Subgroups — #26234494

Order 12032.

1022 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689202	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689164	C₂	1	2	yes	maximal, complemented
3	#20246335	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic
5	#20244151	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244146	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243588	C₂	1	2	yes	maximal, complemented
8	#20243582	C₂	1	2	yes	maximal, complemented
9	#20243545	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243422	C₂	1	2	yes	maximal, complemented
11	C₄×#107×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂×C₄×D₁₈₈	—	2	1	no	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×#13093982	C₂²	1	2	yes	—
16	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
17	#15689202	C₄	1	8	yes	complemented
18	#15689164	—	2	8	no	—
19	C₂×#13093957	C₂²	1	2	yes	—
20	C₂×#13093956	C₂²	1	2	yes	—
21	C₂×#13093956	C₂²	1	2	yes	—
22	C₂×#13093955	C₂²	1	2	yes	—
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
25	#15689025	—	2	1	no	—
26	#15689021	—	2	1	no	—
27	#15689015	—	2	2	no	—
28	#15688997	—	2	2	no	—
29	#15688993	C₂²	1	1	yes	characteristic
30	#15688993	C₂²	1	1	yes	characteristic
31	#15688980	C₂²	1	2	yes	—
32	#15688980	C₂²	1	2	yes	—
33	C₄×C₄⋊Dic₄₇	—	2	1	no	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	1	yes	characteristic
42	C₄₇×#340	C₂²	1	1	yes	characteristic
43	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	—	2	2	no	—
45	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
46	C₂×#10625324	—	2	4	no	—
47	C₂×#10625324	—	2	4	no	—
48	C₂×#10625324	C₂×C₄	1	8	yes	complemented
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₄×D₁₈₈	—	4	4	no	—
51	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
52	C₄×D₁₈₈	Q₈	1	4	yes	—
53	#13093982	—	2	4	no	—
54	#13093982	—	4	2	no	—
55	C₂×C₄⋊Dic₄₇	—	2	1	no	—
56	C₂×C₄⋊Dic₄₇	—	2	1	no	—
57	C₂×C₄⋊Dic₄₇	—	2	1	no	—
58	C₂×C₄⋊Dic₄₇	—	2	1	no	—
59	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
62	C₂×Dic₄₇⋊C₄	—	2	2	no	—
63	C₄⋊C₄×D₄₇	—	2	4	no	—
64	C₄⋊C₄×D₄₇	—	4	2	no	—
65	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
66	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
67	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
68	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
69	C₂×C₄×Dic₄₇	—	2	2	no	—
70	#13093957	—	2	4	no	—
71	#13093956	—	2	4	no	—
72	#13093956	—	4	2	no	—
73	#13093955	—	2	4	no	—
74	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
75	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	complemented
76	C₄₇⋊#95	—	2	2	no	—
77	C₄₇⋊#95	—	2	2	no	—
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	—	2	1	no	—
85	C₂×C₄²×C₄₇	—	2	1	no	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	#107×C₄₇	—	2	2	no	—
88	#107×C₄₇	D₄	1	4	yes	complemented
89	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
90	#95×C₄₇	—	2	1	no	—
91	#95×C₄₇	—	2	1	no	—
92	C₂³×D₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₇	—	2	2	no	—
101	C₂²×Dic₄₇	—	2	2	no	—
102	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
103	C₂×D₁₈₈	—	2	2	no	—
104	C₂×D₁₈₈	—	2	2	no	—
105	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
106	C₂×C₄×D₄₇	—	2	2	no	—
107	C₂×C₄×D₄₇	—	2	2	no	—
108	C₂×C₄×D₄₇	—	2	2	no	—
109	C₂×C₄×D₄₇	—	2	2	no	—
110	C₂×C₄×D₄₇	—	4	4	no	—
111	C₂×C₄×D₄₇	—	4	4	no	—
112	C₂×C₄×D₄₇	—	8	2	no	—
113	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
114	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₇	#41	1	2	yes	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	—	2	1	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
129	C₄²×C₄₇	—	4	2	no	—
130	C₄²×C₄₇	—	4	2	no	—
131	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
132	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
133	(C₂×D₄₇)⋊C₄	—	4	4	no	—
134	(C₂×D₄₇)⋊C₄	—	4	4	no	—
135	(C₂×D₄₇)⋊C₄	—	8	2	no	—
136	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	8	yes	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	—	2	2	no	—
140	C₄⋊Dic₄₇	—	2	2	no	—
141	C₄⋊Dic₄₇	—	4	2	no	—
142	C₄⋊Dic₄₇	—	4	2	no	—
143	C₄⋊Dic₄₇	—	8	1	no	—
144	C₄⋊Dic₄₇	—	8	1	no	—
145	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
146	Dic₄₇⋊C₄	—	4	4	no	—
147	C₄×Dic₄₇	—	4	4	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
151	#10625324	—	2	16	no	—
152	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂²×D₄₇	—	2	2	no	—
154	C₂²×D₄₇	—	2	2	no	—
155	C₂²×D₄₇	—	2	2	no	—
156	C₂²×D₄₇	—	2	2	no	—
157	C₂²×D₄₇	—	2	2	no	—
158	C₂²×D₄₇	—	2	2	no	—
159	C₂²×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₄₇	#137	1	2	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	4	2	no	—
188	C₂×Dic₄₇	—	4	2	no	—
189	C₂×Dic₄₇	—	4	2	no	—
190	C₂×Dic₄₇	—	4	2	no	—
191	C₂×Dic₄₇	—	4	2	no	—
192	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
193	D₁₈₈	—	2	8	no	—
194	C₄×D₄₇	—	2	4	no	—
195	C₄×D₄₇	—	2	4	no	—
196	C₄×D₄₇	—	2	4	no	—
197	C₄×D₄₇	—	2	4	no	—
198	C₄×D₄₇	—	8	8	no	—
199	C₈×C₄₇	—	2	2	no	—
200	C₈×C₄₇	C₄×D₄	1	4	yes	complemented
201	C₄₇⋊C₈	—	2	4	no	—
202	#22663	—	47	1	no	maximal, Sylow
203	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
204	C₂²×C₄₇	D₄²	1	1	yes	characteristic
205	C₂²×C₄₇	#547	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
208	C₂²×C₄₇	#577	1	1	yes	characteristic
209	C₂²×C₄₇	#577	1	1	yes	characteristic
210	C₂×D₄₇	—	2	4	no	—
211	C₂×D₄₇	—	2	4	no	—
212	C₂×D₄₇	—	2	4	no	—
213	C₂×D₄₇	—	4	2	no	—
214	C₂×D₄₇	—	4	2	no	—
215	C₂×D₄₇	—	4	2	no	—
216	C₂×D₄₇	—	4	2	no	—
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	4	2	no	—
219	C₄×C₄₇	—	4	2	no	—
220	C₄×C₄₇	—	8	1	no	—
221	C₄×C₄₇	—	8	1	no	—
222	C₄×C₄₇	#428	1	4	yes	complemented
223	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
224	C₄×C₄₇	#520	1	1	yes	characteristic
225	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
226	C₄×C₄₇	#554	1	1	yes	characteristic
227	Dic₄₇	—	2	4	no	—
228	Dic₄₇	—	8	2	no	—
229	Dic₄₇	—	8	2	no	—
230	C₂×#436	—	47	1	no	—
231	C₂×#428	—	47	2	no	—
232	#2354	—	47	1	no	—
233	D₄×C₄⋊C₄	—	47	1	no	—
234	#1948	—	47	1	no	—
235	#1947	—	47	1	no	—
236	#1854	—	47	2	no	—
237	#1853	—	47	2	no	—
238	#1844	—	47	1	no	—
239	#1809	—	47	2	no	—
240	C₄×#107	D₄₇	1	1	yes	characteristic, complemented
241	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
242	C₂×C₄₇	C₂×#428	1	1	yes	characteristic
243	C₂×C₄₇	#2912	1	1	yes	characteristic
244	C₂×C₄₇	#3272	1	1	yes	characteristic
245	C₂×C₄₇	#3278	1	1	yes	characteristic
246	C₂×C₄₇	#3354	1	1	yes	characteristic
247	C₂×C₄₇	#3356	1	1	yes	characteristic
248	D₄₇	—	4	4	no	—
249	C₂²×M₁₆	—	47	2	no	—
250	C₂×C₄×D₄	—	47	1	no	—
251	C₂×C₄×D₄	—	94	1	no	—
252	C₂×#117	—	47	2	no	—
253	C₂²×C₄⋊C₄	—	47	2	no	—
254	#436	—	47	8	no	—
255	#428	—	94	8	no	—
256	C₂×#107	—	47	2	no	—
257	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
258	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
259	C₂×#106	—	47	2	no	—
260	C₂×#106	—	47	2	no	—
261	C₂×#106	—	47	2	no	—
262	C₂×C₄⋊C₈	—	47	1	no	—
263	C₂×C₂²⋊C₈	—	47	2	no	—
264	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
265	#390	—	94	1	no	—
266	#389	—	94	1	no	—
267	#388	—	94	2	no	—
268	#385	—	94	2	no	—
269	#384	—	47	1	no	—
270	#384	—	47	1	no	—
271	#380	—	47	2	no	—
272	#380	—	47	2	no	—
273	C₄×C₄⋊C₄	—	94	1	no	—
274	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
275	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
276	#340	—	47	2	no	—
277	#340	—	47	2	no	—
278	#340	C₂×D₄₇	1	1	yes	characteristic
279	#340	C₂×D₄₇	1	1	yes	characteristic
280	C₄₇	#22663	1	1	yes	characteristic, complemented, Sylow
281	C₂²×D₄	—	47	1	no	—
282	C₂³×C₄	—	47	2	no	—
283	C₂³×C₄	—	94	2	no	—
284	C₂×M₁₆	—	47	8	no	—
285	C₂×M₁₆	—	94	4	no	—
286	C₂×M₁₆	—	94	4	no	—
287	C₂²×C₈	—	47	2	no	—
288	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
290	C₄×D₄	—	47	4	no	—
291	C₄×D₄	—	47	4	no	—
292	C₄×D₄	—	188	4	no	—
293	#117	—	94	4	no	—
294	#117	—	188	2	no	—
295	C₂×C₄⋊C₄	—	47	1	no	—
296	C₂×C₄⋊C₄	—	47	2	no	—
297	C₂×C₄⋊C₄	—	47	2	no	—
298	C₂×C₄⋊C₄	—	94	4	no	—
299	C₂×C₄⋊C₄	—	94	1	no	—
300	C₂×C₄⋊C₄	—	94	1	no	—
301	C₂×C₄⋊C₄	—	94	2	no	—
302	C₂×C₄⋊C₄	—	94	1	no	—
303	C₂×C₄⋊C₄	—	94	1	no	—
304	C₂×C₄⋊C₄	—	188	2	no	—
305	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	47	2	no	—
310	C₂×C₂²⋊C₄	—	94	2	no	—
311	C₂×C₂²⋊C₄	—	94	2	no	—
312	C₂×C₂²⋊C₄	—	94	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	—	94	2	no	—
316	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
317	#107	—	2	2	no	—
318	#107	—	94	4	no	—
319	#107	D₁₈₈	1	4	yes	complemented
320	#106	—	94	4	no	—
321	#106	—	94	4	no	—
322	#106	—	188	2	no	—
323	C₄⋊C₈	—	47	4	no	—
324	C₂²⋊C₈	—	47	8	no	—
325	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
326	#95	—	2	1	no	—
327	#95	—	2	1	no	—
328	#95	—	94	2	no	—
329	#95	—	94	2	no	—
330	C₂⁴	—	47	2	no	—
331	C₂×D₄	—	47	4	no	—
332	C₂×D₄	—	94	2	no	—
333	C₂×D₄	—	94	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	47	2	no	—
339	C₂²×C₄	—	47	4	no	—
340	C₂²×C₄	—	47	4	no	—
341	C₂²×C₄	—	94	2	no	—
342	C₂²×C₄	—	94	2	no	—
343	C₂²×C₄	—	94	2	no	—
344	C₂²×C₄	—	94	2	no	—
345	C₂²×C₄	—	94	2	no	—
346	C₂²×C₄	—	94	2	no	—
347	C₂²×C₄	—	376	2	no	—
348	C₂²×C₄	—	188	4	no	—
349	C₂²×C₄	—	188	4	no	—
350	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
353	M₁₆	—	94	16	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	47	4	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	—	94	2	no	—
359	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
360	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
361	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
362	C₂×C₈	#10625350	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	47	4	no	—
370	C₄⋊C₄	—	94	2	no	—
371	C₄⋊C₄	—	94	2	no	—
372	C₄⋊C₄	—	94	2	no	—
373	C₄⋊C₄	—	94	2	no	—
374	C₄⋊C₄	—	376	1	no	—
375	C₄⋊C₄	—	376	1	no	—
376	C₄⋊C₄	—	188	4	no	—
377	C₄⋊C₄	—	188	2	no	—
378	C₄⋊C₄	—	188	2	no	—
379	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
380	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
381	C₂²⋊C₄	—	47	8	no	—
382	C₂²⋊C₄	—	376	2	no	—
383	C₂²⋊C₄	—	188	4	no	—
384	C₂²⋊C₄	—	188	4	no	—
385	C₄²	—	4	2	no	—
386	C₄²	—	4	2	no	—
387	C₄²	—	188	4	no	—
388	C₄²	C₂×C₄×D₄₇	1	2	yes	—
389	C₄²	Q₈×D₄₇	1	2	yes	—
390	C₂³	—	47	4	no	—
391	C₂³	—	94	2	no	—
392	C₂³	—	94	2	no	—
393	C₂³	—	94	2	no	—
394	C₂³	—	94	2	no	—
395	C₂³	—	94	2	no	—
396	C₂³	—	94	2	no	—
397	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
398	D₄	—	94	8	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	47	4	no	—
414	C₂×C₄	—	94	2	no	—
415	C₂×C₄	—	94	2	no	—
416	C₂×C₄	—	94	4	no	—
417	C₂×C₄	—	94	4	no	—
418	C₂×C₄	—	94	4	no	—
419	C₂×C₄	—	94	4	no	—
420	C₂×C₄	—	376	8	no	—
421	C₂×C₄	—	188	2	no	—
422	C₂×C₄	—	188	2	no	—
423	C₂×C₄	—	188	2	no	—
424	C₂×C₄	—	188	2	no	—
425	C₂×C₄	—	188	2	no	—
426	C₂×C₄	—	188	2	no	—
427	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
428	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
429	C₂×C₄	#13094048	1	2	yes	—
430	C₂×C₄	#13094056	1	2	yes	—
431	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
433	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
434	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
435	C₂×C₄	#13094070	1	1	yes	characteristic
436	C₂×C₄	#13094071	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	94	4	no	—
439	C₈	C₄×D₁₈₈	1	4	yes	complemented
440	C₂²	—	94	4	no	—
441	C₂²	—	94	4	no	—
442	C₂²	—	94	4	no	—
443	C₂²	—	188	2	no	—
444	C₂²	—	188	2	no	—
445	C₂²	—	188	2	no	—
446	C₂²	—	188	2	no	—
447	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
448	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
449	C₂²	#15689778	1	1	yes	characteristic
450	C₂²	C₂×#13094048	1	1	yes	characteristic
451	C₂²	C₂×#13094056	1	1	yes	characteristic
452	C₂²	#15689930	1	1	yes	characteristic
453	C₂²	#15689930	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	94	4	no	—
460	C₄	—	376	2	no	—
461	C₄	—	376	2	no	—
462	C₄	#15689164	1	4	yes	complemented
463	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
464	C₄	#15689603	1	1	yes	characteristic
465	C₄	Q₈×D₁₈₈	1	1	yes	characteristic
466	C₄	#15689833	1	1	yes	characteristic
467	C₂	—	188	4	no	—
468	C₂	C₄⋊C₄×D₁₈₈	1	1	yes	characteristic
469	C₂	C₂×#15689164	1	1	yes	characteristic
470	C₂	#20251980	1	1	yes	characteristic
471	C₂	#20254989	1	1	yes	characteristic
472	C₂	#20255055	1	1	yes	characteristic
473	C₂	#20255985	1	1	yes	characteristic
474	C₂	#20256005	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#107×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#107	D₄₇
hypocenter	C₄₇	#22663
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
2. C₂×#15689164	C₂	semidirect
5. #20244151	C₂	semidirect
6. #20244146	C₂	semidirect
7. #20243588	C₂	semidirect
8. #20243582	C₂	semidirect
9. #20243545	C₂	semidirect
10. #20243422	C₂	semidirect
11. C₄×#107×C₄₇	C₂	semidirect
17. #15689202	C₄	semidirect
48. C₂×#10625324	C₂×C₄	semidirect
74. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
75. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
88. #107×C₄₇	D₄	semidirect
89. C₄×C₈×C₄₇	C₂×C₄	semidirect
200. C₈×C₄₇	C₄×D₄	semidirect
222. C₄×C₄₇	#428	semidirect
240. C₄×#107	D₄₇	semidirect
280. C₄₇	#22663	semidirect
319. #107	D₁₈₈	semidirect
325. C₄×C₈	C₄×D₄₇	semidirect
439. C₈	C₄×D₁₈₈	semidirect
462. C₄	#15689164	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689202	2
C₂×#15689164	2
#20246335	2
C₄⋊C₄×D₁₈₈	2
#20244151	2
#20244146	2
#20243588	2
#20243582	2
#20243545	2
#20243422	2
C₄×#107×C₄₇	2
#22663	47