Subgroups — #26234735

Order 12032.

858 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×#15689245	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689240	C₂	1	1	yes	maximal, characteristic
3	#20251956	C₂	1	2	yes	maximal, complemented
4	#20244142	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244137	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243665	C₂	1	2	yes	maximal, complemented
7	#20243665	C₂	1	2	yes	maximal, complemented
8	#20243563	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243408	C₂	1	2	yes	maximal, complemented
10	#20243260	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2943	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	2	yes	—
13	C₂×#13094031	C₂²	1	2	yes	—
14	#15689245	—	2	4	no	—
15	#15689240	—	2	4	no	—
16	C₂×#13093960	C₂²	1	1	yes	characteristic
17	C₂×#13093960	C₂²	1	1	yes	characteristic
18	C₂×#13093960	C₂²	1	2	yes	—
19	#15689150	—	2	2	no	—
20	#15689150	—	2	2	no	—
21	#15689150	C₂²	1	2	yes	—
22	#15689150	C₂²	1	2	yes	—
23	#15689147	—	2	2	no	—
24	#15689147	C₂²	1	2	yes	—
25	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×#13093951	C₂²	1	2	yes	—
28	C₂×#13093951	C₂²	1	2	yes	—
29	C₂×#13093934	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688882	C₂²	1	2	yes	—
33	#15688882	C₂²	1	2	yes	—
34	#15688877	C₂²	1	1	yes	characteristic
35	#15688877	C₂²	1	1	yes	characteristic
36	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
37	C₄×#41×C₄₇	C₂²	1	2	yes	—
38	C₄₇×#442	C₄	1	2	yes	complemented
39	C₄₇×#441	C₄	1	2	yes	complemented
40	C₄₇×#440	C₄	1	2	yes	complemented
41	C₄₇×#440	C₄	1	2	yes	complemented
42	C₄₇×#427	C₂²	1	1	yes	characteristic
43	C₄₇×#416	C₂²	1	2	yes	—
44	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
45	#13094031	—	2	4	no	—
46	#13094031	—	2	4	no	—
47	#13094031	—	4	2	no	—
48	#13094031	—	4	2	no	—
49	C₂×#10625329	—	2	2	no	—
50	C₂×#10625329	—	2	2	no	—
51	C₂×#10625329	C₂³	1	2	yes	—
52	C₂×#10625329	C₂³	1	2	yes	—
53	C₂²×C₄₇⋊C₈	—	2	2	no	—
54	C₂²×C₄₇⋊C₈	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊Dic₄₇	—	2	1	no	—
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	#13093960	—	2	2	no	—
61	#13093960	—	2	2	no	—
62	#13093960	—	4	2	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
64	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
68	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
69	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
70	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
71	#13093951	—	2	4	no	—
72	#13093951	—	2	4	no	—
73	#13093934	—	2	2	no	—
74	C₈×Dic₄₇	—	2	2	no	—
75	C₄₇⋊#95	—	2	1	no	—
76	C₂×#41×C₄₇	C₂³	1	2	yes	—
77	#135×C₄₇	D₄	1	4	yes	—
78	#135×C₄₇	Q₈	1	4	yes	—
79	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
86	C₄×D₄×C₄₇	—	2	2	no	—
87	C₄×D₄×C₄₇	—	2	2	no	—
88	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
89	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
90	#117×C₄₇	—	2	2	no	—
91	#117×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₄₇	—	2	2	no	—
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
95	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
96	#106×C₄₇	C₂×C₄	1	2	yes	—
97	#103×C₄₇	C₂×C₄	1	2	yes	—
98	#103×C₄₇	C₂×C₄	1	2	yes	—
99	#102×C₄₇	C₂×C₄	1	2	yes	—
100	#102×C₄₇	C₂×C₄	1	2	yes	—
101	#97×C₄₇	C₂×C₄	1	2	yes	—
102	#97×C₄₇	C₂×C₄	1	2	yes	—
103	#41×C₄₇	—	2	2	no	—
104	#41×C₄₇	—	2	2	no	—
105	#41×C₄₇	C₂×D₄	1	4	yes	—
106	#41×C₄₇	C₂×Q₈	1	4	yes	—
107	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂²×Dic₄₇	—	2	1	no	—
117	C₂²×Dic₄₇	—	2	1	no	—
118	Q₁₆×C₄₇	C₄⋊C₄	1	4	yes	complemented
119	SD₁₆×C₄₇	C₄⋊C₄	1	8	yes	complemented
120	D₈×C₄₇	C₄⋊C₄	1	4	yes	complemented
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
132	C₂²⋊C₄×C₄₇	—	2	2	no	—
133	C₂²⋊C₄×C₄₇	—	2	2	no	—
134	C₂²⋊C₄×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	—	2	2	no	—
138	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₇	C₂×D₄	1	2	yes	—
140	C₄⋊Dic₄₇	—	4	2	no	—
141	C₄×Dic₄₇	—	2	1	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	#10625329	—	2	2	no	—
146	#10625329	—	2	2	no	—
147	#10625329	—	2	2	no	—
148	#10625329	—	2	2	no	—
149	#10625329	—	4	4	no	—
150	#10625329	—	4	4	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	4	4	no	—
158	C₂×C₄₇⋊C₈	—	4	4	no	—
159	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
161	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂³×C₄₇	—	2	2	no	—
163	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
164	Q₈×C₄₇	—	2	2	no	—
165	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
166	D₄×C₄₇	—	2	4	no	—
167	D₄×C₄₇	—	2	4	no	—
168	D₄×C₄₇	—	2	2	no	—
169	D₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	4	no	—
178	C₂×C₄×C₄₇	—	8	2	no	—
179	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	4	1	no	—
189	C₂×Dic₄₇	—	4	1	no	—
190	C₂×Dic₄₇	—	4	1	no	—
191	C₂×Dic₄₇	—	4	1	no	—
192	C₂×Dic₄₇	—	4	1	no	—
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
195	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
196	C₄₇⋊C₈	—	2	1	no	—
197	C₄₇⋊C₈	—	2	2	no	—
198	C₄₇⋊C₈	—	2	1	no	—
199	C₄₇⋊C₈	—	4	2	no	—
200	C₄₇⋊C₈	—	4	2	no	—
201	#22687	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	—	2	4	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₄₇	#547	1	1	yes	characteristic
209	C₂²×C₄₇	#554	1	1	yes	characteristic
210	C₄×C₄₇	—	2	4	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	4	2	no	—
214	C₄×C₄₇	—	4	2	no	—
215	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₄×C₄₇	#520	1	1	yes	characteristic
217	C₄×C₄₇	D₄²	1	1	yes	characteristic
218	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
219	Dic₄₇	—	4	2	no	—
220	Dic₄₇	—	8	1	no	—
221	C₂×#444	—	47	1	no	—
222	C₂×#443	—	47	1	no	—
223	#2943	D₄₇	1	1	yes	characteristic
224	#2906	—	47	2	no	—
225	#1946	—	47	1	no	—
226	#1945	—	47	1	no	—
227	#1866	—	47	2	no	—
228	#1866	—	47	2	no	—
229	#1849	—	47	1	no	—
230	#1806	—	47	2	no	—
231	#1771	—	47	1	no	—
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	—	4	4	no	—
235	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₄₇	#2955	1	1	yes	characteristic
237	C₂×C₄₇	#2956	1	1	yes	characteristic
238	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
239	C₂×#131	—	47	2	no	—
240	C₂×#131	—	47	2	no	—
241	C₄×#41	C₂×D₄₇	1	2	yes	—
242	#444	—	94	4	no	—
243	#443	—	94	4	no	—
244	#442	Dic₄₇	1	2	yes	complemented
245	#441	Dic₄₇	1	2	yes	complemented
246	#440	Dic₄₇	1	2	yes	complemented
247	#440	Dic₄₇	1	2	yes	complemented
248	C₂×#108	—	47	1	no	—
249	C₂×#108	—	47	1	no	—
250	C₂×#108	—	47	2	no	—
251	#427	C₂×D₄₇	1	1	yes	characteristic
252	#424	—	47	2	no	—
253	#424	—	47	2	no	—
254	#424	—	94	2	no	—
255	#424	—	94	2	no	—
256	#423	—	47	2	no	—
257	#423	—	94	2	no	—
258	C₂×C₄⋊C₈	—	47	1	no	—
259	C₂×C₄⋊C₈	—	94	2	no	—
260	C₂×#104	—	47	2	no	—
261	C₂×#104	—	47	2	no	—
262	#416	C₂×D₄₇	1	2	yes	—
263	C₂×#97	—	47	1	no	—
264	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
265	C₂×C₄×C₈	—	47	1	no	—
266	C₄×C₄⋊C₄	—	47	1	no	—
267	#339	—	47	2	no	—
268	#339	—	47	2	no	—
269	#336	—	47	1	no	—
270	#336	—	47	1	no	—
271	C₄₇	#22687	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	C₂²×D₄₇	1	2	yes	—
273	#135	Dic₉₄	1	4	yes	—
274	#135	D₁₈₈	1	4	yes	—
275	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
276	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
277	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
278	#131	—	94	4	no	—
279	#131	—	94	4	no	—
280	#131	—	188	2	no	—
281	#131	—	188	2	no	—
282	C₂×M₁₆	—	47	2	no	—
283	C₂×M₁₆	—	47	2	no	—
284	C₂×M₁₆	—	94	2	no	—
285	C₂×M₁₆	—	94	2	no	—
286	C₂²×C₈	—	47	1	no	—
287	C₂²×C₈	—	47	1	no	—
288	C₂²×C₈	—	94	2	no	—
289	C₂²×C₈	—	94	2	no	—
290	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
292	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
293	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
297	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
298	#117	—	2	2	no	—
299	#117	C₂²×D₄₇	1	2	yes	—
300	C₂×C₄⋊C₄	—	94	1	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	47	1	no	—
303	C₂×C₄²	—	47	1	no	—
304	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
305	#108	—	94	2	no	—
306	#108	—	94	2	no	—
307	#108	—	188	2	no	—
308	#107	C₂×Dic₄₇	1	1	yes	characteristic
309	#107	C₂×Dic₄₇	1	1	yes	characteristic
310	#106	C₂×Dic₄₇	1	2	yes	—
311	C₄⋊C₈	—	47	2	no	—
312	C₄⋊C₈	—	47	2	no	—
313	C₄⋊C₈	—	94	2	no	—
314	C₄⋊C₈	—	94	2	no	—
315	C₄⋊C₈	—	94	2	no	—
316	C₄⋊C₈	—	94	2	no	—
317	C₄⋊C₈	—	94	2	no	—
318	C₄⋊C₈	—	94	2	no	—
319	#104	—	94	4	no	—
320	#104	—	94	4	no	—
321	#103	C₂×Dic₄₇	1	2	yes	—
322	#103	C₂×Dic₄₇	1	2	yes	—
323	#102	C₂×Dic₄₇	1	2	yes	—
324	#102	C₂×Dic₄₇	1	2	yes	—
325	#97	—	94	2	no	—
326	#97	C₂×Dic₄₇	1	2	yes	—
327	#97	C₂×Dic₄₇	1	2	yes	—
328	C₄×C₈	—	94	2	no	—
329	#95	—	94	1	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	C₂×Dic₉₄	1	4	yes	—
333	#41	C₂×D₁₈₈	1	4	yes	—
334	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	94	1	no	—
341	C₂²×C₄	—	94	1	no	—
342	C₂²×C₄	#10625352	1	1	yes	characteristic
343	C₂²×C₄	#10625352	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
345	Q₁₆	C₄⋊Dic₄₇	1	4	yes	complemented
346	SD₁₆	C₄⋊Dic₄₇	1	8	yes	complemented
347	D₈	C₄⋊Dic₄₇	1	4	yes	complemented
348	M₁₆	—	94	2	no	—
349	M₁₆	—	94	2	no	—
350	M₁₆	—	94	2	no	—
351	M₁₆	—	94	2	no	—
352	M₁₆	—	188	4	no	—
353	M₁₆	—	188	4	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	47	1	no	—
357	C₂×C₈	—	47	2	no	—
358	C₂×C₈	—	47	1	no	—
359	C₂×C₈	—	94	1	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	94	1	no	—
362	C₂×C₈	—	94	1	no	—
363	C₂×C₈	—	94	2	no	—
364	C₂×C₈	—	94	2	no	—
365	C₂×C₈	—	188	4	no	—
366	C₂×C₈	—	188	4	no	—
367	C₂×C₈	C₂×Dic₉₄	1	2	yes	—
368	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
369	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
370	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
371	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	188	2	no	—
375	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
376	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	94	1	no	—
384	C₄²	—	94	1	no	—
385	C₄²	—	94	1	no	—
386	C₄²	—	94	1	no	—
387	C₄²	D₄×D₄₇	1	2	yes	—
388	C₄²	C₂²×Dic₄₇	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	C₂×#10625352	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	C₂×C₄⋊Dic₄₇	1	4	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	2	2	no	—
396	D₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	94	2	no	—
407	C₂×C₄	—	188	1	no	—
408	C₂×C₄	—	188	1	no	—
409	C₂×C₄	—	188	1	no	—
410	C₂×C₄	—	188	1	no	—
411	C₂×C₄	—	188	1	no	—
412	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
413	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
414	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
417	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
418	C₂×C₄	#13094070	1	1	yes	characteristic
419	C₂×C₄	#13094071	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	94	1	no	—
422	C₈	—	94	2	no	—
423	C₈	—	94	1	no	—
424	C₈	—	188	2	no	—
425	C₈	—	188	2	no	—
426	C₈	C₂×C₄⋊Dic₄₇	1	2	yes	—
427	C₈	C₂×C₄⋊Dic₄₇	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
434	C₂²	#15689777	1	1	yes	characteristic
435	C₂²	#15689830	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	376	1	no	—
442	C₄	—	188	2	no	—
443	C₄	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
444	C₄	#15689606	1	1	yes	characteristic
445	C₄	D₄×D₁₈₈	1	1	yes	characteristic
446	C₄	D₄×Dic₉₄	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	4	no	—
450	C₂	D₄×C₄⋊Dic₄₇	1	1	yes	characteristic
451	C₂	#20252291	1	1	yes	characteristic
452	C₂	#20252298	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2943	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#135×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2943	D₄₇
hypocenter	C₄₇	#22687
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
3. #20251956	C₂	semidirect
4. #20244142	C₂	semidirect
5. #20244137	C₂	semidirect
6. #20243665	C₂	semidirect
7. #20243665	C₂	semidirect
8. #20243563	C₂	semidirect
9. #20243408	C₂	semidirect
10. #20243260	C₂	semidirect
38. C₄₇×#442	C₄	semidirect
39. C₄₇×#441	C₄	semidirect
40. C₄₇×#440	C₄	semidirect
41. C₄₇×#440	C₄	semidirect
118. Q₁₆×C₄₇	C₄⋊C₄	semidirect
119. SD₁₆×C₄₇	C₄⋊C₄	semidirect
120. D₈×C₄₇	C₄⋊C₄	semidirect
244. #442	Dic₄₇	semidirect
245. #441	Dic₄₇	semidirect
246. #440	Dic₄₇	semidirect
247. #440	Dic₄₇	semidirect
271. C₄₇	#22687	semidirect
345. Q₁₆	C₄⋊Dic₄₇	semidirect
346. SD₁₆	C₄⋊Dic₄₇	semidirect
347. D₈	C₄⋊Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689245	2
C₂×#15689240	2
#20251956	2
#20244142	2
#20244137	2
#20243665	2
#20243563	2
#20243408	2
#20243260	2
C₄₇×#2943	2
#22687	47