Subgroups — #26106392

Order 12032.

630 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689179	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689175	C₂	1	1	yes	maximal, characteristic
3	#20245793	C₂	1	1	yes	maximal, characteristic
4	#20241272	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241272	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241271	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13093982	—	2	1	no	—
9	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
10	#15689179	—	2	2	no	—
11	#15689179	C₄	1	4	yes	complemented
12	#15689175	—	2	2	no	—
13	#15689175	C₄	1	4	yes	complemented
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
17	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
18	C₂×#13093934	—	2	1	no	—
19	C₂×C₈×Dic₄₇	—	2	1	no	—
20	#15688993	C₂²	1	1	yes	characteristic
21	#15688988	—	2	1	no	—
22	#15688980	—	2	1	no	—
23	#15688980	C₄	1	2	yes	—
24	C₄⋊C₄×Dic₄₇	—	2	1	no	—
25	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#384	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
32	C₂²×C₄₇⋊C₈	—	2	1	no	—
33	C₂²×C₄₇⋊C₈	—	2	1	no	—
34	#13093982	—	4	2	no	—
35	#13093982	—	4	2	no	—
36	C₂×C₄⋊Dic₄₇	—	2	1	no	—
37	C₂×C₄⋊Dic₄₇	—	2	1	no	—
38	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
39	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
40	C₂×C₄×Dic₄₇	—	2	2	no	—
41	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
44	C₄²×D₄₇	C₂×C₄	1	2	yes	—
45	C₄²×D₄₇	C₂×C₄	1	2	yes	—
46	C₄²×D₄₇	D₄	1	2	yes	—
47	C₄²×D₄₇	Q₈	1	2	yes	—
48	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
49	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
51	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
52	(C₂×D₄₇)⋊C₈	—	2	4	no	—
53	(C₂×D₄₇)⋊C₈	—	2	4	no	—
54	#13093934	—	2	4	no	—
55	C₈×Dic₄₇	—	2	4	no	—
56	C₄₇⋊#95	—	2	2	no	—
57	C₄₇⋊#95	—	2	2	no	—
58	C₂²×C₈×C₄₇	—	2	1	no	—
59	C₂²×C₈×C₄₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₄₇	—	2	1	no	—
65	C₄⋊C₈×C₄₇	—	2	1	no	—
66	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
67	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
68	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂²×Dic₄₇	—	2	2	no	—
74	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×D₄₇	—	2	1	no	—
78	C₂×C₄×D₄₇	—	2	1	no	—
79	C₂×C₄×D₄₇	—	2	1	no	—
80	C₂×C₄×D₄₇	—	2	1	no	—
81	C₂×C₄×D₄₇	—	2	1	no	—
82	C₂×C₄×D₄₇	—	2	1	no	—
83	C₂×C₄×D₄₇	—	2	1	no	—
84	C₂×C₄×D₄₇	—	2	1	no	—
85	C₂×C₄×D₄₇	—	4	1	no	—
86	C₂×C₄×D₄₇	—	4	1	no	—
87	C₂×C₄×D₄₇	C₄²	1	2	yes	—
88	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
89	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
90	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
91	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
92	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
93	C₂×C₈×C₄₇	—	2	2	no	—
94	C₂×C₈×C₄₇	—	2	2	no	—
95	C₂×C₈×C₄₇	—	4	1	no	—
96	C₂×C₈×C₄₇	—	4	1	no	—
97	C₂×C₈×C₄₇	—	4	1	no	—
98	C₂×C₈×C₄₇	—	4	1	no	—
99	C₄⋊C₄×C₄₇	—	4	2	no	—
100	C₄⋊C₄×C₄₇	—	4	1	no	—
101	C₄⋊C₄×C₄₇	—	4	1	no	—
102	C₄⋊C₄×C₄₇	—	4	1	no	—
103	C₄⋊C₄×C₄₇	—	4	1	no	—
104	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
108	(C₂×D₄₇)⋊C₄	—	4	4	no	—
109	C₄⋊Dic₄₇	—	4	1	no	—
110	C₄⋊Dic₄₇	—	4	1	no	—
111	C₄⋊Dic₄₇	—	4	1	no	—
112	C₄⋊Dic₄₇	—	4	1	no	—
113	C₄⋊Dic₄₇	—	4	2	no	—
114	C₄×Dic₄₇	—	4	4	no	—
115	C₄×Dic₄₇	C₄²	1	2	yes	—
116	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
117	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
118	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
119	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
120	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	4	1	no	—
124	C₂×C₄₇⋊C₈	—	4	1	no	—
125	C₂×C₄₇⋊C₈	—	4	1	no	—
126	C₂×C₄₇⋊C₈	—	4	1	no	—
127	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×D₄₇	—	2	1	no	—
129	C₂²×D₄₇	—	2	1	no	—
130	C₂²×D₄₇	—	2	1	no	—
131	C₂²×D₄₇	—	2	1	no	—
132	C₂²×D₄₇	—	2	1	no	—
133	C₂²×D₄₇	—	2	1	no	—
134	C₂²×D₄₇	#95	1	2	yes	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	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	C₂×C₄²	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
150	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
154	C₂×Dic₄₇	—	2	1	no	—
155	C₂×Dic₄₇	—	2	1	no	—
156	C₂×Dic₄₇	—	2	1	no	—
157	C₂×Dic₄₇	—	2	1	no	—
158	C₂×Dic₄₇	—	2	1	no	—
159	C₂×Dic₄₇	—	2	1	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	#95	1	2	yes	—
164	C₂×Dic₄₇	#95	1	2	yes	—
165	C₂×Dic₄₇	#95	1	2	yes	—
166	C₄×D₄₇	—	2	2	no	—
167	C₄×D₄₇	—	2	2	no	—
168	C₄×D₄₇	—	2	2	no	—
169	C₄×D₄₇	—	2	2	no	—
170	C₄×D₄₇	—	2	2	no	—
171	C₄×D₄₇	—	2	2	no	—
172	C₄×D₄₇	—	2	2	no	—
173	C₄×D₄₇	—	2	2	no	—
174	C₄×D₄₇	—	4	2	no	—
175	C₄×D₄₇	—	4	2	no	—
176	C₈×C₄₇	—	4	2	no	—
177	C₈×C₄₇	—	4	2	no	—
178	C₄₇⋊C₈	—	4	2	no	—
179	C₄₇⋊C₈	—	4	2	no	—
180	#8046	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
182	C₂²×C₄₇	#413	1	1	yes	characteristic
183	C₂²×C₄₇	#413	1	1	yes	characteristic
184	C₂²×C₄₇	#416	1	1	yes	characteristic
185	C₂²×C₄₇	#416	1	1	yes	characteristic
186	C₂²×C₄₇	#418	1	1	yes	characteristic
187	C₂²×C₄₇	#419	1	1	yes	characteristic
188	C₂×D₄₇	—	2	2	no	—
189	C₂×D₄₇	—	2	2	no	—
190	C₂×D₄₇	—	2	2	no	—
191	C₂×D₄₇	—	4	1	no	—
192	C₂×D₄₇	—	4	1	no	—
193	C₂×D₄₇	—	4	1	no	—
194	C₂×D₄₇	—	4	1	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	—	8	2	no	—
198	C₄×C₄₇	#416	1	1	yes	characteristic
199	C₄×C₄₇	#416	1	1	yes	characteristic
200	C₄×C₄₇	#417	1	1	yes	characteristic
201	C₄×C₄₇	#417	1	1	yes	characteristic
202	C₄×C₄₇	#427	1	1	yes	characteristic
203	C₄×C₄₇	#427	1	1	yes	characteristic
204	C₄×C₄₇	#428	1	1	yes	characteristic
205	C₄×C₄₇	#428	1	1	yes	characteristic
206	Dic₄₇	—	2	2	no	—
207	Dic₄₇	—	2	2	no	—
208	Dic₄₇	—	2	2	no	—
209	Dic₄₇	—	8	2	no	—
210	C₂×#432	—	47	1	no	—
211	C₂×#431	—	47	1	no	—
212	#2285	—	47	1	no	—
213	#1296	—	47	1	no	—
214	#1296	—	47	1	no	—
215	#1296	—	47	1	no	—
216	#1296	D₄₇	1	1	yes	characteristic, complemented
217	C₂×C₄₇	#1553	1	1	yes	characteristic
218	C₂×C₄₇	#1553	1	1	yes	characteristic
219	C₂×C₄₇	#1554	1	1	yes	characteristic
220	C₂×C₄₇	#1554	1	1	yes	characteristic
221	C₂×C₄₇	#1735	1	1	yes	characteristic
222	C₂×C₄₇	#1736	1	1	yes	characteristic
223	C₂×C₄₇	#1742	1	1	yes	characteristic
224	D₄₇	—	4	2	no	—
225	C₂×#117	—	94	1	no	—
226	C₂²×C₄²	—	47	1	no	—
227	#432	—	47	4	no	—
228	#432	—	94	2	no	—
229	#431	—	47	4	no	—
230	#431	—	94	2	no	—
231	C₂×C₄⋊C₈	—	47	1	no	—
232	C₂×C₄⋊C₈	—	47	1	no	—
233	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
235	C₂×C₂²⋊C₈	—	94	1	no	—
236	C₂×C₂²⋊C₈	—	94	1	no	—
237	C₂×#97	—	94	1	no	—
238	C₂×C₄×C₈	—	94	1	no	—
239	#384	—	47	1	no	—
240	#384	C₂×D₄₇	1	1	yes	characteristic
241	#382	—	94	1	no	—
242	#380	—	47	2	no	—
243	#380	—	94	1	no	—
244	C₄×C₄⋊C₄	—	47	2	no	—
245	C₄×C₄⋊C₄	—	94	1	no	—
246	C₄₇	#8046	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₄	—	47	1	no	—
248	C₂³×C₄	—	47	1	no	—
249	C₂³×C₄	—	47	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	94	1	no	—
253	C₂²×C₈	—	94	1	no	—
254	#117	—	188	2	no	—
255	#117	—	188	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	47	2	no	—
259	C₂×C₄⋊C₄	—	94	1	no	—
260	C₂×C₄⋊C₄	—	94	1	no	—
261	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
262	C₂×C₂²⋊C₄	—	94	2	no	—
263	C₂×C₄²	—	47	1	no	—
264	C₂×C₄²	—	47	1	no	—
265	C₂×C₄²	—	47	1	no	—
266	C₂×C₄²	—	47	2	no	—
267	C₂×C₄²	—	47	2	no	—
268	C₂×C₄²	—	47	2	no	—
269	C₂×C₄²	—	47	2	no	—
270	C₂×C₄²	—	94	2	no	—
271	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	47	2	no	—
275	C₄⋊C₈	—	47	2	no	—
276	C₄⋊C₈	—	94	1	no	—
277	C₄⋊C₈	—	94	1	no	—
278	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
279	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
280	C₂²⋊C₈	—	94	4	no	—
281	C₂²⋊C₈	—	94	4	no	—
282	#97	—	94	4	no	—
283	C₄×C₈	—	94	4	no	—
284	#95	—	94	2	no	—
285	#95	—	94	2	no	—
286	C₂⁴	—	47	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	47	1	no	—
289	C₂²×C₄	—	47	1	no	—
290	C₂²×C₄	—	47	1	no	—
291	C₂²×C₄	—	47	2	no	—
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	47	2	no	—
295	C₂²×C₄	—	47	2	no	—
296	C₂²×C₄	—	47	2	no	—
297	C₂²×C₄	—	94	1	no	—
298	C₂²×C₄	—	94	1	no	—
299	C₂²×C₄	—	94	1	no	—
300	C₂²×C₄	—	94	1	no	—
301	C₂²×C₄	—	94	1	no	—
302	C₂²×C₄	—	94	1	no	—
303	C₂²×C₄	—	94	1	no	—
304	C₂²×C₄	—	94	1	no	—
305	C₂²×C₄	—	94	2	no	—
306	C₂²×C₄	—	188	1	no	—
307	C₂²×C₄	—	188	1	no	—
308	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
309	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	94	2	no	—
319	C₂×C₈	—	188	1	no	—
320	C₂×C₈	—	188	1	no	—
321	C₂×C₈	—	188	1	no	—
322	C₂×C₈	—	188	1	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	188	2	no	—
329	C₄⋊C₄	—	188	1	no	—
330	C₄⋊C₄	—	188	1	no	—
331	C₄⋊C₄	—	188	1	no	—
332	C₄⋊C₄	—	188	1	no	—
333	C₂²⋊C₄	—	188	4	no	—
334	C₄²	—	47	2	no	—
335	C₄²	—	47	2	no	—
336	C₄²	—	47	2	no	—
337	C₄²	—	47	2	no	—
338	C₄²	—	47	2	no	—
339	C₄²	—	47	2	no	—
340	C₄²	—	188	4	no	—
341	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
342	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
343	C₄²	D₄×D₄₇	1	1	yes	characteristic
344	C₄²	Q₈×D₄₇	1	1	yes	characteristic
345	C₂³	—	47	2	no	—
346	C₂³	—	94	1	no	—
347	C₂³	—	94	1	no	—
348	C₂³	—	94	1	no	—
349	C₂³	—	94	1	no	—
350	C₂³	—	94	1	no	—
351	C₂³	—	94	1	no	—
352	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	47	2	no	—
359	C₂×C₄	—	47	2	no	—
360	C₂×C₄	—	47	2	no	—
361	C₂×C₄	—	94	1	no	—
362	C₂×C₄	—	94	1	no	—
363	C₂×C₄	—	94	1	no	—
364	C₂×C₄	—	94	1	no	—
365	C₂×C₄	—	94	1	no	—
366	C₂×C₄	—	94	1	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	94	2	no	—
369	C₂×C₄	—	94	2	no	—
370	C₂×C₄	—	94	2	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	—	188	2	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
383	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
384	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
385	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
386	C₂×C₄	#13094043	1	1	yes	characteristic
387	C₂×C₄	#13094045	1	1	yes	characteristic
388	C₂×C₄	#13094045	1	1	yes	characteristic
389	C₂×C₄	#13094047	1	1	yes	characteristic
390	C₂×C₄	#13094048	1	1	yes	characteristic
391	C₂×C₄	#13094051	1	1	yes	characteristic
392	C₂×C₄	#13094053	1	1	yes	characteristic
393	C₂×C₄	#13094056	1	1	yes	characteristic
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	188	2	no	—
397	C₈	—	188	2	no	—
398	C₂²	—	94	2	no	—
399	C₂²	—	94	2	no	—
400	C₂²	—	94	2	no	—
401	C₂²	—	188	1	no	—
402	C₂²	—	188	1	no	—
403	C₂²	—	188	1	no	—
404	C₂²	—	188	1	no	—
405	C₂²	#95×D₄₇	1	1	yes	characteristic
406	C₂²	#15689104	1	1	yes	characteristic
407	C₂²	#15689106	1	1	yes	characteristic
408	C₂²	#15689116	1	1	yes	characteristic
409	C₂²	#15689118	1	1	yes	characteristic
410	C₂²	#15689126	1	1	yes	characteristic
411	C₂²	#15689130	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	8	2	no	—
415	C₄	—	94	2	no	—
416	C₄	—	94	2	no	—
417	C₄	—	94	2	no	—
418	C₄	—	376	2	no	—
419	C₄	#15689116	1	1	yes	characteristic
420	C₄	#15689118	1	1	yes	characteristic
421	C₄	#15689121	1	1	yes	characteristic
422	C₄	#15689123	1	1	yes	characteristic
423	C₄	#15689158	1	1	yes	characteristic
424	C₄	#15689160	1	1	yes	characteristic
425	C₄	#15689162	1	1	yes	characteristic
426	C₄	#15689164	1	1	yes	characteristic
427	C₂	—	188	2	no	—
428	C₂	#20242090	1	1	yes	characteristic
429	C₂	#20242092	1	1	yes	characteristic
430	C₂	#20242095	1	1	yes	characteristic
431	C₂	#20242097	1	1	yes	characteristic
432	C₂	#20243103	1	1	yes	characteristic
433	C₂	#20243106	1	1	yes	characteristic
434	C₂	#20243125	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1296	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1296	D₄₇
hypocenter	C₄₇	#8046
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. #20241272	C₂	semidirect
5. #20241272	C₂	semidirect
6. #20241271	C₂	semidirect
7. C₄₇×#1296	C₂	semidirect
11. #15689179	C₄	semidirect
13. #15689175	C₄	semidirect
216. #1296	D₄₇	semidirect
246. C₄₇	#8046	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689179	2
C₂×#15689175	2
#20245793	2
#20241272	2
#20241271	2
C₄₇×#1296	2
#8046	47