Subgroups — #26214309

Order 12032.

1010 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093959	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689159	C₂	1	1	yes	maximal, characteristic
3	#20251807	C₂	1	1	yes	maximal, characteristic
4	#20251806	C₂	1	1	yes	maximal, characteristic
5	C₂×#15689079	C₂	1	1	yes	maximal, characteristic
6	#20243271	C₂	1	4	yes	maximal, complemented
7	#20243266	C₂	1	4	yes	maximal, complemented
8	#20243098	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1733	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×#13093983	C₂²	1	1	yes	characteristic
14	C₂×#13093959	C₄	1	8	yes	complemented
15	C₂×#13093959	C₂²	1	2	yes	—
16	C₂×#13093959	C₂²	1	2	yes	—
17	#15689159	C₄	1	2	yes	complemented
18	#15689159	C₄	1	2	yes	complemented
19	#15689159	C₂²	1	2	yes	—
20	#15689159	C₂²	1	2	yes	—
21	C₂×#13093957	C₄	1	2	yes	complemented
22	C₂×#13093955	C₄	1	2	yes	complemented
23	#15689081	C₂²	1	4	yes	—
24	#15689079	—	2	2	no	—
25	#15689079	C₄	1	8	yes	complemented
26	#15689079	C₂²	1	4	yes	—
27	#15689078	—	2	2	no	—
28	C₄×#10625329	—	2	2	no	—
29	M₁₆×Dic₄₇	—	2	2	no	—
30	C₂×#13093935	C₂²	1	2	yes	—
31	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
32	#15688883	C₂²	1	4	yes	—
33	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#339	C₂²	1	4	yes	—
37	C₂×#10625329	—	2	1	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	C₂×C₄	1	4	yes	—
40	C₂×#10625329	C₂×C₄	1	4	yes	—
41	C₂×#10625329	D₄	1	2	yes	—
42	C₂×#10625329	D₄	1	2	yes	—
43	C₂×#10625329	Q₈	1	4	yes	—
44	C₂×#10625329	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	—	2	1	no	—
46	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
47	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
55	#13093983	—	2	1	no	—
56	#13093983	—	2	1	no	—
57	#13093983	C₂×C₄	1	2	yes	—
58	#13093983	C₂³	1	2	yes	—
59	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	#13093959	C₂×C₄	1	8	yes	complemented
63	#13093959	C₂×C₄	1	8	yes	complemented
64	#13093957	C₂×C₄	1	4	yes	—
65	#13093957	C₂×C₄	1	4	yes	—
66	#13093955	C₂×C₄	1	4	yes	—
67	#13093955	C₂×C₄	1	4	yes	—
68	#13093935	—	2	4	no	—
69	#13093935	C₂×C₄	1	8	yes	complemented
70	#13093934	—	2	4	no	—
71	C₄×C₄₇⋊C₈	—	2	4	no	—
72	C₄×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
73	C₈×Dic₄₇	—	2	4	no	—
74	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₄₇	—	2	1	no	—
76	C₂×M₁₆×C₄₇	—	2	2	no	—
77	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
78	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
79	C₂²×C₈×C₄₇	—	2	1	no	—
80	#117×C₄₇	—	2	1	no	—
81	#117×C₄₇	—	2	1	no	—
82	#117×C₄₇	—	2	2	no	—
83	#117×C₄₇	C₂×C₄	1	2	yes	—
84	#117×C₄₇	C₂×C₄	1	4	yes	—
85	#117×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
88	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
92	C₂⁴×C₄₇	#41	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	—	2	2	no	—
106	M₁₆×C₄₇	—	2	4	no	—
107	M₁₆×C₄₇	—	2	2	no	—
108	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₄₇	—	2	4	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
114	C₂²⋊C₄×C₄₇	—	2	4	no	—
115	C₂²⋊C₄×C₄₇	—	2	2	no	—
116	C₂²⋊C₄×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	—	2	2	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂²⋊Dic₄₇	—	2	2	no	—
122	C₂²⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
125	C₄×Dic₄₇	—	2	2	no	—
126	C₄×Dic₄₇	—	2	2	no	—
127	#10625329	—	2	4	no	—
128	#10625329	—	2	2	no	—
129	#10625329	C₄⋊C₄	1	8	yes	—
130	#10625329	C₄⋊C₄	1	8	yes	—
131	#10625329	C₂²×C₄	1	4	yes	—
132	C₂×C₄₇⋊C₈	—	2	4	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	C₄²	1	4	yes	—
135	C₂×C₄₇⋊C₈	C₄²	1	4	yes	—
136	C₂×C₄₇⋊C₈	C₄²	1	4	yes	—
137	C₂×C₄₇⋊C₈	C₄²	1	4	yes	—
138	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
147	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
148	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
149	C₂³×C₄₇	—	4	2	no	—
150	C₂³×C₄₇	#117	1	2	yes	—
151	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
152	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
153	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
154	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	—	8	2	no	—
159	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₇	#117	1	2	yes	—
164	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
169	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
170	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
171	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂×Dic₄₇	—	2	4	no	—
178	C₂×Dic₄₇	—	8	2	no	—
179	C₈×C₄₇	—	2	4	no	—
180	C₄₇⋊C₈	—	2	4	no	—
181	C₄₇⋊C₈	C₂×C₄²	1	2	yes	—
182	C₄₇⋊C₈	C₂×C₄²	1	2	yes	—
183	C₄₇⋊C₈	C₂×C₄²	1	2	yes	—
184	C₄₇⋊C₈	C₂×C₄²	1	2	yes	—
185	C₄₇⋊C₈	C₂×C₄⋊C₄	1	8	yes	—
186	#20446	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	2	no	—
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
193	C₂²×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
194	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
197	C₄×C₄₇	—	4	4	no	—
198	C₄×C₄₇	—	4	4	no	—
199	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
200	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
201	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
202	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
205	Dic₄₇	—	4	4	no	—
206	C₂²×#108	—	47	1	no	—
207	C₂×#427	—	47	1	no	—
208	#2873	—	47	1	no	—
209	#2873	—	47	1	no	—
210	C₂×#405	—	47	1	no	—
211	#1773	—	47	4	no	—
212	#1772	—	47	4	no	—
213	#1733	—	47	1	no	—
214	#1733	D₄₇	1	1	yes	characteristic
215	C₂×C₄₇	—	2	1	no	—
216	C₂×C₄₇	—	2	1	no	—
217	C₂×C₄₇	—	2	2	no	—
218	C₂×C₄₇	—	2	2	no	—
219	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄₇	#2957	1	2	yes	—
221	C₂²×M₁₆	—	47	1	no	—
222	C₂²×M₁₆	—	47	1	no	—
223	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
224	C₂³×C₈	—	47	1	no	—
225	C₂×#117	—	47	1	no	—
226	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
227	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
228	C₂×#108	—	47	8	no	—
229	C₂×#108	—	47	2	no	—
230	C₂×#108	—	47	2	no	—
231	#427	—	47	2	no	—
232	#427	—	47	2	no	—
233	#427	—	47	2	no	—
234	#427	—	47	2	no	—
235	C₂×#107	—	47	2	no	—
236	C₂×#106	—	47	2	no	—
237	#405	—	47	8	no	—
238	#405	—	47	4	no	—
239	#405	—	47	4	no	—
240	#405	—	94	2	no	—
241	#405	—	94	2	no	—
242	C₄×M₁₆	—	94	2	no	—
243	C₄×M₁₆	—	94	2	no	—
244	C₂×#97	—	47	2	no	—
245	C₂×C₄×C₈	—	47	2	no	—
246	#339	—	47	4	no	—
247	#339	C₂×D₄₇	1	4	yes	—
248	C₄₇	#20446	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	47	4	no	—
253	C₂×M₁₆	—	47	2	no	—
254	C₂×M₁₆	—	47	2	no	—
255	C₂×M₁₆	—	47	4	no	—
256	C₂×M₁₆	—	47	4	no	—
257	C₂×M₁₆	—	47	2	no	—
258	C₂×M₁₆	—	94	1	no	—
259	C₂×M₁₆	—	94	2	no	—
260	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
261	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	47	4	no	—
264	C₂²×C₈	—	47	1	no	—
265	C₂²×C₈	—	47	1	no	—
266	C₂²×C₈	—	47	1	no	—
267	C₂²×C₈	—	47	1	no	—
268	C₂²×C₈	—	47	4	no	—
269	C₂²×C₈	—	47	1	no	—
270	C₂²×C₈	—	47	1	no	—
271	C₂²×C₈	—	47	2	no	—
272	C₂²×C₈	—	94	1	no	—
273	#117	—	2	1	no	—
274	#117	—	2	1	no	—
275	#117	—	2	2	no	—
276	#117	—	47	2	no	—
277	#117	—	47	2	no	—
278	#117	—	94	1	no	—
279	#117	—	94	1	no	—
280	#117	C₄×D₄₇	1	2	yes	—
281	#117	C₄×D₄₇	1	4	yes	—
282	#117	C₂²×D₄₇	1	2	yes	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	47	2	no	—
285	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	94	1	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	94	1	no	—
291	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
292	#108	—	47	8	no	—
293	#108	—	47	8	no	—
294	#107	—	47	4	no	—
295	#107	—	47	4	no	—
296	#106	—	47	4	no	—
297	#106	—	47	4	no	—
298	#97	—	47	8	no	—
299	#97	—	94	4	no	—
300	#97	—	94	4	no	—
301	C₄×C₈	—	47	8	no	—
302	C₄×C₈	—	94	4	no	—
303	C₄×C₈	—	94	4	no	—
304	C₂⁴	#10625352	1	1	yes	characteristic
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	94	2	no	—
308	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
309	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
310	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
312	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
313	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
314	C₂²×C₄	#10625352	1	1	yes	characteristic
315	C₂²×C₄	#10625352	1	2	yes	—
316	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
317	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
318	M₁₆	—	2	4	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	47	8	no	—
321	M₁₆	—	47	8	no	—
322	M₁₆	—	47	4	no	—
323	M₁₆	—	94	4	no	—
324	M₁₆	—	94	2	no	—
325	M₁₆	C₂×C₄×D₄₇	1	4	yes	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	47	4	no	—
329	C₂×C₈	—	47	4	no	—
330	C₂×C₈	—	47	4	no	—
331	C₂×C₈	—	47	4	no	—
332	C₂×C₈	—	47	2	no	—
333	C₂×C₈	—	47	4	no	—
334	C₂×C₈	—	47	2	no	—
335	C₂×C₈	—	47	1	no	—
336	C₂×C₈	—	47	1	no	—
337	C₂×C₈	—	47	1	no	—
338	C₂×C₈	—	47	1	no	—
339	C₂×C₈	—	47	2	no	—
340	C₂×C₈	—	47	2	no	—
341	C₂×C₈	—	47	4	no	—
342	C₂×C₈	—	47	4	no	—
343	C₂×C₈	—	94	4	no	—
344	C₂×C₈	—	94	2	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	47	4	no	—
348	C₄⋊C₄	—	94	2	no	—
349	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	94	2	no	—
354	C₂²⋊C₄	—	94	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	94	2	no	—
359	C₄²	—	94	2	no	—
360	C₄²	C₂×C₄×D₄₇	1	4	yes	—
361	C₂³	—	4	2	no	—
362	C₂³	#13093980	1	2	yes	—
363	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
364	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
365	C₂³	#13093989	1	2	yes	—
366	C₂³	C₂×#10625352	1	1	yes	characteristic
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	—	94	4	no	—
372	C₂×C₄	—	376	2	no	—
373	C₂×C₄	C₄²×D₄₇	1	2	yes	—
374	C₂×C₄	C₄²×D₄₇	1	2	yes	—
375	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
376	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
377	C₂×C₄	#13093980	1	2	yes	—
378	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
379	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
380	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
381	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
382	C₂×C₄	#13093989	1	2	yes	—
383	C₂×C₄	#13093989	1	2	yes	—
384	C₂×C₄	#13093989	1	2	yes	—
385	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
386	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
388	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
390	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	47	2	no	—
393	C₈	—	47	2	no	—
394	C₈	—	47	2	no	—
395	C₈	—	47	2	no	—
396	C₈	—	47	8	no	—
397	C₈	—	94	4	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	#15688974	1	2	yes	—
404	C₂²	#15688974	1	2	yes	—
405	C₂²	C₂×#13093980	1	1	yes	characteristic
406	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
407	C₂²	C₂×#13093989	1	1	yes	characteristic
408	C₄	—	4	4	no	—
409	C₄	—	4	4	no	—
410	C₄	—	188	4	no	—
411	C₄	#15688974	1	2	yes	—
412	C₄	#15688974	1	2	yes	—
413	C₄	C₂×C₄²×D₄₇	1	1	yes	characteristic
414	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
415	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
416	C₄	C₂×#13093989	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	2	no	—
419	C₂	—	2	2	no	—
420	C₂	—	2	1	no	—
421	C₂	C₂×#15688974	1	1	yes	characteristic
422	C₂	#20252301	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1733	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂⁴×C₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1733	D₄₇
hypocenter	C₄₇	#20446
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
6. #20243271	C₂	semidirect
7. #20243266	C₂	semidirect
14. C₂×#13093959	C₄	semidirect
17. #15689159	C₄	semidirect
18. #15689159	C₄	semidirect
21. C₂×#13093957	C₄	semidirect
22. C₂×#13093955	C₄	semidirect
25. #15689079	C₄	semidirect
62. #13093959	C₂×C₄	semidirect
63. #13093959	C₂×C₄	semidirect
69. #13093935	C₂×C₄	semidirect
72. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
248. C₄₇	#20446	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13093959	2
C₂×#15689159	2
#20251807	2
#20251806	2
C₂×#15689079	2
#20243271	2
#20243266	2
#20243098	2
C₄₇×#1733	2
#20446	47