Subgroups — #26198720

Order 12032.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253170	C₂	1	2	yes	maximal
2	C₈×#10625350	C₂	1	1	yes	maximal, characteristic
3	#20242843	C₂	1	2	yes	maximal, complemented
4	#20242836	C₂	1	2	yes	maximal, complemented
5	#20242789	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242784	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242755	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242750	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15688876	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242045	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10625350	C₂²	1	1	yes	characteristic
13	#15689427	—	2	2	no	—
14	#15689420	—	2	2	no	—
15	#15689415	C₂²	1	2	yes	—
16	#15689410	C₂²	1	2	yes	—
17	#15689405	C₂²	1	2	yes	—
18	#15689400	C₂²	1	2	yes	—
19	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
20	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
21	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
22	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₄₇	—	2	1	no	—
24	C₈×C₂²⋊D₄₇	—	2	1	no	—
25	#15689176	C₂²	1	1	yes	characteristic
26	#15689174	—	2	1	no	—
27	#15689159	—	2	2	no	—
28	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
29	#15689117	—	2	2	no	—
30	C₄×C₈×D₄₇	—	2	1	no	—
31	#15688876	C₂²	1	1	yes	characteristic
32	#15688876	C₂²	1	1	yes	characteristic
33	#15688876	C₂²	1	2	yes	—
34	#15688872	C₂²	1	2	yes	—
35	#15688872	C₂²	1	2	yes	—
36	#15688869	C₂²	1	2	yes	—
37	#15688869	C₂²	1	2	yes	—
38	C₄₇×#533	C₂²	1	2	yes	—
39	C₄₇×#500	C₂²	1	1	yes	characteristic
40	C₄₇×#494	C₂²	1	1	yes	characteristic
41	C₄₇×#487	C₂²	1	2	yes	—
42	C₄₇×#467	—	2	1	no	—
43	C₄₇×#467	—	2	1	no	—
44	C₄×Q₁₆×C₄₇	—	2	1	no	—
45	C₄×Q₁₆×C₄₇	—	2	1	no	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	D₄	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	—	2	2	no	—
49	C₂×C₈×D₄₇	—	2	1	no	—
50	C₂×C₈×D₄₇	—	2	1	no	—
51	C₄×Dic₉₄	D₄	1	1	yes	characteristic
52	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
53	C₄×D₁₈₈	D₄	1	1	yes	characteristic
54	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₄₇	—	2	1	no	—
56	C₄×C₂²⋊D₄₇	—	2	1	no	—
57	#13093983	D₄	1	1	yes	characteristic
58	#13093981	—	2	1	no	—
59	C₄²×D₄₇	—	2	1	no	—
60	#13093957	—	2	2	no	—
61	#13093957	—	2	2	no	—
62	#13093955	—	2	2	no	—
63	#13093955	—	2	2	no	—
64	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
66	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
69	Dic₄₇⋊C₈	—	2	1	no	—
70	Dic₄₇⋊C₈	—	2	1	no	—
71	#13093947	—	2	2	no	—
72	#13093947	—	2	2	no	—
73	#13093944	—	2	2	no	—
74	#13093944	—	2	2	no	—
75	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
76	(C₂×D₄₇)⋊C₈	—	2	1	no	—
77	(C₂×D₄₇)⋊C₈	—	2	1	no	—
78	C₄×C₄₇⋊C₈	—	2	1	no	—
79	C₈×Dic₄₇	—	2	1	no	—
80	C₈×Dic₄₇	—	2	1	no	—
81	C₂×Q₁₆×C₄₇	—	2	1	no	—
82	C₂×Q₁₆×C₄₇	—	2	1	no	—
83	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
86	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
87	#125×C₄₇	—	2	2	no	—
88	C₂²⋊Q₈×C₄₇	—	2	2	no	—
89	C₂²⋊Q₈×C₄₇	—	2	2	no	—
90	C₄×Q₈×C₄₇	—	2	2	no	—
91	C₄×Q₈×C₄₇	—	2	2	no	—
92	#117×C₄₇	—	2	2	no	—
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	#107×C₄₇	—	2	1	no	—
95	#107×C₄₇	—	2	1	no	—
96	#103×C₄₇	—	2	2	no	—
97	#103×C₄₇	—	2	2	no	—
98	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
107	C₂×C₂²⋊D₄₇	—	2	1	no	—
108	#10625350	—	2	2	no	—
109	#10625350	Q₁₆	1	4	yes	complemented
110	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×D₄₇	—	2	1	no	—
113	C₂×C₄×D₄₇	—	2	1	no	—
114	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
115	Q₁₆×C₄₇	—	4	2	no	—
116	Q₁₆×C₄₇	—	4	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	4	1	no	—
119	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	4	2	no	—
128	C₄⋊C₄×C₄₇	—	4	2	no	—
129	C₂²⋊C₄×C₄₇	—	4	2	no	—
130	C₄²×C₄₇	—	4	2	no	—
131	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₇	#41	1	1	yes	characteristic
134	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₄₇	—	2	1	no	—
136	(C₂×D₄₇)⋊C₄	—	2	1	no	—
137	(C₂×D₄₇)⋊C₄	—	2	1	no	—
138	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
139	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
140	Dic₄₇⋊C₄	—	2	1	no	—
141	Dic₄₇⋊C₄	—	2	1	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	4	4	no	—
150	C₈×D₄₇	—	4	2	no	—
151	C₈×D₄₇	—	4	2	no	—
152	C₂³×C₄₇	#121	1	1	yes	characteristic
153	C₂²×D₄₇	—	2	1	no	—
154	Q₈×C₄₇	—	4	2	no	—
155	Q₈×C₄₇	—	4	2	no	—
156	Q₈×C₄₇	—	8	2	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
166	C₂×C₄×C₄₇	#135	1	2	yes	—
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂²⋊D₄₇	—	2	4	no	—
171	C₂×Dic₄₇	—	2	1	no	—
172	C₂×Dic₄₇	—	2	1	no	—
173	C₂×Dic₄₇	—	2	1	no	—
174	D₁₈₈	—	2	1	no	—
175	D₁₈₈	C₂×Q₁₆	1	2	yes	—
176	C₄×D₄₇	—	2	4	no	—
177	C₄×D₄₇	—	4	2	no	—
178	C₄×D₄₇	—	4	1	no	—
179	C₄×D₄₇	—	4	1	no	—
180	Dic₉₄	—	2	1	no	—
181	Dic₉₄	C₂×Q₁₆	1	2	yes	—
182	C₈×C₄₇	—	2	1	no	—
183	C₈×C₄₇	—	2	1	no	—
184	C₈×C₄₇	—	2	1	no	—
185	C₈×C₄₇	#135	1	2	yes	—
186	C₄₇⋊C₈	—	4	1	no	—
187	C₄₇⋊C₈	—	4	2	no	—
188	C₄₇⋊C₈	—	4	2	no	—
189	C₄₇⋊C₈	—	4	1	no	—
190	#19126	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	#467	1	2	yes	—
194	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
195	C₂×D₄₇	—	2	2	no	—
196	C₂×D₄₇	—	4	1	no	—
197	C₂×D₄₇	—	4	1	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	8	2	no	—
202	C₄×C₄₇	—	8	2	no	—
203	C₄×C₄₇	#467	1	2	yes	—
204	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
205	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
206	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
207	C₄×C₄₇	#575	1	1	yes	characteristic
208	Dic₄₇	—	2	2	no	—
209	Dic₄₇	—	4	1	no	—
210	Dic₄₇	—	4	1	no	—
211	#3170	D₄₇	1	1	yes	characteristic, complemented
212	#3076	—	47	2	no	—
213	C₈×#41	—	47	1	no	—
214	#1684	—	47	2	no	—
215	#1683	—	47	2	no	—
216	#1676	—	47	1	no	—
217	#1675	—	47	1	no	—
218	#1670	—	47	1	no	—
219	#1669	—	47	1	no	—
220	C₂×#335	—	47	1	no	—
221	#1542	—	47	2	no	—
222	C₂×C₄₇	—	2	2	no	—
223	C₂×C₄₇	#3035	1	1	yes	characteristic
224	C₂×C₄₇	C₂×#467	1	1	yes	characteristic
225	C₂×C₄₇	#3067	1	1	yes	characteristic
226	D₄₇	—	4	2	no	—
227	#533	C₂×D₄₇	1	2	yes	—
228	C₄×#41	—	47	1	no	—
229	#500	C₂×D₄₇	1	1	yes	characteristic
230	#494	C₂×D₄₇	1	1	yes	characteristic
231	#487	C₂×D₄₇	1	2	yes	—
232	#479	—	94	2	no	—
233	#478	—	94	2	no	—
234	#477	—	47	2	no	—
235	#476	—	47	2	no	—
236	#475	—	47	2	no	—
237	#474	—	47	2	no	—
238	#467	—	2	1	no	—
239	#467	—	2	1	no	—
240	C₈×Q₈	—	47	1	no	—
241	C₈×Q₈	—	47	1	no	—
242	C₄×Q₁₆	—	2	1	no	—
243	C₄×Q₁₆	—	2	1	no	—
244	C₈×D₄	—	47	1	no	—
245	C₈×D₄	—	47	1	no	—
246	C₈×D₄	—	94	1	no	—
247	C₈×D₄	—	94	1	no	—
248	#431	—	47	1	no	—
249	#431	—	94	1	no	—
250	#427	—	94	2	no	—
251	C₂×C₄⋊C₈	—	47	2	no	—
252	#416	—	94	2	no	—
253	C₂×C₄×C₈	—	94	1	no	—
254	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
255	#335	—	47	1	no	—
256	#335	—	47	1	no	—
257	#335	—	47	2	no	—
258	#333	—	47	2	no	—
259	#333	—	47	2	no	—
260	#332	—	47	2	no	—
261	#332	—	47	2	no	—
262	C₄₇	#19126	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	47	1	no	—
264	C₂×Q₁₆	—	2	1	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂²×C₈	—	94	2	no	—
267	C₂²×C₈	—	94	1	no	—
268	C₂²×C₈	—	94	1	no	—
269	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
270	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
271	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
272	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
273	#125	—	2	2	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	—	47	1	no	—
279	C₄×Q₈	—	47	1	no	—
280	C₄×D₄	—	47	1	no	—
281	C₄×D₄	—	47	1	no	—
282	C₄×D₄	—	94	1	no	—
283	C₄×D₄	—	94	1	no	—
284	#117	—	2	2	no	—
285	#117	—	47	1	no	—
286	#117	—	94	1	no	—
287	C₂×C₄²	—	94	1	no	—
288	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
289	#107	—	2	1	no	—
290	#107	—	2	1	no	—
291	#107	—	94	2	no	—
292	#107	—	94	2	no	—
293	#106	—	94	2	no	—
294	#106	—	94	2	no	—
295	C₄⋊C₈	—	47	1	no	—
296	C₄⋊C₈	—	47	1	no	—
297	C₄⋊C₈	—	47	2	no	—
298	C₄⋊C₈	—	47	2	no	—
299	C₄⋊C₈	—	94	1	no	—
300	C₄⋊C₈	—	94	1	no	—
301	C₄⋊C₈	—	94	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	—	94	2	no	—
305	#103	—	94	2	no	—
306	#102	—	94	2	no	—
307	#102	—	94	2	no	—
308	C₂²⋊C₈	—	94	1	no	—
309	C₂²⋊C₈	—	94	1	no	—
310	C₂²⋊C₈	—	94	1	no	—
311	C₄×C₈	—	94	1	no	—
312	C₄×C₈	—	94	1	no	—
313	C₄×C₈	—	94	1	no	—
314	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
315	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
318	#41	—	47	4	no	—
319	#41	—	94	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	47	1	no	—
323	C₂×D₄	—	47	1	no	—
324	C₂×D₄	—	94	1	no	—
325	C₂²×C₄	—	94	1	no	—
326	C₂²×C₄	—	94	1	no	—
327	C₂²×C₄	—	94	1	no	—
328	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
329	C₂²×C₄	#10625352	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
331	Q₁₆	—	4	2	no	—
332	Q₁₆	—	4	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	94	2	no	—
336	C₂×C₈	—	94	2	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	188	2	no	—
340	C₂×C₈	—	188	4	no	—
341	C₂×C₈	—	188	2	no	—
342	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	47	1	no	—
353	C₄⋊C₄	—	47	1	no	—
354	C₄⋊C₄	—	94	1	no	—
355	C₄⋊C₄	—	94	1	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	94	1	no	—
358	C₂²⋊C₄	—	94	1	no	—
359	C₂²⋊C₄	—	94	1	no	—
360	C₄²	—	4	2	no	—
361	C₄²	—	94	1	no	—
362	C₄²	—	94	1	no	—
363	C₄²	—	94	1	no	—
364	C₄²	D₄×D₄₇	1	1	yes	characteristic
365	C₄²	#10625352	1	1	yes	characteristic
366	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
367	C₄²	C₂³×D₄₇	1	1	yes	characteristic
368	C₂³	—	94	1	no	—
369	C₂³	#13093995	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	8	2	no	—
373	Q₈	—	47	2	no	—
374	Q₈	—	94	1	no	—
375	D₄	—	47	2	no	—
376	D₄	—	94	4	no	—
377	D₄	—	94	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	94	1	no	—
384	C₂×C₄	—	94	4	no	—
385	C₂×C₄	—	94	1	no	—
386	C₂×C₄	—	94	1	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	1	no	—
389	C₂×C₄	—	188	1	no	—
390	C₂×C₄	#13093995	1	1	yes	characteristic
391	C₂×C₄	#13093995	1	1	yes	characteristic
392	C₂×C₄	#13093995	1	1	yes	characteristic
393	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
394	C₂×C₄	#13094047	1	2	yes	—
395	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	188	1	no	—
402	C₈	—	188	2	no	—
403	C₈	—	188	2	no	—
404	C₈	—	188	1	no	—
405	C₈	#13094044	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	94	2	no	—
409	C₂²	—	188	1	no	—
410	C₂²	—	188	1	no	—
411	C₂²	#15689361	1	2	yes	—
412	C₂²	C₂×#13093995	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	94	2	no	—
419	C₄	—	188	1	no	—
420	C₄	—	188	1	no	—
421	C₄	#15689361	1	2	yes	—
422	C₄	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
423	C₄	C₂×#13094044	1	1	yes	characteristic
424	C₄	C₂×#13094047	1	1	yes	characteristic
425	C₄	#15689921	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	188	2	no	—
428	C₂	#20252837	1	1	yes	characteristic
429	C₂	C₂×#15689361	1	1	yes	characteristic
430	C₂	#20253104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093995
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3170	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#10625350	D₄
hypercenter	#3170	D₄₇
hypocenter	C₄₇	#19126
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

Complements

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

N	H ≅ G/N	type
3. #20242843	C₂	semidirect
4. #20242836	C₂	semidirect
5. #20242789	C₂	semidirect
6. #20242784	C₂	semidirect
7. #20242755	C₂	semidirect
8. #20242750	C₂	semidirect
9. C₂×#15688876	C₂	semidirect
10. #20242045	C₂	semidirect
11. C₄₇×#3170	C₂	semidirect
109. #10625350	Q₁₆	semidirect
211. #3170	D₄₇	semidirect
262. C₄₇	#19126	semidirect

Maximal subgroups

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

subgroup	index
#20253170	2
C₈×#10625350	2
#20242843	2
#20242836	2
#20242789	2
#20242784	2
#20242755	2
#20242750	2
C₂×#15688876	2
#20242045	2
C₄₇×#3170	2
#19126	47