Subgroups — #26230155

Order 12032.

846 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	#20253814	C₂	1	1	yes	maximal, characteristic
2	#20252100	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252099	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244216	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243713	C₂	1	4	yes	maximal, complemented
6	#20243712	C₂	1	4	yes	maximal, complemented
7	#20243525	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243134	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1962	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13094044	C₂²	1	4	yes	—
11	C₂×#13094032	C₂²	1	2	yes	—
12	C₂×#13094031	C₂²	1	2	yes	—
13	#15689673	C₂²	1	1	yes	characteristic
14	#15689505	C₄	1	4	yes	complemented
15	#15689502	C₄	1	1	yes	characteristic, complemented
16	#15689499	C₄	1	1	yes	characteristic, complemented
17	#15689497	C₄	1	1	yes	characteristic, complemented
18	#15689495	C₄	1	1	yes	characteristic, complemented
19	#15689201	—	2	1	no	—
20	#15689201	—	2	1	no	—
21	#15689200	—	2	1	no	—
22	#15689200	—	2	1	no	—
23	D₄×C₄₇⋊C₈	—	2	1	no	—
24	D₄×C₄₇⋊C₈	—	2	1	no	—
25	#15689188	—	2	1	no	—
26	#15689188	—	2	1	no	—
27	#15689147	C₂²	1	1	yes	characteristic
28	C₂×#13093952	C₂²	1	4	yes	—
29	#15689091	C₂²	1	2	yes	—
30	#15689090	C₂²	1	2	yes	—
31	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
33	#15688887	C₂²	1	4	yes	—
34	#15688878	C₂²	1	2	yes	—
35	#15688878	C₂²	1	2	yes	—
36	C₄₇×#532	C₂²	1	1	yes	characteristic
37	C₄₇×#423	C₂²	1	1	yes	characteristic
38	C₂×#104×C₄₇	C₂²	1	4	yes	—
39	C₄³×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#10625350	C₂³	1	2	yes	—
41	#13094044	—	4	4	no	—
42	#13094044	—	4	4	no	—
43	C₂×#10625337	C₂×C₄	1	4	yes	—
44	C₂×#10625335	C₂×C₄	1	4	yes	—
45	C₂×#10625336	C₂×C₄	1	4	yes	—
46	C₂×#10625334	C₂×C₄	1	4	yes	—
47	#13094032	—	4	4	no	—
48	#13094031	—	4	4	no	—
49	C₂×#10625329	—	2	2	no	—
50	C₂×#10625329	C₂³	1	2	yes	—
51	C₂×#10625324	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	—	2	2	no	—
53	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₄₇	—	2	2	no	—
57	#13094024	C₂×C₄	1	1	yes	characteristic
58	#13094021	C₂×C₄	1	1	yes	characteristic
59	#13094012	C₂×C₄	1	2	yes	—
60	#13093998	—	2	1	no	—
61	#13093998	—	2	1	no	—
62	C₄×D₁₈₈	—	2	1	no	—
63	C₄×D₁₈₈	—	2	1	no	—
64	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
66	#13093952	—	4	4	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
68	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
69	(C₂×D₄₇)⋊C₈	—	2	2	no	—
70	(C₂×D₄₇)⋊C₈	—	2	2	no	—
71	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
74	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
75	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
76	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
77	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
78	C₂×#41×C₄₇	C₂³	1	2	yes	—
79	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
80	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
81	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
82	#124×C₄₇	C₂×C₄	1	2	yes	—
83	#121×C₄₇	—	2	1	no	—
84	#121×C₄₇	—	2	1	no	—
85	C₄×D₄×C₄₇	—	2	1	no	—
86	C₄×D₄×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	—	2	1	no	—
92	C₄⋊C₈×C₄₇	—	2	1	no	—
93	#104×C₄₇	—	4	4	no	—
94	#41×C₄₇	—	2	4	no	—
95	#41×C₄₇	—	2	4	no	—
96	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	1	no	—
99	C₂×D₄×C₄₇	—	2	1	no	—
100	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₇	—	2	2	no	—
107	#10625350	—	2	4	no	—
108	#10625350	—	2	4	no	—
109	C₂×D₁₈₈	—	2	1	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₄₇	—	2	2	no	—
113	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
114	M₁₆×C₄₇	—	2	4	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	1	no	—
117	C₄⋊C₄×C₄₇	—	2	1	no	—
118	C₂²⋊C₄×C₄₇	—	2	2	no	—
119	C₂²⋊C₄×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	4	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	—	4	2	no	—
124	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
128	#10625337	—	4	4	no	—
129	#10625336	—	4	4	no	—
130	#10625335	—	4	4	no	—
131	#10625334	—	4	4	no	—
132	(C₂×D₄₇)⋊C₄	—	2	2	no	—
133	(C₂×D₄₇)⋊C₄	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	1	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	#10625329	—	2	4	no	—
137	#10625329	—	4	4	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	4	4	no	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
150	#10625324	—	4	4	no	—
151	C₈×D₄₇	—	4	4	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
154	C₂²×D₄₇	—	2	2	no	—
155	Q₈×C₄₇	—	2	4	no	—
156	D₄×C₄₇	—	2	4	no	—
157	D₄×C₄₇	—	4	4	no	—
158	D₄×C₄₇	—	4	2	no	—
159	D₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
175	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
176	C₂²⋊D₄₇	—	4	4	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	D₁₈₈	—	2	4	no	—
179	D₁₈₈	—	4	2	no	—
180	D₁₈₈	—	4	2	no	—
181	C₄×D₄₇	—	4	2	no	—
182	C₄×D₄₇	—	4	2	no	—
183	Dic₉₄	—	2	4	no	—
184	C₈×C₄₇	—	4	2	no	—
185	C₄₇⋊C₈	—	2	2	no	—
186	C₄₇⋊C₈	—	2	2	no	—
187	C₄₇⋊C₈	—	2	1	no	—
188	C₄₇⋊C₈	—	2	1	no	—
189	C₄₇⋊C₈	—	2	1	no	—
190	C₄₇⋊C₈	—	2	1	no	—
191	C₄₇⋊C₈	—	4	2	no	—
192	#22280	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	—	4	2	no	—
198	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂²×C₄₇	#540	1	2	yes	—
200	C₂×D₄₇	—	4	2	no	—
201	C₂×D₄₇	—	4	2	no	—
202	C₂×D₄₇	—	4	2	no	—
203	C₄×C₄₇	—	2	1	no	—
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	4	4	no	—
206	C₄×C₄₇	—	4	2	no	—
207	C₄×C₄₇	#443	1	2	yes	—
208	C₄×C₄₇	#444	1	2	yes	—
209	C₄×C₄₇	#518	1	2	yes	—
210	C₄×C₄₇	#535	1	1	yes	characteristic
211	C₄×C₄₇	#535	1	1	yes	characteristic
212	Dic₄₇	—	4	2	no	—
213	#3147	—	47	1	no	—
214	#2931	—	47	1	no	—
215	#2931	—	47	1	no	—
216	#1962	—	47	1	no	—
217	#1962	D₄₇	1	1	yes	characteristic, complemented
218	#1876	—	47	4	no	—
219	#1876	—	47	4	no	—
220	#1837	—	47	1	no	—
221	#1744	—	47	1	no	—
222	C₂×C₄₇	—	2	2	no	—
223	C₂×C₄₇	—	8	2	no	—
224	C₂×C₄₇	#2328	1	1	yes	characteristic
225	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
226	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
227	D₄₇	—	8	2	no	—
228	C₂×#135	—	47	4	no	—
229	C₂×#131	—	47	2	no	—
230	C₂×#131	—	47	2	no	—
231	#532	—	47	1	no	—
232	#532	C₂×D₄₇	1	1	yes	characteristic
233	#495	—	47	4	no	—
234	#494	—	47	1	no	—
235	#493	—	47	1	no	—
236	#492	—	47	1	no	—
237	#492	—	47	1	no	—
238	#436	—	94	1	no	—
239	#436	—	94	1	no	—
240	#436	—	94	1	no	—
241	#436	—	94	1	no	—
242	C₈×D₄	—	94	1	no	—
243	C₈×D₄	—	94	1	no	—
244	C₈×D₄	—	94	1	no	—
245	C₈×D₄	—	94	1	no	—
246	#423	—	47	1	no	—
247	#423	C₂×D₄₇	1	1	yes	characteristic
248	C₂×#104	—	47	4	no	—
249	C₂×#104	C₂×D₄₇	1	4	yes	—
250	#408	—	47	2	no	—
251	#408	—	47	2	no	—
252	C₂×C₄×C₈	—	47	1	no	—
253	C₂×C₄×C₈	—	47	1	no	—
254	C₄³	C₂×D₄₇	1	1	yes	characteristic
255	#341	—	47	4	no	—
256	#336	—	47	2	no	—
257	#336	—	47	2	no	—
258	C₄₇	#22280	1	1	yes	characteristic, complemented, Sylow
259	C₂×#41	—	47	2	no	—
260	C₂×#41	C₂²×D₄₇	1	2	yes	—
261	#135	—	188	4	no	—
262	#135	—	188	4	no	—
263	C₂×Q₁₆	—	47	4	no	—
264	C₂×SD₁₆	—	47	4	no	—
265	C₂×SD₁₆	—	47	4	no	—
266	C₂×D₈	—	47	4	no	—
267	#131	—	188	4	no	—
268	#131	—	188	4	no	—
269	C₂×M₁₆	—	47	2	no	—
270	C₂×M₁₆	—	94	2	no	—
271	C₂×M₁₆	—	94	2	no	—
272	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
273	C₂²×C₈	—	47	1	no	—
274	C₂²×C₈	—	47	1	no	—
275	C₂²×C₈	—	47	2	no	—
276	C₂²×C₈	—	94	2	no	—
277	C₂²×C₈	—	94	2	no	—
278	C₄⋊Q₈	—	47	1	no	—
279	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
280	#127	—	47	1	no	—
281	#127	C₄×D₄₇	1	1	yes	characteristic
282	#124	—	47	2	no	—
283	#124	C₄×D₄₇	1	2	yes	—
284	#121	—	2	1	no	—
285	#121	—	2	1	no	—
286	#121	—	94	1	no	—
287	#121	—	94	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	94	1	no	—
291	C₄×D₄	—	94	1	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
295	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	94	1	no	—
299	C₄⋊C₈	—	94	1	no	—
300	#104	—	4	4	no	—
301	#104	—	188	4	no	—
302	C₂²⋊C₈	—	94	2	no	—
303	C₂²⋊C₈	—	94	2	no	—
304	C₂²⋊C₈	—	94	2	no	—
305	C₂²⋊C₈	—	94	2	no	—
306	C₄×C₈	—	47	1	no	—
307	C₄×C₈	—	47	1	no	—
308	C₄×C₈	—	47	2	no	—
309	C₄×C₈	—	47	1	no	—
310	C₄×C₈	—	47	1	no	—
311	C₄×C₈	—	47	1	no	—
312	C₄×C₈	—	47	1	no	—
313	#41	—	2	4	no	—
314	#41	—	2	4	no	—
315	#41	—	94	4	no	—
316	#41	—	94	4	no	—
317	C₂×Q₈	—	47	2	no	—
318	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	47	2	no	—
323	C₂×D₄	—	94	2	no	—
324	C₂×D₄	—	94	1	no	—
325	C₂×D₄	—	94	1	no	—
326	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	94	2	no	—
330	C₂²×C₄	#10625352	1	1	yes	characteristic
331	C₂²×C₄	#10625352	1	1	yes	characteristic
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	Q₁₆	—	188	4	no	—
334	SD₁₆	—	188	4	no	—
335	SD₁₆	—	188	4	no	—
336	D₈	—	188	4	no	—
337	M₁₆	—	2	4	no	—
338	M₁₆	—	94	4	no	—
339	M₁₆	—	188	4	no	—
340	M₁₆	—	188	4	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	47	2	no	—
343	C₂×C₈	—	47	2	no	—
344	C₂×C₈	—	47	1	no	—
345	C₂×C₈	—	47	1	no	—
346	C₂×C₈	—	47	1	no	—
347	C₂×C₈	—	47	1	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	—	94	2	no	—
351	C₂×C₈	—	94	2	no	—
352	C₂×C₈	—	94	2	no	—
353	C₂×C₈	—	188	4	no	—
354	C₂×C₈	—	188	4	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	94	1	no	—
358	C₄⋊C₄	—	94	1	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	94	2	no	—
362	C₂²⋊C₄	—	94	2	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	4	2	no	—
367	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₄²	D₄×D₄₇	1	1	yes	characteristic
370	C₄²	D₄×D₄₇	1	1	yes	characteristic
371	C₂³	—	2	2	no	—
372	C₂³	—	94	2	no	—
373	C₂³	C₂×#10625352	1	1	yes	characteristic
374	Q₈	—	2	4	no	—
375	Q₈	—	94	4	no	—
376	D₄	—	2	4	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	94	4	no	—
381	D₄	—	188	4	no	—
382	D₄	—	188	2	no	—
383	D₄	—	188	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	—	188	2	no	—
395	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
396	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
397	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
398	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	#13094069	1	2	yes	—
402	C₂×C₄	#13094070	1	2	yes	—
403	C₈	—	4	2	no	—
404	C₈	—	94	2	no	—
405	C₈	—	94	2	no	—
406	C₈	—	94	1	no	—
407	C₈	—	94	1	no	—
408	C₈	—	94	1	no	—
409	C₈	—	94	1	no	—
410	C₈	—	188	2	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	188	2	no	—
417	C₂²	—	188	2	no	—
418	C₂²	—	188	2	no	—
419	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
420	C₂²	#15689726	1	2	yes	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	188	2	no	—
426	C₄	#15689237	1	2	yes	—
427	C₄	#15689242	1	2	yes	—
428	C₄	#15689595	1	2	yes	—
429	C₄	#15689686	1	1	yes	characteristic
430	C₄	#15689691	1	1	yes	characteristic
431	C₂	—	2	2	no	—
432	C₂	—	8	2	no	—
433	C₂	—	376	2	no	—
434	C₂	#20246112	1	1	yes	characteristic
435	C₂	C₂×#15689237	1	1	yes	characteristic
436	C₂	C₂×#15689242	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1962	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253814	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1962	D₄₇
hypocenter	C₄₇	#22280
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1962

Complements

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

N	H ≅ G/N	type
2. #20252100	C₂	semidirect
3. #20252099	C₂	semidirect
4. #20244216	C₂	semidirect
5. #20243713	C₂	semidirect
6. #20243712	C₂	semidirect
7. #20243525	C₂	semidirect
8. #20243134	C₂	semidirect
9. C₄₇×#1962	C₂	semidirect
14. #15689505	C₄	semidirect
15. #15689502	C₄	semidirect
16. #15689499	C₄	semidirect
17. #15689497	C₄	semidirect
18. #15689495	C₄	semidirect
217. #1962	D₄₇	semidirect
258. C₄₇	#22280	semidirect

Maximal subgroups

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

subgroup	index
#20253814	2
#20252100	2
#20252099	2
#20244216	2
#20243713	2
#20243712	2
#20243525	2
#20243134	2
C₄₇×#1962	2
#22280	47