Subgroups — C₄×#15689165 #26214345

Order 12032.

1218 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689165	C₂	1	2	yes	maximal
2	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243285	C₂	1	4	yes	maximal, complemented
5	C₄×#13093958	C₂	1	2	yes	maximal, complemented
6	C₄×#13093956	C₂	1	2	yes	maximal, complemented
7	#20243108	C₂	1	2	yes	maximal
8	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#13093983	C₂²	1	2	yes	—
10	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	C₂²×C₄×Dic₄₇	—	2	1	no	—
12	#15689165	C₄	1	16	yes	direct product factor
13	C₂×#13093958	C₂²	1	4	yes	—
14	C₂×#13093956	C₂²	1	4	yes	—
15	C₄×C₄⋊Dic₄₇	—	2	1	no	—
16	C₄×C₄⋊Dic₄₇	—	2	1	no	—
17	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
19	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
21	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
22	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
23	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
24	#15688969	—	2	1	no	—
25	C₂×C₄₇⋊#95	—	2	1	no	—
26	C₄²×Dic₄₇	—	2	1	no	—
27	#15688886	C₂²	1	4	yes	—
28	#15688886	C₂²	1	4	yes	—
29	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₄×M₁₆×C₄₇	C₄	1	8	yes	complemented
33	C₂×#97×C₄₇	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
35	C₂³×Dic₄₇	—	2	2	no	—
36	#13093983	—	2	4	no	—
37	#13093983	C₂×C₄	1	8	yes	—
38	C₂×C₄⋊Dic₄₇	—	2	2	no	—
39	C₂×C₄⋊Dic₄₇	—	2	4	no	—
40	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
41	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
42	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
43	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
44	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
45	C₂×C₄×Dic₄₇	—	2	2	no	—
46	C₂×C₄×Dic₄₇	—	2	2	no	—
47	C₂×C₄×Dic₄₇	—	2	1	no	—
48	C₂×C₄×Dic₄₇	—	2	1	no	—
49	C₂×C₄×Dic₄₇	—	2	2	no	—
50	C₂×C₄×Dic₄₇	—	2	2	no	—
51	C₂×C₄×Dic₄₇	—	4	4	no	—
52	#13093958	C₂×C₄	1	16	yes	complemented
53	#13093956	C₂×C₄	1	16	yes	complemented
54	C₄₇⋊#95	—	2	2	no	—
55	C₄₇⋊#95	—	2	2	no	—
56	C₄₇⋊#95	—	2	1	no	—
57	C₄₇⋊#95	—	2	1	no	—
58	C₄₇⋊#95	—	2	2	no	—
59	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₄₇	—	2	4	no	—
63	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	—
65	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
66	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
69	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	#97×C₄₇	C₂×C₄	1	8	yes	complemented
75	C₄×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
76	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	4	2	no	—
80	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
81	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	4	yes	—
91	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₄₇	—	2	8	no	—
93	C₂²×Dic₄₇	—	2	2	no	—
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	—	2	4	no	—
96	C₂²×Dic₄₇	—	4	4	no	—
97	C₂²×Dic₄₇	—	4	4	no	—
98	M₁₆×C₄₇	—	2	8	no	—
99	M₁₆×C₄₇	C₄²	1	16	yes	complemented
100	C₂×C₈×C₄₇	—	2	4	no	—
101	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
103	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
104	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
105	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
106	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
107	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
108	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
109	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
110	C₂²⋊Dic₄₇	—	2	8	no	—
111	C₄⋊Dic₄₇	—	2	8	no	—
112	C₄⋊Dic₄₇	—	2	4	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	—	2	2	no	—
115	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
116	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
117	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
118	C₄×Dic₄₇	—	2	8	no	—
119	C₄×Dic₄₇	—	4	4	no	—
120	C₄×Dic₄₇	—	4	4	no	—
121	C₄×Dic₄₇	—	4	2	no	—
122	C₄×Dic₄₇	—	4	4	no	—
123	C₄×Dic₄₇	—	4	2	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	—	2	1	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂³×C₄₇	C₄×D₄	1	4	yes	—
129	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	8	no	—
135	C₂×C₄×C₄₇	—	4	4	no	—
136	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
137	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₇	#117	1	4	yes	—
143	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
144	C₂×C₄×C₄₇	C₄×Q₈	1	8	yes	—
145	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
146	C₂×C₄×C₄₇	#137	1	2	yes	—
147	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
151	C₂×Dic₄₇	—	2	4	no	—
152	C₂×Dic₄₇	—	2	4	no	—
153	C₂×Dic₄₇	—	2	8	no	—
154	C₂×Dic₄₇	—	4	16	no	—
155	C₂×Dic₄₇	—	4	4	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	4	no	—
161	C₈×C₄₇	—	2	4	no	—
162	C₈×C₄₇	C₂×C₄²	1	8	yes	complemented
163	C₄×#428	—	47	1	no	maximal, Sylow
164	C₂²×C₄₇	—	2	2	no	—
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	4	no	—
167	C₂²×C₄₇	—	2	4	no	—
168	C₂²×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
169	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
171	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
173	C₂²×C₄₇	#575	1	2	yes	—
174	C₄×C₄₇	—	2	2	no	—
175	C₄×C₄₇	—	2	2	no	—
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
178	C₄×C₄₇	#428	1	4	yes	complemented
179	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
180	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
181	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
182	Dic₄₇	—	4	4	no	—
183	Dic₄₇	—	4	8	no	—
184	Dic₄₇	—	4	4	no	—
185	C₂×#428	—	47	2	no	—
186	C₂×C₄×M₁₆	D₄₇	1	1	yes	characteristic
187	C₄×#117	—	47	1	no	—
188	C₂×C₄×C₄⋊C₄	—	47	1	no	—
189	#1776	—	47	4	no	—
190	C₄×#107	—	47	2	no	—
191	C₄×#106	—	47	2	no	—
192	#1736	—	47	2	no	—
193	C₂×C₄₇	—	2	4	no	—
194	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄₇	C₂×#428	1	1	yes	characteristic
196	C₂×C₄₇	#2911	1	1	yes	characteristic
197	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	2	yes	—
198	C₂×C₄₇	C₄×#137	1	2	yes	—
199	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
200	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
201	C₂×#117	—	47	2	no	—
202	C₂²×C₄⋊C₄	—	47	2	no	—
203	C₂²×C₄²	—	94	1	no	—
204	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
205	#428	—	47	16	no	—
206	C₂×#107	—	47	4	no	—
207	C₂×#106	—	47	4	no	—
208	C₄×M₁₆	Dic₄₇	1	8	yes	complemented
209	C₂×#97	C₂×D₄₇	1	2	yes	—
210	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
211	C₄×C₄⋊C₄	—	47	2	no	—
212	C₄×C₄⋊C₄	—	47	2	no	—
213	C₄×C₄⋊C₄	—	47	1	no	—
214	C₄×C₄⋊C₄	—	47	1	no	—
215	C₄×C₄⋊C₄	—	47	2	no	—
216	C₄×C₄⋊C₄	—	94	1	no	—
217	C₄×C₄⋊C₄	—	94	1	no	—
218	C₄×C₂²⋊C₄	—	94	1	no	—
219	C₄×C₂²⋊C₄	—	94	1	no	—
220	#376	—	94	1	no	—
221	C₂×#95	—	94	1	no	—
222	C₄³	—	94	1	no	—
223	#340	—	47	4	no	—
224	#340	—	47	4	no	—
225	C₄₇	C₄×#428	1	1	yes	characteristic, complemented, Sylow
226	C₂³×C₄	—	94	2	no	—
227	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
228	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
229	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
230	C₂×M₁₆	—	2	4	no	—
231	C₂×M₁₆	C₄×D₄₇	1	8	yes	—
232	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
233	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
234	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
235	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
236	#117	—	47	8	no	—
237	#117	—	94	4	no	—
238	C₂×C₄⋊C₄	—	47	8	no	—
239	C₂×C₄⋊C₄	—	47	4	no	—
240	C₂×C₄⋊C₄	—	47	2	no	—
241	C₂×C₄⋊C₄	—	47	2	no	—
242	C₂×C₄⋊C₄	—	94	2	no	—
243	C₂×C₄⋊C₄	—	94	4	no	—
244	C₂×C₂²⋊C₄	—	94	2	no	—
245	C₂×C₄²	—	94	2	no	—
246	C₂×C₄²	—	94	2	no	—
247	C₂×C₄²	—	94	2	no	—
248	C₂×C₄²	—	94	1	no	—
249	C₂×C₄²	—	94	1	no	—
250	C₂×C₄²	—	94	2	no	—
251	C₂×C₄²	—	188	4	no	—
252	C₂×C₄²	Dic₉₄	1	4	yes	—
253	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
254	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
255	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
256	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
258	#107	—	47	16	no	—
259	#106	—	47	16	no	—
260	#97	C₂×Dic₄₇	1	8	yes	complemented
261	C₄×C₈	C₂×Dic₄₇	1	8	yes	complemented
262	#95	—	94	2	no	—
263	#95	—	94	2	no	—
264	#95	—	94	1	no	—
265	#95	—	94	1	no	—
266	#95	—	94	2	no	—
267	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	94	8	no	—
272	C₂²×C₄	—	94	2	no	—
273	C₂²×C₄	—	94	2	no	—
274	C₂²×C₄	—	94	4	no	—
275	C₂²×C₄	—	188	4	no	—
276	C₂²×C₄	—	188	4	no	—
277	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
278	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
279	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
280	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
281	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
286	C₂²×C₄	#10625350	1	4	yes	—
287	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
288	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
289	M₁₆	—	2	8	no	—
290	M₁₆	C₄×Dic₄₇	1	16	yes	complemented
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	C₂×C₄×D₄₇	1	8	yes	—
293	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
294	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
295	C₄⋊C₄	—	47	4	no	—
296	C₄⋊C₄	—	47	8	no	—
297	C₄⋊C₄	—	47	4	no	—
298	C₄⋊C₄	—	94	8	no	—
299	C₄⋊C₄	—	94	4	no	—
300	C₄⋊C₄	—	94	2	no	—
301	C₄⋊C₄	—	94	2	no	—
302	C₂²⋊C₄	—	94	8	no	—
303	C₄²	—	94	8	no	—
304	C₄²	—	188	4	no	—
305	C₄²	—	188	4	no	—
306	C₄²	—	188	2	no	—
307	C₄²	—	188	4	no	—
308	C₄²	—	188	2	no	—
309	C₄²	C₄⋊Dic₄₇	1	4	yes	—
310	C₄²	C₄⋊Dic₄₇	1	4	yes	—
311	C₄²	C₂×Dic₉₄	1	2	yes	—
312	C₄²	C₂×Dic₉₄	1	2	yes	—
313	C₄²	C₂²×Dic₄₇	1	2	yes	—
314	C₄²	C₂²×Dic₄₇	1	2	yes	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	2	no	—
318	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
319	C₂³	C₄×D₁₈₈	1	4	yes	—
320	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	94	4	no	—
328	C₂×C₄	—	94	4	no	—
329	C₂×C₄	—	94	8	no	—
330	C₂×C₄	—	188	16	no	—
331	C₂×C₄	—	188	4	no	—
332	C₂×C₄	—	188	2	no	—
333	C₂×C₄	—	188	2	no	—
334	C₂×C₄	—	188	2	no	—
335	C₂×C₄	—	188	2	no	—
336	C₂×C₄	—	188	4	no	—
337	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
338	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
339	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
340	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
341	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
342	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
343	C₂×C₄	#13093983	1	4	yes	—
344	C₂×C₄	C₄×D₁₈₈	1	4	yes	—
345	C₂×C₄	C₄×Dic₉₄	1	8	yes	—
346	C₂×C₄	#13094052	1	2	yes	—
347	C₂×C₄	#13094057	1	2	yes	—
348	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
349	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
350	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
351	C₂×C₄	C₂×#10625350	1	2	yes	—
352	C₈	—	2	4	no	—
353	C₈	C₂×C₄×Dic₄₇	1	8	yes	complemented
354	C₂²	—	2	4	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	C₄×C₄⋊Dic₄₇	1	4	yes	—
359	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
360	C₂²	C₂×C₄×D₁₈₈	1	2	yes	—
361	C₂²	C₂×#13094052	1	1	yes	characteristic
362	C₂²	C₂×#13094057	1	1	yes	characteristic
363	C₂²	#15689923	1	2	yes	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	188	8	no	—
368	C₄	—	188	4	no	—
369	C₄	—	188	4	no	—
370	C₄	C₄×C₄⋊Dic₄₇	1	4	yes	—
371	C₄	#15689165	1	4	yes	direct product factor
372	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
373	C₄	C₂×#13093983	1	1	yes	characteristic
374	C₄	C₂×C₄×Dic₉₄	1	2	yes	—
375	C₂	—	2	4	no	—
376	C₂	C₂×C₄×C₄⋊Dic₄₇	1	1	yes	characteristic
377	C₂	C₂×#15689165	1	1	yes	characteristic
378	C₂	#20251978	1	1	yes	characteristic
379	C₂	C₄×#13094052	1	2	yes	—
380	C₂	C₄×#13094057	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×M₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₄₇
hypocenter	C₄₇	C₄×#428
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. #20243285	C₂	semidirect
5. C₄×#13093958	C₂	semidirect
6. C₄×#13093956	C₂	semidirect
12. #15689165	C₄	direct (N × H)
32. C₄×M₁₆×C₄₇	C₄	semidirect
52. #13093958	C₂×C₄	semidirect
53. #13093956	C₂×C₄	semidirect
74. #97×C₄₇	C₂×C₄	semidirect
75. C₄×C₈×C₄₇	C₂×C₄	semidirect
99. M₁₆×C₄₇	C₄²	semidirect
162. C₈×C₄₇	C₂×C₄²	semidirect
178. C₄×C₄₇	#428	semidirect
208. C₄×M₁₆	Dic₄₇	semidirect
225. C₄₇	C₄×#428	semidirect
260. #97	C₂×Dic₄₇	semidirect
261. C₄×C₈	C₂×Dic₄₇	semidirect
290. M₁₆	C₄×Dic₄₇	semidirect
353. C₈	C₂×C₄×Dic₄₇	semidirect
371. C₄	#15689165	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×#15689165	2
C₄×#13093983	2
C₂×C₄×C₄⋊Dic₄₇	2
#20243285	2
C₄×#13093958	2
C₄×#13093956	2
#20243108	2
C₂×C₄×M₁₆×C₄₇	2
C₄×#428	47

Subgroups — C4×#15689165 #26214345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689165 #26214345