Subgroups — #26111033

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689414	C₂	1	1	yes	maximal, characteristic
2	#20246339	C₂	1	1	yes	maximal, characteristic
3	#20244335	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244189	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688850	C₂	1	1	yes	maximal, characteristic
6	#20241227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13094024	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
10	C₂×#13093982	—	2	1	no	—
11	#15689414	—	2	2	no	—
12	#15689414	C₄	1	4	yes	complemented
13	C₂×#13093956	—	2	1	no	—
14	C₂×#13093947	—	2	2	no	—
15	C₂×#13093946	—	2	1	no	—
16	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	#15689024	—	2	1	no	—
18	#15689013	—	2	2	no	—
19	#15688980	—	2	1	no	—
20	C₄⋊C₄×Dic₄₇	—	2	1	no	—
21	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
22	#15688886	—	2	1	no	—
23	#15688886	—	2	1	no	—
24	#15688850	—	2	2	no	—
25	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#384	C₂²	1	1	yes	characteristic
28	C₂²×Dic₉₄	—	2	1	no	—
29	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₇	—	2	1	no	—
31	C₂²×C₄₇⋊C₈	—	2	1	no	—
32	#13094024	—	2	1	no	—
33	#13094024	—	2	1	no	—
34	#13094024	—	2	1	no	—
35	#13094024	C₂×C₄	1	2	yes	—
36	C₄×D₁₈₈	—	2	1	no	—
37	C₄×D₁₈₈	—	2	1	no	—
38	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
39	C₄×D₁₈₈	D₄	1	2	yes	—
40	#13093982	—	4	2	no	—
41	#13093982	—	4	2	no	—
42	C₂×C₄⋊Dic₄₇	—	2	1	no	—
43	C₂×C₄⋊Dic₄₇	—	2	1	no	—
44	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
45	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
47	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
48	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
49	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
50	C₂×C₄×Dic₄₇	—	2	2	no	—
51	C₂×C₄×Dic₄₇	—	2	1	no	—
52	#13093956	—	2	4	no	—
53	#13093947	—	4	4	no	—
54	#13093946	—	2	4	no	—
55	C₄×C₄₇⋊C₈	—	2	1	no	—
56	C₄×C₄₇⋊C₈	—	2	1	no	—
57	C₄₇⋊#95	—	2	2	no	—
58	C₄₇⋊#95	—	2	1	no	—
59	C₂²×C₈×C₄₇	—	2	1	no	—
60	C₂²×C₈×C₄₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
64	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
65	C₄⋊C₈×C₄₇	—	2	1	no	—
66	C₄⋊C₈×C₄₇	—	2	1	no	—
67	C₄⋊C₈×C₄₇	—	2	1	no	—
68	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
69	C₂³×D₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×Dic₄₇	—	2	1	no	—
75	C₂²×Dic₄₇	—	2	1	no	—
76	C₂²×Dic₄₇	—	2	1	no	—
77	C₂²×Dic₄₇	—	4	1	no	—
78	C₂×D₁₈₈	—	2	1	no	—
79	C₂×D₁₈₈	—	2	1	no	—
80	C₂×D₁₈₈	—	2	1	no	—
81	C₂×D₁₈₈	—	2	1	no	—
82	C₂×D₁₈₈	—	2	1	no	—
83	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
84	C₂×C₄×D₄₇	—	2	2	no	—
85	C₂×C₄×D₄₇	—	2	2	no	—
86	C₂×C₄×D₄₇	—	4	1	no	—
87	C₂×C₄×D₄₇	—	4	1	no	—
88	C₂×C₄×D₄₇	—	4	1	no	—
89	C₂×C₄×D₄₇	—	4	1	no	—
90	C₂×Dic₉₄	—	2	2	no	—
91	C₂×Dic₉₄	—	4	2	no	—
92	C₂×Dic₉₄	—	4	2	no	—
93	C₂×Dic₉₄	—	4	1	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	C₂×C₈×C₄₇	—	4	1	no	—
100	C₄⋊C₄×C₄₇	—	4	2	no	—
101	C₄⋊C₄×C₄₇	—	4	1	no	—
102	C₄⋊C₄×C₄₇	—	4	1	no	—
103	C₄⋊C₄×C₄₇	—	4	1	no	—
104	C₄⋊C₄×C₄₇	—	4	1	no	—
105	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₄₇	#41	1	1	yes	characteristic
108	C₄²×C₄₇	#41	1	1	yes	characteristic
109	(C₂×D₄₇)⋊C₄	—	2	2	no	—
110	(C₂×D₄₇)⋊C₄	—	2	2	no	—
111	(C₂×D₄₇)⋊C₄	—	4	4	no	—
112	(C₂×D₄₇)⋊C₄	—	8	2	no	—
113	C₄⋊Dic₄₇	—	2	1	no	—
114	C₄⋊Dic₄₇	—	2	1	no	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	—	2	2	no	—
117	C₄⋊Dic₄₇	—	2	1	no	—
118	C₄⋊Dic₄₇	—	2	1	no	—
119	C₄⋊Dic₄₇	—	4	1	no	—
120	C₄⋊Dic₄₇	—	4	1	no	—
121	C₄⋊Dic₄₇	C₂²⋊C₄	1	2	yes	—
122	C₄⋊Dic₄₇	SD₁₆	1	2	yes	—
123	C₄×Dic₄₇	—	4	4	no	—
124	C₄×Dic₄₇	—	4	1	no	—
125	C₄×Dic₄₇	—	4	1	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	4	1	no	—
128	C₂×C₄₇⋊C₈	—	4	1	no	—
129	C₂³×C₄₇	#120	1	1	yes	characteristic
130	C₂²×D₄₇	—	2	2	no	—
131	C₂²×D₄₇	—	4	1	no	—
132	C₂²×D₄₇	—	4	1	no	—
133	C₂²×D₄₇	—	4	1	no	—
134	C₂²×D₄₇	—	4	1	no	—
135	C₂²×D₄₇	—	4	1	no	—
136	C₂²×D₄₇	—	4	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
152	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	2	2	no	—
158	C₂×Dic₄₇	—	4	1	no	—
159	C₂×Dic₄₇	—	4	1	no	—
160	C₂×Dic₄₇	—	4	1	no	—
161	C₂×Dic₄₇	—	4	1	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	1	no	—
164	C₂×Dic₄₇	—	4	1	no	—
165	C₂×Dic₄₇	—	4	1	no	—
166	C₂×Dic₄₇	—	8	1	no	—
167	C₂×Dic₄₇	—	8	1	no	—
168	D₁₈₈	—	2	2	no	—
169	D₁₈₈	—	2	2	no	—
170	D₁₈₈	—	4	1	no	—
171	D₁₈₈	—	4	1	no	—
172	C₄×D₄₇	—	4	2	no	—
173	C₄×D₄₇	—	4	2	no	—
174	C₄×D₄₇	—	4	2	no	—
175	C₄×D₄₇	—	4	2	no	—
176	Dic₉₄	—	4	4	no	—
177	Dic₉₄	—	8	2	no	—
178	C₈×C₄₇	—	4	2	no	—
179	C₈×C₄₇	—	8	1	no	—
180	C₄₇⋊C₈	—	4	2	no	—
181	#8976	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	#386	1	1	yes	characteristic
183	C₂²×C₄₇	#450	1	1	yes	characteristic
184	C₂²×C₄₇	#452	1	1	yes	characteristic
185	C₂²×C₄₇	#452	1	1	yes	characteristic
186	C₂²×C₄₇	#452	1	1	yes	characteristic
187	C₂²×C₄₇	#453	1	1	yes	characteristic
188	C₂²×C₄₇	#454	1	1	yes	characteristic
189	C₂×D₄₇	—	4	2	no	—
190	C₂×D₄₇	—	4	2	no	—
191	C₂×D₄₇	—	4	2	no	—
192	C₂×D₄₇	—	8	1	no	—
193	C₂×D₄₇	—	8	1	no	—
194	C₂×D₄₇	—	8	1	no	—
195	C₂×D₄₇	—	8	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	8	2	no	—
199	C₄×C₄₇	#416	1	1	yes	characteristic
200	C₄×C₄₇	#419	1	1	yes	characteristic
201	C₄×C₄₇	C₄×SD₁₆	1	1	yes	characteristic
202	C₄×C₄₇	#440	1	1	yes	characteristic
203	C₄×C₄₇	#461	1	1	yes	characteristic
204	C₄×C₄₇	#463	1	1	yes	characteristic
205	C₄×C₄₇	#485	1	1	yes	characteristic
206	C₄×C₄₇	#485	1	1	yes	characteristic
207	Dic₄₇	—	4	2	no	—
208	Dic₄₇	—	4	2	no	—
209	Dic₄₇	—	8	2	no	—
210	Dic₄₇	—	8	1	no	—
211	C₂×#476	—	47	1	no	—
212	#2354	—	47	1	no	—
213	#1987	—	47	1	no	—
214	#1956	—	47	1	no	—
215	C₂×D₄⋊C₈	—	47	1	no	—
216	#1296	D₄₇	1	1	yes	characteristic, complemented
217	#1279	—	47	1	no	—
218	C₂×C₄₇	#1631	1	1	yes	characteristic
219	C₂×C₄₇	#1634	1	1	yes	characteristic
220	C₂×C₄₇	#1635	1	1	yes	characteristic
221	C₂×C₄₇	#1638	1	1	yes	characteristic
222	C₂×C₄₇	#1873	1	1	yes	characteristic
223	C₂×C₄₇	#1877	1	1	yes	characteristic
224	C₂×C₄₇	#1883	1	1	yes	characteristic
225	D₄₇	—	8	2	no	—
226	C₂×C₄⋊Q₈	—	47	1	no	—
227	C₂×C₄×D₄	—	47	1	no	—
228	C₂×#117	—	94	1	no	—
229	#476	—	47	4	no	—
230	#476	—	94	2	no	—
231	C₂×#106	—	94	1	no	—
232	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
234	C₂×#103	—	94	2	no	—
235	C₂×#102	—	94	1	no	—
236	C₂×C₄×C₈	—	47	1	no	—
237	#390	—	94	1	no	—
238	#388	—	94	2	no	—
239	#384	C₂×D₄₇	1	1	yes	characteristic
240	#380	—	94	1	no	—
241	C₄×C₄⋊C₄	—	47	1	no	—
242	C₄×C₄⋊C₄	—	94	1	no	—
243	#340	—	94	1	no	—
244	#340	—	94	1	no	—
245	D₄⋊C₈	—	94	2	no	—
246	C₄₇	#8976	1	1	yes	characteristic, complemented, Sylow
247	C₂²×Q₈	—	94	1	no	—
248	C₂²×D₄	—	47	1	no	—
249	C₂³×C₄	—	94	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	94	1	no	—
253	C₄⋊Q₈	—	47	2	no	—
254	C₄⋊Q₈	—	94	1	no	—
255	C₄⋊Q₈	—	94	1	no	—
256	C₄⋊Q₈	—	94	1	no	—
257	C₄×D₄	—	47	2	no	—
258	C₄×D₄	—	47	2	no	—
259	C₄×D₄	—	94	1	no	—
260	C₄×D₄	—	94	1	no	—
261	#117	—	188	2	no	—
262	#117	—	188	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	47	1	no	—
266	C₂×C₄⋊C₄	—	47	1	no	—
267	C₂×C₄⋊C₄	—	47	1	no	—
268	C₂×C₄⋊C₄	—	94	1	no	—
269	C₂×C₄⋊C₄	—	94	1	no	—
270	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
271	C₂×C₂²⋊C₄	—	94	1	no	—
272	C₂×C₂²⋊C₄	—	94	2	no	—
273	C₂×C₂²⋊C₄	—	94	2	no	—
274	C₂×C₄²	—	94	2	no	—
275	C₂×C₄²	—	94	1	no	—
276	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
277	#106	—	94	4	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
282	#103	—	188	4	no	—
283	#102	—	94	4	no	—
284	C₄×C₈	—	94	1	no	—
285	C₄×C₈	—	94	1	no	—
286	#95	—	94	2	no	—
287	#95	—	94	1	no	—
288	C₂⁴	—	94	1	no	—
289	C₂×Q₈	—	94	2	no	—
290	C₂×Q₈	—	188	2	no	—
291	C₂×Q₈	—	188	2	no	—
292	C₂×Q₈	—	188	1	no	—
293	C₂×D₄	—	47	2	no	—
294	C₂×D₄	—	94	1	no	—
295	C₂×D₄	—	94	1	no	—
296	C₂×D₄	—	94	1	no	—
297	C₂×D₄	—	94	1	no	—
298	C₂×D₄	—	94	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	94	1	no	—
301	C₂²×C₄	—	94	1	no	—
302	C₂²×C₄	—	94	2	no	—
303	C₂²×C₄	—	94	2	no	—
304	C₂²×C₄	—	94	1	no	—
305	C₂²×C₄	—	188	1	no	—
306	C₂²×C₄	—	188	1	no	—
307	C₂²×C₄	—	188	1	no	—
308	C₂²×C₄	—	188	1	no	—
309	C₂²×C₄	—	188	1	no	—
310	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
312	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	188	1	no	—
321	C₂×C₈	—	188	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	47	2	no	—
328	C₄⋊C₄	—	47	2	no	—
329	C₄⋊C₄	—	94	1	no	—
330	C₄⋊C₄	—	94	1	no	—
331	C₄⋊C₄	—	94	2	no	—
332	C₄⋊C₄	—	94	2	no	—
333	C₄⋊C₄	—	94	1	no	—
334	C₄⋊C₄	—	94	1	no	—
335	C₄⋊C₄	—	188	1	no	—
336	C₄⋊C₄	—	188	1	no	—
337	C₂²⋊C₄	—	94	2	no	—
338	C₂²⋊C₄	—	94	2	no	—
339	C₂²⋊C₄	—	376	2	no	—
340	C₂²⋊C₄	—	188	4	no	—
341	C₄²	—	188	4	no	—
342	C₄²	—	188	1	no	—
343	C₄²	—	188	1	no	—
344	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
345	C₄²	#10625350	1	1	yes	characteristic
346	C₄²	D₄×D₄₇	1	1	yes	characteristic
347	C₄²	#10625354	1	1	yes	characteristic
348	C₂³	—	94	2	no	—
349	C₂³	—	188	1	no	—
350	C₂³	—	188	1	no	—
351	C₂³	—	188	1	no	—
352	C₂³	—	188	1	no	—
353	C₂³	—	188	1	no	—
354	C₂³	—	188	1	no	—
355	C₂³	#13093994	1	1	yes	characteristic
356	Q₈	—	376	2	no	—
357	Q₈	—	188	4	no	—
358	D₄	—	94	2	no	—
359	D₄	—	94	2	no	—
360	D₄	—	188	1	no	—
361	D₄	—	188	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	94	2	no	—
369	C₂×C₄	—	376	1	no	—
370	C₂×C₄	—	376	1	no	—
371	C₂×C₄	—	188	2	no	—
372	C₂×C₄	—	188	1	no	—
373	C₂×C₄	—	188	1	no	—
374	C₂×C₄	—	188	1	no	—
375	C₂×C₄	—	188	1	no	—
376	C₂×C₄	—	188	1	no	—
377	C₂×C₄	—	188	1	no	—
378	C₂×C₄	—	188	1	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	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
384	C₂×C₄	#13093986	1	1	yes	characteristic
385	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
386	C₂×C₄	#13093997	1	1	yes	characteristic
387	C₂×C₄	#13093999	1	1	yes	characteristic
388	C₂×C₄	#13094009	1	1	yes	characteristic
389	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
390	C₂×C₄	#13094043	1	1	yes	characteristic
391	C₂×C₄	#13094045	1	1	yes	characteristic
392	C₂×C₄	#13094045	1	1	yes	characteristic
393	C₂×C₄	#13094048	1	1	yes	characteristic
394	C₂×C₄	#13094053	1	1	yes	characteristic
395	C₂×C₄	#13094056	1	1	yes	characteristic
396	C₂×C₄	#13094056	1	1	yes	characteristic
397	C₈	—	4	2	no	—
398	C₈	—	8	1	no	—
399	C₈	—	188	2	no	—
400	C₂²	—	376	1	no	—
401	C₂²	—	376	1	no	—
402	C₂²	—	376	1	no	—
403	C₂²	—	376	1	no	—
404	C₂²	—	188	2	no	—
405	C₂²	—	188	2	no	—
406	C₂²	—	188	2	no	—
407	C₂²	#15689001	1	1	yes	characteristic
408	C₂²	#15689275	1	1	yes	characteristic
409	C₂²	#15689286	1	1	yes	characteristic
410	C₂²	#15689288	1	1	yes	characteristic
411	C₂²	#15689288	1	1	yes	characteristic
412	C₂²	#15689293	1	1	yes	characteristic
413	C₂²	#15689298	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	376	2	no	—
418	C₄	—	376	1	no	—
419	C₄	—	188	2	no	—
420	C₄	—	188	2	no	—
421	C₄	#15689116	1	1	yes	characteristic
422	C₄	#15689130	1	1	yes	characteristic
423	C₄	#15689210	1	1	yes	characteristic
424	C₄	#15689222	1	1	yes	characteristic
425	C₄	#15689327	1	1	yes	characteristic
426	C₄	#15689337	1	1	yes	characteristic
427	C₄	#15689466	1	1	yes	characteristic
428	C₄	#15689467	1	1	yes	characteristic
429	C₂	—	376	2	no	—
430	C₂	#20242516	1	1	yes	characteristic
431	C₂	#20242534	1	1	yes	characteristic
432	C₂	#20242540	1	1	yes	characteristic
433	C₂	#20242561	1	1	yes	characteristic
434	C₂	#20243699	1	1	yes	characteristic
435	C₂	#20243723	1	1	yes	characteristic
436	C₂	#20243763	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093994
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1296	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂²×D₁₈₈	D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1296	D₄₇
hypocenter	C₄₇	#8976
LCS	G ▷ C₄²×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
3. #20244335	C₂	semidirect
4. #20244189	C₂	semidirect
6. #20241227	C₂	semidirect
7. C₄₇×#1296	C₂	semidirect
12. #15689414	C₄	semidirect
216. #1296	D₄₇	semidirect
246. C₄₇	#8976	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689414	2
#20246339	2
#20244335	2
#20244189	2
C₂×#15688850	2
#20241227	2
C₄₇×#1296	2
#8976	47