Subgroups — #26125234

Order 12032.

974 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15688892	C₂	1	1	yes	maximal, characteristic
2	#20243109	C₂	1	2	yes	maximal
3	C₂×#15688882	C₂	1	2	yes	maximal
4	#20241617	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#544	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄₇⋊#95	—	2	2	no	—
10	#15688892	—	2	2	no	—
11	#15688885	—	2	2	no	—
12	#15688885	—	2	2	no	—
13	#15688882	—	2	4	no	—
14	C₄₇×#544	—	2	4	no	—
15	C₄₇×#544	—	2	2	no	—
16	C₄₇×#544	C₄	1	4	yes	complemented
17	C₂×C₄⋊Q₈×C₄₇	—	2	2	no	—
18	C₂×#125×C₄₇	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
20	C₂×#117×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂³×Dic₄₇	—	2	1	no	—
23	C₂³×Dic₄₇	—	2	1	no	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	Q₈	1	4	yes	complemented
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	1	no	—
34	C₂×C₄⋊Dic₄₇	Q₈	1	2	yes	complemented
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	—	2	1	no	—
38	C₂×C₄×Dic₄₇	Q₈	1	2	yes	complemented
39	C₄₇⋊#95	—	4	4	no	—
40	C₂²×Q₈×C₄₇	—	2	2	no	—
41	C₂³×C₄×C₄₇	D₄	1	2	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₄⋊Q₈×C₄₇	—	2	8	no	—
44	C₄⋊Q₈×C₄₇	—	2	8	no	—
45	#125×C₄₇	—	2	8	no	—
46	#125×C₄₇	—	2	8	no	—
47	C₂²⋊Q₈×C₄₇	—	2	8	no	—
48	C₂²⋊Q₈×C₄₇	—	2	8	no	—
49	#117×C₄₇	—	2	2	no	—
50	#117×C₄₇	—	2	2	no	—
51	#117×C₄₇	C₂×C₄	1	4	yes	—
52	#117×C₄₇	D₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	—	2	2	no	—
63	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
64	C₂×Q₈×C₄₇	—	2	8	no	—
65	C₂×Q₈×C₄₇	—	8	2	no	—
66	C₂×Q₈×C₄₇	—	8	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	4	2	no	—
72	C₂²×C₄×C₄₇	—	4	2	no	—
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
74	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	#41	1	2	yes	—
82	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
84	C₂²×Dic₄₇	—	2	2	no	—
85	C₂²×Dic₄₇	—	2	2	no	—
86	C₂²×Dic₄₇	—	2	2	no	—
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	—	4	1	no	—
89	C₂²×Dic₄₇	—	4	1	no	—
90	C₂²×Dic₄₇	—	4	1	no	—
91	C₂²×Dic₄₇	—	4	1	no	—
92	C₂²×Dic₄₇	—	4	2	no	—
93	C₂²×Dic₄₇	—	4	2	no	—
94	C₂²×Dic₄₇	—	4	1	no	—
95	C₂²×Dic₄₇	—	4	1	no	—
96	C₄⋊C₄×C₄₇	—	2	8	no	—
97	C₄⋊C₄×C₄₇	—	2	16	no	—
98	C₄⋊C₄×C₄₇	—	2	4	no	—
99	C₄⋊C₄×C₄₇	—	2	4	no	—
100	C₄⋊C₄×C₄₇	—	2	2	no	—
101	C₄⋊C₄×C₄₇	—	2	2	no	—
102	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
103	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
104	C₂²⋊C₄×C₄₇	—	2	4	no	—
105	C₂²⋊C₄×C₄₇	—	2	4	no	—
106	C₄²×C₄₇	—	2	4	no	—
107	C₄²×C₄₇	—	2	4	no	—
108	C₄⋊Dic₄₇	—	2	4	no	—
109	C₄⋊Dic₄₇	—	4	2	no	—
110	C₄×Dic₄₇	—	2	4	no	—
111	C₄×Dic₄₇	—	4	2	no	—
112	#10625329	—	2	4	no	—
113	#10625329	—	2	4	no	—
114	#10625329	—	4	2	no	—
115	#10625329	—	4	2	no	—
116	C₂×C₄₇⋊C₈	—	2	4	no	—
117	C₂×C₄₇⋊C₈	—	4	2	no	—
118	C₂×C₄₇⋊C₈	—	4	2	no	—
119	C₂³×C₄₇	—	2	1	no	—
120	C₂³×C₄₇	—	2	1	no	—
121	C₂³×C₄₇	—	2	1	no	—
122	C₂³×C₄₇	—	2	1	no	—
123	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂³×C₄₇	#120	1	1	yes	characteristic
125	C₂³×C₄₇	#120	1	1	yes	characteristic
126	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
128	C₂³×C₄₇	#124	1	1	yes	characteristic
129	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
130	Q₈×C₄₇	—	8	8	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	—	4	2	no	—
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	4	4	no	—
141	C₂×C₄×C₄₇	—	8	2	no	—
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
144	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#120	1	2	yes	—
147	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
148	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
150	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
152	C₂×C₄×C₄₇	#124	1	2	yes	—
153	C₂×C₄×C₄₇	#124	1	2	yes	—
154	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
156	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
157	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
158	C₂×Dic₄₇	—	2	4	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	4	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	8	2	no	—
168	C₂×Dic₄₇	—	8	1	no	—
169	C₂×Dic₄₇	—	8	1	no	—
170	C₄₇⋊C₈	—	4	4	no	—
171	#11392	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	2	1	no	—
173	C₂²×C₄₇	—	2	1	no	—
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	#379	1	1	yes	characteristic
185	C₂²×C₄₇	#391	1	1	yes	characteristic
186	C₂²×C₄₇	#391	1	1	yes	characteristic
187	C₂²×C₄₇	#393	1	1	yes	characteristic
188	C₂²×C₄₇	#393	1	1	yes	characteristic
189	C₂²×C₄₇	#395	1	1	yes	characteristic
190	C₂²×C₄₇	#395	1	1	yes	characteristic
191	C₂²×C₄₇	#453	1	1	yes	characteristic
192	C₂²×C₄₇	#454	1	1	yes	characteristic
193	C₂²×C₄₇	#455	1	1	yes	characteristic
194	C₂²×C₄₇	#456	1	1	yes	characteristic
195	C₄×C₄₇	—	4	4	no	—
196	C₄×C₄₇	—	4	4	no	—
197	C₄×C₄₇	—	4	4	no	—
198	C₄×C₄₇	#391	1	2	yes	—
199	C₄×C₄₇	#391	1	2	yes	—
200	C₄×C₄₇	#393	1	2	yes	—
201	C₄×C₄₇	#395	1	2	yes	—
202	Dic₄₇	—	4	4	no	—
203	Dic₄₇	—	8	2	no	—
204	C₂×#544	D₄₇	1	1	yes	characteristic
205	C₂×#343	—	47	1	no	—
206	#1736	—	47	2	no	—
207	C₂×#339	—	47	2	no	—
208	C₄⋊#95	—	47	1	no	—
209	C₂×C₄₇	—	2	1	no	—
210	C₂×C₄₇	—	2	1	no	—
211	C₂×C₄₇	—	2	1	no	—
212	C₂×C₄₇	—	2	1	no	—
213	C₂×C₄₇	#1446	1	1	yes	characteristic
214	C₂×C₄₇	#1792	1	1	yes	characteristic
215	C₂×C₄₇	#1793	1	1	yes	characteristic
216	C₂×C₄₇	#2027	1	1	yes	characteristic
217	C₂×C₄₇	#2028	1	1	yes	characteristic
218	C₂×C₄₇	#2060	1	1	yes	characteristic
219	C₂×C₄₇	#2061	1	1	yes	characteristic
220	C₂²×M₁₆	—	47	2	no	—
221	#544	—	2	4	no	—
222	#544	—	2	2	no	—
223	#544	Dic₄₇	1	4	yes	complemented
224	C₂×C₄⋊Q₈	—	2	2	no	—
225	C₂×#125	—	2	2	no	—
226	C₂×C₂²⋊Q₈	—	2	2	no	—
227	C₂×#117	C₂×D₄₇	1	2	yes	—
228	C₂²×C₄⋊C₄	—	47	1	no	—
229	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
230	C₂²×C₄²	—	47	1	no	—
231	C₂×#95	—	94	2	no	—
232	#343	—	94	2	no	—
233	#340	—	94	2	no	—
234	#340	—	94	2	no	—
235	#339	—	94	4	no	—
236	C₄₇	#11392	1	1	yes	characteristic, complemented, Sylow
237	C₂²×Q₈	—	2	2	no	—
238	C₂³×C₄	—	94	1	no	—
239	C₂³×C₄	—	94	1	no	—
240	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
241	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
242	C₂×M₁₆	—	47	4	no	—
243	C₂×M₁₆	—	94	2	no	—
244	C₂×M₁₆	—	94	2	no	—
245	C₂×M₁₆	—	94	2	no	—
246	C₂×M₁₆	—	94	2	no	—
247	C₂×M₁₆	—	94	2	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₄⋊Q₈	—	2	8	no	—
250	C₄⋊Q₈	—	2	8	no	—
251	#125	—	2	8	no	—
252	#125	—	2	8	no	—
253	C₂²⋊Q₈	—	2	8	no	—
254	C₂²⋊Q₈	—	2	8	no	—
255	#117	—	2	2	no	—
256	#117	—	2	2	no	—
257	#117	C₂×Dic₄₇	1	4	yes	—
258	#117	C₂²⋊D₄₇	1	4	yes	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	47	2	no	—
264	C₂×C₄⋊C₄	—	94	2	no	—
265	C₂×C₄⋊C₄	—	94	2	no	—
266	C₂×C₄⋊C₄	—	94	1	no	—
267	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
268	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	47	2	no	—
274	C₂×C₄²	—	94	2	no	—
275	C₂×C₄²	—	94	2	no	—
276	C₂×C₄²	—	94	1	no	—
277	#95	—	188	4	no	—
278	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	—	8	2	no	—
281	C₂×Q₈	—	8	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	—	94	2	no	—
291	C₂²×C₄	—	94	2	no	—
292	C₂²×C₄	—	188	2	no	—
293	C₂²×C₄	—	188	2	no	—
294	C₂²×C₄	—	188	1	no	—
295	C₂²×C₄	—	188	1	no	—
296	C₂²×C₄	—	188	1	no	—
297	C₂²×C₄	—	188	1	no	—
298	C₂²×C₄	—	188	1	no	—
299	C₂²×C₄	—	188	1	no	—
300	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
301	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
302	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
303	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
304	C₂²×C₄	#10625354	1	2	yes	—
305	C₂²×C₄	#10625354	1	1	yes	characteristic
306	C₂²×C₄	#10625354	1	1	yes	characteristic
307	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
309	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
310	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
311	M₁₆	—	94	4	no	—
312	M₁₆	—	94	4	no	—
313	M₁₆	—	188	2	no	—
314	M₁₆	—	188	2	no	—
315	C₂×C₈	—	94	4	no	—
316	C₂×C₈	—	188	2	no	—
317	C₂×C₈	—	188	2	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	16	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	94	4	no	—
325	C₄⋊C₄	—	188	2	no	—
326	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
327	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	4	no	—
332	C₄²	—	94	4	no	—
333	C₄²	—	188	2	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
339	C₂³	#13093993	1	1	yes	characteristic
340	C₂³	#13093993	1	1	yes	characteristic
341	C₂³	#13094000	1	1	yes	characteristic
342	C₂³	#13094000	1	1	yes	characteristic
343	C₂³	#13094013	1	1	yes	characteristic
344	C₂³	#13094022	1	1	yes	characteristic
345	Q₈	—	8	8	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	8	2	no	—
357	C₂×C₄	—	94	4	no	—
358	C₂×C₄	—	376	2	no	—
359	C₂×C₄	—	376	1	no	—
360	C₂×C₄	—	376	1	no	—
361	C₂×C₄	—	188	4	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	—	188	2	no	—
364	C₂×C₄	—	188	2	no	—
365	C₂×C₄	—	188	2	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	—	188	2	no	—
368	C₂×C₄	—	188	2	no	—
369	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
370	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
371	C₂×C₄	Q₈×Dic₄₇	1	1	yes	characteristic
372	C₂×C₄	Q₈×Dic₄₇	1	1	yes	characteristic
373	C₂×C₄	#13093993	1	2	yes	—
374	C₂×C₄	#13094000	1	2	yes	—
375	C₂×C₄	#13094000	1	2	yes	—
376	C₂×C₄	#13094000	1	2	yes	—
377	C₂×C₄	#13094000	1	2	yes	—
378	C₂×C₄	#13094000	1	2	yes	—
379	C₂×C₄	#13094013	1	2	yes	—
380	C₂×C₄	#13094013	1	2	yes	—
381	C₂×C₄	#13094013	1	1	yes	characteristic
382	C₂×C₄	#13094022	1	2	yes	—
383	C₂×C₄	#13094022	1	2	yes	—
384	C₂×C₄	#13094022	1	1	yes	characteristic
385	C₈	—	188	4	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	#15688979	1	1	yes	characteristic
399	C₂²	#15689030	1	1	yes	characteristic
400	C₂²	#15689030	1	1	yes	characteristic
401	C₂²	#15689034	1	1	yes	characteristic
402	C₂²	#15689034	1	1	yes	characteristic
403	C₂²	#15689042	1	1	yes	characteristic
404	C₂²	#15689042	1	1	yes	characteristic
405	C₂²	#15689291	1	1	yes	characteristic
406	C₂²	#15689296	1	1	yes	characteristic
407	C₂²	#15689301	1	1	yes	characteristic
408	C₂²	#15689306	1	1	yes	characteristic
409	C₄	—	4	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	376	2	no	—
413	C₄	—	188	4	no	—
414	C₄	#15689030	1	2	yes	—
415	C₄	#15689030	1	2	yes	—
416	C₄	#15689034	1	2	yes	—
417	C₄	#15689042	1	2	yes	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	#20241659	1	1	yes	characteristic
423	C₂	#20243342	1	1	yes	characteristic
424	C₂	#20243347	1	1	yes	characteristic
425	C₂	#20244541	1	1	yes	characteristic
426	C₂	#20244546	1	1	yes	characteristic
427	C₂	#20244730	1	1	yes	characteristic
428	C₂	#20244735	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093993
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#544	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#544	D₄₇
hypocenter	C₄₇	#11392
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#544

Complements

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

N	H ≅ G/N	type
16. C₄₇×#544	C₄	semidirect
29. C₂×#10625329	Q₈	semidirect
34. C₂×C₄⋊Dic₄₇	Q₈	semidirect
38. C₂×C₄×Dic₄₇	Q₈	semidirect
223. #544	Dic₄₇	semidirect
236. C₄₇	#11392	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15688892	2
#20243109	2
C₂×#15688882	2
#20241617	2
C₂×C₄₇×#544	2
#11392	47