Subgroups — #26121870

Order 12032.

1164 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689889	C₂	1	1	yes	maximal, characteristic
2	#20251908	C₂	1	1	yes	maximal, characteristic
3	#20251905	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688879	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625350	C₂²	1	1	yes	characteristic
9	#15689889	—	2	2	no	—
10	#15689889	—	2	2	no	—
11	#15689889	—	2	2	no	—
12	#15689889	—	2	2	no	—
13	C₂×#13094032	C₄	1	4	yes	complemented
14	C₂×#13094030	—	2	2	no	—
15	C₂²×#10625329	C₂²	1	1	yes	characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₄₇	—	2	2	no	—
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	#15689133	—	2	1	no	—
20	#15689131	—	2	1	no	—
21	#15689129	—	2	1	no	—
22	#15689127	—	2	1	no	—
23	#15689125	—	2	2	no	—
24	#15689122	—	2	2	no	—
25	#15689120	C₄	1	4	yes	complemented
26	#15689117	C₄	1	4	yes	complemented
27	#15688895	—	2	2	no	—
28	C₄₇⋊#338	—	2	2	no	—
29	#15688879	—	2	2	no	—
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#344	—	2	2	no	—
34	C₂×#10625350	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
41	C₂×#10625350	C₂×C₄	1	2	yes	—
42	C₂×#10625350	C₂×C₄	1	2	yes	—
43	C₂×#10625350	D₄	1	2	yes	—
44	C₂×#10625350	D₄	1	2	yes	—
45	C₂×#10625350	Q₈	1	2	yes	—
46	C₂²×Dic₉₄	D₄	1	1	yes	characteristic
47	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
48	C₂²×C₂²⋊D₄₇	—	2	1	no	—
49	C₂²×C₄×D₄₇	—	2	1	no	—
50	#13094032	—	2	8	no	—
51	#13094032	—	2	8	no	—
52	#13094030	—	2	8	no	—
53	#13094030	—	2	8	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	—	2	1	no	—
57	C₂×#10625329	—	2	1	no	—
58	C₂×#10625329	—	2	1	no	—
59	C₂×#10625329	—	2	1	no	—
60	C₂×#10625329	—	2	1	no	—
61	C₂×#10625329	—	2	1	no	—
62	C₂×#10625329	—	2	1	no	—
63	C₂×#10625329	—	2	1	no	—
64	C₂×#10625329	D₄	1	2	yes	—
65	C₂×#10625329	D₄	1	2	yes	—
66	C₂×#10625324	—	2	4	no	—
67	M₁₆×D₄₇	—	2	8	no	—
68	M₁₆×D₄₇	—	2	8	no	—
69	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
70	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
71	C₂×C₈×D₄₇	—	2	4	no	—
72	#13093983	—	2	1	no	—
73	#13093983	—	2	1	no	—
74	#13093983	—	2	1	no	—
75	#13093983	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊Dic₄₇	—	2	1	no	—
77	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
78	C₂×C₄×Dic₄₇	—	2	1	no	—
79	#13093949	—	2	4	no	—
80	#13093947	—	2	4	no	—
81	#13093946	—	2	4	no	—
82	#13093944	—	2	4	no	—
83	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₇	—	2	1	no	—
85	C₂×M₁₆×C₄₇	—	2	1	no	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
94	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
95	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
96	C₂²×C₈×C₄₇	—	2	1	no	—
97	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
98	#117×C₄₇	—	2	1	no	—
99	#117×C₄₇	—	2	1	no	—
100	#117×C₄₇	—	2	1	no	—
101	#117×C₄₇	C₂×C₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
104	C₂×C₄²×C₄₇	—	2	1	no	—
105	C₂⁴×C₄₇	#41	1	1	yes	characteristic
106	C₂³×D₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	4	1	no	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	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	C₂×Q₈	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	C₂×C₂²⋊D₄₇	—	2	2	no	—
123	C₂×C₂²⋊D₄₇	—	2	2	no	—
124	C₂×C₂²⋊D₄₇	—	2	2	no	—
125	C₂×C₂²⋊D₄₇	—	2	2	no	—
126	C₂×C₂²⋊D₄₇	—	2	2	no	—
127	C₂×C₂²⋊D₄₇	—	2	2	no	—
128	C₂²×Dic₄₇	—	2	1	no	—
129	C₂²×Dic₄₇	—	4	1	no	—
130	#10625350	—	2	2	no	—
131	#10625350	—	2	2	no	—
132	#10625350	—	2	2	no	—
133	#10625350	—	2	2	no	—
134	#10625350	—	2	2	no	—
135	#10625350	—	2	2	no	—
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	C₄²	1	4	yes	—
143	#10625350	C₂²⋊C₄	1	4	yes	—
144	#10625350	C₄⋊C₄	1	4	yes	—
145	#10625350	C₄⋊C₄	1	4	yes	—
146	C₂×D₁₈₈	—	2	1	no	—
147	C₂×D₁₈₈	—	2	1	no	—
148	C₂×D₁₈₈	—	2	1	no	—
149	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
150	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
151	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
152	C₂×C₄×D₄₇	—	2	2	no	—
153	C₂×C₄×D₄₇	—	2	2	no	—
154	C₂×C₄×D₄₇	—	2	2	no	—
155	C₂×C₄×D₄₇	—	2	2	no	—
156	C₂×C₄×D₄₇	—	2	2	no	—
157	C₂×C₄×D₄₇	—	2	2	no	—
158	C₂×Dic₉₄	—	2	1	no	—
159	C₂×Dic₉₄	—	2	1	no	—
160	C₂×Dic₉₄	—	2	1	no	—
161	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
162	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
163	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
164	M₁₆×C₄₇	—	2	2	no	—
165	M₁₆×C₄₇	—	2	2	no	—
166	M₁₆×C₄₇	—	2	2	no	—
167	M₁₆×C₄₇	—	4	1	no	—
168	M₁₆×C₄₇	—	4	1	no	—
169	M₁₆×C₄₇	—	4	1	no	—
170	M₁₆×C₄₇	—	4	1	no	—
171	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₂×C₈×C₄₇	—	2	2	no	—
174	C₂×C₈×C₄₇	—	2	2	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	—	2	2	no	—
177	C₂×C₈×C₄₇	—	2	2	no	—
178	C₄⋊C₄×C₄₇	—	2	2	no	—
179	C₄⋊C₄×C₄₇	—	4	1	no	—
180	C₂²⋊C₄×C₄₇	—	2	2	no	—
181	C₂²⋊C₄×C₄₇	—	4	1	no	—
182	C₄²×C₄₇	—	2	2	no	—
183	C₄²×C₄₇	—	4	1	no	—
184	C₂²⋊Dic₄₇	—	2	2	no	—
185	C₂²⋊Dic₄₇	—	4	1	no	—
186	C₄⋊Dic₄₇	—	2	2	no	—
187	C₄⋊Dic₄₇	—	4	1	no	—
188	C₄×Dic₄₇	—	2	2	no	—
189	C₄×Dic₄₇	—	4	1	no	—
190	#10625329	—	2	2	no	—
191	#10625329	—	2	2	no	—
192	#10625329	—	2	2	no	—
193	#10625329	—	2	2	no	—
194	#10625329	—	4	1	no	—
195	#10625329	—	4	1	no	—
196	#10625329	—	4	1	no	—
197	#10625329	—	4	1	no	—
198	C₂×C₄₇⋊C₈	—	2	2	no	—
199	C₂×C₄₇⋊C₈	—	2	2	no	—
200	C₂×C₄₇⋊C₈	—	2	2	no	—
201	C₂×C₄₇⋊C₈	—	2	2	no	—
202	C₂×C₄₇⋊C₈	—	2	2	no	—
203	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
204	#10625324	—	2	16	no	—
205	C₈×D₄₇	—	2	16	no	—
206	C₂³×C₄₇	—	8	1	no	—
207	C₂³×C₄₇	#117	1	1	yes	characteristic
208	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
209	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
210	C₂³×C₄₇	#121	1	1	yes	characteristic
211	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂³×C₄₇	#123	1	1	yes	characteristic
213	C₂³×C₄₇	#123	1	1	yes	characteristic
214	C₂²×D₄₇	—	2	2	no	—
215	C₂²×D₄₇	—	2	2	no	—
216	C₂²×D₄₇	—	2	2	no	—
217	C₂²×D₄₇	—	8	2	no	—
218	C₂×C₄×C₄₇	—	4	2	no	—
219	C₂×C₄×C₄₇	—	8	2	no	—
220	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
247	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
248	C₂²⋊D₄₇	—	2	4	no	—
249	C₂²⋊D₄₇	—	2	4	no	—
250	C₂²⋊D₄₇	—	2	4	no	—
251	C₂²⋊D₄₇	—	2	4	no	—
252	C₂×Dic₄₇	—	2	2	no	—
253	C₂×Dic₄₇	—	2	2	no	—
254	C₂×Dic₄₇	—	2	2	no	—
255	C₂×Dic₄₇	—	4	2	no	—
256	C₂×Dic₄₇	—	8	2	no	—
257	D₁₈₈	—	2	2	no	—
258	D₁₈₈	—	2	2	no	—
259	D₁₈₈	—	2	2	no	—
260	D₁₈₈	#95	1	4	yes	—
261	C₄×D₄₇	—	2	4	no	—
262	C₄×D₄₇	—	2	4	no	—
263	C₄×D₄₇	—	2	4	no	—
264	C₄×D₄₇	—	2	4	no	—
265	Dic₉₄	—	2	2	no	—
266	Dic₉₄	—	2	2	no	—
267	Dic₉₄	—	2	2	no	—
268	Dic₉₄	#95	1	4	yes	—
269	C₈×C₄₇	—	2	4	no	—
270	C₈×C₄₇	—	4	2	no	—
271	C₄₇⋊C₈	—	2	4	no	—
272	C₄₇⋊C₈	—	4	2	no	—
273	#10793	—	47	1	no	maximal, Sylow
274	C₂²×C₄₇	—	4	1	no	—
275	C₂²×C₄₇	—	4	1	no	—
276	C₂²×C₄₇	—	4	1	no	—
277	C₂²×C₄₇	—	4	1	no	—
278	C₂²×C₄₇	—	4	1	no	—
279	C₂²×C₄₇	—	4	1	no	—
280	C₂²×C₄₇	—	4	1	no	—
281	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
282	C₂²×C₄₇	#380	1	1	yes	characteristic
283	C₂²×C₄₇	#381	1	1	yes	characteristic
284	C₂²×C₄₇	#385	1	1	yes	characteristic
285	C₂²×C₄₇	#385	1	1	yes	characteristic
286	C₂²×C₄₇	#386	1	1	yes	characteristic
287	C₂²×C₄₇	#386	1	1	yes	characteristic
288	C₂×D₄₇	—	2	4	no	—
289	C₂×D₄₇	—	4	4	no	—
290	C₂×D₄₇	—	8	2	no	—
291	C₂×D₄₇	—	8	2	no	—
292	C₄×C₄₇	—	8	2	no	—
293	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
294	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
295	C₄×C₄₇	#379	1	1	yes	characteristic
296	C₄×C₄₇	#380	1	1	yes	characteristic
297	C₄×C₄₇	#385	1	1	yes	characteristic
298	C₄×C₄₇	#385	1	1	yes	characteristic
299	C₄×C₄₇	#386	1	1	yes	characteristic
300	C₄×C₄₇	#386	1	1	yes	characteristic
301	Dic₄₇	—	2	4	no	—
302	Dic₄₇	—	8	2	no	—
303	C₂×#568	—	47	1	no	—
304	#2896	—	47	1	no	—
305	#2896	—	47	1	no	—
306	C₂×#344	—	47	1	no	—
307	C₂×#344	D₄₇	1	1	yes	characteristic, complemented
308	C₂×#338	—	47	1	no	—
309	C₂×H(3,ℤ/4)	—	47	1	no	—
310	C₂×C₄₇	—	2	1	no	—
311	C₂×C₄₇	—	2	1	no	—
312	C₂×C₄₇	—	2	1	no	—
313	C₂×C₄₇	—	2	1	no	—
314	C₂×C₄₇	—	2	1	no	—
315	C₂×C₄₇	—	2	1	no	—
316	C₂×C₄₇	—	2	1	no	—
317	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
318	D₄₇	—	4	4	no	—
319	C₂²×#41	—	47	1	no	—
320	#568	—	94	2	no	—
321	#568	—	94	2	no	—
322	#568	—	94	2	no	—
323	#568	—	94	2	no	—
324	C₂×#131	—	47	4	no	—
325	C₂×#131	—	94	2	no	—
326	C₂²×M₁₆	—	47	1	no	—
327	C₂²×M₁₆	—	47	1	no	—
328	C₂²×M₁₆	—	94	2	no	—
329	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
330	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
331	C₂×#117	—	47	1	no	—
332	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
333	#419	—	94	1	no	—
334	#419	—	94	1	no	—
335	#418	—	94	1	no	—
336	#418	—	94	1	no	—
337	#417	—	94	2	no	—
338	#417	—	94	2	no	—
339	#416	—	47	4	no	—
340	#416	—	47	4	no	—
341	#344	—	2	2	no	—
342	#344	—	94	2	no	—
343	#338	—	94	2	no	—
344	H(3,ℤ/4)	—	94	2	no	—
345	C₄₇	#10793	1	1	yes	characteristic, complemented, Sylow
346	C₂×#41	—	47	2	no	—
347	C₂×#41	—	47	2	no	—
348	C₂×#41	—	47	2	no	—
349	C₂×#41	—	47	2	no	—
350	C₂×#41	—	47	2	no	—
351	C₂×#41	—	47	2	no	—
352	C₂×#41	—	94	1	no	—
353	C₂×#41	—	94	1	no	—
354	C₂×#41	—	94	1	no	—
355	C₂×#41	—	94	1	no	—
356	C₂×#41	—	94	1	no	—
357	C₂×#41	—	94	1	no	—
358	C₂²×Q₈	—	47	1	no	—
359	C₂²×D₄	—	47	1	no	—
360	C₂²×D₄	—	94	1	no	—
361	C₂³×C₄	—	94	1	no	—
362	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
363	#131	—	94	8	no	—
364	#131	—	94	8	no	—
365	#131	—	94	8	no	—
366	#131	—	94	8	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	47	2	no	—
377	C₂×M₁₆	—	47	2	no	—
378	C₂×M₁₆	—	94	4	no	—
379	C₂×M₁₆	—	94	8	no	—
380	C₂×M₁₆	—	94	8	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	—	94	1	no	—
387	C₂×M₁₆	—	94	1	no	—
388	C₂×M₁₆	—	94	1	no	—
389	C₂×M₁₆	—	94	1	no	—
390	C₂×M₁₆	—	94	1	no	—
391	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
392	C₂×M₁₆	D₁₈₈	1	2	yes	—
393	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	—	47	2	no	—
396	C₂²×C₈	—	47	2	no	—
397	C₂²×C₈	—	94	4	no	—
398	C₂²×C₈	C₄×D₄₇	1	2	yes	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	—	2	1	no	—
402	#117	—	47	2	no	—
403	#117	—	94	1	no	—
404	#117	—	94	1	no	—
405	#117	—	94	1	no	—
406	#117	C₄×D₄₇	1	2	yes	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	94	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	94	1	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	94	1	no	—
413	#103	—	94	4	no	—
414	#103	—	94	4	no	—
415	#102	—	94	4	no	—
416	#102	—	94	4	no	—
417	C₂⁴	—	94	1	no	—
418	C₂⁴	#10625350	1	1	yes	characteristic
419	#41	—	47	4	no	—
420	#41	—	47	4	no	—
421	#41	—	47	4	no	—
422	#41	—	47	4	no	—
423	#41	—	94	2	no	—
424	#41	—	94	2	no	—
425	#41	—	94	2	no	—
426	#41	—	94	2	no	—
427	#41	—	94	2	no	—
428	#41	—	94	2	no	—
429	#41	—	94	2	no	—
430	#41	—	94	2	no	—
431	#41	—	94	2	no	—
432	#41	—	94	2	no	—
433	#41	—	94	2	no	—
434	#41	—	94	2	no	—
435	C₂×Q₈	—	47	2	no	—
436	C₂×Q₈	—	47	2	no	—
437	C₂×Q₈	—	47	2	no	—
438	C₂×Q₈	—	94	1	no	—
439	C₂×Q₈	—	94	1	no	—
440	C₂×Q₈	—	94	1	no	—
441	C₂×D₄	—	47	2	no	—
442	C₂×D₄	—	47	2	no	—
443	C₂×D₄	—	47	2	no	—
444	C₂×D₄	—	94	2	no	—
445	C₂×D₄	—	94	2	no	—
446	C₂×D₄	—	94	2	no	—
447	C₂×D₄	—	94	2	no	—
448	C₂×D₄	—	94	2	no	—
449	C₂×D₄	—	94	2	no	—
450	C₂×D₄	—	94	1	no	—
451	C₂×D₄	—	94	1	no	—
452	C₂×D₄	—	94	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	—	94	1	no	—
455	C₂²×C₄	—	94	2	no	—
456	C₂²×C₄	—	94	2	no	—
457	C₂²×C₄	—	94	2	no	—
458	C₂²×C₄	—	94	2	no	—
459	C₂²×C₄	—	94	2	no	—
460	C₂²×C₄	—	94	2	no	—
461	C₂²×C₄	—	188	1	no	—
462	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
466	C₂²×C₄	#10625350	1	1	yes	characteristic
467	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
468	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
469	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
470	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
471	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
472	C₂²×C₄	#10625352	1	1	yes	characteristic
473	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
474	C₂²×C₄	#10625354	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	4	1	no	—
480	M₁₆	—	4	1	no	—
481	M₁₆	—	4	1	no	—
482	M₁₆	—	4	1	no	—
483	M₁₆	—	94	16	no	—
484	M₁₆	—	94	2	no	—
485	M₁₆	—	94	2	no	—
486	M₁₆	—	94	2	no	—
487	M₁₆	—	94	2	no	—
488	M₁₆	—	188	1	no	—
489	M₁₆	—	188	1	no	—
490	M₁₆	—	188	1	no	—
491	M₁₆	—	188	1	no	—
492	M₁₆	(C₂×D₄₇)⋊C₄	1	4	yes	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	47	4	no	—
500	C₂×C₈	—	94	16	no	—
501	C₂×C₈	—	94	2	no	—
502	C₂×C₈	—	94	2	no	—
503	C₂×C₈	—	94	2	no	—
504	C₂×C₈	—	94	2	no	—
505	C₂×C₈	—	94	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	—	94	2	no	—
509	C₄⋊C₄	—	188	1	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	94	2	no	—
513	C₂²⋊C₄	—	188	1	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	4	1	no	—
516	C₄²	—	94	2	no	—
517	C₄²	—	188	1	no	—
518	C₂³	—	8	1	no	—
519	C₂³	—	94	2	no	—
520	C₂³	—	94	2	no	—
521	C₂³	—	94	2	no	—
522	C₂³	—	376	2	no	—
523	C₂³	#13093981	1	1	yes	characteristic
524	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
525	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
526	C₂³	#13093997	1	1	yes	characteristic
527	C₂³	#13094002	1	1	yes	characteristic
528	C₂³	#13094006	1	1	yes	characteristic
529	C₂³	#13094009	1	1	yes	characteristic
530	Q₈	—	47	4	no	—
531	Q₈	—	94	2	no	—
532	Q₈	—	94	2	no	—
533	Q₈	—	94	2	no	—
534	D₄	—	47	4	no	—
535	D₄	—	94	4	no	—
536	D₄	—	94	4	no	—
537	D₄	—	94	4	no	—
538	D₄	—	94	4	no	—
539	D₄	—	94	2	no	—
540	D₄	—	94	2	no	—
541	D₄	—	94	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	94	2	no	—
545	C₂×C₄	—	94	2	no	—
546	C₂×C₄	—	94	2	no	—
547	C₂×C₄	—	94	4	no	—
548	C₂×C₄	—	94	4	no	—
549	C₂×C₄	—	94	4	no	—
550	C₂×C₄	—	94	4	no	—
551	C₂×C₄	—	376	2	no	—
552	C₂×C₄	—	188	2	no	—
553	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
554	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
555	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
556	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
557	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
558	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
559	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
560	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
561	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
562	C₂×C₄	#13093982	1	1	yes	characteristic
563	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
564	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
566	C₂×C₄	#13093986	1	1	yes	characteristic
567	C₂×C₄	#13093986	1	1	yes	characteristic
568	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
569	C₂×C₄	#13093992	1	1	yes	characteristic
570	C₂×C₄	#13093992	1	1	yes	characteristic
571	C₂×C₄	#13093994	1	1	yes	characteristic
572	C₂×C₄	#13093994	1	1	yes	characteristic
573	C₂×C₄	#13093995	1	1	yes	characteristic
574	C₂×C₄	#13093997	1	1	yes	characteristic
575	C₂×C₄	#13093999	1	1	yes	characteristic
576	C₂×C₄	#13094000	1	1	yes	characteristic
577	C₂×C₄	#13094002	1	1	yes	characteristic
578	C₂×C₄	#13094004	1	1	yes	characteristic
579	C₂×C₄	#13094006	1	1	yes	characteristic
580	C₂×C₄	#13094009	1	1	yes	characteristic
581	C₈	—	2	4	no	—
582	C₈	—	4	2	no	—
583	C₈	—	94	4	no	—
584	C₈	—	188	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	94	4	no	—
593	C₂²	—	376	2	no	—
594	C₂²	—	376	2	no	—
595	C₂²	—	188	4	no	—
596	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
597	C₂²	#15688982	1	1	yes	characteristic
598	C₂²	#15688985	1	1	yes	characteristic
599	C₂²	#15688994	1	1	yes	characteristic
600	C₂²	#15688997	1	1	yes	characteristic
601	C₂²	#15688999	1	1	yes	characteristic
602	C₂²	#15689001	1	1	yes	characteristic
603	C₄	—	8	2	no	—
604	C₄	—	94	4	no	—
605	C₄	—	376	2	no	—
606	C₄	#95×D₄₇	1	1	yes	characteristic
607	C₄	#15688970	1	1	yes	characteristic
608	C₄	#15688978	1	1	yes	characteristic
609	C₄	#15688980	1	1	yes	characteristic
610	C₄	#15688994	1	1	yes	characteristic
611	C₄	#15688997	1	1	yes	characteristic
612	C₄	#15688999	1	1	yes	characteristic
613	C₄	#15689001	1	1	yes	characteristic
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	2	1	no	—
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	2	1	no	—
621	C₂	—	188	4	no	—
622	C₂	(C₂×D₄₇)⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15688970
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#344	C₂
socle	C₂×C₄₇	C₂²⋊#95
prime radical	C₂²×#10625350	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#344	D₄₇
hypocenter	C₄₇	#10793
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
4. C₂×#15688895	C₂	semidirect
5. C₂×C₄₇⋊#338	C₂	semidirect
6. C₂×#15688879	C₂	semidirect
7. C₂×C₄₇×#344	C₂	semidirect
13. C₂×#13094032	C₄	semidirect
25. #15689120	C₄	semidirect
26. #15689117	C₄	semidirect
307. C₂×#344	D₄₇	semidirect
345. C₄₇	#10793	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689889	2
#20251908	2
#20251905	2
C₂×#15688895	2
C₂×C₄₇⋊#338	2
C₂×#15688879	2
C₂×C₄₇×#344	2
#10793	47