Subgroups — #26219751

Order 12032.

1082 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689165	C₂	1	2	yes	maximal
2	#20245795	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20244158	C₂	1	4	yes	maximal, complemented
5	#20244152	C₂	1	2	yes	maximal, complemented
6	#20244147	C₂	1	2	yes	maximal, complemented
7	#20243108	C₂	1	2	yes	maximal
8	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic
9	C₂×#13093983	C₂²	1	2	yes	—
10	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₄₇	—	2	1	no	—
13	#15689165	—	2	8	no	—
14	C₂×#13093958	C₂²	1	4	yes	—
15	C₂×#13093956	C₂²	1	4	yes	—
16	#15688993	C₂²	1	1	yes	characteristic
17	#15688993	C₂²	1	1	yes	characteristic
18	#15688989	C₂²	1	2	yes	—
19	#15688983	—	2	1	no	—
20	#15688983	—	2	1	no	—
21	C₄×C₄⋊Dic₄₇	—	2	1	no	—
22	C₄×C₄⋊Dic₄₇	—	2	1	no	—
23	C₄×C₄⋊Dic₄₇	—	2	1	no	—
24	C₄×C₄⋊Dic₄₇	—	2	1	no	—
25	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
27	C₂×C₄₇⋊#95	—	2	1	no	—
28	#15688886	C₂²	1	4	yes	—
29	#15688886	C₂²	1	4	yes	—
30	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#423	C₄	1	8	yes	complemented
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
34	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
35	C₂³×Dic₄₇	—	2	1	no	—
36	C₂³×Dic₄₇	—	2	1	no	—
37	#13093983	—	2	4	no	—
38	#13093983	—	2	4	no	—
39	C₂×C₄⋊Dic₄₇	—	2	1	no	—
40	C₂×C₄⋊Dic₄₇	—	2	1	no	—
41	C₂×C₄⋊Dic₄₇	—	2	2	no	—
42	C₂×C₄⋊Dic₄₇	—	2	2	no	—
43	C₂×C₄⋊Dic₄₇	—	2	1	no	—
44	C₂×C₄⋊Dic₄₇	—	2	1	no	—
45	C₂×C₄⋊Dic₄₇	—	2	1	no	—
46	C₂×C₄⋊Dic₄₇	—	2	1	no	—
47	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
48	C₂×C₄⋊Dic₄₇	Q₈	1	4	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
53	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	—	4	4	no	—
58	#13093958	—	2	8	no	—
59	#13093956	—	2	8	no	—
60	C₄₇⋊#95	—	2	2	no	—
61	C₄₇⋊#95	—	2	2	no	—
62	C₄₇⋊#95	—	2	2	no	—
63	C₄₇⋊#95	—	2	2	no	—
64	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₄₇	—	2	4	no	—
68	C₂×M₁₆×C₄₇	—	2	4	no	—
69	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	—
70	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
72	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₄₇	C₂×C₄	1	8	yes	complemented
78	C₄⋊C₈×C₄₇	C₂×C₄	1	8	yes	complemented
79	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	4	1	no	—
83	C₂²×C₄×C₄₇	—	4	1	no	—
84	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₄₇	#41	1	2	yes	—
96	C₂²×C₄×C₄₇	#41	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	2	4	no	—
99	C₂²×Dic₄₇	—	2	4	no	—
100	C₂²×Dic₄₇	—	2	2	no	—
101	C₂²×Dic₄₇	—	2	2	no	—
102	C₂²×Dic₄₇	—	2	2	no	—
103	C₂²×Dic₄₇	—	2	2	no	—
104	C₂²×Dic₄₇	—	4	2	no	—
105	C₂²×Dic₄₇	—	4	2	no	—
106	C₂²×Dic₄₇	—	4	2	no	—
107	C₂²×Dic₄₇	—	4	2	no	—
108	M₁₆×C₄₇	—	2	16	no	—
109	C₂×C₈×C₄₇	—	2	4	no	—
110	C₂×C₈×C₄₇	—	2	4	no	—
111	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
112	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
113	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
114	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
115	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
116	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
117	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
118	C₂²⋊Dic₄₇	—	4	4	no	—
119	C₄⋊Dic₄₇	—	2	4	no	—
120	C₄⋊Dic₄₇	—	2	4	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	—	2	2	no	—
125	C₄⋊Dic₄₇	—	2	2	no	—
126	C₄⋊Dic₄₇	—	2	2	no	—
127	C₄⋊Dic₄₇	—	4	2	no	—
128	C₄⋊Dic₄₇	—	4	2	no	—
129	C₄⋊Dic₄₇	—	4	2	no	—
130	C₄⋊Dic₄₇	—	4	2	no	—
131	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
132	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	—
133	C₄×Dic₄₇	—	4	4	no	—
134	C₄×Dic₄₇	—	4	4	no	—
135	C₄×Dic₄₇	—	4	4	no	—
136	C₂³×C₄₇	—	2	1	no	—
137	C₂³×C₄₇	—	2	1	no	—
138	C₂³×C₄₇	—	2	1	no	—
139	C₂³×C₄₇	—	2	1	no	—
140	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
141	C₂³×C₄₇	#121	1	2	yes	—
142	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
143	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	8	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
156	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
158	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
159	C₂×C₄×C₄₇	#121	1	2	yes	—
160	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
161	C₂×C₄×C₄₇	#125	1	4	yes	—
162	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
163	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
164	C₂×C₄×C₄₇	#137	1	2	yes	—
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂×Dic₄₇	—	2	4	no	—
172	C₂×Dic₄₇	—	2	4	no	—
173	C₂×Dic₄₇	—	4	8	no	—
174	C₂×Dic₄₇	—	4	8	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	2	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	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₈×C₄₇	—	2	8	no	—
186	#21170	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	2	no	—
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	2	2	no	—
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	#389	1	4	yes	—
194	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
196	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
199	C₂²×C₄₇	#575	1	1	yes	characteristic
200	C₂²×C₄₇	#575	1	1	yes	characteristic
201	C₄×C₄₇	—	2	2	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	#389	1	4	yes	—
205	C₄×C₄₇	#428	1	4	yes	complemented
206	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
208	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
209	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
210	Dic₄₇	—	4	4	no	—
211	Dic₄₇	—	4	4	no	—
212	Dic₄₇	—	8	2	no	—
213	Dic₄₇	—	8	2	no	—
214	C₂×#428	—	47	2	no	—
215	C₂×#423	D₄₇	1	1	yes	characteristic
216	#2285	—	47	1	no	—
217	C₂×C₄×C₄⋊C₄	—	47	1	no	—
218	#1949	—	47	4	no	—
219	#1948	—	47	2	no	—
220	#1947	—	47	2	no	—
221	#1736	—	47	2	no	—
222	C₂×C₄₇	—	2	4	no	—
223	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
224	C₂×C₄₇	C₂×#428	1	1	yes	characteristic
225	C₂×C₄₇	#2911	1	1	yes	characteristic
226	C₂×C₄₇	#3036	1	1	yes	characteristic
227	C₂×C₄₇	#3037	1	1	yes	characteristic
228	C₂×C₄₇	#3077	1	1	yes	characteristic
229	C₂×C₄₇	#3078	1	1	yes	characteristic
230	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
231	C₂×#117	—	47	2	no	—
232	C₂²×C₄⋊C₄	—	47	1	no	—
233	C₂²×C₄⋊C₄	—	47	1	no	—
234	C₂²×C₄²	—	94	1	no	—
235	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
236	#428	—	94	8	no	—
237	C₂×#107	—	47	4	no	—
238	C₂×#106	—	47	4	no	—
239	#423	Dic₄₇	1	8	yes	complemented
240	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
241	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
242	#384	—	47	1	no	—
243	#384	—	47	1	no	—
244	#382	—	47	2	no	—
245	#380	—	94	1	no	—
246	#380	—	94	1	no	—
247	C₄×C₄⋊C₄	—	47	2	no	—
248	C₄×C₄⋊C₄	—	47	2	no	—
249	C₄×C₄⋊C₄	—	94	1	no	—
250	C₄×C₄⋊C₄	—	94	1	no	—
251	C₄×C₄⋊C₄	—	94	1	no	—
252	C₄×C₄⋊C₄	—	94	1	no	—
253	C₂×#95	—	94	1	no	—
254	#340	—	47	4	no	—
255	#340	—	47	4	no	—
256	C₄₇	#21170	1	1	yes	characteristic, complemented, Sylow
257	C₂³×C₄	—	94	1	no	—
258	C₂³×C₄	—	94	1	no	—
259	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
260	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
261	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
262	C₂×M₁₆	—	2	4	no	—
263	C₂×M₁₆	—	2	4	no	—
264	C₂×M₁₆	C₂×Dic₄₇	1	8	yes	—
265	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
266	#117	—	94	4	no	—
267	#117	—	94	4	no	—
268	C₂×C₄⋊C₄	—	47	4	no	—
269	C₂×C₄⋊C₄	—	47	4	no	—
270	C₂×C₄⋊C₄	—	47	2	no	—
271	C₂×C₄⋊C₄	—	47	2	no	—
272	C₂×C₄⋊C₄	—	47	2	no	—
273	C₂×C₄⋊C₄	—	47	2	no	—
274	C₂×C₄⋊C₄	—	94	1	no	—
275	C₂×C₄⋊C₄	—	94	1	no	—
276	C₂×C₄⋊C₄	—	94	2	no	—
277	C₂×C₄⋊C₄	—	94	2	no	—
278	C₂×C₄⋊C₄	—	94	1	no	—
279	C₂×C₄⋊C₄	—	94	1	no	—
280	C₂×C₄⋊C₄	—	94	1	no	—
281	C₂×C₄⋊C₄	—	94	1	no	—
282	C₂×C₂²⋊C₄	—	94	2	no	—
283	C₂×C₄²	—	94	2	no	—
284	C₂×C₄²	—	94	2	no	—
285	C₂×C₄²	—	94	2	no	—
286	C₂×C₄²	—	188	4	no	—
287	C₂×C₄²	Dic₉₄	1	4	yes	—
288	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
289	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
290	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
291	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
292	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
293	#107	—	94	8	no	—
294	#106	—	94	8	no	—
295	C₄⋊C₈	C₂×Dic₄₇	1	8	yes	complemented
296	C₄⋊C₈	C₂×Dic₄₇	1	8	yes	complemented
297	#95	—	94	2	no	—
298	#95	—	94	2	no	—
299	#95	—	94	2	no	—
300	#95	—	94	2	no	—
301	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	94	4	no	—
307	C₂²×C₄	—	94	4	no	—
308	C₂²×C₄	—	94	2	no	—
309	C₂²×C₄	—	94	2	no	—
310	C₂²×C₄	—	94	2	no	—
311	C₂²×C₄	—	94	2	no	—
312	C₂²×C₄	—	188	2	no	—
313	C₂²×C₄	—	188	2	no	—
314	C₂²×C₄	—	188	2	no	—
315	C₂²×C₄	—	188	2	no	—
316	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
317	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
318	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
319	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
324	C₂²×C₄	D₄×D₄₇	1	2	yes	—
325	C₂²×C₄	#10625352	1	2	yes	—
326	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
327	C₂²×C₄	#10625354	1	2	yes	—
328	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
329	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
330	M₁₆	—	2	16	no	—
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	C₂²×Dic₄₇	1	8	yes	—
334	C₄⋊C₄	—	47	4	no	—
335	C₄⋊C₄	—	47	4	no	—
336	C₄⋊C₄	—	94	4	no	—
337	C₄⋊C₄	—	94	4	no	—
338	C₄⋊C₄	—	94	2	no	—
339	C₄⋊C₄	—	94	2	no	—
340	C₄⋊C₄	—	94	2	no	—
341	C₄⋊C₄	—	94	2	no	—
342	C₄⋊C₄	—	94	2	no	—
343	C₄⋊C₄	—	94	2	no	—
344	C₄⋊C₄	—	188	2	no	—
345	C₄⋊C₄	—	188	2	no	—
346	C₄⋊C₄	—	188	2	no	—
347	C₄⋊C₄	—	188	2	no	—
348	C₂²⋊C₄	—	188	4	no	—
349	C₄²	—	188	4	no	—
350	C₄²	—	188	4	no	—
351	C₄²	—	188	4	no	—
352	C₄²	C₄⋊Dic₄₇	1	4	yes	—
353	C₄²	C₄⋊Dic₄₇	1	4	yes	—
354	C₄²	C₂×Dic₉₄	1	2	yes	—
355	C₄²	C₂×Dic₉₄	1	2	yes	—
356	C₄²	C₂²×Dic₄₇	1	2	yes	—
357	C₄²	C₂²×Dic₄₇	1	2	yes	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
363	C₂³	#13093999	1	2	yes	—
364	C₂³	#13094004	1	2	yes	—
365	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	94	4	no	—
375	C₂×C₄	—	94	4	no	—
376	C₂×C₄	—	188	2	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	2	no	—
382	C₂×C₄	—	188	8	no	—
383	C₂×C₄	—	188	8	no	—
384	C₂×C₄	—	188	2	no	—
385	C₂×C₄	—	188	2	no	—
386	C₂×C₄	—	188	2	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
389	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
390	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
391	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
392	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
393	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
394	C₂×C₄	Q₈×Dic₄₇	1	4	yes	—
395	C₂×C₄	#13093999	1	2	yes	—
396	C₂×C₄	#13094004	1	2	yes	—
397	C₂×C₄	#13094015	1	4	yes	—
398	C₂×C₄	#13094023	1	4	yes	—
399	C₂×C₄	#13094052	1	2	yes	—
400	C₂×C₄	#13094057	1	2	yes	—
401	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
405	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
406	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
407	C₈	—	2	8	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	#15689022	1	4	yes	—
415	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
416	C₂²	C₂×#13093999	1	1	yes	characteristic
417	C₂²	C₂×#13094004	1	1	yes	characteristic
418	C₂²	C₂×#13094052	1	1	yes	characteristic
419	C₂²	C₂×#13094057	1	1	yes	characteristic
420	C₂²	#15689923	1	1	yes	characteristic
421	C₂²	#15689923	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	376	2	no	—
426	C₄	—	376	2	no	—
427	C₄	—	188	4	no	—
428	C₄	—	188	4	no	—
429	C₄	#15689022	1	4	yes	—
430	C₄	#15689165	1	4	yes	complemented
431	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
432	C₄	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
433	C₄	C₂×#13094015	1	1	yes	characteristic
434	C₄	C₂×#13094023	1	1	yes	characteristic
435	C₂	—	2	4	no	—
436	C₂	C₂×#15689022	1	1	yes	characteristic
437	C₂	C₂×#15689165	1	1	yes	characteristic
438	C₂	#20251978	1	1	yes	characteristic
439	C₂	#20252854	1	1	yes	characteristic
440	C₂	#20252862	1	1	yes	characteristic
441	C₂	#20253187	1	1	yes	characteristic
442	C₂	#20253195	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#423	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#423	D₄₇
hypocenter	C₄₇	#21170
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
4. #20244158	C₂	semidirect
5. #20244152	C₂	semidirect
6. #20244147	C₂	semidirect
32. C₄₇×#423	C₄	semidirect
77. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
78. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
205. C₄×C₄₇	#428	semidirect
239. #423	Dic₄₇	semidirect
256. C₄₇	#21170	semidirect
295. C₄⋊C₈	C₂×Dic₄₇	semidirect
296. C₄⋊C₈	C₂×Dic₄₇	semidirect
430. C₄	#15689165	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689165	2
#20245795	2
C₂×C₄×C₄⋊Dic₄₇	2
#20244158	2
#20244152	2
#20244147	2
#20243108	2
C₂×C₄₇×#423	2
#21170	47