Subgroups — #26121723

Order 12032.

1148 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	C₂×#15689890	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689107	C₂	1	1	yes	maximal, characteristic
3	#20243115	C₂	1	2	yes	maximal, complemented
4	#20243114	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#413	C₂	1	1	yes	maximal, characteristic
6	#15689890	—	2	4	no	—
7	#15689890	—	2	4	no	—
8	C₂×#13094031	—	2	2	no	—
9	C₂×#13094031	—	2	2	no	—
10	C₂²×#10625329	C₄	1	4	yes	—
11	C₂²×#10625329	C₂²	1	2	yes	—
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	#15689107	—	2	2	no	—
15	#15689107	C₄	1	4	yes	—
16	C₂×#13093943	—	2	1	no	—
17	C₂×#13093941	—	2	1	no	—
18	#15688888	—	2	4	no	—
19	#15688887	—	2	4	no	—
20	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
22	C₄₇×#413	—	2	2	no	—
23	C₄₇×#413	C₄	1	4	yes	—
24	C₂×#101×C₄₇	—	2	1	no	—
25	C₂×#100×C₄₇	—	2	1	no	—
26	#13094031	—	2	16	no	—
27	#13094031	—	2	16	no	—
28	C₂×#10625329	—	2	4	no	—
29	C₂×#10625329	—	2	1	no	—
30	C₂×#10625329	—	2	1	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	4	yes	—
41	C₂×#10625329	C₂×C₄	1	2	yes	—
42	C₂×#10625329	C₂×C₄	1	2	yes	—
43	C₂×#10625329	D₄	1	4	yes	—
44	C₂×#10625329	D₄	1	4	yes	—
45	C₂²×C₄₇⋊C₈	—	2	4	no	—
46	C₂²×C₄₇⋊C₈	—	2	1	no	—
47	C₂²×C₄₇⋊C₈	—	2	1	no	—
48	C₂²×C₄₇⋊C₈	—	2	2	no	—
49	#13093943	—	2	4	no	—
50	#13093941	—	2	4	no	—
51	C₂×#41×C₄₇	—	2	2	no	—
52	C₂×#41×C₄₇	—	2	2	no	—
53	C₂×#41×C₄₇	—	2	2	no	—
54	C₂×#41×C₄₇	—	2	2	no	—
55	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×#41×C₄₇	D₄	1	2	yes	—
58	C₂×#41×C₄₇	D₄	1	2	yes	—
59	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₇	Q₈	1	2	yes	—
62	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₄₇	—	2	2	no	—
65	C₂×M₁₆×C₄₇	—	2	2	no	—
66	C₂×M₁₆×C₄₇	—	2	2	no	—
67	C₂×M₁₆×C₄₇	—	2	2	no	—
68	C₂×M₁₆×C₄₇	—	2	2	no	—
69	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
70	C₂²×C₈×C₄₇	—	2	2	no	—
71	#101×C₄₇	—	2	4	no	—
72	#100×C₄₇	—	2	4	no	—
73	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
74	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
75	#41×C₄₇	—	2	4	no	—
76	#41×C₄₇	—	2	4	no	—
77	#41×C₄₇	—	2	4	no	—
78	#41×C₄₇	—	2	4	no	—
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	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
86	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	2	4	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
92	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
93	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
94	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	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	#41	1	2	yes	—
111	C₂²×C₄×C₄₇	#41	1	2	yes	—
112	M₁₆×C₄₇	—	2	4	no	—
113	M₁₆×C₄₇	—	2	4	no	—
114	M₁₆×C₄₇	—	4	2	no	—
115	M₁₆×C₄₇	—	4	2	no	—
116	C₂×C₈×C₄₇	—	2	4	no	—
117	C₂×C₈×C₄₇	—	4	2	no	—
118	C₂×C₈×C₄₇	—	4	2	no	—
119	#10625329	—	2	16	no	—
120	#10625329	—	2	2	no	—
121	#10625329	—	2	2	no	—
122	#10625329	—	2	4	no	—
123	#10625329	—	2	4	no	—
124	#10625329	—	2	4	no	—
125	#10625329	—	2	4	no	—
126	#10625329	—	4	2	no	—
127	#10625329	—	4	2	no	—
128	#10625329	C₂²⋊C₄	1	4	yes	—
129	#10625329	C₂²⋊C₄	1	4	yes	—
130	C₂×C₄₇⋊C₈	—	2	16	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	4	no	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	2	4	no	—
136	C₂×C₄₇⋊C₈	—	4	2	no	—
137	C₂×C₄₇⋊C₈	—	4	2	no	—
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	8	1	no	—
141	C₂³×C₄₇	—	8	2	no	—
142	C₂³×C₄₇	#95	1	4	yes	—
143	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
147	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
148	Q₈×C₄₇	—	2	4	no	—
149	Q₈×C₄₇	—	2	4	no	—
150	D₄×C₄₇	—	2	8	no	—
151	D₄×C₄₇	—	2	8	no	—
152	D₄×C₄₇	—	2	4	no	—
153	D₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	#95	1	4	yes	—
161	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	#117	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₄₇	#120	1	2	yes	—
174	C₂×C₄×C₄₇	#120	1	2	yes	—
175	C₂×C₄×C₄₇	#121	1	2	yes	—
176	C₂×C₄×C₄₇	#121	1	2	yes	—
177	C₂×C₄×C₄₇	#123	1	2	yes	—
178	C₂×C₄×C₄₇	#123	1	2	yes	—
179	C₈×C₄₇	—	4	4	no	—
180	C₄₇⋊C₈	—	2	4	no	—
181	C₄₇⋊C₈	—	2	4	no	—
182	C₄₇⋊C₈	—	4	4	no	—
183	#10767	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	4	1	no	—
186	C₂²×C₄₇	—	4	1	no	—
187	C₂²×C₄₇	—	4	1	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	4	4	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	—	8	2	no	—
193	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
194	C₂²×C₄₇	#380	1	1	yes	characteristic
195	C₂²×C₄₇	#380	1	1	yes	characteristic
196	C₂²×C₄₇	#385	1	2	yes	—
197	C₂²×C₄₇	#385	1	2	yes	—
198	C₄×C₄₇	—	2	4	no	—
199	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
200	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
201	C₄×C₄₇	#379	1	1	yes	characteristic
202	C₄×C₄₇	#381	1	1	yes	characteristic
203	C₄×C₄₇	#386	1	2	yes	—
204	C₄×C₄₇	#386	1	2	yes	—
205	C₂×#568	—	47	1	no	—
206	C₂×#413	—	47	1	no	—
207	C₂×#413	D₄₇	1	1	yes	characteristic
208	#1738	—	47	2	no	—
209	#1738	—	47	2	no	—
210	C₂×C₄₇	—	2	1	no	—
211	C₂×C₄₇	—	2	1	no	—
212	C₂×C₄₇	—	2	1	no	—
213	C₂×C₄₇	—	2	2	no	—
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	—	4	4	no	—
216	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
217	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
218	#568	—	94	4	no	—
219	#568	—	94	4	no	—
220	C₂×#131	—	94	2	no	—
221	C₂×#131	—	94	2	no	—
222	C₂²×M₁₆	—	47	1	no	—
223	C₂²×M₁₆	—	47	1	no	—
224	C₂²×M₁₆	—	47	4	no	—
225	C₂²×M₁₆	—	47	2	no	—
226	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
227	#413	—	2	2	no	—
228	#413	—	47	4	no	—
229	#413	—	94	2	no	—
230	#413	Dic₄₇	1	4	yes	—
231	C₂×#101	—	2	1	no	—
232	C₂×#101	—	94	1	no	—
233	C₂×#100	—	2	1	no	—
234	C₂×#100	—	94	1	no	—
235	#341	—	94	4	no	—
236	#341	—	94	4	no	—
237	C₄₇	#10767	1	1	yes	characteristic, complemented, Sylow
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	—	2	2	no	—
242	C₂×#41	C₄×D₄₇	1	2	yes	—
243	C₂×#41	D₁₈₈	1	2	yes	—
244	C₂×#41	C₂×Dic₄₇	1	2	yes	—
245	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
246	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
247	C₂²×D₄	Dic₉₄	1	2	yes	—
248	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
249	C₂³×C₄	C₄×D₄₇	1	2	yes	—
250	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
251	#131	—	94	16	no	—
252	#131	—	94	16	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	47	2	no	—
259	C₂×M₁₆	—	47	2	no	—
260	C₂×M₁₆	—	47	4	no	—
261	C₂×M₁₆	—	47	4	no	—
262	C₂×M₁₆	—	47	4	no	—
263	C₂×M₁₆	—	94	8	no	—
264	C₂×M₁₆	—	94	8	no	—
265	C₂×M₁₆	—	94	4	no	—
266	C₂×M₁₆	—	94	1	no	—
267	C₂×M₁₆	—	94	2	no	—
268	C₂×M₁₆	—	94	2	no	—
269	C₂×M₁₆	—	94	1	no	—
270	C₂×M₁₆	—	94	2	no	—
271	C₂×M₁₆	—	94	2	no	—
272	C₂×M₁₆	—	94	2	no	—
273	C₂×M₁₆	—	94	2	no	—
274	C₂×M₁₆	—	94	2	no	—
275	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	94	4	no	—
278	C₂²×C₈	—	94	1	no	—
279	C₂²×C₈	—	94	1	no	—
280	C₂²×C₈	—	94	2	no	—
281	#101	—	2	4	no	—
282	#101	—	94	4	no	—
283	#100	—	2	4	no	—
284	#100	—	94	4	no	—
285	C₂⁴	Dic₄₇⋊C₄	1	2	yes	—
286	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	#41	—	2	4	no	—
290	#41	—	2	4	no	—
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	#41	—	2	4	no	—
294	#41	—	2	4	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
298	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	Dic₄₇⋊C₄	1	4	yes	—
304	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	—
305	C₂×D₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
306	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
312	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
313	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
314	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₄₇	1	2	yes	—
318	C₂²×C₄	D₄×D₄₇	1	2	yes	—
319	C₂²×C₄	#10625352	1	2	yes	—
320	C₂²×C₄	#10625352	1	2	yes	—
321	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
324	M₁₆	—	2	4	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	4	2	no	—
327	M₁₆	—	4	2	no	—
328	M₁₆	—	47	4	no	—
329	M₁₆	—	47	4	no	—
330	M₁₆	—	94	16	no	—
331	M₁₆	—	94	2	no	—
332	M₁₆	—	94	2	no	—
333	M₁₆	—	94	4	no	—
334	M₁₆	—	94	4	no	—
335	M₁₆	—	94	4	no	—
336	M₁₆	—	94	4	no	—
337	M₁₆	—	188	2	no	—
338	M₁₆	—	188	2	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	—	94	16	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	94	4	no	—
346	C₂×C₈	—	94	4	no	—
347	C₂×C₈	—	94	4	no	—
348	C₂×C₈	—	188	2	no	—
349	C₂×C₈	—	188	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	8	1	no	—
353	C₂³	—	8	2	no	—
354	C₂³	C₄₇⋊#95	1	4	yes	—
355	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
356	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
357	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
358	C₂³	#13094001	1	2	yes	—
359	C₂³	#13094001	1	2	yes	—
360	Q₈	—	2	4	no	—
361	Q₈	—	2	4	no	—
362	D₄	—	2	8	no	—
363	D₄	—	2	8	no	—
364	D₄	—	2	4	no	—
365	D₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	C₄₇⋊#95	1	4	yes	—
373	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
376	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
377	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
378	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
379	C₂×C₄	#13093980	1	1	yes	characteristic
380	C₂×C₄	#13093980	1	1	yes	characteristic
381	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
382	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
383	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
384	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
385	C₂×C₄	#13093992	1	2	yes	—
386	C₂×C₄	#13093994	1	2	yes	—
387	C₂×C₄	#13093996	1	2	yes	—
388	C₂×C₄	#13093996	1	2	yes	—
389	C₂×C₄	#13094005	1	2	yes	—
390	C₂×C₄	#13094008	1	2	yes	—
391	C₈	—	4	4	no	—
392	C₈	—	94	4	no	—
393	C₈	—	94	4	no	—
394	C₈	—	188	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
405	C₂²	#15688981	1	1	yes	characteristic
406	C₂²	#15688981	1	1	yes	characteristic
407	C₂²	#15688995	1	2	yes	—
408	C₂²	#15688998	1	2	yes	—
409	C₄	—	2	4	no	—
410	C₄	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
411	C₄	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
412	C₄	#15688978	1	1	yes	characteristic
413	C₄	#15688984	1	1	yes	characteristic
414	C₄	#15689000	1	2	yes	—
415	C₄	#15689003	1	2	yes	—
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	2	no	—
420	C₂	—	2	2	no	—
421	C₂	—	4	4	no	—
422	C₂	#20241610	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15688978
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#413	C₂
socle	C₂×C₄₇	C₂²⋊#95
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#413	D₄₇
hypocenter	C₄₇	#10767
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
3. #20243115	C₂	semidirect
4. #20243114	C₂	semidirect
237. C₄₇	#10767	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×#15689107	2
#20243115	2
#20243114	2
C₂×C₄₇×#413	2
#10767	47