Subgroups — #27080675

Order 12032.

1882 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689680	C₂	1	1	yes	maximal, characteristic
2	#20252339	C₂	1	8	yes	maximal, complemented
3	#20252331	C₂	1	8	yes	maximal, complemented
4	#20252325	C₂	1	4	yes	maximal, complemented
5	#20252318	C₂	1	4	yes	maximal, complemented
6	#20251951	C₂	1	2	yes	maximal
7	#20251806	C₂	1	2	yes	maximal
8	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	#15689680	C₄	1	2	yes	—
13	#15689680	C₄	1	4	yes	—
14	#15689680	C₄	1	2	yes	—
15	#15689680	C₂²	1	2	yes	—
16	#15689680	C₂²	1	2	yes	—
17	#15689680	C₂²	1	4	yes	—
18	C₂×#13094024	C₄	1	2	yes	—
19	C₂×#13094016	C₄	1	2	yes	—
20	C₂×#13094003	C₄	1	4	yes	—
21	C₂×C₄×Dic₉₄	C₂²	1	4	yes	—
22	C₂×#13093983	C₂²	1	2	yes	—
23	#15689252	C₂²	1	32	yes	complemented
24	#15689250	C₂²	1	16	yes	complemented
25	#15689247	C₂²	1	16	yes	complemented
26	#15689151	C₂²	1	8	yes	—
27	#15689149	C₂²	1	8	yes	—
28	#15689146	C₂²	1	8	yes	—
29	#15689081	C₂²	1	8	yes	—
30	#15689078	C₂²	1	8	yes	—
31	C₄×#10625329	C₂²	1	4	yes	—
32	C₄×#10625329	C₂²	1	4	yes	—
33	M₁₆×Dic₄₇	C₂²	1	8	yes	—
34	C₂×#13093935	C₂²	1	2	yes	—
35	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
36	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
37	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#423	C₂²	1	2	yes	—
39	C₄₇×#423	C₂²	1	2	yes	—
40	C₄₇×#423	C₂²	1	4	yes	—
41	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	—
42	C₂²×Dic₉₄	C₂×C₄	1	4	yes	—
43	C₂×#10625329	—	2	4	no	—
44	C₂×#10625329	Q₈	1	8	yes	complemented
45	C₂×#10625329	C₂³	1	2	yes	—
46	C₂×#10625329	C₂³	1	2	yes	—
47	C₂×#10625329	C₂³	1	2	yes	—
48	C₂×#10625329	C₂³	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	#13094024	C₂×C₄	1	4	yes	—
52	#13094024	C₂×C₄	1	4	yes	—
53	#13094024	C₂×C₄	1	4	yes	—
54	#13094024	C₂×C₄	1	4	yes	—
55	#13094016	C₂×C₄	1	4	yes	—
56	#13094016	C₂×C₄	1	4	yes	—
57	#13094016	C₂×C₄	1	8	yes	—
58	#13094003	C₂×C₄	1	8	yes	—
59	#13094003	C₂×C₄	1	8	yes	—
60	#13094003	C₂×C₄	1	8	yes	—
61	#13094003	C₂×C₄	1	8	yes	—
62	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
63	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
64	C₄×Dic₉₄	C₂³	1	8	yes	—
65	C₄×Dic₉₄	C₂³	1	8	yes	—
66	#13093983	C₂×C₄	1	4	yes	—
67	#13093983	C₂×C₄	1	4	yes	—
68	#13093983	C₂³	1	4	yes	—
69	#13093983	C₂³	1	4	yes	—
70	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
71	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
72	C₂×Dic₄₇⋊C₄	C₂×C₄	1	8	yes	—
73	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
74	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
75	Dic₄₇⋊C₈	C₂³	1	32	yes	—
76	#13093935	C₂³	1	8	yes	—
77	#13093934	C₂³	1	16	yes	—
78	C₄×C₄₇⋊C₈	C₂³	1	8	yes	—
79	C₈×Dic₄₇	C₂³	1	16	yes	—
80	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
81	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₄₇	—	2	8	no	—
83	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
84	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
85	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
86	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
94	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
95	C₄⋊C₈×C₄₇	C₂³	1	8	yes	—
96	C₄⋊C₈×C₄₇	C₂³	1	8	yes	—
97	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	—	4	4	no	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	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	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₄₇	#41	1	4	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
114	C₂×Dic₉₄	—	4	8	no	—
115	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
116	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
117	M₁₆×C₄₇	—	2	8	no	—
118	M₁₆×C₄₇	—	2	8	no	—
119	C₂×C₈×C₄₇	—	2	8	no	—
120	C₂×C₈×C₄₇	C₂⁴	1	8	yes	—
121	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
122	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂⁴	1	2	yes	—
130	C₄²×C₄₇	C₂⁴	1	2	yes	—
131	C₂²⋊Dic₄₇	C₂²×C₄	1	8	yes	—
132	C₂²⋊Dic₄₇	C₂²×C₄	1	8	yes	—
133	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
134	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
135	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
136	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
137	Dic₄₇⋊C₄	C₂²×C₄	1	16	yes	—
138	Dic₄₇⋊C₄	C₂²×C₄	1	16	yes	—
139	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
140	C₄×Dic₄₇	C₂⁴	1	8	yes	—
141	#10625329	—	2	4	no	—
142	#10625329	—	2	4	no	—
143	#10625329	C₂×Q₈	1	8	yes	—
144	#10625329	C₂×Q₈	1	8	yes	complemented
145	C₂×C₄₇⋊C₈	—	2	4	no	—
146	C₂×C₄₇⋊C₈	C₂×Q₈	1	8	yes	complemented
147	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
148	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
149	C₂³×C₄₇	—	4	2	no	—
150	C₂³×C₄₇	C₄×Q₈	1	4	yes	—
151	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
161	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
162	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
163	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
171	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
172	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
176	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
177	C₂×Dic₄₇	—	4	8	no	—
178	C₂×Dic₄₇	C₂³×C₄	1	16	yes	—
179	Dic₉₄	—	2	16	no	—
180	Dic₉₄	—	4	8	no	—
181	C₈×C₄₇	—	2	8	no	—
182	C₄₇⋊C₈	—	2	4	no	—
183	C₄₇⋊C₈	C₂²×Q₈	1	8	yes	—
184	#60192	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	4	4	no	—
189	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
190	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
191	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
192	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	2	2	no	—
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
197	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
198	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
199	C₄×C₄₇	#568	1	4	yes	—
200	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
201	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
202	Dic₄₇	—	2	16	no	—
203	C₂×#533	—	47	1	no	—
204	Q₈×M₁₆	—	47	8	no	—
205	#2962	—	47	8	no	—
206	#2961	—	47	4	no	—
207	#2960	—	47	4	no	—
208	#2905	—	47	2	no	—
209	C₂×#423	D₄₇	1	1	yes	characteristic
210	#2873	—	47	2	no	—
211	C₂×C₄×M₁₆	—	47	1	no	—
212	C₂×C₄₇	—	2	2	no	—
213	C₂×C₄₇	—	2	2	no	—
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#568	1	2	yes	—
217	C₂²×M₁₆	—	47	1	no	—
218	C₂²×M₁₆	—	47	1	no	—
219	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
220	#533	—	47	2	no	—
221	#533	—	47	4	no	—
222	#533	—	47	2	no	—
223	#533	—	47	2	no	—
224	#533	—	47	2	no	—
225	#533	—	47	4	no	—
226	C₂×C₄⋊Q₈	—	47	2	no	—
227	C₂×#125	—	47	2	no	—
228	C₂×C₂²⋊Q₈	—	47	4	no	—
229	C₂×C₄×Q₈	—	47	4	no	—
230	C₂×#117	—	47	2	no	—
231	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
232	#446	—	47	16	no	—
233	#446	—	47	32	no	—
234	C₈×Q₈	—	47	16	no	—
235	#424	—	47	8	no	—
236	#424	—	47	8	no	—
237	#423	—	47	8	no	—
238	#423	C₂×D₄₇	1	2	yes	—
239	#423	C₂×D₄₇	1	2	yes	—
240	#423	C₂×D₄₇	1	4	yes	—
241	C₂×C₄⋊C₈	C₂×D₄₇	1	4	yes	—
242	#405	—	47	8	no	—
243	#405	—	47	8	no	—
244	C₄×M₁₆	—	47	8	no	—
245	C₄×M₁₆	—	47	4	no	—
246	C₄×M₁₆	—	47	4	no	—
247	C₂×#97	—	47	2	no	—
248	C₂×C₄×C₈	—	47	2	no	—
249	C₄₇	#60192	1	1	yes	characteristic, complemented, Sylow
250	C₂²×Q₈	—	47	4	no	—
251	C₂³×C₄	C₄×D₄₇	1	2	yes	—
252	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
253	C₂×M₁₆	—	2	8	no	—
254	C₂×M₁₆	—	47	8	no	—
255	C₂×M₁₆	—	47	2	no	—
256	C₂×M₁₆	—	47	2	no	—
257	C₂×M₁₆	—	47	2	no	—
258	C₂×M₁₆	—	47	2	no	—
259	C₂×M₁₆	—	94	4	no	—
260	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
261	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
262	C₂²×C₈	—	47	2	no	—
263	C₂²×C₈	—	47	2	no	—
264	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
265	C₄⋊Q₈	—	47	4	no	—
266	C₄⋊Q₈	—	47	4	no	—
267	C₄⋊Q₈	—	47	4	no	—
268	C₄⋊Q₈	—	47	4	no	—
269	#125	—	47	4	no	—
270	#125	—	47	4	no	—
271	#125	—	47	8	no	—
272	C₂²⋊Q₈	—	47	8	no	—
273	C₂²⋊Q₈	—	47	8	no	—
274	C₂²⋊Q₈	—	47	8	no	—
275	C₂²⋊Q₈	—	47	8	no	—
276	C₄×Q₈	—	47	8	no	—
277	C₄×Q₈	—	47	8	no	—
278	C₄×Q₈	—	47	8	no	—
279	C₄×Q₈	—	47	8	no	—
280	#117	—	47	4	no	—
281	#117	—	47	4	no	—
282	#117	—	47	4	no	—
283	#117	—	47	4	no	—
284	C₂×C₄⋊C₄	—	47	4	no	—
285	C₂×C₄⋊C₄	—	47	8	no	—
286	C₂×C₄⋊C₄	—	47	4	no	—
287	C₂×C₂²⋊C₄	—	47	4	no	—
288	C₂×C₄²	—	47	4	no	—
289	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
290	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
291	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
292	C₂×C₄²	C₄×D₄₇	1	2	yes	—
293	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
294	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
295	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
296	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
297	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
298	C₄⋊C₈	—	47	32	no	—
299	C₄⋊C₈	C₂²×D₄₇	1	8	yes	—
300	C₄⋊C₈	C₂²×D₄₇	1	8	yes	—
301	#97	—	47	16	no	—
302	#97	—	47	8	no	—
303	C₄×C₈	—	47	16	no	—
304	C₄×C₈	—	47	8	no	—
305	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
306	C₂×Q₈	—	47	8	no	—
307	C₂×Q₈	—	47	8	no	—
308	C₂×Q₈	—	188	8	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	—	47	8	no	—
311	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
312	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
313	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
314	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
315	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
316	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
317	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	#10625352	1	4	yes	—
321	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
322	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
325	M₁₆	—	2	8	no	—
326	M₁₆	—	2	8	no	—
327	M₁₆	—	47	8	no	—
328	M₁₆	—	47	8	no	—
329	M₁₆	—	94	4	no	—
330	M₁₆	—	94	4	no	—
331	C₂×C₈	—	2	8	no	—
332	C₂×C₈	—	47	8	no	—
333	C₂×C₈	—	47	4	no	—
334	C₂×C₈	—	47	4	no	—
335	C₂×C₈	—	94	4	no	—
336	C₂×C₈	C₂³×D₄₇	1	8	yes	—
337	C₄⋊C₄	—	47	16	no	—
338	C₄⋊C₄	—	47	16	no	—
339	C₄⋊C₄	—	47	8	no	—
340	C₄⋊C₄	—	47	8	no	—
341	C₄⋊C₄	—	47	8	no	—
342	C₄⋊C₄	—	47	8	no	—
343	C₂²⋊C₄	—	47	8	no	—
344	C₂²⋊C₄	—	47	8	no	—
345	C₄²	—	47	8	no	—
346	C₄²	—	47	8	no	—
347	C₄²	C₂×C₄×D₄₇	1	2	yes	—
348	C₄²	C₂×C₄×D₄₇	1	2	yes	—
349	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
350	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
351	C₄²	C₂×C₄×D₄₇	1	2	yes	—
352	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
353	C₄²	C₂×C₄×D₄₇	1	2	yes	—
354	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
355	C₄²	C₂³×D₄₇	1	2	yes	—
356	C₄²	C₂³×D₄₇	1	2	yes	—
357	C₂³	—	4	2	no	—
358	C₂³	#13093989	1	4	yes	—
359	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
360	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
361	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
362	Q₈	—	94	16	no	—
363	Q₈	—	188	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	47	16	no	—
371	C₂×C₄	—	188	8	no	—
372	C₂×C₄	#13093989	1	4	yes	—
373	C₂×C₄	#13093989	1	4	yes	—
374	C₂×C₄	#13093989	1	4	yes	—
375	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
376	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
377	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
378	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
382	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
383	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
384	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
385	C₂×C₄	C₂×#10625352	1	2	yes	—
386	C₂×C₄	C₂×#10625352	1	2	yes	—
387	C₂×C₄	C₂×#10625352	1	2	yes	—
388	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
389	C₈	—	2	8	no	—
390	C₈	—	47	8	no	—
391	C₈	—	94	4	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	4	no	—
396	C₂²	C₂×#13093989	1	2	yes	—
397	C₂²	C₂×#13093989	1	2	yes	—
398	C₂²	C₂×#13093989	1	2	yes	—
399	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	94	16	no	—
404	C₄	C₂×#13093989	1	2	yes	—
405	C₄	C₂×#13093989	1	2	yes	—
406	C₄	C₂×#13093989	1	2	yes	—
407	C₄	#15689889	1	4	yes	—
408	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
409	C₄	C₂²×#10625352	1	1	yes	characteristic
410	C₂	—	2	2	no	—
411	C₂	—	2	2	no	—
412	C₂	—	2	2	no	—
413	C₂	C₂²×#13093989	1	1	yes	characteristic
414	C₂	C₂×#15689889	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂×C₄₇×#423	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#423	D₄₇
hypocenter	C₄₇	#60192
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
2. #20252339	C₂	semidirect
3. #20252331	C₂	semidirect
4. #20252325	C₂	semidirect
5. #20252318	C₂	semidirect
23. #15689252	C₂²	semidirect
24. #15689250	C₂²	semidirect
25. #15689247	C₂²	semidirect
44. C₂×#10625329	Q₈	semidirect
144. #10625329	C₂×Q₈	semidirect
146. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
249. C₄₇	#60192	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689680	2
#20252339	2
#20252331	2
#20252325	2
#20252318	2
#20251951	2
#20251806	2
C₂×C₄×#10625329	2
C₂×C₄₇×#423	2
#60192	47