Subgroups — #26238538

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689323	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625336	C₂	1	2	yes	maximal, complemented
3	#20246452	C₂	1	1	yes	maximal, characteristic
4	#20244193	C₂	1	1	yes	maximal, characteristic
5	#20244149	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244070	C₂	1	2	yes	maximal, complemented
7	#20243743	C₂	1	2	yes	maximal, complemented
8	#20243648	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093948	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	2	yes	—
13	C₂×#13094021	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
15	C₂×#13093986	—	2	1	no	—
16	#15689323	C₄	1	8	yes	complemented
17	C₄×#10625336	—	2	8	no	—
18	C₂×#13093955	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093948	C₂²	1	1	yes	characteristic
21	C₂×#13093948	C₂²	1	1	yes	characteristic
22	C₂×#13093944	C₂²	1	2	yes	—
23	C₂×#13093944	C₂²	1	2	yes	—
24	C₂×#13093944	C₂²	1	2	yes	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
27	#15689025	C₂²	1	2	yes	—
28	#15689024	—	2	1	no	—
29	#15689001	—	2	2	no	—
30	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688885	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	1	yes	characteristic
33	#15688885	C₂²	1	2	yes	—
34	#15688878	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#389	—	2	2	no	—
38	C₄₇×#389	C₂²	1	2	yes	—
39	C₄₇×#384	—	2	1	no	—
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×D₁₈₈	—	2	1	no	—
44	C₂²×D₁₈₈	—	2	1	no	—
45	C₂²×D₁₈₈	C₂³	1	2	yes	—
46	C₂²×C₄×D₄₇	—	2	2	no	—
47	C₂×#10625336	—	2	4	no	—
48	C₂×#10625336	—	2	4	no	—
49	C₂×#10625336	C₂×C₄	1	8	yes	complemented
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	#13094021	—	2	2	no	—
54	#13094021	C₂×C₄	1	4	yes	—
55	C₄×D₁₈₈	—	2	4	no	—
56	C₄×D₁₈₈	—	4	2	no	—
57	#13093986	—	4	4	no	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
61	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
62	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
63	C₂×C₄×Dic₄₇	—	2	1	no	—
64	#13093955	—	2	4	no	—
65	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
66	#13093948	—	2	2	no	—
67	#13093948	D₄	1	4	yes	complemented
68	#13093944	—	2	4	no	—
69	#13093944	—	4	2	no	—
70	#13093944	C₂×C₄	1	8	yes	complemented
71	C₄×C₄₇⋊C₈	—	2	2	no	—
72	C₄×C₄₇⋊C₈	—	2	4	no	—
73	C₄₇⋊#95	—	2	1	no	—
74	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×Q₈×C₄₇	—	2	2	no	—
76	C₄×Q₈×C₄₇	—	2	4	no	—
77	C₄×Q₈×C₄₇	—	4	2	no	—
78	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	—	2	2	no	—
90	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	#95×C₄₇	—	2	2	no	—
93	#95×C₄₇	D₄	1	2	yes	—
94	C₂³×D₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
100	C₂×Q₈×C₄₇	#41	1	2	yes	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	1	no	—
110	C₂²×Dic₄₇	—	2	1	no	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	—	2	2	no	—
113	C₂×D₁₈₈	—	2	2	no	—
114	C₂×D₁₈₈	—	2	2	no	—
115	C₂×D₁₈₈	—	2	4	no	—
116	C₂×D₁₈₈	—	2	2	no	—
117	C₂×D₁₈₈	—	2	4	no	—
118	C₂×D₁₈₈	—	4	2	no	—
119	C₂×D₁₈₈	—	4	2	no	—
120	C₂×D₁₈₈	—	8	1	no	—
121	C₂×D₁₈₈	—	8	1	no	—
122	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
123	C₂×C₄×D₄₇	—	4	4	no	—
124	C₂×C₄×D₄₇	—	4	4	no	—
125	C₂×C₄×D₄₇	—	8	2	no	—
126	C₄⋊C₄×C₄₇	—	2	4	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	4	4	no	—
132	C₄⋊C₄×C₄₇	—	4	2	no	—
133	C₄⋊C₄×C₄₇	—	8	1	no	—
134	C₄⋊C₄×C₄₇	—	8	2	no	—
135	C₄⋊C₄×C₄₇	SD₁₆	1	4	yes	complemented
136	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
137	C₄²×C₄₇	—	2	4	no	—
138	C₄²×C₄₇	—	2	2	no	—
139	C₄²×C₄₇	—	2	2	no	—
140	C₄²×C₄₇	—	4	4	no	—
141	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
142	C₄²×C₄₇	#41	1	2	yes	—
143	#10625336	—	2	16	no	—
144	(C₂×D₄₇)⋊C₄	—	4	4	no	—
145	(C₂×D₄₇)⋊C₄	—	4	4	no	—
146	(C₂×D₄₇)⋊C₄	—	8	2	no	—
147	C₄⋊Dic₄₇	—	2	1	no	—
148	C₄⋊Dic₄₇	—	2	1	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
151	C₄×Dic₄₇	—	4	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	—	2	1	no	—
158	C₂×C₄₇⋊C₈	—	2	1	no	—
159	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
160	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
161	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂²×D₄₇	—	2	4	no	—
163	C₂²×D₄₇	—	4	2	no	—
164	C₂²×D₄₇	—	4	2	no	—
165	C₂²×D₄₇	—	4	2	no	—
166	C₂²×D₄₇	—	4	2	no	—
167	C₂²×D₄₇	—	4	2	no	—
168	C₂²×D₄₇	—	4	2	no	—
169	Q₈×C₄₇	—	2	2	no	—
170	Q₈×C₄₇	—	2	2	no	—
171	Q₈×C₄₇	—	2	2	no	—
172	Q₈×C₄₇	C₄×D₄	1	4	yes	complemented
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
192	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
193	C₂×C₄×C₄₇	#135	1	2	yes	—
194	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
200	C₂×Dic₄₇	—	2	2	no	—
201	C₂×Dic₄₇	—	4	1	no	—
202	C₂×Dic₄₇	—	4	1	no	—
203	C₂×Dic₄₇	—	4	1	no	—
204	C₂×Dic₄₇	—	4	1	no	—
205	C₂×Dic₄₇	—	4	1	no	—
206	D₁₈₈	—	2	4	no	—
207	D₁₈₈	—	2	4	no	—
208	D₁₈₈	—	4	2	no	—
209	D₁₈₈	—	4	2	no	—
210	D₁₈₈	—	4	8	no	—
211	D₁₈₈	—	8	4	no	—
212	C₄×D₄₇	—	8	8	no	—
213	C₄₇⋊C₈	—	2	4	no	—
214	C₄₇⋊C₈	—	2	2	no	—
215	C₄₇⋊C₈	—	4	1	no	—
216	#22997	—	47	1	no	maximal, Sylow
217	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₄₇	D₄²	1	1	yes	characteristic
219	C₂²×C₄₇	#548	1	1	yes	characteristic
220	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
221	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
222	C₂²×C₄₇	#576	1	1	yes	characteristic
223	C₂²×C₄₇	#577	1	1	yes	characteristic
224	C₂×D₄₇	—	4	4	no	—
225	C₂×D₄₇	—	4	4	no	—
226	C₂×D₄₇	—	4	4	no	—
227	C₂×D₄₇	—	8	2	no	—
228	C₂×D₄₇	—	8	2	no	—
229	C₂×D₄₇	—	8	2	no	—
230	C₂×D₄₇	—	8	2	no	—
231	C₄×C₄₇	—	2	4	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	2	4	no	—
234	C₄×C₄₇	—	4	2	no	—
235	C₄×C₄₇	—	4	2	no	—
236	C₄×C₄₇	—	8	2	no	—
237	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
238	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₄₇	#520	1	1	yes	characteristic
240	C₄×C₄₇	#547	1	1	yes	characteristic
241	C₄×C₄₇	#553	1	1	yes	characteristic
242	Dic₄₇	—	4	2	no	—
243	Dic₄₇	—	8	1	no	—
244	C₂×#460	—	47	1	no	—
245	C₂×C₄×SD₁₆	—	47	2	no	—
246	#2366	—	47	1	no	—
247	Q₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
248	#1957	—	47	1	no	—
249	#1948	—	47	1	no	—
250	#1934	—	47	2	no	—
251	#1880	—	47	2	no	—
252	#1864	—	47	2	no	—
253	C₈×C₄⋊C₄	—	47	1	no	—
254	C₄×#103	—	47	1	no	—
255	C₂×C₄₇	#2361	1	1	yes	characteristic
256	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
257	C₂×C₄₇	#2946	1	1	yes	characteristic
258	C₂×C₄₇	D₄×SD₁₆	1	1	yes	characteristic
259	C₂×C₄₇	#3287	1	1	yes	characteristic
260	C₂×C₄₇	#3362	1	1	yes	characteristic
261	C₂×C₄₇	#3365	1	1	yes	characteristic
262	D₄₇	—	8	4	no	—
263	C₂²×SD₁₆	—	47	2	no	—
264	C₂×#127	—	47	1	no	—
265	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
266	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
267	C₂×C₄×D₄	—	47	2	no	—
268	C₂×C₄×D₄	—	94	1	no	—
269	#460	—	47	8	no	—
270	C₄×SD₁₆	—	94	8	no	—
271	C₂×#106	—	47	2	no	—
272	C₂×C₄⋊C₈	—	47	1	no	—
273	C₂×#103	—	47	1	no	—
274	C₂×#103	—	47	1	no	—
275	C₂×#102	—	47	2	no	—
276	C₂×#102	—	47	2	no	—
277	C₂×#102	—	47	2	no	—
278	C₂×C₄×C₈	—	47	2	no	—
279	C₂×C₄×C₈	—	47	1	no	—
280	#390	—	47	2	no	—
281	#390	—	94	1	no	—
282	#389	—	2	2	no	—
283	#389	C₂×D₄₇	1	2	yes	—
284	#386	—	94	2	no	—
285	#384	—	2	1	no	—
286	#384	C₂×D₄₇	1	1	yes	characteristic
287	C₄×C₄⋊C₄	—	2	1	no	—
288	C₄×C₄⋊C₄	—	47	1	no	—
289	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
290	#340	—	47	1	no	—
291	#340	—	47	2	no	—
292	#340	—	47	1	no	—
293	#336	—	47	2	no	—
294	C₄₇	#22997	1	1	yes	characteristic, complemented, Sylow
295	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
296	C₂²×D₄	—	47	2	no	—
297	C₂²×D₄	—	94	1	no	—
298	C₂²×D₄	—	94	1	no	—
299	C₂³×C₄	—	94	2	no	—
300	C₂×SD₁₆	—	47	8	no	—
301	C₂×SD₁₆	—	94	4	no	—
302	C₂×SD₁₆	—	94	4	no	—
303	C₂²×C₈	—	47	2	no	—
304	C₂²×C₈	—	47	1	no	—
305	C₂²×C₈	—	47	1	no	—
306	#127	—	47	4	no	—
307	#127	—	94	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	4	no	—
310	C₄×Q₈	—	4	2	no	—
311	C₄×Q₈	C₄×D₄₇	1	4	yes	complemented
312	C₄×D₄	—	94	4	no	—
313	C₄×D₄	—	188	2	no	—
314	C₄×D₄	—	188	4	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	47	1	no	—
321	C₂×C₄⋊C₄	—	47	1	no	—
322	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
325	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	94	2	no	—
327	C₂×C₂²⋊C₄	—	94	2	no	—
328	C₂×C₂²⋊C₄	—	94	2	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	2	no	—
331	C₂×C₄²	—	94	1	no	—
332	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
333	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
334	#106	—	94	4	no	—
335	C₄⋊C₈	—	47	4	no	—
336	#103	—	47	4	no	—
337	#103	—	94	2	no	—
338	#102	—	47	8	no	—
339	#102	—	94	4	no	—
340	#102	—	188	2	no	—
341	C₄×C₈	—	94	4	no	—
342	C₄×C₈	—	94	2	no	—
343	#95	—	2	2	no	—
344	#95	—	94	1	no	—
345	#95	C₂²⋊D₄₇	1	2	yes	—
346	C₂⁴	—	94	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
351	C₂×Q₈	D₄×D₄₇	1	2	yes	—
352	C₂×Q₈	#10625354	1	2	yes	—
353	C₂×D₄	—	47	4	no	—
354	C₂×D₄	—	94	4	no	—
355	C₂×D₄	—	94	4	no	—
356	C₂×D₄	—	94	2	no	—
357	C₂×D₄	—	94	2	no	—
358	C₂×D₄	—	94	2	no	—
359	C₂×D₄	—	94	2	no	—
360	C₂×D₄	—	94	2	no	—
361	C₂×D₄	—	376	1	no	—
362	C₂×D₄	—	376	1	no	—
363	C₂×D₄	—	188	2	no	—
364	C₂×D₄	—	188	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	94	1	no	—
369	C₂²×C₄	—	94	1	no	—
370	C₂²×C₄	—	376	2	no	—
371	C₂²×C₄	—	188	4	no	—
372	C₂²×C₄	—	188	4	no	—
373	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
374	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
376	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
377	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
378	SD₁₆	—	94	16	no	—
379	C₂×C₈	—	47	4	no	—
380	C₂×C₈	—	47	2	no	—
381	C₂×C₈	—	94	2	no	—
382	C₂×C₈	—	94	1	no	—
383	C₂×C₈	—	94	2	no	—
384	C₂×C₈	—	94	1	no	—
385	C₂×C₈	—	94	1	no	—
386	C₂×C₈	—	94	1	no	—
387	C₂×C₈	—	94	1	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	8	1	no	—
396	C₄⋊C₄	—	8	2	no	—
397	C₄⋊C₄	—	47	2	no	—
398	C₄⋊C₄	—	94	1	no	—
399	C₄⋊C₄	—	94	1	no	—
400	C₄⋊C₄	—	94	1	no	—
401	C₄⋊C₄	#10625336	1	4	yes	complemented
402	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
403	C₂²⋊C₄	—	376	2	no	—
404	C₂²⋊C₄	—	188	4	no	—
405	C₂²⋊C₄	—	188	4	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	4	4	no	—
410	C₄²	—	188	2	no	—
411	C₄²	C₂×C₄×D₄₇	1	2	yes	—
412	C₄²	#10625350	1	2	yes	—
413	C₂³	—	94	4	no	—
414	C₂³	—	188	2	no	—
415	C₂³	—	188	2	no	—
416	C₂³	—	188	2	no	—
417	C₂³	—	188	2	no	—
418	C₂³	—	188	2	no	—
419	C₂³	—	188	2	no	—
420	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
421	Q₈	—	2	2	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	2	2	no	—
424	Q₈	#13093986	1	4	yes	complemented
425	D₄	—	94	4	no	—
426	D₄	—	94	4	no	—
427	D₄	—	376	4	no	—
428	D₄	—	188	2	no	—
429	D₄	—	188	2	no	—
430	D₄	—	188	8	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	94	2	no	—
448	C₂×C₄	—	376	8	no	—
449	C₂×C₄	—	188	1	no	—
450	C₂×C₄	—	188	1	no	—
451	C₂×C₄	—	188	1	no	—
452	C₂×C₄	—	188	1	no	—
453	C₂×C₄	—	188	1	no	—
454	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
455	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
456	C₂×C₄	C₂×#10625336	1	4	yes	—
457	C₂×C₄	C₂×#10625336	1	2	yes	—
458	C₂×C₄	#13094044	1	2	yes	—
459	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
460	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
461	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
462	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
463	C₂×C₄	#13094069	1	1	yes	characteristic
464	C₂×C₄	#13094072	1	1	yes	characteristic
465	C₈	—	94	2	no	—
466	C₈	—	94	4	no	—
467	C₈	—	188	1	no	—
468	C₂²	—	376	2	no	—
469	C₂²	—	376	2	no	—
470	C₂²	—	376	2	no	—
471	C₂²	—	376	2	no	—
472	C₂²	—	188	4	no	—
473	C₂²	—	188	4	no	—
474	C₂²	—	188	4	no	—
475	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
476	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
477	C₂²	#15689784	1	1	yes	characteristic
478	C₂²	C₂²×#10625336	1	1	yes	characteristic
479	C₂²	C₂×#13094044	1	1	yes	characteristic
480	C₂²	#15689926	1	1	yes	characteristic
481	C₂²	#15689931	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	4	no	—
484	C₄	—	2	4	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	8	2	no	—
488	C₄	—	376	1	no	—
489	C₄	—	188	2	no	—
490	C₄	C₄×#10625336	1	4	yes	complemented
491	C₄	C₂×#13093986	1	1	yes	characteristic
492	C₄	#15689604	1	1	yes	characteristic
493	C₄	#15689774	1	1	yes	characteristic
494	C₄	#15689821	1	1	yes	characteristic
495	C₂	—	376	4	no	—
496	C₂	#20246404	1	1	yes	characteristic
497	C₂	C₂×C₄×#10625336	1	1	yes	characteristic
498	C₂	#20252216	1	1	yes	characteristic
499	C₂	D₄×#10625336	1	1	yes	characteristic
500	C₂	#20255144	1	1	yes	characteristic
501	C₂	#20256059	1	1	yes	characteristic
502	C₂	#20256084	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	Q₈×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#13094021	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	Q₈×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#22997
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ Q₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#10625336	C₂	semidirect
5. #20244149	C₂	semidirect
6. #20244070	C₂	semidirect
7. #20243743	C₂	semidirect
8. #20243648	C₂	semidirect
9. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
10. C₄×#13093948	C₂	semidirect
11. Q₈×C₄⋊C₄×C₄₇	C₂	semidirect
16. #15689323	C₄	semidirect
49. C₂×#10625336	C₂×C₄	semidirect
65. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
67. #13093948	D₄	semidirect
70. #13093944	C₂×C₄	semidirect
78. C₄×Q₈×C₄₇	C₂×C₄	semidirect
135. C₄⋊C₄×C₄₇	SD₁₆	semidirect
172. Q₈×C₄₇	C₄×D₄	semidirect
237. C₄×C₄₇	C₄×SD₁₆	semidirect
247. Q₈×C₄⋊C₄	D₄₇	semidirect
294. C₄₇	#22997	semidirect
311. C₄×Q₈	C₄×D₄₇	semidirect
401. C₄⋊C₄	#10625336	semidirect
424. Q₈	#13093986	semidirect
490. C₄	C₄×#10625336	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689323	2
C₂×C₄×#10625336	2
#20246452	2
#20244193	2
#20244149	2
#20244070	2
#20243743	2
#20243648	2
C₄⋊C₄×C₄₇⋊C₈	2
C₄×#13093948	2
Q₈×C₄⋊C₄×C₄₇	2
#22997	47