	C₂×C₄	#13093951	1	4	yes	complemented
541	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
542	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
543	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
544	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
545	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
546	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
547	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
548	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
549	C₂×C₄	#13093983	1	2	yes	—
550	C₂×C₄	#13093983	1	2	yes	—
551	C₂×C₄	#13093998	1	2	yes	—
552	C₂×C₄	#13093998	1	2	yes	—
553	C₂×C₄	#13093998	1	2	yes	—
554	C₂×C₄	#13094003	1	2	yes	—
555	C₂×C₄	#13094003	1	2	yes	—
556	C₂×C₄	#13094003	1	2	yes	—
557	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
558	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
560	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
561	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
562	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
563	C₈	—	188	4	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	4	no	—
569	C₂²	—	2	4	no	—
570	C₂²	—	2	4	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	8	no	—
574	C₂²	#15688983	1	2	yes	—
575	C₂²	#15688983	1	2	yes	—
576	C₂²	C₂×#13093951	1	2	yes	—
577	C₂²	#15689140	1	2	yes	—
578	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
579	C₂²	C₂×#13093998	1	1	yes	characteristic
580	C₂²	C₂×#13094003	1	1	yes	characteristic
581	C₄	—	2	4	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	188	8	no	—
588	C₄	#15688983	1	2	yes	—
589	C₄	#15688983	1	2	yes	—
590	C₄	C₂×#13093951	1	4	yes	complemented
591	C₄	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
592	C₄	C₂×#13093983	1	1	yes	characteristic
593	C₄	C₂×#13093998	1	1	yes	characteristic
594	C₄	C₂×#13094003	1	1	yes	characteristic
595	C₂	—	2	1	no	—
596	C₂	—	2	2	no	—
597	C₂	—	2	1	no	—
598	C₂	—	4	4	no	—
599	C₂	#20243408	1	4	yes	direct product factor
600	C₂	C₂×#15688983	1	1	yes	characteristic
601	C₂	C₂²×#13093951	1	1	yes	characteristic
602	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×#41×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×#41	D₄₇
hypocenter	C₄₇	C₂×#1806
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#15689147	C₂	semidirect
3. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
4. #20243408	C₂	direct (N × H)
5. C₂×#15688882	C₂	semidirect
11. #15689147	C₂²	semidirect
17. C₄×C₄⋊Dic₄₇	C₂²	semidirect
19. #15688882	C₂²	semidirect
23. C₄×#41×C₄₇	C₄	semidirect
25. C₂×C₄×Q₈×C₄₇	C₄	semidirect
26. C₂×C₄×Q₈×C₄₇	C₄	semidirect
29. C₂×C₄×D₄×C₄₇	C₄	semidirect
30. C₂×C₄×D₄×C₄₇	C₄	semidirect
70. C₄×Q₈×C₄₇	C₂×C₄	semidirect
71. C₄×Q₈×C₄₇	C₂×C₄	semidirect
78. C₄×D₄×C₄₇	C₂×C₄	semidirect
79. C₄×D₄×C₄₇	C₂×C₄	semidirect
115. #41×C₄₇	C₄⋊C₄	semidirect
120. C₂×Q₈×C₄₇	C₄⋊C₄	semidirect
128. C₂×D₄×C₄₇	C₄⋊C₄	semidirect
209. Q₈×C₄₇	C₂×C₄⋊C₄	semidirect
215. D₄×C₄₇	C₂×C₄⋊C₄	semidirect
234. C₂×C₄×C₄₇	#104	semidirect
288. C₄×C₄₇	C₂×#104	semidirect
304. C₂×C₄₇	#1806	semidirect
312. C₄×#41	Dic₄₇	semidirect
314. C₂×C₄×Q₈	Dic₄₇	semidirect
315. C₂×C₄×Q₈	Dic₄₇	semidirect
318. C₂×C₄×D₄	Dic₄₇	semidirect
319. C₂×C₄×D₄	Dic₄₇	semidirect
336. C₄₇	C₂×#1806	semidirect
362. C₄×Q₈	C₂×Dic₄₇	semidirect
363. C₄×Q₈	C₂×Dic₄₇	semidirect
370. C₄×D₄	C₂×Dic₄₇	semidirect
371. C₄×D₄	C₂×Dic₄₇	semidirect
417. #41	C₄⋊Dic₄₇	semidirect
422. C₂×Q₈	C₄⋊Dic₄₇	semidirect
430. C₂×D₄	C₄⋊Dic₄₇	semidirect
511. Q₈	C₂×C₄⋊Dic₄₇	semidirect
517. D₄	C₂×C₄⋊Dic₄₇	semidirect
540. C₂×C₄	#13093951	semidirect
590. C₄	C₂×#13093951	semidirect
599. C₂	#20243408	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂²×#13093951	2
C₂×C₄×C₄⋊Dic₄₇	2
#20243408	2
C₂×#15688882	2
C₂×C₄×#41×C₄₇	2
C₂×#1806	47

Subgroups — C2×#20243408 #26215815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243408 #26215815