Subgroups — #26121605

Order 12032.

1226 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689890	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689097	C₂	1	1	yes	maximal, characteristic
3	#20243107	C₂	1	2	yes	maximal, complemented
4	C₂×#15688879	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2311	C₂	1	1	yes	maximal, characteristic
6	#15689890	—	2	4	no	—
7	#15689890	—	2	2	no	—
8	#15689890	C₄	1	4	yes	complemented
9	C₂×#13094031	—	2	4	no	—
10	C₂²×#10625329	—	2	2	no	—
11	C₂²×#10625329	C₂²	1	2	yes	—
12	C₂×#13093983	C₂²	1	2	yes	—
13	#15689097	—	2	2	no	—
14	#15689097	C₄	1	4	yes	complemented
15	C₂×#13093939	—	2	2	no	—
16	#15688885	—	2	4	no	—
17	#15688879	—	2	4	no	—
18	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#391	C₄	1	2	yes	complemented
22	C₄₇×#390	C₄	1	2	yes	complemented
23	C₄₇×#386	—	2	2	no	—
24	C₄₇×#380	—	2	2	no	—
25	#13094031	—	2	16	no	—
26	#13094031	—	2	16	no	—
27	C₂×#10625329	—	2	4	no	—
28	C₂×#10625329	—	2	8	no	—
29	C₂×#10625329	—	2	8	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	2	no	—
34	C₂×#10625329	C₂×C₄	1	4	yes	—
35	C₂×#10625329	D₄	1	4	yes	—
36	C₂²×C₄₇⋊C₈	—	2	4	no	—
37	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
38	#13093983	—	2	2	no	—
39	#13093983	—	2	2	no	—
40	#13093983	—	2	2	no	—
41	#13093983	C₂×C₄	1	4	yes	—
42	C₂×C₄⋊Dic₄₇	—	2	2	no	—
43	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
44	C₂×C₄×Dic₄₇	—	2	2	no	—
45	#13093939	—	2	8	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	—	2	2	no	—
49	C₂×#41×C₄₇	—	2	2	no	—
50	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×#41×C₄₇	D₄	1	2	yes	—
53	C₂×#41×C₄₇	Q₈	1	2	yes	—
54	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂²×D₄×C₄₇	D₄	1	2	yes	—
57	C₂³×C₄×C₄₇	—	2	1	no	—
58	C₂³×C₄×C₄₇	D₄	1	2	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	#117×C₄₇	—	2	2	no	—
61	#117×C₄₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
70	#95×C₄₇	—	2	4	no	—
71	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
72	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
73	#41×C₄₇	—	2	4	no	—
74	#41×C₄₇	—	2	4	no	—
75	#41×C₄₇	—	2	4	no	—
76	#41×C₄₇	—	2	4	no	—
77	#41×C₄₇	—	2	4	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	C₄²	1	2	yes	—
84	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
85	C₂×D₄×C₄₇	—	2	4	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	C₄²	1	2	yes	—
90	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
91	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
92	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	4	2	no	—
100	C₂²×C₄×C₄₇	—	8	2	no	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	2	yes	—
113	C₂²×C₄×C₄₇	#41	1	2	yes	—
114	C₂²×Dic₄₇	—	4	2	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	—	4	1	no	—
117	C₄⋊C₄×C₄₇	—	4	1	no	—
118	C₄⋊C₄×C₄₇	—	4	1	no	—
119	C₄⋊C₄×C₄₇	—	4	1	no	—
120	C₂²⋊C₄×C₄₇	—	4	2	no	—
121	C₂²⋊C₄×C₄₇	—	8	4	no	—
122	C₄²×C₄₇	—	2	4	no	—
123	C₂²⋊Dic₄₇	—	2	4	no	—
124	C₂²⋊Dic₄₇	—	4	2	no	—
125	C₄⋊Dic₄₇	—	2	4	no	—
126	C₄⋊Dic₄₇	—	4	2	no	—
127	C₄×Dic₄₇	—	2	4	no	—
128	C₄×Dic₄₇	—	4	2	no	—
129	#10625329	—	2	16	no	—
130	#10625329	—	2	4	no	—
131	#10625329	—	2	4	no	—
132	#10625329	—	2	4	no	—
133	#10625329	—	2	4	no	—
134	C₂×C₄₇⋊C₈	—	2	16	no	—
135	C₂×C₄₇⋊C₈	—	2	4	no	—
136	C₂×C₄₇⋊C₈	—	2	4	no	—
137	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	8	yes	complemented
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	4	1	no	—
141	C₂³×C₄₇	—	4	1	no	—
142	C₂³×C₄₇	—	4	2	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	#95	1	4	yes	—
145	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂³×C₄₇	#121	1	2	yes	—
149	C₂³×C₄₇	#121	1	2	yes	—
150	Q₈×C₄₇	—	2	4	no	—
151	Q₈×C₄₇	—	2	4	no	—
152	D₄×C₄₇	—	2	8	no	—
153	D₄×C₄₇	—	2	8	no	—
154	D₄×C₄₇	—	2	4	no	—
155	D₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	4	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	8	4	no	—
168	C₂×C₄×C₄₇	#95	1	4	yes	—
169	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#117	1	2	yes	—
175	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
180	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
181	C₂×C₄×C₄₇	#120	1	2	yes	—
182	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
183	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
184	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
185	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
186	C₂×C₄×C₄₇	#123	1	2	yes	—
187	C₂×Dic₄₇	—	4	4	no	—
188	C₂×Dic₄₇	—	8	2	no	—
189	C₂×Dic₄₇	—	8	2	no	—
190	C₄₇⋊C₈	—	2	8	no	—
191	#10742	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	4	no	—
197	C₂²×C₄₇	—	4	1	no	—
198	C₂²×C₄₇	—	4	1	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	—	4	4	no	—
201	C₂²×C₄₇	—	4	2	no	—
202	C₂²×C₄₇	—	4	2	no	—
203	C₂²×C₄₇	—	8	2	no	—
204	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
205	C₂²×C₄₇	#380	1	2	yes	—
206	C₂²×C₄₇	#386	1	2	yes	—
207	C₂²×C₄₇	#386	1	1	yes	characteristic
208	C₂²×C₄₇	#386	1	1	yes	characteristic
209	C₄×C₄₇	—	2	4	no	—
210	C₄×C₄₇	—	8	2	no	—
211	C₄×C₄₇	—	8	2	no	—
212	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
213	C₄×C₄₇	#379	1	1	yes	characteristic
214	C₄×C₄₇	#381	1	1	yes	characteristic
215	C₄×C₄₇	#385	1	1	yes	characteristic
216	C₄×C₄₇	#385	1	1	yes	characteristic
217	C₄×C₄₇	#385	1	2	yes	—
218	Dic₄₇	—	8	4	no	—
219	C₂×#568	—	47	1	no	—
220	C₂×#410	—	47	1	no	—
221	#2311	D₄₇	1	1	yes	characteristic
222	#1736	—	47	2	no	—
223	C₂×H(3,ℤ/4)	—	47	2	no	—
224	C₂×C₄₇	—	2	2	no	—
225	C₂×C₄₇	—	2	1	no	—
226	C₂×C₄₇	—	2	1	no	—
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	—	4	4	no	—
229	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
230	C₂×C₄₇	#1909	1	1	yes	characteristic
231	C₂×C₄₇	#1910	1	1	yes	characteristic
232	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
233	#568	—	47	4	no	—
234	#568	—	94	4	no	—
235	#568	—	94	2	no	—
236	C₂×#131	—	94	4	no	—
237	C₂²×M₁₆	—	47	2	no	—
238	C₂²×M₁₆	—	94	2	no	—
239	C₂×#117	—	47	2	no	—
240	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
242	#410	—	47	4	no	—
243	#410	—	94	2	no	—
244	C₂×#99	—	94	2	no	—
245	#391	Dic₄₇	1	2	yes	complemented
246	#390	Dic₄₇	1	2	yes	complemented
247	#386	—	2	2	no	—
248	#380	—	2	2	no	—
249	#340	—	94	4	no	—
250	H(3,ℤ/4)	—	94	4	no	—
251	C₄₇	#10742	1	1	yes	characteristic, complemented, Sylow
252	C₂×#41	—	2	2	no	—
253	C₂×#41	—	2	2	no	—
254	C₂×#41	—	2	2	no	—
255	C₂×#41	—	2	2	no	—
256	C₂×#41	Dic₉₄	1	2	yes	—
257	C₂×#41	C₄×D₄₇	1	2	yes	—
258	C₂×#41	C₄×D₄₇	1	2	yes	—
259	C₂×#41	D₁₈₈	1	2	yes	—
260	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
261	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
262	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
265	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
266	#131	—	94	16	no	—
267	#131	—	94	16	no	—
268	C₂×M₁₆	—	47	4	no	—
269	C₂×M₁₆	—	47	4	no	—
270	C₂×M₁₆	—	94	4	no	—
271	C₂×M₁₆	—	94	8	no	—
272	C₂×M₁₆	—	94	8	no	—
273	C₂×M₁₆	—	94	2	no	—
274	C₂×M₁₆	—	94	2	no	—
275	C₂×M₁₆	—	94	2	no	—
276	C₂×M₁₆	—	94	2	no	—
277	C₂²×C₈	—	47	4	no	—
278	C₂²×C₈	—	94	4	no	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	#117	—	47	4	no	—
282	#117	—	94	2	no	—
283	#117	—	94	2	no	—
284	#117	—	94	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	94	2	no	—
290	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	4	no	—
293	C₂×C₂²⋊C₄	—	94	2	no	—
294	C₂×C₄²	—	94	2	no	—
295	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
296	#99	—	94	8	no	—
297	#95	—	2	4	no	—
298	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
299	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	#41	—	2	4	no	—
305	#41	—	2	4	no	—
306	#41	—	2	4	no	—
307	#41	—	2	4	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	C₄×Dic₄₇	1	2	yes	—
311	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	C₄×Dic₄₇	1	2	yes	—
317	C₂×D₄	Dic₄₇⋊C₄	1	4	yes	—
318	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
319	C₂×D₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	8	2	no	—
328	C₂²×C₄	—	188	2	no	—
329	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
330	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
331	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
332	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₄₇	1	2	yes	—
337	C₂²×C₄	D₄×D₄₇	1	2	yes	—
338	C₂²×C₄	#10625352	1	2	yes	—
339	C₂²×C₄	#10625352	1	2	yes	—
340	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
342	M₁₆	—	94	16	no	—
343	M₁₆	—	94	4	no	—
344	M₁₆	—	94	4	no	—
345	M₁₆	—	94	4	no	—
346	M₁₆	—	94	4	no	—
347	C₂×C₈	—	47	8	no	—
348	C₂×C₈	—	94	16	no	—
349	C₂×C₈	—	94	4	no	—
350	C₂×C₈	—	94	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	94	4	no	—
357	C₄⋊C₄	—	188	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	8	4	no	—
360	C₂²⋊C₄	—	94	4	no	—
361	C₂²⋊C₄	—	188	2	no	—
362	C₄²	—	2	4	no	—
363	C₄²	—	94	4	no	—
364	C₄²	—	188	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	C₄₇⋊#95	1	4	yes	—
372	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
373	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
374	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
375	C₂³	#13093996	1	2	yes	—
376	C₂³	#13093996	1	2	yes	—
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	D₄	—	2	8	no	—
380	D₄	—	2	8	no	—
381	D₄	—	2	4	no	—
382	D₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	4	no	—
395	C₂×C₄	—	376	2	no	—
396	C₂×C₄	—	376	2	no	—
397	C₂×C₄	—	188	4	no	—
398	C₂×C₄	C₄₇⋊#95	1	4	yes	—
399	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
401	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
402	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
403	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
404	C₂×C₄	#13093980	1	2	yes	—
405	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
406	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
407	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
408	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
409	C₂×C₄	#13093992	1	1	yes	characteristic
410	C₂×C₄	#13093992	1	1	yes	characteristic
411	C₂×C₄	#13093994	1	2	yes	—
412	C₂×C₄	#13094001	1	2	yes	—
413	C₂×C₄	#13094001	1	2	yes	—
414	C₂×C₄	#13094005	1	1	yes	characteristic
415	C₂×C₄	#13094005	1	1	yes	characteristic
416	C₂×C₄	#13094008	1	2	yes	—
417	C₈	—	94	8	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
431	C₂²	#15688981	1	2	yes	—
432	C₂²	#15689000	1	2	yes	—
433	C₂²	#15689003	1	1	yes	characteristic
434	C₂²	#15689003	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	2	no	—
438	C₄	—	376	4	no	—
439	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
440	C₄	#15688978	1	1	yes	characteristic
441	C₄	#15688984	1	1	yes	characteristic
442	C₄	#15688995	1	1	yes	characteristic
443	C₄	#15688995	1	1	yes	characteristic
444	C₄	#15688998	1	2	yes	—
445	C₂	—	2	1	no	—
446	C₂	—	2	2	no	—
447	C₂	—	2	1	no	—
448	C₂	—	2	2	no	—
449	C₂	—	4	4	no	—
450	C₂	#20241610	1	1	yes	characteristic
451	C₂	#20243911	1	1	yes	characteristic
452	C₂	#20243916	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689003
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#2311	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#2311	D₄₇
hypocenter	C₄₇	#10742
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2311

Complements

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

N	H ≅ G/N	type
3. #20243107	C₂	semidirect
4. C₂×#15688879	C₂	semidirect
8. #15689890	C₄	semidirect
14. #15689097	C₄	semidirect
21. C₄₇×#391	C₄	semidirect
22. C₄₇×#390	C₄	semidirect
137. C₂×C₄₇⋊C₈	C₂²⋊C₄	semidirect
245. #391	Dic₄₇	semidirect
246. #390	Dic₄₇	semidirect
251. C₄₇	#10742	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689890	2
C₂×#15689097	2
#20243107	2
C₂×#15688879	2
C₄₇×#2311	2
#10742	47