Subgroups — #26228242

Order 12032.

708 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689250	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689184	C₂	1	1	yes	maximal, characteristic
3	#20246656	C₂	1	1	yes	maximal, characteristic
4	#20244327	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244110	C₂	1	2	yes	maximal, complemented
6	#20244109	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244004	C₂	1	2	yes	maximal
8	#20243998	C₂	1	2	yes	maximal
9	#20243955	C₂	1	2	yes	maximal, complemented
10	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1798	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
13	#15689250	—	2	4	no	—
14	#15689184	—	2	4	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#13093935	C₂²	1	1	yes	characteristic
22	C₂×#13093934	C₂²	1	2	yes	—
23	C₂×#13093934	C₂²	1	2	yes	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15689062	C₄	1	1	yes	characteristic
26	#15689059	C₄	1	1	yes	characteristic
27	#15689056	C₄	1	2	yes	—
28	#15689046	C₄	1	2	yes	—
29	#15689043	C₄	1	1	yes	characteristic
30	#15689035	C₄	1	1	yes	characteristic
31	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
32	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₄×Dic₉₄	—	2	2	no	—
49	C₄×Dic₉₄	—	2	2	no	—
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
52	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
58	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	Dic₄₇⋊C₈	—	2	4	no	—
62	Dic₄₇⋊C₈	—	4	2	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
65	#13093935	—	2	2	no	—
66	#13093934	—	2	4	no	—
67	#13093934	—	4	2	no	—
68	C₄×C₄₇⋊C₈	D₄	1	4	yes	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₄₇⋊#95	C₂×C₄	1	2	yes	—
71	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
72	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
73	C₄₇⋊#95	C₂×C₄	1	2	yes	—
74	C₄₇⋊#95	C₂×C₄	1	2	yes	—
75	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
78	#117×C₄₇	—	2	2	no	—
79	#117×C₄₇	—	2	2	no	—
80	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₇	—	2	2	no	—
87	C₄⋊C₈×C₄₇	—	2	2	no	—
88	C₂²⋊C₈×C₄₇	—	4	2	no	—
89	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
106	C₂×Dic₉₄	—	2	2	no	—
107	C₂×Dic₉₄	—	4	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₂²⋊C₄×C₄₇	—	2	2	no	—
117	C₂²⋊C₄×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	—	2	1	no	—
119	C₄²×C₄₇	—	2	1	no	—
120	C₄²×C₄₇	C₂×D₄	1	2	yes	—
121	C₄²×C₄₇	#41	1	2	yes	—
122	C₂²⋊Dic₄₇	—	4	2	no	—
123	C₂²⋊Dic₄₇	—	4	2	no	—
124	C₄⋊Dic₄₇	—	2	2	no	—
125	C₄⋊Dic₄₇	—	4	2	no	—
126	Dic₄₇⋊C₄	—	2	4	no	—
127	Dic₄₇⋊C₄	—	4	2	no	—
128	Dic₄₇⋊C₄	—	4	2	no	—
129	C₄×Dic₄₇	—	2	2	no	—
130	C₄×Dic₄₇	—	2	2	no	—
131	C₄×Dic₄₇	—	2	2	no	—
132	C₄×Dic₄₇	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
144	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
145	C₂³×C₄₇	—	2	1	no	—
146	C₂³×C₄₇	—	2	1	no	—
147	C₂³×C₄₇	—	2	1	no	—
148	C₂³×C₄₇	—	2	2	no	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
170	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
171	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	Dic₉₄	—	4	4	no	—
185	C₈×C₄₇	—	4	2	no	—
186	C₈×C₄₇	—	4	2	no	—
187	C₄₇⋊C₈	—	2	2	no	—
188	C₄₇⋊C₈	—	2	2	no	—
189	C₄₇⋊C₈	—	4	1	no	—
190	C₄₇⋊C₈	—	4	1	no	—
191	#22105	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	4	1	no	—
193	C₂²×C₄₇	—	4	1	no	—
194	C₂²×C₄₇	—	4	1	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₄₇	#519	1	1	yes	characteristic
199	C₂²×C₄₇	#520	1	1	yes	characteristic
200	C₂²×C₄₇	#568	1	2	yes	—
201	C₂²×C₄₇	#568	1	2	yes	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	—	4	1	no	—
205	C₄×C₄₇	—	4	1	no	—
206	C₄×C₄₇	—	4	1	no	—
207	C₄×C₄₇	#536	1	1	yes	characteristic
208	C₄×C₄₇	#537	1	1	yes	characteristic
209	C₄×C₄₇	#541	1	1	yes	characteristic
210	C₄×C₄₇	#542	1	1	yes	characteristic
211	Dic₄₇	—	4	2	no	—
212	Dic₄₇	—	4	2	no	—
213	Dic₄₇	—	4	2	no	—
214	Dic₄₇	—	4	2	no	—
215	C₂×#446	—	47	1	no	—
216	C₂×#433	—	47	1	no	—
217	#2396	—	47	1	no	—
218	#1985	—	47	1	no	—
219	#1940	—	47	1	no	—
220	#1940	—	47	2	no	—
221	#1924	—	47	2	no	—
222	#1924	—	47	2	no	—
223	#1917	—	47	2	no	—
224	#1798	D₄₇	1	1	yes	characteristic
225	#1770	—	47	1	no	—
226	C₂×C₄₇	—	8	1	no	—
227	C₂×C₄₇	#2323	1	1	yes	characteristic
228	C₂×C₄₇	#2930	1	1	yes	characteristic
229	C₂×C₄₇	#2932	1	1	yes	characteristic
230	C₂×C₄₇	#2987	1	2	yes	—
231	C₂×C₄₇	#2995	1	2	yes	—
232	C₂×C₄×Q₈	—	47	1	no	—
233	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
234	#446	—	94	4	no	—
235	#433	—	94	4	no	—
236	C₂×C₄⋊C₈	—	47	2	no	—
237	C₂×C₄⋊C₈	—	47	1	no	—
238	C₂×C₄⋊C₈	—	47	1	no	—
239	C₂×C₄⋊C₈	—	47	2	no	—
240	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	—	47	1	no	—
243	C₂×C₂²⋊C₈	—	47	1	no	—
244	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
245	C₂×#97	—	47	2	no	—
246	C₂×#97	—	47	1	no	—
247	C₂×#97	—	47	2	no	—
248	C₂×C₄×C₈	—	47	1	no	—
249	#400	—	47	1	no	—
250	#399	—	47	1	no	—
251	#398	—	47	2	no	—
252	#396	—	47	2	no	—
253	#395	—	47	1	no	—
254	#393	—	47	1	no	—
255	C₄×C₄⋊C₄	—	47	1	no	—
256	C₄×C₄⋊C₄	—	47	2	no	—
257	C₄×C₂²⋊C₄	—	47	2	no	—
258	#336	—	47	2	no	—
259	#336	—	47	2	no	—
260	#336	—	47	2	no	—
261	#336	—	47	2	no	—
262	#336	C₂×D₄₇	1	2	yes	—
263	C₄₇	#22105	1	1	yes	characteristic, complemented, Sylow
264	C₂²×Q₈	—	47	1	no	—
265	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
266	C₂²×C₈	—	47	1	no	—
267	C₂²×C₈	—	47	1	no	—
268	C₂²×C₈	—	47	1	no	—
269	C₂²×C₈	—	47	1	no	—
270	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
271	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
272	C₄×Q₈	—	94	2	no	—
273	C₄×Q₈	—	94	2	no	—
274	#117	—	2	2	no	—
275	#117	—	2	2	no	—
276	C₂×C₄⋊C₄	—	47	2	no	—
277	C₂×C₄⋊C₄	—	47	1	no	—
278	C₂×C₄⋊C₄	—	47	2	no	—
279	C₂×C₄⋊C₄	—	47	2	no	—
280	C₂×C₄⋊C₄	—	47	2	no	—
281	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	—	47	2	no	—
284	C₂×C₂²⋊C₄	—	47	2	no	—
285	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
287	C₂×C₄²	—	47	2	no	—
288	C₂×C₄²	—	47	2	no	—
289	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
290	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	94	2	no	—
294	C₄⋊C₈	—	94	2	no	—
295	C₄⋊C₈	—	94	4	no	—
296	C₄⋊C₈	—	188	2	no	—
297	C₂²⋊C₈	—	4	2	no	—
298	C₂²⋊C₈	—	94	2	no	—
299	C₂²⋊C₈	—	94	2	no	—
300	#97	—	94	4	no	—
301	#97	—	94	2	no	—
302	#97	—	188	2	no	—
303	C₄×C₈	—	47	4	no	—
304	#95	—	47	2	no	—
305	#95	—	47	2	no	—
306	#95	—	47	2	no	—
307	#95	—	47	1	no	—
308	#95	—	47	1	no	—
309	#95	—	47	2	no	—
310	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
311	C₂×Q₈	—	94	2	no	—
312	C₂×Q₈	—	188	2	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	47	2	no	—
320	C₂²×C₄	—	47	2	no	—
321	C₂²×C₄	—	47	2	no	—
322	C₂²×C₄	—	47	2	no	—
323	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	47	2	no	—
336	C₂×C₈	—	47	2	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	94	1	no	—
340	C₂×C₈	—	94	1	no	—
341	C₂×C₈	—	94	1	no	—
342	C₂×C₈	—	94	1	no	—
343	C₂×C₈	—	94	1	no	—
344	C₂×C₈	—	94	1	no	—
345	C₂×C₈	—	94	1	no	—
346	C₂×C₈	—	94	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	94	4	no	—
350	C₄⋊C₄	—	94	2	no	—
351	C₄⋊C₄	—	188	2	no	—
352	C₄⋊C₄	—	188	2	no	—
353	C₄⋊C₄	—	188	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	188	2	no	—
357	C₂²⋊C₄	—	188	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	94	2	no	—
361	C₄²	—	94	2	no	—
362	C₄²	—	94	2	no	—
363	C₄²	—	94	2	no	—
364	C₄²	D₄×D₄₇	1	2	yes	—
365	C₄²	#10625352	1	2	yes	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
372	Q₈	—	188	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	94	2	no	—
389	C₂×C₄	—	94	2	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	94	2	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	94	2	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	94	2	no	—
398	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
399	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
400	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
402	C₂×C₄	#13094069	1	1	yes	characteristic
403	C₂×C₄	#13094071	1	1	yes	characteristic
404	C₂×C₄	#13094071	1	1	yes	characteristic
405	C₂×C₄	#13094072	1	1	yes	characteristic
406	C₈	—	4	2	no	—
407	C₈	—	4	2	no	—
408	C₈	—	94	2	no	—
409	C₈	—	94	2	no	—
410	C₈	—	188	1	no	—
411	C₈	—	188	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
418	C₂²	#15689600	1	1	yes	characteristic
419	C₂²	#15689604	1	1	yes	characteristic
420	C₂²	#15689888	1	2	yes	—
421	C₂²	#15689888	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	188	2	no	—
428	C₄	—	188	2	no	—
429	C₄	—	188	2	no	—
430	C₄	—	188	2	no	—
431	C₄	#15689696	1	1	yes	characteristic
432	C₄	#15689702	1	1	yes	characteristic
433	C₄	#15689733	1	1	yes	characteristic
434	C₄	#15689740	1	1	yes	characteristic
435	C₂	—	8	1	no	—
436	C₂	#20246066	1	1	yes	characteristic
437	C₂	#20252094	1	1	yes	characteristic
438	C₂	#20252103	1	1	yes	characteristic
439	C₂	#20252492	1	2	yes	—
440	C₂	#20252556	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1798	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1798	D₄₇
hypocenter	C₄₇	#22105
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1798

Complements

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

N	H ≅ G/N	type
1. C₂×#15689250	C₂	semidirect
4. #20244327	C₂	semidirect
5. #20244110	C₂	semidirect
6. #20244109	C₂	semidirect
9. #20243955	C₂	semidirect
10. #20243258	C₂	semidirect
263. C₄₇	#22105	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689250	2
C₂×#15689184	2
#20246656	2
#20244327	2
#20244110	2
#20244109	2
#20244004	2
#20243998	2
#20243955	2
#20243258	2
C₄₇×#1798	2
#22105	47