Subgroups — #26224121

Order 12032.

738 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253178	C₂	1	1	yes	maximal, characteristic
2	#20252322	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094030	C₂	1	1	yes	maximal, characteristic
4	#20244331	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244164	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243988	C₂	1	2	yes	maximal, complemented
7	#20243666	C₂	1	2	yes	maximal
8	#20243409	C₂	1	1	yes	maximal, characteristic
9	#20243272	C₂	1	2	yes	maximal, complemented
10	#20243232	C₂	1	2	yes	maximal
11	C₄₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094030	C₂²	1	1	yes	characteristic
13	C₂×#13094030	C₂²	1	1	yes	characteristic
14	#15689680	C₂²	1	1	yes	characteristic
15	C₄×#10625350	C₂²	1	1	yes	characteristic
16	#15689431	C₄	1	2	yes	complemented
17	#15689424	C₄	1	2	yes	complemented
18	#15689419	C₄	1	1	yes	characteristic, complemented
19	#15689414	C₄	1	1	yes	characteristic, complemented
20	#15689409	C₄	1	1	yes	characteristic, complemented
21	#15689404	C₄	1	1	yes	characteristic, complemented
22	#15689253	—	2	1	no	—
23	#15689253	—	2	1	no	—
24	C₈×Dic₉₄	—	2	1	no	—
25	C₈×Dic₉₄	—	2	1	no	—
26	C₂×#13093960	C₂²	1	2	yes	—
27	#15689161	C₂²	1	2	yes	—
28	#15689149	C₂²	1	2	yes	—
29	#15689147	C₂²	1	1	yes	characteristic
30	C₂×#13093952	C₂²	1	2	yes	—
31	#15689120	C₂²	1	2	yes	—
32	#15689078	C₂²	1	1	yes	characteristic
33	#15689078	C₂²	1	2	yes	—
34	#15689078	C₂²	1	1	yes	characteristic
35	#15689077	—	2	1	no	—
36	#15689077	—	2	1	no	—
37	C₄×#10625329	C₂²	1	1	yes	characteristic
38	C₄×#10625324	—	2	1	no	—
39	C₄×C₈×D₄₇	—	2	1	no	—
40	#15688888	C₂²	1	2	yes	—
41	#15688883	C₂²	1	2	yes	—
42	#15688883	C₂²	1	2	yes	—
43	#15688883	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#97×C₄₇	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
48	C₄₇×#336	C₂²	1	2	yes	—
49	C₂×#10625350	C₂³	1	1	yes	characteristic
50	#13094030	—	2	2	no	—
51	#13094030	—	2	2	no	—
52	#13094030	—	2	2	no	—
53	#13094030	Q₈	1	4	yes	complemented
54	C₂×#10625329	C₂³	1	2	yes	—
55	C₂×#10625329	C₂³	1	1	yes	characteristic
56	C₂×#10625329	C₂³	1	1	yes	characteristic
57	C₂×#10625324	—	2	1	no	—
58	C₂×#10625324	—	2	1	no	—
59	C₂×C₈×D₄₇	—	2	1	no	—
60	C₂×C₈×D₄₇	—	2	1	no	—
61	#13094024	C₂×C₄	1	1	yes	characteristic
62	#13094024	C₂×C₄	1	1	yes	characteristic
63	#13094016	C₂×C₄	1	2	yes	—
64	#13094003	—	2	1	no	—
65	#13094003	—	2	1	no	—
66	C₄×Dic₉₄	—	2	1	no	—
67	C₄×Dic₉₄	—	2	1	no	—
68	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
69	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
70	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
71	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₄₇	—	2	1	no	—
73	C₄×C₂²⋊D₄₇	—	2	1	no	—
74	#13093983	C₂³	1	1	yes	characteristic
75	#13093983	C₂³	1	2	yes	—
76	#13093981	—	2	1	no	—
77	C₄²×D₄₇	—	2	1	no	—
78	#13093960	—	2	4	no	—
79	#13093958	C₂×C₄	1	2	yes	—
80	#13093958	C₂×C₄	1	2	yes	—
81	#13093956	C₂×C₄	1	2	yes	—
82	#13093956	C₂×C₄	1	2	yes	—
83	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
84	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
85	Dic₄₇⋊C₈	—	2	2	no	—
86	Dic₄₇⋊C₈	—	2	2	no	—
87	#13093952	—	2	4	no	—
88	#13093949	C₂×C₄	1	2	yes	—
89	#13093949	C₂×C₄	1	2	yes	—
90	#13093946	C₂×C₄	1	2	yes	—
91	#13093946	C₂×C₄	1	2	yes	—
92	#13093935	—	2	1	no	—
93	#13093934	—	2	2	no	—
94	#13093934	—	2	1	no	—
95	#13093934	—	2	1	no	—
96	C₄×C₄₇⋊C₈	—	2	1	no	—
97	C₈×Dic₄₇	—	2	2	no	—
98	C₈×Dic₄₇	—	2	1	no	—
99	C₈×Dic₄₇	—	2	1	no	—
100	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
101	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
104	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
105	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
108	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
109	#97×C₄₇	—	2	4	no	—
110	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
111	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
112	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
113	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
114	#95×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
119	C₂×C₂²⋊D₄₇	—	2	1	no	—
120	#10625350	—	2	1	no	—
121	#10625350	—	2	1	no	—
122	#10625350	C₂×Q₈	1	2	yes	—
123	#10625350	#41	1	2	yes	—
124	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₄₇	—	2	1	no	—
126	C₂×C₄×D₄₇	—	2	1	no	—
127	C₂×C₄×D₄₇	—	2	1	no	—
128	C₂×Dic₉₄	—	2	1	no	—
129	C₂×Dic₉₄	—	2	1	no	—
130	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	—	2	1	no	—
133	C₂×C₈×C₄₇	—	2	1	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
142	C₂×C₈×C₄₇	#41	1	2	yes	—
143	C₄⋊C₄×C₄₇	—	4	2	no	—
144	C₄²×C₄₇	—	2	2	no	—
145	C₄²×C₄₇	—	2	2	no	—
146	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₂²⋊Dic₄₇	—	2	1	no	—
151	C₂²⋊Dic₄₇	—	2	2	no	—
152	(C₂×D₄₇)⋊C₄	—	2	1	no	—
153	(C₂×D₄₇)⋊C₄	—	2	1	no	—
154	C₄⋊Dic₄₇	—	2	1	no	—
155	C₄⋊Dic₄₇	—	2	1	no	—
156	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
157	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
158	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
160	Dic₄₇⋊C₄	—	2	1	no	—
161	Dic₄₇⋊C₄	—	2	1	no	—
162	Dic₄₇⋊C₄	—	2	2	no	—
163	Dic₄₇⋊C₄	—	2	2	no	—
164	C₄×Dic₄₇	—	2	1	no	—
165	C₄×Dic₄₇	—	2	1	no	—
166	C₄×Dic₄₇	—	2	1	no	—
167	C₄×Dic₄₇	—	2	2	no	—
168	#10625329	—	2	1	no	—
169	#10625329	—	2	1	no	—
170	#10625329	—	2	2	no	—
171	#10625329	—	2	2	no	—
172	#10625329	C₂×Q₈	1	2	yes	—
173	#10625329	#41	1	2	yes	—
174	C₂×C₄₇⋊C₈	—	2	1	no	—
175	C₂×C₄₇⋊C₈	—	2	1	no	—
176	C₂×C₄₇⋊C₈	—	2	2	no	—
177	#10625324	—	2	4	no	—
178	#10625324	—	2	4	no	—
179	C₈×D₄₇	—	2	4	no	—
180	C₈×D₄₇	—	2	4	no	—
181	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂²×D₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂²⋊D₄₇	—	2	2	no	—
199	C₂²⋊D₄₇	—	2	2	no	—
200	C₂×Dic₄₇	—	2	1	no	—
201	C₂×Dic₄₇	—	2	1	no	—
202	C₂×Dic₄₇	—	2	1	no	—
203	C₂×Dic₄₇	—	2	2	no	—
204	C₂×Dic₄₇	—	2	2	no	—
205	D₁₈₈	—	2	1	no	—
206	D₁₈₈	C₄×Q₈	1	2	yes	—
207	C₄×D₄₇	—	2	2	no	—
208	C₄×D₄₇	—	2	2	no	—
209	C₄×D₄₇	—	4	2	no	—
210	C₄×D₄₇	—	4	2	no	—
211	Dic₉₄	—	2	1	no	—
212	Dic₉₄	—	4	2	no	—
213	Dic₉₄	—	4	2	no	—
214	Dic₉₄	C₄×Q₈	1	2	yes	—
215	C₈×C₄₇	—	2	2	no	—
216	C₈×C₄₇	—	2	2	no	—
217	C₈×C₄₇	—	2	1	no	—
218	C₈×C₄₇	—	2	1	no	—
219	C₈×C₄₇	C₂²⋊Q₈	1	2	yes	—
220	C₈×C₄₇	C₂²⋊Q₈	1	2	yes	—
221	C₄₇⋊C₈	—	2	2	no	—
222	C₄₇⋊C₈	—	2	2	no	—
223	C₄₇⋊C₈	—	4	2	no	—
224	#21628	—	47	1	no	maximal, Sylow
225	C₂²×C₄₇	—	2	1	no	—
226	C₂²×C₄₇	—	2	1	no	—
227	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₄₇	#529	1	1	yes	characteristic
229	C₂²×C₄₇	#533	1	1	yes	characteristic
230	C₂×D₄₇	—	2	2	no	—
231	C₂×D₄₇	—	4	1	no	—
232	C₂×D₄₇	—	4	1	no	—
233	C₄×C₄₇	—	2	1	no	—
234	C₄×C₄₇	—	2	1	no	—
235	C₄×C₄₇	—	2	1	no	—
236	C₄×C₄₇	—	8	2	no	—
237	C₄×C₄₇	#444	1	2	yes	—
238	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
239	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
240	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
241	C₄×C₄₇	#525	1	1	yes	characteristic
242	Dic₄₇	—	2	2	no	—
243	Dic₄₇	—	4	2	no	—
244	Dic₄₇	—	4	1	no	—
245	Dic₄₇	—	4	2	no	—
246	Dic₄₇	—	4	1	no	—
247	#3076	—	47	1	no	—
248	#2960	—	47	1	no	—
249	C₄×#131	—	47	1	no	—
250	#1986	—	47	1	no	—
251	#1950	—	47	1	no	—
252	#1922	—	47	2	no	—
253	#1866	—	47	2	no	—
254	#1806	—	47	1	no	—
255	#1773	—	47	2	no	—
256	#1770	D₄₇	1	1	yes	characteristic, complemented
257	#1765	—	47	2	no	—
258	C₂×C₄₇	—	2	1	no	—
259	C₂×C₄₇	—	2	1	no	—
260	C₂×C₄₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
262	C₂×C₄₇	#2955	1	1	yes	characteristic
263	D₄₇	—	4	2	no	—
264	C₂×#131	—	47	1	no	—
265	C₂×#131	—	47	1	no	—
266	#533	—	47	1	no	—
267	C₄×#41	—	47	1	no	—
268	#479	—	47	2	no	—
269	#478	—	47	2	no	—
270	#477	—	47	1	no	—
271	#476	—	47	1	no	—
272	#475	—	47	1	no	—
273	#474	—	47	1	no	—
274	#446	—	94	1	no	—
275	#446	—	94	1	no	—
276	C₈×Q₈	—	94	1	no	—
277	C₈×Q₈	—	94	1	no	—
278	C₂×#108	—	47	2	no	—
279	#427	—	47	2	no	—
280	#424	—	47	2	no	—
281	#423	—	47	1	no	—
282	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
283	C₂×#104	—	47	2	no	—
284	#416	—	47	2	no	—
285	#405	—	47	1	no	—
286	#405	—	47	1	no	—
287	#405	—	47	2	no	—
288	#405	—	94	1	no	—
289	#405	—	94	1	no	—
290	C₄×M₁₆	—	47	1	no	—
291	C₄×M₁₆	—	94	1	no	—
292	C₂×#97	C₂×D₄₇	1	2	yes	—
293	C₂×C₄×C₈	—	94	1	no	—
294	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
296	#341	—	47	2	no	—
297	#339	—	47	2	no	—
298	#339	—	47	2	no	—
299	#339	—	47	2	no	—
300	#336	C₂×D₄₇	1	2	yes	—
301	C₄₇	#21628	1	1	yes	characteristic, complemented, Sylow
302	C₂×#41	—	47	1	no	—
303	#131	—	47	4	no	—
304	#131	—	94	2	no	—
305	#131	—	94	2	no	—
306	#131	—	94	2	no	—
307	C₂×M₁₆	—	47	1	no	—
308	C₂×M₁₆	—	47	1	no	—
309	C₂×M₁₆	—	47	2	no	—
310	C₂×M₁₆	—	94	1	no	—
311	C₂×M₁₆	—	94	1	no	—
312	C₂²×C₈	—	94	1	no	—
313	C₂²×C₈	—	94	1	no	—
314	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
315	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
316	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
317	C₄⋊Q₈	—	47	1	no	—
318	C₄⋊Q₈	—	47	1	no	—
319	#125	—	47	2	no	—
320	C₂²⋊Q₈	—	94	1	no	—
321	C₂²⋊Q₈	—	94	1	no	—
322	C₄×Q₈	—	47	1	no	—
323	C₄×Q₈	—	47	1	no	—
324	C₄×Q₈	—	94	1	no	—
325	C₄×Q₈	—	94	1	no	—
326	C₄×D₄	—	47	1	no	—
327	C₄×D₄	—	47	1	no	—
328	C₄×D₄	—	94	1	no	—
329	C₄×D₄	—	94	1	no	—
330	#117	—	47	1	no	—
331	#117	—	47	2	no	—
332	#117	—	94	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄²	—	94	1	no	—
335	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
336	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
337	#108	—	94	4	no	—
338	#107	—	47	2	no	—
339	#107	—	47	2	no	—
340	#106	—	47	2	no	—
341	#106	—	47	2	no	—
342	C₄⋊C₈	—	94	2	no	—
343	C₄⋊C₈	—	94	2	no	—
344	C₄⋊C₈	—	94	1	no	—
345	C₄⋊C₈	—	94	1	no	—
346	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
347	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
348	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
349	#104	—	94	4	no	—
350	#103	—	47	2	no	—
351	#103	—	47	2	no	—
352	#102	—	47	2	no	—
353	#102	—	47	2	no	—
354	#97	—	2	4	no	—
355	#97	—	94	1	no	—
356	#97	—	94	1	no	—
357	#97	—	94	2	no	—
358	#97	—	94	1	no	—
359	C₄×C₈	—	94	1	no	—
360	C₄×C₈	—	94	1	no	—
361	C₄×C₈	—	94	2	no	—
362	C₄×C₈	—	94	1	no	—
363	C₄×C₈	D₁₈₈	1	1	yes	characteristic
364	C₄×C₈	D₁₈₈	1	1	yes	characteristic
365	C₄×C₈	D₁₈₈	1	1	yes	characteristic
366	C₄×C₈	D₁₈₈	1	1	yes	characteristic
367	#95	—	2	1	no	—
368	#41	—	47	2	no	—
369	#41	—	47	2	no	—
370	#41	—	94	1	no	—
371	#41	—	94	1	no	—
372	C₂×Q₈	—	47	1	no	—
373	C₂×Q₈	—	94	1	no	—
374	C₂×Q₈	—	94	1	no	—
375	C₂×D₄	—	47	1	no	—
376	C₂×D₄	—	94	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	94	1	no	—
379	C₂²×C₄	—	94	1	no	—
380	C₂²×C₄	—	94	1	no	—
381	C₂²×C₄	#10625350	1	1	yes	characteristic
382	C₂²×C₄	#10625350	1	1	yes	characteristic
383	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
384	M₁₆	—	47	2	no	—
385	M₁₆	—	47	2	no	—
386	M₁₆	—	94	4	no	—
387	M₁₆	—	94	1	no	—
388	M₁₆	—	94	1	no	—
389	M₁₆	—	94	4	no	—
390	M₁₆	—	94	2	no	—
391	M₁₆	—	94	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	94	4	no	—
397	C₂×C₈	—	94	1	no	—
398	C₂×C₈	—	94	1	no	—
399	C₂×C₈	—	94	4	no	—
400	C₂×C₈	—	94	2	no	—
401	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
402	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
403	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
404	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
405	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
406	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
407	C₂×C₈	#10625352	1	2	yes	—
408	C₂×C₈	Q₈×D₄₇	1	2	yes	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	47	2	no	—
411	C₄⋊C₄	—	47	2	no	—
412	C₄⋊C₄	—	47	1	no	—
413	C₄⋊C₄	—	47	1	no	—
414	C₄⋊C₄	—	94	1	no	—
415	C₄⋊C₄	—	94	1	no	—
416	C₄⋊C₄	—	94	2	no	—
417	C₄⋊C₄	—	94	2	no	—
418	C₄⋊C₄	—	94	1	no	—
419	C₄⋊C₄	—	94	1	no	—
420	C₂²⋊C₄	—	94	1	no	—
421	C₂²⋊C₄	—	94	2	no	—
422	C₂²⋊C₄	—	94	1	no	—
423	C₂²⋊C₄	—	94	1	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	94	1	no	—
427	C₄²	—	94	1	no	—
428	C₄²	—	94	1	no	—
429	C₄²	—	94	2	no	—
430	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
432	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
433	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
434	C₂³	—	94	1	no	—
435	C₂³	C₂×#10625350	1	1	yes	characteristic
436	Q₈	—	47	2	no	—
437	Q₈	—	94	1	no	—
438	Q₈	—	188	2	no	—
439	Q₈	—	188	2	no	—
440	D₄	—	47	2	no	—
441	D₄	—	94	2	no	—
442	D₄	—	94	2	no	—
443	D₄	—	94	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	94	1	no	—
450	C₂×C₄	—	94	2	no	—
451	C₂×C₄	—	94	2	no	—
452	C₂×C₄	—	94	1	no	—
453	C₂×C₄	—	94	1	no	—
454	C₂×C₄	—	94	2	no	—
455	C₂×C₄	—	94	2	no	—
456	C₂×C₄	—	188	2	no	—
457	C₂×C₄	—	188	2	no	—
458	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
459	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
460	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
461	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
464	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
465	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
466	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
467	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	94	2	no	—
473	C₈	—	94	2	no	—
474	C₈	—	188	2	no	—
475	C₈	#13094004	1	2	yes	—
476	C₈	#13094004	1	2	yes	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	94	2	no	—
480	C₂²	—	188	1	no	—
481	C₂²	—	188	1	no	—
482	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
483	C₂²	#15689655	1	1	yes	characteristic
484	C₂²	#15689677	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	8	2	no	—
489	C₄	—	94	2	no	—
490	C₄	—	188	1	no	—
491	C₄	—	188	2	no	—
492	C₄	—	188	1	no	—
493	C₄	—	188	2	no	—
494	C₄	#15689246	1	2	yes	—
495	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
496	C₄	C₄×#10625352	1	1	yes	characteristic
497	C₄	C₂×#13094004	1	1	yes	characteristic
498	C₄	#15689635	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	188	2	no	—
502	C₂	C₄×#13094004	1	1	yes	characteristic
503	C₂	C₂×#15689246	1	1	yes	characteristic
504	C₂	#20252292	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1770	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#10625350	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1770	D₄₇
hypocenter	C₄₇	#21628
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1770

Complements

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

N	H ≅ G/N	type
2. #20252322	C₂	semidirect
4. #20244331	C₂	semidirect
5. #20244164	C₂	semidirect
6. #20243988	C₂	semidirect
9. #20243272	C₂	semidirect
11. C₄₇×#1770	C₂	semidirect
16. #15689431	C₄	semidirect
17. #15689424	C₄	semidirect
18. #15689419	C₄	semidirect
19. #15689414	C₄	semidirect
20. #15689409	C₄	semidirect
21. #15689404	C₄	semidirect
53. #13094030	Q₈	semidirect
256. #1770	D₄₇	semidirect
301. C₄₇	#21628	semidirect

Maximal subgroups

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

subgroup	index
#20253178	2
#20252322	2
C₄×#13094030	2
#20244331	2
#20244164	2
#20243988	2
#20243666	2
#20243409	2
#20243272	2
#20243232	2
C₄₇×#1770	2
#21628	47