Subgroups — #26215933

Order 12032.

1292 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689890	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689171	C₂	1	2	yes	maximal, complemented
3	C₂×#15689107	C₂	1	1	yes	maximal, characteristic
4	#20243436	C₂	1	8	yes	maximal, complemented
5	C₂×C₄₇⋊#338	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#413	C₂	1	1	yes	maximal, characteristic
7	#15689890	—	2	4	no	—
8	#15689890	—	2	4	no	—
9	C₂×#13094031	C₄	1	4	yes	—
10	C₂×#13094031	C₂²	1	4	yes	—
11	C₂²×#10625329	C₄	1	4	yes	—
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	C₂²×#10625329	C₂²	1	1	yes	characteristic
15	#15689171	—	2	4	no	—
16	#15689171	—	2	4	no	—
17	C₂×#13093959	C₂²	1	8	yes	complemented
18	#15689107	—	2	2	no	—
19	#15689107	C₂²	1	4	yes	—
20	C₂×#13093943	—	2	1	no	—
21	C₂×#13093941	—	2	1	no	—
22	C₄₇⋊#338	C₂²	1	8	yes	complemented
23	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
25	C₄₇×#413	—	2	2	no	—
26	C₄₇×#413	C₂²	1	4	yes	—
27	C₂×#101×C₄₇	—	2	1	no	—
28	C₂×#100×C₄₇	—	2	1	no	—
29	#13094031	—	2	16	no	—
30	#13094031	—	2	16	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	8	no	—
34	C₂×#10625329	—	2	8	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	—	2	2	no	—
40	C₂×#10625329	C₂×C₄	1	2	yes	—
41	C₂×#10625329	C₂×C₄	1	8	yes	—
42	C₂×#10625329	C₂×C₄	1	2	yes	—
43	C₂×#10625329	C₂×C₄	1	2	yes	—
44	C₂×#10625329	D₄	1	4	yes	—
45	C₂×#10625329	D₄	1	4	yes	—
46	C₂×#10625329	C₂³	1	4	yes	—
47	C₂×#10625329	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
50	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
52	#13093959	—	2	16	no	—
53	#13093943	—	2	4	no	—
54	#13093941	—	2	4	no	—
55	C₂×#41×C₄₇	—	2	2	no	—
56	C₂×#41×C₄₇	—	2	2	no	—
57	C₂×#41×C₄₇	—	2	2	no	—
58	C₂×#41×C₄₇	—	2	2	no	—
59	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×#41×C₄₇	D₄	1	2	yes	—
61	C₂×#41×C₄₇	Q₈	1	2	yes	—
62	C₂×#41×C₄₇	C₂³	1	2	yes	—
63	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
64	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
65	C₂²×D₄×C₄₇	Q₈	1	2	yes	—
66	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₄₇	—	2	2	no	—
69	C₂×M₁₆×C₄₇	—	2	2	no	—
70	C₂×M₁₆×C₄₇	—	2	2	no	—
71	C₂×M₁₆×C₄₇	—	2	2	no	—
72	C₂×M₁₆×C₄₇	—	2	2	no	—
73	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
74	C₂²×C₈×C₄₇	—	2	2	no	—
75	#101×C₄₇	—	2	4	no	—
76	#100×C₄₇	—	2	4	no	—
77	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
78	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	2	4	no	—
82	#41×C₄₇	—	2	4	no	—
83	#41×C₄₇	—	2	4	no	—
84	#41×C₄₇	—	2	4	no	—
85	#41×C₄₇	—	2	4	no	—
86	#41×C₄₇	—	2	4	no	—
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×Q₈×C₄₇	—	2	2	no	—
89	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
90	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
91	C₂×D₄×C₄₇	—	2	4	no	—
92	C₂×D₄×C₄₇	—	2	4	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
96	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
97	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂×D₄×C₄₇	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	2	yes	—
114	C₂²×C₄×C₄₇	#41	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	M₁₆×C₄₇	—	2	4	no	—
117	M₁₆×C₄₇	—	2	4	no	—
118	M₁₆×C₄₇	—	4	2	no	—
119	M₁₆×C₄₇	—	4	2	no	—
120	C₂×C₈×C₄₇	—	2	4	no	—
121	C₂×C₈×C₄₇	—	4	2	no	—
122	C₂×C₈×C₄₇	—	4	2	no	—
123	#10625329	—	2	2	no	—
124	#10625329	—	2	2	no	—
125	#10625329	—	2	4	no	—
126	#10625329	—	2	16	no	—
127	#10625329	—	2	4	no	—
128	#10625329	—	2	4	no	—
129	#10625329	—	4	2	no	—
130	#10625329	—	4	2	no	—
131	#10625329	C₂²⋊C₄	1	4	yes	—
132	#10625329	C₂²⋊C₄	1	4	yes	—
133	#10625329	C₂²⋊C₄	1	8	yes	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	2	16	no	—
136	C₂×C₄₇⋊C₈	—	2	4	no	—
137	C₂×C₄₇⋊C₈	—	4	2	no	—
138	C₂×C₄₇⋊C₈	—	4	2	no	—
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
141	C₂×C₄₇⋊C₈	C₂×D₄	1	8	yes	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	8	1	no	—
145	C₂³×C₄₇	—	8	2	no	—
146	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
147	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
150	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
151	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
152	Q₈×C₄₇	—	2	4	no	—
153	Q₈×C₄₇	—	2	4	no	—
154	D₄×C₄₇	—	2	8	no	—
155	D₄×C₄₇	—	2	8	no	—
156	D₄×C₄₇	—	2	4	no	—
157	D₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
168	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
172	C₂×C₄×C₄₇	#117	1	2	yes	—
173	C₂×C₄×C₄₇	#121	1	2	yes	—
174	C₂×C₄×C₄₇	#121	1	2	yes	—
175	C₂×C₄×C₄₇	#121	1	2	yes	—
176	C₂×C₄×C₄₇	#121	1	2	yes	—
177	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
183	C₈×C₄₇	—	4	4	no	—
184	C₄₇⋊C₈	—	2	4	no	—
185	C₄₇⋊C₈	—	4	4	no	—
186	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	8	yes	—
187	#20673	—	47	1	no	maximal, Sylow
188	C₂²×C₄₇	—	2	4	no	—
189	C₂²×C₄₇	—	4	1	no	—
190	C₂²×C₄₇	—	4	1	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	—	4	2	no	—
193	C₂²×C₄₇	—	4	1	no	—
194	C₂²×C₄₇	—	4	4	no	—
195	C₂²×C₄₇	—	8	2	no	—
196	C₂²×C₄₇	—	8	2	no	—
197	C₂²×C₄₇	#380	1	1	yes	characteristic
198	C₂²×C₄₇	#380	1	1	yes	characteristic
199	C₂²×C₄₇	#380	1	2	yes	—
200	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
202	C₄×C₄₇	—	2	4	no	—
203	C₄×C₄₇	#380	1	1	yes	characteristic
204	C₄×C₄₇	#380	1	1	yes	characteristic
205	C₄×C₄₇	#380	1	2	yes	—
206	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
207	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
208	C₄×C₄₇	C₂×#121	1	2	yes	—
209	C₂×#568	—	47	1	no	—
210	C₂×#430	—	47	2	no	—
211	C₂×#413	—	47	1	no	—
212	C₂×#413	D₄₇	1	1	yes	characteristic
213	#1813	—	47	8	no	—
214	C₂×#338	—	47	2	no	—
215	C₂×C₄₇	—	2	1	no	—
216	C₂×C₄₇	—	2	1	no	—
217	C₂×C₄₇	—	2	1	no	—
218	C₂×C₄₇	—	2	2	no	—
219	C₂×C₄₇	—	2	2	no	—
220	C₂×C₄₇	—	4	4	no	—
221	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
222	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
223	#568	—	94	4	no	—
224	#568	—	94	4	no	—
225	C₂×#131	—	47	4	no	—
226	C₂×#131	—	47	4	no	—
227	C₂²×M₁₆	—	47	1	no	—
228	C₂²×M₁₆	—	47	4	no	—
229	C₂²×M₁₆	—	47	1	no	—
230	C₂²×M₁₆	—	47	2	no	—
231	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
232	#430	—	94	4	no	—
233	#430	—	94	4	no	—
234	C₂×#108	—	47	8	no	—
235	#413	—	2	2	no	—
236	#413	—	47	4	no	—
237	#413	—	94	2	no	—
238	#413	C₂×D₄₇	1	4	yes	—
239	C₂×#101	—	2	1	no	—
240	C₂×#101	—	94	1	no	—
241	C₂×#100	—	2	1	no	—
242	C₂×#100	—	94	1	no	—
243	#338	—	47	8	no	—
244	C₄₇	#20673	1	1	yes	characteristic, complemented, Sylow
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	—	2	2	no	—
249	C₂×#41	Dic₉₄	1	2	yes	—
250	C₂×#41	C₄×D₄₇	1	2	yes	—
251	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
252	C₂×#41	C₂²×D₄₇	1	2	yes	—
253	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
254	C₂²×D₄	Dic₉₄	1	2	yes	—
255	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
256	C₂³×C₄	C₄×D₄₇	1	2	yes	—
257	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
258	#131	—	94	16	no	—
259	#131	—	94	16	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	47	2	no	—
266	C₂×M₁₆	—	47	2	no	—
267	C₂×M₁₆	—	47	4	no	—
268	C₂×M₁₆	—	47	4	no	—
269	C₂×M₁₆	—	47	2	no	—
270	C₂×M₁₆	—	47	8	no	—
271	C₂×M₁₆	—	47	2	no	—
272	C₂×M₁₆	—	47	4	no	—
273	C₂×M₁₆	—	94	8	no	—
274	C₂×M₁₆	—	94	8	no	—
275	C₂×M₁₆	—	94	2	no	—
276	C₂×M₁₆	—	94	2	no	—
277	C₂×M₁₆	—	94	2	no	—
278	C₂×M₁₆	—	94	2	no	—
279	C₂×M₁₆	—	94	2	no	—
280	C₂×M₁₆	—	94	2	no	—
281	C₂×M₁₆	—	94	2	no	—
282	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	—	47	2	no	—
285	C₂²×C₈	—	47	8	no	—
286	C₂²×C₈	—	47	2	no	—
287	C₂²×C₈	—	94	2	no	—
288	#108	—	94	16	no	—
289	#101	—	2	4	no	—
290	#101	—	94	4	no	—
291	#100	—	2	4	no	—
292	#100	—	94	4	no	—
293	C₂⁴	Dic₄₇⋊C₄	1	2	yes	—
294	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
295	#41	—	2	4	no	—
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	Dic₄₇⋊C₄	1	2	yes	—
306	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	Dic₄₇⋊C₄	1	4	yes	—
312	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
313	C₂×D₄	C₂×Dic₉₄	1	4	yes	—
314	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
320	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
321	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
323	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
325	C₂²×C₄	D₄×D₄₇	1	2	yes	—
326	C₂²×C₄	D₄×D₄₇	1	2	yes	—
327	C₂²×C₄	#10625352	1	2	yes	—
328	C₂²×C₄	#10625352	1	2	yes	—
329	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
332	M₁₆	—	2	4	no	—
333	M₁₆	—	2	4	no	—
334	M₁₆	—	4	2	no	—
335	M₁₆	—	4	2	no	—
336	M₁₆	—	47	4	no	—
337	M₁₆	—	47	4	no	—
338	M₁₆	—	47	8	no	—
339	M₁₆	—	94	16	no	—
340	M₁₆	—	94	2	no	—
341	M₁₆	—	94	2	no	—
342	M₁₆	—	94	4	no	—
343	M₁₆	—	94	4	no	—
344	M₁₆	—	94	4	no	—
345	M₁₆	—	188	2	no	—
346	M₁₆	—	188	2	no	—
347	C₂×C₈	—	2	4	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	47	4	no	—
351	C₂×C₈	—	47	8	no	—
352	C₂×C₈	—	47	4	no	—
353	C₂×C₈	—	94	16	no	—
354	C₂×C₈	—	94	4	no	—
355	C₂×C₈	—	94	4	no	—
356	C₂×C₈	—	188	2	no	—
357	C₂×C₈	—	188	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	8	1	no	—
361	C₂³	—	8	2	no	—
362	C₂³	C₂×Dic₄₇⋊C₄	1	4	yes	—
363	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
364	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
365	C₂³	#13094001	1	2	yes	—
366	C₂³	#13094001	1	2	yes	—
367	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
368	Q₈	—	2	4	no	—
369	Q₈	—	2	4	no	—
370	D₄	—	2	8	no	—
371	D₄	—	2	8	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
381	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
383	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
384	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
385	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
386	C₂×C₄	#13093980	1	1	yes	characteristic
387	C₂×C₄	#13093980	1	1	yes	characteristic
388	C₂×C₄	#13093980	1	2	yes	—
389	C₂×C₄	#13093996	1	2	yes	—
390	C₂×C₄	#13093996	1	2	yes	—
391	C₂×C₄	#13093996	1	2	yes	—
392	C₂×C₄	#13093996	1	2	yes	—
393	C₂×C₄	#13094001	1	2	yes	—
394	C₂×C₄	#13094001	1	2	yes	—
395	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
397	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
398	C₂×C₄	C₂×#10625352	1	2	yes	—
399	C₈	—	4	4	no	—
400	C₈	—	47	8	no	—
401	C₈	—	94	4	no	—
402	C₈	—	188	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	#15688981	1	1	yes	characteristic
413	C₂²	#15688981	1	1	yes	characteristic
414	C₂²	#15688981	1	2	yes	—
415	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
416	C₂²	C₂×#13094001	1	2	yes	—
417	C₄	—	2	4	no	—
418	C₄	#15688981	1	1	yes	characteristic
419	C₄	#15688981	1	1	yes	characteristic
420	C₄	#15688981	1	2	yes	—
421	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
422	C₄	C₂×#13093980	1	1	yes	characteristic
423	C₄	C₂×#13093996	1	2	yes	—
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	2	2	no	—
428	C₂	—	2	2	no	—
429	C₂	—	4	4	no	—
430	C₂	C₂×#15688981	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13093980
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#413	C₂
socle	C₂×C₄₇	C₂×#380
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#413	D₄₇
hypocenter	C₄₇	#20673
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#413

Complements

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

N	H ≅ G/N	type
2. C₂×#15689171	C₂	semidirect
4. #20243436	C₂	semidirect
5. C₂×C₄₇⋊#338	C₂	semidirect
17. C₂×#13093959	C₂²	semidirect
22. C₄₇⋊#338	C₂²	semidirect
244. C₄₇	#20673	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689890	2
C₂×#15689171	2
C₂×#15689107	2
#20243436	2
C₂×C₄₇⋊#338	2
C₂×C₄₇×#413	2
#20673	47