Subgroups — #26122123

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688993	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688885	C₂	1	4	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
7	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
8	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	4	yes	complemented
12	#15688993	—	2	2	no	—
13	#15688993	C₄	1	4	yes	complemented
14	#15688885	—	2	8	no	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₇	—	2	1	no	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
19	C₄×C₄⋊C₄×C₄₇	C₄	1	4	yes	complemented
20	C₂×#95×C₄₇	—	2	1	no	—
21	C₂³×Dic₄₇	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	4	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	4	no	—
26	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
27	C₂×C₄⋊Dic₄₇	—	2	4	no	—
28	C₂×C₄⋊Dic₄₇	—	2	4	no	—
29	C₂×C₄⋊Dic₄₇	—	2	4	no	—
30	C₂×C₄⋊Dic₄₇	—	2	4	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	4	4	no	—
33	C₂×C₄⋊Dic₄₇	—	4	2	no	—
34	C₂×C₄⋊Dic₄₇	—	4	2	no	—
35	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
36	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
37	C₂³×C₄×C₄₇	—	2	2	no	—
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
45	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	—
47	C₂×C₄²×C₄₇	—	2	4	no	—
48	C₂×C₄²×C₄₇	—	4	2	no	—
49	C₂×C₄²×C₄₇	—	4	2	no	—
50	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₄₇	D₄	1	2	yes	—
54	C₂×C₄²×C₄₇	D₄	1	2	yes	—
55	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
56	#95×C₄₇	—	2	4	no	—
57	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₇	—	2	2	no	—
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	4	no	—
61	C₂²×C₄×C₄₇	—	2	4	no	—
62	C₂²×C₄×C₄₇	—	2	4	no	—
63	C₂²×C₄×C₄₇	—	4	2	no	—
64	C₂²×C₄×C₄₇	—	4	2	no	—
65	C₂²×C₄×C₄₇	—	4	2	no	—
66	C₂²×C₄×C₄₇	—	4	2	no	—
67	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₄₇	D₈	1	2	yes	—
74	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
75	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
76	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
77	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₄₇	#41	1	2	yes	—
86	C₂²×C₄×C₄₇	#41	1	2	yes	—
87	C₂²×Dic₄₇	—	2	4	no	—
88	C₂²×Dic₄₇	—	4	4	no	—
89	C₂²×Dic₄₇	—	4	2	no	—
90	C₂²×Dic₄₇	—	4	2	no	—
91	C₂²×Dic₄₇	—	4	4	no	—
92	C₄⋊C₄×C₄₇	—	2	4	no	—
93	C₄⋊C₄×C₄₇	—	2	4	no	—
94	C₄⋊C₄×C₄₇	—	2	4	no	—
95	C₄⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	complemented
96	C₄²×C₄₇	—	4	8	no	—
97	C₄²×C₄₇	C₄²	1	4	yes	—
98	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
99	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
100	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
101	C₄⋊Dic₄₇	—	2	8	no	—
102	C₄⋊Dic₄₇	—	4	8	no	—
103	C₄⋊Dic₄₇	—	4	8	no	—
104	C₄⋊Dic₄₇	—	4	2	no	—
105	C₄⋊Dic₄₇	—	4	2	no	—
106	C₂×C₄₇⋊C₈	—	2	4	no	—
107	C₂×C₄₇⋊C₈	—	2	8	no	—
108	C₂×C₄₇⋊C₈	—	4	4	no	—
109	C₂×C₄₇⋊C₈	—	4	2	no	—
110	C₂×C₄₇⋊C₈	—	4	2	no	—
111	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
113	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₂³×C₄₇	#121	1	2	yes	—
115	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
116	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
117	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
118	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
119	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
120	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
121	C₂³×C₄₇	#137	1	2	yes	—
122	C₂×C₄×C₄₇	—	2	4	no	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	2	no	—
125	C₂×C₄×C₄₇	—	2	4	no	—
126	C₂×C₄×C₄₇	—	2	8	no	—
127	C₂×C₄×C₄₇	—	4	4	no	—
128	C₂×C₄×C₄₇	—	4	4	no	—
129	C₂×C₄×C₄₇	—	4	4	no	—
130	C₂×C₄×C₄₇	—	4	4	no	—
131	C₂×C₄×C₄₇	—	4	4	no	—
132	C₂×C₄×C₄₇	—	4	4	no	—
133	C₂×C₄×C₄₇	#95	1	4	yes	—
134	C₂×C₄×C₄₇	#95	1	4	yes	—
135	C₂×C₄×C₄₇	#102	1	4	yes	—
136	C₂×C₄×C₄₇	#102	1	4	yes	—
137	C₂×C₄×C₄₇	#103	1	4	yes	—
138	C₂×C₄×C₄₇	#103	1	4	yes	—
139	C₂×C₄×C₄₇	#106	1	4	yes	—
140	C₂×C₄×C₄₇	#107	1	4	yes	—
141	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#117	1	2	yes	—
147	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	#121	1	2	yes	—
152	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
153	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#125	1	2	yes	—
156	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
158	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	—	4	4	no	—
161	C₂×Dic₄₇	—	4	4	no	—
162	C₂×Dic₄₇	—	8	4	no	—
163	C₂×Dic₄₇	—	8	4	no	—
164	C₄₇⋊C₈	—	4	4	no	—
165	#10849	—	47	1	no	maximal, Sylow
166	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
167	C₂²×C₄₇	#380	1	2	yes	—
168	C₂²×C₄₇	#389	1	2	yes	—
169	C₂²×C₄₇	#390	1	1	yes	characteristic
170	C₂²×C₄₇	#391	1	1	yes	characteristic
171	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
175	C₂²×C₄₇	#417	1	2	yes	—
176	C₂²×C₄₇	#418	1	1	yes	characteristic
177	C₂²×C₄₇	#419	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
180	C₂²×C₄₇	#428	1	2	yes	—
181	C₂²×C₄₇	#459	1	2	yes	—
182	C₂²×C₄₇	#460	1	2	yes	—
183	C₂²×C₄₇	#461	1	2	yes	—
184	C₂²×C₄₇	#462	1	2	yes	—
185	C₂²×C₄₇	#474	1	2	yes	—
186	C₂²×C₄₇	#475	1	2	yes	—
187	C₂²×C₄₇	#476	1	2	yes	—
188	C₂²×C₄₇	#477	1	2	yes	—
189	C₄×C₄₇	—	2	4	no	—
190	C₄×C₄₇	—	4	8	no	—
191	C₄×C₄₇	#340	1	8	yes	complemented
192	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
193	C₄×C₄₇	#382	1	1	yes	characteristic
194	C₄×C₄₇	#384	1	1	yes	characteristic
195	C₄×C₄₇	#389	1	2	yes	—
196	C₄×C₄₇	#390	1	1	yes	characteristic
197	C₄×C₄₇	#391	1	1	yes	characteristic
198	Dic₄₇	—	8	4	no	—
199	C₂²×C₄⋊C₈	—	47	1	no	—
200	C₂×#384	—	47	1	no	—
201	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
202	C₂×#340	—	47	4	no	—
203	C₂×C₄₇	C₄⋊#95	1	1	yes	characteristic
204	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
205	C₂×C₄₇	#1736	1	1	yes	characteristic
206	C₂×C₄₇	#1802	1	2	yes	—
207	C₂×C₄₇	#1803	1	2	yes	—
208	C₂×C₄₇	#1947	1	2	yes	—
209	C₂×C₄₇	#1948	1	2	yes	—
210	C₂×C₄₇	#1981	1	1	yes	characteristic
211	C₂×C₄₇	#1982	1	1	yes	characteristic
212	C₂×C₄₇	#1987	1	1	yes	characteristic
213	C₂×C₄₇	#1988	1	1	yes	characteristic
214	C₂³×C₈	—	47	2	no	—
215	C₂²×C₄⋊C₄	—	47	2	no	—
216	C₂²×C₄⋊C₄	—	94	1	no	—
217	C₂²×C₄⋊C₄	—	94	1	no	—
218	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
219	C₂²×C₄²	—	2	1	no	—
220	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
221	C₂×C₄⋊C₈	—	47	4	no	—
222	C₂×C₄⋊C₈	—	94	2	no	—
223	C₂×C₄⋊C₈	—	94	2	no	—
224	#384	—	47	4	no	—
225	#384	—	94	2	no	—
226	C₄×C₄⋊C₄	—	2	2	no	—
227	C₄×C₄⋊C₄	Dic₄₇	1	4	yes	complemented
228	C₂×#95	—	2	1	no	—
229	#340	—	94	8	no	—
230	C₄₇	#10849	1	1	yes	characteristic, complemented, Sylow
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	—	94	2	no	—
233	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
234	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
235	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
236	C₂²×C₈	—	47	4	no	—
237	C₂²×C₈	—	94	4	no	—
238	C₂²×C₈	—	94	2	no	—
239	C₂²×C₈	—	94	4	no	—
240	C₂²×C₈	—	94	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	47	4	no	—
245	C₂×C₄⋊C₄	—	94	4	no	—
246	C₂×C₄⋊C₄	—	94	4	no	—
247	C₂×C₄⋊C₄	—	94	4	no	—
248	C₂×C₄⋊C₄	—	94	4	no	—
249	C₂×C₄⋊C₄	—	94	2	no	—
250	C₂×C₄⋊C₄	—	188	4	no	—
251	C₂×C₄⋊C₄	—	188	2	no	—
252	C₂×C₄⋊C₄	—	188	2	no	—
253	C₂×C₄⋊C₄	Dic₉₄	1	4	yes	—
254	C₂×C₄⋊C₄	D₁₈₈	1	4	yes	—
255	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
256	C₂×C₄²	—	2	4	no	—
257	C₂×C₄²	—	4	2	no	—
258	C₂×C₄²	—	4	2	no	—
259	C₂×C₄²	Dic₉₄	1	2	yes	—
260	C₂×C₄²	C₄×D₄₇	1	2	yes	—
261	C₂×C₄²	C₄×D₄₇	1	2	yes	—
262	C₂×C₄²	D₁₈₈	1	2	yes	—
263	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
264	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
265	C₄⋊C₈	—	94	8	no	—
266	#95	—	2	4	no	—
267	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	94	4	no	—
278	C₂²×C₄	—	188	4	no	—
279	C₂²×C₄	—	188	2	no	—
280	C₂²×C₄	—	188	2	no	—
281	C₂²×C₄	—	188	4	no	—
282	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
283	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
284	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
285	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
286	C₂²×C₄	#10625334	1	2	yes	—
287	C₂²×C₄	#10625335	1	2	yes	—
288	C₂²×C₄	#10625336	1	2	yes	—
289	C₂²×C₄	#10625337	1	2	yes	—
290	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
291	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
292	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
293	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
294	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
298	C₂²×C₄	#10625350	1	2	yes	—
299	C₂²×C₄	#10625350	1	2	yes	—
300	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
302	C₂×C₈	—	94	4	no	—
303	C₂×C₈	—	94	8	no	—
304	C₂×C₈	—	188	4	no	—
305	C₂×C₈	—	188	2	no	—
306	C₂×C₈	—	188	2	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	94	8	no	—
311	C₄⋊C₄	—	188	8	no	—
312	C₄⋊C₄	—	188	8	no	—
313	C₄⋊C₄	—	188	2	no	—
314	C₄⋊C₄	—	188	2	no	—
315	C₄⋊C₄	C₄⋊Dic₄₇	1	8	yes	complemented
316	C₄²	—	4	8	no	—
317	C₄²	C₄×Dic₄₇	1	4	yes	—
318	C₄²	Dic₄₇⋊C₄	1	4	yes	—
319	C₄²	C₄⋊Dic₄₇	1	4	yes	—
320	C₄²	(C₂×D₄₇)⋊C₄	1	4	yes	—
321	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
322	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
323	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
324	C₂³	#13093998	1	2	yes	—
325	C₂³	#13094003	1	2	yes	—
326	C₂³	C₂×#10625334	1	1	yes	characteristic
327	C₂³	C₂×#10625336	1	1	yes	characteristic
328	C₂³	C₂×#10625335	1	1	yes	characteristic
329	C₂³	C₂×#10625337	1	1	yes	characteristic
330	C₂³	#13094049	1	2	yes	—
331	C₂³	#13094054	1	2	yes	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	376	4	no	—
344	C₂×C₄	—	376	4	no	—
345	C₂×C₄	—	188	4	no	—
346	C₂×C₄	—	188	4	no	—
347	C₂×C₄	—	188	4	no	—
348	C₂×C₄	C₄₇⋊#95	1	4	yes	—
349	C₂×C₄	C₄₇⋊#95	1	4	yes	—
350	C₂×C₄	#13093944	1	4	yes	—
351	C₂×C₄	#13093945	1	4	yes	—
352	C₂×C₄	#13093947	1	4	yes	—
353	C₂×C₄	#13093948	1	4	yes	—
354	C₂×C₄	#13093955	1	4	yes	—
355	C₂×C₄	#13093957	1	4	yes	—
356	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
358	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
360	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
361	C₂×C₄	#13093983	1	2	yes	—
362	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
363	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
364	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
365	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
366	C₂×C₄	#13093998	1	2	yes	—
367	C₂×C₄	#13094003	1	2	yes	—
368	C₂×C₄	#13094012	1	1	yes	characteristic
369	C₂×C₄	#13094012	1	1	yes	characteristic
370	C₂×C₄	#13094016	1	2	yes	—
371	C₂×C₄	#13094021	1	1	yes	characteristic
372	C₂×C₄	#13094024	1	2	yes	—
373	C₂×C₄	#13094024	1	1	yes	characteristic
374	C₈	—	188	4	no	—
375	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
376	C₂²	#15688983	1	2	yes	—
377	C₂²	#15689021	1	2	yes	—
378	C₂²	#15689025	1	1	yes	characteristic
379	C₂²	#15689029	1	1	yes	characteristic
380	C₂²	C₂×#13093944	1	1	yes	characteristic
381	C₂²	C₂×#13093945	1	1	yes	characteristic
382	C₂²	C₂×#13093947	1	1	yes	characteristic
383	C₂²	C₂×#13093948	1	1	yes	characteristic
384	C₂²	#15689124	1	2	yes	—
385	C₂²	#15689127	1	1	yes	characteristic
386	C₂²	#15689131	1	1	yes	characteristic
387	C₂²	C₂×#13093955	1	1	yes	characteristic
388	C₂²	C₂×#13093957	1	1	yes	characteristic
389	C₂²	#15689166	1	2	yes	—
390	C₂²	#15689318	1	2	yes	—
391	C₂²	#15689323	1	2	yes	—
392	C₂²	#15689328	1	2	yes	—
393	C₂²	#15689333	1	2	yes	—
394	C₂²	#15689403	1	2	yes	—
395	C₂²	#15689408	1	2	yes	—
396	C₂²	#15689413	1	2	yes	—
397	C₂²	#15689418	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	4	8	no	—
400	C₄	—	376	4	no	—
401	C₄	#15688885	1	8	yes	complemented
402	C₄	C₄×C₄⋊Dic₄₇	1	2	yes	—
403	C₄	#15688989	1	1	yes	characteristic
404	C₄	#15688993	1	1	yes	characteristic
405	C₄	#15689021	1	2	yes	—
406	C₄	#15689025	1	1	yes	characteristic
407	C₄	#15689029	1	1	yes	characteristic
408	C₂	#20241618	1	1	yes	characteristic
409	C₂	C₂×#15688885	1	1	yes	characteristic
410	C₂	#20243109	1	1	yes	characteristic
411	C₂	#20243388	1	2	yes	—
412	C₂	#20243393	1	2	yes	—
413	C₂	#20244146	1	2	yes	—
414	C₂	#20244151	1	2	yes	—
415	C₂	#20244311	1	1	yes	characteristic
416	C₂	#20244315	1	1	yes	characteristic
417	C₂	#20244336	1	1	yes	characteristic
418	C₂	#20244340	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#10849
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
11. C₂×C₄⋊(C₄₇⋊C₈)	C₄	semidirect
13. #15688993	C₄	semidirect
19. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
95. C₄⋊C₄×C₄₇	C₄⋊C₄	semidirect
191. C₄×C₄₇	#340	semidirect
227. C₄×C₄⋊C₄	Dic₄₇	semidirect
230. C₄₇	#10849	semidirect
315. C₄⋊C₄	C₄⋊Dic₄₇	semidirect
401. C₄	#15688885	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂×#15688993	2
C₂×#15688885	2
C₂×C₄×C₄⋊C₄×C₄₇	2
#10849	47