Subgroups — #26214011

Order 12032.

1562 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256591	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689140	C₂	1	1	yes	maximal, characteristic
3	#20251806	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243200	C₂	1	4	yes	maximal, complemented
6	#104×Dic₄₇	C₂	1	4	yes	maximal, complemented
7	#20243099	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15688883	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#104×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	#15689606	—	2	2	no	—
12	#15689606	C₄	1	4	yes	complemented
13	#15689601	C₄	1	2	yes	complemented
14	#15689598	—	2	2	no	—
15	#15689598	C₄	1	2	yes	complemented
16	#41×Dic₄₇	—	2	2	no	—
17	#41×Dic₄₇	C₂²	1	4	yes	—
18	C₂×#13093983	—	2	2	no	—
19	C₂×#13093983	C₂²	1	1	yes	characteristic
20	C₂×#13093983	C₂²	1	1	yes	characteristic
21	C₂×#13093983	C₂²	1	1	yes	characteristic
22	#15689140	C₄	1	8	yes	complemented
23	C₂×#13093951	C₂²	1	4	yes	—
24	#15689081	—	2	2	no	—
25	#15689078	—	2	2	no	—
26	M₁₆×Dic₄₇	C₂²	1	4	yes	complemented
27	C₄×C₄⋊Dic₄₇	—	2	2	no	—
28	C₄×C₂²⋊Dic₄₇	—	2	2	no	—
29	#15688969	C₂²	1	2	yes	complemented
30	C₄²×Dic₄₇	C₂²	1	2	yes	complemented
31	#15688884	C₂²	1	4	yes	complemented
32	#15688883	C₂²	1	2	yes	complemented
33	#15688883	C₂²	1	2	yes	complemented
34	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#104×C₄₇	C₄	1	8	yes	complemented
38	C₂×#104×C₄₇	C₂²	1	2	yes	—
39	C₂×#104×C₄₇	C₂²	1	2	yes	—
40	C₂×#10625329	—	2	1	no	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	C₂×C₄	1	4	yes	complemented
43	C₂×#10625329	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	—	2	1	no	—
45	Q₈×Dic₄₇	—	2	4	no	—
46	Q₈×Dic₄₇	C₂×C₄	1	8	yes	complemented
47	D₄×Dic₄₇	—	2	8	no	—
48	D₄×Dic₄₇	—	2	8	no	—
49	D₄×Dic₄₇	—	2	4	no	—
50	D₄×Dic₄₇	C₂×C₄	1	8	yes	complemented
51	#13093983	—	2	1	no	—
52	#13093983	—	2	1	no	—
53	#13093983	—	2	2	no	—
54	#13093983	—	2	4	no	—
55	#13093983	—	2	4	no	—
56	#13093983	—	2	4	no	—
57	#13093983	C₂×C₄	1	2	yes	—
58	#13093983	C₂×C₄	1	2	yes	—
59	#13093983	C₂×C₄	1	2	yes	—
60	#13093983	C₂×C₄	1	4	yes	complemented
61	#13093983	D₄	1	2	yes	—
62	#13093983	D₄	1	2	yes	—
63	#13093983	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₄₇	—	2	1	no	—
65	C₂×C₄⋊Dic₄₇	—	2	4	no	—
66	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
68	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
69	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
70	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
71	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
72	C₂×C₄×Dic₄₇	—	2	1	no	—
73	C₂×C₄×Dic₄₇	—	2	4	no	—
74	C₂×C₄×Dic₄₇	—	2	4	no	—
75	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
76	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
77	#13093951	C₂×C₄	1	16	yes	complemented
78	#13093934	—	2	4	no	—
79	C₈×Dic₄₇	—	2	4	no	—
80	C₄₇⋊#95	—	2	4	no	—
81	C₂×#41×C₄₇	—	2	1	no	—
82	C₂×#41×C₄₇	—	2	1	no	—
83	C₂×#41×C₄₇	—	2	2	no	—
84	C₂×#41×C₄₇	—	2	2	no	—
85	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
86	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
87	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
88	C₂×#41×C₄₇	C₂³	1	2	yes	—
89	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂²×D₄×C₄₇	—	2	1	no	—
91	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂³×C₄×C₄₇	—	2	1	no	—
93	C₂³×C₄×C₄₇	—	2	1	no	—
94	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₄₇	—	2	1	no	—
96	C₂×M₁₆×C₄₇	—	2	2	no	—
97	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
98	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
99	C₂²×C₈×C₄₇	—	2	1	no	—
100	C₂×C₄²×C₄₇	—	2	1	no	—
101	C₂×C₄²×C₄₇	—	2	2	no	—
102	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
103	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
105	#104×C₄₇	C₂×C₄	1	8	yes	complemented
106	#104×C₄₇	C₂×C₄	1	8	yes	complemented
107	C₂⁴×C₄₇	—	2	1	no	—
108	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
109	#41×C₄₇	—	2	4	no	—
110	#41×C₄₇	—	2	4	no	—
111	#41×C₄₇	—	2	4	no	—
112	#41×C₄₇	—	2	4	no	—
113	#41×C₄₇	—	2	4	no	—
114	#41×C₄₇	—	2	2	no	—
115	#41×C₄₇	—	2	2	no	—
116	#41×C₄₇	C₄²	1	8	yes	complemented
117	#41×C₄₇	C₂²×C₄	1	4	yes	—
118	#41×C₄₇	C₂²×C₄	1	4	yes	—
119	C₂×Q₈×C₄₇	—	2	1	no	—
120	C₂×Q₈×C₄₇	—	2	2	no	—
121	C₂×Q₈×C₄₇	C₄²	1	4	yes	complemented
122	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂×D₄×C₄₇	—	2	2	no	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	2	4	no	—
126	C₂×D₄×C₄₇	—	2	2	no	—
127	C₂×D₄×C₄₇	—	2	1	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂×D₄×C₄₇	C₄²	1	4	yes	complemented
130	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	1	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	4	no	—
135	C₂²×C₄×C₄₇	—	2	4	no	—
136	C₂²×C₄×C₄₇	—	2	2	no	—
137	C₂²×C₄×C₄₇	—	2	4	no	—
138	C₂²×C₄×C₄₇	—	2	1	no	—
139	C₂²×C₄×C₄₇	—	4	4	no	—
140	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	#41	1	2	yes	—
148	C₂²×C₄×C₄₇	#41	1	2	yes	—
149	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₂²×Dic₄₇	—	2	2	no	—
151	C₂²×Dic₄₇	—	2	2	no	—
152	C₂²×Dic₄₇	—	2	8	no	—
153	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
154	M₁₆×C₄₇	—	2	4	no	—
155	M₁₆×C₄₇	—	2	2	no	—
156	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
157	C₂×C₈×C₄₇	—	2	4	no	—
158	C₂×C₈×C₄₇	—	2	2	no	—
159	C₄²×C₄₇	—	2	4	no	—
160	C₄²×C₄₇	—	2	1	no	—
161	C₄²×C₄₇	—	2	1	no	—
162	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
163	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
164	C₂²⋊Dic₄₇	—	2	2	no	—
165	C₂²⋊Dic₄₇	—	2	4	no	—
166	C₂²⋊Dic₄₇	—	2	2	no	—
167	C₂²⋊Dic₄₇	—	2	8	no	—
168	C₂²⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
169	C₂²⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
170	C₄⋊Dic₄₇	—	2	2	no	—
171	C₄⋊Dic₄₇	—	2	4	no	—
172	C₄⋊Dic₄₇	—	2	8	no	—
173	C₄⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
174	C₄⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
175	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
176	C₄×Dic₄₇	—	2	2	no	—
177	C₄×Dic₄₇	—	2	2	no	—
178	C₄×Dic₄₇	—	2	2	no	—
179	C₄×Dic₄₇	—	2	8	no	—
180	C₄×Dic₄₇	—	4	8	no	—
181	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
182	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
183	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
184	#10625329	—	2	4	no	—
185	#10625329	—	2	2	no	—
186	#10625329	C₂²×C₄	1	4	yes	—
187	C₂×C₄₇⋊C₈	—	2	4	no	—
188	C₂×C₄₇⋊C₈	—	2	2	no	—
189	C₂³×C₄₇	—	2	2	no	—
190	C₂³×C₄₇	—	2	4	no	—
191	C₂³×C₄₇	—	4	2	no	—
192	C₂³×C₄₇	—	8	2	no	—
193	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₄₇	C₄×D₄	1	2	yes	—
196	C₂³×C₄₇	C₄×D₄	1	2	yes	—
197	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₄₇	—	2	2	no	—
199	Q₈×C₄₇	—	2	4	no	—
200	Q₈×C₄₇	C₂×C₄²	1	4	yes	—
201	D₄×C₄₇	—	2	4	no	—
202	D₄×C₄₇	—	2	4	no	—
203	D₄×C₄₇	—	2	8	no	—
204	D₄×C₄₇	—	2	2	no	—
205	D₄×C₄₇	—	2	4	no	—
206	D₄×C₄₇	C₂×C₄²	1	4	yes	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	4	no	—
211	C₂×C₄×C₄₇	—	2	4	no	—
212	C₂×C₄×C₄₇	—	2	4	no	—
213	C₂×C₄×C₄₇	—	2	8	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	4	8	no	—
216	C₂×C₄×C₄₇	—	4	2	no	—
217	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
218	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
219	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	#117	1	2	yes	—
222	C₂×C₄×C₄₇	#117	1	2	yes	—
223	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
235	C₂×Dic₄₇	—	2	4	no	—
236	C₂×Dic₄₇	—	2	4	no	—
237	C₂×Dic₄₇	—	4	4	no	—
238	C₂×Dic₄₇	—	4	4	no	—
239	C₂×Dic₄₇	—	8	8	no	—
240	C₂×Dic₄₇	—	8	2	no	—
241	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	8	yes	—
242	C₈×C₄₇	—	2	4	no	—
243	C₄₇⋊C₈	—	2	4	no	—
244	#20405	—	47	1	no	maximal, Sylow
245	C₂²×C₄₇	—	2	2	no	—
246	C₂²×C₄₇	—	2	2	no	—
247	C₂²×C₄₇	—	2	2	no	—
248	C₂²×C₄₇	—	2	4	no	—
249	C₂²×C₄₇	—	4	2	no	—
250	C₂²×C₄₇	—	4	2	no	—
251	C₂²×C₄₇	—	4	4	no	—
252	C₂²×C₄₇	—	8	4	no	—
253	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
254	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
255	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
258	C₄×C₄₇	—	2	4	no	—
259	C₄×C₄₇	—	2	4	no	—
260	C₄×C₄₇	—	4	2	no	—
261	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
262	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
263	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
264	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
265	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
266	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
267	Dic₄₇	—	2	8	no	—
268	Dic₄₇	—	4	4	no	—
269	Dic₄₇	—	4	4	no	—
270	#3428	—	47	1	no	—
271	C₂×#421	—	47	1	no	—
272	C₂²×#104	D₄₇	1	1	yes	characteristic
273	#2873	—	47	1	no	—
274	C₄×#117	—	47	1	no	—
275	#1759	—	47	4	no	—
276	C₄×#104	—	47	4	no	—
277	#1733	—	47	1	no	—
278	C₂×#339	—	47	1	no	—
279	C₂×C₄₇	—	2	1	no	—
280	C₂×C₄₇	—	2	1	no	—
281	C₂×C₄₇	—	2	2	no	—
282	C₂×C₄₇	—	2	2	no	—
283	C₂×C₄₇	—	4	4	no	—
284	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₄₇	#2901	1	2	yes	—
286	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
287	C₂²×M₁₆	—	47	1	no	—
288	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
289	#520	—	47	4	no	—
290	#520	—	94	2	no	—
291	#519	—	47	2	no	—
292	#518	—	47	2	no	—
293	#518	—	94	2	no	—
294	C₄×#41	—	47	4	no	—
295	C₄×#41	—	94	2	no	—
296	C₂×#117	—	47	1	no	—
297	C₂×#117	—	47	1	no	—
298	C₂×#117	—	47	1	no	—
299	C₂×#117	—	94	2	no	—
300	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
301	#421	—	47	8	no	—
302	C₂×#104	—	47	4	no	—
303	C₂×#104	Dic₄₇	1	8	yes	complemented
304	C₂×#104	C₂×D₄₇	1	2	yes	—
305	C₂×#104	C₂×D₄₇	1	2	yes	—
306	#405	—	94	2	no	—
307	#405	—	94	2	no	—
308	C₄×M₁₆	—	47	4	no	—
309	C₄×C₄⋊C₄	—	94	2	no	—
310	C₄×C₂²⋊C₄	—	94	2	no	—
311	#376	—	47	2	no	—
312	C₄³	—	47	2	no	—
313	#339	—	47	4	no	—
314	#339	—	47	2	no	—
315	#339	—	47	2	no	—
316	C₄₇	#20405	1	1	yes	characteristic, complemented, Sylow
317	C₂×#41	—	2	1	no	—
318	C₂×#41	—	2	1	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	C₄×D₄₇	1	4	yes	—
322	C₂×#41	C₄×D₄₇	1	2	yes	—
323	C₂×#41	C₂×Dic₄₇	1	4	yes	—
324	C₂×#41	C₂²×D₄₇	1	2	yes	—
325	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	47	4	no	—
334	C₂×M₁₆	—	47	2	no	—
335	C₂×M₁₆	—	94	1	no	—
336	C₂×M₁₆	—	94	2	no	—
337	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	complemented
338	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
339	C₂²×C₈	—	2	1	no	—
340	C₂²×C₈	—	94	1	no	—
341	C₄×Q₈	—	47	8	no	—
342	C₄×Q₈	—	94	4	no	—
343	C₄×D₄	—	47	8	no	—
344	C₄×D₄	—	94	8	no	—
345	C₄×D₄	—	94	4	no	—
346	C₄×D₄	—	94	8	no	—
347	#117	—	47	2	no	—
348	#117	—	47	2	no	—
349	#117	—	47	2	no	—
350	#117	—	47	2	no	—
351	#117	—	47	4	no	—
352	#117	—	47	2	no	—
353	#117	—	47	2	no	—
354	#117	—	94	4	no	—
355	#117	—	94	4	no	—
356	#117	—	94	4	no	—
357	#117	—	94	1	no	—
358	#117	—	94	1	no	—
359	#117	—	94	2	no	—
360	C₂×C₄⋊C₄	—	47	2	no	—
361	C₂×C₄⋊C₄	—	47	2	no	—
362	C₂×C₄⋊C₄	—	94	4	no	—
363	C₂×C₄⋊C₄	—	94	1	no	—
364	C₂×C₂²⋊C₄	—	47	2	no	—
365	C₂×C₂²⋊C₄	—	94	4	no	—
366	C₂×C₂²⋊C₄	—	94	1	no	—
367	C₂×C₂²⋊C₄	—	94	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	—	47	2	no	—
371	C₂×C₄²	—	47	2	no	—
372	C₂×C₄²	—	94	4	no	—
373	C₂×C₄²	—	94	1	no	—
374	C₂×C₄²	—	94	4	no	—
375	C₂×C₄²	C₂×Dic₄₇	1	4	yes	complemented
376	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
377	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
378	#104	—	47	16	no	—
379	#104	C₂×Dic₄₇	1	8	yes	complemented
380	#104	C₂×Dic₄₇	1	8	yes	complemented
381	#97	—	94	4	no	—
382	C₄×C₈	—	94	4	no	—
383	#95	—	94	4	no	—
384	C₂⁴	—	2	1	no	—
385	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
386	#41	—	2	4	no	—
387	#41	—	2	4	no	—
388	#41	—	2	4	no	—
389	#41	—	2	4	no	—
390	#41	—	2	4	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	C₄×Dic₄₇	1	8	yes	complemented
394	#41	C₂×C₄×D₄₇	1	4	yes	—
395	#41	C₂²×Dic₄₇	1	4	yes	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	C₄×Dic₄₇	1	4	yes	complemented
399	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	C₄×Dic₄₇	1	4	yes	complemented
407	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	47	4	no	—
418	C₂²×C₄	—	94	8	no	—
419	C₂²×C₄	—	94	2	no	—
420	C₂²×C₄	—	94	2	no	—
421	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
422	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
423	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
424	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
425	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
426	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
427	C₂²×C₄	#10625352	1	2	yes	—
428	C₂²×C₄	#10625352	1	2	yes	—
429	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
430	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
431	M₁₆	—	2	4	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	47	4	no	—
434	M₁₆	—	94	4	no	—
435	M₁₆	—	94	2	no	—
436	M₁₆	C₂²×Dic₄₇	1	4	yes	—
437	C₂×C₈	—	2	4	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	94	4	no	—
440	C₂×C₈	—	94	2	no	—
441	C₄⋊C₄	—	47	4	no	—
442	C₄⋊C₄	—	47	4	no	—
443	C₄⋊C₄	—	47	4	no	—
444	C₄⋊C₄	—	94	8	no	—
445	C₄⋊C₄	—	94	2	no	—
446	C₄⋊C₄	—	94	4	no	—
447	C₂²⋊C₄	—	47	4	no	—
448	C₂²⋊C₄	—	47	4	no	—
449	C₂²⋊C₄	—	94	8	no	—
450	C₂²⋊C₄	—	94	2	no	—
451	C₂²⋊C₄	—	94	4	no	—
452	C₂²⋊C₄	—	94	2	no	—
453	C₄²	—	2	4	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	47	4	no	—
457	C₄²	—	47	4	no	—
458	C₄²	—	47	4	no	—
459	C₄²	—	94	8	no	—
460	C₄²	—	94	2	no	—
461	C₄²	—	94	2	no	—
462	C₄²	—	94	2	no	—
463	C₄²	—	188	8	no	—
464	C₄²	C₂²×Dic₄₇	1	2	yes	—
465	C₄²	C₂²×Dic₄₇	1	2	yes	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	8	2	no	—
470	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
471	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
472	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
473	C₂³	D₄×Dic₄₇	1	2	yes	—
474	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
475	Q₈	—	2	4	no	—
476	Q₈	—	2	2	no	—
477	Q₈	C₂×C₄×Dic₄₇	1	4	yes	—
478	D₄	—	2	8	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	2	no	—
483	D₄	C₂×C₄×Dic₄₇	1	4	yes	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	8	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	47	8	no	—
495	C₂×C₄	—	94	4	no	—
496	C₂×C₄	—	94	4	no	—
497	C₂×C₄	—	376	8	no	—
498	C₂×C₄	—	376	2	no	—
499	C₂×C₄	—	188	4	no	—
500	C₂×C₄	—	188	4	no	—
501	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
502	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
503	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
504	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
505	C₂×C₄	#13093980	1	2	yes	—
506	C₂×C₄	#13093980	1	2	yes	—
507	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
508	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
509	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
510	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
511	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
512	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
513	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
514	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
515	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
517	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
518	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
519	C₈	—	2	4	no	—
520	C₈	—	94	4	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	8	4	no	—
529	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
530	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
531	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
532	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
533	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
534	C₄	—	2	4	no	—
535	C₄	—	2	4	no	—
536	C₄	—	4	2	no	—
537	C₄	—	94	8	no	—
538	C₄	—	188	4	no	—
539	C₄	—	188	4	no	—
540	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
541	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
542	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
543	C₄	C₂×#13093980	1	1	yes	characteristic
544	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
545	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
546	C₂	—	2	1	no	—
547	C₂	—	2	1	no	—
548	C₂	—	2	2	no	—
549	C₂	—	2	2	no	—
550	C₂	—	4	4	no	—
551	C₂	C₂×C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
552	C₂	#20251932	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#104×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#104	D₄₇
hypocenter	C₄₇	#20405
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#104

Complements

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

N	H ≅ G/N	type
3. #20251806	C₂	semidirect
4. C₄×#13093983	C₂	semidirect
5. #20243200	C₂	semidirect
6. #104×Dic₄₇	C₂	semidirect
7. #20243099	C₂	semidirect
8. C₂×#15688883	C₂	semidirect
12. #15689606	C₄	semidirect
13. #15689601	C₄	semidirect
15. #15689598	C₄	semidirect
22. #15689140	C₄	semidirect
26. M₁₆×Dic₄₇	C₂²	semidirect
29. #15688969	C₂²	semidirect
30. C₄²×Dic₄₇	C₂²	semidirect
31. #15688884	C₂²	semidirect
32. #15688883	C₂²	semidirect
33. #15688883	C₂²	semidirect
37. C₂×#104×C₄₇	C₄	semidirect
42. C₂×#10625329	C₂×C₄	semidirect
46. Q₈×Dic₄₇	C₂×C₄	semidirect
50. D₄×Dic₄₇	C₂×C₄	semidirect
60. #13093983	C₂×C₄	semidirect
77. #13093951	C₂×C₄	semidirect
97. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
102. C₂×C₄²×C₄₇	C₂×C₄	semidirect
105. #104×C₄₇	C₂×C₄	semidirect
106. #104×C₄₇	C₂×C₄	semidirect
116. #41×C₄₇	C₄²	semidirect
121. C₂×Q₈×C₄₇	C₄²	semidirect
129. C₂×D₄×C₄₇	C₄²	semidirect
303. C₂×#104	Dic₄₇	semidirect
316. C₄₇	#20405	semidirect
337. C₂×M₁₆	C₂×Dic₄₇	semidirect
375. C₂×C₄²	C₂×Dic₄₇	semidirect
379. #104	C₂×Dic₄₇	semidirect
380. #104	C₂×Dic₄₇	semidirect
393. #41	C₄×Dic₄₇	semidirect
398. C₂×Q₈	C₄×Dic₄₇	semidirect
406. C₂×D₄	C₄×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20256591	2
C₂×#15689140	2
#20251806	2
C₄×#13093983	2
#20243200	2
#104×Dic₄₇	2
#20243099	2
C₂×#15688883	2
C₂²×#104×C₄₇	2
#20405	47