Subgroups — C₂×#20243421 #26215851

Order 12032.

1662 conjugacy classes of subgroups.

The subgroup lattice has 398 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, complemented
2	C₂²×#13093956	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15688983	C₂	1	2	yes	maximal
4	#20243421	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688886	C₂	1	2	yes	maximal, complemented
6	C₂³×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂²×C₂²⋊Dic₄₇	—	2	2	no	—
10	C₂×#13093958	—	2	4	no	—
11	C₂×#13093958	C₂²	1	4	yes	complemented
12	C₂×#13093956	—	2	4	no	—
13	C₂×#13093956	C₂²	1	4	yes	complemented
14	#15688983	—	2	4	no	—
15	#15688983	C₂²	1	8	yes	—
16	C₂×C₄₇⋊#95	—	2	2	no	—
17	#15688886	C₂²	1	8	yes	complemented
18	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₄₇	—	2	4	no	—
20	C₂²×M₁₆×C₄₇	—	2	4	no	—
21	C₂²×M₁₆×C₄₇	C₄	1	8	yes	complemented
22	C₂²×M₁₆×C₄₇	C₂²	1	4	yes	—
23	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂³×Dic₄₇	—	2	2	no	—
26	C₂³×Dic₄₇	—	2	2	no	—
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	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
34	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
35	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
36	C₂×C₂²⋊Dic₄₇	—	4	8	no	—
37	#13093958	—	2	8	no	—
38	#13093956	—	2	8	no	—
39	C₄₇⋊#95	—	2	8	no	—
40	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	—	2	2	no	—
42	C₂³×C₄×C₄₇	—	2	2	no	—
43	C₂³×C₄×C₄₇	—	2	2	no	—
44	C₂³×C₄×C₄₇	—	2	2	no	—
45	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	D₄	1	2	yes	—
48	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₄₇	—	2	32	no	—
52	C₂×M₁₆×C₄₇	—	2	8	no	—
53	C₂×M₁₆×C₄₇	—	2	8	no	—
54	C₂×M₁₆×C₄₇	C₂×C₄	1	16	yes	complemented
55	C₂²×C₈×C₄₇	—	2	2	no	—
56	C₂²×C₈×C₄₇	—	2	2	no	—
57	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
58	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
59	C₂²×C₈×C₄₇	D₄	1	4	yes	—
60	C₂²×C₈×C₄₇	D₄	1	4	yes	—
61	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
62	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
63	C₂⁴×C₄₇	—	2	2	no	—
64	C₂⁴×C₄₇	—	2	2	no	—
65	C₂⁴×C₄₇	—	2	4	no	—
66	C₂⁴×C₄₇	—	2	4	no	—
67	C₂⁴×C₄₇	C₄⋊C₄	1	4	yes	—
68	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
69	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	8	no	—
73	C₂²×C₄×C₄₇	—	2	8	no	—
74	C₂²×C₄×C₄₇	—	2	4	no	—
75	C₂²×C₄×C₄₇	—	2	4	no	—
76	C₂²×C₄×C₄₇	—	2	8	no	—
77	C₂²×C₄×C₄₇	—	2	8	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
83	C₂²×C₄×C₄₇	C₄⋊C₄	1	8	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	#41	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₇	—	2	4	no	—
96	C₂²×Dic₄₇	—	2	4	no	—
97	C₂²×Dic₄₇	—	4	4	no	—
98	C₂²×Dic₄₇	—	4	4	no	—
99	C₂²×Dic₄₇	—	4	4	no	—
100	C₂²×Dic₄₇	—	4	4	no	—
101	C₂²×Dic₄₇	—	4	4	no	—
102	C₂²×Dic₄₇	—	4	4	no	—
103	M₁₆×C₄₇	—	2	32	no	—
104	C₂×C₈×C₄₇	—	2	8	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	C₂²⋊C₄	1	16	yes	complemented
108	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
110	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
111	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
112	C₂²⋊Dic₄₇	—	4	16	no	—
113	C₄⋊Dic₄₇	—	2	4	no	—
114	C₄⋊Dic₄₇	—	2	4	no	—
115	C₄⋊Dic₄₇	—	2	4	no	—
116	C₄⋊Dic₄₇	—	2	4	no	—
117	C₄⋊Dic₄₇	—	4	4	no	—
118	C₄⋊Dic₄₇	—	4	4	no	—
119	C₂³×C₄₇	—	2	2	no	—
120	C₂³×C₄₇	—	2	2	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	2	4	no	—
123	C₂³×C₄₇	—	2	8	no	—
124	C₂³×C₄₇	—	2	16	no	—
125	C₂³×C₄₇	—	4	8	no	—
126	C₂³×C₄₇	—	4	4	no	—
127	C₂³×C₄₇	—	4	4	no	—
128	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
129	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
130	C₂³×C₄₇	#121	1	2	yes	—
131	C₂³×C₄₇	#121	1	2	yes	—
132	C₂³×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
133	C₂³×C₄₇	#137	1	4	yes	—
134	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	8	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	16	no	—
143	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
145	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₇	#117	1	4	yes	—
147	C₂×C₄×C₄₇	#121	1	2	yes	—
148	C₂×C₄×C₄₇	#121	1	2	yes	—
149	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
150	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×Dic₄₇	—	4	4	no	—
158	C₂×Dic₄₇	—	4	4	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	—	4	4	no	—
161	C₂×Dic₄₇	—	4	4	no	—
162	C₂×Dic₄₇	—	4	4	no	—
163	C₂×Dic₄₇	—	8	8	no	—
164	C₂×Dic₄₇	—	8	8	no	—
165	C₈×C₄₇	—	2	4	no	—
166	C₈×C₄₇	C₂×C₂²⋊C₄	1	8	yes	complemented
167	C₂×#1809	—	47	1	no	maximal, Sylow
168	C₂²×C₄₇	—	2	8	no	—
169	C₂²×C₄₇	—	2	4	no	—
170	C₂²×C₄₇	—	4	16	no	—
171	C₂²×C₄₇	—	4	4	no	—
172	C₂²×C₄₇	—	4	2	no	—
173	C₂²×C₄₇	—	4	2	no	—
174	C₂²×C₄₇	#380	1	4	yes	—
175	C₂²×C₄₇	#428	1	8	yes	—
176	C₂²×C₄₇	#468	1	8	yes	—
177	C₂²×C₄₇	#469	1	4	yes	—
178	C₂²×C₄₇	#470	1	4	yes	—
179	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
181	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
183	C₂²×C₄₇	C₂×#137	1	2	yes	—
184	C₄×C₄₇	—	2	4	no	—
185	C₄×C₄₇	#380	1	4	yes	—
186	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
187	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
188	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
189	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
190	Dic₄₇	—	8	4	no	—
191	Dic₄₇	—	8	4	no	—
192	C₂³×M₁₆	D₄₇	1	1	yes	characteristic
193	C₂²×#107	—	47	1	no	—
194	C₂²×#106	—	47	1	no	—
195	C₂×#380	—	47	2	no	—
196	#1809	—	47	8	no	—
197	C₂×#340	—	47	2	no	—
198	C₂×C₄₇	—	4	4	no	—
199	C₂×C₄₇	#1809	1	8	yes	complemented
200	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
201	C₂×C₄₇	C₂×#428	1	2	yes	—
202	C₂×C₄₇	C₂×#468	1	2	yes	—
203	C₂×C₄₇	C₂×#469	1	1	yes	characteristic
204	C₂×C₄₇	C₂×#470	1	1	yes	characteristic
205	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
206	C₂²×M₁₆	—	2	4	no	—
207	C₂²×M₁₆	—	2	4	no	—
208	C₂²×M₁₆	Dic₄₇	1	8	yes	complemented
209	C₂²×M₁₆	C₂×D₄₇	1	4	yes	—
210	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
211	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
212	C₂²×C₄⋊C₄	—	47	2	no	—
213	C₂²×C₄⋊C₄	—	47	2	no	—
214	C₂²×C₂²⋊C₄	—	94	2	no	—
215	C₂×#107	—	47	4	no	—
216	C₂×#107	—	94	4	no	—
217	C₂×#106	—	47	4	no	—
218	C₂×#106	—	94	4	no	—
219	#380	—	47	8	no	—
220	#380	—	94	4	no	—
221	C₂×#95	—	94	2	no	—
222	#340	—	47	8	no	—
223	C₄₇	C₂×#1809	1	1	yes	characteristic, complemented, Sylow
224	C₂⁵	D₁₈₈	1	1	yes	characteristic
225	C₂³×C₄	—	2	2	no	—
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	—	2	2	no	—
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	—	94	2	no	—
230	C₂³×C₄	—	94	2	no	—
231	C₂³×C₄	Dic₉₄	1	4	yes	—
232	C₂³×C₄	D₁₈₈	1	2	yes	—
233	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
234	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
235	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
236	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
237	C₂×M₁₆	—	2	32	no	—
238	C₂×M₁₆	—	2	8	no	—
239	C₂×M₁₆	—	2	8	no	—
240	C₂×M₁₆	C₂×Dic₄₇	1	16	yes	complemented
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
244	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
245	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
246	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
247	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
248	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
249	C₂×C₄⋊C₄	—	47	4	no	—
250	C₂×C₄⋊C₄	—	47	4	no	—
251	C₂×C₄⋊C₄	—	94	4	no	—
252	C₂×C₄⋊C₄	—	94	4	no	—
253	C₂×C₄⋊C₄	—	94	4	no	—
254	C₂×C₄⋊C₄	—	94	4	no	—
255	C₂×C₄⋊C₄	—	94	2	no	—
256	C₂×C₄⋊C₄	—	94	2	no	—
257	C₂×C₂²⋊C₄	—	94	8	no	—
258	C₂×C₂²⋊C₄	—	188	8	no	—
259	#107	—	94	8	no	—
260	#106	—	94	8	no	—
261	#95	—	94	8	no	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	2	2	no	—
264	C₂⁴	—	2	4	no	—
265	C₂⁴	—	2	4	no	—
266	C₂⁴	C₄⋊Dic₄₇	1	4	yes	—
267	C₂⁴	C₂×D₁₈₈	1	2	yes	—
268	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	94	4	no	—
282	C₂²×C₄	—	94	4	no	—
283	C₂²×C₄	—	188	4	no	—
284	C₂²×C₄	—	188	4	no	—
285	C₂²×C₄	—	188	4	no	—
286	C₂²×C₄	—	188	4	no	—
287	C₂²×C₄	—	188	4	no	—
288	C₂²×C₄	—	188	4	no	—
289	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
290	C₂²×C₄	C₄⋊Dic₄₇	1	8	yes	—
291	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
292	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
293	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
294	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
295	C₂²×C₄	#10625350	1	2	yes	—
296	C₂²×C₄	#10625350	1	2	yes	—
297	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
298	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
300	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
301	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
302	M₁₆	—	2	32	no	—
303	C₂×C₈	—	2	8	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	C₂²⋊Dic₄₇	1	16	yes	complemented
307	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
308	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
309	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
310	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
311	C₄⋊C₄	—	94	4	no	—
312	C₄⋊C₄	—	94	4	no	—
313	C₄⋊C₄	—	94	4	no	—
314	C₄⋊C₄	—	94	4	no	—
315	C₄⋊C₄	—	188	4	no	—
316	C₄⋊C₄	—	188	4	no	—
317	C₂²⋊C₄	—	188	16	no	—
318	C₂³	—	2	8	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	16	no	—
324	C₂³	—	4	8	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	C₂×C₄⋊Dic₄₇	1	4	yes	—
328	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
329	C₂³	#13093998	1	2	yes	—
330	C₂³	#13093998	1	2	yes	—
331	C₂³	#13094052	1	4	yes	—
332	C₂³	#13094057	1	4	yes	—
333	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	16	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	376	8	no	—
343	C₂×C₄	—	376	8	no	—
344	C₂×C₄	—	188	4	no	—
345	C₂×C₄	—	188	4	no	—
346	C₂×C₄	—	188	4	no	—
347	C₂×C₄	—	188	4	no	—
348	C₂×C₄	—	188	4	no	—
349	C₂×C₄	—	188	4	no	—
350	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
351	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
352	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
353	C₂×C₄	#13093983	1	4	yes	—
354	C₂×C₄	#13093998	1	2	yes	—
355	C₂×C₄	#13093998	1	2	yes	—
356	C₂×C₄	#13094003	1	4	yes	—
357	C₂×C₄	#13094003	1	4	yes	—
358	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
362	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
363	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
364	C₈	—	2	4	no	—
365	C₈	C₂×C₂²⋊Dic₄₇	1	8	yes	complemented
366	C₂²	—	2	4	no	—
367	C₂²	—	2	8	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	16	no	—
372	C₂²	#15688983	1	4	yes	—
373	C₂²	#15689165	1	8	yes	—
374	C₂²	#15689369	1	8	yes	—
375	C₂²	#15689376	1	4	yes	—
376	C₂²	#15689381	1	4	yes	—
377	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
378	C₂²	C₂×#13093998	1	1	yes	characteristic
379	C₂²	C₂×#13093998	1	1	yes	characteristic
380	C₂²	C₂×#13094052	1	2	yes	—
381	C₂²	C₂×#13094057	1	2	yes	—
382	C₄	—	2	4	no	—
383	C₄	—	376	4	no	—
384	C₄	—	376	4	no	—
385	C₄	#15688983	1	4	yes	—
386	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
387	C₄	C₂×#13093983	1	1	yes	characteristic
388	C₄	C₂×#13094003	1	1	yes	characteristic
389	C₄	C₂×#13094003	1	1	yes	characteristic
390	C₂	—	4	4	no	—
391	C₂	#20243421	1	8	yes	direct product factor
392	C₂	C₂×#15688983	1	1	yes	characteristic
393	C₂	C₂×#15689165	1	2	yes	—
394	C₂	C₂×#15689369	1	2	yes	—
395	C₂	C₂×#15689376	1	1	yes	characteristic
396	C₂	C₂×#15689381	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂³×M₁₆×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂×D₄
prime radical	C₂⁵×C₄₇	D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂³×M₁₆	D₄₇
hypocenter	C₄₇	C₂×#1809
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂³×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093958	C₂	semidirect
2. C₂²×#13093956	C₂	semidirect
4. #20243421	C₂	direct (N × H)
5. C₂×#15688886	C₂	semidirect
11. C₂×#13093958	C₂²	semidirect
13. C₂×#13093956	C₂²	semidirect
17. #15688886	C₂²	semidirect
21. C₂²×M₁₆×C₄₇	C₄	semidirect
54. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
107. C₂×C₈×C₄₇	C₂²⋊C₄	semidirect
166. C₈×C₄₇	C₂×C₂²⋊C₄	semidirect
199. C₂×C₄₇	#1809	semidirect
208. C₂²×M₁₆	Dic₄₇	semidirect
223. C₄₇	C₂×#1809	semidirect
240. C₂×M₁₆	C₂×Dic₄₇	semidirect
306. C₂×C₈	C₂²⋊Dic₄₇	semidirect
365. C₈	C₂×C₂²⋊Dic₄₇	semidirect
391. C₂	#20243421	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×#13093956	2
C₂×#15688983	2
#20243421	2
C₂×#15688886	2
C₂³×M₁₆×C₄₇	2
C₂×#1809	47

Subgroups — C2×#20243421 #26215851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243421 #26215851