Subgroups — C₂×C₄₇×#2925 #26099820

Order 12032.

2178 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2925	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄₇×#433	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×#432	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#431	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#408	C₂	1	2	yes	maximal
9	C₂×C₄₇×#405	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
12	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
13	C₄×#41×C₄₇	C₄	1	8	yes	—
14	C₄×#41×C₄₇	C₂²	1	8	yes	—
15	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
18	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
20	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic
21	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#117×C₄₇	C₂²	1	2	yes	—
23	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
25	C₄₇×#433	C₂²	1	32	yes	complemented
26	C₄₇×#432	C₂²	1	16	yes	complemented
27	C₄₇×#431	C₂²	1	16	yes	complemented
28	C₄₇×#423	C₂²	1	8	yes	complemented
29	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
32	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
34	C₂×C₄⋊C₈×C₄₇	C₂²	1	8	yes	complemented
35	C₄₇×#408	C₂²	1	16	yes	—
36	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
37	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
38	C₄₇×#405	C₂²	1	16	yes	complemented
39	C₂×#97×C₄₇	C₂²	1	4	yes	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	4	yes	—
41	C₂×#41×C₄₇	—	2	4	no	—
42	C₂×#41×C₄₇	—	2	4	no	—
43	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
44	C₂×#41×C₄₇	C₂³	1	4	yes	—
45	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
51	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₄₇	—	2	8	no	—
55	C₂×M₁₆×C₄₇	C₂³	1	8	yes	—
56	C₂²×C₈×C₄₇	—	2	8	no	—
57	C₂²×C₈×C₄₇	C₂³	1	8	yes	—
58	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
61	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
62	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
63	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	—
64	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
65	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	—
66	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
67	#117×C₄₇	C₂×C₄	1	8	yes	—
68	#117×C₄₇	C₂×C₄	1	4	yes	—
69	#117×C₄₇	C₂³	1	4	yes	—
70	#117×C₄₇	C₂³	1	8	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
83	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
84	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
85	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
90	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
91	C₄⋊C₈×C₄₇	C₂³	1	8	yes	—
92	C₄⋊C₈×C₄₇	C₂³	1	8	yes	—
93	C₄⋊C₈×C₄₇	C₂³	1	8	yes	—
94	C₂²⋊C₈×C₄₇	C₂³	1	16	yes	—
95	C₂²⋊C₈×C₄₇	C₂³	1	16	yes	—
96	#97×C₄₇	C₂³	1	16	yes	—
97	C₄×C₈×C₄₇	C₂³	1	16	yes	—
98	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	#41×C₄₇	—	2	16	no	—
101	#41×C₄₇	—	2	8	no	—
102	#41×C₄₇	—	2	8	no	—
103	C₂×Q₈×C₄₇	—	2	4	no	—
104	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
105	C₂×D₄×C₄₇	—	2	8	no	—
106	C₂×D₄×C₄₇	—	2	4	no	—
107	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
108	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	8	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	4	2	no	—
114	C₂²×C₄×C₄₇	—	4	4	no	—
115	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
123	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
125	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	#41	1	4	yes	—
130	C₂²×C₄×C₄₇	#41	1	4	yes	—
131	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
134	M₁₆×C₄₇	—	2	16	no	—
135	C₂×C₈×C₄₇	—	2	4	no	—
136	C₂×C₈×C₄₇	—	2	4	no	—
137	C₂×C₈×C₄₇	—	2	16	no	—
138	C₂×C₈×C₄₇	—	2	8	no	—
139	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
140	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
141	C₂×C₈×C₄₇	C₂⁴	1	8	yes	—
142	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
143	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
144	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
145	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
146	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
147	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
148	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
149	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
150	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
151	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
152	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
153	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
154	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
155	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
156	C₄²×C₄₇	C₂⁴	1	2	yes	—
157	C₄²×C₄₇	C₂⁴	1	2	yes	—
158	C₄²×C₄₇	C₂⁴	1	4	yes	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	2	4	no	—
162	C₂³×C₄₇	—	2	4	no	—
163	C₂³×C₄₇	—	2	4	no	—
164	C₂³×C₄₇	#117	1	4	yes	—
165	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
166	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
167	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	Q₈×C₄₇	—	2	8	no	—
169	D₄×C₄₇	—	2	16	no	—
170	D₄×C₄₇	—	2	8	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	2	8	no	—
178	C₂×C₄×C₄₇	—	2	8	no	—
179	C₂×C₄×C₄₇	—	2	16	no	—
180	C₂×C₄×C₄₇	—	2	4	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	4	4	no	—
183	C₂×C₄×C₄₇	—	4	8	no	—
184	C₂×C₄×C₄₇	#117	1	4	yes	—
185	C₂×C₄×C₄₇	#117	1	8	yes	—
186	C₂×C₄×C₄₇	#131	1	4	yes	—
187	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
188	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
189	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
191	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
193	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
195	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
196	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
197	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
198	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
199	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
200	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
201	C₈×C₄₇	—	2	4	no	—
202	C₈×C₄₇	—	2	4	no	—
203	C₈×C₄₇	—	2	8	no	—
204	C₂×#2925	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₄₇	—	2	8	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	2	no	—
208	C₂²×C₄₇	—	2	4	no	—
209	C₂²×C₄₇	—	2	4	no	—
210	C₂²×C₄₇	—	2	4	no	—
211	C₂²×C₄₇	—	4	8	no	—
212	C₂²×C₄₇	C₂×#117	1	4	yes	—
213	C₂²×C₄₇	C₂×#117	1	2	yes	—
214	C₂²×C₄₇	C₂×#131	1	2	yes	—
215	C₂²×C₄₇	#568	1	2	yes	—
216	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
217	C₄×C₄₇	—	2	4	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	2	4	no	—
220	C₄×C₄₇	—	2	2	no	—
221	C₄×C₄₇	—	2	2	no	—
222	C₄×C₄₇	—	2	4	no	—
223	C₄×C₄₇	C₂×#117	1	2	yes	—
224	C₄×C₄₇	C₂×#117	1	4	yes	—
225	C₄×C₄₇	C₂×#131	1	4	yes	—
226	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
227	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
228	C₂×C₄×#41	C₂×C₄₇	1	1	yes	characteristic
229	#2925	C₂×C₄₇	1	16	yes	direct product factor
230	C₂×#433	C₂×C₄₇	1	4	yes	complemented
231	C₂×#432	C₂×C₄₇	1	2	yes	complemented
232	C₂×#431	C₂×C₄₇	1	2	yes	complemented
233	C₂×#423	C₂×C₄₇	1	1	yes	characteristic, complemented
234	C₂²×C₄⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
235	C₂×#408	C₂×C₄₇	1	2	yes	—
236	C₂×#405	C₂×C₄₇	1	2	yes	complemented
237	C₂×C₄₇	—	2	4	no	—
238	C₂×C₄₇	—	4	4	no	—
239	C₂×C₄₇	#2925	1	4	yes	direct product factor
240	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
241	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
242	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
243	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
244	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
245	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
246	C₄×#41	C₄×C₄₇	1	8	yes	—
247	C₄×#41	C₂²×C₄₇	1	8	yes	—
248	C₂×C₄×Q₈	C₄×C₄₇	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₄×C₄₇	1	1	yes	characteristic
250	C₂×C₄×D₄	C₄×C₄₇	1	2	yes	—
251	C₂×C₄×D₄	C₄×C₄₇	1	1	yes	characteristic
252	C₂×C₄×D₄	C₄×C₄₇	1	2	yes	—
253	C₂×C₄×D₄	C₄×C₄₇	1	1	yes	characteristic
254	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
255	C₂×#117	C₂²×C₄₇	1	2	yes	—
256	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
257	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
258	#433	C₂²×C₄₇	1	32	yes	complemented
259	#432	C₂²×C₄₇	1	16	yes	complemented
260	#431	C₂²×C₄₇	1	16	yes	complemented
261	#423	C₂²×C₄₇	1	8	yes	complemented
262	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
266	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
267	C₂×C₄⋊C₈	C₂²×C₄₇	1	8	yes	complemented
268	#408	C₂²×C₄₇	1	16	yes	—
269	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
271	#405	C₂²×C₄₇	1	16	yes	complemented
272	C₂×#97	C₂²×C₄₇	1	4	yes	—
273	C₂×C₄×C₈	C₂²×C₄₇	1	4	yes	—
274	C₄₇	C₂×#2925	1	1	yes	characteristic, direct product factor, Sylow
275	C₂×#41	—	2	4	no	—
276	C₂×#41	—	2	4	no	—
277	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
278	C₂×#41	C₂³×C₄₇	1	4	yes	—
279	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
280	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
281	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
282	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
283	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
284	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
285	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
287	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
288	C₂×M₁₆	—	2	8	no	—
289	C₂×M₁₆	C₂³×C₄₇	1	8	yes	—
290	C₂²×C₈	—	2	8	no	—
291	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
292	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
293	C₂²×C₈	C₂³×C₄₇	1	8	yes	—
294	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
295	C₄×Q₈	C₂×C₄×C₄₇	1	8	yes	—
296	C₄×Q₈	C₂×C₄×C₄₇	1	8	yes	—
297	C₄×D₄	C₂×C₄×C₄₇	1	16	yes	—
298	C₄×D₄	C₂×C₄×C₄₇	1	8	yes	—
299	C₄×D₄	C₂×C₄×C₄₇	1	16	yes	—
300	C₄×D₄	C₂×C₄×C₄₇	1	8	yes	—
301	#117	C₂×C₄×C₄₇	1	8	yes	—
302	#117	C₂×C₄×C₄₇	1	4	yes	—
303	#117	C₂³×C₄₇	1	4	yes	—
304	#117	C₂³×C₄₇	1	8	yes	—
305	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
311	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
312	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
313	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
314	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
315	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
316	C₂×C₄²	C₂×C₄×C₄₇	1	8	yes	—
317	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
318	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
319	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
321	C₂×C₄²	C₂³×C₄₇	1	8	yes	—
322	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
323	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
324	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
325	C₄⋊C₈	C₂³×C₄₇	1	8	yes	—
326	C₄⋊C₈	C₂³×C₄₇	1	8	yes	—
327	C₄⋊C₈	C₂³×C₄₇	1	8	yes	—
328	C₂²⋊C₈	C₂³×C₄₇	1	16	yes	—
329	C₂²⋊C₈	C₂³×C₄₇	1	16	yes	—
330	#97	C₂³×C₄₇	1	16	yes	—
331	C₄×C₈	C₂³×C₄₇	1	16	yes	—
332	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
333	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
334	#41	—	2	16	no	—
335	#41	—	2	8	no	—
336	#41	—	2	8	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	C₂²×C₄×C₄₇	1	8	yes	—
342	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
351	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
352	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
353	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
355	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₄₇	1	8	yes	—
357	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
358	C₂²×C₄	C₂²×C₄×C₄₇	1	8	yes	—
359	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
360	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
362	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
363	C₂²×C₄	#41×C₄₇	1	4	yes	—
364	C₂²×C₄	#41×C₄₇	1	4	yes	—
365	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
368	M₁₆	—	2	16	no	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	2	16	no	—
372	C₂×C₈	—	2	8	no	—
373	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
374	C₂×C₈	C₂⁴×C₄₇	1	8	yes	—
375	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
376	C₄⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
377	C₄⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
378	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
379	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
380	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
381	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
382	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
383	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
384	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
385	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
386	C₄²	C₂²×C₄×C₄₇	1	8	yes	—
387	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
388	C₄²	C₂²×C₄×C₄₇	1	8	yes	—
389	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
390	C₄²	C₂⁴×C₄₇	1	4	yes	—
391	C₄²	C₂⁴×C₄₇	1	2	yes	—
392	C₄²	C₂⁴×C₄₇	1	2	yes	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	#117×C₄₇	1	4	yes	—
399	C₂³	C₂³×C₄×C₄₇	1	4	yes	—
400	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
401	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
402	Q₈	—	2	8	no	—
403	D₄	—	2	16	no	—
404	D₄	—	2	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	#117×C₄₇	1	4	yes	—
419	C₂×C₄	#117×C₄₇	1	8	yes	—
420	C₂×C₄	#131×C₄₇	1	4	yes	—
421	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
422	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
423	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
424	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
425	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
426	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
427	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
428	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
429	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
430	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
431	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
432	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
433	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
434	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
435	C₈	—	2	4	no	—
436	C₈	—	2	4	no	—
437	C₈	—	2	8	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	8	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	8	no	—
445	C₂²	C₂×#117×C₄₇	1	4	yes	—
446	C₂²	C₂×#117×C₄₇	1	2	yes	—
447	C₂²	C₂×#131×C₄₇	1	2	yes	—
448	C₂²	C₄₇×#568	1	2	yes	—
449	C₂²	C₂⁴×C₄×C₄₇	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	2	4	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	4	no	—
455	C₄	—	2	4	no	—
456	C₄	C₂×#117×C₄₇	1	2	yes	—
457	C₄	C₂×#117×C₄₇	1	4	yes	—
458	C₄	C₂×#131×C₄₇	1	4	yes	—
459	C₄	C₂²×#41×C₄₇	1	1	yes	characteristic
460	C₄	C₂²×#41×C₄₇	1	1	yes	characteristic
461	C₂	—	2	4	no	—
462	C₂	—	4	4	no	—
463	C₂	C₄₇×#2925	1	4	yes	direct product factor
464	C₂	C₂²×#117×C₄₇	1	1	yes	characteristic
465	C₂	C₂²×#131×C₄₇	1	1	yes	characteristic
466	C₂	C₂×C₄₇×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₄₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2925	C₂	direct (N × H)
3. C₂×C₄₇×#433	C₂	semidirect
4. C₂×C₄₇×#432	C₂	semidirect
5. C₂×C₄₇×#431	C₂	semidirect
6. C₂×C₄₇×#423	C₂	semidirect
7. C₂²×C₄⋊C₈×C₄₇	C₂	semidirect
9. C₂×C₄₇×#405	C₂	semidirect
25. C₄₇×#433	C₂²	semidirect
26. C₄₇×#432	C₂²	semidirect
27. C₄₇×#431	C₂²	semidirect
28. C₄₇×#423	C₂²	semidirect
34. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
38. C₄₇×#405	C₂²	semidirect
204. C₂×#2925	C₄₇	direct (N × H)
229. #2925	C₂×C₄₇	direct (N × H)
230. C₂×#433	C₂×C₄₇	semidirect
231. C₂×#432	C₂×C₄₇	semidirect
232. C₂×#431	C₂×C₄₇	semidirect
233. C₂×#423	C₂×C₄₇	semidirect
234. C₂²×C₄⋊C₈	C₂×C₄₇	semidirect
236. C₂×#405	C₂×C₄₇	semidirect
239. C₂×C₄₇	#2925	direct (N × H)
258. #433	C₂²×C₄₇	semidirect
259. #432	C₂²×C₄₇	semidirect
260. #431	C₂²×C₄₇	semidirect
261. #423	C₂²×C₄₇	semidirect
267. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
271. #405	C₂²×C₄₇	semidirect
274. C₄₇	C₂×#2925	direct (N × H)
463. C₂	C₄₇×#2925	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×C₄×#41×C₄₇	2
C₄₇×#2925	2
C₂×C₄₇×#433	2
C₂×C₄₇×#432	2
C₂×C₄₇×#431	2
C₂×C₄₇×#423	2
C₂²×C₄⋊C₈×C₄₇	2
C₂×C₄₇×#408	2
C₂×C₄₇×#405	2
C₂×#2925	47

Subgroups — C2×C47×#2925 #26099820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2925 #26099820