Subgroups — C₂×#20243434 #26215920

Order 12032.

1346 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689161	C₂	1	2	yes	maximal, complemented
2	C₂×#15689097	C₂	1	2	yes	maximal
3	#20243434	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688880	C₂	1	2	yes	maximal, complemented
5	C₂²×#131×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093983	C₂²	1	4	yes	—
7	#15689161	—	2	4	no	—
8	#15689161	C₂²	1	8	yes	complemented
9	C₂×#13093958	—	2	2	no	—
10	C₂×#13093956	—	2	2	no	—
11	#15689097	—	2	4	no	—
12	#15689097	C₂²	1	8	yes	—
13	C₂×#13093939	—	2	4	no	—
14	#15688880	C₂²	1	8	yes	complemented
15	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#131×C₄₇	—	2	2	no	—
17	C₂×#131×C₄₇	—	2	2	no	—
18	C₂×#131×C₄₇	—	2	4	no	—
19	C₂×#131×C₄₇	C₄	1	4	yes	complemented
20	C₂×#131×C₄₇	C₂²	1	4	yes	—
21	C₂²×M₁₆×C₄₇	C₄	1	2	yes	complemented
22	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₄₇	C₄	1	2	yes	complemented
24	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
25	#13093983	—	2	4	no	—
26	#13093983	—	2	4	no	—
27	#13093983	—	2	4	no	—
28	#13093983	C₂³	1	8	yes	—
29	C₂×C₄⋊Dic₄₇	—	2	4	no	—
30	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
31	C₂×C₄×Dic₄₇	—	2	4	no	—
32	#13093958	—	2	8	no	—
33	#13093956	—	2	8	no	—
34	#13093939	—	2	16	no	—
35	C₂×#41×C₄₇	—	2	2	no	—
36	C₂×#41×C₄₇	—	2	2	no	—
37	C₂×#41×C₄₇	—	2	2	no	—
38	C₂×#41×C₄₇	—	2	2	no	—
39	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
40	C₂×#41×C₄₇	D₄	1	2	yes	—
41	C₂×#41×C₄₇	Q₈	1	2	yes	—
42	C₂×#41×C₄₇	C₂³	1	2	yes	—
43	C₂²×Q₈×C₄₇	Q₈	1	1	yes	characteristic
44	C₂²×D₄×C₄₇	D₄	1	2	yes	—
45	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	#131×C₄₇	—	2	8	no	—
49	#131×C₄₇	—	2	8	no	—
50	#131×C₄₇	—	2	8	no	—
51	#131×C₄₇	—	2	8	no	—
52	C₂×M₁₆×C₄₇	—	2	2	no	—
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	4	no	—
55	C₂×M₁₆×C₄₇	—	2	4	no	—
56	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
58	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₇	—	2	2	no	—
60	C₂²×C₈×C₄₇	—	2	2	no	—
61	C₂²×C₈×C₄₇	—	2	4	no	—
62	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
63	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
67	C₂²×C₈×C₄₇	D₄	1	2	yes	—
68	C₂²×C₈×C₄₇	D₄	1	2	yes	—
69	C₂²×C₈×C₄₇	D₄	1	4	yes	—
70	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
71	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
72	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
73	#41×C₄₇	—	2	4	no	—
74	#41×C₄₇	—	2	4	no	—
75	#41×C₄₇	—	2	4	no	—
76	#41×C₄₇	—	2	4	no	—
77	#41×C₄₇	—	2	4	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
84	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
85	C₂×D₄×C₄₇	—	2	4	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
90	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
91	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
92	C₂×D₄×C₄₇	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
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	C₄⋊C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	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	#41	1	2	yes	—
108	C₂²×C₄×C₄₇	#41	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
110	C₂²×Dic₄₇	—	4	4	no	—
111	M₁₆×C₄₇	—	2	4	no	—
112	M₁₆×C₄₇	—	2	4	no	—
113	M₁₆×C₄₇	—	2	16	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	8	no	—
117	C₂×C₈×C₄₇	—	2	8	no	—
118	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
121	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
122	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
123	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
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	2	yes	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
129	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
130	C₂²⋊Dic₄₇	—	2	8	no	—
131	C₂²⋊Dic₄₇	—	4	4	no	—
132	C₄⋊Dic₄₇	—	2	8	no	—
133	C₄⋊Dic₄₇	—	4	4	no	—
134	C₄×Dic₄₇	—	2	8	no	—
135	C₄×Dic₄₇	—	4	4	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	4	no	—
140	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
142	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₄₇	#121	1	2	yes	—
144	C₂³×C₄₇	#121	1	2	yes	—
145	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₄₇	—	2	4	no	—
147	Q₈×C₄₇	—	2	4	no	—
148	D₄×C₄₇	—	2	8	no	—
149	D₄×C₄₇	—	2	8	no	—
150	D₄×C₄₇	—	2	4	no	—
151	D₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
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	—	2	4	no	—
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#117	1	2	yes	—
166	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#121	1	2	yes	—
168	C₂×C₄×C₄₇	#121	1	2	yes	—
169	C₂×C₄×C₄₇	C₂²⋊Q₈	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	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
177	C₂×Dic₄₇	—	4	8	no	—
178	C₂×Dic₄₇	—	8	8	no	—
179	C₈×C₄₇	—	2	4	no	—
180	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
181	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
182	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂×#1812	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	4	no	—
187	C₂²×C₄₇	—	4	1	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	1	no	—
190	C₂²×C₄₇	—	4	4	no	—
191	C₂²×C₄₇	—	4	4	no	—
192	C₂²×C₄₇	—	4	4	no	—
193	C₂²×C₄₇	#380	1	1	yes	characteristic
194	C₂²×C₄₇	#380	1	2	yes	—
195	C₂²×C₄₇	#380	1	1	yes	characteristic
196	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×#121	1	2	yes	—
198	C₄×C₄₇	—	2	4	no	—
199	C₄×C₄₇	#380	1	1	yes	characteristic
200	C₄×C₄₇	#380	1	1	yes	characteristic
201	C₄×C₄₇	#380	1	2	yes	—
202	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
203	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
204	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
205	Dic₄₇	—	8	8	no	—
206	C₂²×#131	D₄₇	1	1	yes	characteristic
207	C₂×#427	—	47	2	no	—
208	C₂×#410	—	47	2	no	—
209	#1812	—	47	8	no	—
210	C₂×H(3,ℤ/4)	—	47	2	no	—
211	C₂×C₄₇	—	2	2	no	—
212	C₂×C₄₇	—	2	1	no	—
213	C₂×C₄₇	—	2	1	no	—
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	—	4	4	no	—
216	C₂×C₄₇	#1812	1	2	yes	complemented
217	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
218	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
219	C₂×#131	—	2	2	no	—
220	C₂×#131	—	2	2	no	—
221	C₂×#131	—	2	4	no	—
222	C₂×#131	Dic₄₇	1	4	yes	complemented
223	C₂×#131	C₂×D₄₇	1	4	yes	—
224	C₂²×M₁₆	Dic₄₇	1	2	yes	complemented
225	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
226	C₂³×C₈	Dic₄₇	1	2	yes	complemented
227	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
228	C₂×#117	—	47	4	no	—
229	#427	—	47	8	no	—
230	#427	—	94	4	no	—
231	C₂×#107	—	94	2	no	—
232	C₂×#106	—	94	2	no	—
233	#410	—	47	8	no	—
234	#410	—	94	4	no	—
235	C₂×#99	—	94	4	no	—
236	H(3,ℤ/4)	—	47	8	no	—
237	C₄₇	C₂×#1812	1	1	yes	characteristic, complemented, Sylow
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	—	2	2	no	—
242	C₂×#41	Dic₉₄	1	2	yes	—
243	C₂×#41	D₁₈₈	1	2	yes	—
244	C₂×#41	C₂×Dic₄₇	1	2	yes	—
245	C₂×#41	C₂²×D₄₇	1	2	yes	—
246	C₂²×Q₈	Dic₉₄	1	1	yes	characteristic
247	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
248	C₂²×D₄	D₁₈₈	1	2	yes	—
249	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
250	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
251	#131	—	2	8	no	—
252	#131	—	2	8	no	—
253	#131	—	2	8	no	—
254	#131	—	2	8	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	4	no	—
258	C₂×M₁₆	—	2	4	no	—
259	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
260	C₂×M₁₆	C₂×Dic₄₇	1	8	yes	complemented
261	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	2	4	no	—
265	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
266	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
267	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
268	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
269	C₂²×C₈	C₂×Dic₄₇	1	8	yes	complemented
270	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
271	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
272	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
273	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
274	#117	—	47	8	no	—
275	#117	—	94	4	no	—
276	#117	—	94	4	no	—
277	#117	—	94	4	no	—
278	C₂×C₄⋊C₄	—	94	4	no	—
279	C₂×C₂²⋊C₄	—	94	4	no	—
280	C₂×C₄²	—	94	4	no	—
281	#107	—	94	8	no	—
282	#106	—	94	8	no	—
283	#99	—	94	16	no	—
284	C₂⁴	C₄⋊Dic₄₇	1	2	yes	—
285	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	#41	—	2	4	no	—
290	#41	—	2	4	no	—
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	#41	—	2	4	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
297	C₂×Q₈	C₂×Dic₉₄	1	2	yes	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
303	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	—
304	C₂×D₄	C₂×Dic₉₄	1	2	yes	—
305	C₂×D₄	C₂×D₁₈₈	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	188	4	no	—
311	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
312	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
313	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
316	C₂²×C₄	#10625350	1	2	yes	—
317	C₂²×C₄	#10625350	1	2	yes	—
318	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
319	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
323	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
324	M₁₆	—	2	4	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	2	16	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	8	no	—
330	C₂×C₈	—	2	8	no	—
331	C₂×C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
332	C₂×C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
333	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
334	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
335	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
336	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
337	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
338	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
339	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
340	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
341	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
342	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
343	C₄⋊C₄	—	94	8	no	—
344	C₄⋊C₄	—	188	4	no	—
345	C₂²⋊C₄	—	94	8	no	—
346	C₂²⋊C₄	—	188	4	no	—
347	C₄²	—	94	8	no	—
348	C₄²	—	188	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	4	no	—
353	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
354	C₂³	C₂×C₄⋊Dic₄₇	1	4	yes	—
355	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
356	C₂³	#13093998	1	2	yes	—
357	C₂³	#13093998	1	2	yes	—
358	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
359	Q₈	—	2	4	no	—
360	Q₈	—	2	4	no	—
361	D₄	—	2	8	no	—
362	D₄	—	2	8	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	376	8	no	—
372	C₂×C₄	—	188	8	no	—
373	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
376	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
377	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
379	C₂×C₄	#13093983	1	1	yes	characteristic
380	C₂×C₄	#13093983	1	2	yes	—
381	C₂×C₄	#13093983	1	1	yes	characteristic
382	C₂×C₄	#13093998	1	2	yes	—
383	C₂×C₄	#13093998	1	2	yes	—
384	C₂×C₄	#13094003	1	2	yes	—
385	C₂×C₄	#13094003	1	2	yes	—
386	C₂×C₄	#13094003	1	2	yes	—
387	C₂×C₄	#13094003	1	2	yes	—
388	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
390	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
391	C₂×C₄	C₂×#10625350	1	2	yes	—
392	C₈	—	2	4	no	—
393	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
394	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
395	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	#15688983	1	1	yes	characteristic
406	C₂²	#15688983	1	2	yes	—
407	C₂²	#15688983	1	1	yes	characteristic
408	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
409	C₂²	C₂×#13093998	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	376	8	no	—
412	C₄	#15688983	1	1	yes	characteristic
413	C₄	#15688983	1	1	yes	characteristic
414	C₄	#15688983	1	2	yes	—
415	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
416	C₄	C₂×#13093983	1	1	yes	characteristic
417	C₄	C₂×#13094003	1	2	yes	—
418	C₂	—	2	2	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	2	no	—
422	C₂	—	4	4	no	—
423	C₂	#20243434	1	2	yes	direct product factor
424	C₂	C₂×#15688983	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093983
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#131×C₄₇	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#131	D₄₇
hypocenter	C₄₇	C₂×#1812
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
1. C₂×#15689161	C₂	semidirect
3. #20243434	C₂	direct (N × H)
4. C₂×#15688880	C₂	semidirect
8. #15689161	C₂²	semidirect
14. #15688880	C₂²	semidirect
19. C₂×#131×C₄₇	C₄	semidirect
21. C₂²×M₁₆×C₄₇	C₄	semidirect
23. C₂³×C₈×C₄₇	C₄	semidirect
57. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
66. C₂²×C₈×C₄₇	C₂×C₄	semidirect
216. C₂×C₄₇	#1812	semidirect
222. C₂×#131	Dic₄₇	semidirect
224. C₂²×M₁₆	Dic₄₇	semidirect
226. C₂³×C₈	Dic₄₇	semidirect
237. C₄₇	C₂×#1812	semidirect
260. C₂×M₁₆	C₂×Dic₄₇	semidirect
269. C₂²×C₈	C₂×Dic₄₇	semidirect
423. C₂	#20243434	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×#15689161	2
C₂×#15689097	2
#20243434	2
C₂×#15688880	2
C₂²×#131×C₄₇	2
C₂×#1812	47

Subgroups — C2×#20243434 #26215920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243434 #26215920