Subgroups — #27124819

Order 12032.

11534 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689959	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#20257069	C₂	1	8	yes	maximal, complemented
4	#20257058	C₂	1	8	yes	maximal, complemented
5	#20257047	C₂	1	2	yes	maximal, complemented
6	#20257040	C₂	1	2	yes	maximal, complemented
7	#20257033	C₂	1	6	yes	maximal, complemented
8	#20257024	C₂	1	6	yes	maximal, complemented
9	#41×D₁₈₈	C₂	1	16	yes	maximal, complemented
10	#20256721	C₂	1	6	yes	maximal, complemented
11	C₂×#15689635	C₂	1	6	yes	maximal, complemented
12	C₄₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689959	—	2	16	no	—
14	C₂×#13094072	C₂²	1	2	yes	complemented
15	C₂×#13094071	C₂²	1	4	yes	complemented
16	C₂×#13094070	C₂²	1	4	yes	complemented
17	C₂×#13094069	C₂²	1	6	yes	complemented
18	C₂²×#10625354	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#10625350	C₂²	1	3	yes	complemented
20	C₂²×#10625350	C₂²	1	6	yes	complemented
21	C₂²×#10625352	C₂²	1	3	yes	complemented
22	C₂×#41×D₄₇	—	2	16	no	—
23	C₂×#41×D₄₇	C₂²	1	8	yes	complemented
24	C₂×#41×D₄₇	C₂²	1	8	yes	complemented
25	C₂×#41×D₄₇	C₂²	1	8	yes	complemented
26	C₂²×Q₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₄×D₄₇	C₂²	1	3	yes	complemented
28	C₂³×C₄×D₄₇	C₂²	1	3	yes	complemented
29	#15689795	C₂²	1	16	yes	complemented
30	Q₈×D₁₈₈	C₂²	1	16	yes	complemented
31	#15689785	C₂²	1	16	yes	complemented
32	#15689785	C₂²	1	16	yes	complemented
33	#15689777	C₂²	1	48	yes	complemented
34	#15689768	C₂²	1	48	yes	complemented
35	#15689768	C₂²	1	48	yes	complemented
36	D₄×D₁₈₈	C₂²	1	48	yes	complemented
37	#15689704	C₂²	1	24	yes	complemented
38	#15689699	C₂²	1	12	yes	complemented
39	#15689699	C₂²	1	12	yes	complemented
40	#15689692	C₂²	1	12	yes	complemented
41	#15689692	C₂²	1	12	yes	complemented
42	#15689685	C₂²	1	24	yes	complemented
43	#15689673	C₂²	1	24	yes	complemented
44	#15689635	C₂²	1	12	yes	complemented
45	#15689635	C₂²	1	4	yes	complemented
46	#15689635	C₂²	1	12	yes	complemented
47	#15689635	C₂²	1	12	yes	complemented
48	#15689635	C₂²	1	24	yes	complemented
49	#15689635	C₂²	1	24	yes	complemented
50	#15689635	C₂²	1	24	yes	complemented
51	C₂×#13094008	C₂²	1	12	yes	complemented
52	C₂×#13094004	C₂²	1	12	yes	complemented
53	C₂×#13093999	C₂²	1	12	yes	complemented
54	C₂×#13093994	C₂²	1	12	yes	complemented
55	C₂×C₄×D₁₈₈	C₂²	1	24	yes	complemented
56	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
57	C₄₇×#520	C₂²	1	8	yes	complemented
58	C₄₇×#519	C₂²	1	2	yes	complemented
59	C₄₇×#518	C₂²	1	6	yes	complemented
60	C₄×#41×C₄₇	C₂²	1	8	yes	complemented
61	C₂×#117×C₄₇	C₂²	1	6	yes	complemented
62	C₂⁴×D₄₇	C₂³	1	3	yes	—
63	#13094072	—	2	16	no	—
64	#13094071	—	2	32	no	—
65	#13094070	—	2	32	no	—
66	#13094069	—	2	48	no	—
67	C₂×#10625354	—	2	8	no	—
68	C₂×#10625354	C₂³	1	8	yes	—
69	C₂×#10625354	C₂³	1	8	yes	complemented
70	C₂×#10625350	—	2	24	no	—
71	C₂×#10625350	—	2	48	no	—
72	C₂×#10625350	C₂³	1	4	yes	—
73	C₂×#10625350	C₂³	1	12	yes	—
74	C₂×#10625350	C₂³	1	12	yes	—
75	C₂×#10625350	C₂³	1	12	yes	—
76	C₂×#10625350	C₂³	1	12	yes	complemented
77	C₂×#10625350	C₂³	1	12	yes	complemented
78	C₂×#10625352	—	2	24	no	—
79	C₂×#10625352	C₂³	1	24	yes	—
80	C₂×#10625352	C₂³	1	24	yes	complemented
81	#41×D₄₇	—	2	64	no	—
82	#41×D₄₇	—	2	64	no	—
83	#41×D₄₇	—	2	64	no	—
84	C₂²×Dic₉₄	C₂³	1	3	yes	—
85	C₂²×Dic₉₄	C₂³	1	6	yes	complemented
86	C₂×Q₈×D₄₇	—	2	8	no	—
87	C₂×Q₈×D₄₇	C₂³	1	8	yes	—
88	C₂×Q₈×D₄₇	C₂³	1	8	yes	complemented
89	C₂²×D₁₈₈	C₂³	1	3	yes	—
90	C₂²×D₁₈₈	C₂³	1	24	yes	—
91	C₂²×D₁₈₈	C₂³	1	6	yes	complemented
92	C₂²×C₂²⋊D₄₇	C₂³	1	12	yes	—
93	C₂²×C₂²⋊D₄₇	C₂³	1	6	yes	—
94	C₂×D₄×D₄₇	—	2	24	no	—
95	C₂×D₄×D₄₇	C₂³	1	24	yes	—
96	C₂×D₄×D₄₇	C₂³	1	24	yes	complemented
97	C₂³×Dic₄₇	C₂³	1	3	yes	—
98	C₂²×C₄×D₄₇	—	2	24	no	—
99	C₂²×C₄×D₄₇	C₂³	1	12	yes	—
100	C₂²×C₄×D₄₇	C₂³	1	12	yes	—
101	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
103	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
104	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
105	C₂²×C₄×D₄₇	C₂³	1	12	yes	complemented
106	#13094024	C₂³	1	24	yes	complemented
107	#13094021	C₂³	1	24	yes	complemented
108	#13094012	C₂³	1	24	yes	complemented
109	#13094012	C₂³	1	24	yes	complemented
110	#13094008	C₂³	1	8	yes	—
111	#13094008	C₂³	1	24	yes	—
112	#13094008	C₂³	1	48	yes	complemented
113	#13094008	C₂³	1	48	yes	complemented
114	#13094004	C₂³	1	24	yes	—
115	#13094004	C₂³	1	8	yes	—
116	#13094004	C₂³	1	48	yes	complemented
117	#13094004	C₂³	1	24	yes	complemented
118	#13094004	C₂³	1	24	yes	complemented
119	#13093999	C₂³	1	24	yes	—
120	#13093999	C₂³	1	8	yes	—
121	#13093999	C₂³	1	48	yes	complemented
122	#13093999	C₂³	1	24	yes	complemented
123	#13093999	C₂³	1	24	yes	complemented
124	#13093998	C₂³	1	96	yes	complemented
125	#13093994	C₂³	1	48	yes	—
126	#13093994	C₂³	1	8	yes	—
127	#13093994	C₂³	1	24	yes	—
128	#13093994	C₂³	1	48	yes	complemented
129	C₄×D₁₈₈	C₂³	1	48	yes	—
130	C₄×D₁₈₈	C₂³	1	16	yes	—
131	C₄×D₁₈₈	C₂³	1	48	yes	complemented
132	C₄×D₁₈₈	C₂³	1	48	yes	complemented
133	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	complemented
134	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	24	yes	—
135	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	24	yes	complemented
136	C₂×#41×C₄₇	D₄	1	16	yes	complemented
137	C₂×#41×C₄₇	C₂³	1	4	yes	—
138	C₂×#41×C₄₇	C₂³	1	4	yes	—
139	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₄₇	C₂³	1	3	yes	—
141	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
142	C₄×Q₈×C₄₇	C₂³	1	16	yes	complemented
143	C₄×D₄×C₄₇	C₂³	1	48	yes	complemented
144	#117×C₄₇	C₂³	1	4	yes	—
145	#117×C₄₇	C₂³	1	12	yes	—
146	#117×C₄₇	C₂³	1	12	yes	complemented
147	#117×C₄₇	C₂³	1	12	yes	complemented
148	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	complemented
149	C₂×C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
150	C₂×C₄²×C₄₇	C₂³	1	12	yes	complemented
151	C₂⁴×C₄₇	C₂⁴	1	3	yes	—
152	C₂³×D₄₇	—	2	12	no	—
153	C₂³×D₄₇	—	4	12	no	—
154	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
155	C₂³×D₄₇	C₂⁴	1	12	yes	—
156	C₂³×D₄₇	C₂⁴	1	12	yes	—
157	C₂³×D₄₇	C₂⁴	1	3	yes	—
158	#41×C₄₇	C₂×D₄	1	32	yes	complemented
159	#41×C₄₇	C₂×D₄	1	32	yes	complemented
160	C₂×Q₈×C₄₇	C₂×D₄	1	8	yes	complemented
161	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
162	C₂×D₄×C₄₇	C₂×D₄	1	24	yes	complemented
163	C₂×D₄×C₄₇	C₂⁴	1	12	yes	—
164	C₂²×C₄×C₄₇	C₂×D₄	1	24	yes	complemented
165	C₂²×C₄×C₄₇	C₂⁴	1	24	yes	—
166	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
167	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
168	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
170	C₂×C₂²⋊D₄₇	—	2	24	no	—
171	C₂×C₂²⋊D₄₇	—	2	48	no	—
172	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
173	C₂×C₂²⋊D₄₇	C₂⁴	1	24	yes	—
174	C₂×C₂²⋊D₄₇	C₂⁴	1	24	yes	—
175	C₂²×Dic₄₇	—	2	12	no	—
176	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
177	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
178	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
179	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
180	#10625354	—	2	32	no	—
181	#10625354	—	2	32	no	—
182	Q₈×D₄₇	—	2	32	no	—
183	Q₈×D₄₇	—	2	32	no	—
184	#10625352	—	2	96	no	—
185	#10625352	—	2	96	no	—
186	D₄×D₄₇	—	2	96	no	—
187	D₄×D₄₇	—	2	96	no	—
188	#10625350	—	2	48	no	—
189	#10625350	—	2	48	no	—
190	#10625350	—	2	48	no	—
191	#10625350	—	2	16	no	—
192	#10625350	—	2	48	no	—
193	#10625350	—	2	48	no	—
194	C₂×D₁₈₈	—	2	12	no	—
195	C₂×D₁₈₈	—	2	24	no	—
196	C₂×D₁₈₈	—	4	48	no	—
197	C₂×D₁₈₈	C₂⁴	1	16	yes	—
198	C₂×D₁₈₈	C₂⁴	1	4	yes	—
199	C₂×D₁₈₈	C₂⁴	1	12	yes	—
200	C₂×D₁₈₈	C₂⁴	1	12	yes	—
201	C₂×D₁₈₈	C₂⁴	1	48	yes	—
202	C₂×C₄×D₄₇	—	2	4	no	—
203	C₂×C₄×D₄₇	—	2	12	no	—
204	C₂×C₄×D₄₇	—	2	48	no	—
205	C₂×C₄×D₄₇	—	2	48	no	—
206	C₂×C₄×D₄₇	—	2	12	no	—
207	C₂×C₄×D₄₇	—	2	12	no	—
208	C₂×C₄×D₄₇	—	2	48	no	—
209	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
210	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
211	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
212	C₂×C₄×D₄₇	C₂⁴	1	24	yes	—
213	C₂×C₄×D₄₇	C₂⁴	1	6	yes	—
214	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
215	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
216	C₂×C₄×D₄₇	C₂⁴	1	6	yes	—
217	C₂×Dic₉₄	—	2	12	no	—
218	C₂×Dic₉₄	—	2	24	no	—
219	C₂×Dic₉₄	C₂⁴	1	4	yes	—
220	C₂×Dic₉₄	C₂⁴	1	12	yes	—
221	C₂×Dic₉₄	C₂⁴	1	12	yes	—
222	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
223	C₄⋊C₄×C₄₇	C₂⁴	1	24	yes	—
224	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
225	C₂²⋊C₄×C₄₇	C₂⁴	1	24	yes	—
226	C₄²×C₄₇	C₂⁴	1	8	yes	—
227	C₄²×C₄₇	C₂⁴	1	24	yes	—
228	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
229	(C₂×D₄₇)⋊C₄	C₂⁴	1	48	yes	—
230	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
231	(C₂×D₄₇)⋊C₄	C₂⁴	1	48	yes	—
232	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
233	C₄⋊Dic₄₇	C₂⁴	1	48	yes	—
234	C₂³×C₄₇	—	4	6	no	—
235	C₂³×C₄₇	C₂²×D₄	1	12	yes	—
236	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
237	C₂³×C₄₇	C₂⁵	1	6	yes	—
238	C₂²×D₄₇	—	2	2	no	—
239	C₂²×D₄₇	—	2	4	no	—
240	C₂²×D₄₇	—	2	6	no	—
241	C₂²×D₄₇	—	2	24	no	—
242	C₂²×D₄₇	—	2	24	no	—
243	C₂²×D₄₇	—	2	24	no	—
244	C₂²×D₄₇	—	4	12	no	—
245	C₂²×D₄₇	—	4	6	no	—
246	C₂²×D₄₇	—	4	24	no	—
247	C₂²×D₄₇	—	4	48	no	—
248	C₂²×D₄₇	C₂⁵	1	8	yes	—
249	C₂²×D₄₇	C₂⁵	1	6	yes	—
250	C₂²×D₄₇	C₂⁵	1	2	yes	—
251	Q₈×C₄₇	C₂²×D₄	1	16	yes	—
252	D₄×C₄₇	C₂²×D₄	1	48	yes	—
253	C₂×C₄×C₄₇	—	4	24	no	—
254	C₂×C₄×C₄₇	C₂²×D₄	1	12	yes	—
255	C₂×C₄×C₄₇	C₂²×D₄	1	24	yes	—
256	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
257	C₂×C₄×C₄₇	C₂²×D₄	1	24	yes	—
258	C₂×C₄×C₄₇	C₂⁵	1	16	yes	—
259	C₂×C₄×C₄₇	C₂⁵	1	6	yes	—
260	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
262	C₂²⋊D₄₇	—	2	16	no	—
263	C₂²⋊D₄₇	—	2	48	no	—
264	C₂²⋊D₄₇	—	2	48	no	—
265	C₂×Dic₄₇	—	2	6	no	—
266	C₂×Dic₄₇	—	2	24	no	—
267	C₂×Dic₄₇	—	2	2	no	—
268	C₂×Dic₄₇	—	2	24	no	—
269	C₂×Dic₄₇	C₂⁵	1	8	yes	—
270	C₂×Dic₄₇	C₂⁵	1	6	yes	—
271	C₂×Dic₄₇	C₂⁵	1	2	yes	—
272	D₁₈₈	—	2	32	no	—
273	D₁₈₈	—	2	8	no	—
274	D₁₈₈	—	2	24	no	—
275	D₁₈₈	—	2	24	no	—
276	D₁₈₈	—	4	48	no	—
277	C₄×D₄₇	—	2	4	no	—
278	C₄×D₄₇	—	2	4	no	—
279	C₄×D₄₇	—	2	12	no	—
280	C₄×D₄₇	—	2	12	no	—
281	C₄×D₄₇	—	2	16	no	—
282	C₄×D₄₇	—	2	24	no	—
283	C₄×D₄₇	—	2	24	no	—
284	C₄×D₄₇	—	2	48	no	—
285	Dic₉₄	—	2	8	no	—
286	Dic₉₄	—	2	24	no	—
287	Dic₉₄	—	2	24	no	—
288	#62811	—	47	1	no	maximal, Sylow
289	C₂²×C₄₇	—	2	12	no	—
290	C₂²×C₄₇	—	2	2	no	—
291	C₂²×C₄₇	—	4	12	no	—
292	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
293	C₂²×C₄₇	C₂³×D₄	1	12	yes	—
294	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
295	C₂×D₄₇	—	2	8	no	—
296	C₂×D₄₇	—	2	2	no	—
297	C₂×D₄₇	—	2	2	no	—
298	C₂×D₄₇	—	2	6	no	—
299	C₂×D₄₇	—	2	8	no	—
300	C₂×D₄₇	—	2	16	no	—
301	C₂×D₄₇	—	2	12	no	—
302	C₂×D₄₇	—	4	48	no	—
303	C₂×D₄₇	—	4	12	no	—
304	C₂×D₄₇	—	8	24	no	—
305	C₂×D₄₇	#585	1	4	yes	complemented
306	C₄×C₄₇	—	2	16	no	—
307	C₄×C₄₇	C₂³×D₄	1	2	yes	—
308	C₄×C₄₇	C₂³×D₄	1	12	yes	—
309	C₄×C₄₇	C₂³×D₄	1	2	yes	—
310	Dic₄₇	—	2	8	no	—
311	Dic₄₇	—	2	6	no	—
312	Dic₄₇	—	2	2	no	—
313	C₂×#585	—	47	1	no	—
314	C₂³×#41	—	47	1	no	—
315	#3489	—	47	8	no	—
316	#3488	—	47	8	no	—
317	#3487	—	47	2	no	—
318	#3486	—	47	2	no	—
319	#3485	—	47	6	no	—
320	#3484	—	47	6	no	—
321	D₄×#41	—	47	16	no	—
322	#3449	—	47	6	no	—
323	C₂×#525	—	47	6	no	—
324	#3428	D₄₇	1	1	yes	characteristic, complemented
325	C₂×C₄₇	—	2	2	no	—
326	C₂×C₄₇	—	2	12	no	—
327	C₂×C₄₇	C₂⁴×D₄	1	1	yes	characteristic
328	C₂×C₄₇	C₂×#585	1	2	yes	—
329	D₄₇	—	2	4	no	—
330	D₄₇	—	4	6	no	—
331	D₄₇	—	4	8	no	—
332	#585	—	94	16	no	—
333	C₂×2₋¹⁺⁴	—	47	4	no	—
334	C₂×2₋¹⁺⁴	—	47	2	no	—
335	C₂×H(5,𝔽₂)	—	47	4	no	—
336	C₂×H(5,𝔽₂)	—	47	6	no	—
337	C₂²×#41	—	47	8	no	—
338	C₂²×#41	—	47	8	no	—
339	C₂²×#41	—	47	8	no	—
340	C₂²×#41	—	47	1	no	—
341	C₂²×#41	—	47	3	no	—
342	C₂²×#41	—	47	3	no	—
343	C₂²×#41	—	47	6	no	—
344	C₂²×#41	—	94	16	no	—
345	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
346	C₂³×Q₈	—	47	1	no	—
347	C₂³×D₄	—	47	3	no	—
348	C₂⁴×C₄	—	47	3	no	—
349	#550	—	47	16	no	—
350	D₄×Q₈	—	47	16	no	—
351	#548	—	47	16	no	—
352	#548	—	47	16	no	—
353	#547	—	47	48	no	—
354	#546	—	47	48	no	—
355	#546	—	47	48	no	—
356	D₄²	—	47	48	no	—
357	#537	—	47	24	no	—
358	#536	—	47	12	no	—
359	#536	—	47	12	no	—
360	#535	—	47	12	no	—
361	#535	—	47	12	no	—
362	#534	—	47	24	no	—
363	#532	—	47	24	no	—
364	#525	—	47	4	no	—
365	#525	—	47	12	no	—
366	#525	—	47	12	no	—
367	#525	—	47	12	no	—
368	#525	—	47	24	no	—
369	#525	—	47	24	no	—
370	#525	—	47	24	no	—
371	C₂×#123	—	47	12	no	—
372	C₂×C₂²⋊Q₈	—	47	12	no	—
373	C₂×#121	—	47	12	no	—
374	C₂×#120	—	47	12	no	—
375	#520	C₂×D₄₇	1	8	yes	complemented
376	#519	C₂×D₄₇	1	2	yes	complemented
377	#518	C₂×D₄₇	1	6	yes	complemented
378	C₄×#41	C₂×D₄₇	1	8	yes	complemented
379	C₂×C₄×D₄	—	47	24	no	—
380	C₂×#117	C₂×D₄₇	1	6	yes	complemented
381	C₄₇	#62811	1	1	yes	characteristic, complemented, Sylow
382	C₂⁵	—	47	3	no	—
383	2₋¹⁺⁴	—	94	32	no	—
384	2₋¹⁺⁴	—	94	16	no	—
385	H(5,𝔽₂)	—	94	32	no	—
386	H(5,𝔽₂)	—	94	48	no	—
387	C₂×#41	—	47	8	no	—
388	C₂×#41	—	47	8	no	—
389	C₂×#41	—	47	24	no	—
390	C₂×#41	—	47	24	no	—
391	C₂×#41	—	47	4	no	—
392	C₂×#41	—	47	12	no	—
393	C₂×#41	—	47	12	no	—
394	C₂×#41	—	47	12	no	—
395	C₂×#41	—	47	12	no	—
396	C₂×#41	—	47	12	no	—
397	C₂×#41	—	94	64	no	—
398	C₂×#41	—	94	64	no	—
399	C₂×#41	—	94	64	no	—
400	C₂×#41	—	94	8	no	—
401	C₂×#41	—	94	24	no	—
402	C₂×#41	—	94	24	no	—
403	C₂×#41	—	94	48	no	—
404	C₂×#41	D₁₈₈	1	16	yes	complemented
405	C₂×#41	C₂²×D₄₇	1	4	yes	—
406	C₂×#41	C₂²×D₄₇	1	4	yes	—
407	C₂²×Q₈	—	47	8	no	—
408	C₂²×Q₈	—	47	8	no	—
409	C₂²×Q₈	—	47	6	no	—
410	C₂²×Q₈	—	47	3	no	—
411	C₂²×Q₈	—	94	8	no	—
412	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
413	C₂²×D₄	—	47	12	no	—
414	C₂²×D₄	—	47	6	no	—
415	C₂²×D₄	—	47	24	no	—
416	C₂²×D₄	—	47	24	no	—
417	C₂²×D₄	—	47	6	no	—
418	C₂²×D₄	—	47	3	no	—
419	C₂²×D₄	—	47	24	no	—
420	C₂²×D₄	—	94	24	no	—
421	C₂²×D₄	C₂²×D₄₇	1	3	yes	—
422	C₂³×C₄	—	47	3	no	—
423	C₂³×C₄	—	47	12	no	—
424	C₂³×C₄	—	47	12	no	—
425	C₂³×C₄	—	47	12	no	—
426	C₂³×C₄	—	47	1	no	—
427	C₂³×C₄	—	47	3	no	—
428	C₂³×C₄	—	47	3	no	—
429	C₂³×C₄	—	47	3	no	—
430	C₂³×C₄	—	94	24	no	—
431	C₂³×C₄	C₂²×D₄₇	1	3	yes	—
432	C₄⋊Q₈	—	47	24	no	—
433	#127	—	47	24	no	—
434	#124	—	47	24	no	—
435	#124	—	47	24	no	—
436	#123	—	47	8	no	—
437	#123	—	47	24	no	—
438	#123	—	47	48	no	—
439	#123	—	47	48	no	—
440	C₂²⋊Q₈	—	47	8	no	—
441	C₂²⋊Q₈	—	47	24	no	—
442	C₂²⋊Q₈	—	47	24	no	—
443	C₂²⋊Q₈	—	47	24	no	—
444	C₂²⋊Q₈	—	47	48	no	—
445	#121	—	47	96	no	—
446	#121	—	47	8	no	—
447	#121	—	47	24	no	—
448	#121	—	47	24	no	—
449	#121	—	47	24	no	—
450	#121	—	47	48	no	—
451	#120	—	47	8	no	—
452	#120	—	47	24	no	—
453	#120	—	47	48	no	—
454	#120	—	47	48	no	—
455	C₄×Q₈	C₂²×D₄₇	1	16	yes	complemented
456	C₄×D₄	—	47	16	no	—
457	C₄×D₄	—	47	48	no	—
458	C₄×D₄	—	47	48	no	—
459	C₄×D₄	—	47	48	no	—
460	C₄×D₄	C₂²×D₄₇	1	48	yes	complemented
461	#117	C₂²×D₄₇	1	4	yes	—
462	#117	C₂²×D₄₇	1	12	yes	—
463	#117	C₂²×D₄₇	1	12	yes	complemented
464	#117	C₂²×D₄₇	1	12	yes	complemented
465	C₂×C₄⋊C₄	—	47	24	no	—
466	C₂×C₄⋊C₄	C₂²×D₄₇	1	12	yes	complemented
467	C₂×C₂²⋊C₄	—	47	24	no	—
468	C₂×C₂²⋊C₄	—	47	24	no	—
469	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
470	C₂×C₄²	C₂²×D₄₇	1	12	yes	complemented
471	C₂⁴	—	47	1	no	—
472	C₂⁴	—	47	12	no	—
473	C₂⁴	—	47	12	no	—
474	C₂⁴	—	47	3	no	—
475	C₂⁴	—	94	12	no	—
476	C₂⁴	—	188	12	no	—
477	C₂⁴	C₂³×D₄₇	1	3	yes	—
478	#41	—	94	32	no	—
479	#41	—	94	32	no	—
480	#41	—	94	96	no	—
481	#41	—	94	96	no	—
482	#41	—	94	16	no	—
483	#41	—	94	48	no	—
484	#41	—	94	48	no	—
485	#41	—	94	48	no	—
486	#41	—	94	48	no	—
487	#41	—	94	48	no	—
488	#41	C₂×D₁₈₈	1	32	yes	complemented
489	#41	C₂×D₁₈₈	1	32	yes	complemented
490	C₂×Q₈	—	47	4	no	—
491	C₂×Q₈	—	47	12	no	—
492	C₂×Q₈	—	47	12	no	—
493	C₂×Q₈	—	94	32	no	—
494	C₂×Q₈	—	94	32	no	—
495	C₂×Q₈	—	94	12	no	—
496	C₂×Q₈	—	94	24	no	—
497	C₂×Q₈	C₂×D₁₈₈	1	8	yes	complemented
498	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
499	C₂×D₄	—	47	8	no	—
500	C₂×D₄	—	47	24	no	—
501	C₂×D₄	—	47	24	no	—
502	C₂×D₄	—	47	16	no	—
503	C₂×D₄	—	47	4	no	—
504	C₂×D₄	—	47	12	no	—
505	C₂×D₄	—	47	12	no	—
506	C₂×D₄	—	47	48	no	—
507	C₂×D₄	—	94	24	no	—
508	C₂×D₄	—	94	48	no	—
509	C₂×D₄	—	94	96	no	—
510	C₂×D₄	—	94	96	no	—
511	C₂×D₄	—	94	12	no	—
512	C₂×D₄	—	94	24	no	—
513	C₂×D₄	—	188	48	no	—
514	C₂×D₄	C₂×D₁₈₈	1	24	yes	complemented
515	C₂×D₄	C₂³×D₄₇	1	12	yes	—
516	C₂²×C₄	—	47	12	no	—
517	C₂²×C₄	—	47	12	no	—
518	C₂²×C₄	—	47	1	no	—
519	C₂²×C₄	—	47	3	no	—
520	C₂²×C₄	—	47	12	no	—
521	C₂²×C₄	—	47	12	no	—
522	C₂²×C₄	—	47	24	no	—
523	C₂²×C₄	—	47	2	no	—
524	C₂²×C₄	—	47	6	no	—
525	C₂²×C₄	—	47	2	no	—
526	C₂²×C₄	—	47	8	no	—
527	C₂²×C₄	—	47	6	no	—
528	C₂²×C₄	—	94	12	no	—
529	C₂²×C₄	—	94	4	no	—
530	C₂²×C₄	—	94	12	no	—
531	C₂²×C₄	—	94	12	no	—
532	C₂²×C₄	—	94	12	no	—
533	C₂²×C₄	—	94	48	no	—
534	C₂²×C₄	—	94	48	no	—
535	C₂²×C₄	—	94	48	no	—
536	C₂²×C₄	C₂×D₁₈₈	1	24	yes	complemented
537	C₂²×C₄	C₂³×D₄₇	1	24	yes	—
538	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
539	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
540	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
541	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
542	C₄⋊C₄	—	47	16	no	—
543	C₄⋊C₄	—	47	48	no	—
544	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
545	C₄⋊C₄	C₂³×D₄₇	1	24	yes	—
546	C₂²⋊C₄	—	47	16	no	—
547	C₂²⋊C₄	—	47	16	no	—
548	C₂²⋊C₄	—	47	48	no	—
549	C₂²⋊C₄	—	47	48	no	—
550	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
551	C₂²⋊C₄	C₂³×D₄₇	1	24	yes	—
552	C₄²	C₂³×D₄₇	1	24	yes	—
553	C₄²	C₂³×D₄₇	1	8	yes	—
554	C₂³	—	4	6	no	—
555	C₂³	—	47	2	no	—
556	C₂³	—	47	8	no	—
557	C₂³	—	47	6	no	—
558	C₂³	—	94	4	no	—
559	C₂³	—	94	24	no	—
560	C₂³	—	94	2	no	—
561	C₂³	—	94	24	no	—
562	C₂³	—	94	24	no	—
563	C₂³	—	94	6	no	—
564	C₂³	—	188	24	no	—
565	C₂³	—	188	12	no	—
566	C₂³	—	188	6	no	—
567	C₂³	—	188	48	no	—
568	C₂³	C₂²×D₁₈₈	1	12	yes	—
569	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
570	C₂³	C₂⁴×D₄₇	1	6	yes	—
571	Q₈	—	94	8	no	—
572	Q₈	—	94	24	no	—
573	Q₈	—	94	24	no	—
574	Q₈	C₂²×D₁₈₈	1	16	yes	—
575	D₄	—	94	32	no	—
576	D₄	—	94	16	no	—
577	D₄	—	94	48	no	—
578	D₄	—	94	48	no	—
579	D₄	—	94	8	no	—
580	D₄	—	94	24	no	—
581	D₄	—	94	24	no	—
582	D₄	—	188	48	no	—
583	D₄	C₂²×D₁₈₈	1	48	yes	—
584	C₂×C₄	—	4	24	no	—
585	C₂×C₄	—	47	2	no	—
586	C₂×C₄	—	47	8	no	—
587	C₂×C₄	—	47	6	no	—
588	C₂×C₄	—	94	2	no	—
589	C₂×C₄	—	94	6	no	—
590	C₂×C₄	—	94	24	no	—
591	C₂×C₄	—	94	24	no	—
592	C₂×C₄	—	94	4	no	—
593	C₂×C₄	—	94	4	no	—
594	C₂×C₄	—	94	24	no	—
595	C₂×C₄	—	94	24	no	—
596	C₂×C₄	—	94	12	no	—
597	C₂×C₄	—	94	16	no	—
598	C₂×C₄	—	94	12	no	—
599	C₂×C₄	—	94	48	no	—
600	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
601	C₂×C₄	C₂²×D₁₈₈	1	24	yes	—
602	C₂×C₄	C₂²×D₁₈₈	1	12	yes	—
603	C₂×C₄	C₂²×D₁₈₈	1	24	yes	—
604	C₂×C₄	C₂⁴×D₄₇	1	16	yes	—
605	C₂×C₄	C₂⁴×D₄₇	1	6	yes	—
606	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
607	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
608	C₂²	—	2	12	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	4	12	no	—
611	C₂²	—	47	4	no	—
612	C₂²	—	94	8	no	—
613	C₂²	—	94	2	no	—
614	C₂²	—	94	2	no	—
615	C₂²	—	94	8	no	—
616	C₂²	—	94	6	no	—
617	C₂²	—	94	16	no	—
618	C₂²	—	94	12	no	—
619	C₂²	—	376	24	no	—
620	C₂²	—	188	48	no	—
621	C₂²	—	188	12	no	—
622	C₂²	C₂³×D₁₈₈	1	2	yes	—
623	C₂²	C₂³×D₁₈₈	1	12	yes	—
624	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
625	C₄	—	2	16	no	—
626	C₄	—	94	2	no	—
627	C₄	—	94	6	no	—
628	C₄	—	94	8	no	—
629	C₄	C₂³×D₁₈₈	1	2	yes	—
630	C₄	C₂³×D₁₈₈	1	2	yes	—
631	C₄	C₂³×D₁₈₈	1	12	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	2	12	no	—
634	C₂	—	94	4	no	—
635	C₂	—	188	8	no	—
636	C₂	—	188	6	no	—
637	C₂	C₂⁴×D₁₈₈	1	1	yes	characteristic
638	C₂	#585×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₄₇×#3428	C₂
hypercenter	#3428	D₄₇
hypocenter	C₄₇	#62811
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #3428

Complements

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

N	H ≅ G/N	type
1. C₂×#15689959	C₂	semidirect
2. C₂²×#41×D₄₇	C₂	semidirect
3. #20257069	C₂	semidirect
4. #20257058	C₂	semidirect
5. #20257047	C₂	semidirect
6. #20257040	C₂	semidirect
7. #20257033	C₂	semidirect
8. #20257024	C₂	semidirect
9. #41×D₁₈₈	C₂	semidirect
10. #20256721	C₂	semidirect
11. C₂×#15689635	C₂	semidirect
12. C₄₇×#3428	C₂	semidirect
14. C₂×#13094072	C₂²	semidirect
15. C₂×#13094071	C₂²	semidirect
16. C₂×#13094070	C₂²	semidirect
17. C₂×#13094069	C₂²	semidirect
18. C₂²×#10625354	C₂²	semidirect
19. C₂²×#10625350	C₂²	semidirect
20. C₂²×#10625350	C₂²	semidirect
21. C₂²×#10625352	C₂²	semidirect
23. C₂×#41×D₄₇	C₂²	semidirect
24. C₂×#41×D₄₇	C₂²	semidirect
25. C₂×#41×D₄₇	C₂²	semidirect
26. C₂²×Q₈×D₄₇	C₂²	semidirect
27. C₂²×D₄×D₄₇	C₂²	semidirect
28. C₂³×C₄×D₄₇	C₂²	semidirect
29. #15689795	C₂²	semidirect
30. Q₈×D₁₈₈	C₂²	semidirect
31. #15689785	C₂²	semidirect
32. #15689785	C₂²	semidirect
33. #15689777	C₂²	semidirect
34. #15689768	C₂²	semidirect
35. #15689768	C₂²	semidirect
36. D₄×D₁₈₈	C₂²	semidirect
37. #15689704	C₂²	semidirect
38. #15689699	C₂²	semidirect
39. #15689699	C₂²	semidirect
40. #15689692	C₂²	semidirect
41. #15689692	C₂²	semidirect
42. #15689685	C₂²	semidirect
43. #15689673	C₂²	semidirect
44. #15689635	C₂²	semidirect
45. #15689635	C₂²	semidirect
46. #15689635	C₂²	semidirect
47. #15689635	C₂²	semidirect
48. #15689635	C₂²	semidirect
49. #15689635	C₂²	semidirect
50. #15689635	C₂²	semidirect
51. C₂×#13094008	C₂²	semidirect
52. C₂×#13094004	C₂²	semidirect
53. C₂×#13093999	C₂²	semidirect
54. C₂×#13093994	C₂²	semidirect
55. C₂×C₄×D₁₈₈	C₂²	semidirect
57. C₄₇×#520	C₂²	semidirect
58. C₄₇×#519	C₂²	semidirect
59. C₄₇×#518	C₂²	semidirect
60. C₄×#41×C₄₇	C₂²	semidirect
61. C₂×#117×C₄₇	C₂²	semidirect
69. C₂×#10625354	C₂³	semidirect
76. C₂×#10625350	C₂³	semidirect
77. C₂×#10625350	C₂³	semidirect
80. C₂×#10625352	C₂³	semidirect
85. C₂²×Dic₉₄	C₂³	semidirect
88. C₂×Q₈×D₄₇	C₂³	semidirect
91. C₂²×D₁₈₈	C₂³	semidirect
96. C₂×D₄×D₄₇	C₂³	semidirect
105. C₂²×C₄×D₄₇	C₂³	semidirect
106. #13094024	C₂³	semidirect
107. #13094021	C₂³	semidirect
108. #13094012	C₂³	semidirect
109. #13094012	C₂³	semidirect
112. #13094008	C₂³	semidirect
113. #13094008	C₂³	semidirect
116. #13094004	C₂³	semidirect
117. #13094004	C₂³	semidirect
118. #13094004	C₂³	semidirect
121. #13093999	C₂³	semidirect
122. #13093999	C₂³	semidirect
123. #13093999	C₂³	semidirect
124. #13093998	C₂³	semidirect
128. #13093994	C₂³	semidirect
131. C₄×D₁₈₈	C₂³	semidirect
132. C₄×D₁₈₈	C₂³	semidirect
133. C₂×C₄⋊Dic₄₇	C₂³	semidirect
135. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
136. C₂×#41×C₄₇	D₄	semidirect
142. C₄×Q₈×C₄₇	C₂³	semidirect
143. C₄×D₄×C₄₇	C₂³	semidirect
146. #117×C₄₇	C₂³	semidirect
147. #117×C₄₇	C₂³	semidirect
148. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
150. C₂×C₄²×C₄₇	C₂³	semidirect
158. #41×C₄₇	C₂×D₄	semidirect
159. #41×C₄₇	C₂×D₄	semidirect
160. C₂×Q₈×C₄₇	C₂×D₄	semidirect
162. C₂×D₄×C₄₇	C₂×D₄	semidirect
164. C₂²×C₄×C₄₇	C₂×D₄	semidirect
305. C₂×D₄₇	#585	semidirect
324. #3428	D₄₇	semidirect
375. #520	C₂×D₄₇	semidirect
376. #519	C₂×D₄₇	semidirect
377. #518	C₂×D₄₇	semidirect
378. C₄×#41	C₂×D₄₇	semidirect
380. C₂×#117	C₂×D₄₇	semidirect
381. C₄₇	#62811	semidirect
404. C₂×#41	D₁₈₈	semidirect
455. C₄×Q₈	C₂²×D₄₇	semidirect
460. C₄×D₄	C₂²×D₄₇	semidirect
463. #117	C₂²×D₄₇	semidirect
464. #117	C₂²×D₄₇	semidirect
466. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
470. C₂×C₄²	C₂²×D₄₇	semidirect
488. #41	C₂×D₁₈₈	semidirect
489. #41	C₂×D₁₈₈	semidirect
497. C₂×Q₈	C₂×D₁₈₈	semidirect
514. C₂×D₄	C₂×D₁₈₈	semidirect
536. C₂²×C₄	C₂×D₁₈₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689959	2
C₂²×#41×D₄₇	2
#20257069	2
#20257058	2
#20257047	2
#20257040	2
#20257033	2
#20257024	2
#41×D₁₈₈	2
#20256721	2
C₂×#15689635	2
C₄₇×#3428	2
#62811	47