Subgroups — C₂²×#15689813 #27123270

Order 12032.

7934 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689813	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#13094017	C₂	1	2	yes	maximal, complemented
3	C₂²×#13094016	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13094014	C₂	1	2	yes	maximal, complemented
5	C₂²×#13094005	C₂	1	2	yes	maximal
6	C₂²×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#13093980	C₂	1	2	yes	maximal, complemented
11	C₂³×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
13	C₂³×Dic₉₄	C₂²	1	1	yes	characteristic
14	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
15	#15689813	C₂²	1	256	yes	direct product factor
16	C₂×#13094017	C₂²	1	48	yes	complemented
17	C₂×#13094016	C₂²	1	24	yes	complemented
18	C₂×#13094014	C₂²	1	48	yes	complemented
19	C₂×#13094005	C₂²	1	48	yes	—
20	C₂×#13094003	C₂²	1	24	yes	complemented
21	C₂×#13094003	C₂²	1	24	yes	complemented
22	C₂×C₄×Dic₉₄	C₂²	1	24	yes	complemented
23	C₂×#13093983	C₂²	1	24	yes	complemented
24	C₂×#13093980	C₂²	1	48	yes	complemented
25	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
28	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊Dic₄₇	C₂²	1	24	yes	complemented
30	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	—
31	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	—
32	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	—
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×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
37	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
38	C₂²×C₄×Dic₄₇	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	—
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	C₂²×Dic₉₄	—	2	8	no	—
49	C₂²×Dic₉₄	C₂³	1	12	yes	—
50	C₂³×Dic₄₇	—	2	16	no	—
51	C₂³×Dic₄₇	C₂³	1	2	yes	—
52	C₂³×Dic₄₇	C₂³	1	2	yes	—
53	C₂³×Dic₄₇	C₂³	1	2	yes	—
54	C₂³×Dic₄₇	C₂³	1	2	yes	—
55	C₂³×Dic₄₇	C₂³	1	24	yes	—
56	#13094017	C₂³	1	128	yes	complemented
57	#13094016	C₂³	1	64	yes	complemented
58	#13094014	C₂³	1	128	yes	complemented
59	#13094005	C₂³	1	128	yes	—
60	#13094003	C₂³	1	64	yes	complemented
61	#13094003	C₂³	1	64	yes	complemented
62	C₄×Dic₉₄	C₂³	1	64	yes	complemented
63	#13093983	C₂³	1	64	yes	complemented
64	#13093980	C₂³	1	128	yes	complemented
65	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
66	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
67	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	—
68	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	64	yes	complemented
70	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
71	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
72	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
73	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
74	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
75	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	—
76	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	—
77	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	—
78	C₂×C₄×Dic₄₇	C₂³	1	24	yes	—
79	C₂×C₄×Dic₄₇	C₂³	1	24	yes	—
80	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
81	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₄₇	—	2	8	no	—
83	C₂²×D₄×C₄₇	C₂³	1	12	yes	—
84	C₂³×C₄×C₄₇	—	2	8	no	—
85	C₂³×C₄×C₄₇	—	2	8	no	—
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	12	yes	—
92	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₄₇	C₂³	1	64	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	C₂⁴×C₄₇	—	2	4	no	—
99	C₂⁴×C₄₇	—	2	4	no	—
100	C₂⁴×C₄₇	—	2	4	no	—
101	C₂⁴×C₄₇	—	2	4	no	—
102	C₂⁴×C₄₇	—	2	4	no	—
103	C₂⁴×C₄₇	#41	1	8	yes	—
104	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
105	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
106	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂×D₄×C₄₇	—	2	48	no	—
108	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
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	—	2	48	no	—
115	C₂²×C₄×C₄₇	#41	1	8	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	16	yes	—
122	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
123	C₂²×Dic₄₇	—	2	96	no	—
124	C₂²×Dic₄₇	—	2	8	no	—
125	C₂²×Dic₄₇	—	2	8	no	—
126	C₂²×Dic₄₇	—	2	8	no	—
127	C₂²×Dic₄₇	—	2	8	no	—
128	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
129	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
130	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
131	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
132	C₂²×Dic₄₇	C₂⁴	1	32	yes	—
133	C₂×Dic₉₄	—	2	48	no	—
134	C₂×Dic₉₄	C₂⁴	1	16	yes	—
135	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
136	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
137	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
138	C₄²×C₄₇	C₂⁴	1	16	yes	—
139	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
140	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
141	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
142	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
143	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
144	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
145	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
146	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
147	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
148	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
149	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
150	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
151	C₄×Dic₄₇	C₂⁴	1	32	yes	—
152	C₄×Dic₄₇	C₂⁴	1	32	yes	—
153	C₂³×C₄₇	—	2	32	no	—
154	C₂³×C₄₇	—	2	12	no	—
155	C₂³×C₄₇	—	2	12	no	—
156	C₂³×C₄₇	—	2	12	no	—
157	C₂³×C₄₇	—	2	12	no	—
158	C₂³×C₄₇	—	2	12	no	—
159	C₂³×C₄₇	—	4	16	no	—
160	C₂³×C₄₇	C₂×#41	1	4	yes	—
161	C₂³×C₄₇	C₂×#41	1	24	yes	—
162	C₂³×C₄₇	C₂×#41	1	4	yes	—
163	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
164	C₂³×C₄₇	C₂⁵	1	4	yes	—
165	C₂³×C₄₇	C₂⁵	1	4	yes	—
166	C₂³×C₄₇	C₂⁵	1	3	yes	—
167	D₄×C₄₇	—	2	32	no	—
168	C₂×C₄×C₄₇	—	2	12	no	—
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	32	no	—
173	C₂×C₄×C₄₇	—	2	32	no	—
174	C₂×C₄×C₄₇	C₂×#41	1	24	yes	—
175	C₂×C₄×C₄₇	C₂⁵	1	4	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×Dic₄₇	—	2	24	no	—
181	C₂×Dic₄₇	—	2	64	no	—
182	C₂×Dic₄₇	—	2	24	no	—
183	C₂×Dic₄₇	—	2	24	no	—
184	C₂×Dic₄₇	—	2	24	no	—
185	C₂×Dic₄₇	C₂⁵	1	8	yes	—
186	C₂×Dic₄₇	C₂⁵	1	8	yes	—
187	C₂×Dic₄₇	C₂⁵	1	8	yes	—
188	C₂×Dic₄₇	C₂⁵	1	8	yes	—
189	Dic₉₄	—	2	32	no	—
190	C₂²×#552	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	—	2	4	no	—
192	C₂²×C₄₇	—	2	4	no	—
193	C₂²×C₄₇	—	2	48	no	—
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	#552	1	16	yes	complemented
199	C₂²×C₄₇	C₂²×#41	1	6	yes	—
200	C₂²×C₄₇	C₂²×#41	1	8	yes	—
201	C₂²×C₄₇	C₂²×#41	1	6	yes	—
202	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	6	yes	—
203	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
204	C₄×C₄₇	—	2	4	no	—
205	C₄×C₄₇	—	2	4	no	—
206	C₄×C₄₇	—	2	4	no	—
207	C₄×C₄₇	—	2	4	no	—
208	C₄×C₄₇	C₂²×#41	1	8	yes	—
209	Dic₄₇	—	2	8	no	—
210	Dic₄₇	—	2	8	no	—
211	Dic₄₇	—	2	8	no	—
212	Dic₄₇	—	2	8	no	—
213	C₂×#552	—	47	48	no	—
214	C₂²×#126	—	47	2	no	—
215	C₂²×#125	—	47	1	no	—
216	C₂²×#125	—	47	2	no	—
217	C₂²×#123	—	47	2	no	—
218	C₂²×C₂²⋊Q₈	—	47	1	no	—
219	C₂²×C₂²⋊Q₈	—	47	1	no	—
220	C₂²×C₄×Q₈	—	47	1	no	—
221	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
222	C₂²×#117	—	47	1	no	—
223	C₂²×#117	—	47	2	no	—
224	C₂³×C₄⋊C₄	—	47	1	no	—
225	C₂×C₄₇	—	2	8	no	—
226	C₂×C₄₇	—	4	4	no	—
227	C₂×C₄₇	C₂×#552	1	12	yes	complemented
228	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
229	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
230	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
231	C₂³×Q₈	—	47	1	no	—
232	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
233	C₂⁴×C₄	—	47	2	no	—
234	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
235	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
236	#552	—	47	256	no	—
237	C₂×#126	—	47	48	no	—
238	C₂×#125	—	47	48	no	—
239	C₂×#125	—	47	24	no	—
240	C₂×#123	—	47	48	no	—
241	C₂×C₂²⋊Q₈	—	47	24	no	—
242	C₂×C₂²⋊Q₈	—	47	24	no	—
243	C₂×C₄×Q₈	—	47	24	no	—
244	C₂×C₄×D₄	C₂×D₄₇	1	24	yes	—
245	C₂×#117	—	47	24	no	—
246	C₂×#117	—	47	48	no	—
247	C₂²×C₄⋊C₄	—	47	1	no	—
248	C₂²×C₄⋊C₄	—	47	1	no	—
249	C₂²×C₄⋊C₄	—	47	2	no	—
250	C₂²×C₄⋊C₄	—	47	24	no	—
251	C₂²×C₄⋊C₄	—	47	2	no	—
252	C₂²×C₄⋊C₄	—	47	2	no	—
253	C₂²×C₄⋊C₄	—	47	1	no	—
254	C₂²×C₄⋊C₄	—	47	2	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×C₂²⋊C₄	—	47	2	no	—
259	C₂²×C₂²⋊C₄	—	47	2	no	—
260	C₂²×C₂²⋊C₄	—	47	2	no	—
261	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
263	C₂²×C₄²	—	47	2	no	—
264	C₂²×C₄²	—	47	2	no	—
265	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
266	C₄₇	C₂²×#552	1	1	yes	characteristic, complemented, Sylow
267	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
268	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
269	C₂²×Q₈	—	47	12	no	—
270	C₂²×Q₈	—	94	8	no	—
271	C₂²×D₄	—	2	8	no	—
272	C₂²×D₄	C₂²×D₄₇	1	12	yes	—
273	C₂³×C₄	—	2	8	no	—
274	C₂³×C₄	—	2	8	no	—
275	C₂³×C₄	—	47	24	no	—
276	C₂³×C₄	—	47	2	no	—
277	C₂³×C₄	—	47	2	no	—
278	C₂³×C₄	—	47	2	no	—
279	C₂³×C₄	—	47	2	no	—
280	C₂³×C₄	—	94	16	no	—
281	C₂³×C₄	C₂²×D₄₇	1	12	yes	—
282	C₂³×C₄	C₂²×D₄₇	1	12	yes	—
283	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
284	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
285	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
286	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
287	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
288	#126	—	47	128	no	—
289	#125	—	47	128	no	—
290	#125	—	47	64	no	—
291	#123	—	47	128	no	—
292	C₂²⋊Q₈	—	47	64	no	—
293	C₂²⋊Q₈	—	47	64	no	—
294	C₄×Q₈	—	47	64	no	—
295	C₄×D₄	C₂²×D₄₇	1	64	yes	—
296	#117	—	47	64	no	—
297	#117	—	47	128	no	—
298	C₂×C₄⋊C₄	—	47	12	no	—
299	C₂×C₄⋊C₄	—	47	12	no	—
300	C₂×C₄⋊C₄	—	47	24	no	—
301	C₂×C₄⋊C₄	—	47	64	no	—
302	C₂×C₄⋊C₄	—	47	24	no	—
303	C₂×C₄⋊C₄	—	47	12	no	—
304	C₂×C₄⋊C₄	—	47	24	no	—
305	C₂×C₄⋊C₄	—	47	24	no	—
306	C₂×C₄⋊C₄	—	47	24	no	—
307	C₂×C₄⋊C₄	—	47	24	no	—
308	C₂×C₄⋊C₄	C₂²×D₄₇	1	12	yes	—
309	C₂×C₂²⋊C₄	—	47	24	no	—
310	C₂×C₂²⋊C₄	—	47	24	no	—
311	C₂×C₂²⋊C₄	—	47	24	no	—
312	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
313	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
314	C₂×C₄²	—	47	24	no	—
315	C₂×C₄²	—	47	24	no	—
316	C₂×C₄²	C₂²×D₄₇	1	12	yes	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	—	2	4	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	#10625350	1	8	yes	—
323	C₂⁴	C₂³×D₄₇	1	6	yes	—
324	C₂⁴	C₂³×D₄₇	1	6	yes	—
325	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
326	C₂×Q₈	—	47	16	no	—
327	C₂×Q₈	—	94	48	no	—
328	C₂×D₄	—	2	48	no	—
329	C₂×D₄	C₂³×D₄₇	1	16	yes	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	48	no	—
335	C₂²×C₄	—	2	48	no	—
336	C₂²×C₄	—	47	12	no	—
337	C₂²×C₄	—	47	12	no	—
338	C₂²×C₄	—	47	12	no	—
339	C₂²×C₄	—	47	12	no	—
340	C₂²×C₄	—	47	32	no	—
341	C₂²×C₄	—	94	8	no	—
342	C₂²×C₄	—	94	96	no	—
343	C₂²×C₄	—	94	8	no	—
344	C₂²×C₄	—	94	8	no	—
345	C₂²×C₄	—	94	8	no	—
346	C₂²×C₄	#10625352	1	8	yes	—
347	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
348	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
349	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
350	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
351	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
352	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
353	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
354	C₄⋊C₄	—	47	32	no	—
355	C₄⋊C₄	—	47	32	no	—
356	C₄⋊C₄	—	47	32	no	—
357	C₄⋊C₄	—	47	32	no	—
358	C₄⋊C₄	—	47	32	no	—
359	C₄⋊C₄	—	47	16	no	—
360	C₄⋊C₄	—	47	16	no	—
361	C₄⋊C₄	—	47	32	no	—
362	C₄⋊C₄	—	47	16	no	—
363	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
364	C₂²⋊C₄	—	47	32	no	—
365	C₂²⋊C₄	—	47	32	no	—
366	C₂²⋊C₄	—	47	32	no	—
367	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
368	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
369	C₄²	—	47	32	no	—
370	C₄²	—	47	32	no	—
371	C₄²	C₂³×D₄₇	1	16	yes	—
372	C₂³	—	2	32	no	—
373	C₂³	—	2	12	no	—
374	C₂³	—	2	12	no	—
375	C₂³	—	2	12	no	—
376	C₂³	—	2	12	no	—
377	C₂³	—	2	12	no	—
378	C₂³	—	4	16	no	—
379	C₂³	C₂×#10625352	1	4	yes	—
380	C₂³	C₂×#10625350	1	24	yes	—
381	C₂³	C₂×#10625350	1	4	yes	—
382	C₂³	#13094071	1	4	yes	—
383	C₂³	C₂⁴×D₄₇	1	4	yes	—
384	C₂³	C₂⁴×D₄₇	1	4	yes	—
385	C₂³	C₂⁴×D₄₇	1	3	yes	—
386	Q₈	—	94	32	no	—
387	D₄	—	2	32	no	—
388	C₂×C₄	—	2	12	no	—
389	C₂×C₄	—	2	12	no	—
390	C₂×C₄	—	2	12	no	—
391	C₂×C₄	—	2	12	no	—
392	C₂×C₄	—	2	32	no	—
393	C₂×C₄	—	2	32	no	—
394	C₂×C₄	—	47	8	no	—
395	C₂×C₄	—	47	8	no	—
396	C₂×C₄	—	47	8	no	—
397	C₂×C₄	—	47	8	no	—
398	C₂×C₄	—	94	24	no	—
399	C₂×C₄	—	94	64	no	—
400	C₂×C₄	—	94	24	no	—
401	C₂×C₄	—	94	24	no	—
402	C₂×C₄	—	94	24	no	—
403	C₂×C₄	C₂×#10625352	1	24	yes	—
404	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
405	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
406	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
407	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
408	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
409	C₂²	—	2	48	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	4	24	no	—
416	C₂²	#15689813	1	16	yes	direct product factor
417	C₂²	C₂²×#10625352	1	6	yes	—
418	C₂²	C₂²×#10625350	1	8	yes	—
419	C₂²	C₂²×#10625350	1	6	yes	—
420	C₂²	C₂×#13094071	1	6	yes	—
421	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	4	no	—
426	C₄	—	94	8	no	—
427	C₄	—	94	8	no	—
428	C₄	—	94	8	no	—
429	C₄	—	94	8	no	—
430	C₄	C₂²×#10625352	1	8	yes	—
431	C₂	—	2	8	no	—
432	C₂	—	4	4	no	—
433	C₂	C₂×#15689813	1	12	yes	direct product factor
434	C₂	C₂³×#10625352	1	1	yes	characteristic
435	C₂	C₂³×#10625350	1	1	yes	characteristic
436	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×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂³×D₄×C₄₇	C₂²
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂²×#552
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×#15689813	C₂	direct (N × H)
2. C₂²×#13094017	C₂	semidirect
3. C₂²×#13094016	C₂	semidirect
4. C₂²×#13094014	C₂	semidirect
6. C₂²×#13094003	C₂	semidirect
7. C₂²×#13094003	C₂	semidirect
8. C₂²×C₄×Dic₉₄	C₂	semidirect
9. C₂²×#13093983	C₂	semidirect
10. C₂²×#13093980	C₂	semidirect
11. C₂³×C₄⋊Dic₄₇	C₂	semidirect
15. #15689813	C₂²	direct (N × H)
16. C₂×#13094017	C₂²	semidirect
17. C₂×#13094016	C₂²	semidirect
18. C₂×#13094014	C₂²	semidirect
20. C₂×#13094003	C₂²	semidirect
21. C₂×#13094003	C₂²	semidirect
22. C₂×C₄×Dic₉₄	C₂²	semidirect
23. C₂×#13093983	C₂²	semidirect
24. C₂×#13093980	C₂²	semidirect
29. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
56. #13094017	C₂³	semidirect
57. #13094016	C₂³	semidirect
58. #13094014	C₂³	semidirect
60. #13094003	C₂³	semidirect
61. #13094003	C₂³	semidirect
62. C₄×Dic₉₄	C₂³	semidirect
63. #13093983	C₂³	semidirect
64. #13093980	C₂³	semidirect
69. C₂×C₄⋊Dic₄₇	C₂³	semidirect
198. C₂²×C₄₇	#552	semidirect
227. C₂×C₄₇	C₂×#552	semidirect
266. C₄₇	C₂²×#552	semidirect
416. C₂²	#15689813	direct (N × H)
433. C₂	C₂×#15689813	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×#15689813	2
C₂²×#13094017	2
C₂²×#13094016	2
C₂²×#13094014	2
C₂²×#13094005	2
C₂²×#13094003	2
C₂²×C₄×Dic₉₄	2
C₂²×#13093983	2
C₂²×#13093980	2
C₂³×C₄⋊Dic₄₇	2
C₂²×C₄×D₄×C₄₇	2
C₂²×#552	47

Subgroups — C22×#15689813 #27123270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689813 #27123270