Subgroups — #26232492

Order 12032.

1474 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244350	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244341	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243817	C₂	1	2	yes	maximal, complemented
6	#20243706	C₂	1	2	yes	maximal, complemented
7	#20243474	C₂	1	2	yes	maximal, complemented
8	#20243388	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13093945	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688885	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#547	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	—	2	1	no	—
14	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
15	D₄×C₄₇⋊C₈	—	2	4	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#13093945	C₂²	1	1	yes	characteristic
18	C₂×#13093945	C₂²	1	1	yes	characteristic
19	C₂×#13093945	C₂²	1	2	yes	—
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	#15689022	—	2	1	no	—
23	#15688998	—	2	2	no	—
24	#15688993	C₂²	1	1	yes	characteristic
25	#15688983	C₂²	1	2	yes	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	#15688885	C₂²	1	1	yes	characteristic
28	#15688885	C₂²	1	1	yes	characteristic
29	#15688885	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	C₂²×#41×C₄₇	—	2	1	no	—
35	C₄₇×#547	—	2	4	no	—
36	C₄₇×#547	C₄	1	8	yes	complemented
37	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#123×C₄₇	—	2	2	no	—
39	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
40	C₂×#121×C₄₇	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
44	C₂³×Dic₄₇	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	—	2	4	no	—
46	C₂²×C₄₇⋊C₈	—	2	4	no	—
47	C₂²×C₄₇⋊C₈	—	4	2	no	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	D₄×Dic₄₇	—	4	4	no	—
52	C₂×C₄⋊Dic₄₇	—	2	4	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	—	2	2	no	—
55	C₂×C₄⋊Dic₄₇	—	2	1	no	—
56	C₂×C₄⋊Dic₄₇	—	4	2	no	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
63	#13093945	—	2	2	no	—
64	#13093945	—	2	2	no	—
65	#13093945	—	4	2	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
67	C₄×C₄₇⋊C₈	—	2	2	no	—
68	C₄₇⋊#95	—	2	1	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₂×#41×C₄₇	—	2	8	no	—
71	C₂×#41×C₄₇	—	4	4	no	—
72	C₂×#41×C₄₇	—	4	4	no	—
73	C₂²×Q₈×C₄₇	—	2	1	no	—
74	C₂²×D₄×C₄₇	—	2	2	no	—
75	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
76	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₄₇	—	2	2	no	—
78	C₂³×C₄×C₄₇	—	2	1	no	—
79	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
80	C₄⋊Q₈×C₄₇	—	2	2	no	—
81	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
82	#123×C₄₇	—	2	16	no	—
83	C₂²⋊Q₈×C₄₇	—	2	8	no	—
84	#121×C₄₇	—	2	4	no	—
85	#121×C₄₇	C₂×C₄	1	8	yes	complemented
86	C₄×D₄×C₄₇	—	2	2	no	—
87	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
88	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
89	C₄×D₄×C₄₇	D₄	1	4	yes	—
90	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
91	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
92	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
94	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₂⁴×C₄₇	—	2	1	no	—
102	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
103	#41×C₄₇	—	4	32	no	—
104	C₂×Q₈×C₄₇	—	2	4	no	—
105	C₂×Q₈×C₄₇	—	4	2	no	—
106	C₂×Q₈×C₄₇	—	4	2	no	—
107	C₂×D₄×C₄₇	—	2	8	no	—
108	C₂×D₄×C₄₇	—	2	1	no	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	—	2	1	no	—
113	C₂×D₄×C₄₇	—	4	4	no	—
114	C₂×D₄×C₄₇	—	4	4	no	—
115	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
116	C₂×D₄×C₄₇	D₈	1	4	yes	—
117	C₂×D₄×C₄₇	SD₁₆	1	4	yes	—
118	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	8	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	4	no	—
127	C₂²×C₄×C₄₇	—	4	4	no	—
128	C₂²×C₄×C₄₇	—	4	4	no	—
129	C₂²×C₄×C₄₇	—	4	2	no	—
130	C₂²×C₄×C₄₇	—	4	2	no	—
131	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
137	C₂²×Dic₄₇	—	2	1	no	—
138	C₂²×Dic₄₇	—	2	1	no	—
139	C₂²×Dic₄₇	—	2	2	no	—
140	C₂²×Dic₄₇	—	4	4	no	—
141	C₂²×Dic₄₇	—	4	4	no	—
142	C₂²×Dic₄₇	—	8	2	no	—
143	C₄⋊C₄×C₄₇	—	2	8	no	—
144	C₄⋊C₄×C₄₇	—	2	4	no	—
145	C₄⋊C₄×C₄₇	—	2	1	no	—
146	C₄⋊C₄×C₄₇	—	2	2	no	—
147	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
148	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
149	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
150	C₂²⋊C₄×C₄₇	—	2	4	no	—
151	C₂²⋊C₄×C₄₇	—	2	8	no	—
152	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
153	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
154	C₄²×C₄₇	C₂×D₄	1	2	yes	—
155	C₂²⋊Dic₄₇	—	4	4	no	—
156	C₄⋊Dic₄₇	—	2	1	no	—
157	C₄⋊Dic₄₇	—	2	1	no	—
158	C₄⋊Dic₄₇	—	2	2	no	—
159	C₄⋊Dic₄₇	—	2	2	no	—
160	C₄⋊Dic₄₇	—	2	1	no	—
161	C₄⋊Dic₄₇	—	4	4	no	—
162	C₄⋊Dic₄₇	—	4	2	no	—
163	C₄⋊Dic₄₇	—	8	1	no	—
164	C₄⋊Dic₄₇	#41	1	2	yes	complemented
165	C₄×Dic₄₇	—	4	2	no	—
166	C₂×C₄₇⋊C₈	—	2	1	no	—
167	C₂×C₄₇⋊C₈	—	2	1	no	—
168	C₂×C₄₇⋊C₈	—	2	1	no	—
169	C₂×C₄₇⋊C₈	—	2	2	no	—
170	C₂×C₄₇⋊C₈	—	2	1	no	—
171	C₂×C₄₇⋊C₈	—	2	2	no	—
172	C₂×C₄₇⋊C₈	—	2	2	no	—
173	C₂×C₄₇⋊C₈	—	2	1	no	—
174	C₂×C₄₇⋊C₈	—	4	8	no	—
175	C₂×C₄₇⋊C₈	#41	1	2	yes	complemented
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	2	no	—
178	C₂³×C₄₇	—	2	2	no	—
179	C₂³×C₄₇	—	2	2	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	4	1	no	—
182	C₂³×C₄₇	—	4	1	no	—
183	C₂³×C₄₇	—	4	1	no	—
184	C₂³×C₄₇	—	4	1	no	—
185	C₂³×C₄₇	—	4	1	no	—
186	C₂³×C₄₇	—	4	1	no	—
187	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
188	C₂³×C₄₇	C₂×D₈	1	4	yes	—
189	C₂³×C₄₇	C₂×SD₁₆	1	4	yes	—
190	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₄₇	—	4	8	no	—
192	D₄×C₄₇	—	2	2	no	—
193	D₄×C₄₇	—	2	2	no	—
194	D₄×C₄₇	—	4	16	no	—
195	D₄×C₄₇	—	4	1	no	—
196	D₄×C₄₇	—	4	1	no	—
197	D₄×C₄₇	#102	1	16	yes	complemented
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	1	no	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	4	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	4	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	—	4	2	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	16	no	—
213	C₂×C₄×C₄₇	—	4	8	no	—
214	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
216	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
218	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
219	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
225	C₂×Dic₄₇	—	2	2	no	—
226	C₂×Dic₄₇	—	4	1	no	—
227	C₂×Dic₄₇	—	4	1	no	—
228	C₂×Dic₄₇	—	4	2	no	—
229	C₂×Dic₄₇	—	4	1	no	—
230	C₂×Dic₄₇	—	4	1	no	—
231	C₂×Dic₄₇	—	4	2	no	—
232	C₂×Dic₄₇	—	4	2	no	—
233	C₂×Dic₄₇	—	4	1	no	—
234	C₂×Dic₄₇	—	8	8	no	—
235	C₄₇⋊C₈	—	2	2	no	—
236	C₄₇⋊C₈	—	4	2	no	—
237	C₄₇⋊C₈	—	4	1	no	—
238	#22485	—	47	1	no	maximal, Sylow
239	C₂²×C₄₇	—	2	4	no	—
240	C₂²×C₄₇	—	2	4	no	—
241	C₂²×C₄₇	—	2	4	no	—
242	C₂²×C₄₇	—	2	4	no	—
243	C₂²×C₄₇	—	2	4	no	—
244	C₂²×C₄₇	—	2	4	no	—
245	C₂²×C₄₇	—	4	2	no	—
246	C₂²×C₄₇	—	4	2	no	—
247	C₂²×C₄₇	—	4	2	no	—
248	C₂²×C₄₇	—	8	1	no	—
249	C₂²×C₄₇	—	8	1	no	—
250	C₂²×C₄₇	—	8	1	no	—
251	C₂²×C₄₇	—	8	1	no	—
252	C₂²×C₄₇	C₂×#102	1	8	yes	—
253	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₄₇	#546	1	1	yes	characteristic
255	C₂²×C₄₇	#547	1	1	yes	characteristic
256	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
257	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
258	C₂²×C₄₇	#577	1	1	yes	characteristic
259	C₂²×C₄₇	#578	1	1	yes	characteristic
260	C₄×C₄₇	—	2	4	no	—
261	C₄×C₄₇	—	2	2	no	—
262	C₄×C₄₇	—	4	2	no	—
263	C₄×C₄₇	—	4	4	no	—
264	C₄×C₄₇	C₂×#102	1	4	yes	—
265	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
266	C₄×C₄₇	#520	1	1	yes	characteristic
267	C₄×C₄₇	#546	1	1	yes	characteristic
268	C₄×C₄₇	#547	1	1	yes	characteristic
269	Dic₄₇	—	4	2	no	—
270	Dic₄₇	—	8	1	no	—
271	Dic₄₇	—	8	2	no	—
272	C₂×#547	D₄₇	1	1	yes	characteristic
273	C₂×C₈×D₄	—	47	1	no	—
274	D₄×C₄⋊C₄	—	47	1	no	—
275	#1990	—	47	1	no	—
276	#1988	—	47	1	no	—
277	#1893	—	47	2	no	—
278	#1874	—	47	2	no	—
279	#1823	—	47	2	no	—
280	#1802	—	47	1	no	—
281	C₄×#102	—	47	1	no	—
282	C₂×#340	—	47	2	no	—
283	C₂×C₄₇	—	2	8	no	—
284	C₂×C₄₇	—	8	2	no	—
285	C₂×C₄₇	#2339	1	1	yes	characteristic
286	C₂×C₄₇	C₂²×#102	1	1	yes	characteristic
287	C₂×C₄₇	#2898	1	1	yes	characteristic
288	C₂×C₄₇	#3294	1	1	yes	characteristic
289	C₂×C₄₇	#3298	1	1	yes	characteristic
290	C₂×C₄₇	#3334	1	1	yes	characteristic
291	C₂×C₄₇	#3335	1	1	yes	characteristic
292	C₂²×#41	—	2	1	no	—
293	C₂³×C₈	—	47	2	no	—
294	#547	—	2	4	no	—
295	#547	Dic₄₇	1	8	yes	complemented
296	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
297	C₂×#123	—	2	2	no	—
298	C₂×C₂²⋊Q₈	—	2	1	no	—
299	C₂×#121	C₂×D₄₇	1	2	yes	—
300	C₂×C₄×D₄	—	94	1	no	—
301	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
302	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
303	C₂²×C₄⋊C₄	—	47	2	no	—
304	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
305	C₈×D₄	—	94	4	no	—
306	C₂×C₄⋊C₈	—	47	1	no	—
307	C₂×#102	—	47	1	no	—
308	C₂×#102	—	47	1	no	—
309	C₂×#102	—	47	2	no	—
310	C₂×C₂²⋊C₈	—	47	2	no	—
311	C₂×C₄×C₈	—	47	1	no	—
312	#389	—	94	1	no	—
313	#385	—	94	2	no	—
314	#384	—	47	1	no	—
315	#380	—	47	2	no	—
316	C₄×C₄⋊C₄	—	47	1	no	—
317	#340	—	47	2	no	—
318	#340	—	47	1	no	—
319	#340	—	47	2	no	—
320	#340	—	47	2	no	—
321	#340	—	47	2	no	—
322	#340	—	47	2	no	—
323	#340	—	47	1	no	—
324	C₄₇	#22485	1	1	yes	characteristic, complemented, Sylow
325	C₂×#41	—	2	8	no	—
326	C₂×#41	—	4	4	no	—
327	C₂×#41	—	4	4	no	—
328	C₂²×Q₈	—	2	1	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
331	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	—	94	2	no	—
335	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
336	C₂²×C₈	—	47	1	no	—
337	C₂²×C₈	—	47	2	no	—
338	C₂²×C₈	—	47	1	no	—
339	C₂²×C₈	—	94	4	no	—
340	C₂²×C₈	—	94	4	no	—
341	C₂²×C₈	—	188	2	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
344	#123	—	2	16	no	—
345	C₂²⋊Q₈	—	2	8	no	—
346	#121	—	2	4	no	—
347	#121	C₂×Dic₄₇	1	8	yes	complemented
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	188	4	no	—
350	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
351	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
352	C₄×D₄	C₂²⋊D₄₇	1	4	yes	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	47	1	no	—
357	C₂×C₄⋊C₄	—	47	2	no	—
358	C₂×C₄⋊C₄	—	47	1	no	—
359	C₂×C₄⋊C₄	—	94	4	no	—
360	C₂×C₄⋊C₄	—	94	1	no	—
361	C₂×C₄⋊C₄	—	94	2	no	—
362	C₂×C₄⋊C₄	—	94	1	no	—
363	C₂×C₄⋊C₄	—	188	2	no	—
364	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
365	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	94	2	no	—
371	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
372	C₂×C₄²	—	94	1	no	—
373	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
374	C₄⋊C₈	—	94	2	no	—
375	#102	—	94	2	no	—
376	#102	—	94	2	no	—
377	#102	—	188	2	no	—
378	C₂²⋊C₈	—	94	4	no	—
379	C₄×C₈	—	94	2	no	—
380	#95	—	94	1	no	—
381	#95	—	94	2	no	—
382	C₂⁴	—	2	1	no	—
383	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
384	#41	—	4	32	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	4	2	no	—
387	C₂×Q₈	—	4	2	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	4	4	no	—
395	C₂×D₄	—	4	4	no	—
396	C₂×D₄	#10625334	1	4	yes	—
397	C₂×D₄	#10625335	1	4	yes	—
398	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
399	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	4	4	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	94	1	no	—
413	C₂²×C₄	—	94	1	no	—
414	C₂²×C₄	—	94	2	no	—
415	C₂²×C₄	—	376	2	no	—
416	C₂²×C₄	—	188	4	no	—
417	C₂²×C₄	—	188	4	no	—
418	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
419	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
420	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
421	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
422	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
423	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
424	C₂×C₈	—	47	2	no	—
425	C₂×C₈	—	94	1	no	—
426	C₂×C₈	—	94	1	no	—
427	C₂×C₈	—	94	1	no	—
428	C₂×C₈	—	94	2	no	—
429	C₂×C₈	—	94	1	no	—
430	C₂×C₈	—	94	2	no	—
431	C₂×C₈	—	94	2	no	—
432	C₂×C₈	—	94	1	no	—
433	C₂×C₈	—	188	8	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	47	2	no	—
439	C₄⋊C₄	—	94	1	no	—
440	C₄⋊C₄	—	94	1	no	—
441	C₄⋊C₄	—	94	2	no	—
442	C₄⋊C₄	—	94	2	no	—
443	C₄⋊C₄	—	94	1	no	—
444	C₄⋊C₄	—	376	1	no	—
445	C₄⋊C₄	—	188	4	no	—
446	C₄⋊C₄	—	188	2	no	—
447	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
448	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
449	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	188	4	no	—
453	C₂²⋊C₄	C₂²⋊Dic₄₇	1	8	yes	—
454	C₄²	—	188	2	no	—
455	C₄²	C₂²×Dic₄₇	1	2	yes	—
456	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
469	C₂³	C₂×#10625334	1	4	yes	—
470	C₂³	C₂×#10625335	1	4	yes	—
471	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
472	Q₈	—	4	8	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	16	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	1	no	—
478	D₄	#13093945	1	16	yes	complemented
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	4	16	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	94	2	no	—
496	C₂×C₄	—	376	8	no	—
497	C₂×C₄	—	188	2	no	—
498	C₂×C₄	—	188	1	no	—
499	C₂×C₄	—	188	1	no	—
500	C₂×C₄	—	188	2	no	—
501	C₂×C₄	—	188	2	no	—
502	C₂×C₄	—	188	1	no	—
503	C₂×C₄	—	188	1	no	—
504	C₂×C₄	—	188	1	no	—
505	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
506	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
507	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
508	C₂×C₄	C₂×#10625334	1	2	yes	—
509	C₂×C₄	C₂×#10625335	1	2	yes	—
510	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
511	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
512	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
513	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
514	C₂×C₄	#13094070	1	1	yes	characteristic
515	C₂×C₄	#13094071	1	1	yes	characteristic
516	C₈	—	94	2	no	—
517	C₈	—	188	2	no	—
518	C₈	—	188	1	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	C₂×#13093945	1	8	yes	—
533	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
534	C₂²	#15689761	1	1	yes	characteristic
535	C₂²	#15689772	1	1	yes	characteristic
536	C₂²	C₂²×#10625334	1	1	yes	characteristic
537	C₂²	C₂²×#10625335	1	1	yes	characteristic
538	C₂²	#15689931	1	1	yes	characteristic
539	C₂²	#15689938	1	1	yes	characteristic
540	C₄	—	2	2	no	—
541	C₄	—	2	4	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	4	no	—
544	C₄	—	376	2	no	—
545	C₄	—	376	1	no	—
546	C₄	—	188	2	no	—
547	C₄	C₂×#13093945	1	4	yes	—
548	C₄	#41×Dic₄₇	1	1	yes	characteristic
549	C₄	#15689606	1	1	yes	characteristic
550	C₄	#15689761	1	1	yes	characteristic
551	C₄	#15689772	1	1	yes	characteristic
552	C₂	—	2	8	no	—
553	C₂	—	8	2	no	—
554	C₂	#20246218	1	1	yes	characteristic
555	C₂	C₂²×#13093945	1	1	yes	characteristic
556	C₂	#20251921	1	1	yes	characteristic
557	C₂	#20255195	1	1	yes	characteristic
558	C₂	#20255247	1	1	yes	characteristic
559	C₂	#20255731	1	1	yes	characteristic
560	C₂	#20255745	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#547	C₂
socle	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#547	D₄₇
hypocenter	C₄₇	#22485
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄ ◁ C₂×#547

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
2. D₄×C₄⋊Dic₄₇	C₂	semidirect
3. #20244350	C₂	semidirect
4. #20244341	C₂	semidirect
5. #20243817	C₂	semidirect
6. #20243706	C₂	semidirect
7. #20243474	C₂	semidirect
8. #20243388	C₂	semidirect
9. C₄×#13093945	C₂	semidirect
10. C₂×#15688885	C₂	semidirect
36. C₄₇×#547	C₄	semidirect
81. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
85. #121×C₄₇	C₂×C₄	semidirect
88. C₄×D₄×C₄₇	C₂×C₄	semidirect
93. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
164. C₄⋊Dic₄₇	#41	semidirect
175. C₂×C₄₇⋊C₈	#41	semidirect
197. D₄×C₄₇	#102	semidirect
295. #547	Dic₄₇	semidirect
324. C₄₇	#22485	semidirect
343. C₄⋊Q₈	C₂×Dic₄₇	semidirect
347. #121	C₂×Dic₄₇	semidirect
351. C₄×D₄	C₂×Dic₄₇	semidirect
364. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
478. D₄	#13093945	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₄₇⋊C₈	2
D₄×C₄⋊Dic₄₇	2
#20244350	2
#20244341	2
#20243817	2
#20243706	2
#20243474	2
#20243388	2
C₄×#13093945	2
C₂×#15688885	2
C₂×C₄₇×#547	2
#22485	47