Subgroups — C₂×#135×Dic₄₇ #27080303

Order 12032.

2894 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	#135×Dic₄₇	C₂	1	16	yes	maximal, direct product factor
3	C₂×Q₁₆×Dic₄₇	C₂	1	2	yes	maximal, complemented
4	C₂×SD₁₆×Dic₄₇	C₂	1	4	yes	maximal, complemented
5	C₂×D₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
6	C₂×#15689161	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689119	C₂	1	2	yes	maximal, complemented
8	C₂²×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#135×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	#41×Dic₄₇	—	2	8	no	—
12	#41×Dic₄₇	C₂²	1	16	yes	complemented
13	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	—
14	C₂×D₄×Dic₄₇	—	2	4	no	—
15	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
16	C₂×#13093983	—	2	2	no	—
17	C₂×#13093983	C₂²	1	2	yes	—
18	C₂²×C₄×Dic₄₇	—	2	2	no	—
19	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	Q₁₆×Dic₄₇	C₂²	1	16	yes	complemented
21	SD₁₆×Dic₄₇	C₂²	1	32	yes	complemented
22	D₈×Dic₄₇	C₂²	1	16	yes	complemented
23	#15689161	C₂²	1	8	yes	complemented
24	C₂×#13093958	C₂²	1	2	yes	—
25	C₂×#13093956	C₂²	1	2	yes	—
26	#15689119	C₂²	1	16	yes	complemented
27	C₂×#13093948	C₂²	1	4	yes	—
28	C₂×#13093945	C₂²	1	4	yes	—
29	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
30	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
31	C₂×C₈×Dic₄₇	C₂²	1	8	yes	complemented
32	C₂²×#41×C₄₇	C₂²	1	2	yes	—
33	C₂×#135×C₄₇	C₄	1	16	yes	complemented
34	C₂×#135×C₄₇	C₂²	1	8	yes	—
35	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
37	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂³×Dic₄₇	—	2	4	no	—
40	C₂³×Dic₄₇	D₄	1	2	yes	—
41	C₂²×C₄₇⋊C₈	—	2	4	no	—
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
44	Q₈×Dic₄₇	—	2	8	no	—
45	Q₈×Dic₄₇	C₂³	1	16	yes	—
46	D₄×Dic₄₇	—	2	32	no	—
47	D₄×Dic₄₇	—	2	8	no	—
48	D₄×Dic₄₇	C₂³	1	16	yes	—
49	#13093983	—	2	4	no	—
50	#13093983	—	2	16	no	—
51	#13093983	C₂³	1	8	yes	—
52	C₂×C₄⋊Dic₄₇	—	2	4	no	—
53	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
54	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
55	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	—	2	4	no	—
58	C₂×C₄×Dic₄₇	—	2	16	no	—
59	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	D₄	1	4	yes	—
62	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
63	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
64	#13093958	C₂³	1	8	yes	—
65	#13093956	C₂³	1	8	yes	—
66	#13093948	C₂³	1	16	yes	—
67	#13093945	C₂³	1	16	yes	—
68	C₈×Dic₄₇	C₂³	1	8	yes	—
69	C₈×Dic₄₇	C₂³	1	8	yes	—
70	C₂×#41×C₄₇	—	2	4	no	—
71	C₂×#41×C₄₇	—	2	8	no	—
72	C₂×#41×C₄₇	C₂×C₄	1	16	yes	complemented
73	C₂×#41×C₄₇	C₂³	1	8	yes	—
74	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
75	C₂²×D₄×C₄₇	—	2	2	no	—
76	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
77	C₂³×C₄×C₄₇	—	2	2	no	—
78	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	#135×C₄₇	C₂×C₄	1	64	yes	complemented
80	C₂×Q₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
81	C₂×Q₁₆×C₄₇	C₂³	1	4	yes	—
82	C₂×SD₁₆×C₄₇	C₂×C₄	1	16	yes	complemented
83	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
84	C₂×D₈×C₄₇	C₂×C₄	1	8	yes	complemented
85	C₂×D₈×C₄₇	C₂³	1	4	yes	—
86	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
87	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
90	C₂⁴×C₄₇	—	2	2	no	—
91	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
92	#41×C₄₇	—	2	32	no	—
93	#41×C₄₇	—	2	16	no	—
94	#41×C₄₇	C₂²×C₄	1	32	yes	complemented
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	4	no	—
97	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
98	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
99	C₂×D₄×C₄₇	—	2	16	no	—
100	C₂×D₄×C₄₇	—	2	8	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	4	no	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
104	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	16	no	—
107	C₂²×C₄×C₄₇	—	2	8	no	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	4	yes	—
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
114	C₂²×Dic₄₇	—	2	8	no	—
115	C₂²×Dic₄₇	—	2	4	no	—
116	C₂²×Dic₄₇	—	2	16	no	—
117	C₂²×Dic₄₇	—	4	16	no	—
118	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
119	C₂²×Dic₄₇	C₂×D₄	1	8	yes	—
120	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
121	Q₁₆×C₄₇	C₂²×C₄	1	16	yes	complemented
122	SD₁₆×C₄₇	C₂²×C₄	1	32	yes	complemented
123	D₈×C₄₇	C₂²×C₄	1	16	yes	complemented
124	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	16	yes	complemented
127	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
128	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
129	C₂²⋊Dic₄₇	—	2	8	no	—
130	C₂²⋊Dic₄₇	—	2	16	no	—
131	C₄⋊Dic₄₇	—	2	4	no	—
132	C₄⋊Dic₄₇	—	2	16	no	—
133	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
134	C₄×Dic₄₇	—	2	8	no	—
135	C₄×Dic₄₇	—	2	16	no	—
136	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
137	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
138	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
139	C₄×Dic₄₇	C₂⁴	1	4	yes	—
140	C₂×C₄₇⋊C₈	—	2	4	no	—
141	C₂×C₄₇⋊C₈	—	2	8	no	—
142	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
143	C₂³×C₄₇	—	2	4	no	—
144	C₂³×C₄₇	—	2	8	no	—
145	C₂³×C₄₇	—	2	4	no	—
146	C₂³×C₄₇	—	4	8	no	—
147	C₂³×C₄₇	C₄×D₄	1	4	yes	—
148	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₄₇	—	2	8	no	—
151	Q₈×C₄₇	—	2	4	no	—
152	Q₈×C₄₇	C₂³×C₄	1	8	yes	—
153	D₄×C₄₇	—	2	32	no	—
154	D₄×C₄₇	—	2	8	no	—
155	D₄×C₄₇	—	2	4	no	—
156	D₄×C₄₇	C₂³×C₄	1	8	yes	—
157	C₂×C₄×C₄₇	—	2	8	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	32	no	—
160	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
161	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
162	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
164	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
168	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
169	C₂×Dic₄₇	—	2	4	no	—
170	C₂×Dic₄₇	—	2	16	no	—
171	C₂×Dic₄₇	—	2	8	no	—
172	C₂×Dic₄₇	—	4	8	no	—
173	C₂×Dic₄₇	—	4	32	no	—
174	C₂×Dic₄₇	#135	1	8	yes	direct product factor
175	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
176	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
177	C₈×C₄₇	C₂³×C₄	1	4	yes	—
178	C₈×C₄₇	C₂³×C₄	1	4	yes	—
179	C₄₇⋊C₈	—	2	4	no	—
180	C₂×C₄×#135	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	—	2	8	no	—
182	C₂²×C₄₇	—	2	4	no	—
183	C₂²×C₄₇	—	2	8	no	—
184	C₂²×C₄₇	—	4	16	no	—
185	C₂²×C₄₇	—	4	8	no	—
186	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
187	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
188	C₂²×C₄₇	C₂×#135	1	4	yes	—
189	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
190	C₄×C₄₇	—	2	8	no	—
191	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
192	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
193	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
194	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
195	Dic₄₇	—	2	4	no	—
196	Dic₄₇	—	4	8	no	—
197	Dic₄₇	C₂×#135	1	8	yes	direct product factor
198	C₂²×#135	D₄₇	1	1	yes	characteristic
199	C₂×C₄×#41	—	47	2	no	—
200	C₄×#135	—	47	16	no	—
201	C₂×C₄×Q₁₆	—	47	2	no	—
202	C₂×C₄×SD₁₆	—	47	4	no	—
203	C₂×C₄×D₈	—	47	2	no	—
204	C₂×#427	—	47	1	no	—
205	C₂×#416	—	47	2	no	—
206	C₂²×C₄×C₈	—	47	1	no	—
207	C₂×C₄₇	—	2	4	no	—
208	C₂×C₄₇	—	4	8	no	—
209	C₂×C₄₇	C₄×#135	1	4	yes	complemented
210	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
211	C₂×C₄₇	C₂²×#135	1	2	yes	—
212	C₂²×#41	C₂×D₄₇	1	2	yes	—
213	C₂×#135	Dic₄₇	1	16	yes	direct product factor
214	C₂×#135	C₂×D₄₇	1	8	yes	—
215	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
216	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
217	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
218	C₂³×C₈	—	47	1	no	—
219	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₄×#41	—	47	16	no	—
221	C₄×#41	—	94	8	no	—
222	C₂×C₄×Q₈	—	47	4	no	—
223	C₂×C₄×D₄	—	47	4	no	—
224	C₂×C₄×D₄	—	94	4	no	—
225	C₂×#117	—	47	2	no	—
226	C₂×#117	—	94	2	no	—
227	C₂²×C₄²	—	47	1	no	—
228	C₂²×C₄²	—	94	2	no	—
229	C₄×Q₁₆	—	47	16	no	—
230	C₄×SD₁₆	—	47	32	no	—
231	C₄×D₈	—	47	16	no	—
232	#427	—	47	8	no	—
233	C₂×#107	—	47	2	no	—
234	C₂×#106	—	47	2	no	—
235	#416	—	47	16	no	—
236	C₂×#103	—	47	4	no	—
237	C₂×#102	—	47	4	no	—
238	C₂×C₄×C₈	—	47	2	no	—
239	C₂×C₄×C₈	—	47	2	no	—
240	C₂×C₄×C₈	—	47	8	no	—
241	C₄₇	C₂×C₄×#135	1	1	yes	characteristic, complemented, Sylow
242	C₂×#41	—	2	4	no	—
243	C₂×#41	—	2	8	no	—
244	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
245	C₂×#41	C₂²×D₄₇	1	8	yes	—
246	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	—	47	2	no	—
251	C₂³×C₄	—	94	4	no	—
252	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
253	#135	C₂×Dic₄₇	1	64	yes	direct product factor
254	C₂×Q₁₆	C₂×Dic₄₇	1	8	yes	complemented
255	C₂×Q₁₆	C₂²×D₄₇	1	4	yes	—
256	C₂×SD₁₆	C₂×Dic₄₇	1	16	yes	complemented
257	C₂×SD₁₆	C₂²×D₄₇	1	8	yes	—
258	C₂×D₈	C₂×Dic₄₇	1	8	yes	complemented
259	C₂×D₈	C₂²×D₄₇	1	4	yes	—
260	C₂²×C₈	—	47	2	no	—
261	C₂²×C₈	—	47	4	no	—
262	C₂²×C₈	—	94	4	no	—
263	C₂²×C₈	C₂×Dic₄₇	1	8	yes	complemented
264	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
267	C₄×Q₈	—	47	16	no	—
268	C₄×Q₈	—	94	8	no	—
269	C₄×D₄	—	47	16	no	—
270	C₄×D₄	—	94	8	no	—
271	C₄×D₄	—	94	32	no	—
272	#117	—	47	8	no	—
273	#117	—	94	16	no	—
274	#117	—	94	4	no	—
275	C₂×C₄⋊C₄	—	47	4	no	—
276	C₂×C₄⋊C₄	—	94	4	no	—
277	C₂×C₂²⋊C₄	—	94	4	no	—
278	C₂×C₂²⋊C₄	—	94	2	no	—
279	C₂×C₄²	—	47	4	no	—
280	C₂×C₄²	—	47	1	no	—
281	C₂×C₄²	—	47	1	no	—
282	C₂×C₄²	—	47	2	no	—
283	C₂×C₄²	—	47	4	no	—
284	C₂×C₄²	—	94	16	no	—
285	C₂×C₄²	—	94	4	no	—
286	C₂×C₄²	—	94	2	no	—
287	#107	—	47	8	no	—
288	#106	—	47	8	no	—
289	#103	—	47	16	no	—
290	#102	—	47	16	no	—
291	C₄×C₈	—	47	8	no	—
292	C₄×C₈	—	47	8	no	—
293	C₂⁴	—	2	2	no	—
294	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
295	#41	—	2	32	no	—
296	#41	—	2	16	no	—
297	#41	C₂²×Dic₄₇	1	32	yes	complemented
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
301	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
302	C₂×D₄	—	2	16	no	—
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
307	C₂×D₄	C₂³×D₄₇	1	4	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	16	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	47	2	no	—
312	C₂²×C₄	—	47	2	no	—
313	C₂²×C₄	—	47	8	no	—
314	C₂²×C₄	—	94	8	no	—
315	C₂²×C₄	—	94	16	no	—
316	C₂²×C₄	—	94	4	no	—
317	C₂²×C₄	—	188	16	no	—
318	C₂²×C₄	D₄×D₄₇	1	2	yes	—
319	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	#10625352	1	4	yes	—
321	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
322	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
324	Q₁₆	C₂²×Dic₄₇	1	16	yes	complemented
325	SD₁₆	C₂²×Dic₄₇	1	32	yes	complemented
326	D₈	C₂²×Dic₄₇	1	16	yes	complemented
327	C₂×C₈	—	47	4	no	—
328	C₂×C₈	—	94	4	no	—
329	C₂×C₈	—	94	8	no	—
330	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
331	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
332	C₂×C₈	C₂²×Dic₄₇	1	16	yes	complemented
333	C₂×C₈	C₂³×D₄₇	1	2	yes	—
334	C₂×C₈	C₂³×D₄₇	1	2	yes	—
335	C₄⋊C₄	—	47	8	no	—
336	C₄⋊C₄	—	94	16	no	—
337	C₄⋊C₄	—	94	4	no	—
338	C₂²⋊C₄	—	94	16	no	—
339	C₂²⋊C₄	—	94	8	no	—
340	C₄²	—	47	4	no	—
341	C₄²	—	47	4	no	—
342	C₄²	—	47	4	no	—
343	C₄²	—	47	4	no	—
344	C₄²	—	94	16	no	—
345	C₄²	—	94	8	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	8	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	4	8	no	—
350	C₂³	D₄×Dic₄₇	1	4	yes	—
351	C₂³	C₂×D₄×D₄₇	1	2	yes	—
352	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
353	Q₈	—	2	8	no	—
354	Q₈	—	2	4	no	—
355	Q₈	C₂³×Dic₄₇	1	8	yes	—
356	D₄	—	2	32	no	—
357	D₄	—	2	8	no	—
358	D₄	—	2	4	no	—
359	D₄	C₂³×Dic₄₇	1	8	yes	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	32	no	—
363	C₂×C₄	—	47	8	no	—
364	C₂×C₄	—	47	4	no	—
365	C₂×C₄	—	47	4	no	—
366	C₂×C₄	—	94	16	no	—
367	C₂×C₄	—	94	4	no	—
368	C₂×C₄	—	94	8	no	—
369	C₂×C₄	—	188	32	no	—
370	C₂×C₄	—	188	8	no	—
371	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
372	C₂×C₄	D₄×Dic₄₇	1	8	yes	—
373	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
374	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
375	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
376	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
377	C₂×C₄	C₂×#10625352	1	2	yes	—
378	C₂×C₄	C₂×#10625352	1	4	yes	—
379	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
380	C₈	—	94	4	no	—
381	C₈	C₂³×Dic₄₇	1	4	yes	—
382	C₈	C₂³×Dic₄₇	1	4	yes	—
383	C₂²	—	2	8	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	4	16	no	—
387	C₂²	—	4	8	no	—
388	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
389	C₂²	C₂×D₄×Dic₄₇	1	2	yes	—
390	C₂²	#135×D₄₇	1	4	yes	—
391	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
392	C₄	—	2	8	no	—
393	C₄	—	47	8	no	—
394	C₄	—	94	4	no	—
395	C₄	—	188	8	no	—
396	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
397	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
398	C₄	C₂⁴×Dic₄₇	1	1	yes	characteristic
399	C₄	C₂²×#10625352	1	1	yes	characteristic
400	C₂	—	2	4	no	—
401	C₂	—	4	8	no	—
402	C₂	#135×Dic₄₇	1	4	yes	direct product factor
403	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
404	C₂	C₂×#135×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting, prime radical	C₂²×#135×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂²×#135	D₄₇
hypocenter	C₄₇	C₂×C₄×#135
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#41×Dic₄₇	C₂	semidirect
2. #135×Dic₄₇	C₂	direct (N × H)
3. C₂×Q₁₆×Dic₄₇	C₂	semidirect
4. C₂×SD₁₆×Dic₄₇	C₂	semidirect
5. C₂×D₈×Dic₄₇	C₂	semidirect
6. C₂×#15689161	C₂	semidirect
7. C₂×#15689119	C₂	semidirect
8. C₂²×C₈×Dic₄₇	C₂	semidirect
12. #41×Dic₄₇	C₂²	semidirect
20. Q₁₆×Dic₄₇	C₂²	semidirect
21. SD₁₆×Dic₄₇	C₂²	semidirect
22. D₈×Dic₄₇	C₂²	semidirect
23. #15689161	C₂²	semidirect
26. #15689119	C₂²	semidirect
31. C₂×C₈×Dic₄₇	C₂²	semidirect
33. C₂×#135×C₄₇	C₄	semidirect
72. C₂×#41×C₄₇	C₂×C₄	semidirect
79. #135×C₄₇	C₂×C₄	semidirect
80. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
82. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
84. C₂×D₈×C₄₇	C₂×C₄	semidirect
86. C₂²×C₈×C₄₇	C₂×C₄	semidirect
94. #41×C₄₇	C₂²×C₄	semidirect
121. Q₁₆×C₄₇	C₂²×C₄	semidirect
122. SD₁₆×C₄₇	C₂²×C₄	semidirect
123. D₈×C₄₇	C₂²×C₄	semidirect
126. C₂×C₈×C₄₇	C₂²×C₄	semidirect
174. C₂×Dic₄₇	#135	direct (N × H)
197. Dic₄₇	C₂×#135	direct (N × H)
209. C₂×C₄₇	C₄×#135	semidirect
213. C₂×#135	Dic₄₇	direct (N × H)
241. C₄₇	C₂×C₄×#135	semidirect
244. C₂×#41	C₂×Dic₄₇	semidirect
253. #135	C₂×Dic₄₇	direct (N × H)
254. C₂×Q₁₆	C₂×Dic₄₇	semidirect
256. C₂×SD₁₆	C₂×Dic₄₇	semidirect
258. C₂×D₈	C₂×Dic₄₇	semidirect
263. C₂²×C₈	C₂×Dic₄₇	semidirect
297. #41	C₂²×Dic₄₇	semidirect
324. Q₁₆	C₂²×Dic₄₇	semidirect
325. SD₁₆	C₂²×Dic₄₇	semidirect
326. D₈	C₂²×Dic₄₇	semidirect
332. C₂×C₈	C₂²×Dic₄₇	semidirect
402. C₂	#135×Dic₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#41×Dic₄₇	2
#135×Dic₄₇	2
C₂×Q₁₆×Dic₄₇	2
C₂×SD₁₆×Dic₄₇	2
C₂×D₈×Dic₄₇	2
C₂×#15689161	2
C₂×#15689119	2
C₂²×C₈×Dic₄₇	2
C₂²×#135×C₄₇	2
C₂×C₄×#135	47

Subgroups — C2×#135×Dic47 #27080303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#135×Dic₄₇ #27080303