Subgroups — #26219699

Order 12032.

882 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093959	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689159	C₂	1	1	yes	maximal, characteristic
3	#20251952	C₂	1	1	yes	maximal, characteristic
4	#20251951	C₂	1	1	yes	maximal, characteristic
5	C₂×#15689079	C₂	1	1	yes	maximal, characteristic
6	#20244140	C₂	1	4	yes	maximal, complemented
7	#20244135	C₂	1	4	yes	maximal, complemented
8	#20243098	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1733	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×#13093983	C₂²	1	1	yes	characteristic
14	C₂×#13093959	—	2	4	no	—
15	C₂×#13093959	C₂²	1	2	yes	—
16	C₂×#13093959	C₂²	1	2	yes	—
17	#15689159	C₄	1	2	yes	complemented
18	#15689159	C₄	1	2	yes	complemented
19	#15689159	C₂²	1	2	yes	—
20	#15689159	C₂²	1	2	yes	—
21	C₂×#13093957	C₄	1	2	yes	complemented
22	C₂×#13093955	C₄	1	2	yes	complemented
23	#15689151	C₂²	1	4	yes	—
24	#15689150	—	2	2	no	—
25	#15689150	C₂²	1	4	yes	—
26	#15689149	—	2	2	no	—
27	#15689147	—	2	2	no	—
28	#15689146	—	2	2	no	—
29	#15689079	—	2	4	no	—
30	C₂×#13093935	C₂²	1	2	yes	—
31	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
32	#15688883	C₂²	1	4	yes	—
33	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#339	C₂²	1	4	yes	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	—	2	1	no	—
40	C₂×#10625329	—	2	2	no	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	D₄	1	2	yes	—
43	C₂×#10625329	D₄	1	2	yes	—
44	C₂×#10625329	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	—	2	1	no	—
46	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
51	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	—
52	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	#13093983	—	2	1	no	—
56	#13093983	—	2	1	no	—
57	#13093983	C₂×C₄	1	2	yes	—
58	#13093983	C₂³	1	2	yes	—
59	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	#13093959	—	2	4	no	—
63	#13093959	—	2	4	no	—
64	#13093957	C₂×C₄	1	4	yes	—
65	#13093957	C₂×C₄	1	4	yes	—
66	#13093955	C₂×C₄	1	4	yes	—
67	#13093955	C₂×C₄	1	4	yes	—
68	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
69	Dic₄₇⋊C₈	—	2	8	no	—
70	#13093935	—	2	4	no	—
71	C₄×C₄₇⋊C₈	—	2	4	no	—
72	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₄₇	—	2	1	no	—
74	C₂×M₁₆×C₄₇	—	2	2	no	—
75	C₂×M₁₆×C₄₇	—	2	2	no	—
76	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₇	—	2	1	no	—
78	#117×C₄₇	—	2	2	no	—
79	#117×C₄₇	—	2	1	no	—
80	#117×C₄₇	—	2	1	no	—
81	#117×C₄₇	C₂×C₄	1	2	yes	—
82	#117×C₄₇	Q₈	1	4	yes	—
83	#117×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
90	C₂⁴×C₄₇	#41	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	#41	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₄₇	—	2	2	no	—
104	M₁₆×C₄₇	—	2	2	no	—
105	M₁₆×C₄₇	—	2	2	no	—
106	M₁₆×C₄₇	—	4	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	4	2	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	4	no	—
111	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
112	C₂²⋊C₄×C₄₇	—	2	2	no	—
113	C₂²⋊C₄×C₄₇	—	2	4	no	—
114	C₂²⋊C₄×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	C₂×Q₈	1	4	yes	—
119	C₂²⋊Dic₄₇	—	2	2	no	—
120	C₂²⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	#10625329	—	2	4	no	—
126	#10625329	—	2	4	no	—
127	#10625329	—	2	2	no	—
128	#10625329	—	2	2	no	—
129	#10625329	—	4	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	4	2	no	—
134	C₂×C₄₇⋊C₈	C₄⋊C₄	1	4	yes	—
135	C₂×C₄₇⋊C₈	C₄⋊C₄	1	4	yes	—
136	C₂×C₄₇⋊C₈	C₄⋊C₄	1	4	yes	—
137	C₂×C₄₇⋊C₈	C₄⋊C₄	1	4	yes	—
138	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
143	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
144	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
146	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
147	C₂³×C₄₇	—	4	2	no	—
148	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
149	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
150	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
151	C₂³×C₄₇	#125	1	2	yes	—
152	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	8	2	no	—
157	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
162	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
163	C₂×C₄×C₄₇	#121	1	2	yes	—
164	C₂×C₄×C₄₇	#121	1	2	yes	—
165	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₄₇	#125	1	2	yes	—
167	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
168	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
169	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×Dic₄₇	—	2	4	no	—
176	C₂×Dic₄₇	—	8	2	no	—
177	C₈×C₄₇	—	4	2	no	—
178	C₄₇⋊C₈	—	2	4	no	—
179	C₄₇⋊C₈	—	4	2	no	—
180	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
181	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
182	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
183	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
184	#21163	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	#389	1	2	yes	—
191	C₂²×C₄₇	#389	1	2	yes	—
192	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
195	C₄×C₄₇	—	4	4	no	—
196	C₄×C₄₇	—	4	4	no	—
197	C₄×C₄₇	#389	1	2	yes	—
198	C₄×C₄₇	#389	1	2	yes	—
199	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
200	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
201	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
202	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
203	Dic₄₇	—	4	4	no	—
204	C₂²×#108	—	47	1	no	—
205	C₂×#427	—	47	1	no	—
206	#2905	—	47	1	no	—
207	#2905	—	47	1	no	—
208	C₂×#405	—	47	1	no	—
209	#1946	—	47	4	no	—
210	#1945	—	47	4	no	—
211	#1733	—	47	1	no	—
212	#1733	D₄₇	1	1	yes	characteristic
213	C₂×C₄₇	—	2	1	no	—
214	C₂×C₄₇	—	2	1	no	—
215	C₂×C₄₇	—	2	2	no	—
216	C₂×C₄₇	—	2	2	no	—
217	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
218	C₂×C₄₇	#2957	1	2	yes	—
219	C₂²×M₁₆	—	47	1	no	—
220	C₂²×M₁₆	—	47	1	no	—
221	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
222	C₂³×C₈	—	47	1	no	—
223	C₂×#117	—	47	1	no	—
224	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
226	C₂×#108	—	47	2	no	—
227	C₂×#108	—	47	2	no	—
228	C₂×#108	—	94	4	no	—
229	#427	—	47	2	no	—
230	#427	—	47	2	no	—
231	#427	—	47	2	no	—
232	#427	—	47	2	no	—
233	C₂×#107	—	47	2	no	—
234	C₂×#106	—	47	2	no	—
235	#424	—	47	4	no	—
236	#424	—	47	4	no	—
237	#424	—	94	2	no	—
238	#424	—	94	2	no	—
239	#423	—	94	2	no	—
240	#423	—	94	2	no	—
241	#405	—	94	4	no	—
242	C₂×#97	—	47	2	no	—
243	C₂×C₄×C₈	—	47	2	no	—
244	#339	—	47	4	no	—
245	#339	C₂×D₄₇	1	4	yes	—
246	C₄₇	#21163	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	47	2	no	—
252	C₂×M₁₆	—	47	2	no	—
253	C₂×M₁₆	—	47	2	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂×M₁₆	—	94	2	no	—
256	C₂×M₁₆	—	94	1	no	—
257	C₂×M₁₆	—	94	2	no	—
258	C₂×M₁₆	—	94	2	no	—
259	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	47	1	no	—
262	C₂²×C₈	—	47	1	no	—
263	C₂²×C₈	—	47	1	no	—
264	C₂²×C₈	—	47	1	no	—
265	C₂²×C₈	—	47	4	no	—
266	C₂²×C₈	—	47	4	no	—
267	C₂²×C₈	—	47	1	no	—
268	C₂²×C₈	—	47	1	no	—
269	C₂²×C₈	—	47	2	no	—
270	C₂²×C₈	—	94	1	no	—
271	#117	—	2	2	no	—
272	#117	—	2	1	no	—
273	#117	—	2	1	no	—
274	#117	—	47	2	no	—
275	#117	—	47	2	no	—
276	#117	—	94	1	no	—
277	#117	—	94	1	no	—
278	#117	Dic₉₄	1	4	yes	—
279	#117	C₄×D₄₇	1	2	yes	—
280	#117	C₂²×D₄₇	1	2	yes	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	47	2	no	—
283	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	94	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	94	1	no	—
289	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
290	#108	—	94	4	no	—
291	#108	—	94	4	no	—
292	#107	—	47	4	no	—
293	#107	—	47	4	no	—
294	#106	—	47	4	no	—
295	#106	—	47	4	no	—
296	C₄⋊C₈	—	94	8	no	—
297	C₄⋊C₈	—	94	8	no	—
298	#97	—	94	4	no	—
299	C₄×C₈	—	94	4	no	—
300	C₂⁴	#10625352	1	1	yes	characteristic
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	94	2	no	—
304	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
305	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	#10625350	1	2	yes	—
308	C₂²×C₄	D₄×D₄₇	1	2	yes	—
309	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	#10625352	1	1	yes	characteristic
312	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
313	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	4	2	no	—
317	M₁₆	—	94	4	no	—
318	M₁₆	—	94	4	no	—
319	M₁₆	—	94	2	no	—
320	M₁₆	—	94	2	no	—
321	M₁₆	—	188	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	47	4	no	—
325	C₂×C₈	—	47	4	no	—
326	C₂×C₈	—	47	4	no	—
327	C₂×C₈	—	47	4	no	—
328	C₂×C₈	—	47	1	no	—
329	C₂×C₈	—	47	1	no	—
330	C₂×C₈	—	47	1	no	—
331	C₂×C₈	—	47	1	no	—
332	C₂×C₈	—	47	2	no	—
333	C₂×C₈	—	47	2	no	—
334	C₂×C₈	—	47	2	no	—
335	C₂×C₈	—	47	2	no	—
336	C₂×C₈	—	47	4	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	188	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	47	4	no	—
344	C₄⋊C₄	—	94	2	no	—
345	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	94	2	no	—
350	C₂²⋊C₄	—	94	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	94	2	no	—
355	C₄²	—	94	2	no	—
356	C₄²	C₂×Dic₉₄	1	4	yes	—
357	C₂³	—	4	2	no	—
358	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
359	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
360	C₂³	#13094001	1	2	yes	—
361	C₂³	#13094014	1	2	yes	—
362	C₂³	C₂×#10625352	1	1	yes	characteristic
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	8	2	no	—
367	C₂×C₄	—	94	4	no	—
368	C₂×C₄	—	376	2	no	—
369	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
370	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
371	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
372	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
373	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
374	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
375	C₂×C₄	#13093997	1	2	yes	—
376	C₂×C₄	#13093997	1	2	yes	—
377	C₂×C₄	#13094001	1	2	yes	—
378	C₂×C₄	#13094014	1	2	yes	—
379	C₂×C₄	#13094023	1	2	yes	—
380	C₂×C₄	#13094023	1	2	yes	—
381	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
383	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
384	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
385	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
386	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
387	C₈	—	4	2	no	—
388	C₈	—	47	2	no	—
389	C₈	—	47	2	no	—
390	C₈	—	47	2	no	—
391	C₈	—	47	2	no	—
392	C₈	—	94	4	no	—
393	C₈	—	188	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	#15689020	1	2	yes	—
400	C₂²	#15689020	1	2	yes	—
401	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
402	C₂²	C₂×#13094001	1	1	yes	characteristic
403	C₂²	C₂×#13094014	1	1	yes	characteristic
404	C₄	—	4	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	188	4	no	—
407	C₄	#15689020	1	2	yes	—
408	C₄	#15689020	1	2	yes	—
409	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
410	C₄	C₂×C₄×Dic₉₄	1	1	yes	characteristic
411	C₄	C₂×#13093997	1	1	yes	characteristic
412	C₄	C₂×#13094023	1	1	yes	characteristic
413	C₂	—	2	1	no	—
414	C₂	—	2	2	no	—
415	C₂	—	2	2	no	—
416	C₂	—	2	1	no	—
417	C₂	C₂×#15689020	1	1	yes	characteristic
418	C₂	#20252301	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1733	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂⁴×C₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1733	D₄₇
hypocenter	C₄₇	#21163
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
6. #20244140	C₂	semidirect
7. #20244135	C₂	semidirect
17. #15689159	C₄	semidirect
18. #15689159	C₄	semidirect
21. C₂×#13093957	C₄	semidirect
22. C₂×#13093955	C₄	semidirect
246. C₄₇	#21163	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13093959	2
C₂×#15689159	2
#20251952	2
#20251951	2
C₂×#15689079	2
#20244140	2
#20244135	2
#20243098	2
C₄₇×#1733	2
#21163	47