Subgroups — C₂²×#15689819 #27123282

Order 12032.

8798 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689819	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#13094019	C₂	1	2	yes	maximal, complemented
3	C₂²×#13094016	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13094006	C₂	1	2	yes	maximal, complemented
5	C₂²×#13093998	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13093998	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13093996	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×(C₂²⋊D₄₇)⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₂²×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
14	C₂³×C₂²⋊D₄₇	C₂²	1	2	yes	—
15	C₂³×C₂²⋊D₄₇	C₂²	1	2	yes	—
16	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
17	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
18	#15689819	C₂²	1	256	yes	direct product factor
19	C₂×#13094019	C₂²	1	48	yes	complemented
20	C₂×#13094016	C₂²	1	24	yes	complemented
21	C₂×#13094006	C₂²	1	48	yes	complemented
22	C₂×#13093998	C₂²	1	24	yes	complemented
23	C₂×#13093998	C₂²	1	24	yes	complemented
24	C₂×#13093996	C₂²	1	48	yes	complemented
25	C₂×C₄×D₁₈₈	C₂²	1	24	yes	complemented
26	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	48	yes	complemented
27	C₂×#13093983	C₂²	1	24	yes	complemented
28	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
31	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊Dic₄₇	C₂²	1	24	yes	complemented
33	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	—
34	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
36	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
37	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
38	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
40	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₄₇	C₂²	1	24	yes	complemented
44	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
48	C₂⁴×D₄₇	C₂³	1	2	yes	—
49	C₂²×D₁₈₈	—	2	8	no	—
50	C₂²×D₁₈₈	C₂³	1	12	yes	—
51	C₂²×C₂²⋊D₄₇	—	2	16	no	—
52	C₂²×C₂²⋊D₄₇	—	4	8	no	—
53	C₂²×C₂²⋊D₄₇	C₂³	1	24	yes	—
54	C₂²×C₂²⋊D₄₇	C₂³	1	24	yes	—
55	C₂³×Dic₄₇	—	4	8	no	—
56	C₂³×Dic₄₇	C₂³	1	2	yes	—
57	C₂³×Dic₄₇	C₂³	1	2	yes	—
58	C₂³×Dic₄₇	C₂³	1	2	yes	—
59	C₂³×Dic₄₇	C₂³	1	24	yes	—
60	C₂²×C₄×D₄₇	—	4	8	no	—
61	C₂²×C₄×D₄₇	C₂³	1	24	yes	—
62	#13094019	C₂³	1	128	yes	complemented
63	#13094016	C₂³	1	64	yes	complemented
64	#13094006	C₂³	1	128	yes	complemented
65	#13093998	C₂³	1	64	yes	complemented
66	#13093998	C₂³	1	64	yes	complemented
67	#13093996	C₂³	1	128	yes	complemented
68	C₄×D₁₈₈	C₂³	1	64	yes	complemented
69	(C₂²⋊D₄₇)⋊C₄	C₂³	1	128	yes	complemented
70	#13093983	C₂³	1	64	yes	complemented
71	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
72	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
73	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	—
74	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
75	C₂×C₄⋊Dic₄₇	C₂³	1	64	yes	complemented
76	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
77	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
78	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	—
79	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	24	yes	—
80	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	24	yes	—
81	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	24	yes	—
82	C₂×C₄×Dic₄₇	C₂³	1	24	yes	—
83	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
84	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₄₇	—	2	8	no	—
86	C₂²×D₄×C₄₇	C₂³	1	12	yes	—
87	C₂³×C₄×C₄₇	—	2	8	no	—
88	C₂³×C₄×C₄₇	—	2	8	no	—
89	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₄₇	C₂³	1	12	yes	—
94	C₂³×C₄×C₄₇	C₂³	1	12	yes	—
95	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₄₇	C₂³	1	64	yes	complemented
97	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
98	C₂×C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
99	C₂×C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
100	C₂×C₄²×C₄₇	C₂³	1	12	yes	—
101	C₂⁴×C₄₇	—	2	4	no	—
102	C₂⁴×C₄₇	—	2	4	no	—
103	C₂⁴×C₄₇	—	2	4	no	—
104	C₂⁴×C₄₇	—	2	4	no	—
105	C₂⁴×C₄₇	—	2	4	no	—
106	C₂⁴×C₄₇	#41	1	8	yes	—
107	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
108	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
109	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
110	C₂³×D₄₇	—	2	8	no	—
111	C₂³×D₄₇	—	2	8	no	—
112	C₂³×D₄₇	—	2	8	no	—
113	C₂³×D₄₇	C₂⁴	1	12	yes	—
114	C₂×D₄×C₄₇	—	2	48	no	—
115	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
116	C₂²×C₄×C₄₇	—	2	4	no	—
117	C₂²×C₄×C₄₇	—	2	4	no	—
118	C₂²×C₄×C₄₇	—	2	4	no	—
119	C₂²×C₄×C₄₇	—	2	4	no	—
120	C₂²×C₄×C₄₇	—	2	48	no	—
121	C₂²×C₄×C₄₇	—	2	48	no	—
122	C₂²×C₄×C₄₇	#41	1	8	yes	—
123	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
125	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
126	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
127	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
128	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
129	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
130	C₂×C₂²⋊D₄₇	—	2	96	no	—
131	C₂×C₂²⋊D₄₇	—	4	48	no	—
132	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
133	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
134	C₂²×Dic₄₇	—	2	8	no	—
135	C₂²×Dic₄₇	—	2	8	no	—
136	C₂²×Dic₄₇	—	2	8	no	—
137	C₂²×Dic₄₇	—	4	48	no	—
138	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
139	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
140	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
141	C₂²×Dic₄₇	C₂⁴	1	32	yes	—
142	C₂×D₁₈₈	—	2	48	no	—
143	C₂×D₁₈₈	C₂⁴	1	16	yes	—
144	C₂×C₄×D₄₇	—	4	48	no	—
145	C₂×C₄×D₄₇	C₂⁴	1	32	yes	—
146	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
147	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
148	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
149	C₄²×C₄₇	C₂⁴	1	16	yes	—
150	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
151	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
152	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
153	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
154	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
155	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
156	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
157	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
158	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
159	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
160	C₄×Dic₄₇	C₂⁴	1	32	yes	—
161	C₂³×C₄₇	—	2	32	no	—
162	C₂³×C₄₇	—	2	12	no	—
163	C₂³×C₄₇	—	2	12	no	—
164	C₂³×C₄₇	—	2	12	no	—
165	C₂³×C₄₇	—	2	12	no	—
166	C₂³×C₄₇	—	2	12	no	—
167	C₂³×C₄₇	—	4	16	no	—
168	C₂³×C₄₇	C₂×#41	1	4	yes	—
169	C₂³×C₄₇	C₂×#41	1	24	yes	—
170	C₂³×C₄₇	C₂×#41	1	4	yes	—
171	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
172	C₂³×C₄₇	C₂⁵	1	4	yes	—
173	C₂³×C₄₇	C₂⁵	1	4	yes	—
174	C₂³×C₄₇	C₂⁵	1	3	yes	—
175	C₂²×D₄₇	—	2	24	no	—
176	C₂²×D₄₇	—	2	24	no	—
177	C₂²×D₄₇	—	2	24	no	—
178	C₂²×D₄₇	—	4	32	no	—
179	C₂²×D₄₇	C₂⁵	1	8	yes	—
180	D₄×C₄₇	—	2	32	no	—
181	C₂×C₄×C₄₇	—	2	12	no	—
182	C₂×C₄×C₄₇	—	2	12	no	—
183	C₂×C₄×C₄₇	—	2	12	no	—
184	C₂×C₄×C₄₇	—	2	12	no	—
185	C₂×C₄×C₄₇	—	2	32	no	—
186	C₂×C₄×C₄₇	—	2	32	no	—
187	C₂×C₄×C₄₇	C₂×#41	1	24	yes	—
188	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
189	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
190	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
191	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
192	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
193	C₂²⋊D₄₇	—	2	64	no	—
194	C₂²⋊D₄₇	—	4	32	no	—
195	C₂×Dic₄₇	—	2	24	no	—
196	C₂×Dic₄₇	—	2	24	no	—
197	C₂×Dic₄₇	—	2	24	no	—
198	C₂×Dic₄₇	—	4	32	no	—
199	C₂×Dic₄₇	C₂⁵	1	8	yes	—
200	C₂×Dic₄₇	C₂⁵	1	8	yes	—
201	C₂×Dic₄₇	C₂⁵	1	8	yes	—
202	D₁₈₈	—	2	32	no	—
203	C₄×D₄₇	—	4	32	no	—
204	C₂²×#553	—	47	1	no	maximal, Sylow
205	C₂²×C₄₇	—	2	4	no	—
206	C₂²×C₄₇	—	2	4	no	—
207	C₂²×C₄₇	—	2	48	no	—
208	C₂²×C₄₇	—	2	4	no	—
209	C₂²×C₄₇	—	2	4	no	—
210	C₂²×C₄₇	—	2	4	no	—
211	C₂²×C₄₇	—	4	24	no	—
212	C₂²×C₄₇	#553	1	16	yes	complemented
213	C₂²×C₄₇	C₂²×#41	1	6	yes	—
214	C₂²×C₄₇	C₂²×#41	1	8	yes	—
215	C₂²×C₄₇	C₂²×#41	1	6	yes	—
216	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	6	yes	—
217	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
218	C₂×D₄₇	—	2	8	no	—
219	C₂×D₄₇	—	2	8	no	—
220	C₂×D₄₇	—	2	8	no	—
221	C₂×D₄₇	—	4	48	no	—
222	C₄×C₄₇	—	2	4	no	—
223	C₄×C₄₇	—	2	4	no	—
224	C₄×C₄₇	—	2	4	no	—
225	C₄×C₄₇	—	2	4	no	—
226	C₄×C₄₇	C₂²×#41	1	8	yes	—
227	Dic₄₇	—	2	8	no	—
228	Dic₄₇	—	2	8	no	—
229	Dic₄₇	—	2	8	no	—
230	C₂×#553	—	47	48	no	—
231	C₂²×#126	—	47	2	no	—
232	C₂²×#125	—	47	1	no	—
233	C₂²×#123	—	47	2	no	—
234	C₂²×#121	—	47	2	no	—
235	C₂²×#121	—	47	1	no	—
236	C₂²×#121	—	47	1	no	—
237	C₂²×C₄×D₄	—	47	1	no	—
238	C₂²×C₄×D₄	—	47	2	no	—
239	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic, complemented
240	C₂²×#117	—	47	1	no	—
241	C₂³×C₄⋊C₄	—	47	1	no	—
242	C₂×C₄₇	—	2	8	no	—
243	C₂×C₄₇	—	4	4	no	—
244	C₂×C₄₇	C₂×#553	1	12	yes	complemented
245	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
246	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
247	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
248	D₄₇	—	4	8	no	—
249	C₂³×D₄	—	47	2	no	—
250	C₂³×D₄	—	47	2	no	—
251	C₂³×D₄	—	47	1	no	—
252	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
253	C₂⁴×C₄	—	47	2	no	—
254	C₂⁴×C₄	—	47	2	no	—
255	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
256	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
257	#553	—	47	256	no	—
258	C₂×#126	—	47	48	no	—
259	C₂×#125	—	47	24	no	—
260	C₂×#123	—	47	48	no	—
261	C₂×#121	—	47	48	no	—
262	C₂×#121	—	47	24	no	—
263	C₂×#121	—	47	24	no	—
264	C₂×C₄×D₄	—	47	48	no	—
265	C₂×C₄×D₄	—	47	24	no	—
266	C₂×C₄×D₄	C₂×D₄₇	1	24	yes	complemented
267	C₂×#117	—	47	24	no	—
268	C₂²×C₄⋊C₄	—	47	1	no	—
269	C₂²×C₄⋊C₄	—	47	1	no	—
270	C₂²×C₄⋊C₄	—	47	2	no	—
271	C₂²×C₄⋊C₄	—	47	24	no	—
272	C₂²×C₄⋊C₄	—	47	1	no	—
273	C₂²×C₄⋊C₄	—	47	2	no	—
274	C₂²×C₄⋊C₄	—	47	2	no	—
275	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	—	47	2	no	—
277	C₂²×C₂²⋊C₄	—	47	2	no	—
278	C₂²×C₂²⋊C₄	—	47	2	no	—
279	C₂²×C₂²⋊C₄	—	47	2	no	—
280	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
282	C₂²×C₄²	—	47	2	no	—
283	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
284	C₄₇	C₂²×#553	1	1	yes	characteristic, complemented, Sylow
285	C₂⁵	—	47	2	no	—
286	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
287	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
288	C₂²×D₄	—	2	8	no	—
289	C₂²×D₄	—	47	24	no	—
290	C₂²×D₄	—	47	24	no	—
291	C₂²×D₄	—	47	12	no	—
292	C₂²×D₄	—	94	16	no	—
293	C₂²×D₄	—	94	8	no	—
294	C₂²×D₄	—	188	8	no	—
295	C₂²×D₄	C₂²×D₄₇	1	12	yes	—
296	C₂³×C₄	—	2	8	no	—
297	C₂³×C₄	—	2	8	no	—
298	C₂³×C₄	—	47	2	no	—
299	C₂³×C₄	—	47	2	no	—
300	C₂³×C₄	—	47	2	no	—
301	C₂³×C₄	—	47	24	no	—
302	C₂³×C₄	—	47	24	no	—
303	C₂³×C₄	—	188	8	no	—
304	C₂³×C₄	—	188	8	no	—
305	C₂³×C₄	C₂²×D₄₇	1	12	yes	—
306	C₂³×C₄	C₂²×D₄₇	1	12	yes	—
307	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
308	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
309	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
310	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
311	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
312	#126	—	47	128	no	—
313	#125	—	47	64	no	—
314	#123	—	47	128	no	—
315	#121	—	47	128	no	—
316	#121	—	47	64	no	—
317	#121	—	47	64	no	—
318	C₄×D₄	—	47	128	no	—
319	C₄×D₄	—	47	64	no	—
320	C₄×D₄	C₂²×D₄₇	1	64	yes	complemented
321	#117	—	47	64	no	—
322	C₂×C₄⋊C₄	—	47	12	no	—
323	C₂×C₄⋊C₄	—	47	12	no	—
324	C₂×C₄⋊C₄	—	47	24	no	—
325	C₂×C₄⋊C₄	—	47	64	no	—
326	C₂×C₄⋊C₄	—	47	12	no	—
327	C₂×C₄⋊C₄	—	47	24	no	—
328	C₂×C₄⋊C₄	—	47	24	no	—
329	C₂×C₄⋊C₄	C₂²×D₄₇	1	12	yes	—
330	C₂×C₂²⋊C₄	—	47	24	no	—
331	C₂×C₂²⋊C₄	—	47	24	no	—
332	C₂×C₂²⋊C₄	—	47	24	no	—
333	C₂×C₂²⋊C₄	—	47	24	no	—
334	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
335	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
336	C₂×C₄²	—	47	24	no	—
337	C₂×C₄²	C₂²×D₄₇	1	12	yes	—
338	C₂⁴	—	2	4	no	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	2	4	no	—
341	C₂⁴	—	2	4	no	—
342	C₂⁴	—	2	4	no	—
343	C₂⁴	—	47	12	no	—
344	C₂⁴	—	94	8	no	—
345	C₂⁴	—	94	8	no	—
346	C₂⁴	—	94	8	no	—
347	C₂⁴	#10625350	1	8	yes	—
348	C₂⁴	C₂³×D₄₇	1	6	yes	—
349	C₂⁴	C₂³×D₄₇	1	6	yes	—
350	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
351	C₂×D₄	—	2	48	no	—
352	C₂×D₄	—	47	32	no	—
353	C₂×D₄	—	47	32	no	—
354	C₂×D₄	—	47	16	no	—
355	C₂×D₄	—	94	96	no	—
356	C₂×D₄	—	94	48	no	—
357	C₂×D₄	—	188	48	no	—
358	C₂×D₄	C₂³×D₄₇	1	16	yes	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	48	no	—
364	C₂²×C₄	—	2	48	no	—
365	C₂²×C₄	—	47	12	no	—
366	C₂²×C₄	—	47	12	no	—
367	C₂²×C₄	—	47	12	no	—
368	C₂²×C₄	—	47	32	no	—
369	C₂²×C₄	—	47	32	no	—
370	C₂²×C₄	—	94	8	no	—
371	C₂²×C₄	—	94	8	no	—
372	C₂²×C₄	—	94	8	no	—
373	C₂²×C₄	—	188	48	no	—
374	C₂²×C₄	—	188	48	no	—
375	C₂²×C₄	#10625352	1	8	yes	—
376	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
377	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
378	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
379	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
380	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
381	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
382	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
383	C₄⋊C₄	—	47	32	no	—
384	C₄⋊C₄	—	47	32	no	—
385	C₄⋊C₄	—	47	16	no	—
386	C₄⋊C₄	—	47	16	no	—
387	C₄⋊C₄	—	47	32	no	—
388	C₄⋊C₄	—	47	16	no	—
389	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
390	C₂²⋊C₄	—	47	32	no	—
391	C₂²⋊C₄	—	47	32	no	—
392	C₂²⋊C₄	—	47	32	no	—
393	C₂²⋊C₄	—	47	32	no	—
394	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
395	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
396	C₄²	—	47	32	no	—
397	C₄²	C₂³×D₄₇	1	16	yes	—
398	C₂³	—	2	32	no	—
399	C₂³	—	2	12	no	—
400	C₂³	—	2	12	no	—
401	C₂³	—	2	12	no	—
402	C₂³	—	2	12	no	—
403	C₂³	—	2	12	no	—
404	C₂³	—	4	16	no	—
405	C₂³	—	47	8	no	—
406	C₂³	—	94	24	no	—
407	C₂³	—	94	24	no	—
408	C₂³	—	94	24	no	—
409	C₂³	—	188	32	no	—
410	C₂³	C₂×#10625352	1	4	yes	—
411	C₂³	C₂×#10625350	1	24	yes	—
412	C₂³	C₂×#10625350	1	4	yes	—
413	C₂³	#13094070	1	4	yes	—
414	C₂³	C₂⁴×D₄₇	1	4	yes	—
415	C₂³	C₂⁴×D₄₇	1	4	yes	—
416	C₂³	C₂⁴×D₄₇	1	3	yes	—
417	D₄	—	2	32	no	—
418	D₄	—	94	64	no	—
419	D₄	—	94	32	no	—
420	D₄	—	188	32	no	—
421	C₂×C₄	—	2	12	no	—
422	C₂×C₄	—	2	12	no	—
423	C₂×C₄	—	2	12	no	—
424	C₂×C₄	—	2	12	no	—
425	C₂×C₄	—	2	32	no	—
426	C₂×C₄	—	2	32	no	—
427	C₂×C₄	—	47	8	no	—
428	C₂×C₄	—	47	8	no	—
429	C₂×C₄	—	47	8	no	—
430	C₂×C₄	—	94	24	no	—
431	C₂×C₄	—	94	24	no	—
432	C₂×C₄	—	94	24	no	—
433	C₂×C₄	—	188	32	no	—
434	C₂×C₄	—	188	32	no	—
435	C₂×C₄	C₂×#10625352	1	24	yes	—
436	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
437	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
438	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
439	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
440	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	48	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	4	24	no	—
448	C₂²	—	94	8	no	—
449	C₂²	—	94	8	no	—
450	C₂²	—	94	8	no	—
451	C₂²	—	188	48	no	—
452	C₂²	#15689819	1	16	yes	direct product factor
453	C₂²	C₂²×#10625352	1	6	yes	—
454	C₂²	C₂²×#10625350	1	8	yes	—
455	C₂²	C₂²×#10625350	1	6	yes	—
456	C₂²	C₂×#13094070	1	6	yes	—
457	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
458	C₄	—	2	4	no	—
459	C₄	—	2	4	no	—
460	C₄	—	2	4	no	—
461	C₄	—	2	4	no	—
462	C₄	—	94	8	no	—
463	C₄	—	94	8	no	—
464	C₄	—	94	8	no	—
465	C₄	C₂²×#10625352	1	8	yes	—
466	C₂	—	2	8	no	—
467	C₂	—	4	4	no	—
468	C₂	—	188	8	no	—
469	C₂	C₂×#15689819	1	12	yes	direct product factor
470	C₂	C₂³×#10625352	1	1	yes	characteristic
471	C₂	C₂³×#10625350	1	1	yes	characteristic
472	C₂	C₂²×#13094070	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂²×#553
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#15689819	C₂	direct (N × H)
2. C₂²×#13094019	C₂	semidirect
3. C₂²×#13094016	C₂	semidirect
4. C₂²×#13094006	C₂	semidirect
5. C₂²×#13093998	C₂	semidirect
6. C₂²×#13093998	C₂	semidirect
7. C₂²×#13093996	C₂	semidirect
8. C₂²×C₄×D₁₈₈	C₂	semidirect
9. C₂²×(C₂²⋊D₄₇)⋊C₄	C₂	semidirect
10. C₂²×#13093983	C₂	semidirect
11. C₂³×C₄⋊Dic₄₇	C₂	semidirect
12. C₂²×C₄×D₄×C₄₇	C₂	semidirect
18. #15689819	C₂²	direct (N × H)
19. C₂×#13094019	C₂²	semidirect
20. C₂×#13094016	C₂²	semidirect
21. C₂×#13094006	C₂²	semidirect
22. C₂×#13093998	C₂²	semidirect
23. C₂×#13093998	C₂²	semidirect
24. C₂×#13093996	C₂²	semidirect
25. C₂×C₄×D₁₈₈	C₂²	semidirect
26. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
27. C₂×#13093983	C₂²	semidirect
32. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
43. C₂×C₄×D₄×C₄₇	C₂²	semidirect
62. #13094019	C₂³	semidirect
63. #13094016	C₂³	semidirect
64. #13094006	C₂³	semidirect
65. #13093998	C₂³	semidirect
66. #13093998	C₂³	semidirect
67. #13093996	C₂³	semidirect
68. C₄×D₁₈₈	C₂³	semidirect
69. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
70. #13093983	C₂³	semidirect
75. C₂×C₄⋊Dic₄₇	C₂³	semidirect
96. C₄×D₄×C₄₇	C₂³	semidirect
212. C₂²×C₄₇	#553	semidirect
239. C₂²×C₄×D₄	D₄₇	semidirect
244. C₂×C₄₇	C₂×#553	semidirect
266. C₂×C₄×D₄	C₂×D₄₇	semidirect
284. C₄₇	C₂²×#553	semidirect
320. C₄×D₄	C₂²×D₄₇	semidirect
452. C₂²	#15689819	direct (N × H)
469. C₂	C₂×#15689819	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×#15689819	2
C₂²×#13094019	2
C₂²×#13094016	2
C₂²×#13094006	2
C₂²×#13093998	2
C₂²×#13093996	2
C₂²×C₄×D₁₈₈	2
C₂²×(C₂²⋊D₄₇)⋊C₄	2
C₂²×#13093983	2
C₂³×C₄⋊Dic₄₇	2
C₂²×C₄×D₄×C₄₇	2
C₂²×#553	47

Subgroups — C22×#15689819 #27123282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689819 #27123282