Subgroups — #26235056

Order 12032.

796 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#10625329	C₂	1	2	yes	maximal
2	#20244164	C₂	1	2	yes	maximal, complemented
3	#20243595	C₂	1	2	yes	maximal, complemented
4	#20243595	C₂	1	2	yes	maximal, complemented
5	#20243529	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243430	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243426	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243294	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243115	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688888	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#435	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂²×#10625329	C₂²	1	2	yes	—
14	#15689201	—	2	2	no	—
15	#15689195	—	2	2	no	—
16	#15689195	—	2	2	no	—
17	D₄×C₄₇⋊C₈	—	2	2	no	—
18	C₂×#13093960	C₂²	1	2	yes	—
19	C₂×#13093960	C₂²	1	2	yes	—
20	C₂×#13093960	C₂²	1	2	yes	—
21	#15689147	C₂²	1	2	yes	—
22	#15689087	C₂²	1	2	yes	—
23	#15689087	C₂²	1	2	yes	—
24	C₄×#10625329	C₂²	1	2	yes	—
25	#15688888	C₂²	1	2	yes	—
26	#15688888	C₂²	1	1	yes	characteristic
27	#15688888	C₂²	1	1	yes	characteristic
28	#15688888	C₂²	1	1	yes	characteristic
29	#15688888	C₂²	1	1	yes	characteristic
30	#15688888	C₂²	1	2	yes	—
31	#15688888	C₂²	1	2	yes	—
32	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
33	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#435	C₄	1	4	yes	—
36	C₄₇×#435	C₄	1	4	yes	—
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	—	2	2	no	—
43	C₂×#10625329	—	2	4	no	—
44	C₂×#10625329	—	2	4	no	—
45	C₂×#10625329	—	4	2	no	—
46	C₂×#10625329	—	4	2	no	—
47	C₂×#10625329	C₂³	1	2	yes	—
48	C₂×#10625329	C₂³	1	2	yes	—
49	C₂×#10625329	C₂³	1	2	yes	—
50	C₂×#10625329	C₂³	1	2	yes	—
51	C₂²×C₄₇⋊C₈	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	—	2	2	no	—
53	#13093960	—	2	4	no	—
54	#13093960	—	4	2	no	—
55	#13093960	—	4	2	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
58	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
62	#13093935	—	2	2	no	—
63	C₄×C₄₇⋊C₈	—	2	2	no	—
64	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₄₇	—	4	2	no	—
68	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
69	C₂²×C₈×C₄₇	—	4	2	no	—
70	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
77	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
78	C₄×D₄×C₄₇	D₄	1	2	yes	—
79	C₄×D₄×C₄₇	D₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₇	Q₈	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₄₇	Q₈	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	Q₈	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
85	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
86	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
87	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
88	#97×C₄₇	C₂×C₄	1	4	yes	—
89	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
90	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
91	C₂×D₄×C₄₇	—	4	2	no	—
92	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
93	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
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	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	M₁₆×C₄₇	—	4	4	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	4	2	no	—
115	C₂×C₈×C₄₇	—	4	2	no	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
121	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
122	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
123	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
124	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
125	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
126	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
127	C₄²×C₄₇	C₂×D₄	1	2	yes	—
128	#10625329	—	2	2	no	—
129	#10625329	—	2	2	no	—
130	#10625329	—	2	2	no	—
131	#10625329	—	2	2	no	—
132	#10625329	—	2	2	no	—
133	#10625329	—	2	2	no	—
134	#10625329	—	2	2	no	—
135	#10625329	—	4	4	no	—
136	#10625329	—	4	4	no	—
137	#10625329	#41	1	4	yes	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	4	4	no	—
143	C₂×C₄₇⋊C₈	—	4	4	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	—	2	2	no	—
147	C₂³×C₄₇	—	4	1	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	—	4	1	no	—
150	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
151	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
154	D₄×C₄₇	—	2	4	no	—
155	D₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
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	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
178	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
179	C₈×C₄₇	—	2	2	no	—
180	C₈×C₄₇	—	2	2	no	—
181	C₈×C₄₇	—	2	2	no	—
182	C₈×C₄₇	—	2	2	no	—
183	C₄₇⋊C₈	—	2	4	no	—
184	C₄₇⋊C₈	—	4	2	no	—
185	C₄₇⋊C₈	—	4	2	no	—
186	C₄₇⋊C₈	—	4	2	no	—
187	#22718	—	47	1	no	maximal, Sylow
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	2	no	—
198	C₂²×C₄₇	—	4	4	no	—
199	C₂²×C₄₇	—	8	2	no	—
200	C₂²×C₄₇	#430	1	2	yes	—
201	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₂²×C₄₇	#554	1	2	yes	—
203	C₄×C₄₇	—	2	1	no	—
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
209	C₄×C₄₇	#518	1	1	yes	characteristic
210	C₄×C₄₇	#546	1	2	yes	—
211	D₄×M₁₆	—	47	2	no	—
212	C₂×#435	D₄₇	1	1	yes	characteristic
213	#1950	—	47	2	no	—
214	#1855	—	47	2	no	—
215	#1855	—	47	2	no	—
216	#1838	—	47	1	no	—
217	#1811	—	47	1	no	—
218	#1810	—	47	1	no	—
219	#1778	—	47	1	no	—
220	#1738	—	47	1	no	—
221	C₂×#341	—	47	1	no	—
222	C₂×C₄₇	—	2	2	no	—
223	C₂×C₄₇	—	2	2	no	—
224	C₂×C₄₇	—	4	1	no	—
225	C₂×C₄₇	—	4	2	no	—
226	C₂×C₄₇	#2349	1	1	yes	characteristic
227	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
228	C₂×C₄₇	#2916	1	1	yes	characteristic
229	C₂²×M₁₆	—	47	2	no	—
230	C₂²×M₁₆	—	47	2	no	—
231	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
232	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
233	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
234	#436	—	94	2	no	—
235	#435	—	94	2	no	—
236	#435	—	94	2	no	—
237	#435	Dic₄₇	1	4	yes	—
238	#435	Dic₄₇	1	4	yes	—
239	C₈×D₄	—	94	2	no	—
240	C₂×#108	—	47	2	no	—
241	C₂×#108	—	47	2	no	—
242	C₂×#108	—	47	2	no	—
243	#423	—	47	2	no	—
244	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
245	#407	—	47	2	no	—
246	#407	—	47	2	no	—
247	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
248	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
249	C₄×M₁₆	—	47	2	no	—
250	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
251	#341	—	47	1	no	—
252	#341	—	47	1	no	—
253	#341	—	47	1	no	—
254	#341	—	47	2	no	—
255	#341	—	47	2	no	—
256	#341	—	47	2	no	—
257	#341	—	47	1	no	—
258	C₄₇	#22718	1	1	yes	characteristic, complemented, Sylow
259	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
260	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
261	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
262	C₂×M₁₆	—	4	2	no	—
263	C₂×M₁₆	—	47	2	no	—
264	C₂×M₁₆	—	47	2	no	—
265	C₂×M₁₆	—	47	2	no	—
266	C₂×M₁₆	—	47	2	no	—
267	C₂×M₁₆	—	94	2	no	—
268	C₂×M₁₆	—	94	2	no	—
269	C₂×M₁₆	—	94	4	no	—
270	C₂×M₁₆	—	94	4	no	—
271	C₂×M₁₆	—	188	2	no	—
272	C₂×M₁₆	—	188	2	no	—
273	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
274	C₂²×C₈	—	4	2	no	—
275	C₂²×C₈	—	94	2	no	—
276	C₂²×C₈	—	94	2	no	—
277	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
278	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
279	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
280	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
282	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
283	C₄×D₄	D₁₈₈	1	2	yes	—
284	C₄×D₄	D₁₈₈	1	2	yes	—
285	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
286	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
287	C₂×C₄⋊C₄	Dic₉₄	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	Dic₉₄	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	Dic₉₄	1	1	yes	characteristic
290	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
291	#108	—	94	4	no	—
292	#108	—	188	2	no	—
293	#108	—	188	2	no	—
294	C₄⋊C₈	—	94	2	no	—
295	C₄⋊C₈	—	94	2	no	—
296	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	—
297	C₂²⋊C₈	—	94	2	no	—
298	C₂²⋊C₈	—	94	2	no	—
299	C₂²⋊C₈	—	94	2	no	—
300	C₂²⋊C₈	—	94	2	no	—
301	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	—
302	C₂²⋊C₈	C₂×Dic₄₇	1	2	yes	—
303	C₂²⋊C₈	C₂×Dic₄₇	1	2	yes	—
304	#97	—	94	2	no	—
305	#97	C₂×Dic₄₇	1	4	yes	—
306	C₄×C₈	—	94	2	no	—
307	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
308	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
311	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
317	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
319	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
322	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
323	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
326	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
327	M₁₆	—	4	4	no	—
328	M₁₆	—	47	4	no	—
329	M₁₆	—	94	2	no	—
330	M₁₆	—	94	2	no	—
331	M₁₆	—	94	2	no	—
332	M₁₆	—	94	2	no	—
333	M₁₆	—	94	2	no	—
334	M₁₆	—	94	2	no	—
335	M₁₆	—	94	2	no	—
336	M₁₆	—	188	4	no	—
337	M₁₆	—	188	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	94	2	no	—
346	C₂×C₈	—	94	2	no	—
347	C₂×C₈	—	94	2	no	—
348	C₂×C₈	—	188	4	no	—
349	C₂×C₈	—	188	4	no	—
350	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
351	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
352	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
353	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
354	C₄⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
355	C₄⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
356	C₂²⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
357	C₂²⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
358	C₂²⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
359	C₂²⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
360	C₄²	C₂×D₁₈₈	1	2	yes	—
361	C₄²	C₂²×Dic₄₇	1	2	yes	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
369	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
370	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
371	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
372	D₄	—	2	4	no	—
373	D₄	—	4	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	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	1	yes	characteristic
391	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
392	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
395	C₂×C₄	#41×D₄₇	1	2	yes	—
396	C₂×C₄	#13094069	1	2	yes	—
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	—	2	2	no	—
401	C₈	—	94	4	no	—
402	C₈	—	188	2	no	—
403	C₈	—	188	2	no	—
404	C₈	—	188	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	8	2	no	—
417	C₂²	#15689172	1	2	yes	—
418	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
419	C₂²	#15689832	1	2	yes	—
420	C₄	—	2	1	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	#41×Dic₄₇	1	1	yes	characteristic
426	C₄	#15689598	1	1	yes	characteristic
427	C₄	#15689768	1	2	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	2	2	no	—
430	C₂	—	4	1	no	—
431	C₂	—	4	2	no	—
432	C₂	#20246298	1	1	yes	characteristic
433	C₂	C₂×#15689172	1	1	yes	characteristic
434	C₂	#20251999	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#435	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₄₇	Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#435	D₄₇
hypocenter	C₄₇	#22718
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
2. #20244164	C₂	semidirect
3. #20243595	C₂	semidirect
4. #20243595	C₂	semidirect
5. #20243529	C₂	semidirect
6. #20243430	C₂	semidirect
7. #20243426	C₂	semidirect
8. #20243294	C₂	semidirect
9. #20243115	C₂	semidirect
10. C₂×#15688888	C₂	semidirect
258. C₄₇	#22718	semidirect

Maximal subgroups

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

subgroup	index
D₄×#10625329	2
#20244164	2
#20243595	2
#20243529	2
#20243430	2
#20243426	2
#20243294	2
#20243115	2
C₂×#15688888	2
C₂×C₄₇×#435	2
#22718	47