Subgroups — #26216126

Order 12032.

1260 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256589	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689105	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689096	C₂	1	1	yes	maximal, characteristic
4	#20243490	C₂	1	8	yes	maximal, complemented
5	#20243099	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243097	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688879	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625350	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	#15689604	—	2	2	no	—
12	#15689603	—	2	2	no	—
13	#15689600	—	2	1	no	—
14	#15689597	—	2	1	no	—
15	#15689596	—	2	2	no	—
16	C₄×#10625350	C₄	1	4	yes	complemented
17	#15689591	C₂²	1	4	yes	—
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	C₂×#13093983	C₂²	1	1	yes	characteristic
20	#117×D₄₇	C₄	1	4	yes	complemented
21	#15689105	—	2	2	no	—
22	#15689105	C₂²	1	4	yes	—
23	C₂×#13093942	—	2	1	no	—
24	C₂×#13093940	—	2	1	no	—
25	#15689096	—	2	2	no	—
26	#15689096	C₂²	1	4	yes	—
27	C₂×#13093938	—	2	2	no	—
28	#15688884	C₂²	1	4	yes	complemented
29	#15688882	C₂²	1	4	yes	complemented
30	#15688879	C₂²	1	4	yes	complemented
31	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×H(3,ℤ/4)	C₂²	1	4	yes	complemented
35	C₂×#10625350	—	2	1	no	—
36	C₂×#10625350	—	2	1	no	—
37	C₂×#10625350	—	2	1	no	—
38	C₂×#10625350	—	2	1	no	—
39	C₂×#10625350	—	2	1	no	—
40	C₂×#10625350	—	2	1	no	—
41	C₂×#10625350	—	2	1	no	—
42	C₂×#10625350	—	2	1	no	—
43	C₂×#10625350	C₂×C₄	1	2	yes	—
44	C₂×#10625350	D₄	1	2	yes	—
45	C₂×#10625350	D₄	1	2	yes	—
46	C₂×#10625350	C₂³	1	2	yes	—
47	C₂²×Dic₉₄	D₄	1	1	yes	characteristic
48	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
49	C₂²×C₂²⋊D₄₇	D₄	1	2	yes	—
50	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	C₂³	1	2	yes	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₄×Dic₉₄	—	2	4	no	—
59	#13093989	—	2	4	no	—
60	C₄×D₁₈₈	—	2	4	no	—
61	#13093986	—	2	4	no	—
62	C₄×C₂²⋊D₄₇	—	2	8	no	—
63	(C₂²⋊D₄₇)⋊C₄	—	2	8	no	—
64	#13093983	—	2	1	no	—
65	#13093983	—	2	1	no	—
66	#13093983	—	2	1	no	—
67	#13093983	—	2	1	no	—
68	#13093983	—	2	1	no	—
69	#13093983	C₂×C₄	1	2	yes	—
70	#13093983	C₂×C₄	1	2	yes	—
71	#13093983	C₂³	1	2	yes	—
72	#13093982	—	2	4	no	—
73	#13093981	C₂×C₄	1	8	yes	complemented
74	#13093980	—	2	4	no	—
75	C₂×C₄⋊Dic₄₇	—	2	1	no	—
76	C₂×C₄⋊Dic₄₇	—	2	1	no	—
77	C₄⋊C₄×D₄₇	—	2	4	no	—
78	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
79	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
80	C₂²⋊C₄×D₄₇	—	2	4	no	—
81	C₂×C₄×Dic₄₇	—	2	1	no	—
82	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
83	C₄²×D₄₇	C₂×C₄	1	8	yes	complemented
84	#13093942	—	2	4	no	—
85	#13093940	—	2	4	no	—
86	#13093938	—	2	8	no	—
87	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₄₇	—	2	1	no	—
89	C₂×M₁₆×C₄₇	—	2	1	no	—
90	C₂×M₁₆×C₄₇	—	2	1	no	—
91	C₂×M₁₆×C₄₇	—	2	1	no	—
92	C₂×M₁₆×C₄₇	—	2	1	no	—
93	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
94	C₂²×C₈×C₄₇	—	2	1	no	—
95	#117×C₄₇	—	2	1	no	—
96	#117×C₄₇	—	2	1	no	—
97	#117×C₄₇	—	2	1	no	—
98	#117×C₄₇	—	2	1	no	—
99	#117×C₄₇	—	2	1	no	—
100	#117×C₄₇	C₂×C₄	1	2	yes	—
101	#117×C₄₇	C₂³	1	2	yes	—
102	#117×C₄₇	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
104	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
107	C₂×C₄²×C₄₇	—	2	1	no	—
108	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
109	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂³×D₄₇	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	4	1	no	—
113	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂×C₂²⋊D₄₇	—	2	2	no	—
128	C₂×C₂²⋊D₄₇	—	2	2	no	—
129	C₂×C₂²⋊D₄₇	—	2	2	no	—
130	C₂×C₂²⋊D₄₇	—	2	2	no	—
131	C₂×C₂²⋊D₄₇	C₂²⋊C₄	1	4	yes	—
132	C₂×C₂²⋊D₄₇	C₂×D₄	1	4	yes	—
133	C₂²×Dic₄₇	—	2	2	no	—
134	C₂²×Dic₄₇	—	4	1	no	—
135	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
136	#10625350	—	2	2	no	—
137	#10625350	—	2	2	no	—
138	#10625350	—	2	2	no	—
139	#10625350	—	2	2	no	—
140	#10625350	—	2	2	no	—
141	#10625350	—	2	2	no	—
142	#10625350	—	2	2	no	—
143	#10625350	—	2	2	no	—
144	#10625350	—	2	2	no	—
145	#10625350	—	2	2	no	—
146	#10625350	—	2	2	no	—
147	#10625350	—	2	2	no	—
148	#10625350	—	2	2	no	—
149	#10625350	—	2	2	no	—
150	#10625350	—	2	2	no	—
151	#10625350	—	2	2	no	—
152	C₂×D₁₈₈	—	2	1	no	—
153	C₂×D₁₈₈	—	2	1	no	—
154	C₂×D₁₈₈	—	2	1	no	—
155	C₂×D₁₈₈	—	2	1	no	—
156	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
157	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
158	C₂×C₄×D₄₇	—	2	2	no	—
159	C₂×C₄×D₄₇	—	2	2	no	—
160	C₂×C₄×D₄₇	—	2	2	no	—
161	C₂×C₄×D₄₇	—	2	2	no	—
162	C₂×C₄×D₄₇	—	2	8	no	—
163	C₂×C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
164	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
165	C₂×Dic₉₄	—	2	1	no	—
166	C₂×Dic₉₄	—	2	1	no	—
167	C₂×Dic₉₄	—	2	1	no	—
168	C₂×Dic₉₄	—	2	1	no	—
169	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
170	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
171	M₁₆×C₄₇	—	2	2	no	—
172	M₁₆×C₄₇	—	2	2	no	—
173	M₁₆×C₄₇	—	4	1	no	—
174	M₁₆×C₄₇	—	4	1	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	—	4	1	no	—
177	C₂×C₈×C₄₇	—	4	1	no	—
178	C₄⋊C₄×C₄₇	—	2	2	no	—
179	C₄⋊C₄×C₄₇	—	2	2	no	—
180	C₄⋊C₄×C₄₇	—	2	2	no	—
181	C₄⋊C₄×C₄₇	—	4	1	no	—
182	C₂²⋊C₄×C₄₇	—	2	2	no	—
183	C₂²⋊C₄×C₄₇	—	2	2	no	—
184	C₂²⋊C₄×C₄₇	—	2	2	no	—
185	C₂²⋊C₄×C₄₇	—	4	1	no	—
186	C₄²×C₄₇	—	2	2	no	—
187	C₄²×C₄₇	—	2	2	no	—
188	C₄²×C₄₇	—	4	1	no	—
189	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
190	C₂²⋊Dic₄₇	—	2	2	no	—
191	C₂²⋊Dic₄₇	—	2	2	no	—
192	C₂²⋊Dic₄₇	—	2	2	no	—
193	C₂²⋊Dic₄₇	—	4	1	no	—
194	(C₂×D₄₇)⋊C₄	—	2	8	no	—
195	C₄⋊Dic₄₇	—	2	2	no	—
196	C₄⋊Dic₄₇	—	2	2	no	—
197	C₄⋊Dic₄₇	—	2	2	no	—
198	C₄⋊Dic₄₇	—	4	1	no	—
199	Dic₄₇⋊C₄	—	2	8	no	—
200	C₄×Dic₄₇	—	2	2	no	—
201	C₄×Dic₄₇	—	2	8	no	—
202	C₄×Dic₄₇	—	2	2	no	—
203	C₄×Dic₄₇	—	4	1	no	—
204	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
205	#10625329	—	2	2	no	—
206	#10625329	—	2	2	no	—
207	#10625329	—	4	1	no	—
208	#10625329	—	4	1	no	—
209	C₂×C₄₇⋊C₈	—	2	2	no	—
210	C₂×C₄₇⋊C₈	—	4	1	no	—
211	C₂×C₄₇⋊C₈	—	4	1	no	—
212	C₂³×C₄₇	—	8	1	no	—
213	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×C₄₇	#123	1	1	yes	characteristic
216	C₂³×C₄₇	#123	1	1	yes	characteristic
217	C₂³×C₄₇	#123	1	1	yes	characteristic
218	C₂³×C₄₇	#123	1	1	yes	characteristic
219	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
220	C₂²×D₄₇	—	2	2	no	—
221	C₂²×D₄₇	—	2	2	no	—
222	C₂²×D₄₇	—	8	2	no	—
223	C₂²×D₄₇	C₂×C₂²⋊C₄	1	4	yes	—
224	C₂×C₄×C₄₇	—	2	4	no	—
225	C₂×C₄×C₄₇	—	4	2	no	—
226	C₂×C₄×C₄₇	—	8	2	no	—
227	C₂×C₄×C₄₇	—	8	2	no	—
228	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
243	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
244	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
247	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
248	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
249	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
256	C₂²⋊D₄₇	—	2	4	no	—
257	C₂²⋊D₄₇	—	2	4	no	—
258	C₂²⋊D₄₇	—	2	4	no	—
259	C₂²⋊D₄₇	—	2	4	no	—
260	C₂×Dic₄₇	—	2	2	no	—
261	C₂×Dic₄₇	—	2	2	no	—
262	C₂×Dic₄₇	—	2	4	no	—
263	C₂×Dic₄₇	—	4	2	no	—
264	C₂×Dic₄₇	—	8	2	no	—
265	C₂×Dic₄₇	—	8	2	no	—
266	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	4	yes	—
267	D₁₈₈	—	2	2	no	—
268	D₁₈₈	—	2	2	no	—
269	D₁₈₈	—	2	2	no	—
270	D₁₈₈	—	2	2	no	—
271	C₄×D₄₇	—	2	4	no	—
272	C₄×D₄₇	—	2	4	no	—
273	C₄×D₄₇	—	2	4	no	—
274	C₄×D₄₇	—	2	4	no	—
275	C₄×D₄₇	—	8	8	no	—
276	Dic₉₄	—	2	2	no	—
277	Dic₉₄	—	2	2	no	—
278	Dic₉₄	—	2	2	no	—
279	Dic₉₄	—	2	2	no	—
280	C₈×C₄₇	—	4	2	no	—
281	C₄₇⋊C₈	—	4	2	no	—
282	#20708	—	47	1	no	maximal, Sylow
283	C₂²×C₄₇	—	4	1	no	—
284	C₂²×C₄₇	—	4	1	no	—
285	C₂²×C₄₇	—	4	1	no	—
286	C₂²×C₄₇	—	4	1	no	—
287	C₂²×C₄₇	—	4	1	no	—
288	C₂²×C₄₇	—	4	1	no	—
289	C₂²×C₄₇	—	4	1	no	—
290	C₂²×C₄₇	#381	1	1	yes	characteristic
291	C₂²×C₄₇	#381	1	1	yes	characteristic
292	C₂²×C₄₇	#381	1	1	yes	characteristic
293	C₂²×C₄₇	#381	1	1	yes	characteristic
294	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
295	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
296	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
297	C₂×D₄₇	—	2	4	no	—
298	C₂×D₄₇	—	4	4	no	—
299	C₂×D₄₇	—	8	2	no	—
300	C₂×D₄₇	—	8	2	no	—
301	C₄×C₄₇	—	4	4	no	—
302	C₄×C₄₇	—	8	2	no	—
303	C₄×C₄₇	#381	1	1	yes	characteristic
304	C₄×C₄₇	#381	1	1	yes	characteristic
305	C₄×C₄₇	#381	1	1	yes	characteristic
306	C₄×C₄₇	#381	1	1	yes	characteristic
307	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
308	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
309	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
310	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
311	Dic₄₇	—	2	4	no	—
312	Dic₄₇	—	4	4	no	—
313	Dic₄₇	—	8	2	no	—
314	#3428	—	47	1	no	—
315	C₂×#413	—	47	1	no	—
316	C₂×#410	—	47	1	no	—
317	#1827	—	47	8	no	—
318	#1733	—	47	1	no	—
319	#1733	—	47	1	no	—
320	C₂×H(3,ℤ/4)	—	47	1	no	—
321	C₂×H(3,ℤ/4)	D₄₇	1	1	yes	characteristic, complemented
322	C₂×C₄₇	—	2	1	no	—
323	C₂×C₄₇	—	2	1	no	—
324	C₂×C₄₇	—	2	1	no	—
325	C₂×C₄₇	—	2	1	no	—
326	C₂×C₄₇	—	2	1	no	—
327	C₂×C₄₇	—	2	1	no	—
328	C₂×C₄₇	—	2	1	no	—
329	C₂×C₄₇	C₂×#381	1	1	yes	characteristic
330	D₄₇	—	4	4	no	—
331	C₂²×#41	—	47	1	no	—
332	C₂²×M₁₆	—	47	1	no	—
333	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
334	#520	—	94	2	no	—
335	#520	—	94	2	no	—
336	#519	—	94	1	no	—
337	#518	—	94	2	no	—
338	#518	—	94	1	no	—
339	C₄×#41	—	47	4	no	—
340	C₄×#41	—	47	4	no	—
341	C₂×#117	—	47	1	no	—
342	C₂×#117	—	47	4	no	—
343	C₂×#117	—	47	1	no	—
344	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
345	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
346	#413	—	47	4	no	—
347	#413	—	94	2	no	—
348	C₂×#101	—	94	1	no	—
349	C₂×#100	—	94	1	no	—
350	#410	—	47	4	no	—
351	#410	—	94	2	no	—
352	C₂×#99	—	94	2	no	—
353	#339	—	47	4	no	—
354	#339	—	47	4	no	—
355	H(3,ℤ/4)	—	47	4	no	—
356	H(3,ℤ/4)	C₂×D₄₇	1	4	yes	complemented
357	C₄₇	#20708	1	1	yes	characteristic, complemented, Sylow
358	C₂×#41	—	47	2	no	—
359	C₂×#41	—	47	2	no	—
360	C₂×#41	—	47	2	no	—
361	C₂×#41	—	47	2	no	—
362	C₂×#41	—	94	1	no	—
363	C₂×#41	—	94	1	no	—
364	C₂×#41	—	94	1	no	—
365	C₂×#41	—	94	1	no	—
366	C₂×#41	—	94	1	no	—
367	C₂×#41	—	94	1	no	—
368	C₂×#41	—	94	1	no	—
369	C₂×#41	—	94	1	no	—
370	C₂²×Q₈	—	47	1	no	—
371	C₂²×D₄	—	47	2	no	—
372	C₂²×D₄	—	47	1	no	—
373	C₂³×C₄	—	47	2	no	—
374	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	47	2	no	—
381	C₂×M₁₆	—	94	1	no	—
382	C₂×M₁₆	—	94	1	no	—
383	C₂×M₁₆	—	94	1	no	—
384	C₂×M₁₆	—	94	1	no	—
385	C₂×M₁₆	—	94	1	no	—
386	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
387	C₂²×C₈	—	2	1	no	—
388	C₂²×C₈	—	94	1	no	—
389	C₄×Q₈	—	94	4	no	—
390	C₄×Q₈	—	94	4	no	—
391	C₄×D₄	—	94	4	no	—
392	C₄×D₄	—	94	8	no	—
393	C₄×D₄	—	94	4	no	—
394	C₄×D₄	—	94	8	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	47	2	no	—
401	#117	—	47	2	no	—
402	#117	—	47	8	no	—
403	#117	—	47	2	no	—
404	#117	—	94	4	no	—
405	#117	—	94	4	no	—
406	#117	—	94	1	no	—
407	#117	—	94	1	no	—
408	#117	—	94	1	no	—
409	#117	—	94	1	no	—
410	#117	—	94	1	no	—
411	#117	C₄×D₄₇	1	2	yes	—
412	#117	C₂²×D₄₇	1	2	yes	—
413	#117	C₂²×D₄₇	1	2	yes	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	94	4	no	—
417	C₂×C₄⋊C₄	—	94	1	no	—
418	C₂×C₄⋊C₄	—	94	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	94	4	no	—
422	C₂×C₂²⋊C₄	—	94	1	no	—
423	C₂×C₂²⋊C₄	—	94	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	47	2	no	—
426	C₂×C₄²	—	47	8	no	—
427	C₂×C₄²	—	94	1	no	—
428	C₂×C₄²	C₄×D₄₇	1	2	yes	—
429	#101	—	94	4	no	—
430	#100	—	94	4	no	—
431	#99	—	94	8	no	—
432	C₂⁴	—	47	2	no	—
433	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
434	#41	—	94	2	no	—
435	#41	—	94	2	no	—
436	#41	—	94	2	no	—
437	#41	—	94	2	no	—
438	#41	—	94	2	no	—
439	#41	—	94	2	no	—
440	#41	—	94	2	no	—
441	#41	—	94	2	no	—
442	#41	—	94	2	no	—
443	#41	—	94	2	no	—
444	#41	—	94	2	no	—
445	#41	—	94	2	no	—
446	#41	—	94	2	no	—
447	#41	—	94	2	no	—
448	#41	—	94	2	no	—
449	#41	—	94	2	no	—
450	C₂×Q₈	—	47	2	no	—
451	C₂×Q₈	—	47	2	no	—
452	C₂×Q₈	—	94	1	no	—
453	C₂×Q₈	—	94	1	no	—
454	C₂×Q₈	—	94	1	no	—
455	C₂×Q₈	—	94	1	no	—
456	C₂×D₄	—	47	4	no	—
457	C₂×D₄	—	47	4	no	—
458	C₂×D₄	—	47	2	no	—
459	C₂×D₄	—	47	2	no	—
460	C₂×D₄	—	94	2	no	—
461	C₂×D₄	—	94	2	no	—
462	C₂×D₄	—	94	2	no	—
463	C₂×D₄	—	94	2	no	—
464	C₂×D₄	—	94	1	no	—
465	C₂×D₄	—	94	1	no	—
466	C₂×D₄	—	94	1	no	—
467	C₂×D₄	—	94	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	47	2	no	—
471	C₂²×C₄	—	47	4	no	—
472	C₂²×C₄	—	47	4	no	—
473	C₂²×C₄	—	94	8	no	—
474	C₂²×C₄	—	94	2	no	—
475	C₂²×C₄	—	94	2	no	—
476	C₂²×C₄	—	94	2	no	—
477	C₂²×C₄	—	94	2	no	—
478	C₂²×C₄	—	94	2	no	—
479	C₂²×C₄	—	188	1	no	—
480	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
482	C₂²×C₄	#10625350	1	1	yes	characteristic
483	C₂²×C₄	#10625350	1	1	yes	characteristic
484	C₂²×C₄	#10625350	1	1	yes	characteristic
485	C₂²×C₄	#10625350	1	1	yes	characteristic
486	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
487	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
488	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
489	C₂²×C₄	#10625352	1	1	yes	characteristic
490	C₂²×C₄	#10625352	1	1	yes	characteristic
491	C₂²×C₄	#10625354	1	1	yes	characteristic
492	C₂²×C₄	#10625354	1	1	yes	characteristic
493	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	4	1	no	—
497	M₁₆	—	4	1	no	—
498	M₁₆	—	94	2	no	—
499	M₁₆	—	94	2	no	—
500	M₁₆	—	188	1	no	—
501	M₁₆	—	188	1	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	4	1	no	—
504	C₂×C₈	—	4	1	no	—
505	C₂×C₈	—	94	2	no	—
506	C₂×C₈	—	188	1	no	—
507	C₂×C₈	—	188	1	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	—	94	8	no	—
513	C₄⋊C₄	—	94	2	no	—
514	C₄⋊C₄	—	94	2	no	—
515	C₄⋊C₄	—	94	2	no	—
516	C₄⋊C₄	—	188	1	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	94	8	no	—
522	C₂²⋊C₄	—	94	2	no	—
523	C₂²⋊C₄	—	94	2	no	—
524	C₂²⋊C₄	—	94	2	no	—
525	C₂²⋊C₄	—	188	1	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	4	1	no	—
529	C₄²	—	47	4	no	—
530	C₄²	—	94	8	no	—
531	C₄²	—	94	2	no	—
532	C₄²	—	94	2	no	—
533	C₄²	—	188	1	no	—
534	C₄²	C₂×C₄×D₄₇	1	4	yes	—
535	C₂³	—	8	1	no	—
536	C₂³	—	47	4	no	—
537	C₂³	—	94	2	no	—
538	C₂³	—	94	2	no	—
539	C₂³	—	376	2	no	—
540	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
541	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
542	C₂³	#13094006	1	1	yes	characteristic
543	C₂³	#13094006	1	1	yes	characteristic
544	C₂³	#13094009	1	1	yes	characteristic
545	C₂³	#13094009	1	1	yes	characteristic
546	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
547	Q₈	—	94	2	no	—
548	Q₈	—	94	2	no	—
549	Q₈	—	94	2	no	—
550	Q₈	—	94	2	no	—
551	D₄	—	94	4	no	—
552	D₄	—	94	4	no	—
553	D₄	—	94	4	no	—
554	D₄	—	94	4	no	—
555	D₄	—	94	2	no	—
556	D₄	—	94	2	no	—
557	D₄	—	94	2	no	—
558	D₄	—	94	2	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	—	47	4	no	—
564	C₂×C₄	—	94	2	no	—
565	C₂×C₄	—	94	2	no	—
566	C₂×C₄	—	94	4	no	—
567	C₂×C₄	—	94	4	no	—
568	C₂×C₄	—	94	4	no	—
569	C₂×C₄	—	94	4	no	—
570	C₂×C₄	—	94	4	no	—
571	C₂×C₄	—	376	8	no	—
572	C₂×C₄	—	376	2	no	—
573	C₂×C₄	—	376	2	no	—
574	C₂×C₄	—	188	2	no	—
575	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
576	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
577	C₂×C₄	#13093981	1	1	yes	characteristic
578	C₂×C₄	#13093981	1	1	yes	characteristic
579	C₂×C₄	#13093981	1	1	yes	characteristic
580	C₂×C₄	#13093981	1	1	yes	characteristic
581	C₂×C₄	#13093982	1	1	yes	characteristic
582	C₂×C₄	#13093982	1	1	yes	characteristic
583	C₂×C₄	#13093982	1	1	yes	characteristic
584	C₂×C₄	#13093982	1	1	yes	characteristic
585	C₂×C₄	#13094006	1	1	yes	characteristic
586	C₂×C₄	#13094006	1	1	yes	characteristic
587	C₂×C₄	#13094006	1	1	yes	characteristic
588	C₂×C₄	#13094006	1	1	yes	characteristic
589	C₂×C₄	#13094006	1	1	yes	characteristic
590	C₂×C₄	#13094006	1	1	yes	characteristic
591	C₂×C₄	#13094009	1	1	yes	characteristic
592	C₂×C₄	#13094009	1	1	yes	characteristic
593	C₂×C₄	#13094009	1	1	yes	characteristic
594	C₂×C₄	#13094009	1	1	yes	characteristic
595	C₂×C₄	#13094009	1	1	yes	characteristic
596	C₂×C₄	#13094009	1	1	yes	characteristic
597	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
598	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
599	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
600	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
601	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
602	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
603	C₈	—	4	2	no	—
604	C₈	—	188	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	94	4	no	—
613	C₂²	—	376	2	no	—
614	C₂²	—	376	2	no	—
615	C₂²	—	188	4	no	—
616	C₂²	#15688985	1	1	yes	characteristic
617	C₂²	#15688985	1	1	yes	characteristic
618	C₂²	#15688985	1	1	yes	characteristic
619	C₂²	#15688985	1	1	yes	characteristic
620	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
621	C₂²	C₂×#13094006	1	1	yes	characteristic
622	C₂²	C₂×#13094009	1	1	yes	characteristic
623	C₄	—	4	4	no	—
624	C₄	—	8	2	no	—
625	C₄	—	94	4	no	—
626	C₄	—	376	2	no	—
627	C₄	—	188	4	no	—
628	C₄	#15688985	1	1	yes	characteristic
629	C₄	#15688985	1	1	yes	characteristic
630	C₄	#15688985	1	1	yes	characteristic
631	C₄	#15688985	1	1	yes	characteristic
632	C₄	C₂×#13093981	1	1	yes	characteristic
633	C₄	C₂×#13093982	1	1	yes	characteristic
634	C₄	C₂×#13094006	1	1	yes	characteristic
635	C₄	C₂×#13094009	1	1	yes	characteristic
636	C₂	—	2	1	no	—
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	2	1	no	—
642	C₂	—	2	1	no	—
643	C₂	—	188	4	no	—
644	C₂	C₂×#15688985	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13093981
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×H(3,ℤ/4)	C₂
socle	C₂×C₄₇	C₂×#381
prime radical	C₂²×#10625350	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×H(3,ℤ/4)	D₄₇
hypocenter	C₄₇	#20708
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×#117 ◁ C₂×H(3,ℤ/4)

Complements

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

N	H ≅ G/N	type
4. #20243490	C₂	semidirect
5. #20243099	C₂	semidirect
6. #20243097	C₂	semidirect
7. C₂×#15688879	C₂	semidirect
8. C₂×C₄₇×H(3,ℤ/4)	C₂	semidirect
16. C₄×#10625350	C₄	semidirect
20. #117×D₄₇	C₄	semidirect
28. #15688884	C₂²	semidirect
29. #15688882	C₂²	semidirect
30. #15688879	C₂²	semidirect
34. C₄₇×H(3,ℤ/4)	C₂²	semidirect
73. #13093981	C₂×C₄	semidirect
83. C₄²×D₄₇	C₂×C₄	semidirect
321. C₂×H(3,ℤ/4)	D₄₇	semidirect
356. H(3,ℤ/4)	C₂×D₄₇	semidirect
357. C₄₇	#20708	semidirect

Maximal subgroups

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

subgroup	index
#20256589	2
C₂×#15689105	2
C₂×#15689096	2
#20243490	2
#20243099	2
#20243097	2
C₂×#15688879	2
C₂×C₄₇×H(3,ℤ/4)	2
#20708	47