Subgroups — C₂×#20244875 #26245249

Order 12032.

998 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093958	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093955	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689019	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688988	C₂	1	1	yes	maximal, characteristic
5	#20244875	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688885	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688877	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#340	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂²×Dic₄₇⋊C₄	—	2	1	no	—
13	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13093958	—	2	4	no	—
15	C₂×#13093958	C₂²	1	4	yes	—
16	C₂×#13093955	—	2	4	no	—
17	C₂×#13093955	C₂²	1	4	yes	—
18	#15689019	—	2	2	no	—
19	#15689019	C₂²	1	4	yes	—
20	#15688988	—	2	2	no	—
21	#15688988	C₂²	1	4	yes	—
22	C₂×C₄₇⋊#95	—	2	1	no	—
23	C₂×C₄₇⋊#95	—	2	1	no	—
24	C₂×C₄₇⋊#95	—	2	1	no	—
25	#15688885	C₂²	1	4	yes	—
26	#15688877	C₂²	1	4	yes	—
27	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#340	C₂²	1	4	yes	—
31	C₂³×Dic₄₇	—	2	1	no	—
32	C₂³×Dic₄₇	—	2	1	no	—
33	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
34	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	C₂²×C₄₇⋊C₈	—	2	2	no	—
37	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	—
38	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
39	C₂×C₄⋊Dic₄₇	—	2	1	no	—
40	C₂×C₄⋊Dic₄₇	—	2	2	no	—
41	C₂×C₄⋊Dic₄₇	—	2	2	no	—
42	C₂×C₄⋊Dic₄₇	—	2	2	no	—
43	C₂×C₄⋊Dic₄₇	—	2	1	no	—
44	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
47	C₂×Dic₄₇⋊C₄	—	2	4	no	—
48	C₂×Dic₄₇⋊C₄	—	4	4	no	—
49	C₂×C₄×Dic₄₇	—	2	2	no	—
50	C₂×C₄×Dic₄₇	—	2	2	no	—
51	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
52	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
53	#13093958	—	2	8	no	—
54	#13093955	—	2	8	no	—
55	C₄₇⋊#95	—	2	4	no	—
56	C₄₇⋊#95	—	2	4	no	—
57	C₄₇⋊#95	—	2	4	no	—
58	C₂³×C₄×C₄₇	—	2	1	no	—
59	C₂³×C₄×C₄₇	—	2	1	no	—
60	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₇	—	2	2	no	—
62	C₂²×C₈×C₄₇	—	2	2	no	—
63	C₂²×C₈×C₄₇	Q₈	1	4	yes	—
64	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
73	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	4	2	no	—
77	C₂²×C₄×C₄₇	—	4	2	no	—
78	C₂²×C₄×C₄₇	—	4	2	no	—
79	C₂²×C₄×C₄₇	—	4	2	no	—
80	C₂²×C₄×C₄₇	—	4	2	no	—
81	C₂²×C₄×C₄₇	—	4	2	no	—
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₄₇	#41	1	2	yes	—
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₂²×C₄×C₄₇	#41	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂²×Dic₄₇	—	2	4	no	—
91	C₂²×Dic₄₇	—	2	2	no	—
92	C₂²×Dic₄₇	—	2	2	no	—
93	C₂²×Dic₄₇	—	2	2	no	—
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	—	4	2	no	—
100	C₂²×Dic₄₇	—	4	2	no	—
101	C₂²×Dic₄₇	—	4	2	no	—
102	C₂²×Dic₄₇	—	4	2	no	—
103	C₂²×Dic₄₇	—	4	2	no	—
104	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
105	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₄₇	—	2	8	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	4	2	no	—
115	C₄⋊C₄×C₄₇	—	4	2	no	—
116	C₄⋊Dic₄₇	—	2	4	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	4	2	no	—
121	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
122	Dic₄₇⋊C₄	—	4	8	no	—
123	C₄×Dic₄₇	—	2	4	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	8	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
130	C₂³×C₄₇	#121	1	2	yes	—
131	C₂³×C₄₇	#123	1	2	yes	—
132	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
133	C₂³×C₄₇	#135	1	2	yes	—
134	C₂³×C₄₇	#135	1	2	yes	—
135	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
136	C₂³×C₄₇	#137	1	2	yes	—
137	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	8	4	no	—
145	C₂×C₄×C₄₇	—	8	4	no	—
146	C₂×C₄×C₄₇	#121	1	2	yes	—
147	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
148	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
149	C₂×C₄×C₄₇	#123	1	2	yes	—
150	C₂×C₄×C₄₇	#125	1	4	yes	—
151	C₂×C₄×C₄₇	#125	1	4	yes	—
152	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×Dic₄₇	—	2	4	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	8	no	—
169	C₂×Dic₄₇	—	4	4	no	—
170	C₂×Dic₄₇	—	4	4	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	8	4	no	—
175	C₈×C₄₇	—	2	4	no	—
176	C₄₇⋊C₈	—	2	4	no	—
177	C₂×#2085	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	#398	1	4	yes	—
179	C₂²×C₄₇	#463	1	4	yes	—
180	C₂²×C₄₇	#464	1	4	yes	—
181	C₂²×C₄₇	#482	1	4	yes	—
182	C₂²×C₄₇	#485	1	4	yes	—
183	C₂²×C₄₇	#499	1	4	yes	—
184	C₂²×C₄₇	#501	1	4	yes	—
185	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
192	C₄×C₄₇	—	8	2	no	—
193	C₄×C₄₇	—	8	2	no	—
194	C₄×C₄₇	#398	1	4	yes	—
195	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
196	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
197	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
198	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
199	Dic₄₇	—	4	2	no	—
200	Dic₄₇	—	4	2	no	—
201	Dic₄₇	—	4	4	no	—
202	Dic₄₇	—	8	2	no	—
203	C₂²×#107	—	47	1	no	—
204	C₂²×#106	—	47	1	no	—
205	C₂×#389	—	47	1	no	—
206	C₂×#382	—	47	1	no	—
207	#2085	—	47	8	no	—
208	C₂×#340	—	47	1	no	—
209	C₂×#340	D₄₇	1	1	yes	characteristic
210	C₂×#336	—	47	1	no	—
211	C₂×C₄₇	#2085	1	8	yes	complemented
212	C₂×C₄₇	C₂×#398	1	1	yes	characteristic
213	C₂×C₄₇	C₂×#463	1	1	yes	characteristic
214	C₂×C₄₇	C₂×#464	1	1	yes	characteristic
215	C₂×C₄₇	C₂×#482	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#485	1	1	yes	characteristic
217	C₂×C₄₇	C₂×#499	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#501	1	1	yes	characteristic
219	C₂³×C₈	—	47	1	no	—
220	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	—	47	1	no	—
222	C₂²×C₄⋊C₄	—	47	1	no	—
223	C₂²×C₄⋊C₄	—	94	1	no	—
224	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
226	C₂²×C₄²	—	47	1	no	—
227	C₂×#107	—	47	4	no	—
228	C₂×#107	—	94	4	no	—
229	C₂×#106	—	47	4	no	—
230	C₂×#106	—	94	4	no	—
231	#389	—	47	4	no	—
232	#389	—	94	2	no	—
233	#382	—	47	4	no	—
234	#382	—	94	2	no	—
235	C₂×#95	—	94	1	no	—
236	C₂×#95	—	94	1	no	—
237	C₂×#95	—	94	1	no	—
238	#340	—	47	4	no	—
239	#340	C₂×D₄₇	1	4	yes	—
240	#336	—	47	4	no	—
241	C₄₇	C₂×#2085	1	1	yes	characteristic, complemented, Sylow
242	C₂³×C₄	—	2	1	no	—
243	C₂³×C₄	—	2	1	no	—
244	C₂³×C₄	—	47	1	no	—
245	C₂³×C₄	—	47	1	no	—
246	C₂³×C₄	—	94	1	no	—
247	C₂³×C₄	—	94	1	no	—
248	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	47	4	no	—
252	C₂²×C₈	—	47	2	no	—
253	C₂²×C₈	—	94	2	no	—
254	C₂²×C₈	—	94	2	no	—
255	C₂²×C₈	Dic₉₄	1	4	yes	—
256	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	47	4	no	—
264	C₂×C₄⋊C₄	—	47	2	no	—
265	C₂×C₄⋊C₄	—	47	2	no	—
266	C₂×C₄⋊C₄	—	94	2	no	—
267	C₂×C₄⋊C₄	—	94	1	no	—
268	C₂×C₄⋊C₄	—	94	2	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	C₂×C₄⋊C₄	—	94	4	no	—
271	C₂×C₄⋊C₄	—	94	1	no	—
272	C₂×C₄⋊C₄	—	188	4	no	—
273	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
274	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
275	C₂×C₄²	—	47	2	no	—
276	C₂×C₄²	—	47	2	no	—
277	C₂×C₄²	—	94	2	no	—
278	C₂×C₄²	—	94	2	no	—
279	#107	—	94	8	no	—
280	#106	—	94	8	no	—
281	#95	—	94	4	no	—
282	#95	—	94	4	no	—
283	#95	—	94	4	no	—
284	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	47	2	no	—
295	C₂²×C₄	—	94	4	no	—
296	C₂²×C₄	—	94	2	no	—
297	C₂²×C₄	—	94	2	no	—
298	C₂²×C₄	—	94	2	no	—
299	C₂²×C₄	—	94	2	no	—
300	C₂²×C₄	—	94	2	no	—
301	C₂²×C₄	—	94	2	no	—
302	C₂²×C₄	—	94	2	no	—
303	C₂²×C₄	—	94	2	no	—
304	C₂²×C₄	—	188	2	no	—
305	C₂²×C₄	—	188	2	no	—
306	C₂²×C₄	—	188	2	no	—
307	C₂²×C₄	—	188	2	no	—
308	C₂²×C₄	—	188	2	no	—
309	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
310	C₂²×C₄	#10625350	1	2	yes	—
311	C₂²×C₄	#10625350	1	2	yes	—
312	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
313	C₂²×C₄	D₄×D₄₇	1	2	yes	—
314	C₂²×C₄	#10625352	1	2	yes	—
315	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
316	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
317	C₂×C₈	—	2	8	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	47	4	no	—
321	C₂×C₈	—	94	8	no	—
322	C₂×C₈	—	94	2	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	C₂×Dic₉₄	1	4	yes	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	47	4	no	—
332	C₄⋊C₄	—	94	4	no	—
333	C₄⋊C₄	—	94	2	no	—
334	C₄⋊C₄	—	94	2	no	—
335	C₄⋊C₄	—	94	2	no	—
336	C₄⋊C₄	—	188	8	no	—
337	C₄⋊C₄	—	188	2	no	—
338	C₄²	—	94	4	no	—
339	C₄²	—	94	2	no	—
340	C₄²	—	94	2	no	—
341	C₂³	#13093997	1	2	yes	—
342	C₂³	#13094006	1	2	yes	—
343	C₂³	#13094023	1	2	yes	—
344	C₂³	#13094043	1	2	yes	—
345	C₂³	#13094047	1	2	yes	—
346	C₂³	#13094051	1	2	yes	—
347	C₂³	#13094053	1	2	yes	—
348	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	8	4	no	—
356	C₂×C₄	—	8	4	no	—
357	C₂×C₄	—	94	4	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	94	2	no	—
363	C₂×C₄	—	94	2	no	—
364	C₂×C₄	—	376	4	no	—
365	C₂×C₄	—	188	2	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	—	188	2	no	—
368	C₂×C₄	—	188	8	no	—
369	C₂×C₄	—	188	2	no	—
370	C₂×C₄	—	188	2	no	—
371	C₂×C₄	—	188	4	no	—
372	C₂×C₄	—	188	4	no	—
373	C₂×C₄	#13093997	1	2	yes	—
374	C₂×C₄	#13094001	1	4	yes	—
375	C₂×C₄	#13094002	1	4	yes	—
376	C₂×C₄	#13094006	1	2	yes	—
377	C₂×C₄	#13094014	1	4	yes	—
378	C₂×C₄	#13094016	1	4	yes	—
379	C₂×C₄	#13094023	1	2	yes	—
380	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
383	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
384	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
385	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
386	C₈	—	2	4	no	—
387	C₈	—	94	4	no	—
388	C₂²	#15689057	1	4	yes	—
389	C₂²	#15689341	1	4	yes	—
390	C₂²	#15689344	1	4	yes	—
391	C₂²	#15689445	1	4	yes	—
392	C₂²	#15689463	1	4	yes	—
393	C₂²	#15689524	1	4	yes	—
394	C₂²	#15689530	1	4	yes	—
395	C₂²	C₂×#13093997	1	1	yes	characteristic
396	C₂²	C₂×#13094006	1	1	yes	characteristic
397	C₂²	C₂×#13094023	1	1	yes	characteristic
398	C₂²	C₂×#13094043	1	1	yes	characteristic
399	C₂²	C₂×#13094047	1	1	yes	characteristic
400	C₂²	C₂×#13094051	1	1	yes	characteristic
401	C₂²	C₂×#13094053	1	1	yes	characteristic
402	C₄	—	8	2	no	—
403	C₄	—	8	2	no	—
404	C₄	—	376	2	no	—
405	C₄	—	188	2	no	—
406	C₄	—	188	2	no	—
407	C₄	—	188	4	no	—
408	C₄	#15689057	1	4	yes	—
409	C₄	C₂×#13094001	1	1	yes	characteristic
410	C₄	C₂×#13094002	1	1	yes	characteristic
411	C₄	C₂×#13094014	1	1	yes	characteristic
412	C₄	C₂×#13094016	1	1	yes	characteristic
413	C₂	#20244875	1	8	yes	direct product factor
414	C₂	C₂×#15689057	1	1	yes	characteristic
415	C₂	C₂×#15689341	1	1	yes	characteristic
416	C₂	C₂×#15689344	1	1	yes	characteristic
417	C₂	C₂×#15689445	1	1	yes	characteristic
418	C₂	C₂×#15689463	1	1	yes	characteristic
419	C₂	C₂×#15689524	1	1	yes	characteristic
420	C₂	C₂×#15689530	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#340	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
hypercenter	C₂×#340	D₄₇
hypocenter	C₄₇	C₂×#2085
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
5. #20244875	C₂	direct (N × H)
211. C₂×C₄₇	#2085	semidirect
241. C₄₇	C₂×#2085	semidirect
413. C₂	#20244875	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13093958	2
C₂²×#13093955	2
C₂×#15689019	2
C₂×#15688988	2
#20244875	2
C₂×#15688885	2
C₂×#15688877	2
C₂×C₄₇×#340	2
C₂×#2085	47

Subgroups — C2×#20244875 #26245249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244875 #26245249