Subgroups — C₂×#20256777 #27123131

Order 12032.

7302 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256777	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689742	C₂	1	4	yes	maximal, complemented
3	C₂×#15689734	C₂	1	2	yes	maximal, complemented
4	C₂×#15689727	C₂	1	2	yes	maximal, complemented
5	C₂×#15689718	C₂	1	4	yes	maximal, complemented
6	C₂×#15689710	C₂	1	4	yes	maximal, complemented
7	C₂×#15689680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689653	C₂	1	8	yes	maximal, complemented
9	C₂×#15689630	C₂	1	2	yes	maximal, complemented
10	C₂×#41×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₂²×#13093981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic
14	#15689742	C₂²	1	64	yes	complemented
15	#15689734	C₂²	1	32	yes	complemented
16	#15689727	C₂²	1	32	yes	complemented
17	#15689718	C₂²	1	64	yes	complemented
18	#15689710	C₂²	1	64	yes	complemented
19	#15689680	C₂²	1	16	yes	complemented
20	C₂×#13094024	C₂²	1	2	yes	complemented
21	#15689653	C₂²	1	128	yes	complemented
22	C₂×#13094019	C₂²	1	8	yes	—
23	C₂×#13094017	C₂²	1	8	yes	complemented
24	C₂×#13094016	C₂²	1	2	yes	complemented
25	C₂×#13094014	C₂²	1	8	yes	complemented
26	C₂×#13094010	C₂²	1	8	yes	—
27	#15689630	C₂²	1	32	yes	complemented
28	C₂×#13094008	C₂²	1	8	yes	—
29	C₂×#13094005	C₂²	1	4	yes	—
30	C₂×#13094005	C₂²	1	8	yes	complemented
31	C₂×#13094003	C₂²	1	4	yes	—
32	C₂×#13094001	C₂²	1	8	yes	complemented
33	C₂×#13094000	C₂²	1	4	yes	—
34	C₂×#13093996	C₂²	1	8	yes	—
35	C₂×#13093995	C₂²	1	4	yes	—
36	C₂×#13093992	C₂²	1	4	yes	—
37	#41×Dic₄₇	C₂²	1	32	yes	complemented
38	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	complemented
39	C₂×C₄×Dic₉₄	C₂²	1	4	yes	complemented
40	C₂×D₄×Dic₄₇	C₂²	1	8	yes	—
41	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
42	C₂×C₄×C₂²⋊D₄₇	C₂²	1	8	yes	—
43	C₂×#13093983	C₂²	1	2	yes	—
44	C₂×#13093983	C₂²	1	4	yes	complemented
45	C₂×#13093981	C₂²	1	4	yes	—
46	C₂×#13093981	C₂²	1	2	yes	—
47	C₂×#13093981	C₂²	1	2	yes	—
48	C₂×#13093981	C₂²	1	16	yes	complemented
49	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	—
50	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
51	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
52	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	complemented
53	C₂²×#41×C₄₇	C₂²	1	2	yes	—
54	C₄₇×#532	C₂²	1	16	yes	complemented
55	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic, complemented
57	C₂×#124×C₄₇	C₂²	1	2	yes	complemented
58	C₂×#121×C₄₇	C₂²	1	4	yes	—
59	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
60	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
61	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
62	C₂²×Dic₉₄	C₂³	1	4	yes	—
63	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
64	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂³×Dic₄₇	C₂³	1	2	yes	—
66	C₂³×Dic₄₇	C₂³	1	8	yes	—
67	C₂²×C₄×D₄₇	—	2	8	no	—
68	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
69	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
70	C₂²×C₄×D₄₇	C₂³	1	8	yes	—
71	#13094024	C₂³	1	16	yes	complemented
72	#13094019	C₂³	1	64	yes	—
73	#13094017	C₂³	1	64	yes	complemented
74	#13094016	C₂³	1	16	yes	complemented
75	#13094014	C₂³	1	64	yes	complemented
76	#13094010	C₂³	1	64	yes	—
77	#13094008	C₂³	1	64	yes	—
78	#13094005	C₂³	1	32	yes	—
79	#13094005	C₂³	1	64	yes	complemented
80	#13094003	C₂³	1	32	yes	—
81	#13094001	C₂³	1	64	yes	complemented
82	#13094000	C₂³	1	32	yes	—
83	#13093996	C₂³	1	64	yes	—
84	#13093995	C₂³	1	32	yes	—
85	#13093992	C₂³	1	32	yes	—
86	Q₈×Dic₄₇	C₂³	1	32	yes	complemented
87	C₄×Dic₉₄	C₂³	1	32	yes	complemented
88	D₄×Dic₄₇	C₂³	1	64	yes	—
89	D₄×Dic₄₇	C₂³	1	32	yes	complemented
90	C₄×C₂²⋊D₄₇	C₂³	1	64	yes	—
91	#13093983	C₂³	1	16	yes	—
92	#13093983	C₂³	1	32	yes	complemented
93	#13093981	C₂³	1	16	yes	—
94	#13093981	C₂³	1	16	yes	—
95	#13093981	C₂³	1	32	yes	—
96	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
97	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
98	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
99	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
100	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
101	C₂×Dic₄₇⋊C₄	C₂³	1	16	yes	—
102	C₂×Dic₄₇⋊C₄	C₂³	1	8	yes	—
103	C₂×Dic₄₇⋊C₄	C₂³	1	8	yes	—
104	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
105	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
106	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
107	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
108	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
109	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	—
110	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
111	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
112	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
113	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
114	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
115	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
116	C₂×C₄×Dic₄₇	C₂³	1	32	yes	complemented
117	C₂×#41×C₄₇	—	2	16	no	—
118	C₂×#41×C₄₇	C₂³	1	16	yes	—
119	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
120	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
121	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
123	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
124	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
127	#127×C₄₇	C₂³	1	8	yes	complemented
128	#124×C₄₇	C₂³	1	16	yes	complemented
129	#121×C₄₇	C₂³	1	32	yes	—
130	C₄×D₄×C₄₇	C₂³	1	32	yes	complemented
131	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
133	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
134	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
137	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
138	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
139	C₂³×D₄₇	—	2	4	no	—
140	C₂³×D₄₇	—	4	4	no	—
141	C₂³×D₄₇	C₂⁴	1	2	yes	—
142	C₂³×D₄₇	C₂⁴	1	4	yes	—
143	#41×C₄₇	—	2	64	no	—
144	C₂×Q₈×C₄₇	—	2	8	no	—
145	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
146	C₂×D₄×C₄₇	—	2	16	no	—
147	C₂×D₄×C₄₇	—	2	8	no	—
148	C₂×D₄×C₄₇	—	4	8	no	—
149	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
150	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
151	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
152	C₂²×C₄×C₄₇	—	2	16	no	—
153	C₂²×C₄×C₄₇	—	4	4	no	—
154	C₂²×C₄×C₄₇	#41	1	8	yes	—
155	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
159	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
160	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
163	C₂×C₂²⋊D₄₇	—	4	16	no	—
164	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
165	C₂²×Dic₄₇	—	2	4	no	—
166	C₂²×Dic₄₇	—	4	16	no	—
167	C₂²×Dic₄₇	—	4	4	no	—
168	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
169	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
170	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
171	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
172	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
173	C₂²×Dic₄₇	C₂⁴	1	32	yes	—
174	C₂×C₄×D₄₇	—	2	8	no	—
175	C₂×C₄×D₄₇	—	2	8	no	—
176	C₂×C₄×D₄₇	—	2	32	no	—
177	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
178	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
179	C₂×Dic₉₄	—	4	8	no	—
180	C₂×Dic₉₄	C₂⁴	1	16	yes	—
181	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
182	C₂²⋊C₄×C₄₇	C₂⁴	1	32	yes	—
183	C₄²×C₄₇	C₂⁴	1	8	yes	—
184	C₄²×C₄₇	C₂⁴	1	4	yes	—
185	C₄²×C₄₇	C₂⁴	1	4	yes	—
186	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
187	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
188	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
189	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
190	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
191	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
192	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
193	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
194	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
195	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
196	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
197	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
198	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
199	C₄×Dic₄₇	C₂⁴	1	8	yes	—
200	C₄×Dic₄₇	C₂⁴	1	8	yes	—
201	C₄×Dic₄₇	C₂⁴	1	16	yes	—
202	C₄×Dic₄₇	C₂⁴	1	32	yes	—
203	C₂³×C₄₇	—	2	4	no	—
204	C₂³×C₄₇	—	2	8	no	—
205	C₂³×C₄₇	—	2	16	no	—
206	C₂³×C₄₇	C₂×#41	1	4	yes	—
207	C₂³×C₄₇	C₂⁵	1	8	yes	—
208	C₂³×C₄₇	C₂⁵	1	2	yes	—
209	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
210	C₂²×D₄₇	—	2	8	no	—
211	C₂²×D₄₇	—	2	4	no	—
212	C₂²×D₄₇	—	2	8	no	—
213	C₂²×D₄₇	—	4	8	no	—
214	C₂²×D₄₇	—	4	16	no	—
215	C₂²×D₄₇	C₂⁵	1	4	yes	—
216	Q₈×C₄₇	—	2	16	no	—
217	D₄×C₄₇	—	2	32	no	—
218	D₄×C₄₇	—	2	16	no	—
219	D₄×C₄₇	—	4	16	no	—
220	C₂×C₄×C₄₇	—	2	8	no	—
221	C₂×C₄×C₄₇	—	2	4	no	—
222	C₂×C₄×C₄₇	—	2	4	no	—
223	C₂×C₄×C₄₇	—	2	32	no	—
224	C₂×C₄×C₄₇	—	4	8	no	—
225	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
226	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
227	C₂×C₄×C₄₇	C₂×#41	1	16	yes	—
228	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
229	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
230	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
231	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
232	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
233	C₂²⋊D₄₇	—	4	32	no	—
234	C₂×Dic₄₇	—	2	8	no	—
235	C₂×Dic₄₇	—	2	4	no	—
236	C₂×Dic₄₇	—	2	16	no	—
237	C₂×Dic₄₇	—	2	8	no	—
238	C₂×Dic₄₇	—	4	32	no	—
239	C₂×Dic₄₇	—	4	8	no	—
240	C₂×Dic₄₇	C₂⁵	1	8	yes	—
241	C₂×Dic₄₇	C₂⁵	1	16	yes	—
242	C₂×Dic₄₇	C₂⁵	1	4	yes	—
243	C₄×D₄₇	—	2	16	no	—
244	C₄×D₄₇	—	2	16	no	—
245	Dic₉₄	—	4	16	no	—
246	C₂×#3455	—	47	1	no	maximal, Sylow
247	C₂²×C₄₇	—	2	4	no	—
248	C₂²×C₄₇	—	2	8	no	—
249	C₂²×C₄₇	—	2	8	no	—
250	C₂²×C₄₇	—	2	16	no	—
251	C₂²×C₄₇	—	4	16	no	—
252	C₂²×C₄₇	C₂²×#41	1	4	yes	—
253	C₂²×C₄₇	C₂²×#41	1	2	yes	—
254	C₂²×C₄₇	#585	1	4	yes	—
255	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
256	C₂×D₄₇	—	2	4	no	—
257	C₂×D₄₇	—	2	8	no	—
258	C₂×D₄₇	—	4	16	no	—
259	C₂×D₄₇	—	4	8	no	—
260	C₄×C₄₇	—	2	8	no	—
261	C₄×C₄₇	—	2	4	no	—
262	C₄×C₄₇	—	2	4	no	—
263	C₄×C₄₇	C₂²×#41	1	4	yes	—
264	C₄×C₄₇	C₂²×#41	1	4	yes	—
265	Dic₄₇	—	2	4	no	—
266	Dic₄₇	—	2	16	no	—
267	Dic₄₇	—	2	8	no	—
268	#3455	—	47	32	no	—
269	C₂×#542	—	47	4	no	—
270	C₂×#541	—	47	2	no	—
271	C₂×#540	—	47	2	no	—
272	C₂×#539	—	47	4	no	—
273	C₂×#538	—	47	4	no	—
274	C₂×#533	—	47	1	no	—
275	C₂×#532	D₄₇	1	1	yes	characteristic, complemented
276	C₂×#529	—	47	8	no	—
277	C₂×#525	—	47	2	no	—
278	C₂×C₄×#41	—	47	2	no	—
279	C₂²×#117	—	47	1	no	—
280	C₂×C₄₇	—	2	4	no	—
281	C₂×C₄₇	—	4	8	no	—
282	C₂×C₄₇	#3455	1	4	yes	complemented
283	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
284	C₂×C₄₇	C₂×#585	1	2	yes	—
285	D₄₇	—	4	4	no	—
286	C₂²×#41	C₂×D₄₇	1	2	yes	—
287	C₂⁴×C₄	—	47	1	no	—
288	#542	—	47	64	no	—
289	#541	—	47	32	no	—
290	#540	—	47	32	no	—
291	#539	—	47	64	no	—
292	#538	—	47	64	no	—
293	#533	—	47	16	no	—
294	#532	C₂×D₄₇	1	16	yes	complemented
295	C₂×C₄⋊Q₈	—	47	2	no	—
296	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
297	C₂×#127	C₂×D₄₇	1	1	yes	characteristic, complemented
298	#529	—	47	128	no	—
299	C₂×#126	—	47	8	no	—
300	C₂×#126	—	47	8	no	—
301	C₂×#125	—	47	8	no	—
302	C₂×#125	—	47	2	no	—
303	C₂×#124	—	47	8	no	—
304	C₂×#124	C₂×D₄₇	1	2	yes	complemented
305	#525	—	47	32	no	—
306	C₂×#123	—	47	4	no	—
307	C₂×#123	—	47	8	no	—
308	C₂×#123	—	47	8	no	—
309	C₂×C₂²⋊Q₈	—	47	4	no	—
310	C₂×C₂²⋊Q₈	—	47	4	no	—
311	C₂×C₂²⋊Q₈	—	47	8	no	—
312	C₂×#121	—	47	4	no	—
313	C₂×#121	—	47	8	no	—
314	C₂×#121	C₂×D₄₇	1	4	yes	—
315	C₂×#120	—	47	4	no	—
316	C₄×#41	—	47	32	no	—
317	C₂×C₄×Q₈	—	47	4	no	—
318	C₂×C₄×Q₈	—	47	4	no	—
319	C₂×C₄×D₄	—	47	8	no	—
320	C₂×C₄×D₄	—	47	4	no	—
321	C₂×C₄×D₄	—	47	8	no	—
322	C₂×C₄×D₄	C₂×D₄₇	1	4	yes	complemented
323	C₂×#117	—	47	2	no	—
324	C₂×#117	—	47	4	no	—
325	C₂×#117	—	47	4	no	—
326	C₂×#117	—	47	2	no	—
327	C₂×#117	—	47	2	no	—
328	C₂×#117	—	47	16	no	—
329	C₂²×C₄⋊C₄	—	47	2	no	—
330	C₂²×C₂²⋊C₄	—	47	2	no	—
331	C₂²×C₄²	—	47	1	no	—
332	C₂²×C₄²	—	47	4	no	—
333	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
334	C₄₇	C₂×#3455	1	1	yes	characteristic, complemented, Sylow
335	C₂⁵	—	47	1	no	—
336	C₂×#41	—	2	16	no	—
337	C₂×#41	C₂²×D₄₇	1	16	yes	—
338	C₂²×Q₈	—	47	4	no	—
339	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
340	C₂²×D₄	—	47	8	no	—
341	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
342	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
343	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
344	C₂³×C₄	—	47	1	no	—
345	C₂³×C₄	—	47	2	no	—
346	C₂³×C₄	—	47	8	no	—
347	C₂³×C₄	—	47	2	no	—
348	C₂³×C₄	—	47	8	no	—
349	C₂³×C₄	—	47	2	no	—
350	C₂³×C₄	—	94	8	no	—
351	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
352	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
353	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
354	C₄⋊Q₈	—	47	16	no	—
355	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
356	#127	C₂²×D₄₇	1	8	yes	complemented
357	#126	—	47	64	no	—
358	#126	—	47	64	no	—
359	#125	—	47	64	no	—
360	#125	—	47	16	no	—
361	#124	—	47	64	no	—
362	#124	C₂²×D₄₇	1	16	yes	complemented
363	#123	—	47	32	no	—
364	#123	—	47	64	no	—
365	#123	—	47	64	no	—
366	C₂²⋊Q₈	—	47	32	no	—
367	C₂²⋊Q₈	—	47	32	no	—
368	C₂²⋊Q₈	—	47	64	no	—
369	#121	—	47	32	no	—
370	#121	—	47	64	no	—
371	#121	C₂²×D₄₇	1	32	yes	—
372	#120	—	47	32	no	—
373	C₄×Q₈	—	47	32	no	—
374	C₄×Q₈	—	47	32	no	—
375	C₄×D₄	—	47	64	no	—
376	C₄×D₄	—	47	32	no	—
377	C₄×D₄	—	47	64	no	—
378	C₄×D₄	C₂²×D₄₇	1	32	yes	complemented
379	#117	—	47	16	no	—
380	#117	—	47	32	no	—
381	#117	—	47	32	no	—
382	#117	—	47	16	no	—
383	#117	—	47	16	no	—
384	C₂×C₄⋊C₄	—	47	4	no	—
385	C₂×C₄⋊C₄	—	47	4	no	—
386	C₂×C₄⋊C₄	—	47	16	no	—
387	C₂×C₄⋊C₄	—	47	4	no	—
388	C₂×C₄⋊C₄	—	47	8	no	—
389	C₂×C₄⋊C₄	—	47	8	no	—
390	C₂×C₄⋊C₄	—	47	8	no	—
391	C₂×C₄⋊C₄	—	47	4	no	—
392	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
393	C₂×C₂²⋊C₄	—	47	4	no	—
394	C₂×C₂²⋊C₄	—	47	8	no	—
395	C₂×C₂²⋊C₄	—	47	8	no	—
396	C₂×C₂²⋊C₄	—	47	4	no	—
397	C₂×C₂²⋊C₄	—	47	4	no	—
398	C₂×C₂²⋊C₄	—	47	16	no	—
399	C₂×C₂²⋊C₄	—	47	8	no	—
400	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
401	C₂×C₄²	—	47	2	no	—
402	C₂×C₄²	—	47	8	no	—
403	C₂×C₄²	—	47	8	no	—
404	C₂×C₄²	—	47	32	no	—
405	C₂×C₄²	—	47	2	no	—
406	C₂×C₄²	—	47	4	no	—
407	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
408	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
409	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
410	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
411	C₂⁴	—	47	2	no	—
412	C₂⁴	—	47	4	no	—
413	C₂⁴	—	94	4	no	—
414	C₂⁴	—	188	4	no	—
415	C₂⁴	C₂³×D₄₇	1	4	yes	—
416	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
417	#41	—	2	64	no	—
418	C₂×Q₈	—	2	8	no	—
419	C₂×Q₈	—	47	16	no	—
420	C₂×Q₈	—	188	8	no	—
421	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
422	C₂×D₄	—	2	16	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	4	8	no	—
425	C₂×D₄	—	47	32	no	—
426	C₂×D₄	—	188	16	no	—
427	C₂×D₄	C₂³×D₄₇	1	16	yes	—
428	C₂×D₄	C₂³×D₄₇	1	8	yes	—
429	C₂×D₄	C₂³×D₄₇	1	16	yes	—
430	C₂²×C₄	—	2	16	no	—
431	C₂²×C₄	—	4	4	no	—
432	C₂²×C₄	—	47	4	no	—
433	C₂²×C₄	—	47	8	no	—
434	C₂²×C₄	—	47	2	no	—
435	C₂²×C₄	—	47	4	no	—
436	C₂²×C₄	—	47	8	no	—
437	C₂²×C₄	—	47	32	no	—
438	C₂²×C₄	—	47	8	no	—
439	C₂²×C₄	—	47	8	no	—
440	C₂²×C₄	—	94	4	no	—
441	C₂²×C₄	—	94	8	no	—
442	C₂²×C₄	—	94	8	no	—
443	C₂²×C₄	—	94	32	no	—
444	C₂²×C₄	—	188	4	no	—
445	C₂²×C₄	—	188	16	no	—
446	C₂²×C₄	#10625352	1	8	yes	—
447	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
448	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
449	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
450	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
451	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
452	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
453	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
454	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
455	C₄⋊C₄	—	47	16	no	—
456	C₄⋊C₄	—	47	16	no	—
457	C₄⋊C₄	—	47	32	no	—
458	C₄⋊C₄	—	47	32	no	—
459	C₄⋊C₄	—	47	16	no	—
460	C₄⋊C₄	—	47	32	no	—
461	C₄⋊C₄	—	47	16	no	—
462	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
463	C₂²⋊C₄	—	47	16	no	—
464	C₂²⋊C₄	—	47	32	no	—
465	C₂²⋊C₄	—	47	32	no	—
466	C₂²⋊C₄	—	47	16	no	—
467	C₂²⋊C₄	—	47	16	no	—
468	C₂²⋊C₄	—	47	32	no	—
469	C₂²⋊C₄	C₂³×D₄₇	1	32	yes	—
470	C₄²	—	47	8	no	—
471	C₄²	—	47	8	no	—
472	C₄²	—	47	16	no	—
473	C₄²	—	47	32	no	—
474	C₄²	C₂³×D₄₇	1	8	yes	—
475	C₄²	C₂³×D₄₇	1	4	yes	—
476	C₄²	C₂³×D₄₇	1	4	yes	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	2	16	no	—
480	C₂³	—	47	4	no	—
481	C₂³	—	94	8	no	—
482	C₂³	—	94	4	no	—
483	C₂³	—	94	8	no	—
484	C₂³	—	188	8	no	—
485	C₂³	—	188	16	no	—
486	C₂³	C₂×#10625352	1	4	yes	—
487	C₂³	C₂⁴×D₄₇	1	8	yes	—
488	C₂³	C₂⁴×D₄₇	1	2	yes	—
489	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
490	Q₈	—	2	16	no	—
491	Q₈	—	188	16	no	—
492	D₄	—	2	32	no	—
493	D₄	—	2	16	no	—
494	D₄	—	4	16	no	—
495	D₄	—	188	32	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	32	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	47	8	no	—
502	C₂×C₄	—	47	16	no	—
503	C₂×C₄	—	47	4	no	—
504	C₂×C₄	—	94	8	no	—
505	C₂×C₄	—	94	4	no	—
506	C₂×C₄	—	94	8	no	—
507	C₂×C₄	—	94	16	no	—
508	C₂×C₄	—	94	16	no	—
509	C₂×C₄	—	94	16	no	—
510	C₂×C₄	—	188	8	no	—
511	C₂×C₄	—	188	32	no	—
512	C₂×C₄	C₂×#10625352	1	4	yes	—
513	C₂×C₄	C₂×#10625352	1	4	yes	—
514	C₂×C₄	C₂×#10625352	1	16	yes	—
515	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
516	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
517	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
518	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
519	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
520	C₂²	—	2	8	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	2	16	no	—
524	C₂²	—	4	16	no	—
525	C₂²	—	94	4	no	—
526	C₂²	—	94	8	no	—
527	C₂²	—	188	16	no	—
528	C₂²	—	188	8	no	—
529	C₂²	C₂²×#10625352	1	4	yes	—
530	C₂²	C₂²×#10625352	1	2	yes	—
531	C₂²	#15689959	1	4	yes	—
532	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
533	C₄	—	2	8	no	—
534	C₄	—	2	4	no	—
535	C₄	—	2	4	no	—
536	C₄	—	94	4	no	—
537	C₄	—	94	8	no	—
538	C₄	—	94	16	no	—
539	C₄	C₂²×#10625352	1	4	yes	—
540	C₄	C₂²×#10625352	1	4	yes	—
541	C₂	—	2	4	no	—
542	C₂	—	4	8	no	—
543	C₂	—	188	4	no	—
544	C₂	#20256777	1	4	yes	direct product factor
545	C₂	C₂³×#10625352	1	1	yes	characteristic
546	C₂	C₂×#15689959	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#532	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	C₂×#3455
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #20256777	C₂	direct (N × H)
2. C₂×#15689742	C₂	semidirect
3. C₂×#15689734	C₂	semidirect
4. C₂×#15689727	C₂	semidirect
5. C₂×#15689718	C₂	semidirect
6. C₂×#15689710	C₂	semidirect
7. C₂×#15689680	C₂	semidirect
8. C₂×#15689653	C₂	semidirect
9. C₂×#15689630	C₂	semidirect
10. C₂×#41×Dic₄₇	C₂	semidirect
11. C₂²×#13093981	C₂	semidirect
12. C₂×C₄₇×#532	C₂	semidirect
14. #15689742	C₂²	semidirect
15. #15689734	C₂²	semidirect
16. #15689727	C₂²	semidirect
17. #15689718	C₂²	semidirect
18. #15689710	C₂²	semidirect
19. #15689680	C₂²	semidirect
20. C₂×#13094024	C₂²	semidirect
21. #15689653	C₂²	semidirect
23. C₂×#13094017	C₂²	semidirect
24. C₂×#13094016	C₂²	semidirect
25. C₂×#13094014	C₂²	semidirect
27. #15689630	C₂²	semidirect
30. C₂×#13094005	C₂²	semidirect
32. C₂×#13094001	C₂²	semidirect
37. #41×Dic₄₇	C₂²	semidirect
38. C₂×Q₈×Dic₄₇	C₂²	semidirect
39. C₂×C₄×Dic₉₄	C₂²	semidirect
41. C₂×D₄×Dic₄₇	C₂²	semidirect
44. C₂×#13093983	C₂²	semidirect
48. C₂×#13093981	C₂²	semidirect
52. C₂²×C₄×Dic₄₇	C₂²	semidirect
54. C₄₇×#532	C₂²	semidirect
55. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
56. C₂×#127×C₄₇	C₂²	semidirect
57. C₂×#124×C₄₇	C₂²	semidirect
59. C₂×C₄×D₄×C₄₇	C₂²	semidirect
71. #13094024	C₂³	semidirect
73. #13094017	C₂³	semidirect
74. #13094016	C₂³	semidirect
75. #13094014	C₂³	semidirect
79. #13094005	C₂³	semidirect
81. #13094001	C₂³	semidirect
86. Q₈×Dic₄₇	C₂³	semidirect
87. C₄×Dic₉₄	C₂³	semidirect
89. D₄×Dic₄₇	C₂³	semidirect
92. #13093983	C₂³	semidirect
116. C₂×C₄×Dic₄₇	C₂³	semidirect
126. C₄⋊Q₈×C₄₇	C₂³	semidirect
127. #127×C₄₇	C₂³	semidirect
128. #124×C₄₇	C₂³	semidirect
130. C₄×D₄×C₄₇	C₂³	semidirect
275. C₂×#532	D₄₇	semidirect
282. C₂×C₄₇	#3455	semidirect
294. #532	C₂×D₄₇	semidirect
296. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
297. C₂×#127	C₂×D₄₇	semidirect
304. C₂×#124	C₂×D₄₇	semidirect
322. C₂×C₄×D₄	C₂×D₄₇	semidirect
334. C₄₇	C₂×#3455	semidirect
355. C₄⋊Q₈	C₂²×D₄₇	semidirect
356. #127	C₂²×D₄₇	semidirect
362. #124	C₂²×D₄₇	semidirect
378. C₄×D₄	C₂²×D₄₇	semidirect
544. C₂	#20256777	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20256777	2
C₂×#15689742	2
C₂×#15689734	2
C₂×#15689727	2
C₂×#15689718	2
C₂×#15689710	2
C₂×#15689680	2
C₂×#15689653	2
C₂×#15689630	2
C₂×#41×Dic₄₇	2
C₂²×#13093981	2
C₂×C₄₇×#532	2
C₂×#3455	47

Subgroups — C2×#20256777 #27123131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20256777 #27123131