Subgroups — #26228248

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×#15689254	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689184	C₂	1	1	yes	maximal, characteristic
3	#20244329	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244112	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244112	C₂	1	2	yes	maximal, complemented
6	#20244003	C₂	1	2	yes	maximal
7	#20244003	C₂	1	2	yes	maximal
8	#20243954	C₂	1	2	yes	maximal, complemented
9	#20243372	C₂	1	1	yes	maximal, characteristic
10	#20243257	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2396	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	4	no	—
13	#15689184	—	2	4	no	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
23	C₂×#13093935	C₂²	1	2	yes	—
24	C₂×#13093935	C₂²	1	1	yes	characteristic
25	C₂×#13093935	C₂²	1	2	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	#15688878	C₂²	1	2	yes	—
28	#15688878	C₂²	1	2	yes	—
29	#15688878	C₂²	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	#15688878	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#400	C₄	1	1	yes	characteristic
35	C₄₇×#399	C₄	1	1	yes	characteristic
36	C₄₇×#398	C₄	1	2	yes	—
37	C₄₇×#396	C₄	1	2	yes	—
38	C₄₇×#395	C₄	1	1	yes	characteristic
39	C₄₇×#393	C₄	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
42	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
50	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
54	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
55	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
58	#13093935	—	2	2	no	—
59	#13093935	—	2	4	no	—
60	#13093935	—	4	2	no	—
61	C₄×C₄₇⋊C₈	D₄	1	4	yes	—
62	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₄₇	—	2	2	no	—
65	C₄×Q₈×C₄₇	—	2	2	no	—
66	#117×C₄₇	—	2	2	no	—
67	#117×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	#95×C₄₇	C₂×C₄	1	2	yes	—
84	#95×C₄₇	C₂×C₄	1	2	yes	—
85	#95×C₄₇	C₂×C₄	1	2	yes	—
86	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
87	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
88	#95×C₄₇	C₂×C₄	1	2	yes	—
89	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	4	2	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	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
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	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	—	4	2	no	—
113	C₄⋊C₄×C₄₇	—	4	2	no	—
114	C₄⋊C₄×C₄₇	—	4	2	no	—
115	C₂²⋊C₄×C₄₇	—	2	2	no	—
116	C₂²⋊C₄×C₄₇	—	2	2	no	—
117	C₂²⋊C₄×C₄₇	—	4	2	no	—
118	C₂²⋊C₄×C₄₇	—	4	2	no	—
119	C₄²×C₄₇	—	2	1	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	1	no	—
122	C₄²×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	C₂×D₄	1	2	yes	—
126	C₄²×C₄₇	#41	1	2	yes	—
127	C₂×C₄₇⋊C₈	—	2	1	no	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	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	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	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	Q₈×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
183	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
185	C₄₇⋊C₈	—	2	2	no	—
186	C₄₇⋊C₈	—	2	2	no	—
187	C₄₇⋊C₈	—	4	1	no	—
188	C₄₇⋊C₈	—	4	1	no	—
189	C₄₇⋊C₈	—	4	2	no	—
190	C₄₇⋊C₈	—	4	2	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	2	no	—
207	C₄×C₄₇	—	4	1	no	—
208	C₄×C₄₇	—	4	2	no	—
209	C₄×C₄₇	—	4	2	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	#536	1	1	yes	characteristic
212	C₄×C₄₇	#537	1	1	yes	characteristic
213	C₄×C₄₇	#541	1	1	yes	characteristic
214	C₄×C₄₇	#542	1	1	yes	characteristic
215	C₂×#446	—	47	1	no	—
216	C₂×#433	—	47	1	no	—
217	#2396	D₄₇	1	1	yes	characteristic
218	#1985	—	47	1	no	—
219	#1940	—	47	2	no	—
220	#1940	—	47	1	no	—
221	#1924	—	47	2	no	—
222	#1924	—	47	2	no	—
223	#1917	—	47	2	no	—
224	#1798	—	47	1	no	—
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	C₂×D₄₇	1	1	yes	characteristic
233	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
234	#446	—	94	4	no	—
235	#433	—	94	4	no	—
236	C₂×C₄⋊C₈	—	47	1	no	—
237	C₂×C₄⋊C₈	—	47	1	no	—
238	C₂×C₄⋊C₈	—	47	1	no	—
239	C₂×C₄⋊C₈	—	47	1	no	—
240	C₂×C₄⋊C₈	—	47	2	no	—
241	C₂×C₄⋊C₈	—	47	2	no	—
242	C₂×C₂²⋊C₈	—	47	1	no	—
243	C₂×C₂²⋊C₈	—	47	1	no	—
244	C₂×C₂²⋊C₈	—	47	2	no	—
245	C₂×#97	—	47	1	no	—
246	C₂×#97	—	47	2	no	—
247	C₂×#97	—	47	2	no	—
248	C₂×C₄×C₈	—	47	1	no	—
249	#400	Dic₄₇	1	1	yes	characteristic
250	#399	Dic₄₇	1	1	yes	characteristic
251	#398	Dic₄₇	1	2	yes	—
252	#396	Dic₄₇	1	2	yes	—
253	#395	Dic₄₇	1	1	yes	characteristic
254	#393	Dic₄₇	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
256	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
257	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
258	#336	—	47	2	no	—
259	#336	—	47	2	no	—
260	#336	—	47	2	no	—
261	#336	—	47	2	no	—
262	#336	—	47	2	no	—
263	C₄₇	#22105	1	1	yes	characteristic, complemented, Sylow
264	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
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	2	no	—
270	C₂²×C₈	—	47	1	no	—
271	C₂²×C₈	—	47	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	2	no	—
274	#117	—	2	2	no	—
275	#117	—	2	2	no	—
276	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
279	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
281	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
282	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
287	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
288	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
289	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
290	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
291	C₄⋊C₈	—	94	2	no	—
292	C₄⋊C₈	—	94	2	no	—
293	C₄⋊C₈	—	94	4	no	—
294	C₄⋊C₈	—	94	2	no	—
295	C₄⋊C₈	—	94	2	no	—
296	C₄⋊C₈	—	188	2	no	—
297	C₂²⋊C₈	—	94	2	no	—
298	C₂²⋊C₈	—	94	2	no	—
299	C₂²⋊C₈	—	188	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	C₂×Dic₄₇	1	2	yes	—
305	#95	C₂×Dic₄₇	1	2	yes	—
306	#95	C₂×Dic₄₇	1	2	yes	—
307	#95	C₂×Dic₄₇	1	1	yes	characteristic
308	#95	C₂×Dic₄₇	1	1	yes	characteristic
309	#95	C₂×Dic₄₇	1	2	yes	—
310	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	4	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	C₂²×Dic₄₇	1	2	yes	—
320	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
324	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
325	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
326	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
329	C₂×C₈	—	47	2	no	—
330	C₂×C₈	—	47	2	no	—
331	C₂×C₈	—	94	1	no	—
332	C₂×C₈	—	94	1	no	—
333	C₂×C₈	—	94	1	no	—
334	C₂×C₈	—	94	1	no	—
335	C₂×C₈	—	94	1	no	—
336	C₂×C₈	—	94	1	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	1	no	—
342	C₂×C₈	—	94	1	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	—	94	1	no	—
345	C₂×C₈	—	94	1	no	—
346	C₂×C₈	—	94	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	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	C₂³×Dic₄₇	1	1	yes	characteristic
372	Q₈	—	4	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	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
399	C₂×C₄	D₄×Dic₄₇	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	#13094070	1	1	yes	characteristic
403	C₂×C₄	#13094071	1	1	yes	characteristic
404	C₂×C₄	#13094072	1	1	yes	characteristic
405	C₂×C₄	#13094072	1	1	yes	characteristic
406	C₈	—	94	2	no	—
407	C₈	—	94	2	no	—
408	C₈	—	188	2	no	—
409	C₈	—	188	1	no	—
410	C₈	—	188	1	no	—
411	C₈	—	188	2	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×D₄×Dic₄₇	1	1	yes	characteristic
418	C₂²	#15689601	1	1	yes	characteristic
419	C₂²	#15689606	1	1	yes	characteristic
420	C₂²	#15689890	1	2	yes	—
421	C₂²	#15689890	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	2	no	—
431	C₄	#15689696	1	1	yes	characteristic
432	C₄	#15689703	1	1	yes	characteristic
433	C₄	#15689733	1	1	yes	characteristic
434	C₄	#15689746	1	1	yes	characteristic
435	C₂	—	8	1	no	—
436	C₂	#20246072	1	1	yes	characteristic
437	C₂	#20252092	1	1	yes	characteristic
438	C₂	#20252106	1	1	yes	characteristic
439	C₂	#20252494	1	2	yes	—
440	C₂	#20252558	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#2396	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2396	D₄₇
hypocenter	C₄₇	#22105
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2396

Complements

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

N	H ≅ G/N	type
1. C₂×#15689254	C₂	semidirect
3. #20244329	C₂	semidirect
4. #20244112	C₂	semidirect
5. #20244112	C₂	semidirect
8. #20243954	C₂	semidirect
10. #20243257	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×#15689254	2
C₂×#15689184	2
#20244329	2
#20244112	2
#20244003	2
#20243954	2
#20243372	2
#20243257	2
C₄₇×#2396	2
#22105	47