Subgroups — C₂×#20241935 #26183538

Order 12032.

1302 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689180	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15688991	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241935	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688857	C₂	1	4	yes	maximal, complemented
5	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
6	#15689180	—	2	2	no	—
7	#15689180	C₂²	1	4	yes	complemented
8	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
9	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
10	C₂×#13093935	—	2	1	no	—
11	#15688991	—	2	2	no	—
12	#15688991	C₂²	1	4	yes	complemented
13	C₂×C₄₇⋊#95	—	2	1	no	—
14	C₂×C₄₇⋊#95	—	2	1	no	—
15	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
16	#15688857	C₂²	1	16	yes	complemented
17	C₂²×#41×C₄₇	—	2	1	no	—
18	C₄₇×#532	—	2	2	no	—
19	C₄₇×#532	—	2	2	no	—
20	C₄₇×#532	C₄	1	4	yes	complemented
21	C₄₇×#532	C₂²	1	4	yes	—
22	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
23	C₂×#127×C₄₇	C₄	1	1	yes	characteristic, complemented
24	C₂×#124×C₄₇	—	2	1	no	—
25	C₂×#121×C₄₇	—	2	1	no	—
26	C₂×#121×C₄₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₄₇	—	2	1	no	—
28	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	complemented
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂³×Dic₄₇	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
33	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
35	#13093935	—	2	4	no	—
36	C₄₇⋊#95	—	2	4	no	—
37	C₄₇⋊#95	—	2	4	no	—
38	C₄₇⋊#95	—	2	2	no	—
39	C₄₇⋊#95	C₂³	1	4	yes	—
40	C₂×#41×C₄₇	—	2	4	no	—
41	C₂×#41×C₄₇	—	2	4	no	—
42	C₂×#41×C₄₇	—	4	8	no	—
43	C₂²×Q₈×C₄₇	—	2	1	no	—
44	C₂²×D₄×C₄₇	—	2	2	no	—
45	C₂²×D₄×C₄₇	—	2	1	no	—
46	C₂²×D₄×C₄₇	—	2	1	no	—
47	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₄₇	—	2	2	no	—
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₄⋊Q₈×C₄₇	—	2	2	no	—
53	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
54	#127×C₄₇	—	2	2	no	—
55	#127×C₄₇	C₂×C₄	1	4	yes	complemented
56	#124×C₄₇	—	2	4	no	—
57	#124×C₄₇	—	2	4	no	—
58	#121×C₄₇	—	2	4	no	—
59	#121×C₄₇	—	2	4	no	—
60	#121×C₄₇	—	2	2	no	—
61	#121×C₄₇	—	2	2	no	—
62	#121×C₄₇	C₂×C₄	1	4	yes	—
63	#121×C₄₇	C₂³	1	4	yes	—
64	C₄×D₄×C₄₇	—	2	4	no	—
65	C₄×D₄×C₄₇	—	2	4	no	—
66	C₄×D₄×C₄₇	—	2	4	no	—
67	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₄₇	D₄	1	2	yes	—
76	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	D₄	1	2	yes	—
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	C₂⁴×C₄₇	—	2	2	no	—
81	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
82	#41×C₄₇	—	4	16	no	—
83	#41×C₄₇	—	4	16	no	—
84	C₂×Q₈×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	—	4	4	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	4	no	—
90	C₂×D₄×C₄₇	—	2	4	no	—
91	C₂×D₄×C₄₇	—	4	4	no	—
92	C₂×D₄×C₄₇	—	4	4	no	—
93	C₂×D₄×C₄₇	—	4	4	no	—
94	C₂×D₄×C₄₇	—	4	8	no	—
95	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	8	no	—
99	C₂²×C₄×C₄₇	—	4	2	no	—
100	C₂²×C₄×C₄₇	—	4	2	no	—
101	C₂²×C₄×C₄₇	—	4	8	no	—
102	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
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	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂²×Dic₄₇	—	2	4	no	—
117	C₂²×Dic₄₇	—	4	4	no	—
118	C₂²×Dic₄₇	—	4	4	no	—
119	C₂²×Dic₄₇	—	4	4	no	—
120	C₄⋊C₄×C₄₇	—	2	4	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
123	C₂²⋊C₄×C₄₇	—	2	4	no	—
124	C₂²⋊C₄×C₄₇	—	2	8	no	—
125	C₂²⋊C₄×C₄₇	—	2	4	no	—
126	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
131	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
132	C₄²×C₄₇	C₂×D₄	1	2	yes	—
133	C₄²×C₄₇	C₂×D₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	4	4	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	2	4	no	—
139	C₂³×C₄₇	—	4	4	no	—
140	C₂³×C₄₇	—	4	4	no	—
141	C₂³×C₄₇	—	4	4	no	—
142	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
145	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₄₇	—	4	8	no	—
147	D₄×C₄₇	—	4	4	no	—
148	D₄×C₄₇	—	4	4	no	—
149	D₄×C₄₇	—	4	8	no	—
150	D₄×C₄₇	—	4	8	no	—
151	D₄×C₄₇	—	4	8	no	—
152	D₄×C₄₇	—	4	8	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	16	no	—
169	C₂×C₄×C₄₇	—	4	4	no	—
170	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×Dic₄₇	—	4	4	no	—
179	C₂×Dic₄₇	—	4	4	no	—
180	C₂×Dic₄₇	—	4	4	no	—
181	C₂×Dic₄₇	—	8	8	no	—
182	C₄₇⋊C₈	—	4	4	no	—
183	C₂×#1514	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	1	no	—
186	C₂²×C₄₇	—	2	1	no	—
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	8	no	—
189	C₂²×C₄₇	—	4	4	no	—
190	C₂²×C₄₇	—	4	4	no	—
191	C₂²×C₄₇	—	4	4	no	—
192	C₂²×C₄₇	—	8	8	no	—
193	C₂²×C₄₇	#410	1	2	yes	—
194	C₂²×C₄₇	#418	1	2	yes	—
195	C₂²×C₄₇	#418	1	2	yes	—
196	C₂²×C₄₇	#421	1	2	yes	—
197	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	2	1	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	4	4	no	—
208	Dic₄₇	—	8	4	no	—
209	C₂×#532	D₄₇	1	1	yes	characteristic
210	C₂×#432	—	47	1	no	—
211	C₂×#383	—	47	1	no	—
212	#1514	—	47	8	no	—
213	C₂×#327	—	47	4	no	—
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	—	2	2	no	—
216	C₂×C₄₇	—	8	4	no	—
217	C₂×C₄₇	#1514	1	4	yes	complemented
218	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
220	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
221	C₂²×#41	—	2	1	no	—
222	#532	—	2	2	no	—
223	#532	—	2	2	no	—
224	#532	Dic₄₇	1	4	yes	complemented
225	#532	C₂×D₄₇	1	4	yes	—
226	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
227	C₂×#127	Dic₄₇	1	1	yes	characteristic, complemented
228	C₂×#124	—	2	1	no	—
229	C₂×#121	—	2	1	no	—
230	C₂×#121	C₂×D₄₇	1	2	yes	—
231	C₂×C₄×D₄	—	2	1	no	—
232	C₂×C₄×D₄	Dic₄₇	1	2	yes	complemented
233	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
234	#432	—	47	4	no	—
235	#432	—	94	2	no	—
236	C₂×C₄⋊C₈	—	94	1	no	—
237	C₂×C₂²⋊C₈	—	47	2	no	—
238	C₂×#97	—	94	1	no	—
239	#383	—	47	4	no	—
240	#383	—	94	2	no	—
241	C₂×#95	—	47	2	no	—
242	C₂×#95	—	94	1	no	—
243	C₂×#95	—	94	1	no	—
244	#327	—	47	16	no	—
245	C₄₇	C₂×#1514	1	1	yes	characteristic, complemented, Sylow
246	C₂×#41	—	2	4	no	—
247	C₂×#41	—	2	4	no	—
248	C₂×#41	—	4	8	no	—
249	C₂²×Q₈	—	2	1	no	—
250	C₂²×D₄	—	2	2	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	—	94	2	no	—
256	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
257	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
258	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
259	C₂²×C₈	—	94	2	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
262	#127	—	2	2	no	—
263	#127	C₂×Dic₄₇	1	4	yes	complemented
264	#124	—	2	4	no	—
265	#124	—	2	4	no	—
266	#121	—	2	4	no	—
267	#121	—	2	4	no	—
268	#121	—	2	2	no	—
269	#121	—	2	2	no	—
270	#121	C₂×Dic₄₇	1	4	yes	—
271	#121	C₂²×D₄₇	1	4	yes	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
281	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
282	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
283	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
284	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
285	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
286	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
287	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
288	C₄⋊C₈	—	94	4	no	—
289	C₂²⋊C₈	—	47	4	no	—
290	C₂²⋊C₈	—	94	2	no	—
291	#97	—	94	4	no	—
292	#95	—	47	4	no	—
293	#95	—	94	2	no	—
294	#95	—	94	4	no	—
295	#95	—	94	4	no	—
296	C₂⁴	—	2	2	no	—
297	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
298	#41	—	4	16	no	—
299	#41	—	4	16	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	4	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	8	no	—
311	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	8	no	—
318	C₂²×C₄	—	94	4	no	—
319	C₂²×C₄	—	188	4	no	—
320	C₂²×C₄	—	188	4	no	—
321	C₂²×C₄	—	188	4	no	—
322	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
323	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂²⋊Dic₄₇	1	2	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	1	yes	characteristic
332	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
334	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
335	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
336	C₂×C₈	—	94	4	no	—
337	C₂×C₈	—	188	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
345	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
346	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
347	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
348	C₄²	C₂²×Dic₄₇	1	2	yes	—
349	C₄²	C₂²×Dic₄₇	1	2	yes	—
350	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
351	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
359	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
360	C₂³	#13094050	1	4	yes	—
361	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
362	Q₈	—	4	8	no	—
363	D₄	—	4	4	no	—
364	D₄	—	4	8	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	8	no	—
367	D₄	—	4	8	no	—
368	D₄	—	4	8	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	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	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	376	8	no	—
387	C₂×C₄	—	188	4	no	—
388	C₂×C₄	—	188	4	no	—
389	C₂×C₄	—	188	4	no	—
390	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
393	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
394	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
395	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
396	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
398	C₈	—	188	4	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	8	no	—
408	C₂²	#15689097	1	2	yes	—
409	C₂²	#15689128	1	2	yes	—
410	C₂²	#15689128	1	2	yes	—
411	C₂²	#15689140	1	2	yes	—
412	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
413	C₂²	C₂×#13094050	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	4	no	—
423	C₄	—	376	4	no	—
424	C₂	—	2	2	no	—
425	C₂	—	2	2	no	—
426	C₂	—	8	4	no	—
427	C₂	#20241935	1	4	yes	direct product factor
428	C₂	C₂×#15689097	1	1	yes	characteristic
429	C₂	C₂×#15689128	1	1	yes	characteristic
430	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	C₂×#1514
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂×#15689180	C₂	semidirect
2. C₂×#15688991	C₂	semidirect
3. #20241935	C₂	direct (N × H)
4. C₂×#15688857	C₂	semidirect
7. #15689180	C₂²	semidirect
12. #15688991	C₂²	semidirect
16. #15688857	C₂²	semidirect
20. C₄₇×#532	C₄	semidirect
22. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
23. C₂×#127×C₄₇	C₄	semidirect
28. C₂×C₄×D₄×C₄₇	C₄	semidirect
53. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
55. #127×C₄₇	C₂×C₄	semidirect
67. C₄×D₄×C₄₇	C₂×C₄	semidirect
217. C₂×C₄₇	#1514	semidirect
224. #532	Dic₄₇	semidirect
226. C₂×C₄⋊Q₈	Dic₄₇	semidirect
227. C₂×#127	Dic₄₇	semidirect
232. C₂×C₄×D₄	Dic₄₇	semidirect
245. C₄₇	C₂×#1514	semidirect
261. C₄⋊Q₈	C₂×Dic₄₇	semidirect
263. #127	C₂×Dic₄₇	semidirect
275. C₄×D₄	C₂×Dic₄₇	semidirect
427. C₂	#20241935	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×#15689180	2
C₂×#15688991	2
#20241935	2
C₂×#15688857	2
C₂×C₄₇×#532	2
C₂×#1514	47

Subgroups — C2×#20241935 #26183538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241935 #26183538