Subgroups — #26184473

Order 12032.

876 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252402	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252039	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242026	C₂	1	2	yes	maximal, complemented
4	#20242019	C₂	1	2	yes	maximal, complemented
5	#20242008	C₂	1	2	yes	maximal, complemented
6	#20242003	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242003	C₂	1	2	yes	maximal, complemented
8	#20241995	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241983	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241976	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3518	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	1	no	—
13	#15689195	—	2	2	no	—
14	D₄×C₄₇⋊C₈	—	2	1	no	—
15	#15689184	—	2	2	no	—
16	#15689180	C₂²	1	1	yes	characteristic
17	#15689180	C₂²	1	2	yes	—
18	#15689180	C₂²	1	2	yes	—
19	#15689180	C₂²	1	2	yes	—
20	#15689150	—	2	1	no	—
21	#15689090	—	2	1	no	—
22	C₄×#10625329	C₂²	1	1	yes	characteristic
23	C₄×#10625329	C₂²	1	1	yes	characteristic
24	C₂×#13093935	C₂²	1	1	yes	characteristic
25	C₂×#13093935	C₂²	1	2	yes	—
26	#15688865	C₂²	1	1	yes	characteristic
27	#15688865	C₂²	1	1	yes	characteristic
28	#15688865	C₂²	1	2	yes	—
29	#15688865	C₂²	1	2	yes	—
30	#15688865	C₂²	1	2	yes	—
31	#15688865	C₂²	1	2	yes	—
32	#15688865	C₂²	1	2	yes	—
33	#15688863	C₂²	1	1	yes	characteristic
34	#15688863	C₂²	1	1	yes	characteristic
35	#15688863	C₂²	1	2	yes	—
36	Q₈²×C₄₇	C₄	1	1	yes	characteristic
37	C₄₇×#556	—	2	1	no	—
38	C₄₇×#556	—	2	2	no	—
39	C₄₇×#556	C₄	1	2	yes	—
40	C₄₇×#556	C₄	1	1	yes	characteristic
41	C₄₇×#555	C₄	1	2	yes	—
42	C₄₇×#555	C₄	1	1	yes	characteristic
43	D₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
44	C₄₇×#548	—	2	1	no	—
45	C₄₇×#542	—	2	1	no	—
46	C₄₇×#542	—	2	2	no	—
47	C₄₇×#533	C₂²	1	1	yes	characteristic
48	C₄₇×#533	C₂²	1	2	yes	—
49	C₄₇×#529	C₂²	1	1	yes	characteristic
50	C₄₇×#529	C₂²	1	2	yes	—
51	C₄₇×#519	—	2	1	no	—
52	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₂²×C₄₇⋊C₈	—	2	2	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
65	#13093935	—	2	2	no	—
66	#13093935	—	2	1	no	—
67	#13093935	C₂³	1	1	yes	characteristic
68	#13093935	C₂³	1	1	yes	characteristic
69	#13093935	C₂³	1	1	yes	characteristic
70	#13093935	C₂³	1	2	yes	—
71	#13093935	C₂³	1	1	yes	characteristic
72	#13093935	C₂³	1	2	yes	—
73	C₄×C₄₇⋊C₈	—	2	1	no	—
74	C₄×C₄₇⋊C₈	—	2	1	no	—
75	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
76	C₂²×Q₈×C₄₇	—	2	1	no	—
77	C₄⋊Q₈×C₄₇	—	2	2	no	—
78	C₄⋊Q₈×C₄₇	—	2	1	no	—
79	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
81	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
83	#126×C₄₇	—	2	2	no	—
84	#126×C₄₇	—	2	2	no	—
85	#126×C₄₇	—	2	2	no	—
86	#126×C₄₇	—	2	1	no	—
87	#126×C₄₇	—	2	2	no	—
88	#125×C₄₇	C₂³	1	1	yes	characteristic
89	#125×C₄₇	C₂³	1	2	yes	—
90	#124×C₄₇	—	2	1	no	—
91	#124×C₄₇	—	2	2	no	—
92	#124×C₄₇	—	2	2	no	—
93	#124×C₄₇	—	2	2	no	—
94	#124×C₄₇	—	2	2	no	—
95	#124×C₄₇	C₂³	1	1	yes	characteristic
96	#123×C₄₇	—	2	2	no	—
97	#123×C₄₇	—	2	1	no	—
98	C₂²⋊Q₈×C₄₇	—	2	2	no	—
99	C₂²⋊Q₈×C₄₇	—	2	1	no	—
100	C₂²⋊Q₈×C₄₇	—	2	1	no	—
101	C₂²⋊Q₈×C₄₇	—	2	2	no	—
102	C₂²⋊Q₈×C₄₇	—	2	2	no	—
103	C₂²⋊Q₈×C₄₇	—	2	1	no	—
104	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
106	#121×C₄₇	—	2	1	no	—
107	#121×C₄₇	—	2	2	no	—
108	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
109	#121×C₄₇	C₂×C₄	1	2	yes	—
110	C₄×Q₈×C₄₇	—	2	1	no	—
111	C₄×Q₈×C₄₇	—	2	2	no	—
112	C₄×Q₈×C₄₇	—	2	1	no	—
113	C₄×Q₈×C₄₇	—	2	1	no	—
114	C₄×Q₈×C₄₇	—	2	2	no	—
115	C₄×Q₈×C₄₇	—	2	1	no	—
116	C₄×Q₈×C₄₇	—	2	2	no	—
117	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
118	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
119	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
121	C₄×D₄×C₄₇	—	2	1	no	—
122	C₄×D₄×C₄₇	—	2	2	no	—
123	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
124	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
125	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
126	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
127	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
128	C₄×D₄×C₄₇	D₄	1	2	yes	—
129	#117×C₄₇	—	2	2	no	—
130	#117×C₄₇	—	2	1	no	—
131	#117×C₄₇	—	2	1	no	—
132	#117×C₄₇	—	2	2	no	—
133	#117×C₄₇	C₂×C₄	1	2	yes	—
134	#117×C₄₇	C₂×C₄	1	2	yes	—
135	#117×C₄₇	C₂×C₄	1	2	yes	—
136	#117×C₄₇	D₄	1	1	yes	characteristic
137	#117×C₄₇	D₄	1	2	yes	—
138	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
140	#41×C₄₇	—	4	2	no	—
141	C₂×Q₈×C₄₇	—	2	2	no	—
142	C₂×Q₈×C₄₇	—	2	1	no	—
143	C₂×Q₈×C₄₇	—	2	1	no	—
144	C₂×Q₈×C₄₇	—	2	2	no	—
145	C₂×Q₈×C₄₇	—	4	4	no	—
146	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₄₇	—	2	1	no	—
149	C₂×D₄×C₄₇	—	2	2	no	—
150	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
152	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	—	2	2	no	—
154	C₂²×C₄×C₄₇	—	2	1	no	—
155	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₄⋊C₄×C₄₇	—	2	2	no	—
162	C₄⋊C₄×C₄₇	—	2	1	no	—
163	C₄⋊C₄×C₄₇	—	2	1	no	—
164	C₄⋊C₄×C₄₇	—	2	2	no	—
165	C₄⋊C₄×C₄₇	—	2	1	no	—
166	C₄⋊C₄×C₄₇	—	2	2	no	—
167	C₄⋊C₄×C₄₇	—	2	1	no	—
168	C₄⋊C₄×C₄₇	—	2	2	no	—
169	C₄⋊C₄×C₄₇	—	2	1	no	—
170	C₄⋊C₄×C₄₇	—	2	2	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	—	2	2	no	—
173	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
174	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
175	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
176	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
177	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
178	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
180	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
181	C₂²⋊C₄×C₄₇	—	2	2	no	—
182	C₂²⋊C₄×C₄₇	—	2	2	no	—
183	C₂²⋊C₄×C₄₇	—	2	2	no	—
184	C₂²⋊C₄×C₄₇	—	2	1	no	—
185	C₂²⋊C₄×C₄₇	—	2	2	no	—
186	C₂²⋊C₄×C₄₇	—	2	1	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	—	2	1	no	—
189	C₂²⋊C₄×C₄₇	—	2	2	no	—
190	C₂²⋊C₄×C₄₇	—	2	1	no	—
191	C₂²⋊C₄×C₄₇	—	2	1	no	—
192	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
193	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
194	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
195	C₄²×C₄₇	—	2	2	no	—
196	C₄²×C₄₇	—	2	2	no	—
197	C₄²×C₄₇	—	2	2	no	—
198	C₄²×C₄₇	—	2	2	no	—
199	C₄²×C₄₇	—	2	1	no	—
200	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
201	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₄₇	C₂×D₄	1	2	yes	—
204	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₄₇	C₂×D₄	1	2	yes	—
206	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
207	#10625329	—	4	2	no	—
208	#10625329	—	4	2	no	—
209	C₂×C₄₇⋊C₈	—	2	1	no	—
210	C₂×C₄₇⋊C₈	—	2	1	no	—
211	C₂×C₄₇⋊C₈	—	2	2	no	—
212	C₂×C₄₇⋊C₈	—	2	2	no	—
213	C₂×C₄₇⋊C₈	—	2	1	no	—
214	C₂×C₄₇⋊C₈	—	2	1	no	—
215	C₂×C₄₇⋊C₈	—	4	4	no	—
216	C₂×C₄₇⋊C₈	—	4	2	no	—
217	C₂³×C₄₇	—	2	1	no	—
218	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
220	Q₈×C₄₇	—	2	2	no	—
221	Q₈×C₄₇	—	4	1	no	—
222	Q₈×C₄₇	—	4	4	no	—
223	Q₈×C₄₇	—	4	2	no	—
224	Q₈×C₄₇	—	8	2	no	—
225	Q₈×C₄₇	—	8	1	no	—
226	D₄×C₄₇	—	2	2	no	—
227	D₄×C₄₇	—	4	2	no	—
228	D₄×C₄₇	—	4	1	no	—
229	D₄×C₄₇	—	8	2	no	—
230	D₄×C₄₇	—	8	1	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	2	1	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	4	2	no	—
238	C₂×C₄×C₄₇	—	4	1	no	—
239	C₂×C₄×C₄₇	—	4	1	no	—
240	C₂×C₄×C₄₇	—	4	2	no	—
241	C₂×C₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	—	4	4	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
247	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	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	C₂²×D₄	1	1	yes	characteristic
253	C₄₇⋊C₈	—	2	2	no	—
254	C₄₇⋊C₈	—	4	1	no	—
255	C₄₇⋊C₈	—	4	1	no	—
256	C₄₇⋊C₈	—	4	2	no	—
257	C₄₇⋊C₈	—	4	2	no	—
258	C₄₇⋊C₈	—	4	1	no	—
259	#17683	—	47	1	no	maximal, Sylow
260	C₂²×C₄₇	—	2	1	no	—
261	C₂²×C₄₇	—	2	2	no	—
262	C₂²×C₄₇	—	2	1	no	—
263	C₂²×C₄₇	—	2	2	no	—
264	C₂²×C₄₇	—	2	2	no	—
265	C₂²×C₄₇	—	2	1	no	—
266	C₂²×C₄₇	—	4	1	no	—
267	C₂²×C₄₇	—	4	1	no	—
268	C₂²×C₄₇	—	4	1	no	—
269	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
270	C₄×C₄₇	—	2	1	no	—
271	C₄×C₄₇	—	2	1	no	—
272	C₄×C₄₇	—	2	2	no	—
273	C₄×C₄₇	—	2	1	no	—
274	C₄×C₄₇	—	2	2	no	—
275	C₄×C₄₇	—	2	1	no	—
276	C₄×C₄₇	—	2	2	no	—
277	C₄×C₄₇	—	2	1	no	—
278	C₄×C₄₇	—	4	1	no	—
279	C₄×C₄₇	—	4	2	no	—
280	C₄×C₄₇	—	4	1	no	—
281	C₄×C₄₇	—	4	2	no	—
282	C₄×C₄₇	—	4	1	no	—
283	C₄×C₄₇	#421	1	2	yes	—
284	#3518	D₄₇	1	1	yes	characteristic
285	#2970	—	47	1	no	—
286	#2923	—	47	1	no	—
287	#1537	—	47	2	no	—
288	#1535	—	47	2	no	—
289	#1532	—	47	2	no	—
290	#1531	—	47	2	no	—
291	#1531	—	47	1	no	—
292	#1529	—	47	1	no	—
293	#1526	—	47	1	no	—
294	#1524	—	47	1	no	—
295	C₂×C₄₇	—	4	1	no	—
296	C₂×C₄₇	—	4	2	no	—
297	C₂×C₄₇	—	8	1	no	—
298	C₂×C₄₇	#2889	1	1	yes	characteristic
299	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
300	C₂×C₄₇	#2901	1	1	yes	characteristic
301	Q₈²	Dic₄₇	1	1	yes	characteristic
302	#556	—	2	1	no	—
303	#556	—	2	2	no	—
304	#556	Dic₄₇	1	1	yes	characteristic
305	#556	Dic₄₇	1	2	yes	—
306	#555	Dic₄₇	1	1	yes	characteristic
307	#555	Dic₄₇	1	2	yes	—
308	D₄×Q₈	Dic₄₇	1	1	yes	characteristic
309	#548	—	2	1	no	—
310	#542	—	2	1	no	—
311	#542	—	2	2	no	—
312	#533	C₂×D₄₇	1	2	yes	—
313	#533	C₂×D₄₇	1	1	yes	characteristic
314	#529	C₂×D₄₇	1	1	yes	characteristic
315	#529	C₂×D₄₇	1	2	yes	—
316	#519	—	2	1	no	—
317	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
318	#446	—	94	1	no	—
319	#435	—	94	2	no	—
320	C₈×D₄	—	94	1	no	—
321	#433	—	94	2	no	—
322	#432	—	47	2	no	—
323	#432	—	47	2	no	—
324	#432	—	47	2	no	—
325	#432	—	47	1	no	—
326	#424	—	94	1	no	—
327	#408	—	94	1	no	—
328	C₄×M₁₆	—	47	1	no	—
329	C₄×M₁₆	—	47	1	no	—
330	C₂×#97	—	47	1	no	—
331	C₂×#97	—	47	2	no	—
332	#330	—	47	1	no	—
333	#330	—	47	2	no	—
334	#330	—	47	2	no	—
335	#330	—	47	2	no	—
336	#330	—	47	1	no	—
337	#330	—	47	2	no	—
338	#330	—	47	2	no	—
339	#329	—	47	1	no	—
340	#329	—	47	1	no	—
341	#329	—	47	2	no	—
342	C₄₇	#17683	1	1	yes	characteristic, complemented, Sylow
343	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
344	C₂²×Q₈	—	2	1	no	—
345	C₂×M₁₆	—	94	1	no	—
346	C₂×M₁₆	—	94	1	no	—
347	C₂²×C₈	—	94	1	no	—
348	C₂²×C₈	—	94	2	no	—
349	C₄⋊Q₈	—	2	2	no	—
350	C₄⋊Q₈	—	2	1	no	—
351	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
352	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
353	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
354	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
355	#126	—	2	2	no	—
356	#126	—	2	2	no	—
357	#126	—	2	2	no	—
358	#126	—	2	1	no	—
359	#126	—	2	2	no	—
360	#125	C₂²×D₄₇	1	1	yes	characteristic
361	#125	C₂²×D₄₇	1	2	yes	—
362	#124	—	2	1	no	—
363	#124	—	2	2	no	—
364	#124	—	2	2	no	—
365	#124	—	2	2	no	—
366	#124	—	2	2	no	—
367	#124	C₂²×D₄₇	1	1	yes	characteristic
368	#123	—	2	2	no	—
369	#123	—	2	1	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
377	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
378	#121	—	2	1	no	—
379	#121	—	2	2	no	—
380	#121	C₂×Dic₄₇	1	1	yes	characteristic
381	#121	C₂×Dic₄₇	1	2	yes	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	2	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
390	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
391	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
392	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
396	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
397	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
398	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
399	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
400	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
401	#117	—	2	2	no	—
402	#117	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	—	2	2	no	—
405	#117	C₂×Dic₄₇	1	2	yes	—
406	#117	C₂×Dic₄₇	1	2	yes	—
407	#117	C₂×Dic₄₇	1	2	yes	—
408	#117	C₂²⋊D₄₇	1	1	yes	characteristic
409	#117	C₂²⋊D₄₇	1	2	yes	—
410	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
411	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
412	C₄⋊C₈	—	94	2	no	—
413	C₄⋊C₈	—	94	2	no	—
414	C₄⋊C₈	—	94	1	no	—
415	C₄⋊C₈	—	94	2	no	—
416	C₂²⋊C₈	—	94	2	no	—
417	C₂²⋊C₈	—	94	2	no	—
418	C₂²⋊C₈	—	94	2	no	—
419	C₂²⋊C₈	—	94	1	no	—
420	#97	—	47	1	no	—
421	#97	—	47	1	no	—
422	#97	—	47	1	no	—
423	#97	—	47	2	no	—
424	#97	—	47	1	no	—
425	#97	—	47	2	no	—
426	#97	—	94	1	no	—
427	#97	—	94	2	no	—
428	C₄×C₈	—	94	1	no	—
429	C₄×C₈	—	94	1	no	—
430	#41	—	4	2	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	4	4	no	—
436	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
437	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
441	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
442	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
446	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
447	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
449	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
450	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
451	M₁₆	—	188	2	no	—
452	M₁₆	—	188	2	no	—
453	C₂×C₈	—	94	1	no	—
454	C₂×C₈	—	94	2	no	—
455	C₂×C₈	—	94	1	no	—
456	C₂×C₈	—	94	1	no	—
457	C₂×C₈	—	94	1	no	—
458	C₂×C₈	—	94	2	no	—
459	C₂×C₈	—	188	4	no	—
460	C₂×C₈	—	188	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
474	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
475	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
476	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
479	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
493	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
494	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	1	no	—
500	C₄²	C₂²×Dic₄₇	1	2	yes	—
501	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
502	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
503	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
504	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
505	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
506	C₄²	C₂³×D₄₇	1	1	yes	characteristic
507	C₂³	—	2	1	no	—
508	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
509	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
510	Q₈	—	2	2	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	4	4	no	—
513	Q₈	—	4	2	no	—
514	Q₈	—	8	2	no	—
515	Q₈	—	8	1	no	—
516	D₄	—	2	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	1	no	—
519	D₄	—	8	2	no	—
520	D₄	—	8	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
535	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
536	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
537	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
538	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
539	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
540	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
541	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
542	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
543	C₈	—	94	2	no	—
544	C₈	—	188	1	no	—
545	C₈	—	188	1	no	—
546	C₈	—	188	2	no	—
547	C₈	—	188	2	no	—
548	C₈	—	188	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	#15689140	1	2	yes	—
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	8	1	no	—
576	C₂	#20251871	1	1	yes	characteristic
577	C₂	C₂×#15689140	1	1	yes	characteristic
578	C₂	#20251935	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3518	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3518	D₄₇
hypocenter	C₄₇	#17683
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3518

Complements

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

N	H ≅ G/N	type
1. #20252402	C₂	semidirect
2. #20252039	C₂	semidirect
3. #20242026	C₂	semidirect
4. #20242019	C₂	semidirect
5. #20242008	C₂	semidirect
6. #20242003	C₂	semidirect
7. #20242003	C₂	semidirect
8. #20241995	C₂	semidirect
9. #20241983	C₂	semidirect
10. #20241976	C₂	semidirect
342. C₄₇	#17683	semidirect

Maximal subgroups

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

subgroup	index
#20252402	2
#20252039	2
#20242026	2
#20242019	2
#20242008	2
#20242003	2
#20241995	2
#20241983	2
#20241976	2
C₄₇×#3518	2
#17683	47