Subgroups — C₂×#20242300 #26186046

Order 12032.

806 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625334	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689202	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242300	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688850	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688845	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625334	C₄	1	1	yes	characteristic
10	C₂²×#10625324	—	2	1	no	—
11	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
12	C₄×#10625334	C₄	1	4	yes	—
13	C₄×#10625334	C₂²	1	4	yes	—
14	#15689202	—	2	2	no	—
15	#15689202	C₂²	1	4	yes	complemented
16	C₂×#13093957	C₄	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×#13093945	C₄	1	1	yes	characteristic
19	C₂×#13093944	C₄	1	1	yes	characteristic
20	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	#15688873	C₂²	1	4	yes	complemented
24	D₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
25	#15688850	C₂²	1	4	yes	complemented
26	#15688845	C₂²	1	4	yes	complemented
27	C₂²×M₁₆×C₄₇	—	2	1	no	—
28	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#436	—	2	2	no	—
30	C₄₇×#436	C₂²	1	4	yes	complemented
31	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
33	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₇	—	2	1	no	—
36	C₂×#10625334	—	2	4	no	—
37	C₂×#10625334	C₂×C₄	1	4	yes	—
38	C₂×#10625324	—	2	4	no	—
39	C₂×#10625324	—	4	4	no	—
40	C₂²×C₄₇⋊C₈	—	2	1	no	—
41	C₂²×C₄₇⋊C₈	—	2	1	no	—
42	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
44	C₄×D₁₈₈	—	2	1	no	—
45	C₄×D₁₈₈	—	2	1	no	—
46	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
47	C₄×D₁₈₈	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
50	#13093957	C₂×C₄	1	4	yes	—
51	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
53	#13093945	C₂×C₄	1	4	yes	—
54	#13093944	C₂×C₄	1	4	yes	—
55	(C₂×D₄₇)⋊C₈	—	2	4	no	—
56	C₄×C₄₇⋊C₈	—	2	1	no	—
57	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
58	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
59	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
60	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	—	2	1	no	—
62	C₂×M₁₆×C₄₇	—	2	4	no	—
63	C₂×M₁₆×C₄₇	—	4	4	no	—
64	C₂²×C₈×C₄₇	—	2	1	no	—
65	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
67	C₄×D₄×C₄₇	—	2	1	no	—
68	C₄×D₄×C₄₇	—	2	1	no	—
69	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
70	C₄×D₄×C₄₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₇	—	2	1	no	—
75	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
76	C₂²⋊C₈×C₄₇	—	2	4	no	—
77	C₄×C₈×C₄₇	D₄	1	2	yes	—
78	C₄×C₈×C₄₇	C₂³	1	2	yes	—
79	C₂⁴×C₄₇	—	2	1	no	—
80	C₂³×D₄₇	—	2	1	no	—
81	C₂×D₄×C₄₇	—	2	1	no	—
82	C₂×D₄×C₄₇	—	2	2	no	—
83	C₂×D₄×C₄₇	—	2	2	no	—
84	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	—	4	2	no	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
93	C₂²×Dic₄₇	—	2	1	no	—
94	C₂×D₁₈₈	—	2	2	no	—
95	C₂×D₁₈₈	—	2	2	no	—
96	C₂×D₁₈₈	—	2	1	no	—
97	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
98	C₂×C₄×D₄₇	—	2	2	no	—
99	C₂×C₄×D₄₇	—	2	2	no	—
100	C₂×C₄×D₄₇	—	4	2	no	—
101	C₂×C₄×D₄₇	—	4	2	no	—
102	M₁₆×C₄₇	—	4	8	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	4	2	no	—
107	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
109	C₄⋊C₄×C₄₇	—	2	1	no	—
110	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²⋊C₄×C₄₇	—	2	2	no	—
112	C₂²⋊C₄×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₇	#41	1	1	yes	characteristic
116	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
117	#10625334	—	2	8	no	—
118	(C₂×D₄₇)⋊C₄	—	2	2	no	—
119	(C₂×D₄₇)⋊C₄	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	1	no	—
121	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	4	2	no	—
126	C₂×C₄₇⋊C₈	—	4	2	no	—
127	C₂×C₄₇⋊C₈	M₁₆	1	4	yes	complemented
128	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
130	#10625324	—	4	8	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	4	2	no	—
133	C₂³×C₄₇	—	4	2	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
136	C₂²×D₄₇	—	2	2	no	—
137	C₂²×D₄₇	—	4	2	no	—
138	C₂²×D₄₇	—	4	2	no	—
139	C₂²×D₄₇	—	4	2	no	—
140	D₄×C₄₇	—	2	2	no	—
141	D₄×C₄₇	—	2	2	no	—
142	D₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	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	4	no	—
149	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
153	C₂×C₄×C₄₇	#131	1	2	yes	—
154	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	D₁₈₈	—	2	2	no	—
162	D₁₈₈	—	2	2	no	—
163	D₁₈₈	—	4	2	no	—
164	C₄×D₄₇	—	4	2	no	—
165	C₄×D₄₇	—	4	2	no	—
166	C₄×D₄₇	—	4	4	no	—
167	C₈×C₄₇	—	2	2	no	—
168	C₈×C₄₇	—	2	2	no	—
169	C₈×C₄₇	—	4	2	no	—
170	C₄₇⋊C₈	—	2	2	no	—
171	C₄₇⋊C₈	—	4	2	no	—
172	C₄₇⋊C₈	—	4	2	no	—
173	C₄₇⋊C₈	C₂×M₁₆	1	4	yes	complemented
174	C₂×#1594	—	47	1	no	maximal, Sylow
175	C₂²×C₄₇	—	4	2	no	—
176	C₂²×C₄₇	—	4	2	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	—	8	4	no	—
179	C₂²×C₄₇	#436	1	2	yes	—
180	C₂²×C₄₇	#442	1	2	yes	—
181	C₂²×C₄₇	#444	1	2	yes	—
182	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂×D₄₇	—	4	2	no	—
184	C₂×D₄₇	—	4	2	no	—
185	C₂×D₄₇	—	4	2	no	—
186	C₂×D₄₇	—	8	4	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	#436	1	2	yes	—
191	C₄×C₄₇	#442	1	2	yes	—
192	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
193	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
194	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	Dic₄₇	—	4	2	no	—
197	C₂×C₄×D₈	—	47	1	no	—
198	C₂×#436	—	47	1	no	—
199	C₂×#436	D₄₇	1	1	yes	characteristic, complemented
200	#1594	—	47	8	no	—
201	C₂×#334	—	47	1	no	—
202	C₂×D₄⋊C₈	—	47	1	no	—
203	C₂×D₄⋊C₈	—	47	1	no	—
204	C₂×#322	—	47	1	no	—
205	C₂×C₄₇	—	8	2	no	—
206	C₂×C₄₇	#1594	1	4	yes	complemented
207	C₂×C₄₇	C₂×#436	1	1	yes	characteristic
208	C₂×C₄₇	C₂×#442	1	1	yes	characteristic
209	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
210	D₄₇	—	8	2	no	—
211	C₂²×D₈	—	47	1	no	—
212	C₂²×M₁₆	—	2	1	no	—
213	C₂²×M₁₆	—	94	1	no	—
214	C₂×C₄×D₄	—	47	1	no	—
215	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
216	C₄×D₈	—	47	4	no	—
217	C₄×D₈	—	47	4	no	—
218	#436	—	2	2	no	—
219	#436	—	47	4	no	—
220	#436	—	94	2	no	—
221	#436	C₂×D₄₇	1	4	yes	complemented
222	C₂×#107	—	47	1	no	—
223	C₂×C₄⋊C₈	—	47	1	no	—
224	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#102	—	47	1	no	—
226	C₂×#102	—	47	1	no	—
227	C₂×C₂²⋊C₈	—	2	1	no	—
228	C₂×C₂²⋊C₈	—	94	1	no	—
229	C₂×C₄×C₈	—	47	1	no	—
230	C₂×C₄×C₈	—	47	1	no	—
231	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
232	#334	—	47	4	no	—
233	D₄⋊C₈	—	47	4	no	—
234	D₄⋊C₈	—	47	4	no	—
235	#322	—	47	4	no	—
236	C₄₇	C₂×#1594	1	1	yes	characteristic, complemented, Sylow
237	C₂²×D₄	—	47	1	no	—
238	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	—	94	1	no	—
241	C₂×D₈	—	47	4	no	—
242	C₂×D₈	—	94	4	no	—
243	C₂×M₁₆	—	2	4	no	—
244	C₂×M₁₆	—	4	4	no	—
245	C₂×M₁₆	—	94	4	no	—
246	C₂×M₁₆	—	188	4	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	47	1	no	—
249	C₂²×C₈	—	47	1	no	—
250	C₂²×C₈	—	94	1	no	—
251	C₂²×C₈	—	94	1	no	—
252	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
253	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	47	2	no	—
257	C₄×D₄	—	47	2	no	—
258	C₄×D₄	—	94	1	no	—
259	C₄×D₄	—	94	1	no	—
260	C₄×D₄	C₄×D₄₇	1	2	yes	—
261	C₄×D₄	C₂²×D₄₇	1	2	yes	—
262	C₂×C₄⋊C₄	—	47	1	no	—
263	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	94	1	no	—
266	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
267	#107	—	47	4	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	47	2	no	—
270	C₄⋊C₈	—	94	1	no	—
271	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
272	#102	—	47	4	no	—
273	#102	—	47	4	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	94	4	no	—
276	C₄×C₈	—	47	2	no	—
277	C₄×C₈	—	47	2	no	—
278	C₄×C₈	—	47	2	no	—
279	C₄×C₈	—	94	1	no	—
280	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
281	C₄×C₈	C₂²×D₄₇	1	2	yes	—
282	C₂⁴	—	2	1	no	—
283	C₂⁴	—	94	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	47	2	no	—
288	C₂×D₄	—	94	1	no	—
289	C₂×D₄	—	94	2	no	—
290	C₂×D₄	—	94	2	no	—
291	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	94	1	no	—
298	C₂²×C₄	—	94	2	no	—
299	C₂²×C₄	—	94	2	no	—
300	C₂²×C₄	—	188	2	no	—
301	C₂²×C₄	—	188	2	no	—
302	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
303	C₂²×C₄	#10625350	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
305	D₈	—	94	8	no	—
306	M₁₆	—	4	8	no	—
307	M₁₆	—	188	8	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	47	4	no	—
313	C₂×C₈	—	47	2	no	—
314	C₂×C₈	—	47	2	no	—
315	C₂×C₈	—	94	2	no	—
316	C₂×C₈	—	94	2	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	188	2	no	—
319	C₂×C₈	—	188	2	no	—
320	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
321	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	47	2	no	—
324	C₄⋊C₄	—	94	1	no	—
325	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	94	2	no	—
329	C₂²⋊C₄	—	94	2	no	—
330	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
331	C₄²	#10625350	1	1	yes	characteristic
332	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
333	C₄²	C₂³×D₄₇	1	1	yes	characteristic
334	C₂³	—	2	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	94	2	no	—
339	C₂³	—	188	2	no	—
340	C₂³	—	188	2	no	—
341	C₂³	—	188	2	no	—
342	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
343	D₄	—	2	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	4	2	no	—
346	D₄	—	94	2	no	—
347	D₄	—	94	2	no	—
348	D₄	—	188	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	—	188	4	no	—
358	C₂×C₄	—	188	2	no	—
359	C₂×C₄	—	188	2	no	—
360	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
362	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
363	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
364	C₂×C₄	#13094032	1	2	yes	—
365	C₂×C₄	#13094049	1	2	yes	—
366	C₂×C₄	#13094050	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
369	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	47	4	no	—
374	C₈	—	94	2	no	—
375	C₈	—	188	2	no	—
376	C₈	—	188	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	8	4	no	—
381	C₂²	—	376	4	no	—
382	C₂²	—	188	2	no	—
383	C₂²	—	188	2	no	—
384	C₂²	—	188	2	no	—
385	C₂²	#15689199	1	2	yes	—
386	C₂²	#15689233	1	2	yes	—
387	C₂²	#15689243	1	2	yes	—
388	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	188	2	no	—
393	C₄	#15689199	1	2	yes	—
394	C₄	#15689233	1	2	yes	—
395	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
396	C₄	C₂×#13094032	1	1	yes	characteristic
397	C₄	C₂×#13094049	1	1	yes	characteristic
398	C₄	C₂×#13094050	1	1	yes	characteristic
399	C₂	—	8	2	no	—
400	C₂	—	376	2	no	—
401	C₂	#20242300	1	4	yes	direct product factor
402	C₂	C₂×#15689199	1	1	yes	characteristic
403	C₂	C₂×#15689233	1	1	yes	characteristic
404	C₂	C₂×#15689243	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#436	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×#10625334	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×#436	D₄₇
hypocenter	C₄₇	C₂×#1594
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
2. C₂×#15689202	C₂	semidirect
3. #20242300	C₂	direct (N × H)
4. C₂×#15688873	C₂	semidirect
5. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
6. C₂×#15688850	C₂	semidirect
7. C₂×#15688845	C₂	semidirect
8. C₂×C₄₇×#436	C₂	semidirect
15. #15689202	C₂²	semidirect
23. #15688873	C₂²	semidirect
24. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
25. #15688850	C₂²	semidirect
26. #15688845	C₂²	semidirect
30. C₄₇×#436	C₂²	semidirect
127. C₂×C₄₇⋊C₈	M₁₆	semidirect
173. C₄₇⋊C₈	C₂×M₁₆	semidirect
199. C₂×#436	D₄₇	semidirect
206. C₂×C₄₇	#1594	semidirect
221. #436	C₂×D₄₇	semidirect
236. C₄₇	C₂×#1594	semidirect
401. C₂	#20242300	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625334	2
C₂×#15689202	2
#20242300	2
C₂×#15688873	2
C₂×D₄⋊(C₄₇⋊C₈)	2
C₂×#15688850	2
C₂×#15688845	2
C₂×C₄₇×#436	2
C₂×#1594	47

Subgroups — C2×#20242300 #26186046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242300 #26186046