Subgroups — #26316693

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20251751	C₂	1	1	yes	maximal, characteristic, complemented
2	#20244776	C₂	1	4	yes	maximal, complemented
3	#20244195	C₂	1	1	yes	maximal, characteristic
4	#20244195	C₂	1	1	yes	maximal, characteristic
5	#20243635	C₂	1	4	yes	maximal, complemented
6	#20243547	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243515	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#127×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂×#13094016	—	2	1	no	—
11	C₂×#13093957	C₂²	1	4	yes	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×#13093945	C₂²	1	4	yes	—
14	C₂×#13093945	C₂²	1	4	yes	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	#15689021	—	2	1	no	—
18	#15689021	—	2	1	no	—
19	#15689021	C₂²	1	2	yes	—
20	#15689021	C₂²	1	2	yes	—
21	#15688993	C₂²	1	1	yes	characteristic
22	#15688993	C₂²	1	1	yes	characteristic
23	#15688989	—	2	1	no	—
24	#15688885	C₂²	1	4	yes	—
25	#15688878	C₂²	1	2	yes	—
26	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₇	—	2	1	no	—
28	C₂×C₄×D₄×C₄₇	—	2	1	no	—
29	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
30	C₄₇×#390	—	2	1	no	—
31	C₄₇×#390	—	2	1	no	—
32	C₄₇×#390	C₂²	1	2	yes	—
33	C₄₇×#384	C₂²	1	1	yes	characteristic
34	C₄³×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
36	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
37	#13094016	—	4	4	no	—
38	C₂×C₄⋊Dic₄₇	—	2	1	no	—
39	C₂×C₄⋊Dic₄₇	—	2	1	no	—
40	C₂×C₄⋊Dic₄₇	—	2	1	no	—
41	C₂×C₄⋊Dic₄₇	—	2	1	no	—
42	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
43	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
44	C₂×Dic₄₇⋊C₄	—	2	2	no	—
45	C₂×Dic₄₇⋊C₄	—	2	2	no	—
46	#13093957	—	4	4	no	—
47	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
48	#13093945	—	2	8	no	—
49	#13093945	—	4	4	no	—
50	C₄×C₄₇⋊C₈	—	2	2	no	—
51	C₄×C₄₇⋊C₈	—	2	2	no	—
52	C₄₇⋊#95	—	2	2	no	—
53	C₄₇⋊#95	—	2	2	no	—
54	C₂²×D₄×C₄₇	—	2	1	no	—
55	C₂²×D₄×C₄₇	—	2	1	no	—
56	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₄₇	—	2	2	no	—
58	#127×C₄₇	—	2	2	no	—
59	#127×C₄₇	Q₈	1	4	yes	—
60	C₄×D₄×C₄₇	—	4	4	no	—
61	C₄×D₄×C₄₇	—	4	4	no	—
62	C₄×D₄×C₄₇	—	4	4	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₂⁴×C₄₇	—	2	2	no	—
77	C₂×D₄×C₄₇	—	2	4	no	—
78	C₂×D₄×C₄₇	—	2	4	no	—
79	C₂×D₄×C₄₇	—	2	4	no	—
80	C₂×D₄×C₄₇	—	2	2	no	—
81	C₂×D₄×C₄₇	—	2	4	no	—
82	C₂×D₄×C₄₇	—	4	2	no	—
83	C₂×D₄×C₄₇	—	4	2	no	—
84	C₂×D₄×C₄₇	—	4	2	no	—
85	C₂×D₄×C₄₇	—	4	2	no	—
86	C₂×D₄×C₄₇	C₂×Q₈	1	4	yes	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	4	4	no	—
89	C₂²×C₄×C₄₇	—	4	4	no	—
90	C₂²×C₄×C₄₇	—	4	4	no	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	—	2	2	no	—
100	C₄⋊C₄×C₄₇	—	2	4	no	—
101	C₄⋊C₄×C₄₇	—	4	2	no	—
102	C₄⋊C₄×C₄₇	—	4	2	no	—
103	C₂²⋊C₄×C₄₇	—	4	4	no	—
104	C₂²⋊C₄×C₄₇	—	4	4	no	—
105	C₂²⋊C₄×C₄₇	—	4	4	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	—	2	2	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	D₈	1	4	yes	—
112	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
113	C₄²×C₄₇	#41	1	2	yes	—
114	C₄⋊Dic₄₇	—	2	4	no	—
115	C₄⋊Dic₄₇	—	2	4	no	—
116	C₄⋊Dic₄₇	—	4	2	no	—
117	C₄⋊Dic₄₇	—	4	2	no	—
118	C₄⋊Dic₄₇	—	4	2	no	—
119	C₄⋊Dic₄₇	—	4	2	no	—
120	Dic₄₇⋊C₄	—	4	4	no	—
121	Dic₄₇⋊C₄	—	4	4	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	#41	1	4	yes	—
128	C₂³×C₄₇	—	2	4	no	—
129	C₂³×C₄₇	—	4	2	no	—
130	C₂³×C₄₇	—	4	2	no	—
131	C₂³×C₄₇	—	4	2	no	—
132	C₂³×C₄₇	—	4	2	no	—
133	C₂³×C₄₇	—	4	2	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
136	D₄×C₄₇	—	2	8	no	—
137	D₄×C₄₇	—	4	4	no	—
138	D₄×C₄₇	—	4	8	no	—
139	D₄×C₄₇	—	4	8	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	8	8	no	—
154	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
159	C₂×C₄×C₄₇	#135	1	2	yes	—
160	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₄₇	#137	1	2	yes	—
162	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₄₇⋊C₈	—	2	4	no	—
173	C₄₇⋊C₈	—	4	2	no	—
174	#29192	—	47	1	no	maximal, Sylow
175	C₂²×C₄₇	—	4	4	no	—
176	C₂²×C₄₇	—	4	4	no	—
177	C₂²×C₄₇	—	4	4	no	—
178	C₂²×C₄₇	—	8	2	no	—
179	C₂²×C₄₇	—	8	2	no	—
180	C₂²×C₄₇	—	8	2	no	—
181	C₂²×C₄₇	—	8	2	no	—
182	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
183	C₂²×C₄₇	#532	1	1	yes	characteristic
184	C₂²×C₄₇	#535	1	1	yes	characteristic
185	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	—	4	1	no	—
192	C₄×C₄₇	—	4	1	no	—
193	C₄×C₄₇	—	8	2	no	—
194	C₄×C₄₇	#474	1	4	yes	—
195	C₄×C₄₇	#478	1	4	yes	—
196	C₄×C₄₇	#553	1	2	yes	—
197	C₄×C₄₇	#554	1	2	yes	—
198	Dic₄₇	—	8	2	no	—
199	Dic₄₇	—	8	2	no	—
200	#2859	—	47	1	no	—
201	C₄×#127	D₄₇	1	1	yes	characteristic
202	#2067	—	47	4	no	—
203	#1957	—	47	1	no	—
204	#1957	—	47	1	no	—
205	#1862	—	47	4	no	—
206	#1845	—	47	1	no	—
207	#1834	—	47	1	no	—
208	C₄×C₄⋊C₈	—	47	1	no	—
209	C₂×C₄₇	—	8	4	no	—
210	C₂×C₄₇	#2566	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#474	1	1	yes	characteristic
212	C₂×C₄₇	C₂×#478	1	1	yes	characteristic
213	C₂×C₄₇	#3169	1	1	yes	characteristic
214	C₂×C₄₇	#3182	1	1	yes	characteristic
215	C₂×C₄₇	#3205	1	1	yes	characteristic
216	C₂×C₄₇	#3210	1	1	yes	characteristic
217	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
218	C₂×#125	—	94	1	no	—
219	C₂×C₄×D₄	—	2	1	no	—
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
222	C₂×#107	—	47	4	no	—
223	C₂×C₄⋊C₈	—	47	2	no	—
224	C₂×#102	—	47	4	no	—
225	C₂×#102	—	47	4	no	—
226	C₂×C₄×C₈	—	47	1	no	—
227	C₂×C₄×C₈	—	47	1	no	—
228	#390	—	2	1	no	—
229	#390	—	2	1	no	—
230	#390	C₂×D₄₇	1	2	yes	—
231	#389	—	47	2	no	—
232	#389	—	47	2	no	—
233	#389	—	94	1	no	—
234	#389	—	94	1	no	—
235	#384	—	47	1	no	—
236	#384	—	47	1	no	—
237	#384	C₂×D₄₇	1	1	yes	characteristic
238	#382	—	94	1	no	—
239	C₄³	C₂×D₄₇	1	1	yes	characteristic
240	#340	—	47	4	no	—
241	#336	—	47	2	no	—
242	C₄₇	#29192	1	1	yes	characteristic, complemented, Sylow
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
246	C₂³×C₄	—	2	2	no	—
247	C₂²×C₈	—	47	2	no	—
248	C₂²×C₈	—	47	2	no	—
249	#127	—	2	2	no	—
250	#127	Dic₉₄	1	4	yes	—
251	#125	—	188	4	no	—
252	C₄×D₄	—	4	4	no	—
253	C₄×D₄	—	4	4	no	—
254	C₄×D₄	—	4	4	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	47	2	no	—
258	C₂×C₄⋊C₄	—	47	2	no	—
259	C₂×C₄⋊C₄	—	94	2	no	—
260	C₂×C₄⋊C₄	—	94	2	no	—
261	C₂×C₄⋊C₄	—	94	1	no	—
262	C₂×C₄⋊C₄	—	94	1	no	—
263	C₂×C₄⋊C₄	—	94	1	no	—
264	C₂×C₄⋊C₄	—	94	1	no	—
265	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
270	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
271	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
272	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
273	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
276	#107	—	188	4	no	—
277	C₄⋊C₈	—	94	4	no	—
278	#102	—	94	8	no	—
279	#102	—	188	4	no	—
280	C₄×C₈	—	94	2	no	—
281	C₄×C₈	—	94	2	no	—
282	#95	—	94	2	no	—
283	#95	—	94	2	no	—
284	C₂⁴	—	2	2	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	C₂×Dic₉₄	1	4	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	94	2	no	—
300	C₂²×C₄	—	94	2	no	—
301	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
308	C₂×C₈	—	47	4	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	—	94	2	no	—
311	C₂×C₈	—	94	2	no	—
312	C₂×C₈	—	94	2	no	—
313	C₂×C₈	—	94	2	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	94	4	no	—
318	C₄⋊C₄	—	94	4	no	—
319	C₄⋊C₄	—	188	4	no	—
320	C₄⋊C₄	—	188	4	no	—
321	C₄⋊C₄	—	188	2	no	—
322	C₄⋊C₄	—	188	2	no	—
323	C₄⋊C₄	—	188	2	no	—
324	C₄⋊C₄	—	188	2	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₂²⋊C₄	—	4	4	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	#10625334	1	4	yes	—
334	C₄²	C₂×Dic₉₄	1	2	yes	—
335	C₄²	#10625350	1	2	yes	—
336	C₂³	—	2	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
344	D₄	—	2	8	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	8	no	—
347	D₄	—	4	8	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	8	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	#13094003	1	2	yes	—
369	C₂×C₄	#13094003	1	2	yes	—
370	C₂×C₄	C₂×#10625334	1	2	yes	—
371	C₂×C₄	C₂×#10625334	1	2	yes	—
372	C₂×C₄	C₂×#10625334	1	2	yes	—
373	C₂×C₄	#13094044	1	2	yes	—
374	C₂×C₄	#13094050	1	2	yes	—
375	C₂×C₄	#13094054	1	2	yes	—
376	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
377	C₂×C₄	#41×D₄₇	1	2	yes	—
378	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
379	C₂×C₄	#13094069	1	2	yes	—
380	C₈	—	94	4	no	—
381	C₈	—	188	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	C₂×#13094003	1	1	yes	characteristic
390	C₂²	#15689669	1	1	yes	characteristic
391	C₂²	#15689690	1	1	yes	characteristic
392	C₂²	C₂²×#10625334	1	1	yes	characteristic
393	C₂²	C₂×#13094044	1	1	yes	characteristic
394	C₂²	C₂×#13094050	1	1	yes	characteristic
395	C₂²	C₂×#13094054	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	376	2	no	—
402	C₄	—	376	2	no	—
403	C₄	#15689403	1	4	yes	—
404	C₄	#15689423	1	4	yes	—
405	C₄	#15689823	1	2	yes	—
406	C₄	#15689832	1	2	yes	—
407	C₂	—	8	4	no	—
408	C₂	#20248584	1	1	yes	characteristic
409	C₂	C₂×#15689403	1	1	yes	characteristic
410	C₂	C₂×#15689423	1	1	yes	characteristic
411	C₂	#20253963	1	1	yes	characteristic
412	C₂	#20254102	1	1	yes	characteristic
413	C₂	#20254306	1	1	yes	characteristic
414	C₂	#20254344	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#127×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#127×C₄₇	C₂²
hypercenter	C₄×#127	D₄₇
hypocenter	C₄₇	#29192
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#127

Complements

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

N	H ≅ G/N	type
1. #20251751	C₂	semidirect
2. #20244776	C₂	semidirect
5. #20243635	C₂	semidirect
6. #20243547	C₂	semidirect
7. #20243515	C₂	semidirect
8. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
242. C₄₇	#29192	semidirect

Maximal subgroups

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

subgroup	index
#20251751	2
#20244776	2
#20244195	2
#20243635	2
#20243547	2
#20243515	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄×#127×C₄₇	2
#29192	47