Subgroups — C₂×#20253936 #27085930

Order 12032.

1902 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689679	C₂	1	1	yes	maximal, characteristic
2	C₂×#125×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20253936	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689531	C₂	1	2	yes	maximal, complemented
5	C₂×#15689530	C₂	1	2	yes	maximal, complemented
6	C₂×#15689525	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689522	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689522	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689164	C₂	1	2	yes	maximal
10	C₂×#15689162	C₂	1	2	yes	maximal
11	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10625324	C₂²	1	1	yes	characteristic
14	C₂²×#10625324	C₂²	1	1	yes	characteristic
15	#15689679	—	2	4	no	—
16	#15689679	C₂²	1	8	yes	—
17	C₂×#13094023	C₂²	1	2	yes	—
18	C₂×#13094016	C₂²	1	1	yes	characteristic
19	C₂×#13094016	C₂²	1	1	yes	characteristic
20	C₂×#13094015	C₂²	1	2	yes	—
21	C₂×#13094014	—	2	2	no	—
22	#125×D₄₇	—	2	4	no	—
23	#125×D₄₇	C₂²	1	8	yes	—
24	C₂×#13094002	—	2	2	no	—
25	C₂×#13093989	—	2	2	no	—
26	C₂×#13093982	C₂²	1	2	yes	—
27	C₂×C₄⋊C₄×D₄₇	—	2	2	no	—
28	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
29	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
30	#15689531	C₂²	1	16	yes	complemented
31	#15689530	C₂²	1	16	yes	complemented
32	#15689525	C₂²	1	8	yes	complemented
33	#15689522	C₂²	1	8	yes	complemented
34	#15689522	C₂²	1	8	yes	complemented
35	#15689164	C₂²	1	16	yes	—
36	#15689162	C₂²	1	16	yes	—
37	C₂×#13093958	C₂²	1	2	yes	—
38	C₂×#13093957	C₂²	1	2	yes	—
39	C₂×#13093957	C₂²	1	2	yes	—
40	C₂×#13093956	C₂²	1	2	yes	—
41	C₂×#13093955	C₂²	1	2	yes	—
42	C₂×#13093955	C₂²	1	2	yes	—
43	C₄×#10625324	C₂²	1	8	yes	—
44	C₂×#13093934	C₂²	1	1	yes	characteristic
45	C₂×#13093934	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
48	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
49	C₄₇×#499	C₂²	1	8	yes	complemented
50	C₂×#107×C₄₇	C₂²	1	2	yes	—
51	C₂×#106×C₄₇	C₂²	1	2	yes	—
52	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂²×Dic₉₄	—	2	2	no	—
54	C₂²×C₄×D₄₇	—	2	2	no	—
55	C₂²×C₄×D₄₇	D₄	1	2	yes	—
56	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
57	C₂×#10625324	Q₈	1	8	yes	complemented
58	C₂×#10625324	Q₈	1	8	yes	complemented
59	C₂×#10625324	C₂³	1	4	yes	—
60	C₂×#10625324	C₂³	1	4	yes	—
61	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
63	#13094023	—	2	4	no	—
64	#13094023	C₂³	1	8	yes	—
65	#13094016	—	2	2	no	—
66	#13094016	—	2	2	no	—
67	#13094016	C₂³	1	4	yes	—
68	#13094016	C₂³	1	4	yes	—
69	#13094015	—	2	4	no	—
70	#13094015	C₂³	1	8	yes	—
71	#13094014	—	2	16	no	—
72	#13094002	—	2	16	no	—
73	#13093989	—	2	16	no	—
74	#13093982	—	2	4	no	—
75	#13093982	C₂³	1	8	yes	—
76	C₂×C₄⋊Dic₄₇	—	2	2	no	—
77	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
78	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
79	C₂×Dic₄₇⋊C₄	—	2	2	no	—
80	C₂×Dic₄₇⋊C₄	—	2	2	no	—
81	C₂×Dic₄₇⋊C₄	—	2	2	no	—
82	C₂×Dic₄₇⋊C₄	—	2	2	no	—
83	C₂×Dic₄₇⋊C₄	—	2	2	no	—
84	C₄⋊C₄×D₄₇	—	2	16	no	—
85	C₄⋊C₄×D₄₇	—	2	4	no	—
86	C₄⋊C₄×D₄₇	C₂³	1	8	yes	—
87	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
88	C₂×C₄×Dic₄₇	—	2	2	no	—
89	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
90	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
91	C₄²×D₄₇	D₄	1	4	yes	—
92	C₄²×D₄₇	C₂³	1	4	yes	—
93	#13093958	C₂³	1	8	yes	—
94	#13093957	C₂³	1	8	yes	—
95	#13093957	C₂³	1	8	yes	—
96	#13093956	C₂³	1	8	yes	—
97	#13093955	C₂³	1	8	yes	—
98	#13093955	C₂³	1	8	yes	—
99	#13093934	C₂³	1	4	yes	—
100	#13093934	C₂³	1	4	yes	—
101	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
102	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	#125×C₄₇	—	2	2	no	—
105	#125×C₄₇	—	2	2	no	—
106	#125×C₄₇	C₂³	1	4	yes	—
107	#125×C₄₇	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
113	#107×C₄₇	C₂³	1	8	yes	—
114	#106×C₄₇	C₂³	1	8	yes	—
115	C₄×C₈×C₄₇	C₂³	1	4	yes	—
116	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
121	C₂²×Dic₄₇	—	2	2	no	—
122	C₂²×Dic₄₇	—	2	2	no	—
123	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
124	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×D₄₇	—	2	8	no	—
126	C₂×C₄×D₄₇	—	4	4	no	—
127	C₂×C₄×D₄₇	—	4	8	no	—
128	C₂×C₄×D₄₇	C₂×D₄	1	8	yes	—
129	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
130	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
131	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
132	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
133	C₂×Dic₉₄	—	2	8	no	—
134	C₂×Dic₉₄	—	4	8	no	—
135	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	—
136	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	—
137	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
138	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
139	C₄⋊C₄×C₄₇	—	2	8	no	—
140	C₄⋊C₄×C₄₇	—	2	8	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₄⋊C₄×C₄₇	—	2	2	no	—
143	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
144	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
145	C₄²×C₄₇	C₂×D₄	1	2	yes	—
146	C₄²×C₄₇	C₂⁴	1	2	yes	—
147	(C₂×D₄₇)⋊C₄	—	2	8	no	—
148	C₄⋊Dic₄₇	—	2	2	no	—
149	C₄⋊Dic₄₇	—	2	2	no	—
150	C₄⋊Dic₄₇	—	2	8	no	—
151	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
152	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
153	Dic₄₇⋊C₄	—	2	8	no	—
154	Dic₄₇⋊C₄	—	2	8	no	—
155	Dic₄₇⋊C₄	—	2	8	no	—
156	Dic₄₇⋊C₄	—	2	8	no	—
157	Dic₄₇⋊C₄	—	2	8	no	—
158	C₄×Dic₄₇	—	2	8	no	—
159	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
160	C₄×Dic₄₇	C₂×D₄	1	8	yes	—
161	C₄×Dic₄₇	C₂⁴	1	2	yes	—
162	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
163	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
164	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
165	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
166	#10625324	C₂×Q₈	1	16	yes	complemented
167	#10625324	C₂×Q₈	1	16	yes	complemented
168	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂²×D₄₇	—	2	4	no	—
170	C₂²×D₄₇	C₄⋊Q₈	1	4	yes	—
171	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	4	4	no	—
176	C₂×C₄×C₄₇	—	4	4	no	—
177	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
180	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
181	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
182	C₂×Dic₄₇	—	2	4	no	—
183	C₂×Dic₄₇	—	2	4	no	—
184	C₂×Dic₄₇	—	2	4	no	—
185	C₂×Dic₄₇	—	4	4	no	—
186	C₂×Dic₄₇	—	4	4	no	—
187	C₂×Dic₄₇	C₄⋊Q₈	1	4	yes	—
188	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
189	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
190	C₄×D₄₇	—	4	8	no	—
191	C₄×D₄₇	—	4	16	no	—
192	C₄×D₄₇	C₄⋊Q₈	1	8	yes	—
193	C₄×D₄₇	C₂²×Q₈	1	4	yes	—
194	C₄×D₄₇	C₂²×Q₈	1	4	yes	—
195	Dic₉₄	—	4	16	no	—
196	C₈×C₄₇	C₂²×Q₈	1	4	yes	—
197	C₈×C₄₇	C₂²×Q₈	1	4	yes	—
198	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	—
199	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	—
200	C₂×#3166	—	47	1	no	maximal, Sylow
201	C₂²×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
202	C₂²×C₄₇	#575	1	4	yes	—
203	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
204	C₂×D₄₇	—	2	8	no	—
205	C₂×D₄₇	—	2	4	no	—
206	C₂×D₄₇	C₂×C₄⋊Q₈	1	4	yes	—
207	C₄×C₄₇	—	2	4	no	—
208	C₄×C₄₇	—	4	4	no	—
209	C₄×C₄₇	—	4	4	no	—
210	C₄×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
211	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
212	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
213	Dic₄₇	—	2	4	no	—
214	Dic₄₇	—	4	4	no	—
215	Dic₄₇	—	4	4	no	—
216	Dic₄₇	C₂×C₄⋊Q₈	1	4	yes	—
217	C₂×#533	—	47	1	no	—
218	C₂²×#125	—	47	1	no	—
219	#3166	—	47	16	no	—
220	C₂×#501	—	47	2	no	—
221	C₂×#501	—	47	2	no	—
222	C₂×#499	—	47	1	no	—
223	C₂×#499	—	47	1	no	—
224	C₂×#499	—	47	1	no	—
225	C₂×#499	D₄₇	1	1	yes	characteristic, complemented
226	C₂×#428	—	47	2	no	—
227	C₂×#428	—	47	2	no	—
228	C₂×C₄×M₁₆	—	47	1	no	—
229	C₂×C₄₇	#3166	1	4	yes	complemented
230	C₂×C₄₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#575	1	2	yes	—
232	D₄₇	—	2	4	no	—
233	C₂²×M₁₆	—	47	1	no	—
234	C₂²×M₁₆	—	47	1	no	—
235	#533	—	47	8	no	—
236	#533	—	94	4	no	—
237	C₂×C₄⋊Q₈	—	47	2	no	—
238	C₂×#125	—	47	8	no	—
239	C₂×#125	—	47	2	no	—
240	C₂×#125	—	47	1	no	—
241	C₂×#125	—	47	1	no	—
242	C₂×#125	—	94	2	no	—
243	C₂×#125	—	94	4	no	—
244	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
245	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
246	C₂×C₂²⋊Q₈	—	94	2	no	—
247	C₂×C₄×Q₈	—	94	2	no	—
248	C₂×#117	—	47	2	no	—
249	C₂²×C₄⋊C₄	—	47	2	no	—
250	C₂²×C₄⋊C₄	—	94	2	no	—
251	C₂²×C₄²	—	47	1	no	—
252	#501	—	47	16	no	—
253	#501	—	47	16	no	—
254	#499	—	47	8	no	—
255	#499	—	47	8	no	—
256	#499	—	47	8	no	—
257	#499	C₂×D₄₇	1	8	yes	complemented
258	#428	—	47	16	no	—
259	#428	—	47	16	no	—
260	C₂×#107	—	47	2	no	—
261	C₂×#107	—	47	2	no	—
262	C₂×#107	—	47	2	no	—
263	C₂×#107	C₂×D₄₇	1	2	yes	—
264	C₂×#106	—	47	2	no	—
265	C₂×#106	—	47	2	no	—
266	C₂×#106	—	47	2	no	—
267	C₂×#106	C₂×D₄₇	1	2	yes	—
268	C₄×M₁₆	—	47	8	no	—
269	C₂×#97	—	47	1	no	—
270	C₂×#97	—	47	1	no	—
271	C₂×C₄×C₈	—	47	1	no	—
272	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
273	C₄₇	C₂×#3166	1	1	yes	characteristic, complemented, Sylow
274	C₂²×Q₈	—	94	2	no	—
275	C₂³×C₄	—	47	1	no	—
276	C₂³×C₄	—	47	2	no	—
277	C₂³×C₄	—	94	2	no	—
278	C₂×M₁₆	—	47	8	no	—
279	C₂×M₁₆	—	47	8	no	—
280	C₂×M₁₆	—	47	4	no	—
281	C₂×M₁₆	—	47	4	no	—
282	C₂²×C₈	—	47	1	no	—
283	C₂²×C₈	—	47	1	no	—
284	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
285	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
286	C₄⋊Q₈	—	47	8	no	—
287	C₄⋊Q₈	—	94	4	no	—
288	#125	—	2	2	no	—
289	#125	—	2	2	no	—
290	#125	—	47	8	no	—
291	#125	—	47	4	no	—
292	#125	—	47	4	no	—
293	#125	—	94	16	no	—
294	#125	—	94	4	no	—
295	#125	—	94	2	no	—
296	#125	—	94	2	no	—
297	#125	C₂²×D₄₇	1	4	yes	—
298	#125	C₂²×D₄₇	1	4	yes	—
299	C₂²⋊Q₈	—	94	16	no	—
300	C₄×Q₈	—	94	16	no	—
301	#117	—	47	8	no	—
302	#117	—	94	4	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	47	2	no	—
306	C₂×C₄⋊C₄	—	47	2	no	—
307	C₂×C₄⋊C₄	—	47	8	no	—
308	C₂×C₄⋊C₄	—	94	4	no	—
309	C₂×C₄⋊C₄	—	94	16	no	—
310	C₂×C₄⋊C₄	—	94	2	no	—
311	C₂×C₄⋊C₄	—	94	2	no	—
312	C₂×C₄⋊C₄	—	94	2	no	—
313	C₂×C₄⋊C₄	—	94	2	no	—
314	C₂×C₄⋊C₄	—	94	2	no	—
315	C₂×C₄⋊C₄	—	94	2	no	—
316	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
317	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
318	C₂×C₂²⋊C₄	—	94	2	no	—
319	C₂×C₄²	—	47	2	no	—
320	C₂×C₄²	—	47	1	no	—
321	C₂×C₄²	—	47	4	no	—
322	C₂×C₄²	—	47	4	no	—
323	C₂×C₄²	—	94	2	no	—
324	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
325	#107	—	47	8	no	—
326	#107	—	47	8	no	—
327	#107	—	47	8	no	—
328	#107	C₂²×D₄₇	1	8	yes	—
329	#106	—	47	8	no	—
330	#106	—	47	8	no	—
331	#106	—	47	8	no	—
332	#106	C₂²×D₄₇	1	8	yes	—
333	#97	—	47	4	no	—
334	#97	—	47	4	no	—
335	C₄×C₈	—	47	4	no	—
336	C₄×C₈	C₂²×D₄₇	1	4	yes	—
337	C₂⁴	—	47	1	no	—
338	C₂×Q₈	—	94	8	no	—
339	C₂×Q₈	—	188	8	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	47	1	no	—
343	C₂²×C₄	—	47	2	no	—
344	C₂²×C₄	—	47	4	no	—
345	C₂²×C₄	—	47	4	no	—
346	C₂²×C₄	—	47	2	no	—
347	C₂²×C₄	—	47	2	no	—
348	C₂²×C₄	—	47	8	no	—
349	C₂²×C₄	—	94	8	no	—
350	C₂²×C₄	—	94	2	no	—
351	C₂²×C₄	—	94	2	no	—
352	C₂²×C₄	—	188	4	no	—
353	C₂²×C₄	—	188	8	no	—
354	C₂²×C₄	D₄×D₄₇	1	2	yes	—
355	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
356	M₁₆	—	47	16	no	—
357	M₁₆	—	47	16	no	—
358	C₂×C₈	—	47	4	no	—
359	C₂×C₈	—	47	4	no	—
360	C₂×C₈	—	47	2	no	—
361	C₂×C₈	—	47	2	no	—
362	C₂×C₈	Q₈×D₄₇	1	4	yes	—
363	C₂×C₈	Q₈×D₄₇	1	4	yes	—
364	C₂×C₈	C₂³×D₄₇	1	2	yes	—
365	C₂×C₈	C₂³×D₄₇	1	2	yes	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	47	4	no	—
371	C₄⋊C₄	—	47	4	no	—
372	C₄⋊C₄	—	94	8	no	—
373	C₄⋊C₄	—	94	8	no	—
374	C₄⋊C₄	—	94	8	no	—
375	C₄⋊C₄	—	94	8	no	—
376	C₄⋊C₄	—	94	8	no	—
377	C₄⋊C₄	—	94	8	no	—
378	C₄⋊C₄	—	94	2	no	—
379	C₄⋊C₄	—	94	2	no	—
380	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
381	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
382	C₂²⋊C₄	—	94	8	no	—
383	C₄²	—	47	8	no	—
384	C₄²	—	47	2	no	—
385	C₄²	—	47	2	no	—
386	C₄²	—	94	8	no	—
387	C₄²	D₄×D₄₇	1	2	yes	—
388	C₄²	C₂³×D₄₇	1	2	yes	—
389	C₂³	—	47	4	no	—
390	C₂³	—	47	2	no	—
391	C₂³	—	94	4	no	—
392	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
393	Q₈	—	188	16	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	47	4	no	—
400	C₂×C₄	—	47	2	no	—
401	C₂×C₄	—	47	8	no	—
402	C₂×C₄	—	47	4	no	—
403	C₂×C₄	—	47	4	no	—
404	C₂×C₄	—	47	4	no	—
405	C₂×C₄	—	94	4	no	—
406	C₂×C₄	—	94	4	no	—
407	C₂×C₄	—	94	4	no	—
408	C₂×C₄	—	188	8	no	—
409	C₂×C₄	—	188	16	no	—
410	C₂×C₄	—	188	4	no	—
411	C₂×C₄	—	188	4	no	—
412	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
413	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
415	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
416	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
417	C₈	—	47	4	no	—
418	C₈	—	47	4	no	—
419	C₈	C₂×Q₈×D₄₇	1	4	yes	—
420	C₈	C₂×Q₈×D₄₇	1	4	yes	—
421	C₂²	—	47	4	no	—
422	C₂²	—	94	4	no	—
423	C₂²	—	94	8	no	—
424	C₂²	C₄⋊Q₈×D₄₇	1	2	yes	—
425	C₂²	#15689920	1	4	yes	—
426	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
427	C₄	—	2	4	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	4	no	—
430	C₄	—	47	4	no	—
431	C₄	—	94	4	no	—
432	C₄	—	188	4	no	—
433	C₄	—	188	4	no	—
434	C₄	C₄⋊Q₈×D₄₇	1	2	yes	—
435	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
436	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
437	C₂	—	94	4	no	—
438	C₂	#20253936	1	4	yes	direct product factor
439	C₂	C₂×C₄⋊Q₈×D₄₇	1	1	yes	characteristic
440	C₂	C₂×#15689920	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#499	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
hypercenter	C₂×#499	D₄₇
hypocenter	C₄₇	C₂×#3166
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#499

Complements

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

N	H ≅ G/N	type
3. #20253936	C₂	direct (N × H)
4. C₂×#15689531	C₂	semidirect
5. C₂×#15689530	C₂	semidirect
6. C₂×#15689525	C₂	semidirect
7. C₂×#15689522	C₂	semidirect
8. C₂×#15689522	C₂	semidirect
12. C₂×C₄₇×#499	C₂	semidirect
30. #15689531	C₂²	semidirect
31. #15689530	C₂²	semidirect
32. #15689525	C₂²	semidirect
33. #15689522	C₂²	semidirect
34. #15689522	C₂²	semidirect
49. C₄₇×#499	C₂²	semidirect
57. C₂×#10625324	Q₈	semidirect
58. C₂×#10625324	Q₈	semidirect
166. #10625324	C₂×Q₈	semidirect
167. #10625324	C₂×Q₈	semidirect
225. C₂×#499	D₄₇	semidirect
229. C₂×C₄₇	#3166	semidirect
257. #499	C₂×D₄₇	semidirect
273. C₄₇	C₂×#3166	semidirect
438. C₂	#20253936	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×#15689679	2
C₂×#125×D₄₇	2
#20253936	2
C₂×#15689531	2
C₂×#15689530	2
C₂×#15689525	2
C₂×#15689522	2
C₂×#15689164	2
C₂×#15689162	2
C₂×C₄×#10625324	2
C₂×C₄₇×#499	2
C₂×#3166	47

Subgroups — C2×#20253936 #27085930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20253936 #27085930