Subgroups — C₂²×#15689744 #27123067

Order 12032.

7974 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689744	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#13094024	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13094019	C₂	1	2	yes	maximal, complemented
4	C₂²×#13094012	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13094010	C₂	1	2	yes	maximal, complemented
6	C₂²×#13094006	C₂	1	2	yes	maximal, complemented
7	C₂²×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13094002	C₂	1	2	yes	maximal, complemented
9	C₂²×#13093998	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Dic₉₄	C₂²	1	1	yes	characteristic
14	C₂³×Dic₉₄	C₂²	1	2	yes	—
15	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
16	C₂³×C₂²⋊D₄₇	C₂²	1	2	yes	—
17	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
18	#15689744	C₂²	1	256	yes	direct product factor
19	C₂×#13094024	C₂²	1	24	yes	complemented
20	C₂×#13094019	C₂²	1	48	yes	complemented
21	C₂×#13094012	C₂²	1	24	yes	complemented
22	C₂×#13094010	C₂²	1	48	yes	complemented
23	C₂×#13094006	C₂²	1	48	yes	complemented
24	C₂×#13094003	C₂²	1	24	yes	complemented
25	C₂×#13094002	C₂²	1	48	yes	complemented
26	C₂×#13093998	C₂²	1	24	yes	—
27	C₂×C₄×Dic₉₄	C₂²	1	24	yes	complemented
28	C₂×C₄×D₁₈₈	C₂²	1	24	yes	complemented
29	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
32	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	—
33	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
35	C₂²×(C₂×D₄₇)⋊C₄	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	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#117×C₄₇	C₂²	1	24	yes	complemented
42	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
48	C₂⁴×D₄₇	C₂³	1	2	yes	—
49	C₂²×Dic₉₄	—	2	8	no	—
50	C₂²×Dic₉₄	—	4	8	no	—
51	C₂²×Dic₉₄	C₂³	1	12	yes	—
52	C₂²×Dic₉₄	C₂³	1	24	yes	—
53	C₂²×D₁₈₈	—	2	8	no	—
54	C₂²×D₁₈₈	C₂³	1	12	yes	—
55	C₂²×C₂²⋊D₄₇	—	4	8	no	—
56	C₂²×C₂²⋊D₄₇	C₂³	1	24	yes	—
57	C₂³×Dic₄₇	C₂³	1	2	yes	—
58	C₂³×Dic₄₇	C₂³	1	2	yes	—
59	C₂³×Dic₄₇	C₂³	1	2	yes	—
60	C₂²×C₄×D₄₇	—	4	8	no	—
61	C₂²×C₄×D₄₇	C₂³	1	24	yes	—
62	#13094024	C₂³	1	64	yes	complemented
63	#13094019	C₂³	1	128	yes	complemented
64	#13094012	C₂³	1	64	yes	complemented
65	#13094010	C₂³	1	128	yes	complemented
66	#13094006	C₂³	1	128	yes	complemented
67	#13094003	C₂³	1	64	yes	complemented
68	#13094002	C₂³	1	128	yes	complemented
69	#13093998	C₂³	1	64	yes	—
70	C₄×Dic₉₄	C₂³	1	64	yes	complemented
71	C₄×D₁₈₈	C₂³	1	64	yes	complemented
72	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
73	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
74	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	—
75	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
76	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
77	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	—
78	C₂×(C₂×D₄₇)⋊C₄	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	C₂³×C₄×C₄₇	—	2	8	no	—
85	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₇	C₂³	1	12	yes	—
91	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	#117×C₄₇	C₂³	1	64	yes	complemented
93	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
94	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
95	C₂×C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
96	C₂×C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
97	C₂×C₄²×C₄₇	C₂³	1	12	yes	—
98	C₂×C₄²×C₄₇	C₂³	1	12	yes	—
99	C₂⁴×C₄₇	—	2	4	no	—
100	C₂⁴×C₄₇	—	2	4	no	—
101	C₂⁴×C₄₇	—	2	4	no	—
102	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
103	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₂³×D₄₇	—	2	8	no	—
105	C₂³×D₄₇	—	2	8	no	—
106	C₂³×D₄₇	—	2	8	no	—
107	C₂³×D₄₇	C₂⁴	1	12	yes	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	4	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	48	no	—
114	C₂²×C₄×C₄₇	#41	1	8	yes	—
115	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
116	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
117	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
118	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
119	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
120	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
121	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
122	C₂×C₂²⋊D₄₇	—	4	48	no	—
123	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
124	C₂²×Dic₄₇	—	2	8	no	—
125	C₂²×Dic₄₇	—	2	8	no	—
126	C₂²×Dic₄₇	—	2	8	no	—
127	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
128	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
129	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
130	C₂×D₁₈₈	—	2	48	no	—
131	C₂×D₁₈₈	C₂⁴	1	16	yes	—
132	C₂×C₄×D₄₇	—	4	48	no	—
133	C₂×C₄×D₄₇	C₂⁴	1	32	yes	—
134	C₂×Dic₉₄	—	2	48	no	—
135	C₂×Dic₉₄	—	4	48	no	—
136	C₂×Dic₉₄	C₂⁴	1	16	yes	—
137	C₂×Dic₉₄	C₂⁴	1	32	yes	—
138	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
139	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
140	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
141	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
142	C₄²×C₄₇	C₂⁴	1	16	yes	—
143	C₄²×C₄₇	C₂⁴	1	16	yes	—
144	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
145	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
146	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
147	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
148	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
149	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
150	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
151	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
152	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
153	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
154	C₄×Dic₄₇	C₂⁴	1	32	yes	—
155	C₂³×C₄₇	—	2	12	no	—
156	C₂³×C₄₇	—	2	12	no	—
157	C₂³×C₄₇	—	2	12	no	—
158	C₂³×C₄₇	—	4	16	no	—
159	C₂³×C₄₇	C₂×#41	1	4	yes	—
160	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
161	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
162	C₂³×C₄₇	C₂⁵	1	4	yes	—
163	C₂³×C₄₇	C₂⁵	1	3	yes	—
164	C₂²×D₄₇	—	2	24	no	—
165	C₂²×D₄₇	—	2	24	no	—
166	C₂²×D₄₇	—	2	24	no	—
167	C₂²×D₄₇	—	4	32	no	—
168	C₂²×D₄₇	C₂⁵	1	8	yes	—
169	C₂×C₄×C₄₇	—	2	12	no	—
170	C₂×C₄×C₄₇	—	2	12	no	—
171	C₂×C₄×C₄₇	—	2	12	no	—
172	C₂×C₄×C₄₇	—	2	12	no	—
173	C₂×C₄×C₄₇	—	2	12	no	—
174	C₂×C₄×C₄₇	—	2	32	no	—
175	C₂×C₄×C₄₇	C₂×#41	1	24	yes	—
176	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
177	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
178	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
179	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
180	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
181	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
182	C₂²⋊D₄₇	—	4	32	no	—
183	C₂×Dic₄₇	—	2	24	no	—
184	C₂×Dic₄₇	—	2	24	no	—
185	C₂×Dic₄₇	—	2	24	no	—
186	C₂×Dic₄₇	C₂⁵	1	8	yes	—
187	C₂×Dic₄₇	C₂⁵	1	8	yes	—
188	C₂×Dic₄₇	C₂⁵	1	8	yes	—
189	D₁₈₈	—	2	32	no	—
190	C₄×D₄₇	—	4	32	no	—
191	Dic₉₄	—	2	32	no	—
192	Dic₉₄	—	4	32	no	—
193	C₂²×#542	—	47	1	no	maximal, Sylow
194	C₂²×C₄₇	—	2	4	no	—
195	C₂²×C₄₇	—	2	4	no	—
196	C₂²×C₄₇	—	2	4	no	—
197	C₂²×C₄₇	—	4	24	no	—
198	C₂²×C₄₇	#542	1	16	yes	complemented
199	C₂²×C₄₇	C₂²×#41	1	6	yes	—
200	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	6	yes	—
201	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	6	yes	—
202	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
203	C₂×D₄₇	—	2	8	no	—
204	C₂×D₄₇	—	2	8	no	—
205	C₂×D₄₇	—	2	8	no	—
206	C₂×D₄₇	—	4	48	no	—
207	C₄×C₄₇	—	2	4	no	—
208	C₄×C₄₇	—	2	4	no	—
209	C₄×C₄₇	—	2	4	no	—
210	C₄×C₄₇	—	2	4	no	—
211	C₄×C₄₇	—	2	4	no	—
212	C₄×C₄₇	C₂²×#41	1	8	yes	—
213	Dic₄₇	—	2	8	no	—
214	Dic₄₇	—	2	8	no	—
215	Dic₄₇	—	2	8	no	—
216	C₂×#542	—	47	48	no	—
217	C₂²×C₄⋊Q₈	—	47	1	no	—
218	C₂²×#126	—	47	2	no	—
219	C₂²×#124	—	47	1	no	—
220	C₂²×#124	—	47	2	no	—
221	C₂²×#123	—	47	2	no	—
222	C₂²×C₂²⋊Q₈	—	47	1	no	—
223	C₂²×C₂²⋊Q₈	—	47	2	no	—
224	C₂²×#121	—	47	1	no	—
225	C₂²×C₄×Q₈	—	47	1	no	—
226	C₂²×C₄×D₄	—	47	1	no	—
227	C₂²×#117	D₄₇	1	1	yes	characteristic, complemented
228	C₂×C₄₇	—	4	4	no	—
229	C₂×C₄₇	C₂×#542	1	12	yes	complemented
230	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
231	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
233	D₄₇	—	4	8	no	—
234	C₂³×Q₈	—	47	1	no	—
235	C₂³×Q₈	—	47	2	no	—
236	C₂³×D₄	—	47	2	no	—
237	C₂³×D₄	—	47	1	no	—
238	C₂⁴×C₄	—	47	2	no	—
239	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
240	#542	—	47	256	no	—
241	C₂×C₄⋊Q₈	—	47	24	no	—
242	C₂×#126	—	47	48	no	—
243	C₂×#124	—	47	48	no	—
244	C₂×#124	—	47	24	no	—
245	C₂×#123	—	47	48	no	—
246	C₂×C₂²⋊Q₈	—	47	24	no	—
247	C₂×C₂²⋊Q₈	—	47	48	no	—
248	C₂×#121	—	47	24	no	—
249	C₂×C₄×Q₈	—	47	24	no	—
250	C₂×C₄×D₄	—	47	24	no	—
251	C₂×#117	C₂×D₄₇	1	24	yes	complemented
252	C₂²×C₄⋊C₄	—	47	1	no	—
253	C₂²×C₄⋊C₄	—	47	2	no	—
254	C₂²×C₄⋊C₄	—	47	1	no	—
255	C₂²×C₄⋊C₄	—	47	2	no	—
256	C₂²×C₄⋊C₄	—	47	2	no	—
257	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	—	47	2	no	—
260	C₂²×C₂²⋊C₄	—	47	2	no	—
261	C₂²×C₂²⋊C₄	—	47	2	no	—
262	C₂²×C₂²⋊C₄	—	47	2	no	—
263	C₂²×C₂²⋊C₄	—	47	2	no	—
264	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
266	C₂²×C₄²	—	47	2	no	—
267	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
268	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
269	C₄₇	C₂²×#542	1	1	yes	characteristic, complemented, Sylow
270	C₂⁵	—	47	2	no	—
271	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
272	C₂²×Q₈	—	47	12	no	—
273	C₂²×Q₈	—	47	24	no	—
274	C₂²×Q₈	—	94	8	no	—
275	C₂²×Q₈	—	188	8	no	—
276	C₂²×D₄	—	47	24	no	—
277	C₂²×D₄	—	47	12	no	—
278	C₂²×D₄	—	94	8	no	—
279	C₂²×D₄	—	188	8	no	—
280	C₂³×C₄	—	2	8	no	—
281	C₂³×C₄	—	47	2	no	—
282	C₂³×C₄	—	47	2	no	—
283	C₂³×C₄	—	47	2	no	—
284	C₂³×C₄	—	47	24	no	—
285	C₂³×C₄	—	188	8	no	—
286	C₂³×C₄	C₂²×D₄₇	1	12	yes	—
287	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
288	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
289	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
290	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
291	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
292	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
293	C₄⋊Q₈	—	47	64	no	—
294	#126	—	47	128	no	—
295	#124	—	47	128	no	—
296	#124	—	47	64	no	—
297	#123	—	47	128	no	—
298	C₂²⋊Q₈	—	47	64	no	—
299	C₂²⋊Q₈	—	47	128	no	—
300	#121	—	47	64	no	—
301	C₄×Q₈	—	47	64	no	—
302	C₄×D₄	—	47	64	no	—
303	#117	C₂²×D₄₇	1	64	yes	complemented
304	C₂×C₄⋊C₄	—	47	12	no	—
305	C₂×C₄⋊C₄	—	47	12	no	—
306	C₂×C₄⋊C₄	—	47	24	no	—
307	C₂×C₄⋊C₄	—	47	24	no	—
308	C₂×C₄⋊C₄	—	47	24	no	—
309	C₂×C₄⋊C₄	C₂²×D₄₇	1	12	yes	—
310	C₂×C₄⋊C₄	C₂²×D₄₇	1	12	yes	—
311	C₂×C₂²⋊C₄	—	47	24	no	—
312	C₂×C₂²⋊C₄	—	47	24	no	—
313	C₂×C₂²⋊C₄	—	47	24	no	—
314	C₂×C₂²⋊C₄	—	47	24	no	—
315	C₂×C₂²⋊C₄	—	47	24	no	—
316	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
317	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
318	C₂×C₄²	—	47	24	no	—
319	C₂×C₄²	C₂²×D₄₇	1	12	yes	—
320	C₂×C₄²	C₂²×D₄₇	1	12	yes	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	4	no	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	—	47	12	no	—
325	C₂⁴	—	94	8	no	—
326	C₂⁴	—	94	8	no	—
327	C₂⁴	—	94	8	no	—
328	C₂⁴	C₂³×D₄₇	1	6	yes	—
329	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
330	C₂×Q₈	—	47	16	no	—
331	C₂×Q₈	—	47	32	no	—
332	C₂×Q₈	—	94	48	no	—
333	C₂×Q₈	—	188	48	no	—
334	C₂×D₄	—	47	32	no	—
335	C₂×D₄	—	47	16	no	—
336	C₂×D₄	—	94	48	no	—
337	C₂×D₄	—	188	48	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	48	no	—
344	C₂²×C₄	—	47	12	no	—
345	C₂²×C₄	—	47	12	no	—
346	C₂²×C₄	—	47	12	no	—
347	C₂²×C₄	—	47	32	no	—
348	C₂²×C₄	—	94	8	no	—
349	C₂²×C₄	—	94	8	no	—
350	C₂²×C₄	—	94	8	no	—
351	C₂²×C₄	—	188	48	no	—
352	C₂²×C₄	#10625350	1	8	yes	—
353	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
354	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
355	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
356	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
357	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
358	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
359	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
360	C₄⋊C₄	—	47	32	no	—
361	C₄⋊C₄	—	47	32	no	—
362	C₄⋊C₄	—	47	16	no	—
363	C₄⋊C₄	—	47	16	no	—
364	C₄⋊C₄	—	47	32	no	—
365	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
366	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
367	C₂²⋊C₄	—	47	32	no	—
368	C₂²⋊C₄	—	47	32	no	—
369	C₂²⋊C₄	—	47	32	no	—
370	C₂²⋊C₄	—	47	32	no	—
371	C₂²⋊C₄	—	47	32	no	—
372	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
373	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
374	C₄²	—	47	32	no	—
375	C₄²	C₂³×D₄₇	1	16	yes	—
376	C₄²	C₂³×D₄₇	1	16	yes	—
377	C₂³	—	2	12	no	—
378	C₂³	—	2	12	no	—
379	C₂³	—	2	12	no	—
380	C₂³	—	4	16	no	—
381	C₂³	—	47	8	no	—
382	C₂³	—	94	24	no	—
383	C₂³	—	94	24	no	—
384	C₂³	—	94	24	no	—
385	C₂³	—	188	32	no	—
386	C₂³	C₂×#10625350	1	4	yes	—
387	C₂³	#13094070	1	4	yes	—
388	C₂³	#13094071	1	4	yes	—
389	C₂³	C₂⁴×D₄₇	1	4	yes	—
390	C₂³	C₂⁴×D₄₇	1	3	yes	—
391	Q₈	—	94	32	no	—
392	Q₈	—	188	32	no	—
393	D₄	—	94	32	no	—
394	D₄	—	188	32	no	—
395	C₂×C₄	—	2	12	no	—
396	C₂×C₄	—	2	12	no	—
397	C₂×C₄	—	2	12	no	—
398	C₂×C₄	—	2	12	no	—
399	C₂×C₄	—	2	12	no	—
400	C₂×C₄	—	2	32	no	—
401	C₂×C₄	—	47	8	no	—
402	C₂×C₄	—	47	8	no	—
403	C₂×C₄	—	47	8	no	—
404	C₂×C₄	—	94	24	no	—
405	C₂×C₄	—	94	24	no	—
406	C₂×C₄	—	94	24	no	—
407	C₂×C₄	—	188	32	no	—
408	C₂×C₄	C₂×#10625350	1	24	yes	—
409	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
410	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
411	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
412	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
413	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
414	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	24	no	—
419	C₂²	—	94	8	no	—
420	C₂²	—	94	8	no	—
421	C₂²	—	94	8	no	—
422	C₂²	—	188	48	no	—
423	C₂²	#15689744	1	16	yes	direct product factor
424	C₂²	C₂²×#10625350	1	6	yes	—
425	C₂²	C₂×#13094070	1	6	yes	—
426	C₂²	C₂×#13094071	1	6	yes	—
427	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
428	C₄	—	2	4	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	2	4	no	—
433	C₄	—	94	8	no	—
434	C₄	—	94	8	no	—
435	C₄	—	94	8	no	—
436	C₄	C₂²×#10625350	1	8	yes	—
437	C₂	—	4	4	no	—
438	C₂	—	188	8	no	—
439	C₂	C₂×#15689744	1	12	yes	direct product factor
440	C₂	C₂³×#10625350	1	1	yes	characteristic
441	C₂	C₂²×#13094070	1	1	yes	characteristic
442	C₂	C₂²×#13094071	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×#117×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂²×#13093998	C₂
hypercenter	C₂²×#117	D₄₇
hypocenter	C₄₇	C₂²×#542
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. C₂×#15689744	C₂	direct (N × H)
2. C₂²×#13094024	C₂	semidirect
3. C₂²×#13094019	C₂	semidirect
4. C₂²×#13094012	C₂	semidirect
5. C₂²×#13094010	C₂	semidirect
6. C₂²×#13094006	C₂	semidirect
7. C₂²×#13094003	C₂	semidirect
8. C₂²×#13094002	C₂	semidirect
10. C₂²×C₄×Dic₉₄	C₂	semidirect
11. C₂²×C₄×D₁₈₈	C₂	semidirect
12. C₂²×#117×C₄₇	C₂	semidirect
18. #15689744	C₂²	direct (N × H)
19. C₂×#13094024	C₂²	semidirect
20. C₂×#13094019	C₂²	semidirect
21. C₂×#13094012	C₂²	semidirect
22. C₂×#13094010	C₂²	semidirect
23. C₂×#13094006	C₂²	semidirect
24. C₂×#13094003	C₂²	semidirect
25. C₂×#13094002	C₂²	semidirect
27. C₂×C₄×Dic₉₄	C₂²	semidirect
28. C₂×C₄×D₁₈₈	C₂²	semidirect
41. C₂×#117×C₄₇	C₂²	semidirect
62. #13094024	C₂³	semidirect
63. #13094019	C₂³	semidirect
64. #13094012	C₂³	semidirect
65. #13094010	C₂³	semidirect
66. #13094006	C₂³	semidirect
67. #13094003	C₂³	semidirect
68. #13094002	C₂³	semidirect
70. C₄×Dic₉₄	C₂³	semidirect
71. C₄×D₁₈₈	C₂³	semidirect
92. #117×C₄₇	C₂³	semidirect
198. C₂²×C₄₇	#542	semidirect
227. C₂²×#117	D₄₇	semidirect
229. C₂×C₄₇	C₂×#542	semidirect
251. C₂×#117	C₂×D₄₇	semidirect
269. C₄₇	C₂²×#542	semidirect
303. #117	C₂²×D₄₇	semidirect
423. C₂²	#15689744	direct (N × H)
439. C₂	C₂×#15689744	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×#15689744	2
C₂²×#13094024	2
C₂²×#13094019	2
C₂²×#13094012	2
C₂²×#13094010	2
C₂²×#13094006	2
C₂²×#13094003	2
C₂²×#13094002	2
C₂²×#13093998	2
C₂²×C₄×Dic₉₄	2
C₂²×C₄×D₁₈₈	2
C₂²×#117×C₄₇	2
C₂²×#542	47

Subgroups — C22×#15689744 #27123067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689744 #27123067