Subgroups — #26198709

Order 12032.

726 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252837	C₂	1	2	yes	maximal, complemented
2	C₈×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242829	C₂	1	2	yes	maximal, complemented
4	#20242822	C₂	1	2	yes	maximal, complemented
5	#20242779	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242774	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242745	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242740	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15688876	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242037	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094044	—	2	2	no	—
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689342	—	2	2	no	—
15	#15689335	—	2	2	no	—
16	#15689330	C₂²	1	2	yes	—
17	#15689325	C₂²	1	2	yes	—
18	#15689320	C₂²	1	2	yes	—
19	#15689315	C₂²	1	2	yes	—
20	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
21	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
22	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
23	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
24	C₈×C₂²⋊D₄₇	—	2	1	no	—
25	C₈×C₂²⋊D₄₇	—	2	1	no	—
26	#15689176	C₂²	1	1	yes	characteristic
27	#15689174	—	2	1	no	—
28	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
29	#15689119	—	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	#15688869	C₂²	1	2	yes	—
35	#15688869	C₂²	1	2	yes	—
36	#15688867	C₂²	1	2	yes	—
37	#15688867	C₂²	1	2	yes	—
38	C₄₇×#532	C₂²	1	2	yes	—
39	C₄₇×#500	C₂²	1	1	yes	characteristic
40	C₄₇×#493	C₂²	1	1	yes	characteristic
41	C₄₇×#486	C₂²	1	2	yes	—
42	C₄₇×#466	—	2	1	no	—
43	C₄₇×#466	—	2	1	no	—
44	C₄×D₈×C₄₇	—	2	1	no	—
45	C₄×D₈×C₄₇	—	2	1	no	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	D₄	1	1	yes	characteristic
48	#13094044	—	4	8	no	—
49	C₂×#10625337	—	2	2	no	—
50	C₂×#10625335	—	2	2	no	—
51	C₂×#10625336	—	2	2	no	—
52	C₂×#10625334	—	2	2	no	—
53	C₂²×C₄₇⋊C₈	—	2	2	no	—
54	C₂×C₈×D₄₇	—	2	1	no	—
55	C₂×C₈×D₄₇	—	2	1	no	—
56	C₄×Dic₉₄	D₄	1	1	yes	characteristic
57	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
58	C₄×D₁₈₈	D₄	1	1	yes	characteristic
59	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
60	C₄×C₂²⋊D₄₇	—	2	1	no	—
61	C₄×C₂²⋊D₄₇	—	2	1	no	—
62	#13093983	D₄	1	1	yes	characteristic
63	#13093981	—	2	1	no	—
64	C₄²×D₄₇	—	2	1	no	—
65	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
70	Dic₄₇⋊C₈	—	2	1	no	—
71	Dic₄₇⋊C₈	—	2	1	no	—
72	#13093948	—	2	2	no	—
73	#13093948	—	2	2	no	—
74	#13093945	—	2	2	no	—
75	#13093945	—	2	2	no	—
76	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
77	(C₂×D₄₇)⋊C₈	—	2	1	no	—
78	(C₂×D₄₇)⋊C₈	—	2	1	no	—
79	C₄×C₄₇⋊C₈	—	2	1	no	—
80	C₈×Dic₄₇	—	2	1	no	—
81	C₈×Dic₄₇	—	2	1	no	—
82	C₂×#41×C₄₇	—	2	2	no	—
83	C₂×D₈×C₄₇	—	2	1	no	—
84	C₂×D₈×C₄₇	—	2	1	no	—
85	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
88	#127×C₄₇	C₂³	1	2	yes	—
89	#124×C₄₇	—	2	2	no	—
90	#121×C₄₇	—	2	2	no	—
91	#121×C₄₇	—	2	2	no	—
92	C₄×D₄×C₄₇	—	2	2	no	—
93	C₄×D₄×C₄₇	—	2	2	no	—
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	#107×C₄₇	—	2	1	no	—
96	#107×C₄₇	—	2	1	no	—
97	#102×C₄₇	—	2	2	no	—
98	#102×C₄₇	—	2	2	no	—
99	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	#41×C₄₇	—	4	4	no	—
104	#41×C₄₇	—	4	4	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	2	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	4	2	no	—
110	C₂²×C₄×C₄₇	—	4	2	no	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₇	—	2	1	no	—
115	#10625350	—	2	2	no	—
116	#10625350	D₈	1	4	yes	complemented
117	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₄₇	—	2	1	no	—
119	C₂×C₄×D₄₇	—	2	1	no	—
120	C₂×C₄×D₄₇	—	2	1	no	—
121	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
122	D₈×C₄₇	—	4	2	no	—
123	D₈×C₄₇	—	4	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	4	1	no	—
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₂²⋊C₄×C₄₇	—	4	2	no	—
133	C₂²⋊C₄×C₄₇	—	4	2	no	—
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₇	#41	1	1	yes	characteristic
137	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂²⋊Dic₄₇	—	2	1	no	—
139	#10625337	—	4	4	no	—
140	#10625336	—	4	4	no	—
141	#10625335	—	4	4	no	—
142	#10625334	—	4	4	no	—
143	(C₂×D₄₇)⋊C₄	—	2	1	no	—
144	(C₂×D₄₇)⋊C₄	—	2	1	no	—
145	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
146	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
147	Dic₄₇⋊C₄	—	2	1	no	—
148	Dic₄₇⋊C₄	—	2	1	no	—
149	C₄×Dic₄₇	—	2	1	no	—
150	C₄×Dic₄₇	—	2	1	no	—
151	C₄×Dic₄₇	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	4	4	no	—
157	C₈×D₄₇	—	4	2	no	—
158	C₈×D₄₇	—	4	2	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	#121	1	1	yes	characteristic
161	C₂²×D₄₇	—	2	1	no	—
162	Q₈×C₄₇	—	4	2	no	—
163	Q₈×C₄₇	—	4	2	no	—
164	D₄×C₄₇	—	4	2	no	—
165	D₄×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	4	2	no	—
167	D₄×C₄₇	—	4	2	no	—
168	D₄×C₄₇	—	8	2	no	—
169	D₄×C₄₇	—	8	4	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	8	4	no	—
175	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
176	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
177	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
179	C₂×C₄×C₄₇	#135	1	2	yes	—
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂²⋊D₄₇	—	2	4	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	D₁₈₈	—	2	1	no	—
188	D₁₈₈	C₂×D₈	1	2	yes	—
189	C₄×D₄₇	—	2	4	no	—
190	C₄×D₄₇	—	4	2	no	—
191	C₄×D₄₇	—	4	1	no	—
192	C₄×D₄₇	—	4	1	no	—
193	Dic₉₄	—	2	1	no	—
194	Dic₉₄	C₂×D₈	1	2	yes	—
195	C₈×C₄₇	—	2	1	no	—
196	C₈×C₄₇	—	2	1	no	—
197	C₈×C₄₇	—	2	1	no	—
198	C₈×C₄₇	#135	1	2	yes	complemented
199	C₄₇⋊C₈	—	4	2	no	—
200	C₄₇⋊C₈	—	4	2	no	—
201	C₄₇⋊C₈	—	4	1	no	—
202	C₄₇⋊C₈	—	4	1	no	—
203	#19125	—	47	1	no	maximal, Sylow
204	C₂²×C₄₇	—	2	1	no	—
205	C₂²×C₄₇	—	2	1	no	—
206	C₂²×C₄₇	—	8	2	no	—
207	C₂²×C₄₇	—	8	2	no	—
208	C₂²×C₄₇	—	8	2	no	—
209	C₂²×C₄₇	#466	1	2	yes	—
210	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
211	C₂×D₄₇	—	2	2	no	—
212	C₂×D₄₇	—	4	1	no	—
213	C₂×D₄₇	—	4	1	no	—
214	C₄×C₄₇	—	2	1	no	—
215	C₄×C₄₇	—	2	1	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	—	8	2	no	—
218	C₄×C₄₇	#466	1	2	yes	—
219	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
220	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
221	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
222	C₄×C₄₇	#575	1	1	yes	characteristic
223	Dic₄₇	—	2	2	no	—
224	Dic₄₇	—	4	1	no	—
225	Dic₄₇	—	4	1	no	—
226	#3169	D₄₇	1	1	yes	characteristic, complemented
227	#3035	—	47	2	no	—
228	C₈×#41	—	47	1	no	—
229	#1682	—	47	2	no	—
230	#1681	—	47	2	no	—
231	#1674	—	47	1	no	—
232	#1673	—	47	1	no	—
233	#1668	—	47	1	no	—
234	#1667	—	47	1	no	—
235	C₂×#335	—	47	1	no	—
236	#1540	—	47	2	no	—
237	C₂×C₄₇	—	2	2	no	—
238	C₂×C₄₇	—	16	2	no	—
239	C₂×C₄₇	#3035	1	1	yes	characteristic
240	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
241	C₂×C₄₇	#3067	1	1	yes	characteristic
242	D₄₇	—	4	2	no	—
243	C₂×#135	—	94	2	no	—
244	#532	C₂×D₄₇	1	2	yes	—
245	C₄×#41	—	47	1	no	—
246	#500	C₂×D₄₇	1	1	yes	characteristic
247	#493	C₂×D₄₇	1	1	yes	characteristic
248	#486	C₂×D₄₇	1	2	yes	—
249	#466	—	2	1	no	—
250	#466	—	2	1	no	—
251	#464	—	94	2	no	—
252	#463	—	94	2	no	—
253	#462	—	47	2	no	—
254	#461	—	47	2	no	—
255	#460	—	47	2	no	—
256	#459	—	47	2	no	—
257	C₈×Q₈	—	47	1	no	—
258	C₈×Q₈	—	47	1	no	—
259	C₄×D₈	—	2	1	no	—
260	C₄×D₈	—	2	1	no	—
261	C₈×D₄	—	47	1	no	—
262	C₈×D₄	—	47	1	no	—
263	C₈×D₄	—	94	1	no	—
264	C₈×D₄	—	94	1	no	—
265	#431	—	47	1	no	—
266	#431	—	94	1	no	—
267	C₂×C₄⋊C₈	—	47	2	no	—
268	#416	—	94	2	no	—
269	C₂×C₄×C₈	—	94	1	no	—
270	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
271	#335	—	47	1	no	—
272	#335	—	47	1	no	—
273	#335	—	47	2	no	—
274	#332	—	47	2	no	—
275	#332	—	47	2	no	—
276	#331	—	47	2	no	—
277	#331	—	47	2	no	—
278	C₄₇	#19125	1	1	yes	characteristic, complemented, Sylow
279	C₂×#41	—	2	2	no	—
280	C₂×#41	—	47	1	no	—
281	#135	—	188	8	no	—
282	C₂×Q₁₆	—	94	2	no	—
283	C₂×SD₁₆	—	94	2	no	—
284	C₂×SD₁₆	—	94	2	no	—
285	C₂×D₈	—	2	1	no	—
286	C₂×D₈	—	2	1	no	—
287	C₂×D₈	—	94	2	no	—
288	C₂²×C₈	—	94	2	no	—
289	C₂²×C₈	—	94	1	no	—
290	C₂²×C₈	—	94	1	no	—
291	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
292	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
293	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
294	#127	C₂²×D₄₇	1	2	yes	—
295	#124	—	2	2	no	—
296	#121	—	2	2	no	—
297	#121	—	2	2	no	—
298	C₄×Q₈	—	47	1	no	—
299	C₄×Q₈	—	47	1	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	47	1	no	—
303	C₄×D₄	—	47	1	no	—
304	C₄×D₄	—	94	1	no	—
305	C₄×D₄	—	94	1	no	—
306	#117	—	47	1	no	—
307	#117	—	94	1	no	—
308	C₂×C₄²	—	94	1	no	—
309	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
310	#107	—	2	1	no	—
311	#107	—	2	1	no	—
312	C₄⋊C₈	—	47	1	no	—
313	C₄⋊C₈	—	47	1	no	—
314	C₄⋊C₈	—	47	2	no	—
315	C₄⋊C₈	—	47	2	no	—
316	C₄⋊C₈	—	94	1	no	—
317	C₄⋊C₈	—	94	1	no	—
318	C₄⋊C₈	—	94	2	no	—
319	#103	—	94	2	no	—
320	#103	—	94	2	no	—
321	#102	—	2	2	no	—
322	#102	—	2	2	no	—
323	#102	—	94	2	no	—
324	#102	—	94	2	no	—
325	C₂²⋊C₈	—	94	1	no	—
326	C₂²⋊C₈	—	94	1	no	—
327	C₂²⋊C₈	—	94	1	no	—
328	C₄×C₈	—	94	1	no	—
329	C₄×C₈	—	94	1	no	—
330	C₄×C₈	—	94	1	no	—
331	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
332	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
335	#41	—	4	4	no	—
336	#41	—	4	4	no	—
337	#41	—	47	4	no	—
338	#41	—	94	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	47	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	47	1	no	—
346	C₂×D₄	—	94	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	94	1	no	—
349	C₂²×C₄	—	94	1	no	—
350	C₂²×C₄	—	94	1	no	—
351	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	#10625352	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
354	Q₁₆	—	188	4	no	—
355	SD₁₆	—	188	4	no	—
356	SD₁₆	—	188	4	no	—
357	D₈	—	4	2	no	—
358	D₈	—	4	2	no	—
359	D₈	—	188	4	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	94	2	no	—
363	C₂×C₈	—	94	2	no	—
364	C₂×C₈	—	94	1	no	—
365	C₂×C₈	—	94	1	no	—
366	C₂×C₈	—	188	2	no	—
367	C₂×C₈	—	188	4	no	—
368	C₂×C₈	—	188	2	no	—
369	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
370	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
371	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
372	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	47	1	no	—
376	C₄⋊C₄	—	47	1	no	—
377	C₄⋊C₄	—	94	1	no	—
378	C₄⋊C₄	—	94	1	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	94	1	no	—
382	C₂²⋊C₄	—	94	1	no	—
383	C₂²⋊C₄	—	94	1	no	—
384	C₄²	—	94	1	no	—
385	C₄²	—	94	1	no	—
386	C₄²	—	94	1	no	—
387	C₄²	D₄×D₄₇	1	1	yes	characteristic
388	C₄²	#10625352	1	1	yes	characteristic
389	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
390	C₄²	C₂³×D₄₇	1	1	yes	characteristic
391	C₂³	—	4	2	no	—
392	C₂³	—	94	1	no	—
393	C₂³	#13093995	1	1	yes	characteristic
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	47	2	no	—
397	Q₈	—	94	1	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	8	4	no	—
404	D₄	—	47	2	no	—
405	D₄	—	94	4	no	—
406	D₄	—	94	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	8	4	no	—
412	C₂×C₄	—	94	1	no	—
413	C₂×C₄	—	94	4	no	—
414	C₂×C₄	—	94	1	no	—
415	C₂×C₄	—	94	1	no	—
416	C₂×C₄	—	188	2	no	—
417	C₂×C₄	—	188	1	no	—
418	C₂×C₄	—	188	1	no	—
419	C₂×C₄	#13093995	1	1	yes	characteristic
420	C₂×C₄	#13093995	1	1	yes	characteristic
421	C₂×C₄	#13093995	1	1	yes	characteristic
422	C₂×C₄	D₈×D₄₇	1	2	yes	—
423	C₂×C₄	#13094043	1	2	yes	—
424	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	188	2	no	—
431	C₈	—	188	2	no	—
432	C₈	—	188	1	no	—
433	C₈	—	188	1	no	—
434	C₈	#13094044	1	2	yes	complemented
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	94	2	no	—
441	C₂²	—	188	1	no	—
442	C₂²	—	188	1	no	—
443	C₂²	#15689356	1	2	yes	—
444	C₂²	C₂×#13093995	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	8	2	no	—
449	C₄	—	94	2	no	—
450	C₄	—	188	1	no	—
451	C₄	—	188	1	no	—
452	C₄	#15689356	1	2	yes	—
453	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
454	C₄	C₂×#13094043	1	1	yes	characteristic
455	C₄	C₂×#13094044	1	1	yes	characteristic
456	C₄	#15689921	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	16	2	no	—
459	C₂	—	188	2	no	—
460	C₂	#20252837	1	1	yes	characteristic
461	C₂	C₂×#15689356	1	1	yes	characteristic
462	C₂	#20253104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093995
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3169	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	#3169	D₄₇
hypocenter	C₄₇	#19125
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #20252837	C₂	semidirect
2. C₈×#10625350	C₂	semidirect
3. #20242829	C₂	semidirect
4. #20242822	C₂	semidirect
5. #20242779	C₂	semidirect
6. #20242774	C₂	semidirect
7. #20242745	C₂	semidirect
8. #20242740	C₂	semidirect
9. C₂×#15688876	C₂	semidirect
10. #20242037	C₂	semidirect
11. C₄₇×#3169	C₂	semidirect
116. #10625350	D₈	semidirect
198. C₈×C₄₇	#135	semidirect
226. #3169	D₄₇	semidirect
278. C₄₇	#19125	semidirect
434. C₈	#13094044	semidirect

Maximal subgroups

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

subgroup	index
#20252837	2
C₈×#10625350	2
#20242829	2
#20242822	2
#20242779	2
#20242774	2
#20242745	2
#20242740	2
C₂×#15688876	2
#20242037	2
C₄₇×#3169	2
#19125	47