Subgroups — #26224291

Order 12032.

890 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689470	C₂	1	1	yes	maximal, characteristic
2	#20246136	C₂	1	1	yes	maximal, characteristic, complemented
3	#20246113	C₂	1	1	yes	maximal, characteristic
4	#20244361	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244212	C₂	1	1	yes	maximal, characteristic
6	#20244085	C₂	1	2	yes	maximal, complemented
7	#20244071	C₂	1	2	yes	maximal, complemented
8	#20243519	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243214	C₂	1	2	yes	maximal, complemented
10	C₄×#13093946	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094024	C₂²	1	1	yes	characteristic
13	C₂×#13094021	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
15	#15689470	C₄	1	8	yes	complemented
16	C₂×#13093946	C₂²	1	2	yes	—
17	C₂×#13093946	C₂²	1	2	yes	—
18	C₂×#13093946	C₂²	1	2	yes	—
19	C₂×#13093946	C₂²	1	2	yes	—
20	#15689027	—	2	2	no	—
21	#15689025	C₂²	1	2	yes	—
22	#15689021	C₂²	1	2	yes	—
23	#15689006	—	2	2	no	—
24	#15689001	—	2	2	no	—
25	#15689001	—	2	2	no	—
26	#15688989	C₂²	1	1	yes	characteristic
27	#15688989	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
29	#15688886	C₂²	1	2	yes	—
30	#15688886	C₂²	1	2	yes	—
31	#15688886	C₂²	1	2	yes	—
32	#15688886	C₂²	1	2	yes	—
33	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#376	C₂²	1	1	yes	characteristic
40	C₂²×Dic₉₄	—	2	1	no	—
41	C₂²×D₁₈₈	—	2	1	no	—
42	C₂²×D₁₈₈	—	2	1	no	—
43	C₂²×D₁₈₈	C₂³	1	2	yes	—
44	C₂²×C₄×D₄₇	—	2	2	no	—
45	#13094024	—	2	2	no	—
46	#13094024	C₂×C₄	1	4	yes	complemented
47	#13094021	—	2	2	no	—
48	#13094021	C₂×C₄	1	4	yes	—
49	C₄×D₁₈₈	—	2	4	no	—
50	C₄×D₁₈₈	—	2	4	no	—
51	C₂×C₄⋊Dic₄₇	—	2	1	no	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×Dic₄₇⋊C₄	—	2	2	no	—
56	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
57	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
59	C₂×C₄×Dic₄₇	—	2	2	no	—
60	#13093946	—	2	4	no	—
61	#13093946	—	2	4	no	—
62	#13093946	C₂×C₄	1	8	yes	complemented
63	#13093946	C₂×C₄	1	8	yes	complemented
64	C₄₇⋊#95	—	2	2	no	—
65	C₄₇⋊#95	—	2	1	no	—
66	C₄₇⋊#95	—	2	1	no	—
67	C₄₇⋊#95	—	2	1	no	—
68	C₄₇⋊#95	—	2	1	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×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	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	#97×C₄₇	—	2	2	no	—
78	#97×C₄₇	—	2	2	no	—
79	#97×C₄₇	—	2	2	no	—
80	C₄×C₈×C₄₇	—	2	2	no	—
81	C₄×C₈×C₄₇	—	2	2	no	—
82	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
83	#95×C₄₇	D₄	1	2	yes	—
84	#95×C₄₇	D₄	1	2	yes	—
85	C₂³×D₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₇	—	2	2	no	—
92	C₂²×Dic₄₇	—	2	2	no	—
93	C₂²×Dic₄₇	—	2	2	no	—
94	C₂×D₁₈₈	—	2	2	no	—
95	C₂×D₁₈₈	—	2	2	no	—
96	C₂×D₁₈₈	—	2	2	no	—
97	C₂×D₁₈₈	—	2	2	no	—
98	C₂×D₁₈₈	—	2	2	no	—
99	C₂×D₁₈₈	—	2	4	no	—
100	C₂×D₁₈₈	—	2	4	no	—
101	C₂×D₁₈₈	—	8	2	no	—
102	C₂×D₁₈₈	—	8	2	no	—
103	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
104	C₂×C₄×D₄₇	—	4	4	no	—
105	C₂×C₄×D₄₇	—	8	2	no	—
106	C₂×C₄×D₄₇	—	8	2	no	—
107	C₂×Dic₉₄	—	2	4	no	—
108	C₂×Dic₉₄	—	8	2	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₇	#41	1	2	yes	—
120	C₂×C₈×C₄₇	#41	1	2	yes	—
121	C₄²×C₄₇	—	2	1	no	—
122	C₄²×C₄₇	—	2	1	no	—
123	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
124	C₄²×C₄₇	#41	1	2	yes	—
125	C₄²×C₄₇	#41	1	2	yes	—
126	C₄²×C₄₇	#41	1	2	yes	—
127	(C₂×D₄₇)⋊C₄	—	4	4	no	—
128	(C₂×D₄₇)⋊C₄	—	8	2	no	—
129	(C₂×D₄₇)⋊C₄	—	8	2	no	—
130	C₄⋊Dic₄₇	—	2	4	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
137	Dic₄₇⋊C₄	—	8	2	no	—
138	C₄×Dic₄₇	—	8	2	no	—
139	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
140	C₂²×D₄₇	—	2	4	no	—
141	C₂²×D₄₇	—	4	2	no	—
142	C₂²×D₄₇	—	4	2	no	—
143	C₂²×D₄₇	—	4	2	no	—
144	C₂²×D₄₇	—	4	2	no	—
145	C₂²×D₄₇	—	4	2	no	—
146	C₂²×D₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₇	#124	1	4	yes	—
157	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×Dic₄₇	—	2	4	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
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	D₁₈₈	—	2	4	no	—
173	D₁₈₈	—	2	4	no	—
174	D₁₈₈	—	4	2	no	—
175	D₁₈₈	—	4	2	no	—
176	D₁₈₈	—	8	4	no	—
177	D₁₈₈	—	8	4	no	—
178	C₄×D₄₇	—	8	8	no	—
179	Dic₉₄	—	8	4	no	—
180	C₈×C₄₇	—	2	2	no	—
181	C₈×C₄₇	—	2	2	no	—
182	C₈×C₄₇	—	2	2	no	—
183	C₈×C₄₇	—	2	2	no	—
184	#21644	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
187	C₂²×C₄₇	#532	1	1	yes	characteristic
188	C₂²×C₄₇	#576	1	2	yes	—
189	C₂²×C₄₇	#577	1	2	yes	—
190	C₂×D₄₇	—	4	4	no	—
191	C₂×D₄₇	—	4	4	no	—
192	C₂×D₄₇	—	4	4	no	—
193	C₂×D₄₇	—	8	2	no	—
194	C₂×D₄₇	—	8	2	no	—
195	C₂×D₄₇	—	8	2	no	—
196	C₂×D₄₇	—	8	2	no	—
197	C₄×C₄₇	—	2	4	no	—
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	2	2	no	—
200	C₄×C₄₇	—	4	2	no	—
201	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
202	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
203	C₄×C₄₇	#529	1	1	yes	characteristic
204	C₄×C₄₇	#529	1	1	yes	characteristic
205	Dic₄₇	—	4	4	no	—
206	Dic₄₇	—	8	2	no	—
207	Dic₄₇	—	8	2	no	—
208	C₂×#486	—	47	1	no	—
209	#2331	—	47	1	no	—
210	#2328	—	47	1	no	—
211	#1993	—	47	1	no	—
212	#1961	—	47	1	no	—
213	#1936	—	47	2	no	—
214	#1934	—	47	2	no	—
215	#1835	—	47	1	no	—
216	#1762	—	47	2	no	—
217	C₄×#102	—	47	2	no	—
218	#1726	D₄₇	1	1	yes	characteristic, complemented
219	C₂×C₄₇	C₄×#124	1	1	yes	characteristic
220	C₂×C₄₇	#2948	1	1	yes	characteristic
221	C₂×C₄₇	#2949	1	1	yes	characteristic
222	C₂×C₄₇	#3136	1	2	yes	—
223	C₂×C₄₇	#3179	1	2	yes	—
224	D₄₇	—	8	4	no	—
225	C₂×C₄⋊Q₈	—	47	1	no	—
226	C₂×#127	—	47	1	no	—
227	C₂×C₄×D₄	—	47	2	no	—
228	#486	—	47	8	no	—
229	C₂×#102	—	47	2	no	—
230	C₂×#102	—	47	2	no	—
231	C₂×#102	—	47	2	no	—
232	C₂×#102	—	47	2	no	—
233	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
234	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
235	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
239	#391	—	94	2	no	—
240	#390	—	47	2	no	—
241	#389	—	47	2	no	—
242	#387	—	94	2	no	—
243	#386	—	94	2	no	—
244	#386	—	94	2	no	—
245	#382	—	47	1	no	—
246	#382	—	47	1	no	—
247	C₄×C₄⋊C₄	—	47	2	no	—
248	#376	C₂×D₄₇	1	1	yes	characteristic
249	#340	—	47	2	no	—
250	#340	—	47	2	no	—
251	#340	—	47	2	no	—
252	#340	—	47	2	no	—
253	C₄₇	#21644	1	1	yes	characteristic, complemented, Sylow
254	C₂²×Q₈	—	94	1	no	—
255	C₂²×D₄	—	47	2	no	—
256	C₂²×D₄	—	94	1	no	—
257	C₂²×D₄	—	94	1	no	—
258	C₂³×C₄	—	94	2	no	—
259	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
261	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
262	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
263	C₄⋊Q₈	—	47	4	no	—
264	C₄⋊Q₈	—	94	2	no	—
265	#127	—	47	4	no	—
266	#127	—	94	2	no	—
267	C₄×D₄	—	94	4	no	—
268	C₄×D₄	—	94	4	no	—
269	C₂×C₄⋊C₄	—	47	2	no	—
270	C₂×C₄⋊C₄	—	47	2	no	—
271	C₂×C₄⋊C₄	—	47	2	no	—
272	C₂×C₄⋊C₄	—	94	1	no	—
273	C₂×C₄⋊C₄	—	94	2	no	—
274	C₂×C₂²⋊C₄	—	94	2	no	—
275	C₂×C₂²⋊C₄	—	94	2	no	—
276	C₂×C₂²⋊C₄	—	94	2	no	—
277	C₂×C₄²	—	94	2	no	—
278	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
279	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
280	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
281	#102	—	47	8	no	—
282	#102	—	47	8	no	—
283	#102	—	94	4	no	—
284	#102	—	94	4	no	—
285	#97	—	2	2	no	—
286	#97	—	2	2	no	—
287	#97	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	C₄×C₈	—	2	2	no	—
290	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
291	#95	—	94	2	no	—
292	#95	—	94	1	no	—
293	#95	—	94	1	no	—
294	#95	—	94	1	no	—
295	#95	—	94	1	no	—
296	#95	—	94	2	no	—
297	#95	D₁₈₈	1	2	yes	—
298	#95	D₁₈₈	1	2	yes	—
299	C₂⁴	—	94	2	no	—
300	C₂×Q₈	—	94	4	no	—
301	C₂×Q₈	—	376	2	no	—
302	C₂×D₄	—	47	4	no	—
303	C₂×D₄	—	94	4	no	—
304	C₂×D₄	—	94	4	no	—
305	C₂×D₄	—	94	2	no	—
306	C₂×D₄	—	94	2	no	—
307	C₂×D₄	—	94	2	no	—
308	C₂×D₄	—	94	2	no	—
309	C₂×D₄	—	94	2	no	—
310	C₂×D₄	—	376	2	no	—
311	C₂×D₄	—	376	2	no	—
312	C₂²×C₄	—	94	2	no	—
313	C₂²×C₄	—	94	2	no	—
314	C₂²×C₄	—	94	2	no	—
315	C₂²×C₄	—	376	2	no	—
316	C₂²×C₄	—	376	2	no	—
317	C₂²×C₄	—	188	4	no	—
318	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
319	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
322	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
332	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
333	C₂×C₈	#10625350	1	2	yes	—
334	C₂×C₈	#10625350	1	2	yes	—
335	C₄⋊C₄	—	47	4	no	—
336	C₄⋊C₄	—	94	4	no	—
337	C₄⋊C₄	—	94	2	no	—
338	C₄⋊C₄	—	94	2	no	—
339	C₄⋊C₄	—	94	2	no	—
340	C₄⋊C₄	—	94	2	no	—
341	C₄⋊C₄	—	94	2	no	—
342	C₄⋊C₄	—	376	2	no	—
343	C₂²⋊C₄	—	376	2	no	—
344	C₂²⋊C₄	—	376	2	no	—
345	C₂²⋊C₄	—	188	4	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	376	2	no	—
349	C₄²	C₂×C₄×D₄₇	1	2	yes	—
350	C₄²	#10625350	1	2	yes	—
351	C₄²	#10625350	1	2	yes	—
352	C₄²	#10625350	1	2	yes	—
353	C₂³	—	94	4	no	—
354	C₂³	—	188	2	no	—
355	C₂³	—	188	2	no	—
356	C₂³	—	188	2	no	—
357	C₂³	—	188	2	no	—
358	C₂³	—	188	2	no	—
359	C₂³	—	188	2	no	—
360	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
361	Q₈	—	376	4	no	—
362	D₄	—	94	4	no	—
363	D₄	—	94	4	no	—
364	D₄	—	376	4	no	—
365	D₄	—	376	4	no	—
366	D₄	—	188	2	no	—
367	D₄	—	188	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	94	4	no	—
376	C₂×C₄	—	376	8	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	2	no	—
382	C₂×C₄	—	188	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	—	188	2	no	—
385	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
386	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
387	C₂×C₄	#13094012	1	4	yes	—
388	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
390	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
391	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
392	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
393	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₂²	—	376	2	no	—
399	C₂²	—	376	2	no	—
400	C₂²	—	376	2	no	—
401	C₂²	—	376	2	no	—
402	C₂²	—	188	4	no	—
403	C₂²	—	188	4	no	—
404	C₂²	—	188	4	no	—
405	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
406	C₂²	C₂×#13094012	1	1	yes	characteristic
407	C₂²	#15689673	1	1	yes	characteristic
408	C₂²	#15689928	1	2	yes	—
409	C₂²	#15689935	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	376	2	no	—
415	C₄	—	376	2	no	—
416	C₄	—	188	4	no	—
417	C₄	C₄×#10625350	1	1	yes	characteristic
418	C₄	C₄×#10625350	1	1	yes	characteristic
419	C₄	#15689657	1	1	yes	characteristic
420	C₄	#15689657	1	1	yes	characteristic
421	C₂	—	376	4	no	—
422	C₂	C₄×#13094012	1	1	yes	characteristic
423	C₂	#20252241	1	1	yes	characteristic
424	C₂	#20252249	1	1	yes	characteristic
425	C₂	#20253744	1	2	yes	—
426	C₂	#20254071	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1726	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#13094021	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1726	D₄₇
hypocenter	C₄₇	#21644
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #376 ◁ #1726

Complements

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

N	H ≅ G/N	type
2. #20246136	C₂	semidirect
4. #20244361	C₂	semidirect
6. #20244085	C₂	semidirect
7. #20244071	C₂	semidirect
8. #20243519	C₂	semidirect
9. #20243214	C₂	semidirect
10. C₄×#13093946	C₂	semidirect
11. C₄₇×#1726	C₂	semidirect
15. #15689470	C₄	semidirect
46. #13094024	C₂×C₄	semidirect
62. #13093946	C₂×C₄	semidirect
63. #13093946	C₂×C₄	semidirect
82. C₄×C₈×C₄₇	C₂×C₄	semidirect
218. #1726	D₄₇	semidirect
253. C₄₇	#21644	semidirect
290. C₄×C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689470	2
#20246136	2
#20246113	2
#20244361	2
#20244212	2
#20244085	2
#20244071	2
#20243519	2
#20243214	2
C₄×#13093946	2
C₄₇×#1726	2
#21644	47