Subgroups — C₂×#20244304 #26220279

Order 12032.

1438 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093960	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689132	C₂	1	2	yes	maximal
3	C₂²×#13093943	C₂	1	2	yes	maximal
4	C₂×#15689078	C₂	1	1	yes	maximal, characteristic
5	#20244304	C₂	1	8	yes	maximal, direct product factor
6	C₂³×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂²×#10625329	C₂²	1	1	yes	characteristic
9	C₂×#13093983	C₂²	1	1	yes	characteristic
10	C₂×#13093960	—	2	4	no	—
11	C₂×#13093960	C₂²	1	4	yes	—
12	#15689132	—	2	4	no	—
13	#15689132	C₂²	1	8	yes	—
14	C₂×#13093948	—	2	4	no	—
15	C₂×#13093943	—	2	8	no	—
16	C₂×#13093943	C₂²	1	8	yes	—
17	#15689078	—	2	2	no	—
18	#15689078	C₂²	1	4	yes	—
19	C₂×#13093934	—	2	1	no	—
20	C₂×C₈×Dic₄₇	—	2	1	no	—
21	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
22	C₂²×Q₁₆×C₄₇	—	2	1	no	—
23	C₂²×Q₁₆×C₄₇	—	2	1	no	—
24	C₂²×Q₁₆×C₄₇	—	2	2	no	—
25	C₂²×Q₁₆×C₄₇	—	2	4	no	—
26	C₂²×Q₁₆×C₄₇	C₄	1	8	yes	complemented
27	C₂²×Q₁₆×C₄₇	C₂²	1	4	yes	—
28	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#10625329	—	2	1	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	4	no	—
33	C₂×#10625329	—	2	4	no	—
34	C₂×#10625329	D₄	1	4	yes	—
35	C₂×#10625329	C₂³	1	4	yes	—
36	C₂×#10625329	C₂³	1	2	yes	—
37	C₂²×C₄₇⋊C₈	—	2	1	no	—
38	C₂²×C₄₇⋊C₈	—	2	2	no	—
39	#13093983	—	2	1	no	—
40	#13093983	—	2	1	no	—
41	#13093983	D₄	1	2	yes	—
42	#13093983	C₂³	1	2	yes	—
43	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
44	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
45	C₂×C₄×Dic₄₇	—	2	1	no	—
46	#13093960	—	2	8	no	—
47	#13093948	—	2	16	no	—
48	#13093943	—	2	16	no	—
49	#13093934	—	2	4	no	—
50	C₈×Dic₄₇	—	2	4	no	—
51	C₂²×Q₈×C₄₇	—	2	4	no	—
52	C₂²×Q₈×C₄₇	—	2	2	no	—
53	C₂²×Q₈×C₄₇	—	2	2	no	—
54	C₂²×Q₈×C₄₇	—	2	2	no	—
55	C₂²×Q₈×C₄₇	—	2	4	no	—
56	C₂²×Q₈×C₄₇	—	2	2	no	—
57	C₂²×Q₈×C₄₇	—	2	2	no	—
58	C₂²×Q₈×C₄₇	—	2	4	no	—
59	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	—
60	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
61	C₂³×C₄×C₄₇	—	2	2	no	—
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂×Q₁₆×C₄₇	—	2	8	no	—
64	C₂×Q₁₆×C₄₇	—	2	8	no	—
65	C₂×Q₁₆×C₄₇	—	2	16	no	—
66	C₂×Q₁₆×C₄₇	—	2	4	no	—
67	C₂×Q₁₆×C₄₇	—	2	4	no	—
68	C₂×Q₁₆×C₄₇	—	2	8	no	—
69	C₂×Q₁₆×C₄₇	C₂×C₄	1	16	yes	complemented
70	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
71	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	D₄	1	2	yes	—
74	C₂²×C₈×C₄₇	D₄	1	4	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂⁴×C₄₇	#41	1	1	yes	characteristic
77	C₂×Q₈×C₄₇	—	2	8	no	—
78	C₂×Q₈×C₄₇	—	2	4	no	—
79	C₂×Q₈×C₄₇	—	2	8	no	—
80	C₂×Q₈×C₄₇	—	2	8	no	—
81	C₂×Q₈×C₄₇	—	2	8	no	—
82	C₂×Q₈×C₄₇	—	2	8	no	—
83	C₂×Q₈×C₄₇	—	2	4	no	—
84	C₂×Q₈×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	—	2	4	no	—
87	C₂×Q₈×C₄₇	—	4	2	no	—
88	C₂×Q₈×C₄₇	—	4	2	no	—
89	C₂×Q₈×C₄₇	—	4	4	no	—
90	C₂×Q₈×C₄₇	—	4	4	no	—
91	C₂×Q₈×C₄₇	—	4	4	no	—
92	C₂×Q₈×C₄₇	—	4	4	no	—
93	C₂×Q₈×C₄₇	—	4	4	no	—
94	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
95	C₂²×C₄×C₄₇	—	2	8	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	4	2	no	—
98	C₂²×C₄×C₄₇	—	4	2	no	—
99	C₂²×C₄×C₄₇	—	4	4	no	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	#41	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
110	C₂²×Dic₄₇	—	2	2	no	—
111	Q₁₆×C₄₇	—	2	16	no	—
112	Q₁₆×C₄₇	—	2	16	no	—
113	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
114	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
115	C₂×C₈×C₄₇	C₂²⋊C₄	1	8	yes	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
120	C₂²⋊Dic₄₇	—	2	2	no	—
121	C₂²⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	—	2	2	no	—
126	#10625329	—	2	4	no	—
127	#10625329	—	2	2	no	—
128	#10625329	—	2	4	no	—
129	#10625329	—	2	4	no	—
130	#10625329	—	4	4	no	—
131	#10625329	C₂×D₄	1	4	yes	—
132	C₂×C₄₇⋊C₈	—	2	4	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	4	4	no	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	C₄×D₄	1	2	yes	—
138	C₂³×C₄₇	#121	1	1	yes	characteristic
139	C₂³×C₄₇	#121	1	1	yes	characteristic
140	C₂³×C₄₇	#124	1	2	yes	—
141	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
142	Q₈×C₄₇	—	2	8	no	—
143	Q₈×C₄₇	—	2	8	no	—
144	Q₈×C₄₇	—	4	4	no	—
145	Q₈×C₄₇	—	4	4	no	—
146	Q₈×C₄₇	—	4	8	no	—
147	Q₈×C₄₇	—	4	8	no	—
148	C₂×C₄×C₄₇	—	2	8	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	8	no	—
152	C₂×C₄×C₄₇	—	4	8	no	—
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₇	#121	1	2	yes	—
159	C₂×C₄×C₄₇	#121	1	2	yes	—
160	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#124	1	2	yes	—
163	C₂×C₄×C₄₇	#127	1	2	yes	—
164	C₂×C₄×C₄₇	#127	1	2	yes	—
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂×Dic₄₇	—	2	4	no	—
172	C₂×Dic₄₇	—	4	4	no	—
173	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
174	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
175	C₄₇⋊C₈	—	2	4	no	—
176	C₄₇⋊C₈	—	4	4	no	—
177	C₂×#1979	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	4	no	—
179	C₂²×C₄₇	—	2	4	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	#390	1	2	yes	—
183	C₂²×C₄₇	#390	1	2	yes	—
184	C₂²×C₄₇	#473	1	4	yes	—
185	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
188	C₄×C₄₇	—	4	8	no	—
189	C₄×C₄₇	#390	1	2	yes	—
190	C₄×C₄₇	#390	1	2	yes	—
191	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
192	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
194	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
195	Dic₄₇	—	4	4	no	—
196	C₂³×Q₁₆	D₄₇	1	1	yes	characteristic
197	C₂²×#108	—	47	1	no	—
198	C₂×#419	—	47	2	no	—
199	C₂²×#101	—	47	2	no	—
200	C₂×#405	—	47	1	no	—
201	#1979	—	47	8	no	—
202	C₂×C₄₇	—	2	1	no	—
203	C₂×C₄₇	—	2	1	no	—
204	C₂×C₄₇	—	2	2	no	—
205	C₂×C₄₇	#1979	1	4	yes	complemented
206	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
207	C₂×C₄₇	C₂×#473	1	2	yes	—
208	C₂³×Q₈	C₂×D₄₇	1	2	yes	—
209	C₂²×Q₁₆	—	2	1	no	—
210	C₂²×Q₁₆	—	2	1	no	—
211	C₂²×Q₁₆	—	2	2	no	—
212	C₂²×Q₁₆	—	2	4	no	—
213	C₂²×Q₁₆	Dic₄₇	1	8	yes	complemented
214	C₂²×Q₁₆	C₂×D₄₇	1	4	yes	—
215	C₂²×M₁₆	—	47	1	no	—
216	C₂²×M₁₆	—	47	2	no	—
217	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
218	C₂×#117	—	47	1	no	—
219	C₂×#108	—	47	4	no	—
220	C₂×#108	—	94	4	no	—
221	#419	—	47	8	no	—
222	#419	—	94	4	no	—
223	C₂×#103	—	94	4	no	—
224	C₂×#101	—	47	8	no	—
225	C₂×#101	—	94	8	no	—
226	#405	—	47	4	no	—
227	#405	—	94	2	no	—
228	C₂×#97	—	94	1	no	—
229	C₂×C₄×C₈	—	94	1	no	—
230	C₄₇	C₂×#1979	1	1	yes	characteristic, complemented, Sylow
231	C₂²×Q₈	—	2	4	no	—
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	2	no	—
235	C₂²×Q₈	—	2	4	no	—
236	C₂²×Q₈	—	2	2	no	—
237	C₂²×Q₈	—	2	2	no	—
238	C₂²×Q₈	—	2	4	no	—
239	C₂²×Q₈	C₂×Dic₄₇	1	8	yes	—
240	C₂²×Q₈	C₂²×D₄₇	1	4	yes	—
241	C₂³×C₄	—	2	2	no	—
242	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
243	C₂×Q₁₆	—	2	8	no	—
244	C₂×Q₁₆	—	2	8	no	—
245	C₂×Q₁₆	—	2	16	no	—
246	C₂×Q₁₆	—	2	4	no	—
247	C₂×Q₁₆	—	2	4	no	—
248	C₂×Q₁₆	—	2	8	no	—
249	C₂×Q₁₆	C₂×Dic₄₇	1	16	yes	complemented
250	C₂×M₁₆	—	47	4	no	—
251	C₂×M₁₆	—	47	2	no	—
252	C₂×M₁₆	—	47	4	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	—	94	1	no	—
255	C₂×M₁₆	—	94	2	no	—
256	C₂×M₁₆	—	94	4	no	—
257	C₂×M₁₆	—	94	4	no	—
258	C₂²×C₈	—	94	1	no	—
259	C₂²×C₈	—	94	2	no	—
260	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
261	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
262	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
263	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
264	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
265	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
266	#117	—	47	2	no	—
267	#117	—	47	2	no	—
268	#117	—	94	1	no	—
269	#117	—	94	1	no	—
270	C₂×C₄⋊C₄	—	47	2	no	—
271	C₂×C₂²⋊C₄	—	94	1	no	—
272	C₂×C₄²	—	94	1	no	—
273	#108	—	94	8	no	—
274	#103	—	94	16	no	—
275	#101	—	94	16	no	—
276	#97	—	94	4	no	—
277	C₄×C₈	—	94	4	no	—
278	C₂⁴	#10625352	1	1	yes	characteristic
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	2	8	no	—
284	C₂×Q₈	—	2	8	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	4	4	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	—	4	4	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	—	94	2	no	—
303	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
304	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₄₇	1	2	yes	—
306	C₂²×C₄	#10625352	1	1	yes	characteristic
307	C₂²×C₄	#10625352	1	2	yes	—
308	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
309	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
312	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
313	Q₁₆	—	2	16	no	—
314	Q₁₆	—	2	16	no	—
315	M₁₆	—	47	4	no	—
316	M₁₆	—	94	4	no	—
317	M₁₆	—	94	2	no	—
318	M₁₆	—	94	4	no	—
319	M₁₆	—	94	4	no	—
320	M₁₆	—	188	4	no	—
321	C₂×C₈	—	94	4	no	—
322	C₂×C₈	—	94	2	no	—
323	C₂×C₈	—	94	4	no	—
324	C₂×C₈	—	188	4	no	—
325	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
326	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
327	C₂×C₈	C₂²⋊Dic₄₇	1	8	yes	—
328	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
329	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
330	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
331	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
332	C₄⋊C₄	—	47	4	no	—
333	C₄⋊C₄	—	94	2	no	—
334	C₂²⋊C₄	—	94	2	no	—
335	C₂²⋊C₄	—	94	2	no	—
336	C₄²	—	94	2	no	—
337	C₄²	—	94	2	no	—
338	C₂³	—	2	4	no	—
339	C₂³	D₄×Dic₄₇	1	2	yes	—
340	C₂³	#13093995	1	1	yes	characteristic
341	C₂³	#13093995	1	1	yes	characteristic
342	C₂³	#13094011	1	2	yes	—
343	C₂³	C₂×#10625352	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	2	8	no	—
346	Q₈	—	4	8	no	—
347	Q₈	—	4	8	no	—
348	Q₈	—	4	4	no	—
349	Q₈	—	4	4	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	94	4	no	—
356	C₂×C₄	—	188	4	no	—
357	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
358	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
359	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
360	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
361	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
362	C₂×C₄	#13093995	1	1	yes	characteristic
363	C₂×C₄	#13093995	1	1	yes	characteristic
364	C₂×C₄	#13093995	1	2	yes	—
365	C₂×C₄	#13093995	1	2	yes	—
366	C₂×C₄	#13094011	1	2	yes	—
367	C₂×C₄	#13094020	1	2	yes	—
368	C₂×C₄	#13094020	1	2	yes	—
369	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
375	C₈	—	94	4	no	—
376	C₈	—	188	4	no	—
377	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
378	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	#15689026	1	2	yes	—
384	C₂²	#15689026	1	2	yes	—
385	C₂²	#15689395	1	4	yes	—
386	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
387	C₂²	C₂×#13093995	1	1	yes	characteristic
388	C₂²	C₂×#13094011	1	1	yes	characteristic
389	C₄	—	4	8	no	—
390	C₄	—	188	4	no	—
391	C₄	#15689026	1	2	yes	—
392	C₄	#15689026	1	2	yes	—
393	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
394	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
395	C₄	C₂×#13093995	1	1	yes	characteristic
396	C₄	C₂×#13094020	1	1	yes	characteristic
397	C₂	—	2	2	no	—
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	#20244304	1	4	yes	direct product factor
401	C₂	C₂×#15689026	1	1	yes	characteristic
402	C₂	C₂×#15689395	1	2	yes	—

	subgroup	G/H
center	C₂³	#13093995
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂³×Q₁₆×C₄₇	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂⁴×C₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂³×Q₁₆	D₄₇
hypocenter	C₄₇	C₂×#1979
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×Q₁₆

Complements

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

N	H ≅ G/N	type
5. #20244304	C₂	direct (N × H)
26. C₂²×Q₁₆×C₄₇	C₄	semidirect
69. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
205. C₂×C₄₇	#1979	semidirect
213. C₂²×Q₁₆	Dic₄₇	semidirect
230. C₄₇	C₂×#1979	semidirect
249. C₂×Q₁₆	C₂×Dic₄₇	semidirect
400. C₂	#20244304	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×#13093960	2
C₂×#15689132	2
C₂²×#13093943	2
C₂×#15689078	2
#20244304	2
C₂³×Q₁₆×C₄₇	2
C₂×#1979	47

Subgroups — C2×#20244304 #26220279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244304 #26220279