Subgroups — #26226298

Order 12032.

1058 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252026	C₂	1	1	yes	maximal, characteristic, complemented
2	#20245872	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244333	C₂	1	2	yes	maximal, complemented
4	#20244308	C₂	1	2	yes	maximal, complemented
5	#20243837	C₂	1	2	yes	maximal, complemented
6	#20243832	C₂	1	2	yes	maximal, complemented
7	#20243408	C₂	1	4	yes	maximal, complemented
8	C₄₇×#3455	C₂	1	1	yes	maximal, characteristic
9	C₂×#13093983	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
11	#15689184	—	2	4	no	—
12	#15689147	C₂²	1	2	yes	—
13	C₂×#13093951	C₂²	1	4	yes	—
14	C₂×#13093951	C₂²	1	4	yes	—
15	#15689087	C₂²	1	2	yes	—
16	C₄×#10625329	C₂²	1	2	yes	—
17	#15689022	—	2	2	no	—
18	#15688998	—	2	2	no	—
19	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
21	#15688882	C₂²	1	4	yes	—
22	#15688882	C₂²	1	4	yes	—
23	C₄₇×#542	C₄	1	4	yes	complemented
24	C₄₇×#541	C₄	1	2	yes	complemented
25	C₄₇×#540	C₄	1	2	yes	complemented
26	C₄₇×#539	—	2	2	no	—
27	C₄₇×#538	—	2	2	no	—
28	C₄₇×#533	C₂²	1	1	yes	characteristic
29	C₄₇×#532	C₂²	1	1	yes	characteristic
30	C₄₇×#529	—	2	4	no	—
31	C₄₇×#525	C₂²	1	2	yes	—
32	C₄×#41×C₄₇	C₂²	1	2	yes	—
33	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
34	C₂³×Dic₄₇	—	2	1	no	—
35	C₂×#10625329	C₂³	1	4	yes	—
36	#13093983	—	4	2	no	—
37	C₂×C₄⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄⋊Dic₄₇	—	2	2	no	—
39	C₂×C₄⋊Dic₄₇	—	2	1	no	—
40	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
41	C₂×C₄×Dic₄₇	—	2	1	no	—
42	C₂×C₄×Dic₄₇	—	4	2	no	—
43	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
44	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
45	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
46	#13093951	—	4	4	no	—
47	#13093951	—	4	4	no	—
48	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
49	#13093935	—	2	2	no	—
50	C₄×C₄₇⋊C₈	—	2	2	no	—
51	C₄₇⋊#95	—	2	2	no	—
52	C₄₇⋊#95	—	2	2	no	—
53	C₂×#41×C₄₇	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
56	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
57	#127×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
58	#126×C₄₇	—	2	4	no	—
59	#126×C₄₇	—	2	4	no	—
60	#125×C₄₇	—	2	4	no	—
61	#125×C₄₇	C₂×C₄	1	2	yes	complemented
62	#124×C₄₇	—	2	4	no	—
63	#124×C₄₇	C₂×C₄	1	2	yes	complemented
64	#123×C₄₇	—	2	2	no	—
65	#123×C₄₇	—	2	4	no	—
66	#123×C₄₇	—	2	4	no	—
67	C₂²⋊Q₈×C₄₇	—	2	2	no	—
68	C₂²⋊Q₈×C₄₇	—	2	4	no	—
69	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
70	#121×C₄₇	—	2	2	no	—
71	#121×C₄₇	—	2	4	no	—
72	#121×C₄₇	C₂×C₄	1	4	yes	—
73	#120×C₄₇	—	2	2	no	—
74	C₄×Q₈×C₄₇	—	2	2	no	—
75	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
76	C₄×D₄×C₄₇	—	2	4	no	—
77	C₄×D₄×C₄₇	—	2	4	no	—
78	C₄×D₄×C₄₇	—	2	2	no	—
79	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
80	#117×C₄₇	—	2	2	no	—
81	#117×C₄₇	C₂×C₄	1	2	yes	—
82	#117×C₄₇	C₂×C₄	1	2	yes	—
83	#117×C₄₇	D₄	1	4	yes	—
84	#117×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
87	C₂×C₄²×C₄₇	—	2	2	no	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
91	#41×C₄₇	—	2	4	no	—
92	#41×C₄₇	—	2	4	no	—
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	2	4	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	2	no	—
110	C₂²×Dic₄₇	—	2	2	no	—
111	C₂²×Dic₄₇	—	4	4	no	—
112	C₂²×Dic₄₇	—	4	2	no	—
113	C₄⋊C₄×C₄₇	—	2	4	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
119	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
120	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₄₇	—	2	4	no	—
122	C₂²⋊C₄×C₄₇	—	2	2	no	—
123	C₂²⋊C₄×C₄₇	—	2	4	no	—
124	C₂²⋊C₄×C₄₇	—	2	4	no	—
125	C₂²⋊C₄×C₄₇	—	2	4	no	—
126	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
127	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
128	C₄²×C₄₇	—	2	4	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
131	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₄₇	C₂×D₄	1	2	yes	—
134	C₄²×C₄₇	C₂×D₄	1	2	yes	—
135	C₂²⋊Dic₄₇	—	4	2	no	—
136	C₄⋊Dic₄₇	—	4	4	no	—
137	C₄⋊Dic₄₇	—	4	4	no	—
138	C₄⋊Dic₄₇	—	4	2	no	—
139	C₄×Dic₄₇	—	2	4	no	—
140	C₄×Dic₄₇	—	2	4	no	—
141	C₄×Dic₄₇	—	4	2	no	—
142	#10625329	—	2	4	no	—
143	#10625329	—	2	4	no	—
144	C₂×C₄₇⋊C₈	—	2	4	no	—
145	C₂³×C₄₇	—	2	1	no	—
146	C₂³×C₄₇	—	2	1	no	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	—	4	2	no	—
149	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₄₇	—	2	4	no	—
152	Q₈×C₄₇	—	8	2	no	—
153	D₄×C₄₇	—	2	4	no	—
154	D₄×C₄₇	—	4	2	no	—
155	D₄×C₄₇	—	4	2	no	—
156	D₄×C₄₇	—	8	2	no	—
157	D₄×C₄₇	—	8	4	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	4	no	—
167	C₂×C₄×C₄₇	—	8	4	no	—
168	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
169	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
175	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
176	C₂×Dic₄₇	—	2	4	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	8	no	—
179	C₂×Dic₄₇	—	4	2	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	2	no	—
183	C₄₇⋊C₈	—	4	4	no	—
184	#21901	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	4	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	4	no	—
192	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₄₇	#535	1	1	yes	characteristic
194	C₂²×C₄₇	#536	1	1	yes	characteristic
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	—	2	4	no	—
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	4	2	no	—
200	C₄×C₄₇	—	4	4	no	—
201	C₄×C₄₇	#520	1	2	yes	—
202	C₄×C₄₇	#537	1	2	yes	—
203	Dic₄₇	—	4	4	no	—
204	Dic₄₇	—	8	2	no	—
205	#3455	D₄₇	1	1	yes	characteristic
206	#2921	—	47	1	no	—
207	#2296	—	47	1	no	—
208	#1986	—	47	2	no	—
209	#1980	—	47	2	no	—
210	#1897	—	47	2	no	—
211	#1896	—	47	2	no	—
212	#1806	—	47	4	no	—
213	C₂×C₄₇	—	2	1	no	—
214	C₂×C₄₇	—	2	1	no	—
215	C₂×C₄₇	—	4	2	no	—
216	C₂×C₄₇	—	8	2	no	—
217	C₂×C₄₇	#2311	1	1	yes	characteristic
218	C₂×C₄₇	#2901	1	2	yes	—
219	#542	Dic₄₇	1	4	yes	complemented
220	#541	Dic₄₇	1	2	yes	complemented
221	#540	Dic₄₇	1	2	yes	complemented
222	#539	—	2	2	no	—
223	#538	—	2	2	no	—
224	#533	C₂×D₄₇	1	1	yes	characteristic
225	#532	C₂×D₄₇	1	1	yes	characteristic
226	#529	—	2	4	no	—
227	#525	C₂×D₄₇	1	2	yes	—
228	C₄×#41	C₂×D₄₇	1	2	yes	—
229	C₂×#117	—	47	1	no	—
230	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
231	C₂²×C₄²	—	47	1	no	—
232	#433	—	94	4	no	—
233	#423	—	47	2	no	—
234	C₂×#104	—	47	4	no	—
235	C₂×#104	—	47	4	no	—
236	#407	—	47	2	no	—
237	C₄×M₁₆	—	47	2	no	—
238	#389	—	94	2	no	—
239	#385	—	94	2	no	—
240	C₄×C₄⋊C₄	—	47	2	no	—
241	C₄×C₄⋊C₄	—	47	2	no	—
242	#339	—	47	4	no	—
243	#339	—	47	4	no	—
244	C₄₇	#21901	1	1	yes	characteristic, complemented, Sylow
245	C₂×#41	C₂²×D₄₇	1	2	yes	—
246	C₂³×C₄	—	94	1	no	—
247	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
248	C₂×M₁₆	—	47	4	no	—
249	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
250	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
251	#127	C₂×Dic₄₇	1	1	yes	characteristic, complemented
252	#126	—	2	4	no	—
253	#126	—	2	4	no	—
254	#125	—	2	4	no	—
255	#125	C₂×Dic₄₇	1	2	yes	complemented
256	#124	—	2	4	no	—
257	#124	C₂×Dic₄₇	1	2	yes	complemented
258	#123	—	2	2	no	—
259	#123	—	2	4	no	—
260	#123	—	2	4	no	—
261	C₂²⋊Q₈	—	2	2	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
264	#121	—	2	2	no	—
265	#121	—	2	4	no	—
266	#121	C₂×Dic₄₇	1	4	yes	—
267	#120	—	2	2	no	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
270	C₄×D₄	—	2	4	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
274	#117	—	2	2	no	—
275	#117	—	188	2	no	—
276	#117	C₂×Dic₄₇	1	2	yes	—
277	#117	C₂×Dic₄₇	1	2	yes	—
278	#117	C₂²⋊D₄₇	1	4	yes	—
279	#117	C₂²×D₄₇	1	2	yes	—
280	C₂×C₄⋊C₄	—	94	1	no	—
281	C₂×C₄⋊C₄	—	94	2	no	—
282	C₂×C₄⋊C₄	—	94	2	no	—
283	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
284	C₂×C₂²⋊C₄	—	94	1	no	—
285	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	47	2	no	—
288	C₂×C₄²	—	47	2	no	—
289	C₂×C₄²	—	94	1	no	—
290	C₂×C₄²	—	188	2	no	—
291	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
292	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
293	C₄⋊C₈	—	94	4	no	—
294	#104	—	188	4	no	—
295	#104	—	188	4	no	—
296	C₂²⋊C₈	—	94	4	no	—
297	#97	—	94	2	no	—
298	C₄×C₈	—	94	2	no	—
299	#95	—	94	2	no	—
300	#95	—	94	2	no	—
301	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	94	2	no	—
315	C₂²×C₄	—	94	2	no	—
316	C₂²×C₄	—	188	4	no	—
317	C₂²×C₄	—	188	2	no	—
318	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
319	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
321	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
323	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
324	M₁₆	—	94	4	no	—
325	M₁₆	—	94	4	no	—
326	C₂×C₈	—	94	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	188	2	no	—
333	C₄⋊C₄	—	188	4	no	—
334	C₄⋊C₄	—	188	4	no	—
335	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
336	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
337	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	188	2	no	—
344	C₂²⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
345	C₂²⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
346	C₄²	—	2	4	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	94	4	no	—
349	C₄²	—	94	4	no	—
350	C₄²	—	188	2	no	—
351	C₄²	C₂²×Dic₄₇	1	2	yes	—
352	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
353	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
354	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
355	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
361	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
362	Q₈	—	2	4	no	—
363	Q₈	—	8	2	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	4	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	8	4	no	—
379	C₂×C₄	—	94	4	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	2	no	—
382	C₂×C₄	—	188	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	—	188	8	no	—
385	C₂×C₄	—	188	2	no	—
386	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
387	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
388	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
389	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
390	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
392	C₂×C₄	#13094070	1	2	yes	—
393	C₂×C₄	#13094071	1	2	yes	—
394	C₈	—	188	4	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	2	no	—
402	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
403	C₂²	#15689687	1	1	yes	characteristic
404	C₂²	#15689694	1	1	yes	characteristic
405	C₄	—	2	4	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	2	no	—
411	C₄	—	376	2	no	—
412	C₄	—	188	4	no	—
413	C₄	#15689606	1	2	yes	—
414	C₄	#15689701	1	2	yes	—
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	—	4	2	no	—
418	C₂	—	8	2	no	—
419	C₂	#20245980	1	1	yes	characteristic
420	C₂	#20251935	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3455	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3455	D₄₇
hypocenter	C₄₇	#21901
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ #3455

Complements

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

N	H ≅ G/N	type
1. #20252026	C₂	semidirect
2. #20245872	C₂	semidirect
3. #20244333	C₂	semidirect
4. #20244308	C₂	semidirect
5. #20243837	C₂	semidirect
6. #20243832	C₂	semidirect
7. #20243408	C₂	semidirect
23. C₄₇×#542	C₄	semidirect
24. C₄₇×#541	C₄	semidirect
25. C₄₇×#540	C₄	semidirect
55. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
56. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
57. #127×C₄₇	C₂×C₄	semidirect
61. #125×C₄₇	C₂×C₄	semidirect
63. #124×C₄₇	C₂×C₄	semidirect
75. C₄×Q₈×C₄₇	C₂×C₄	semidirect
79. C₄×D₄×C₄₇	C₂×C₄	semidirect
219. #542	Dic₄₇	semidirect
220. #541	Dic₄₇	semidirect
221. #540	Dic₄₇	semidirect
244. C₄₇	#21901	semidirect
249. C₄⋊Q₈	C₂×Dic₄₇	semidirect
250. C₄⋊Q₈	C₂×Dic₄₇	semidirect
251. #127	C₂×Dic₄₇	semidirect
255. #125	C₂×Dic₄₇	semidirect
257. #124	C₂×Dic₄₇	semidirect
269. C₄×Q₈	C₂×Dic₄₇	semidirect
273. C₄×D₄	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252026	2
#20245872	2
#20244333	2
#20244308	2
#20243837	2
#20243832	2
#20243408	2
C₄₇×#3455	2
#21901	47