Subgroups — #26122477

Order 12032.

826 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689021	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688891	C₂	1	2	yes	maximal
4	C₂×#15688891	C₂	1	2	yes	maximal
5	C₄₇×#1728	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₇⋊C₄	C₄	1	2	yes	—
10	C₄×#10625329	—	2	4	no	—
11	C₂×#13093935	—	2	1	no	—
12	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
13	#15689021	—	2	1	no	—
14	#15689021	—	2	1	no	—
15	#15689021	—	2	1	no	—
16	#15689021	—	2	1	no	—
17	C₂×C₄₇⋊#95	C₄	1	2	yes	—
18	#15688891	—	2	4	no	—
19	#15688891	C₄	1	8	yes	complemented
20	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#336	—	2	1	no	—
23	C₄₇×#336	—	2	1	no	—
24	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
25	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	C₂×C₄	1	4	yes	—
30	C₂×#10625329	D₄	1	4	yes	—
31	C₂×#10625329	Q₈	1	4	yes	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	1	no	—
34	C₂×C₄⋊Dic₄₇	—	2	1	no	—
35	C₂×C₄⋊Dic₄₇	—	2	2	no	—
36	C₂×C₄⋊Dic₄₇	—	2	1	no	—
37	C₂×C₄⋊Dic₄₇	—	2	1	no	—
38	C₂×C₄⋊Dic₄₇	—	2	2	no	—
39	C₂×C₄⋊Dic₄₇	—	2	2	no	—
40	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
41	C₂×Dic₄₇⋊C₄	—	2	2	no	—
42	C₂×Dic₄₇⋊C₄	—	2	2	no	—
43	C₂×Dic₄₇⋊C₄	—	4	4	no	—
44	#13093935	—	2	4	no	—
45	C₄×C₄₇⋊C₈	—	2	4	no	—
46	C₄₇⋊#95	—	2	2	no	—
47	C₄₇⋊#95	—	2	2	no	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₄₇	—	2	2	no	—
52	C₂×M₁₆×C₄₇	—	2	2	no	—
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	2	no	—
55	C₂×M₁₆×C₄₇	—	2	2	no	—
56	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
57	C₂²×C₈×C₄₇	—	2	2	no	—
58	C₂×C₄²×C₄₇	—	2	2	no	—
59	C₂×C₄²×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
64	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	—	2	2	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	4	1	no	—
70	C₂²×C₄×C₄₇	—	4	1	no	—
71	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₄₇	#41	1	2	yes	—
81	C₂²×C₄×C₄₇	#41	1	2	yes	—
82	C₂²×C₄×C₄₇	#41	1	2	yes	—
83	C₂²×Dic₄₇	—	2	2	no	—
84	C₂²×Dic₄₇	—	2	2	no	—
85	C₂²×Dic₄₇	—	2	2	no	—
86	C₂²×Dic₄₇	—	2	4	no	—
87	C₂²×Dic₄₇	—	4	2	no	—
88	C₂²×Dic₄₇	—	4	2	no	—
89	C₂²×Dic₄₇	—	4	2	no	—
90	C₂²×Dic₄₇	—	4	2	no	—
91	C₂²×Dic₄₇	C₄²	1	4	yes	—
92	M₁₆×C₄₇	—	2	4	no	—
93	M₁₆×C₄₇	—	2	4	no	—
94	M₁₆×C₄₇	—	4	2	no	—
95	M₁₆×C₄₇	—	4	2	no	—
96	C₂×C₈×C₄₇	—	2	4	no	—
97	C₂×C₈×C₄₇	—	4	2	no	—
98	C₂×C₈×C₄₇	—	4	2	no	—
99	C₄²×C₄₇	—	2	1	no	—
100	C₄²×C₄₇	—	2	1	no	—
101	C₄²×C₄₇	—	2	2	no	—
102	C₄²×C₄₇	—	2	2	no	—
103	C₄²×C₄₇	—	2	1	no	—
104	C₄²×C₄₇	—	2	1	no	—
105	C₄⋊Dic₄₇	—	2	4	no	—
106	C₄⋊Dic₄₇	—	2	4	no	—
107	C₄⋊Dic₄₇	—	4	1	no	—
108	C₄⋊Dic₄₇	—	4	2	no	—
109	C₄⋊Dic₄₇	—	4	1	no	—
110	Dic₄₇⋊C₄	—	4	4	no	—
111	Dic₄₇⋊C₄	—	4	4	no	—
112	#10625329	—	2	4	no	—
113	#10625329	—	2	4	no	—
114	#10625329	—	2	4	no	—
115	#10625329	C₄⋊C₄	1	8	yes	complemented
116	C₂×C₄₇⋊C₈	—	2	4	no	—
117	C₂×C₄₇⋊C₈	—	2	4	no	—
118	C₂×C₄₇⋊C₈	—	2	4	no	—
119	C₂³×C₄₇	—	2	1	no	—
120	C₂³×C₄₇	—	2	1	no	—
121	C₂³×C₄₇	—	2	1	no	—
122	C₂³×C₄₇	—	2	1	no	—
123	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
124	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₄₇	#117	1	1	yes	characteristic
126	C₂³×C₄₇	C₄×D₄	1	2	yes	—
127	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
128	C₂×C₄×C₄₇	—	2	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	4	4	no	—
139	C₂×C₄×C₄₇	—	4	4	no	—
140	C₂×C₄×C₄₇	#100	1	2	yes	—
141	C₂×C₄×C₄₇	#101	1	2	yes	—
142	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₇	#117	1	2	yes	—
144	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
147	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
148	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#121	1	2	yes	—
150	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
152	C₂×C₄×C₄₇	#123	1	2	yes	—
153	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#125	1	2	yes	—
156	C₂×C₄×C₄₇	#126	1	2	yes	—
157	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
158	C₂×Dic₄₇	—	2	4	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	4	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	8	4	no	—
167	C₈×C₄₇	—	4	4	no	—
168	C₄₇⋊C₈	—	2	8	no	—
169	#10913	—	47	1	no	maximal, Sylow
170	C₂²×C₄₇	—	2	2	no	—
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
180	C₂²×C₄₇	#386	1	1	yes	characteristic
181	C₂²×C₄₇	#387	1	2	yes	—
182	C₂²×C₄₇	#391	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
185	C₂²×C₄₇	#413	1	1	yes	characteristic
186	C₂²×C₄₇	#413	1	1	yes	characteristic
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	4	1	no	—
190	C₄×C₄₇	—	4	1	no	—
191	C₄×C₄₇	#385	1	2	yes	—
192	C₄×C₄₇	#387	1	2	yes	—
193	C₄×C₄₇	#388	1	2	yes	—
194	C₄×C₄₇	#389	1	2	yes	—
195	Dic₄₇	—	4	4	no	—
196	Dic₄₇	—	8	2	no	—
197	C₂×C₄×M₁₆	—	47	1	no	—
198	C₂×#389	—	47	1	no	—
199	C₂×#343	—	47	2	no	—
200	C₂×#343	—	47	2	no	—
201	#1728	D₄₇	1	1	yes	characteristic
202	C₂×C₄₇	—	2	2	no	—
203	C₂×C₄₇	—	2	2	no	—
204	C₂×C₄₇	#1436	1	1	yes	characteristic
205	C₂×C₄₇	C₄×#100	1	1	yes	characteristic
206	C₂×C₄₇	C₄×#101	1	1	yes	characteristic
207	C₂×C₄₇	#1900	1	1	yes	characteristic
208	C₂×C₄₇	#1901	1	1	yes	characteristic
209	C₂×C₄₇	#1997	1	1	yes	characteristic
210	C₂×C₄₇	#1998	1	1	yes	characteristic
211	C₂²×M₁₆	—	47	2	no	—
212	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
213	C₂²×C₄⋊C₄	—	47	1	no	—
214	C₂²×C₄⋊C₄	—	47	1	no	—
215	C₂²×C₄⋊C₄	—	47	2	no	—
216	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
217	C₄×M₁₆	—	94	4	no	—
218	C₂×#97	—	94	1	no	—
219	C₂×C₄×C₈	—	94	1	no	—
220	#389	—	94	1	no	—
221	#389	—	94	1	no	—
222	#389	—	94	1	no	—
223	#389	—	94	1	no	—
224	C₂×#95	—	47	2	no	—
225	#343	—	47	8	no	—
226	#343	—	94	4	no	—
227	#336	—	2	1	no	—
228	#336	—	2	1	no	—
229	C₄₇	#10913	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₄	—	47	2	no	—
231	C₂³×C₄	—	47	2	no	—
232	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
233	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
234	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	47	4	no	—
241	C₂×M₁₆	—	47	4	no	—
242	C₂×M₁₆	—	47	4	no	—
243	C₂×M₁₆	—	94	2	no	—
244	C₂×M₁₆	—	94	2	no	—
245	C₂×M₁₆	—	94	2	no	—
246	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₂×C₄⋊C₄	—	47	4	no	—
250	C₂×C₄⋊C₄	—	94	1	no	—
251	C₂×C₄⋊C₄	—	94	2	no	—
252	C₂×C₄⋊C₄	—	94	1	no	—
253	C₂×C₄⋊C₄	—	94	2	no	—
254	C₂×C₄⋊C₄	—	94	2	no	—
255	C₂×C₄⋊C₄	—	94	1	no	—
256	C₂×C₄⋊C₄	—	94	2	no	—
257	C₂×C₄⋊C₄	—	94	2	no	—
258	C₂×C₄⋊C₄	—	94	1	no	—
259	C₂×C₄⋊C₄	—	188	4	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
263	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
264	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
266	#97	—	94	4	no	—
267	C₄×C₈	—	94	4	no	—
268	#95	—	94	2	no	—
269	#95	—	94	2	no	—
270	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	47	4	no	—
278	C₂²×C₄	—	94	2	no	—
279	C₂²×C₄	—	94	2	no	—
280	C₂²×C₄	—	94	4	no	—
281	C₂²×C₄	—	94	2	no	—
282	C₂²×C₄	—	188	2	no	—
283	C₂²×C₄	—	188	2	no	—
284	C₂²×C₄	—	188	2	no	—
285	C₂²×C₄	—	188	2	no	—
286	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
288	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
289	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
291	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
292	C₂²×C₄	#10625350	1	2	yes	—
293	C₂²×C₄	D₄×D₄₇	1	2	yes	—
294	C₂²×C₄	#10625352	1	2	yes	—
295	C₂²×C₄	#10625352	1	2	yes	—
296	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
297	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
298	M₁₆	—	2	4	no	—
299	M₁₆	—	2	4	no	—
300	M₁₆	—	4	2	no	—
301	M₁₆	—	4	2	no	—
302	M₁₆	—	47	8	no	—
303	M₁₆	—	94	4	no	—
304	M₁₆	—	94	4	no	—
305	M₁₆	—	94	4	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	—	94	4	no	—
310	C₂×C₈	—	94	4	no	—
311	C₂×C₈	—	94	4	no	—
312	C₄⋊C₄	—	94	4	no	—
313	C₄⋊C₄	—	94	4	no	—
314	C₄⋊C₄	—	188	4	no	—
315	C₄⋊C₄	—	188	4	no	—
316	C₄⋊C₄	—	188	1	no	—
317	C₄⋊C₄	—	188	2	no	—
318	C₄⋊C₄	—	188	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	C₄²×D₄₇	1	1	yes	characteristic
330	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
331	C₂³	#13093981	1	1	yes	characteristic
332	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
333	C₂³	#13093989	1	2	yes	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	94	4	no	—
347	C₂×C₄	—	376	4	no	—
348	C₂×C₄	—	188	2	no	—
349	C₂×C₄	—	188	2	no	—
350	C₂×C₄	—	188	2	no	—
351	C₂×C₄	—	188	4	no	—
352	C₂×C₄	—	188	2	no	—
353	C₂×C₄	—	188	2	no	—
354	C₂×C₄	—	188	4	no	—
355	C₂×C₄	#13093940	1	2	yes	—
356	C₂×C₄	#13093942	1	2	yes	—
357	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
358	C₂×C₄	#13093980	1	2	yes	—
359	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
360	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
361	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
362	C₂×C₄	#13093989	1	2	yes	—
363	C₂×C₄	#13093994	1	1	yes	characteristic
364	C₂×C₄	#13093996	1	2	yes	—
365	C₂×C₄	#13094002	1	2	yes	—
366	C₂×C₄	#13094004	1	2	yes	—
367	C₂×C₄	#13094006	1	2	yes	—
368	C₂×C₄	#13094008	1	1	yes	characteristic
369	C₂×C₄	#13094011	1	1	yes	characteristic
370	C₂×C₄	#13094014	1	2	yes	—
371	C₂×C₄	#13094017	1	2	yes	—
372	C₂×C₄	#13094022	1	1	yes	characteristic
373	C₈	—	4	4	no	—
374	C₈	—	94	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
384	C₂²	#15688974	1	2	yes	—
385	C₂²	#15689000	1	1	yes	characteristic
386	C₂²	#15689005	1	2	yes	—
387	C₂²	#15689028	1	1	yes	characteristic
388	C₂²	C₂×#13093940	1	1	yes	characteristic
389	C₂²	C₂×#13093942	1	1	yes	characteristic
390	C₂²	#15689105	1	1	yes	characteristic
391	C₂²	#15689105	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	376	2	no	—
397	C₄	—	188	4	no	—
398	C₄	#15688997	1	2	yes	—
399	C₄	#15689008	1	2	yes	—
400	C₄	#15689017	1	2	yes	—
401	C₄	#15689018	1	2	yes	—
402	C₂	—	2	2	no	—
403	C₂	—	2	2	no	—
404	C₂	#20241623	1	1	yes	characteristic
405	C₂	C₄×#13093940	1	1	yes	characteristic
406	C₂	C₄×#13093942	1	1	yes	characteristic
407	C₂	#20243849	1	1	yes	characteristic
408	C₂	#20243854	1	1	yes	characteristic
409	C₂	#20244376	1	1	yes	characteristic
410	C₂	#20244380	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#1728	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#1728	D₄₇
hypocenter	C₄₇	#10913
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1728

Complements

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

N	H ≅ G/N	type
19. #15688891	C₄	semidirect
115. #10625329	C₄⋊C₄	semidirect
229. C₄₇	#10913	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625329	2
C₂×#15689021	2
C₂×#15688891	2
C₄₇×#1728	2
#10913	47