Subgroups — C₂×#20253913 #27085896

Order 12032.

1854 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689750	C₂	1	2	yes	maximal
2	#20253913	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689530	C₂	1	2	yes	maximal, complemented
4	C₂×#15689529	C₂	1	2	yes	maximal, complemented
5	C₂×#15689525	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15689523	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689520	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689162	C₂	1	2	yes	maximal
9	C₂×#15689158	C₂	1	1	yes	maximal, characteristic
10	C₂×#106×D₄₇	C₂	1	1	yes	maximal, characteristic
11	C₂×#15689077	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10625324	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
15	#15689750	—	2	8	no	—
16	#15689750	C₂²	1	16	yes	—
17	C₂×#13094023	C₂²	1	2	yes	—
18	C₂×#13094022	—	2	2	no	—
19	C₂×#13094016	C₂²	1	2	yes	—
20	C₂×#13094015	C₂²	1	2	yes	—
21	C₂×#13094014	—	2	2	no	—
22	C₂×#13094002	—	2	2	no	—
23	C₂×#13094000	—	2	2	no	—
24	C₂×#13093982	C₂²	1	2	yes	—
25	C₂×#13093981	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
27	#15689530	C₂²	1	16	yes	complemented
28	#15689529	C₂²	1	16	yes	complemented
29	#15689525	C₂²	1	8	yes	complemented
30	#15689523	C₂²	1	8	yes	complemented
31	#15689520	C₂²	1	8	yes	complemented
32	#15689162	C₂²	1	16	yes	—
33	#15689158	C₂²	1	8	yes	—
34	C₂×#13093958	C₂²	1	2	yes	—
35	C₂×#13093957	C₂²	1	2	yes	—
36	C₂×#13093957	C₂²	1	2	yes	—
37	C₂×#13093956	C₂²	1	1	yes	characteristic
38	C₂×#13093956	C₂²	1	1	yes	characteristic
39	C₂×#13093955	C₂²	1	2	yes	—
40	C₂×#13093955	C₂²	1	2	yes	—
41	#106×D₄₇	C₂²	1	8	yes	—
42	#15689077	C₂²	1	8	yes	—
43	C₂×#13093935	C₂²	1	1	yes	characteristic
44	C₂×#13093934	C₂²	1	1	yes	characteristic
45	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
47	C₄₇×#498	C₂²	1	8	yes	complemented
48	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
50	C₂×#106×C₄₇	C₂²	1	2	yes	—
51	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
52	C₂²×Dic₉₄	—	2	2	no	—
53	C₂²×C₄×D₄₇	—	2	2	no	—
54	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
55	C₂×#10625324	Q₈	1	8	yes	complemented
56	C₂×#10625324	C₂³	1	4	yes	—
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₄₇	Q₈	1	8	yes	complemented
60	C₂×C₈×D₄₇	C₂³	1	4	yes	—
61	#13094023	—	2	4	no	—
62	#13094023	C₂³	1	8	yes	—
63	#13094022	—	2	16	no	—
64	#13094016	—	2	4	no	—
65	#13094016	C₂³	1	8	yes	—
66	#13094015	—	2	4	no	—
67	#13094015	C₂³	1	8	yes	—
68	#13094014	—	2	16	no	—
69	#13094002	—	2	16	no	—
70	#13094000	—	2	16	no	—
71	#13093982	—	2	4	no	—
72	#13093982	C₂³	1	8	yes	—
73	#13093981	D₄	1	4	yes	—
74	#13093981	C₂³	1	4	yes	—
75	C₂×C₄⋊Dic₄₇	—	2	2	no	—
76	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
77	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
78	C₂×Dic₄₇⋊C₄	—	2	2	no	—
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	D₄	1	2	yes	—
84	C₄⋊C₄×D₄₇	—	2	4	no	—
85	C₄⋊C₄×D₄₇	C₂³	1	8	yes	—
86	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
87	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
88	C₂×C₄×Dic₄₇	—	2	2	no	—
89	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
90	#13093958	C₂³	1	8	yes	—
91	#13093957	C₂³	1	8	yes	—
92	#13093957	C₂³	1	8	yes	—
93	#13093956	C₂³	1	4	yes	—
94	#13093956	C₂³	1	4	yes	—
95	#13093955	C₂³	1	8	yes	—
96	#13093955	C₂³	1	8	yes	—
97	#13093935	C₂³	1	4	yes	—
98	#13093934	C₂³	1	4	yes	—
99	C₈×Dic₄₇	C₂³	1	4	yes	—
100	C₂²×Q₈×C₄₇	—	2	2	no	—
101	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₄₇	—	2	4	no	—
104	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	—
105	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
106	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
109	#106×C₄₇	C₂³	1	4	yes	—
110	#106×C₄₇	C₂³	1	4	yes	—
111	#106×C₄₇	C₂³	1	8	yes	—
112	C₄×C₈×C₄₇	C₂³	1	4	yes	—
113	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂×Q₈×C₄₇	—	2	8	no	—
115	C₂×Q₈×C₄₇	—	8	4	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂²×Dic₄₇	—	2	2	no	—
121	C₂²×Dic₄₇	—	2	2	no	—
122	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
123	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×D₄₇	—	2	8	no	—
125	C₂×C₄×D₄₇	—	8	4	no	—
126	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
127	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
128	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
129	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
130	C₂×Dic₉₄	—	2	8	no	—
131	C₂×Dic₉₄	—	8	4	no	—
132	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	—
133	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	—
134	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
135	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
136	C₄⋊C₄×C₄₇	—	2	8	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
140	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
141	C₄²×C₄₇	C₂×D₄	1	2	yes	—
142	C₄²×C₄₇	C₂⁴	1	2	yes	—
143	(C₂×D₄₇)⋊C₄	—	2	8	no	—
144	(C₂×D₄₇)⋊C₄	C₂×D₄	1	8	yes	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	—	2	2	no	—
147	C₄⋊Dic₄₇	—	2	8	no	—
148	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
149	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
150	Dic₄₇⋊C₄	—	2	8	no	—
151	Dic₄₇⋊C₄	—	2	8	no	—
152	Dic₄₇⋊C₄	—	2	8	no	—
153	Dic₄₇⋊C₄	—	2	8	no	—
154	Dic₄₇⋊C₄	—	2	8	no	—
155	Dic₄₇⋊C₄	C₂×D₄	1	8	yes	—
156	C₄×Dic₄₇	—	2	8	no	—
157	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
158	C₄×Dic₄₇	C₂⁴	1	2	yes	—
159	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
160	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
161	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
162	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
163	#10625324	C₂×Q₈	1	16	yes	complemented
164	C₈×D₄₇	C₂×Q₈	1	16	yes	complemented
165	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂²×D₄₇	—	2	4	no	—
167	C₂²×D₄₇	C₄⋊Q₈	1	4	yes	—
168	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
169	Q₈×C₄₇	—	8	8	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	4	4	no	—
174	C₂×C₄×C₄₇	—	4	4	no	—
175	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
178	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
179	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
180	C₂×Dic₄₇	—	2	4	no	—
181	C₂×Dic₄₇	—	2	4	no	—
182	C₂×Dic₄₇	—	2	4	no	—
183	C₂×Dic₄₇	—	4	4	no	—
184	C₂×Dic₄₇	—	4	4	no	—
185	C₂×Dic₄₇	C₄⋊Q₈	1	4	yes	—
186	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
187	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
188	C₄×D₄₇	—	8	8	no	—
189	C₄×D₄₇	C₄⋊Q₈	1	8	yes	—
190	C₄×D₄₇	C₂²×Q₈	1	4	yes	—
191	C₄×D₄₇	C₂²×Q₈	1	4	yes	—
192	Dic₉₄	—	8	8	no	—
193	C₈×C₄₇	C₂²×Q₈	1	4	yes	—
194	C₈×C₄₇	C₂²×Q₈	1	4	yes	—
195	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	—
196	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	—
197	C₂×#3163	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
199	C₂²×C₄₇	#577	1	4	yes	—
200	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
201	C₂×D₄₇	—	2	8	no	—
202	C₂×D₄₇	—	2	4	no	—
203	C₂×D₄₇	C₂×C₄⋊Q₈	1	4	yes	—
204	C₄×C₄₇	—	2	4	no	—
205	C₄×C₄₇	—	4	4	no	—
206	C₄×C₄₇	—	4	4	no	—
207	C₄×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
208	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
209	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
210	Dic₄₇	—	2	4	no	—
211	Dic₄₇	—	4	4	no	—
212	Dic₄₇	—	4	4	no	—
213	Dic₄₇	C₂×C₄⋊Q₈	1	4	yes	—
214	C₂×#544	—	47	2	no	—
215	#3163	—	47	16	no	—
216	C₂×#501	—	47	2	no	—
217	C₂×#501	—	47	2	no	—
218	C₂×#499	—	47	1	no	—
219	C₂×#499	—	47	1	no	—
220	C₂×#498	—	47	1	no	—
221	C₂×#498	D₄₇	1	1	yes	characteristic, complemented
222	C₂×#428	—	47	2	no	—
223	C₂×#427	—	47	1	no	—
224	C₂²×#106	—	47	1	no	—
225	C₂×#405	—	47	1	no	—
226	C₂×C₄₇	#3163	1	4	yes	complemented
227	C₂×C₄₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
228	C₂×C₄₇	C₂×#577	1	2	yes	—
229	D₄₇	—	2	4	no	—
230	C₂²×M₁₆	—	47	1	no	—
231	C₂³×C₈	—	47	1	no	—
232	#544	—	47	16	no	—
233	#544	—	94	8	no	—
234	C₂×C₄⋊Q₈	—	47	2	no	—
235	C₂×C₄⋊Q₈	—	94	2	no	—
236	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
237	C₂×#125	—	47	2	no	—
238	C₂×#125	—	47	2	no	—
239	C₂×#125	—	94	2	no	—
240	C₂×C₂²⋊Q₈	—	94	2	no	—
241	C₂×C₂²⋊Q₈	—	94	2	no	—
242	C₂×#117	—	47	1	no	—
243	C₂×#117	—	47	2	no	—
244	C₂²×C₄⋊C₄	—	47	2	no	—
245	#501	—	47	16	no	—
246	#501	—	47	16	no	—
247	#499	—	47	8	no	—
248	#499	—	47	8	no	—
249	#498	—	47	8	no	—
250	#498	C₂×D₄₇	1	8	yes	complemented
251	#428	—	47	16	no	—
252	#427	—	47	8	no	—
253	C₂×#107	—	47	2	no	—
254	C₂×#107	—	47	2	no	—
255	C₂×#107	—	47	2	no	—
256	C₂×#106	—	47	1	no	—
257	C₂×#106	—	47	1	no	—
258	C₂×#106	—	47	2	no	—
259	C₂×#106	—	47	2	no	—
260	C₂×#106	—	47	8	no	—
261	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
262	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
263	C₂×#106	C₂×D₄₇	1	2	yes	—
264	#405	—	47	8	no	—
265	C₂×#97	—	47	1	no	—
266	C₂×#97	—	47	1	no	—
267	C₂×C₄×C₈	—	47	1	no	—
268	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
269	C₄₇	C₂×#3163	1	1	yes	characteristic, complemented, Sylow
270	C₂²×Q₈	—	2	2	no	—
271	C₂²×Q₈	—	94	2	no	—
272	C₂³×C₄	—	47	1	no	—
273	C₂³×C₄	—	94	2	no	—
274	C₂×M₁₆	—	47	8	no	—
275	C₂×M₁₆	—	47	4	no	—
276	C₂²×C₈	—	47	1	no	—
277	C₂²×C₈	—	47	1	no	—
278	C₂²×C₈	—	47	8	no	—
279	C₂²×C₈	—	47	4	no	—
280	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
282	C₄⋊Q₈	—	2	4	no	—
283	C₄⋊Q₈	—	47	8	no	—
284	C₄⋊Q₈	—	94	4	no	—
285	C₄⋊Q₈	—	94	16	no	—
286	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	—
287	#125	—	47	8	no	—
288	#125	—	47	8	no	—
289	#125	—	94	4	no	—
290	#125	—	94	16	no	—
291	#125	—	94	4	no	—
292	C₂²⋊Q₈	—	94	16	no	—
293	C₂²⋊Q₈	—	94	16	no	—
294	#117	—	47	4	no	—
295	#117	—	47	4	no	—
296	#117	—	47	8	no	—
297	#117	—	94	4	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	47	2	no	—
300	C₂×C₄⋊C₄	—	47	2	no	—
301	C₂×C₄⋊C₄	—	47	2	no	—
302	C₂×C₄⋊C₄	—	47	8	no	—
303	C₂×C₄⋊C₄	—	94	4	no	—
304	C₂×C₄⋊C₄	—	94	2	no	—
305	C₂×C₄⋊C₄	—	94	2	no	—
306	C₂×C₄⋊C₄	—	94	2	no	—
307	C₂×C₄⋊C₄	—	94	2	no	—
308	C₂×C₄⋊C₄	—	94	2	no	—
309	C₂×C₄⋊C₄	—	94	2	no	—
310	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
311	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
312	C₂×C₂²⋊C₄	—	47	2	no	—
313	C₂×C₂²⋊C₄	—	94	2	no	—
314	C₂×C₄²	—	47	1	no	—
315	C₂×C₄²	—	94	2	no	—
316	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
317	#107	—	47	8	no	—
318	#107	—	47	8	no	—
319	#107	—	47	8	no	—
320	#106	—	47	4	no	—
321	#106	—	47	4	no	—
322	#106	—	47	8	no	—
323	#106	—	47	8	no	—
324	#106	C₂²×D₄₇	1	4	yes	—
325	#106	C₂²×D₄₇	1	4	yes	—
326	#106	C₂²×D₄₇	1	8	yes	—
327	#97	—	47	4	no	—
328	#97	—	47	4	no	—
329	C₄×C₈	—	47	4	no	—
330	C₄×C₈	C₂²×D₄₇	1	4	yes	—
331	C₂⁴	—	47	1	no	—
332	C₂×Q₈	—	2	8	no	—
333	C₂×Q₈	—	8	4	no	—
334	C₂×Q₈	—	94	8	no	—
335	C₂×Q₈	—	376	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	47	1	no	—
339	C₂²×C₄	—	47	2	no	—
340	C₂²×C₄	—	47	4	no	—
341	C₂²×C₄	—	47	4	no	—
342	C₂²×C₄	—	47	2	no	—
343	C₂²×C₄	—	47	2	no	—
344	C₂²×C₄	—	94	8	no	—
345	C₂²×C₄	—	94	2	no	—
346	C₂²×C₄	—	94	2	no	—
347	C₂²×C₄	—	376	4	no	—
348	C₂²×C₄	D₄×D₄₇	1	2	yes	—
349	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
350	M₁₆	—	47	16	no	—
351	C₂×C₈	—	47	4	no	—
352	C₂×C₈	—	47	4	no	—
353	C₂×C₈	—	47	2	no	—
354	C₂×C₈	—	47	2	no	—
355	C₂×C₈	—	47	16	no	—
356	C₂×C₈	Q₈×D₄₇	1	4	yes	—
357	C₂×C₈	Q₈×D₄₇	1	4	yes	—
358	C₂×C₈	C₂³×D₄₇	1	2	yes	—
359	C₂×C₈	C₂³×D₄₇	1	2	yes	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	47	8	no	—
364	C₄⋊C₄	—	47	4	no	—
365	C₄⋊C₄	—	47	4	no	—
366	C₄⋊C₄	—	94	8	no	—
367	C₄⋊C₄	—	94	8	no	—
368	C₄⋊C₄	—	94	8	no	—
369	C₄⋊C₄	—	94	8	no	—
370	C₄⋊C₄	—	94	8	no	—
371	C₄⋊C₄	—	94	8	no	—
372	C₄⋊C₄	—	94	2	no	—
373	C₄⋊C₄	—	94	2	no	—
374	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
375	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
376	C₂²⋊C₄	—	47	8	no	—
377	C₂²⋊C₄	—	94	8	no	—
378	C₄²	—	47	2	no	—
379	C₄²	—	47	2	no	—
380	C₄²	—	94	8	no	—
381	C₄²	D₄×D₄₇	1	2	yes	—
382	C₄²	C₂³×D₄₇	1	2	yes	—
383	C₂³	—	47	4	no	—
384	C₂³	—	47	2	no	—
385	C₂³	—	94	4	no	—
386	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
387	Q₈	—	8	8	no	—
388	Q₈	—	376	8	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	47	4	no	—
395	C₂×C₄	—	47	2	no	—
396	C₂×C₄	—	47	8	no	—
397	C₂×C₄	—	47	4	no	—
398	C₂×C₄	—	47	4	no	—
399	C₂×C₄	—	47	4	no	—
400	C₂×C₄	—	94	4	no	—
401	C₂×C₄	—	94	4	no	—
402	C₂×C₄	—	94	4	no	—
403	C₂×C₄	—	376	8	no	—
404	C₂×C₄	—	188	4	no	—
405	C₂×C₄	—	188	4	no	—
406	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
407	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
409	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
410	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
411	C₈	—	47	4	no	—
412	C₈	—	47	4	no	—
413	C₈	C₂×Q₈×D₄₇	1	4	yes	—
414	C₈	C₂×Q₈×D₄₇	1	4	yes	—
415	C₂²	—	47	4	no	—
416	C₂²	—	94	4	no	—
417	C₂²	—	94	8	no	—
418	C₂²	C₄⋊Q₈×D₄₇	1	2	yes	—
419	C₂²	#15689929	1	4	yes	—
420	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
421	C₄	—	2	4	no	—
422	C₄	—	4	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	47	4	no	—
425	C₄	—	94	4	no	—
426	C₄	—	188	4	no	—
427	C₄	—	188	4	no	—
428	C₄	C₄⋊Q₈×D₄₇	1	2	yes	—
429	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
430	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
431	C₂	—	94	4	no	—
432	C₂	#20253913	1	4	yes	direct product factor
433	C₂	C₂×C₄⋊Q₈×D₄₇	1	1	yes	characteristic
434	C₂	C₂×#15689929	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×#498	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
hypercenter	C₂×#498	D₄₇
hypocenter	C₄₇	C₂×#3163
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#498

Complements

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

N	H ≅ G/N	type
2. #20253913	C₂	direct (N × H)
3. C₂×#15689530	C₂	semidirect
4. C₂×#15689529	C₂	semidirect
5. C₂×#15689525	C₂	semidirect
6. C₂×#15689523	C₂	semidirect
7. C₂×#15689520	C₂	semidirect
12. C₂×C₄₇×#498	C₂	semidirect
27. #15689530	C₂²	semidirect
28. #15689529	C₂²	semidirect
29. #15689525	C₂²	semidirect
30. #15689523	C₂²	semidirect
31. #15689520	C₂²	semidirect
47. C₄₇×#498	C₂²	semidirect
55. C₂×#10625324	Q₈	semidirect
59. C₂×C₈×D₄₇	Q₈	semidirect
163. #10625324	C₂×Q₈	semidirect
164. C₈×D₄₇	C₂×Q₈	semidirect
221. C₂×#498	D₄₇	semidirect
226. C₂×C₄₇	#3163	semidirect
250. #498	C₂×D₄₇	semidirect
269. C₄₇	C₂×#3163	semidirect
432. C₂	#20253913	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×#15689750	2
#20253913	2
C₂×#15689530	2
C₂×#15689529	2
C₂×#15689525	2
C₂×#15689523	2
C₂×#15689520	2
C₂×#15689162	2
C₂×#15689158	2
C₂×#106×D₄₇	2
C₂×#15689077	2
C₂×C₄₇×#498	2
C₂×#3163	47

Subgroups — C2×#20253913 #27085896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20253913 #27085896