Subgroups — #26185434

Order 12032.

640 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	#20252018	C₂	1	1	yes	maximal, characteristic
2	#432×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689174	C₂	1	1	yes	maximal, characteristic
4	#20242167	C₂	1	2	yes	maximal, complemented
5	#20242165	C₂	1	2	yes	maximal, complemented
6	#20242161	C₂	1	2	yes	maximal, complemented
7	#20242157	C₂	1	2	yes	maximal, complemented
8	#20242151	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242149	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242149	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
13	#15689180	C₂²	1	1	yes	characteristic
14	#15689180	C₂²	1	1	yes	characteristic
15	#15689179	C₂²	1	2	yes	—
16	#15689178	—	2	1	no	—
17	#15689178	—	2	1	no	—
18	#15689177	—	2	1	no	—
19	#15689175	C₂²	1	2	yes	—
20	#15689174	C₄	1	2	yes	—
21	#15689174	C₄	1	2	yes	—
22	#15689174	C₂²	1	1	yes	characteristic
23	#15689174	C₂²	1	1	yes	characteristic
24	#15689174	C₂²	1	1	yes	characteristic
25	#15689174	C₂²	1	1	yes	characteristic
26	#15689173	—	2	1	no	—
27	#15689145	C₂²	1	2	yes	—
28	C₂×Dic₄₇⋊C₈	C₄	1	2	yes	—
29	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
30	#15689085	—	2	1	no	—
31	C₂×(C₂×D₄₇)⋊C₈	C₄	1	2	yes	—
32	C₂²⋊C₈×D₄₇	—	2	1	no	—
33	#15689075	—	2	1	no	—
34	#97×D₄₇	—	2	1	no	—
35	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
36	#15688876	C₂²	1	2	yes	complemented
37	#15688875	C₂²	1	2	yes	complemented
38	#15688875	C₂²	1	2	yes	complemented
39	#15688874	C₂²	1	2	yes	complemented
40	#15688873	C₂²	1	2	yes	complemented
41	#15688873	C₂²	1	2	yes	complemented
42	C₄₇×#432	C₂²	1	1	yes	characteristic
43	C₄₇×#432	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	2	yes	complemented
46	C₄₇×#334	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
50	C₂×#10625324	—	2	2	no	—
51	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
52	C₂×C₈×D₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
56	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₄₇	D₄	1	1	yes	characteristic
59	C₄²×D₄₇	D₄	1	1	yes	characteristic
60	C₄²×D₄₇	Q₈	1	1	yes	characteristic
61	C₄²×D₄₇	Q₈	1	1	yes	characteristic
62	C₄²×D₄₇	C₂³	1	1	yes	characteristic
63	C₄²×D₄₇	C₂³	1	1	yes	characteristic
64	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
65	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
66	Dic₄₇⋊C₈	—	2	2	no	—
67	Dic₄₇⋊C₈	—	2	2	no	—
68	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
69	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
70	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
71	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
72	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
73	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
74	(C₂×D₄₇)⋊C₈	—	2	2	no	—
75	(C₂×D₄₇)⋊C₈	—	2	2	no	—
76	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
77	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
78	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
79	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
80	#13093935	—	2	1	no	—
81	#13093935	—	2	1	no	—
82	#13093934	—	2	2	no	—
83	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
84	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₈×Dic₄₇	—	2	2	no	—
87	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
90	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
91	C₂²⋊C₈×C₄₇	—	2	1	no	—
92	C₂²⋊C₈×C₄₇	—	2	1	no	—
93	#97×C₄₇	—	2	1	no	—
94	#97×C₄₇	—	2	1	no	—
95	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
96	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₂³×D₄₇	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	—	2	4	no	—
106	C₂×C₄×D₄₇	—	4	2	no	—
107	C₂×C₄×D₄₇	—	4	2	no	—
108	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	4	2	no	—
123	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
125	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
128	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
129	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
138	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
140	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	4	2	no	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
146	#10625324	—	4	4	no	—
147	C₈×D₄₇	—	4	4	no	—
148	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂²×D₄₇	—	2	2	no	—
150	C₂²×D₄₇	—	2	2	no	—
151	C₂²×D₄₇	—	4	1	no	—
152	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	4	1	no	—
166	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₄×D₄₇	—	2	2	no	—
173	C₄×D₄₇	—	2	2	no	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	2	2	no	—
176	C₄×D₄₇	—	2	2	no	—
177	C₄×D₄₇	—	4	1	no	—
178	C₄×D₄₇	—	4	1	no	—
179	C₄×D₄₇	—	4	1	no	—
180	C₄×D₄₇	—	4	1	no	—
181	C₄×D₄₇	—	4	1	no	—
182	C₄×D₄₇	—	4	1	no	—
183	C₄×D₄₇	#135	1	4	yes	—
184	C₈×C₄₇	—	2	2	no	—
185	C₈×C₄₇	—	2	2	no	—
186	C₈×C₄₇	—	4	2	no	—
187	C₈×C₄₇	—	4	2	no	—
188	C₄₇⋊C₈	—	2	2	no	—
189	C₄₇⋊C₈	—	2	2	no	—
190	C₄₇⋊C₈	—	4	2	no	—
191	C₄₇⋊C₈	—	4	2	no	—
192	#17816	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	#430	1	2	yes	—
196	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
197	C₂×D₄₇	—	2	1	no	—
198	C₂×D₄₇	—	2	1	no	—
199	C₂×D₄₇	—	2	1	no	—
200	C₂×D₄₇	—	2	1	no	—
201	C₂×D₄₇	—	2	1	no	—
202	C₂×D₄₇	—	4	4	no	—
203	C₂×D₄₇	#427	1	2	yes	—
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	#568	1	2	yes	—
209	C₄×C₄₇	C₂×#135	1	2	yes	—
210	Dic₄₇	—	2	1	no	—
211	Dic₄₇	—	2	1	no	—
212	Dic₄₇	—	2	1	no	—
213	Dic₄₇	—	2	1	no	—
214	Dic₄₇	—	2	1	no	—
215	Dic₄₇	#427	1	2	yes	—
216	#2920	—	47	1	no	—
217	C₂×#432	—	47	1	no	—
218	C₂×#431	—	47	1	no	—
219	#1572	—	47	2	no	—
220	#1572	—	47	2	no	—
221	#1571	—	47	2	no	—
222	#1570	—	47	2	no	—
223	#1568	—	47	1	no	—
224	#1568	—	47	1	no	—
225	#1568	—	47	1	no	—
226	#1568	D₄₇	1	1	yes	characteristic, complemented
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	#2905	1	1	yes	characteristic
229	C₂×C₄₇	C₂×#427	1	1	yes	characteristic
230	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
231	D₄₇	—	2	2	no	—
232	D₄₇	—	4	1	no	—
233	C₂²×C₄²	—	47	1	no	—
234	#432	—	47	1	no	—
235	#432	—	47	1	no	—
236	#432	—	47	2	no	—
237	#432	—	94	1	no	—
238	#432	—	94	1	no	—
239	#432	—	94	1	no	—
240	#432	C₂×D₄₇	1	1	yes	characteristic
241	#432	C₂×D₄₇	1	1	yes	characteristic
242	#431	—	47	2	no	—
243	#431	—	47	2	no	—
244	#431	—	47	1	no	—
245	#431	—	47	1	no	—
246	#431	—	47	1	no	—
247	#431	—	47	1	no	—
248	#431	—	47	2	no	—
249	#431	—	94	1	no	—
250	#423	—	47	2	no	—
251	C₂×C₄⋊C₈	—	47	2	no	—
252	C₂×C₄⋊C₈	—	47	2	no	—
253	#407	—	94	1	no	—
254	C₂×C₂²⋊C₈	—	47	2	no	—
255	C₂×C₂²⋊C₈	—	94	1	no	—
256	C₄×M₁₆	—	94	1	no	—
257	C₂×#97	—	94	1	no	—
258	C₂×C₄×C₈	—	47	1	no	—
259	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
260	#335	—	47	2	no	—
261	#335	—	47	2	no	—
262	#335	—	47	2	no	—
263	#335	C₂×D₄₇	1	2	yes	complemented
264	#334	—	47	2	no	—
265	#334	—	47	2	no	—
266	#334	—	47	2	no	—
267	#334	C₂×D₄₇	1	2	yes	complemented
268	C₄₇	#17816	1	1	yes	characteristic, complemented, Sylow
269	C₂³×C₄	—	47	1	no	—
270	C₂³×C₄	—	47	1	no	—
271	C₂³×C₄	—	47	1	no	—
272	C₂×M₁₆	—	94	2	no	—
273	C₂²×C₈	—	47	2	no	—
274	C₂²×C₈	—	94	2	no	—
275	C₂²×C₈	C₄×D₄₇	1	2	yes	—
276	C₂×C₄²	—	47	1	no	—
277	C₂×C₄²	—	47	1	no	—
278	C₂×C₄²	—	47	1	no	—
279	C₂×C₄²	—	47	1	no	—
280	C₂×C₄²	—	47	1	no	—
281	C₂×C₄²	—	47	1	no	—
282	C₂×C₄²	—	47	1	no	—
283	C₂×C₄²	—	47	1	no	—
284	C₂×C₄²	—	47	1	no	—
285	C₂×C₄²	—	47	1	no	—
286	C₂×C₄²	—	47	1	no	—
287	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
288	C₄⋊C₈	—	47	2	no	—
289	C₄⋊C₈	—	47	2	no	—
290	C₄⋊C₈	—	47	2	no	—
291	C₄⋊C₈	—	47	2	no	—
292	C₄⋊C₈	—	47	2	no	—
293	C₄⋊C₈	—	47	2	no	—
294	C₄⋊C₈	—	94	2	no	—
295	C₄⋊C₈	—	94	2	no	—
296	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
297	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
298	C₂²⋊C₈	—	2	1	no	—
299	C₂²⋊C₈	—	2	1	no	—
300	C₂²⋊C₈	—	47	2	no	—
301	C₂²⋊C₈	—	47	2	no	—
302	C₂²⋊C₈	—	47	2	no	—
303	C₂²⋊C₈	—	47	2	no	—
304	C₂²⋊C₈	—	94	2	no	—
305	C₂²⋊C₈	—	94	2	no	—
306	C₂²⋊C₈	—	94	1	no	—
307	C₂²⋊C₈	—	94	1	no	—
308	#97	—	2	1	no	—
309	#97	—	2	1	no	—
310	#97	—	94	2	no	—
311	#97	—	94	1	no	—
312	#97	—	94	1	no	—
313	C₄×C₈	—	47	2	no	—
314	C₄×C₈	—	47	1	no	—
315	C₄×C₈	—	47	1	no	—
316	C₄×C₈	—	94	2	no	—
317	C₄×C₈	C₄×D₄₇	1	2	yes	—
318	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
320	C₂⁴	—	47	1	no	—
321	C₂²×C₄	—	47	1	no	—
322	C₂²×C₄	—	47	1	no	—
323	C₂²×C₄	—	47	1	no	—
324	C₂²×C₄	—	47	1	no	—
325	C₂²×C₄	—	47	1	no	—
326	C₂²×C₄	—	47	1	no	—
327	C₂²×C₄	—	47	1	no	—
328	C₂²×C₄	—	47	1	no	—
329	C₂²×C₄	—	47	1	no	—
330	C₂²×C₄	—	47	1	no	—
331	C₂²×C₄	—	47	1	no	—
332	C₂²×C₄	—	47	1	no	—
333	C₂²×C₄	—	47	1	no	—
334	C₂²×C₄	—	47	1	no	—
335	C₂²×C₄	—	47	1	no	—
336	C₂²×C₄	—	94	4	no	—
337	C₂²×C₄	—	188	2	no	—
338	C₂²×C₄	—	188	2	no	—
339	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
341	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
342	M₁₆	—	188	4	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	—	47	2	no	—
347	C₂×C₈	—	47	2	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	—	188	4	no	—
351	C₂×C₈	—	188	2	no	—
352	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
353	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
354	C₄²	—	47	1	no	—
355	C₄²	—	47	1	no	—
356	C₄²	—	47	1	no	—
357	C₄²	—	47	1	no	—
358	C₄²	—	47	1	no	—
359	C₄²	—	47	1	no	—
360	C₄²	—	47	1	no	—
361	C₄²	—	47	1	no	—
362	C₄²	—	47	1	no	—
363	C₄²	—	47	1	no	—
364	C₄²	—	47	1	no	—
365	C₄²	—	47	1	no	—
366	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₄²	D₄×D₄₇	1	1	yes	characteristic
368	C₄²	Q₈×D₄₇	1	1	yes	characteristic
369	C₄²	C₂³×D₄₇	1	1	yes	characteristic
370	C₂³	—	47	1	no	—
371	C₂³	—	47	1	no	—
372	C₂³	—	94	2	no	—
373	C₂³	—	94	2	no	—
374	C₂³	—	188	1	no	—
375	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	47	1	no	—
380	C₂×C₄	—	47	4	no	—
381	C₂×C₄	—	47	1	no	—
382	C₂×C₄	—	47	1	no	—
383	C₂×C₄	—	47	1	no	—
384	C₂×C₄	—	47	1	no	—
385	C₂×C₄	—	47	1	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	94	2	no	—
389	C₂×C₄	—	94	2	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	188	1	no	—
394	C₂×C₄	—	188	1	no	—
395	C₂×C₄	—	188	1	no	—
396	C₂×C₄	—	188	1	no	—
397	C₂×C₄	—	188	1	no	—
398	C₂×C₄	—	188	1	no	—
399	C₂×C₄	—	188	1	no	—
400	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
402	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	94	2	no	—
411	C₈	—	94	2	no	—
412	C₈	—	188	2	no	—
413	C₈	—	188	2	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	47	2	no	—
417	C₂²	—	94	1	no	—
418	C₂²	—	94	1	no	—
419	C₂²	—	94	1	no	—
420	C₂²	—	94	1	no	—
421	C₂²	—	94	1	no	—
422	C₂²	—	188	4	no	—
423	C₂²	#15689170	1	2	yes	—
424	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	47	2	no	—
430	C₄	—	94	1	no	—
431	C₄	—	94	1	no	—
432	C₄	—	94	1	no	—
433	C₄	—	94	1	no	—
434	C₄	—	94	1	no	—
435	C₄	#15689889	1	2	yes	—
436	C₄	#135×D₄₇	1	2	yes	—
437	C₂	—	2	2	no	—
438	C₂	—	94	2	no	—
439	C₂	—	188	1	no	—
440	C₂	#20251950	1	1	yes	characteristic
441	C₂	#427×D₄₇	1	1	yes	characteristic
442	C₂	C₂×#15689170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1568	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₇	C₄⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1568	D₄₇
hypocenter	C₄₇	#17816
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
4. #20242167	C₂	semidirect
5. #20242165	C₂	semidirect
6. #20242161	C₂	semidirect
7. #20242157	C₂	semidirect
8. #20242151	C₂	semidirect
9. #20242149	C₂	semidirect
10. #20242149	C₂	semidirect
11. C₄₇×#1568	C₂	semidirect
36. #15688876	C₂²	semidirect
37. #15688875	C₂²	semidirect
38. #15688875	C₂²	semidirect
39. #15688874	C₂²	semidirect
40. #15688873	C₂²	semidirect
41. #15688873	C₂²	semidirect
45. C₄₇×#335	C₂²	semidirect
46. C₄₇×#334	C₂²	semidirect
226. #1568	D₄₇	semidirect
263. #335	C₂×D₄₇	semidirect
267. #334	C₂×D₄₇	semidirect
268. C₄₇	#17816	semidirect

Maximal subgroups

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

subgroup	index
#20252018	2
#432×D₄₇	2
C₂×#15689174	2
#20242167	2
#20242165	2
#20242161	2
#20242157	2
#20242151	2
#20242149	2
C₄₇×#1568	2
#17816	47