Subgroups — #26122289

Order 12032.

986 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688885	C₂	1	2	yes	maximal
3	C₂×#15688885	C₂	1	2	yes	maximal
4	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₄₇	—	2	1	no	—
9	C₄×C₄⋊Dic₄₇	—	2	4	no	—
10	C₂×C₄₇⋊#95	—	2	1	no	—
11	#15688885	—	2	4	no	—
12	#15688885	C₄	1	8	yes	complemented
13	#15688878	—	2	2	no	—
14	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#389	—	2	2	no	—
19	C₄₇×#389	C₄	1	4	yes	complemented
20	C₂×#95×C₄₇	—	2	1	no	—
21	C₂³×Dic₄₇	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
33	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
34	C₂×C₄⋊Dic₄₇	Q₈	1	4	yes	—
35	C₂×C₄×Dic₄₇	—	2	4	no	—
36	C₂×C₄×Dic₄₇	—	4	2	no	—
37	C₂×C₄×Dic₄₇	—	4	2	no	—
38	C₄₇⋊#95	—	2	4	no	—
39	C₂³×C₄×C₄₇	—	2	1	no	—
40	C₂³×C₄×C₄₇	—	2	1	no	—
41	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
52	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₄₇	—	2	2	no	—
56	C₂×C₄²×C₄₇	—	2	2	no	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₄₇	D₄	1	2	yes	—
59	#95×C₄₇	—	2	4	no	—
60	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₇	—	2	1	no	—
62	C₂²×C₄×C₄₇	—	2	1	no	—
63	C₂²×C₄×C₄₇	—	2	1	no	—
64	C₂²×C₄×C₄₇	—	2	1	no	—
65	C₂²×C₄×C₄₇	—	2	2	no	—
66	C₂²×C₄×C₄₇	—	2	4	no	—
67	C₂²×C₄×C₄₇	—	2	1	no	—
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	4	1	no	—
73	C₂²×C₄×C₄₇	—	4	1	no	—
74	C₂²×C₄×C₄₇	—	4	2	no	—
75	C₂²×C₄×C₄₇	—	4	1	no	—
76	C₂²×C₄×C₄₇	—	4	1	no	—
77	C₂²×C₄×C₄₇	—	4	1	no	—
78	C₂²×C₄×C₄₇	—	4	1	no	—
79	C₂²×C₄×C₄₇	—	4	1	no	—
80	C₂²×C₄×C₄₇	—	4	1	no	—
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	D₈	1	2	yes	—
84	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₄₇	#41	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×Dic₄₇	—	2	4	no	—
94	C₂²×Dic₄₇	—	2	4	no	—
95	C₂²×Dic₄₇	—	2	4	no	—
96	C₂²×Dic₄₇	—	4	2	no	—
97	C₂²×Dic₄₇	—	4	2	no	—
98	C₂²×Dic₄₇	—	4	2	no	—
99	C₂²×Dic₄₇	—	4	2	no	—
100	C₄⋊C₄×C₄₇	—	2	2	no	—
101	C₄⋊C₄×C₄₇	—	2	4	no	—
102	C₄⋊C₄×C₄₇	—	2	4	no	—
103	C₄⋊C₄×C₄₇	—	4	8	no	—
104	C₄⋊C₄×C₄₇	—	4	2	no	—
105	C₄⋊C₄×C₄₇	C₄²	1	4	yes	complemented
106	C₄²×C₄₇	—	2	4	no	—
107	C₄²×C₄₇	—	2	4	no	—
108	C₄⋊Dic₄₇	—	2	4	no	—
109	C₄⋊Dic₄₇	—	2	4	no	—
110	C₄⋊Dic₄₇	—	2	4	no	—
111	C₄⋊Dic₄₇	C₄⋊C₄	1	8	yes	complemented
112	C₄×Dic₄₇	—	4	8	no	—
113	C₂×C₄₇⋊C₈	—	2	4	no	—
114	C₂×C₄₇⋊C₈	—	2	4	no	—
115	C₂×C₄₇⋊C₈	—	2	4	no	—
116	C₂×C₄₇⋊C₈	—	4	2	no	—
117	C₂×C₄₇⋊C₈	—	4	2	no	—
118	C₂×C₄₇⋊C₈	—	4	2	no	—
119	C₂×C₄₇⋊C₈	—	4	2	no	—
120	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₄₇	C₄×D₄	1	2	yes	—
122	C₂³×C₄₇	#120	1	1	yes	characteristic
123	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
124	C₂³×C₄₇	#123	1	1	yes	characteristic
125	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
126	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
127	C₂³×C₄₇	#135	1	2	yes	—
128	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
129	C₂³×C₄₇	#137	1	1	yes	characteristic
130	C₂³×C₄₇	#137	1	2	yes	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	4	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	8	1	no	—
151	C₂×C₄×C₄₇	—	8	1	no	—
152	C₂×C₄×C₄₇	—	8	1	no	—
153	C₂×C₄×C₄₇	—	8	1	no	—
154	C₂×C₄×C₄₇	#102	1	4	yes	—
155	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	#117	1	2	yes	—
158	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
163	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
164	C₂×C₄×C₄₇	#121	1	2	yes	—
165	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₄₇	#123	1	2	yes	—
167	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#125	1	2	yes	—
169	C₂×C₄×C₄₇	#126	1	2	yes	—
170	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
171	C₂×Dic₄₇	—	2	8	no	—
172	C₂×Dic₄₇	—	4	4	no	—
173	C₂×Dic₄₇	—	4	4	no	—
174	C₂×Dic₄₇	—	4	4	no	—
175	C₂×Dic₄₇	—	4	4	no	—
176	C₂×Dic₄₇	—	4	4	no	—
177	C₂×Dic₄₇	—	4	4	no	—
178	C₄₇⋊C₈	—	4	4	no	—
179	#10884	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₄₇	#385	1	2	yes	—
182	C₂²×C₄₇	#386	1	1	yes	characteristic
183	C₂²×C₄₇	#387	1	2	yes	—
184	C₂²×C₄₇	#391	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
186	C₂²×C₄₇	#416	1	1	yes	characteristic
187	C₂²×C₄₇	#417	1	1	yes	characteristic
188	C₂²×C₄₇	#419	1	1	yes	characteristic
189	C₂²×C₄₇	C₄×D₈	1	2	yes	—
190	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
191	C₂²×C₄₇	#440	1	2	yes	—
192	C₂²×C₄₇	#441	1	2	yes	—
193	C₂²×C₄₇	#447	1	1	yes	characteristic
194	C₂²×C₄₇	#448	1	1	yes	characteristic
195	C₂²×C₄₇	#452	1	2	yes	—
196	C₂²×C₄₇	#474	1	2	yes	—
197	C₂²×C₄₇	#475	1	2	yes	—
198	C₂²×C₄₇	#478	1	2	yes	—
199	C₂²×C₄₇	#479	1	2	yes	—
200	C₂²×C₄₇	#480	1	1	yes	characteristic
201	C₂²×C₄₇	#481	1	1	yes	characteristic
202	C₂²×C₄₇	#485	1	2	yes	—
203	C₄×C₄₇	—	2	4	no	—
204	C₄×C₄₇	—	4	2	no	—
205	C₄×C₄₇	—	4	4	no	—
206	C₄×C₄₇	—	8	2	no	—
207	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
208	C₄×C₄₇	#387	1	2	yes	—
209	C₄×C₄₇	#388	1	2	yes	—
210	C₄×C₄₇	#389	1	2	yes	—
211	Dic₄₇	—	4	8	no	—
212	C₂×#389	D₄₇	1	1	yes	characteristic
213	C₂×C₄×C₄⋊C₄	—	47	1	no	—
214	C₂×#340	—	47	2	no	—
215	C₂×#340	—	47	2	no	—
216	C₂×#336	—	47	1	no	—
217	C₂×C₄₇	#1436	1	1	yes	characteristic
218	C₂×C₄₇	C₄×#102	1	1	yes	characteristic
219	C₂×C₄₇	#1763	1	1	yes	characteristic
220	C₂×C₄₇	#1862	1	2	yes	—
221	C₂×C₄₇	#1865	1	2	yes	—
222	C₂×C₄₇	#1873	1	1	yes	characteristic
223	C₂×C₄₇	#1874	1	1	yes	characteristic
224	C₂×C₄₇	#1918	1	2	yes	—
225	C₂×C₄₇	#1919	1	2	yes	—
226	C₂×C₄₇	#1988	1	1	yes	characteristic
227	C₂×C₄₇	#1989	1	1	yes	characteristic
228	C₂³×C₈	—	47	2	no	—
229	C₂²×C₄⋊C₄	—	2	1	no	—
230	C₂²×C₄⋊C₄	—	47	2	no	—
231	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
233	C₂²×C₄²	—	94	1	no	—
234	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
235	#389	—	2	2	no	—
236	#389	Dic₄₇	1	4	yes	complemented
237	C₄×C₄⋊C₄	—	94	4	no	—
238	C₂×#95	—	2	1	no	—
239	C₂×#95	—	94	1	no	—
240	#340	—	47	8	no	—
241	#340	—	94	4	no	—
242	#336	—	94	2	no	—
243	C₄₇	#10884	1	1	yes	characteristic, complemented, Sylow
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	94	2	no	—
247	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
248	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
249	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
250	C₂²×C₈	—	47	4	no	—
251	C₂²×C₈	—	94	2	no	—
252	C₂²×C₈	—	94	2	no	—
253	C₂²×C₈	—	94	2	no	—
254	C₂²×C₈	—	94	2	no	—
255	C₂²×C₈	—	94	2	no	—
256	C₂²×C₈	—	94	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	4	2	no	—
264	C₂×C₄⋊C₄	—	4	2	no	—
265	C₂×C₄⋊C₄	—	47	4	no	—
266	C₂×C₄⋊C₄	—	47	4	no	—
267	C₂×C₄⋊C₄	—	47	4	no	—
268	C₂×C₄⋊C₄	—	94	2	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	C₂×C₄⋊C₄	—	94	2	no	—
271	C₂×C₄⋊C₄	C₄×D₄₇	1	4	yes	—
272	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
273	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	94	4	no	—
277	C₂×C₄²	—	188	2	no	—
278	C₂×C₄²	—	188	2	no	—
279	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
280	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
281	#95	—	2	4	no	—
282	#95	—	94	4	no	—
283	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	94	4	no	—
305	C₂²×C₄	—	94	4	no	—
306	C₂²×C₄	—	94	4	no	—
307	C₂²×C₄	—	188	2	no	—
308	C₂²×C₄	—	188	2	no	—
309	C₂²×C₄	—	188	2	no	—
310	C₂²×C₄	—	188	2	no	—
311	C₂²×C₄	#10625334	1	2	yes	—
312	C₂²×C₄	#10625335	1	2	yes	—
313	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
314	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
315	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
316	C₂²×C₄	#10625350	1	2	yes	—
317	C₂²×C₄	D₄×D₄₇	1	2	yes	—
318	C₂²×C₄	#10625352	1	2	yes	—
319	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
320	C₂²×C₄	#10625354	1	2	yes	—
321	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂×C₈	—	94	4	no	—
324	C₂×C₈	—	94	4	no	—
325	C₂×C₈	—	94	4	no	—
326	C₂×C₈	—	188	2	no	—
327	C₂×C₈	—	188	2	no	—
328	C₂×C₈	—	188	2	no	—
329	C₂×C₈	—	188	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	4	8	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	47	8	no	—
336	C₄⋊C₄	—	94	4	no	—
337	C₄⋊C₄	—	94	4	no	—
338	C₄⋊C₄	—	94	4	no	—
339	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	complemented
340	C₄²	—	2	4	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	188	8	no	—
343	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
344	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
345	C₂³	#13093992	1	1	yes	characteristic
346	C₂³	#13094000	1	2	yes	—
347	C₂³	#13094005	1	1	yes	characteristic
348	C₂³	C₂×#10625334	1	1	yes	characteristic
349	C₂³	C₂×#10625335	1	1	yes	characteristic
350	C₂³	#13094044	1	2	yes	—
351	C₂³	#13094049	1	1	yes	characteristic
352	C₂³	#13094054	1	1	yes	characteristic
353	C₂³	#13094055	1	2	yes	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	1	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	—	8	1	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	—	94	8	no	—
378	C₂×C₄	—	188	4	no	—
379	C₂×C₄	—	188	4	no	—
380	C₂×C₄	—	188	4	no	—
381	C₂×C₄	—	188	4	no	—
382	C₂×C₄	—	188	4	no	—
383	C₂×C₄	—	188	4	no	—
384	C₂×C₄	#13093945	1	4	yes	—
385	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
386	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
387	C₂×C₄	#13093982	1	2	yes	—
388	C₂×C₄	#13093983	1	1	yes	characteristic
389	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
390	C₂×C₄	#13093986	1	2	yes	—
391	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
392	C₂×C₄	#13093989	1	2	yes	—
393	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
394	C₂×C₄	#13093996	1	2	yes	—
395	C₂×C₄	#13094002	1	2	yes	—
396	C₂×C₄	#13094009	1	2	yes	—
397	C₂×C₄	#13094013	1	1	yes	characteristic
398	C₂×C₄	#13094014	1	2	yes	—
399	C₂×C₄	#13094019	1	2	yes	—
400	C₂×C₄	#13094022	1	1	yes	characteristic
401	C₈	—	188	4	no	—
402	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
403	C₂²	#15688994	1	2	yes	—
404	C₂²	#15689003	1	1	yes	characteristic
405	C₂²	#15689004	1	2	yes	—
406	C₂²	#15689030	1	1	yes	characteristic
407	C₂²	C₂×#13093945	1	1	yes	characteristic
408	C₂²	#15689119	1	1	yes	characteristic
409	C₂²	#15689124	1	1	yes	characteristic
410	C₂²	#15689132	1	1	yes	characteristic
411	C₂²	C₄×#10625334	1	2	yes	—
412	C₂²	C₄×#10625335	1	2	yes	—
413	C₂²	#15689221	1	2	yes	—
414	C₂²	#15689228	1	2	yes	—
415	C₂²	#15689256	1	1	yes	characteristic
416	C₂²	#15689261	1	1	yes	characteristic
417	C₂²	#15689283	1	2	yes	—
418	C₂²	#15689400	1	2	yes	—
419	C₂²	#15689405	1	2	yes	—
420	C₂²	#15689420	1	2	yes	—
421	C₂²	#15689427	1	2	yes	—
422	C₂²	#15689434	1	1	yes	characteristic
423	C₂²	#15689439	1	1	yes	characteristic
424	C₂²	#15689461	1	2	yes	—
425	C₄	—	2	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	2	no	—
429	C₄	—	188	8	no	—
430	C₄	C₄⋊C₄×Dic₄₇	1	2	yes	—
431	C₄	#15689009	1	2	yes	—
432	C₄	#15689013	1	2	yes	—
433	C₄	#15689018	1	2	yes	—
434	C₂	#20241620	1	1	yes	characteristic
435	C₂	C₄×#13093945	1	1	yes	characteristic
436	C₂	#20243218	1	1	yes	characteristic
437	C₂	#20243634	1	2	yes	—
438	C₂	#20243655	1	2	yes	—
439	C₂	#20243701	1	1	yes	characteristic
440	C₂	#20243706	1	1	yes	characteristic
441	C₂	#20243956	1	2	yes	—
442	C₂	#20243963	1	2	yes	—
443	C₂	#20244341	1	1	yes	characteristic
444	C₂	#20244346	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×C₄₇×#389	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#389	D₄₇
hypocenter	C₄₇	#10884
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#389

Complements

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

N	H ≅ G/N	type
12. #15688885	C₄	semidirect
19. C₄₇×#389	C₄	semidirect
105. C₄⋊C₄×C₄₇	C₄²	semidirect
111. C₄⋊Dic₄₇	C₄⋊C₄	semidirect
236. #389	Dic₄₇	semidirect
243. C₄₇	#10884	semidirect
339. C₄⋊C₄	C₄×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₄⋊Dic₄₇	2
C₂×#15688885	2
C₂×#15688878	2
C₂×C₄₇×#389	2
#10884	47