Subgroups — #26213982

Order 12032.

1444 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689107	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689097	C₂	1	1	yes	maximal, characteristic
3	#20251806	C₂	1	2	yes	maximal, complemented
4	#20243188	C₂	1	8	yes	maximal, complemented
5	C₂×#15688894	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#568	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂×#13093983	C₂²	1	2	yes	—
9	#15689107	C₄	1	4	yes	complemented
10	#15689107	C₂²	1	4	yes	—
11	C₂×#13093943	C₄	1	2	yes	complemented
12	C₂×#13093941	C₄	1	2	yes	complemented
13	#15689097	C₄	1	4	yes	—
14	#15689097	C₂²	1	4	yes	—
15	C₂×#13093939	C₄	1	4	yes	—
16	#15689081	—	2	4	no	—
17	#15689078	C₂²	1	8	yes	complemented
18	M₁₆×Dic₄₇	—	2	4	no	—
19	#15688894	C₂²	1	8	yes	complemented
20	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#568	—	2	4	no	—
22	C₄₇×#568	—	2	4	no	—
23	C₂×#131×C₄₇	C₄	1	4	yes	complemented
24	C₂×#131×C₄₇	C₂²	1	4	yes	—
25	C₂²×M₁₆×C₄₇	C₄	1	4	yes	complemented
26	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	C₂×C₄	1	4	yes	—
32	C₂×#10625329	C₂×C₄	1	4	yes	—
33	C₂×#10625329	C₂³	1	4	yes	—
34	C₂²×C₄₇⋊C₈	—	2	2	no	—
35	#13093983	—	2	2	no	—
36	#13093983	—	2	2	no	—
37	#13093983	C₂×C₄	1	4	yes	—
38	#13093983	C₂³	1	4	yes	—
39	C₂×C₄⋊Dic₄₇	—	2	2	no	—
40	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
41	C₂×C₄×Dic₄₇	—	2	2	no	—
42	#13093943	C₂×C₄	1	8	yes	complemented
43	#13093941	C₂×C₄	1	8	yes	complemented
44	#13093939	C₂×C₄	1	16	yes	—
45	#13093934	—	2	8	no	—
46	C₈×Dic₄₇	—	2	8	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	—	2	2	no	—
51	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
54	C₂×#41×C₄₇	C₂³	1	2	yes	—
55	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
57	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	#131×C₄₇	—	2	16	no	—
61	#131×C₄₇	—	2	16	no	—
62	C₂×M₁₆×C₄₇	—	2	2	no	—
63	C₂×M₁₆×C₄₇	—	2	2	no	—
64	C₂×M₁₆×C₄₇	—	2	8	no	—
65	C₂×M₁₆×C₄₇	—	2	8	no	—
66	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
70	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
71	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
72	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
74	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
75	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂⁴×C₄₇	C₄²	1	2	yes	—
77	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	2	4	no	—
82	#41×C₄₇	—	2	4	no	—
83	#41×C₄₇	—	2	4	no	—
84	#41×C₄₇	—	2	4	no	—
85	#41×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×Q₈×C₄₇	C₄²	1	2	yes	—
89	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂×D₄×C₄₇	—	2	4	no	—
91	C₂×D₄×C₄₇	—	2	4	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	C₄²	1	4	yes	—
95	C₂×D₄×C₄₇	C₄²	1	2	yes	—
96	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
103	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	#41	1	2	yes	—
113	C₂²×C₄×C₄₇	#41	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
115	C₂²×Dic₄₇	—	2	4	no	—
116	M₁₆×C₄₇	—	2	2	no	—
117	M₁₆×C₄₇	—	2	2	no	—
118	M₁₆×C₄₇	—	2	4	no	—
119	M₁₆×C₄₇	—	2	16	no	—
120	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
121	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
122	M₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
123	C₂×C₈×C₄₇	—	2	4	no	—
124	C₂×C₈×C₄₇	—	2	16	no	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₄₇	C₂×D₄	1	8	yes	—
128	C₂²⋊Dic₄₇	—	2	4	no	—
129	C₂²⋊Dic₄₇	C₂²×C₄	1	8	yes	—
130	C₄⋊Dic₄₇	—	2	4	no	—
131	C₄⋊Dic₄₇	—	2	4	no	—
132	C₄×Dic₄₇	—	2	4	no	—
133	C₄×Dic₄₇	—	2	4	no	—
134	#10625329	—	2	4	no	—
135	#10625329	—	2	4	no	—
136	#10625329	—	2	4	no	—
137	#10625329	C₂²×C₄	1	8	yes	—
138	C₂×C₄₇⋊C₈	—	2	4	no	—
139	C₂×C₄₇⋊C₈	—	2	4	no	—
140	C₂×C₄₇⋊C₈	—	2	4	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	8	1	no	—
144	C₂³×C₄₇	—	8	2	no	—
145	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
146	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
147	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
148	C₂³×C₄₇	C₄×D₄	1	2	yes	—
149	C₂³×C₄₇	C₄×D₄	1	2	yes	—
150	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	Q₈×C₄₇	—	2	4	no	—
152	Q₈×C₄₇	—	2	4	no	—
153	D₄×C₄₇	—	2	8	no	—
154	D₄×C₄₇	—	2	8	no	—
155	D₄×C₄₇	—	2	4	no	—
156	D₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	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	—	2	4	no	—
163	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
164	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
170	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#117	1	2	yes	—
172	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₄×D₄	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	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
182	C₂×Dic₄₇	—	2	8	no	—
183	C₂×Dic₄₇	—	8	4	no	—
184	C₈×C₄₇	—	2	4	no	—
185	C₈×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
186	C₄₇⋊C₈	—	2	8	no	—
187	#20401	—	47	1	no	maximal, Sylow
188	C₂²×C₄₇	—	2	4	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	4	1	no	—
191	C₂²×C₄₇	—	4	1	no	—
192	C₂²×C₄₇	—	4	2	no	—
193	C₂²×C₄₇	—	4	1	no	—
194	C₂²×C₄₇	—	4	4	no	—
195	C₂²×C₄₇	—	8	2	no	—
196	C₂²×C₄₇	—	8	2	no	—
197	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
200	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
202	C₄×C₄₇	—	2	4	no	—
203	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
204	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
205	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
206	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
207	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
208	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
209	Dic₄₇	—	4	8	no	—
210	C₂×#568	D₄₇	1	1	yes	characteristic
211	C₂×#413	—	47	1	no	—
212	C₂×#410	—	47	1	no	—
213	#2873	—	47	2	no	—
214	#1757	—	47	8	no	—
215	C₂×#344	—	47	2	no	—
216	C₂×C₄₇	—	2	2	no	—
217	C₂×C₄₇	—	2	1	no	—
218	C₂×C₄₇	—	2	1	no	—
219	C₂×C₄₇	—	2	1	no	—
220	C₂×C₄₇	—	2	2	no	—
221	C₂×C₄₇	—	4	4	no	—
222	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
223	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
224	#568	—	2	4	no	—
225	#568	—	2	4	no	—
226	C₂×#131	Dic₄₇	1	4	yes	complemented
227	C₂×#131	C₂×D₄₇	1	4	yes	—
228	C₂²×M₁₆	—	47	2	no	—
229	C₂²×M₁₆	Dic₄₇	1	4	yes	complemented
230	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
231	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
232	C₂×#117	—	47	2	no	—
233	#413	—	47	4	no	—
234	#413	—	47	4	no	—
235	C₂×#101	—	47	2	no	—
236	C₂×#100	—	47	2	no	—
237	#410	—	47	4	no	—
238	#410	—	47	4	no	—
239	C₂×#99	—	47	4	no	—
240	#405	—	47	8	no	—
241	#405	—	94	4	no	—
242	C₄×M₁₆	—	94	4	no	—
243	#344	—	47	8	no	—
244	C₄₇	#20401	1	1	yes	characteristic, complemented, Sylow
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	—	2	2	no	—
249	C₂×#41	C₄×D₄₇	1	2	yes	—
250	C₂×#41	C₄×D₄₇	1	2	yes	—
251	C₂×#41	C₂×Dic₄₇	1	2	yes	—
252	C₂×#41	C₂²×D₄₇	1	2	yes	—
253	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
254	C₂²×D₄	C₄×D₄₇	1	2	yes	—
255	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
256	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
257	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
258	#131	—	2	16	no	—
259	#131	—	2	16	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	8	no	—
263	C₂×M₁₆	—	2	8	no	—
264	C₂×M₁₆	—	47	4	no	—
265	C₂×M₁₆	—	47	4	no	—
266	C₂×M₁₆	—	47	4	no	—
267	C₂×M₁₆	—	94	2	no	—
268	C₂×M₁₆	—	94	2	no	—
269	C₂×M₁₆	—	94	2	no	—
270	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
271	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
272	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
273	C₂×M₁₆	C₂×Dic₄₇	1	8	yes	complemented
274	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
275	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
276	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
277	C₂²×C₈	—	94	2	no	—
278	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
279	C₂²×C₈	C₂×Dic₄₇	1	8	yes	complemented
280	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
281	#117	—	47	4	no	—
282	#117	—	47	4	no	—
283	#117	—	94	2	no	—
284	#117	—	94	2	no	—
285	C₂×C₄⋊C₄	—	94	2	no	—
286	C₂×C₂²⋊C₄	—	47	4	no	—
287	C₂×C₄²	—	94	2	no	—
288	#101	—	47	8	no	—
289	#100	—	47	8	no	—
290	#99	—	47	16	no	—
291	#97	—	94	8	no	—
292	C₄×C₈	—	94	8	no	—
293	C₂⁴	C₄×Dic₄₇	1	2	yes	—
294	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
295	#41	—	2	4	no	—
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	C₄×Dic₄₇	1	2	yes	—
306	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
312	C₂×D₄	C₄×Dic₄₇	1	2	yes	—
313	C₂×D₄	C₂×C₄×D₄₇	1	4	yes	—
314	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	94	4	no	—
320	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
321	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
322	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
325	C₂²×C₄	#10625350	1	2	yes	—
326	C₂²×C₄	#10625350	1	2	yes	—
327	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
328	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
329	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
331	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	4	no	—
336	M₁₆	—	2	16	no	—
337	M₁₆	—	47	8	no	—
338	M₁₆	—	94	4	no	—
339	M₁₆	—	94	4	no	—
340	M₁₆	—	94	4	no	—
341	M₁₆	C₂²⋊Dic₄₇	1	4	yes	—
342	M₁₆	C₂²⋊Dic₄₇	1	4	yes	—
343	M₁₆	C₂²⋊Dic₄₇	1	8	yes	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	2	16	no	—
346	C₂×C₈	—	94	4	no	—
347	C₂×C₈	—	94	4	no	—
348	C₂×C₈	—	94	4	no	—
349	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
350	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
351	C₂×C₈	C₂×C₂²⋊D₄₇	1	8	yes	—
352	C₄⋊C₄	—	94	4	no	—
353	C₄⋊C₄	—	94	4	no	—
354	C₂²⋊C₄	—	47	8	no	—
355	C₂²⋊C₄	—	94	4	no	—
356	C₄²	—	94	4	no	—
357	C₄²	—	94	4	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	8	1	no	—
361	C₂³	—	8	2	no	—
362	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
363	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
364	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
365	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
366	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
367	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
368	Q₈	—	2	4	no	—
369	Q₈	—	2	4	no	—
370	D₄	—	2	8	no	—
371	D₄	—	2	8	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	94	8	no	—
381	C₂×C₄	—	376	4	no	—
382	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
383	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
384	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
385	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
386	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
388	C₂×C₄	#13093983	1	1	yes	characteristic
389	C₂×C₄	#13093983	1	1	yes	characteristic
390	C₂×C₄	#13093983	1	2	yes	—
391	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
392	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
393	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
394	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
395	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
396	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
397	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
398	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
400	C₂×C₄	C₂×#10625350	1	2	yes	—
401	C₈	—	2	4	no	—
402	C₈	—	94	8	no	—
403	C₈	C₂×C₂²⋊Dic₄₇	1	8	yes	—
404	C₂²	—	2	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
414	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
415	C₂²	C₄×C₂²⋊Dic₄₇	1	2	yes	—
416	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
417	C₂²	C₂×C₄×C₂²⋊D₄₇	1	2	yes	—
418	C₄	—	2	4	no	—
419	C₄	—	188	8	no	—
420	C₄	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
421	C₄	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
422	C₄	C₄×C₂²⋊Dic₄₇	1	2	yes	—
423	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
424	C₄	C₂×#13093983	1	1	yes	characteristic
425	C₄	C₂×C₄×C₂²⋊D₄₇	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	2	1	no	—
430	C₂	—	2	2	no	—
431	C₂	—	4	4	no	—
432	C₂	C₂×C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×C₂²⋊Dic₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#568	C₂
socle	C₂×C₄₇	C₂×C₄×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#568	D₄₇
hypocenter	C₄₇	#20401
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×M₁₆ ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
3. #20251806	C₂	semidirect
4. #20243188	C₂	semidirect
5. C₂×#15688894	C₂	semidirect
9. #15689107	C₄	semidirect
11. C₂×#13093943	C₄	semidirect
12. C₂×#13093941	C₄	semidirect
17. #15689078	C₂²	semidirect
19. #15688894	C₂²	semidirect
23. C₂×#131×C₄₇	C₄	semidirect
25. C₂²×M₁₆×C₄₇	C₄	semidirect
42. #13093943	C₂×C₄	semidirect
43. #13093941	C₂×C₄	semidirect
69. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
74. C₂²×C₈×C₄₇	C₂×C₄	semidirect
226. C₂×#131	Dic₄₇	semidirect
229. C₂²×M₁₆	Dic₄₇	semidirect
244. C₄₇	#20401	semidirect
273. C₂×M₁₆	C₂×Dic₄₇	semidirect
279. C₂²×C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689107	2
C₂×#15689097	2
#20251806	2
#20243188	2
C₂×#15688894	2
C₂×C₄₇×#568	2
#20401	47