Subgroups — #26105860

Order 12032.

838 conjugacy classes of subgroups.

The subgroup lattice has 408 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×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20241229	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241228	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625324	—	2	1	no	—
9	C₂×C₄⋊C₄×D₄₇	C₄	1	2	yes	—
10	C₂×C₄²×D₄₇	—	2	1	no	—
11	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
12	#15689179	—	2	2	no	—
13	#15689179	C₄	1	4	yes	complemented
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
16	C₄×#10625324	—	2	2	no	—
17	C₄×#10625324	C₄	1	4	yes	complemented
18	C₂×#13093934	—	2	1	no	—
19	C₂×#13093934	—	2	1	no	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
22	C₄×Dic₄₇⋊C₄	—	2	1	no	—
23	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	#15688974	—	2	1	no	—
25	#95×D₄₇	—	2	1	no	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₄₇	—	2	2	no	—
30	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
33	C₂×#10625324	—	2	8	no	—
34	C₂×#10625324	—	2	4	no	—
35	C₂²×C₄₇⋊C₈	—	2	1	no	—
36	C₂²×C₄₇⋊C₈	—	2	1	no	—
37	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
38	C₂×Dic₄₇⋊C₄	—	2	2	no	—
39	C₄⋊C₄×D₄₇	—	2	4	no	—
40	C₄⋊C₄×D₄₇	—	2	4	no	—
41	C₂×C₄×Dic₄₇	—	2	1	no	—
42	C₂×C₄×Dic₄₇	—	2	2	no	—
43	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
46	C₄²×D₄₇	—	4	2	no	—
47	C₄²×D₄₇	—	4	2	no	—
48	C₄²×D₄₇	C₂×C₄	1	2	yes	—
49	C₄²×D₄₇	C₂×C₄	1	2	yes	—
50	C₄²×D₄₇	D₄	1	2	yes	—
51	C₄²×D₄₇	Q₈	1	2	yes	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	complemented
54	(C₂×D₄₇)⋊C₈	—	2	4	no	—
55	#13093934	—	2	4	no	—
56	#13093934	—	2	4	no	—
57	C₄×C₄₇⋊C₈	—	2	1	no	—
58	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	complemented
59	C₄₇⋊#95	—	2	1	no	—
60	C₄₇⋊#95	—	2	2	no	—
61	C₂²×C₈×C₄₇	—	2	1	no	—
62	C₂²×C₈×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₄₇	—	2	1	no	—
65	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₄₇	—	2	1	no	—
67	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	complemented
68	C₄×C₈×C₄₇	—	2	1	no	—
69	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	complemented
70	#95×C₄₇	—	2	1	no	—
71	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×Dic₄₇	—	2	2	no	—
77	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₄₇	—	2	4	no	—
81	C₂×C₄×D₄₇	—	2	2	no	—
82	C₂×C₄×D₄₇	—	2	2	no	—
83	C₂×C₄×D₄₇	—	2	1	no	—
84	C₂×C₄×D₄₇	—	2	1	no	—
85	C₂×C₄×D₄₇	—	2	1	no	—
86	C₂×C₄×D₄₇	—	2	1	no	—
87	C₂×C₄×D₄₇	—	2	8	no	—
88	C₂×C₄×D₄₇	—	4	4	no	—
89	C₂×C₄×D₄₇	—	4	4	no	—
90	C₂×C₄×D₄₇	C₄²	1	2	yes	—
91	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
92	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
93	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
94	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
95	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
96	C₂×C₈×C₄₇	—	2	4	no	—
97	C₂×C₈×C₄₇	—	2	2	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	—	4	1	no	—
100	C₂×C₈×C₄₇	—	4	1	no	—
101	C₄⋊C₄×C₄₇	—	2	2	no	—
102	C₄⋊C₄×C₄₇	M₁₆	1	4	yes	complemented
103	C₄²×C₄₇	—	4	1	no	—
104	C₄²×C₄₇	—	4	1	no	—
105	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
109	C₄⋊Dic₄₇	—	2	2	no	—
110	C₄⋊Dic₄₇	M₁₆	1	4	yes	complemented
111	Dic₄₇⋊C₄	—	2	8	no	—
112	C₄×Dic₄₇	—	4	4	no	—
113	C₄×Dic₄₇	—	4	1	no	—
114	C₄×Dic₄₇	—	4	1	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	4	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	4	1	no	—
125	C₂×C₄₇⋊C₈	—	4	1	no	—
126	#10625324	—	2	16	no	—
127	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×D₄₇	—	2	2	no	—
129	C₂²×D₄₇	—	2	1	no	—
130	C₂²×D₄₇	—	2	1	no	—
131	C₂²×D₄₇	#95	1	2	yes	—
132	C₂²×D₄₇	#104	1	4	yes	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
145	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
149	C₂×Dic₄₇	—	2	2	no	—
150	C₂×Dic₄₇	—	2	1	no	—
151	C₂×Dic₄₇	—	2	1	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	2	4	no	—
154	C₂×Dic₄₇	—	4	2	no	—
155	C₂×Dic₄₇	—	4	2	no	—
156	C₂×Dic₄₇	#95	1	2	yes	—
157	C₂×Dic₄₇	#95	1	2	yes	—
158	C₂×Dic₄₇	#95	1	2	yes	—
159	C₄×D₄₇	—	2	4	no	—
160	C₄×D₄₇	—	2	4	no	—
161	C₄×D₄₇	—	2	2	no	—
162	C₄×D₄₇	—	2	2	no	—
163	C₄×D₄₇	—	2	2	no	—
164	C₄×D₄₇	—	2	2	no	—
165	C₄×D₄₇	—	2	4	no	—
166	C₄×D₄₇	—	2	2	no	—
167	C₄×D₄₇	—	2	2	no	—
168	C₄×D₄₇	—	4	16	no	—
169	C₈×C₄₇	—	2	4	no	—
170	C₈×C₄₇	—	4	2	no	—
171	C₄₇⋊C₈	—	2	4	no	—
172	C₄₇⋊C₈	—	4	2	no	—
173	#7904	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
175	C₂²×C₄₇	#407	1	2	yes	—
176	C₂²×C₄₇	#418	1	1	yes	characteristic
177	C₂²×C₄₇	#419	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#104	1	2	yes	—
179	C₂×D₄₇	—	2	2	no	—
180	C₂×D₄₇	—	2	2	no	—
181	C₂×D₄₇	—	2	4	no	—
182	C₂×D₄₇	—	2	4	no	—
183	C₂×D₄₇	#339	1	4	yes	—
184	C₄×C₄₇	—	2	1	no	—
185	C₄×C₄₇	—	2	1	no	—
186	C₄×C₄₇	—	4	4	no	—
187	C₄×C₄₇	C₄×M₁₆	1	1	yes	characteristic
188	C₄×C₄₇	C₄×M₁₆	1	1	yes	characteristic
189	C₄×C₄₇	#417	1	1	yes	characteristic
190	C₄×C₄₇	#417	1	1	yes	characteristic
191	C₄×C₄₇	#423	1	2	yes	—
192	C₄×C₄₇	#428	1	1	yes	characteristic
193	C₄×C₄₇	#428	1	1	yes	characteristic
194	Dic₄₇	—	2	2	no	—
195	Dic₄₇	—	2	2	no	—
196	Dic₄₇	—	2	2	no	—
197	Dic₄₇	—	4	4	no	—
198	C₂×#432	—	47	1	no	—
199	C₂×C₄×M₁₆	—	47	1	no	—
200	C₂×C₄×C₄⋊C₄	—	47	1	no	—
201	#1279	—	47	1	no	—
202	#1279	—	47	1	no	—
203	#1279	—	47	1	no	—
204	#1279	D₄₇	1	1	yes	characteristic, complemented
205	C₂×C₄₇	#1490	1	2	yes	—
206	C₂×C₄₇	#1491	1	2	yes	—
207	C₂×C₄₇	#1728	1	1	yes	characteristic
208	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
209	C₂×C₄₇	#1736	1	1	yes	characteristic
210	D₄₇	—	2	4	no	—
211	C₂²×M₁₆	—	94	1	no	—
212	C₂²×C₄⋊C₄	—	47	2	no	—
213	C₂²×C₄²	—	47	1	no	—
214	C₂²×C₄²	—	94	1	no	—
215	#432	—	47	4	no	—
216	#432	—	94	2	no	—
217	C₂×C₄⋊C₈	—	47	1	no	—
218	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
219	C₂×C₂²⋊C₈	—	94	1	no	—
220	C₄×M₁₆	—	47	4	no	—
221	C₄×M₁₆	—	94	2	no	—
222	C₂×#97	—	94	1	no	—
223	C₂×#97	—	94	1	no	—
224	C₂×C₄×C₈	—	47	1	no	—
225	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
226	C₄×C₄⋊C₄	—	47	2	no	—
227	C₄×C₄⋊C₄	—	47	1	no	—
228	C₄×C₄⋊C₄	—	94	1	no	—
229	C₄×C₄⋊C₄	—	94	1	no	—
230	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
231	C₂×#95	—	94	1	no	—
232	C₄₇	#7904	1	1	yes	characteristic, complemented, Sylow
233	C₂³×C₄	—	47	1	no	—
234	C₂³×C₄	—	47	1	no	—
235	C₂³×C₄	—	47	1	no	—
236	C₂³×C₄	—	94	2	no	—
237	C₂×M₁₆	—	94	4	no	—
238	C₂×M₁₆	—	94	8	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	94	1	no	—
242	C₂²×C₈	—	94	1	no	—
243	C₂×C₄⋊C₄	—	47	2	no	—
244	C₂×C₄⋊C₄	—	94	4	no	—
245	C₂×C₄⋊C₄	—	94	2	no	—
246	C₂×C₄⋊C₄	—	94	4	no	—
247	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
248	C₂×C₄²	—	2	1	no	—
249	C₂×C₄²	—	47	1	no	—
250	C₂×C₄²	—	47	1	no	—
251	C₂×C₄²	—	47	1	no	—
252	C₂×C₄²	—	47	2	no	—
253	C₂×C₄²	—	47	2	no	—
254	C₂×C₄²	—	47	2	no	—
255	C₂×C₄²	—	47	2	no	—
256	C₂×C₄²	—	94	2	no	—
257	C₂×C₄²	—	94	1	no	—
258	C₂×C₄²	—	188	2	no	—
259	C₂×C₄²	—	188	2	no	—
260	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	47	2	no	—
263	C₄⋊C₈	—	94	1	no	—
264	C₄⋊C₈	C₄×D₄₇	1	2	yes	complemented
265	C₂²⋊C₈	—	94	4	no	—
266	#97	—	94	4	no	—
267	#97	—	94	4	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	47	2	no	—
270	C₄×C₈	—	94	1	no	—
271	C₄×C₈	C₄×D₄₇	1	2	yes	complemented
272	#95	—	2	1	no	—
273	#95	—	94	2	no	—
274	#95	—	94	1	no	—
275	C₂⁴	—	47	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	47	1	no	—
278	C₂²×C₄	—	47	1	no	—
279	C₂²×C₄	—	47	1	no	—
280	C₂²×C₄	—	47	2	no	—
281	C₂²×C₄	—	47	2	no	—
282	C₂²×C₄	—	47	2	no	—
283	C₂²×C₄	—	47	2	no	—
284	C₂²×C₄	—	47	2	no	—
285	C₂²×C₄	—	47	2	no	—
286	C₂²×C₄	—	94	4	no	—
287	C₂²×C₄	—	94	8	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	—	94	1	no	—
291	C₂²×C₄	—	94	1	no	—
292	C₂²×C₄	—	94	1	no	—
293	C₂²×C₄	—	94	1	no	—
294	C₂²×C₄	—	94	2	no	—
295	C₂²×C₄	—	188	4	no	—
296	C₂²×C₄	—	188	4	no	—
297	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
299	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
300	M₁₆	—	94	16	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	94	4	no	—
307	C₂×C₈	—	94	2	no	—
308	C₂×C₈	—	94	2	no	—
309	C₂×C₈	—	188	1	no	—
310	C₂×C₈	—	188	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	47	4	no	—
313	C₄⋊C₄	—	94	8	no	—
314	C₄⋊C₄	—	94	2	no	—
315	C₄⋊C₄	#10625324	1	4	yes	complemented
316	C₄²	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	47	2	no	—
319	C₄²	—	47	2	no	—
320	C₄²	—	47	2	no	—
321	C₄²	—	47	2	no	—
322	C₄²	—	47	2	no	—
323	C₄²	—	47	2	no	—
324	C₄²	—	188	4	no	—
325	C₄²	—	188	1	no	—
326	C₄²	—	188	1	no	—
327	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
328	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
329	C₄²	D₄×D₄₇	1	1	yes	characteristic
330	C₄²	Q₈×D₄₇	1	1	yes	characteristic
331	C₂³	—	47	2	no	—
332	C₂³	—	47	4	no	—
333	C₂³	—	94	2	no	—
334	C₂³	—	94	1	no	—
335	C₂³	—	94	1	no	—
336	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	47	2	no	—
342	C₂×C₄	—	47	2	no	—
343	C₂×C₄	—	47	2	no	—
344	C₂×C₄	—	94	4	no	—
345	C₂×C₄	—	94	4	no	—
346	C₂×C₄	—	94	2	no	—
347	C₂×C₄	—	94	1	no	—
348	C₂×C₄	—	94	1	no	—
349	C₂×C₄	—	94	2	no	—
350	C₂×C₄	—	94	2	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	94	2	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	4	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	4	no	—
358	C₂×C₄	—	188	16	no	—
359	C₂×C₄	—	188	2	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
362	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
363	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
367	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
368	C₂×C₄	C₂×#10625324	1	2	yes	—
369	C₂×C₄	#13094048	1	1	yes	characteristic
370	C₂×C₄	#13094051	1	1	yes	characteristic
371	C₂×C₄	#13094053	1	1	yes	characteristic
372	C₂×C₄	#13094056	1	1	yes	characteristic
373	C₈	—	2	4	no	—
374	C₈	—	4	2	no	—
375	C₈	—	94	4	no	—
376	C₈	—	188	2	no	—
377	C₂²	—	47	4	no	—
378	C₂²	—	94	2	no	—
379	C₂²	—	94	2	no	—
380	C₂²	—	94	4	no	—
381	C₂²	—	94	4	no	—
382	C₂²	#95×D₄₇	1	1	yes	characteristic
383	C₂²	#15689085	1	2	yes	—
384	C₂²	#15689126	1	1	yes	characteristic
385	C₂²	#15689130	1	1	yes	characteristic
386	C₂²	#104×D₄₇	1	2	yes	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	4	4	no	—
390	C₄	—	94	2	no	—
391	C₄	—	94	2	no	—
392	C₄	—	94	2	no	—
393	C₄	—	188	4	no	—
394	C₄	C₄×#10625324	1	1	yes	characteristic
395	C₄	#15689075	1	1	yes	characteristic
396	C₄	#15689121	1	1	yes	characteristic
397	C₄	#15689123	1	1	yes	characteristic
398	C₄	#15689145	1	2	yes	—
399	C₄	#15689162	1	1	yes	characteristic
400	C₄	#15689164	1	1	yes	characteristic
401	C₂	—	94	4	no	—
402	C₂	#20241829	1	2	yes	—
403	C₂	#20241833	1	2	yes	—
404	C₂	#20243080	1	1	yes	characteristic
405	C₂	#339×D₄₇	1	1	yes	characteristic
406	C₂	#20243106	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1279	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1279	D₄₇
hypocenter	C₄₇	#7904
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #20241229	C₂	semidirect
5. #20241228	C₂	semidirect
6. #20241227	C₂	semidirect
7. C₄₇×#1279	C₂	semidirect
13. #15689179	C₄	semidirect
17. C₄×#10625324	C₄	semidirect
53. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
58. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
67. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
69. C₄×C₈×C₄₇	C₂×C₄	semidirect
102. C₄⋊C₄×C₄₇	M₁₆	semidirect
110. C₄⋊Dic₄₇	M₁₆	semidirect
204. #1279	D₄₇	semidirect
232. C₄₇	#7904	semidirect
264. C₄⋊C₈	C₄×D₄₇	semidirect
271. C₄×C₈	C₄×D₄₇	semidirect
315. C₄⋊C₄	#10625324	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×C₄×#10625324	2
C₄×C₄⋊C₄×D₄₇	2
#20241229	2
#20241228	2
#20241227	2
C₄₇×#1279	2
#7904	47