Subgroups — C₂×#20241291 #26106567

Order 12032.

810 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
3	#20241291	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10625329	—	2	1	no	—
6	#15689176	—	2	1	no	—
7	#15689176	—	2	1	no	—
8	#15689176	C₄	1	2	yes	complemented
9	#15689176	C₂²	1	2	yes	—
10	#15689147	—	2	1	no	—
11	#15689147	—	2	1	no	—
12	#15689147	C₄	1	2	yes	complemented
13	#15689147	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	2	yes	complemented
16	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	2	yes	complemented
17	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
18	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
19	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
20	C₂²×C₄²×C₄₇	—	2	1	no	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
23	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
24	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
26	C₂×#95×C₄₇	C₄	1	2	yes	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	4	2	no	—
30	C₂×#10625329	—	4	2	no	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
34	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
35	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
36	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
37	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
38	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
39	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
41	C₄×C₄₇⋊C₈	—	2	2	no	—
42	C₄×C₄₇⋊C₈	—	2	2	no	—
43	C₂³×C₄×C₄₇	—	2	2	no	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄²×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	—	2	2	no	—
52	C₂×C₄²×C₄₇	—	4	2	no	—
53	C₂×C₄²×C₄₇	—	4	2	no	—
54	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	#95×C₄₇	—	2	2	no	—
67	#95×C₄₇	C₂×C₄	1	4	yes	—
68	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	—	2	4	no	—
70	C₂²×C₄×C₄₇	—	2	8	no	—
71	C₂²×C₄×C₄₇	—	2	4	no	—
72	C₂²×C₄×C₄₇	—	4	2	no	—
73	C₂²×C₄×C₄₇	—	4	4	no	—
74	C₂²×C₄×C₄₇	—	4	4	no	—
75	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	D₈	1	2	yes	—
91	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₄⋊C₄×C₄₇	—	2	8	no	—
98	C₄⋊C₄×C₄₇	—	2	8	no	—
99	C₄²×C₄₇	—	4	4	no	—
100	C₄²×C₄₇	—	4	2	no	—
101	C₄²×C₄₇	—	4	2	no	—
102	C₄²×C₄₇	C₄²	1	1	yes	characteristic
103	C₄²×C₄₇	C₄²	1	1	yes	characteristic
104	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
118	#10625329	—	4	4	no	—
119	#10625329	—	4	2	no	—
120	#10625329	—	4	2	no	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	—	2	4	no	—
123	C₂×C₄₇⋊C₈	—	4	4	no	—
124	C₂×C₄₇⋊C₈	—	4	4	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	#95	1	1	yes	characteristic
128	C₂³×C₄₇	#95	1	1	yes	characteristic
129	C₂³×C₄₇	#102	1	2	yes	—
130	C₂³×C₄₇	#103	1	2	yes	—
131	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	4	1	no	—
141	C₂×C₄×C₄₇	—	4	1	no	—
142	C₂×C₄×C₄₇	—	4	1	no	—
143	C₂×C₄×C₄₇	—	4	1	no	—
144	C₂×C₄×C₄₇	—	4	16	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
152	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#102	1	2	yes	—
154	C₂×C₄×C₄₇	#102	1	2	yes	—
155	C₂×C₄×C₄₇	#102	1	2	yes	—
156	C₂×C₄×C₄₇	#103	1	2	yes	—
157	C₂×C₄×C₄₇	#103	1	2	yes	—
158	C₂×C₄×C₄₇	#103	1	2	yes	—
159	C₂×C₄×C₄₇	#104	1	4	yes	—
160	C₂×C₄×C₄₇	#106	1	2	yes	—
161	C₂×C₄×C₄₇	#106	1	2	yes	—
162	C₂×C₄×C₄₇	#107	1	2	yes	—
163	C₂×C₄×C₄₇	#107	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
174	C₄₇⋊C₈	—	4	4	no	—
175	C₄₇⋊C₈	—	4	4	no	—
176	C₂×#1303	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	—	2	4	no	—
178	C₂²×C₄₇	—	2	4	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	#339	1	2	yes	—
184	C₂²×C₄₇	#340	1	2	yes	—
185	C₂²×C₄₇	#340	1	2	yes	—
186	C₂²×C₄₇	#344	1	2	yes	—
187	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	4	8	no	—
197	C₄×C₄₇	#339	1	2	yes	—
198	C₄×C₄₇	#340	1	2	yes	—
199	C₄×C₄₇	#340	1	2	yes	—
200	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
201	C₄×C₄₇	C₂×#103	1	1	yes	characteristic
202	C₄×C₄₇	C₂×#104	1	2	yes	—
203	C₄×C₄₇	C₂×#106	1	1	yes	characteristic
204	C₄×C₄₇	C₂×#107	1	1	yes	characteristic
205	C₂×#431	—	47	1	no	—
206	C₂×#423	—	47	1	no	—
207	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
208	#1303	—	47	4	no	—
209	C₂×C₄₇	—	2	1	no	—
210	C₂×C₄₇	—	2	2	no	—
211	C₂×C₄₇	—	2	1	no	—
212	C₂×C₄₇	#1303	1	4	yes	complemented
213	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
214	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
215	C₂×C₄₇	C₂×#344	1	1	yes	characteristic
216	C₂²×M₁₆	—	94	1	no	—
217	C₂²×C₄⋊C₄	—	2	1	no	—
218	C₂²×C₄²	—	2	1	no	—
219	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
220	#431	—	47	2	no	—
221	#431	—	47	2	no	—
222	#431	—	94	1	no	—
223	#431	—	94	1	no	—
224	#423	—	47	2	no	—
225	#423	—	47	2	no	—
226	#423	—	94	1	no	—
227	#423	—	94	1	no	—
228	C₂×C₄⋊C₈	—	47	2	no	—
229	C₂×C₄⋊C₈	—	47	2	no	—
230	C₂×C₄⋊C₈	—	94	1	no	—
231	C₂×C₂²⋊C₈	—	94	1	no	—
232	C₂×C₄×C₈	—	94	1	no	—
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	—	2	1	no	—
235	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
236	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
237	C₂×#95	Dic₄₇	1	2	yes	—
238	C₄₇	C₂×#1303	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₄	—	2	2	no	—
240	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
241	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
242	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
243	C₂×M₁₆	—	94	2	no	—
244	C₂×M₁₆	—	94	2	no	—
245	C₂×M₁₆	—	188	2	no	—
246	C₂×M₁₆	—	188	2	no	—
247	C₂²×C₈	—	94	2	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₂×C₄⋊C₄	—	2	8	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	4	2	no	—
255	C₂×C₄²	—	4	2	no	—
256	C₂×C₄²	Dic₉₄	1	1	yes	characteristic
257	C₂×C₄²	Dic₉₄	1	1	yes	characteristic
258	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
259	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
260	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
261	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
262	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
263	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
264	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
266	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
268	C₄⋊C₈	—	47	4	no	—
269	C₄⋊C₈	—	47	4	no	—
270	C₄⋊C₈	—	94	2	no	—
271	C₄⋊C₈	—	94	2	no	—
272	C₄⋊C₈	—	94	2	no	—
273	C₄⋊C₈	—	94	2	no	—
274	C₂²⋊C₈	—	94	2	no	—
275	C₂²⋊C₈	—	94	2	no	—
276	C₄×C₈	—	94	2	no	—
277	C₄×C₈	—	94	2	no	—
278	#95	—	2	2	no	—
279	#95	C₂×Dic₄₇	1	4	yes	—
280	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	8	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
289	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
295	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	#10625334	1	2	yes	—
300	C₂²×C₄	#10625335	1	2	yes	—
301	C₂²×C₄	#10625336	1	2	yes	—
302	C₂²×C₄	#10625337	1	2	yes	—
303	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
305	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
306	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
309	M₁₆	—	188	4	no	—
310	M₁₆	—	188	2	no	—
311	M₁₆	—	188	2	no	—
312	C₂×C₈	—	94	4	no	—
313	C₂×C₈	—	94	4	no	—
314	C₂×C₈	—	188	4	no	—
315	C₂×C₈	—	188	4	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄²	—	4	4	no	—
319	C₄²	—	4	2	no	—
320	C₄²	—	4	2	no	—
321	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
322	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
323	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
324	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
325	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
326	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
327	C₄²	C₄⋊Dic₄₇	1	1	yes	characteristic
328	C₄²	C₄⋊Dic₄₇	1	1	yes	characteristic
329	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
330	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
331	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
332	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
333	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
334	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
335	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
336	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	C₄₇⋊#95	1	1	yes	characteristic
340	C₂³	C₄₇⋊#95	1	1	yes	characteristic
341	C₂³	#13093945	1	2	yes	—
342	C₂³	#13093948	1	2	yes	—
343	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
360	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
361	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
362	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
363	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
364	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
365	C₂×C₄	#13093944	1	2	yes	—
366	C₂×C₄	#13093944	1	2	yes	—
367	C₂×C₄	#13093945	1	2	yes	—
368	C₂×C₄	#13093947	1	2	yes	—
369	C₂×C₄	#13093947	1	2	yes	—
370	C₂×C₄	#13093948	1	2	yes	—
371	C₂×C₄	#13093952	1	4	yes	—
372	C₂×C₄	#13093955	1	2	yes	—
373	C₂×C₄	#13093955	1	2	yes	—
374	C₂×C₄	#13093957	1	2	yes	—
375	C₂×C₄	#13093957	1	2	yes	—
376	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
377	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
378	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
379	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
380	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
383	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
384	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
385	C₂×C₄	C₂×#10625337	1	1	yes	characteristic
386	C₈	—	188	4	no	—
387	C₈	—	188	4	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	#15688883	1	2	yes	—
395	C₂²	#15688885	1	2	yes	—
396	C₂²	#15688885	1	2	yes	—
397	C₂²	#15688893	1	2	yes	—
398	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
399	C₂²	C₂×#13093945	1	1	yes	characteristic
400	C₂²	C₂×#13093948	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	4	8	no	—
408	C₄	#15688883	1	2	yes	—
409	C₄	#15688885	1	2	yes	—
410	C₄	#15688885	1	2	yes	—
411	C₄	C₂×#13093944	1	1	yes	characteristic
412	C₄	C₂×#13093947	1	1	yes	characteristic
413	C₄	C₂×#13093952	1	2	yes	—
414	C₄	C₂×#13093955	1	1	yes	characteristic
415	C₄	C₂×#13093957	1	1	yes	characteristic
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	2	no	—
419	C₂	#20241291	1	4	yes	direct product factor
420	C₂	C₂×#15688883	1	1	yes	characteristic
421	C₂	C₂×#15688885	1	1	yes	characteristic
422	C₂	C₂×#15688893	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	#95
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₂×#1303
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #20241291	C₂	direct (N × H)
8. #15689176	C₄	semidirect
12. #15689147	C₄	semidirect
15. C₂×C₄⋊(C₄₇⋊C₈)	C₄	semidirect
16. C₂×C₄⋊(C₄₇⋊C₈)	C₄	semidirect
37. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
38. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
212. C₂×C₄₇	#1303	semidirect
238. C₄₇	C₂×#1303	semidirect
419. C₂	#20241291	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×#15689176	2
C₂×#15689147	2
#20241291	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₂×#1303	47

Subgroups — C2×#20241291 #26106567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241291 #26106567