Subgroups — C₂×#20242560 #26192031

Order 12032.

946 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689418	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689413	C₂	1	1	yes	maximal, characteristic
4	#20242560	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688869	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#556	C₂	1	1	yes	maximal, characteristic
9	C₂×#13094024	C₂²	1	1	yes	characteristic
10	#15689475	—	2	2	no	—
11	#15689475	C₂²	1	4	yes	complemented
12	#15689418	—	2	2	no	—
13	#15689418	C₂²	1	4	yes	complemented
14	#15689413	—	2	2	no	—
15	#15689413	C₂²	1	4	yes	—
16	C₂×#13093957	—	2	1	no	—
17	C₂×#13093955	—	2	1	no	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093948	—	2	1	no	—
21	C₂×#13093947	—	2	2	no	—
22	C₂×#13093945	—	2	1	no	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	#15688869	C₂²	1	4	yes	complemented
25	Q₈⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
26	D₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
27	C₄₇×#556	—	2	2	no	—
28	C₄₇×#556	—	2	2	no	—
29	C₄₇×#556	—	2	2	no	—
30	C₄₇×#556	C₂²	1	4	yes	—
31	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#126×C₄₇	—	2	2	no	—
33	C₂×#124×C₄₇	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
35	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₄₇	—	2	1	no	—
39	C₂²×Dic₉₄	—	2	1	no	—
40	C₂²×C₄₇⋊C₈	—	2	1	no	—
41	C₂²×C₄₇⋊C₈	—	2	1	no	—
42	C₂²×C₄₇⋊C₈	—	2	1	no	—
43	#13094024	—	2	1	no	—
44	#13094024	—	2	1	no	—
45	#13094024	—	2	1	no	—
46	#13094024	C₂³	1	2	yes	—
47	C₂×C₄⋊Dic₄₇	—	2	1	no	—
48	C₂×C₄⋊Dic₄₇	—	2	1	no	—
49	#13093957	—	2	4	no	—
50	#13093955	—	2	4	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
54	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
55	#13093948	—	2	4	no	—
56	#13093947	—	2	8	no	—
57	#13093945	—	2	4	no	—
58	C₄×C₄₇⋊C₈	—	2	1	no	—
59	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
60	C₂²×Q₈×C₄₇	—	2	1	no	—
61	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	—	2	1	no	—
64	C₄⋊Q₈×C₄₇	—	2	1	no	—
65	C₄⋊Q₈×C₄₇	—	2	1	no	—
66	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
67	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
68	#126×C₄₇	—	2	8	no	—
69	#126×C₄₇	—	2	8	no	—
70	#124×C₄₇	—	2	4	no	—
71	#124×C₄₇	—	2	4	no	—
72	C₂²⋊Q₈×C₄₇	—	2	4	no	—
73	C₂²⋊Q₈×C₄₇	—	2	4	no	—
74	C₄×Q₈×C₄₇	—	2	4	no	—
75	C₄×Q₈×C₄₇	—	2	4	no	—
76	C₄×Q₈×C₄₇	—	2	1	no	—
77	C₄×Q₈×C₄₇	—	2	1	no	—
78	C₄×Q₈×C₄₇	D₄	1	2	yes	—
79	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
80	C₄×D₄×C₄₇	—	2	1	no	—
81	C₄×D₄×C₄₇	—	2	1	no	—
82	C₄×D₄×C₄₇	D₄	1	2	yes	—
83	C₄×D₄×C₄₇	C₂³	1	2	yes	—
84	#117×C₄₇	—	2	4	no	—
85	#117×C₄₇	—	2	4	no	—
86	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
92	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	—	2	2	no	—
96	C₂×C₄²×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₂⁴×C₄₇	—	2	1	no	—
99	C₂×Q₈×C₄₇	—	2	1	no	—
100	C₂×Q₈×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	—	2	2	no	—
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	4	2	no	—
105	C₂×Q₈×C₄₇	—	4	2	no	—
106	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₄₇	—	2	1	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	2	2	no	—
110	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	4	2	no	—
118	C₂²×C₄×C₄₇	—	4	2	no	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×Dic₄₇	—	4	1	no	—
123	C₂×Dic₉₄	—	2	2	no	—
124	C₂×Dic₉₄	—	4	4	no	—
125	C₂×Dic₉₄	—	4	1	no	—
126	C₄⋊C₄×C₄₇	—	2	8	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
137	C₂²⋊C₄×C₄₇	—	2	8	no	—
138	C₂²⋊C₄×C₄₇	—	2	8	no	—
139	C₂²⋊C₄×C₄₇	—	2	2	no	—
140	C₂²⋊C₄×C₄₇	—	2	2	no	—
141	C₄²×C₄₇	—	2	8	no	—
142	C₄²×C₄₇	—	2	2	no	—
143	C₄²×C₄₇	—	2	2	no	—
144	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₄⋊Dic₄₇	—	2	2	no	—
149	C₄⋊Dic₄₇	—	2	2	no	—
150	C₄⋊Dic₄₇	—	4	1	no	—
151	C₄⋊Dic₄₇	—	4	1	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	4	2	no	—
156	C₂×C₄₇⋊C₈	—	4	2	no	—
157	C₂×C₄₇⋊C₈	—	4	2	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	#120	1	1	yes	characteristic
163	Q₈×C₄₇	—	2	2	no	—
164	Q₈×C₄₇	—	2	2	no	—
165	Q₈×C₄₇	—	4	2	no	—
166	Q₈×C₄₇	—	4	2	no	—
167	Q₈×C₄₇	—	4	2	no	—
168	Q₈×C₄₇	—	4	4	no	—
169	D₄×C₄₇	—	2	2	no	—
170	D₄×C₄₇	—	2	2	no	—
171	D₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	4	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	4	no	—
184	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
185	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
186	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
187	C₂×C₄×C₄₇	#135	1	2	yes	—
188	C₂×C₄×C₄₇	#135	1	2	yes	—
189	C₂×C₄×C₄₇	#137	1	2	yes	—
190	C₂×C₄×C₄₇	#137	1	2	yes	—
191	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×Dic₄₇	—	4	2	no	—
195	C₂×Dic₄₇	—	8	2	no	—
196	Dic₉₄	—	4	4	no	—
197	Dic₉₄	—	8	2	no	—
198	C₄₇⋊C₈	—	4	2	no	—
199	C₄₇⋊C₈	—	4	2	no	—
200	C₄₇⋊C₈	—	4	2	no	—
201	C₂×#1638	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	4	2	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	8	4	no	—
206	C₂²×C₄₇	#452	1	2	yes	—
207	C₂²×C₄₇	#452	1	2	yes	—
208	C₂²×C₄₇	#454	1	2	yes	—
209	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	4	2	no	—
213	C₄×C₄₇	—	4	2	no	—
214	C₄×C₄₇	—	4	4	no	—
215	C₄×C₄₇	—	4	2	no	—
216	C₄×C₄₇	#452	1	2	yes	—
217	C₄×C₄₇	#452	1	2	yes	—
218	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
219	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
220	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
221	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
222	Dic₄₇	—	8	2	no	—
223	C₂×#556	D₄₇	1	1	yes	characteristic
224	C₂×#487	—	47	1	no	—
225	C₂×#477	—	47	1	no	—
226	C₂×#476	—	47	1	no	—
227	#1638	—	47	8	no	—
228	C₂×#332	—	47	1	no	—
229	C₂×Q₈⋊C₈	—	47	1	no	—
230	C₂×D₄⋊C₈	—	47	1	no	—
231	C₂×C₄₇	—	8	2	no	—
232	C₂×C₄₇	#1638	1	4	yes	complemented
233	C₂×C₄₇	C₂×#452	1	1	yes	characteristic
234	C₂×C₄₇	C₂×#452	1	1	yes	characteristic
235	C₂×C₄₇	C₂×#454	1	1	yes	characteristic
236	#556	—	2	2	no	—
237	#556	—	2	2	no	—
238	#556	—	2	2	no	—
239	#556	C₂×D₄₇	1	4	yes	—
240	C₂×C₄⋊Q₈	—	47	1	no	—
241	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
242	C₂×#126	—	2	2	no	—
243	C₂×#124	—	2	1	no	—
244	C₂×C₂²⋊Q₈	—	2	1	no	—
245	C₂×C₄×Q₈	—	2	1	no	—
246	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
248	C₂×#117	—	2	1	no	—
249	#487	—	47	4	no	—
250	#487	—	94	2	no	—
251	#477	—	47	4	no	—
252	#477	—	94	2	no	—
253	#476	—	47	4	no	—
254	#476	—	94	2	no	—
255	C₂×#107	—	94	1	no	—
256	C₂×#106	—	94	1	no	—
257	C₂×C₄⋊C₈	—	47	1	no	—
258	C₂×C₄⋊C₈	—	47	1	no	—
259	C₂×#103	—	94	1	no	—
260	C₂×#103	—	94	2	no	—
261	C₂×#102	—	94	1	no	—
262	C₂×C₄×C₈	—	47	1	no	—
263	#332	—	47	4	no	—
264	Q₈⋊C₈	—	47	4	no	—
265	D₄⋊C₈	—	47	4	no	—
266	C₄₇	C₂×#1638	1	1	yes	characteristic, complemented, Sylow
267	C₂²×Q₈	—	2	1	no	—
268	C₂²×Q₈	—	94	1	no	—
269	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
270	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
271	C₂³×C₄	—	2	1	no	—
272	C₂²×C₈	—	94	1	no	—
273	C₂²×C₈	—	94	1	no	—
274	C₂²×C₈	—	94	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	47	2	no	—
278	C₄⋊Q₈	—	94	1	no	—
279	C₄⋊Q₈	—	94	1	no	—
280	C₄⋊Q₈	—	94	1	no	—
281	C₄⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
282	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
283	#126	—	2	8	no	—
284	#126	—	2	8	no	—
285	#124	—	2	4	no	—
286	#124	—	2	4	no	—
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	C₄×Q₈	—	2	4	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
294	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
298	C₄×D₄	C₂²×D₄₇	1	2	yes	—
299	#117	—	2	4	no	—
300	#117	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	94	1	no	—
305	C₂×C₄⋊C₄	—	94	1	no	—
306	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
315	#107	—	94	4	no	—
316	#106	—	94	4	no	—
317	C₄⋊C₈	—	47	2	no	—
318	C₄⋊C₈	—	47	2	no	—
319	C₄⋊C₈	—	94	1	no	—
320	C₄⋊C₈	—	94	1	no	—
321	#103	—	94	4	no	—
322	#103	—	94	8	no	—
323	#102	—	94	4	no	—
324	C₄×C₈	—	47	2	no	—
325	C₄×C₈	—	94	1	no	—
326	C₂⁴	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	94	2	no	—
335	C₂×Q₈	—	188	4	no	—
336	C₂×Q₈	—	188	1	no	—
337	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	188	1	no	—
351	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂×C₈	—	94	2	no	—
355	C₂×C₈	—	94	2	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	188	2	no	—
358	C₂×C₈	—	188	2	no	—
359	C₂×C₈	—	188	2	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	94	2	no	—
369	C₄⋊C₄	—	94	2	no	—
370	C₄⋊C₄	—	188	1	no	—
371	C₄⋊C₄	—	188	1	no	—
372	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
373	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
374	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	2	8	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₄²	—	2	8	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
383	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
384	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
385	C₄²	C₂³×D₄₇	1	1	yes	characteristic
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	#13093993	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	4	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	376	2	no	—
398	Q₈	—	188	4	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	376	2	no	—
415	C₂×C₄	—	188	2	no	—
416	C₂×C₄	#13093993	1	1	yes	characteristic
417	C₂×C₄	#13093993	1	1	yes	characteristic
418	C₂×C₄	#13093993	1	1	yes	characteristic
419	C₂×C₄	#13094044	1	2	yes	—
420	C₂×C₄	#13094044	1	2	yes	—
421	C₂×C₄	#13094054	1	2	yes	—
422	C₂×C₄	#13094054	1	2	yes	—
423	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
426	C₈	—	188	2	no	—
427	C₈	—	188	2	no	—
428	C₈	—	188	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	8	4	no	—
433	C₂²	#15689285	1	2	yes	—
434	C₂²	#15689285	1	2	yes	—
435	C₂²	#15689296	1	2	yes	—
436	C₂²	C₂×#13093993	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	4	no	—
443	C₄	—	376	2	no	—
444	C₄	#15689285	1	2	yes	—
445	C₄	#15689285	1	2	yes	—
446	C₄	C₂×#13094044	1	1	yes	characteristic
447	C₄	C₂×#13094044	1	1	yes	characteristic
448	C₄	C₂×#13094054	1	1	yes	characteristic
449	C₄	C₂×#13094054	1	1	yes	characteristic
450	C₂	—	8	2	no	—
451	C₂	#20242560	1	4	yes	direct product factor
452	C₂	C₂×#15689285	1	1	yes	characteristic
453	C₂	C₂×#15689285	1	1	yes	characteristic
454	C₂	C₂×#15689296	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093993
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#556	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂²×D₄×C₄₇	D₄
hypercenter	C₂×#556	D₄₇
hypocenter	C₄₇	C₂×#1638
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#556

Complements

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

N	H ≅ G/N	type
1. C₂×#15689475	C₂	semidirect
2. C₂×#15689418	C₂	semidirect
4. #20242560	C₂	direct (N × H)
5. C₂×#15688869	C₂	semidirect
6. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
11. #15689475	C₂²	semidirect
13. #15689418	C₂²	semidirect
24. #15688869	C₂²	semidirect
25. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
232. C₂×C₄₇	#1638	semidirect
266. C₄₇	C₂×#1638	semidirect
451. C₂	#20242560	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×#15689475	2
C₂×#15689418	2
C₂×#15689413	2
#20242560	2
C₂×#15688869	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₂×D₄⋊(C₄₇⋊C₈)	2
C₂×C₄₇×#556	2
C₂×#1638	47

Subgroups — C2×#20242560 #26192031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242560 #26192031