Subgroups — #26186259

Order 12032.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253468	C₂	1	1	yes	maximal, characteristic
2	#20252363	C₂	1	1	yes	maximal, characteristic
3	#20242266	C₂	1	2	yes	maximal, complemented
4	#20242259	C₂	1	2	yes	maximal, complemented
5	C₈×#10625337	C₂	1	2	yes	maximal, complemented
6	C₈×#10625336	C₂	1	2	yes	maximal, complemented
7	#20242171	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241835	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241799	C₂	1	1	yes	maximal, characteristic
10	C₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689657	C₂²	1	1	yes	characteristic
13	#15689453	C₄	1	1	yes	characteristic
14	#15689436	C₄	1	1	yes	characteristic
15	#15689430	C₄	1	2	yes	—
16	#15689345	C₄	1	2	yes	—
17	#15689279	C₄	1	1	yes	characteristic
18	#15689262	C₄	1	1	yes	characteristic
19	#15689253	C₂²	1	1	yes	characteristic
20	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
21	C₄×#10625337	C₂²	1	2	yes	—
22	C₄×#10625336	C₂²	1	2	yes	—
23	#15689202	C₂²	1	1	yes	characteristic
24	#15689194	—	2	1	no	—
25	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₄₇	—	2	1	no	—
27	#15689182	—	2	1	no	—
28	#15689180	C₂²	1	1	yes	characteristic
29	#15689176	C₂²	1	1	yes	characteristic
30	#15689077	—	2	1	no	—
31	C₄×#10625329	C₂²	1	1	yes	characteristic
32	#15688875	C₂²	1	2	yes	—
33	#15688873	C₂²	1	2	yes	—
34	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
35	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
36	#15688853	C₂²	1	2	yes	—
37	#15688850	C₂²	1	2	yes	—
38	#15688845	C₂²	1	2	yes	—
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₈×Q₈×C₄₇	—	2	1	no	—
42	C₈×Q₈×C₄₇	—	2	1	no	—
43	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
44	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
46	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₄₇	—	2	1	no	—
48	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#10625337	C₂×C₄	1	2	yes	—
50	C₂×#10625336	C₂×C₄	1	2	yes	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625324	—	2	1	no	—
53	C₂×C₈×D₄₇	—	2	1	no	—
54	#13094018	—	2	1	no	—
55	#13094016	C₂×C₄	1	1	yes	characteristic
56	#13094012	C₂×C₄	1	1	yes	characteristic
57	#13094007	—	2	1	no	—
58	#13094003	C₂×C₄	1	1	yes	characteristic
59	#13093998	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
61	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
62	C₄×C₂²⋊D₄₇	—	2	1	no	—
63	#13093981	—	2	1	no	—
64	#13093957	C₂×C₄	1	2	yes	—
65	#13093955	C₂×C₄	1	2	yes	—
66	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	Dic₄₇⋊C₈	—	2	1	no	—
70	Dic₄₇⋊C₈	—	2	1	no	—
71	#13093948	C₂×C₄	1	2	yes	—
72	#13093948	C₂×C₄	1	2	yes	—
73	#13093947	C₂×C₄	1	2	yes	—
74	#13093944	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
76	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
77	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
78	(C₂×D₄₇)⋊C₈	—	2	1	no	—
79	(C₂×D₄₇)⋊C₈	—	2	1	no	—
80	#13093935	—	2	1	no	—
81	#13093935	—	2	1	no	—
82	#13093934	—	2	1	no	—
83	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
84	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
85	C₈×Dic₄₇	—	2	1	no	—
86	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	—	2	1	no	—
88	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
89	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₄₇	—	2	1	no	—
91	C₄×Q₈×C₄₇	—	2	1	no	—
92	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₇	—	2	2	no	—
99	C₄⋊C₈×C₄₇	—	2	2	no	—
100	C₄⋊C₈×C₄₇	—	2	1	no	—
101	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
102	C₄×C₈×C₄₇	—	2	2	no	—
103	C₄×C₈×C₄₇	—	2	2	no	—
104	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
105	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₄₇	—	2	4	no	—
109	C₂×Q₈×C₄₇	—	2	1	no	—
110	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
116	C₂×C₂²⋊D₄₇	—	2	1	no	—
117	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₄₇	—	2	1	no	—
119	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	4	1	no	—
123	C₂×C₈×C₄₇	—	4	2	no	—
124	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	C₂²×C₄	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	—	2	4	no	—
140	#10625336	—	2	4	no	—
141	(C₂×D₄₇)⋊C₄	—	2	1	no	—
142	(C₂×D₄₇)⋊C₄	—	2	1	no	—
143	(C₂×D₄₇)⋊C₄	—	2	1	no	—
144	(C₂×D₄₇)⋊C₄	—	2	1	no	—
145	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
147	Dic₄₇⋊C₄	—	2	1	no	—
148	Dic₄₇⋊C₄	—	2	1	no	—
149	Dic₄₇⋊C₄	—	2	1	no	—
150	Dic₄₇⋊C₄	—	2	1	no	—
151	C₄×Dic₄₇	—	2	1	no	—
152	#10625329	—	2	4	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
157	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
158	#10625324	—	4	2	no	—
159	C₈×D₄₇	—	4	2	no	—
160	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₄₇	—	2	1	no	—
162	Q₈×C₄₇	—	2	4	no	—
163	Q₈×C₄₇	—	2	2	no	—
164	Q₈×C₄₇	#131	1	4	yes	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
179	C₂²⋊D₄₇	—	4	2	no	—
180	C₂×Dic₄₇	—	2	1	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	D₁₈₈	—	2	2	no	—
184	C₄×D₄₇	—	4	1	no	—
185	C₄×D₄₇	—	4	1	no	—
186	Dic₉₄	—	2	2	no	—
187	C₈×C₄₇	—	2	1	no	—
188	C₈×C₄₇	—	2	1	no	—
189	C₈×C₄₇	—	2	1	no	—
190	C₈×C₄₇	—	4	2	no	—
191	C₈×C₄₇	#137	1	2	yes	—
192	C₄₇⋊C₈	—	2	4	no	—
193	C₄₇⋊C₈	—	2	2	no	—
194	C₄₇⋊C₈	—	2	2	no	—
195	C₄₇⋊C₈	—	4	1	no	—
196	C₄₇⋊C₈	—	4	1	no	—
197	#17911	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	#443	1	2	yes	—
201	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂×D₄₇	—	4	1	no	—
203	C₂×D₄₇	—	4	1	no	—
204	C₂×D₄₇	—	4	1	no	—
205	C₄×C₄₇	—	2	4	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	C₂×#131	1	2	yes	—
212	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
213	C₄×C₄₇	#575	1	1	yes	characteristic
214	Dic₄₇	—	4	1	no	—
215	Dic₄₇	—	4	1	no	—
216	Dic₄₇	—	4	1	no	—
217	#3108	—	47	1	no	—
218	#2966	—	47	1	no	—
219	C₂×C₈×Q₈	D₄₇	1	1	yes	characteristic, complemented
220	#1588	—	47	2	no	—
221	#1587	—	47	2	no	—
222	C₈×Q₁₆	—	47	2	no	—
223	C₈×SD₁₆	—	47	2	no	—
224	#1573	—	47	1	no	—
225	#1491	—	47	1	no	—
226	#1483	—	47	1	no	—
227	C₈×M₁₆	—	47	1	no	—
228	C₂×C₄₇	—	2	2	no	—
229	C₂×C₄₇	#2929	1	1	yes	characteristic
230	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
232	D₄₇	—	8	1	no	—
233	#529	—	47	1	no	—
234	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
235	#483	—	47	1	no	—
236	#480	—	47	1	no	—
237	#479	—	47	2	no	—
238	#464	—	47	2	no	—
239	#451	—	47	1	no	—
240	#448	—	47	1	no	—
241	#446	—	47	1	no	—
242	C₈×Q₈	—	2	1	no	—
243	C₈×Q₈	—	2	1	no	—
244	C₈×Q₈	—	47	1	no	—
245	C₈×Q₈	C₂×D₄₇	1	2	yes	—
246	C₈×Q₈	C₂×D₄₇	1	2	yes	—
247	C₄×Q₁₆	—	47	2	no	—
248	C₄×SD₁₆	—	47	2	no	—
249	#436	—	47	1	no	—
250	#435	—	94	1	no	—
251	C₈×D₄	—	47	1	no	—
252	C₈×D₄	—	94	1	no	—
253	#433	—	94	1	no	—
254	#432	—	47	1	no	—
255	#431	—	47	1	no	—
256	C₂×C₄⋊C₈	—	2	1	no	—
257	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
258	#405	—	94	1	no	—
259	C₄×M₁₆	—	47	1	no	—
260	C₂×C₄×C₈	—	2	1	no	—
261	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
262	#335	—	47	2	no	—
263	#334	—	47	2	no	—
264	Q₈⋊C₈	—	47	2	no	—
265	Q₈⋊C₈	—	47	2	no	—
266	Q₈⋊C₈	—	47	2	no	—
267	D₄⋊C₈	—	47	2	no	—
268	#322	—	47	2	no	—
269	C₈²	—	47	2	no	—
270	C₄₇	#17911	1	1	yes	characteristic, complemented, Sylow
271	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
272	C₂×Q₁₆	—	47	2	no	—
273	C₂×SD₁₆	—	47	2	no	—
274	C₂×M₁₆	—	94	1	no	—
275	C₂×M₁₆	—	94	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	94	1	no	—
278	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
279	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
280	#126	—	94	1	no	—
281	#125	—	47	1	no	—
282	#124	—	47	1	no	—
283	#123	—	94	1	no	—
284	C₂²⋊Q₈	—	47	1	no	—
285	#121	—	47	1	no	—
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	47	1	no	—
289	C₄×Q₈	C₄×D₄₇	1	2	yes	—
290	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
291	C₄×D₄	—	47	1	no	—
292	C₄×D₄	—	94	1	no	—
293	#117	—	94	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
298	#107	—	47	2	no	—
299	#106	—	47	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	47	2	no	—
304	C₄⋊C₈	—	47	1	no	—
305	C₄⋊C₈	—	47	1	no	—
306	C₄⋊C₈	—	94	1	no	—
307	C₄⋊C₈	—	94	1	no	—
308	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
309	#103	—	47	2	no	—
310	#103	—	47	2	no	—
311	#103	—	47	2	no	—
312	#102	—	47	2	no	—
313	C₂²⋊C₈	—	47	1	no	—
314	C₂²⋊C₈	—	47	1	no	—
315	C₂²⋊C₈	—	94	1	no	—
316	C₂²⋊C₈	—	94	1	no	—
317	C₂²⋊C₈	—	94	1	no	—
318	#97	—	94	1	no	—
319	#97	—	94	1	no	—
320	#97	—	94	1	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	47	2	no	—
324	C₄×C₈	—	47	2	no	—
325	C₄×C₈	—	94	1	no	—
326	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
327	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	47	1	no	—
333	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
334	C₂×D₄	—	47	1	no	—
335	C₂×D₄	—	94	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	94	1	no	—
339	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
340	C₂²×C₄	#10625350	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
342	Q₁₆	—	94	4	no	—
343	SD₁₆	—	94	4	no	—
344	M₁₆	—	94	4	no	—
345	M₁₆	—	188	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	47	2	no	—
351	C₂×C₈	—	47	2	no	—
352	C₂×C₈	—	94	2	no	—
353	C₂×C₈	—	94	1	no	—
354	C₂×C₈	—	94	1	no	—
355	C₂×C₈	—	188	2	no	—
356	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
357	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
358	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	47	1	no	—
364	C₄⋊C₄	—	47	1	no	—
365	C₄⋊C₄	—	94	1	no	—
366	C₄⋊C₄	—	94	1	no	—
367	C₄⋊C₄	—	94	1	no	—
368	C₄⋊C₄	—	94	1	no	—
369	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
370	C₂²⋊C₄	—	94	1	no	—
371	C₂²⋊C₄	—	94	1	no	—
372	C₂²⋊C₄	—	94	1	no	—
373	C₂²⋊C₄	—	94	1	no	—
374	C₂²⋊C₄	—	94	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	94	1	no	—
378	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
379	C₄²	#10625350	1	1	yes	characteristic
380	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
381	C₄²	C₂³×D₄₇	1	1	yes	characteristic
382	C₂³	—	94	1	no	—
383	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	94	2	no	—
387	Q₈	#13094030	1	4	yes	—
388	D₄	—	94	2	no	—
389	D₄	—	188	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	94	1	no	—
399	C₂×C₄	—	94	1	no	—
400	C₂×C₄	—	94	1	no	—
401	C₂×C₄	—	188	1	no	—
402	C₂×C₄	—	188	1	no	—
403	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	4	2	no	—
413	C₈	—	94	4	no	—
414	C₈	—	94	2	no	—
415	C₈	—	94	2	no	—
416	C₈	—	188	1	no	—
417	C₈	—	188	1	no	—
418	C₈	#13094055	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	188	1	no	—
422	C₂²	—	188	1	no	—
423	C₂²	—	188	1	no	—
424	C₂²	#15689238	1	2	yes	—
425	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	188	1	no	—
433	C₄	—	188	1	no	—
434	C₄	—	188	1	no	—
435	C₄	C₂×#13094030	1	2	yes	—
436	C₄	C₂×#13094055	1	1	yes	characteristic
437	C₄	#15689921	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	376	1	no	—
440	C₂	#20252082	1	1	yes	characteristic
441	C₂	C₄×#13094055	1	1	yes	characteristic
442	C₂	C₂×#15689238	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₈×Q₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#13093998	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×C₈×Q₈	D₄₇
hypocenter	C₄₇	#17911
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
3. #20242266	C₂	semidirect
4. #20242259	C₂	semidirect
5. C₈×#10625337	C₂	semidirect
6. C₈×#10625336	C₂	semidirect
7. #20242171	C₂	semidirect
8. #20241835	C₂	semidirect
10. C₈×#10625329	C₂	semidirect
11. C₂×C₈×Q₈×C₄₇	C₂	semidirect
219. C₂×C₈×Q₈	D₄₇	semidirect
270. C₄₇	#17911	semidirect

Maximal subgroups

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

subgroup	index
#20253468	2
#20252363	2
#20242266	2
#20242259	2
C₈×#10625337	2
C₈×#10625336	2
#20242171	2
#20241835	2
#20241799	2
C₈×#10625329	2
C₂×C₈×Q₈×C₄₇	2
#17911	47