Subgroups — C₂×#20244333 #26220761

Order 12032.

1290 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20244333	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688882	C₂	1	4	yes	maximal
5	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
8	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
9	C₄×#10625329	—	2	2	no	—
10	C₄×#10625329	C₂²	1	4	yes	—
11	C₂×#13093935	—	2	1	no	—
12	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
13	C₄×C₄⋊Dic₄₇	—	2	2	no	—
14	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	—
15	C₂×C₄₇⋊#95	—	2	1	no	—
16	#15688882	C₂²	1	16	yes	—
17	C₄₇×#533	—	2	2	no	—
18	C₄₇×#533	—	2	2	no	—
19	C₄₇×#533	C₄	1	4	yes	complemented
20	C₄₇×#533	C₂²	1	4	yes	—
21	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
22	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
23	C₂×#125×C₄₇	C₄	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
26	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
27	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
28	C₂×#117×C₄₇	C₂²	1	2	yes	—
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂³×Dic₄₇	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	4	no	—
33	C₂×#10625329	Q₈	1	8	yes	complemented
34	C₂×#10625329	C₂³	1	4	yes	—
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	C₂×C₄⋊Dic₄₇	—	2	8	no	—
37	C₂×C₄⋊Dic₄₇	—	2	4	no	—
38	C₂×C₄×Dic₄₇	—	2	8	no	—
39	C₂×C₄×Dic₄₇	—	2	2	no	—
40	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
41	#13093935	—	2	4	no	—
42	C₄×C₄₇⋊C₈	—	2	4	no	—
43	C₄₇⋊#95	—	2	4	no	—
44	C₂²×Q₈×C₄₇	—	2	1	no	—
45	C₂²×Q₈×C₄₇	—	2	1	no	—
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₄₇	—	2	2	no	—
50	C₄⋊Q₈×C₄₇	—	2	2	no	—
51	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
52	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
53	#125×C₄₇	—	2	4	no	—
54	#125×C₄₇	C₂×C₄	1	8	yes	complemented
55	C₂²⋊Q₈×C₄₇	—	2	4	no	—
56	C₂²⋊Q₈×C₄₇	—	2	4	no	—
57	C₂²⋊Q₈×C₄₇	—	2	4	no	—
58	C₂²⋊Q₈×C₄₇	—	2	4	no	—
59	C₄×Q₈×C₄₇	—	2	4	no	—
60	C₄×Q₈×C₄₇	—	2	4	no	—
61	C₄×Q₈×C₄₇	—	2	4	no	—
62	C₄×Q₈×C₄₇	—	2	4	no	—
63	#117×C₄₇	—	2	2	no	—
64	#117×C₄₇	—	2	2	no	—
65	#117×C₄₇	C₂×C₄	1	4	yes	—
66	#117×C₄₇	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	—	2	2	no	—
75	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₄₇	D₄	1	2	yes	—
79	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	D₄	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
83	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	—	4	4	no	—
87	C₂×Q₈×C₄₇	—	4	4	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	4	2	no	—
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
106	C₂²×C₄×C₄₇	#41	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
108	C₂²×Dic₄₇	—	2	8	no	—
109	C₂²×Dic₄₇	—	2	4	no	—
110	C₂²×Dic₄₇	—	4	4	no	—
111	C₂²×Dic₄₇	—	4	4	no	—
112	C₄⋊C₄×C₄₇	—	2	8	no	—
113	C₄⋊C₄×C₄₇	—	2	8	no	—
114	C₄⋊C₄×C₄₇	—	2	4	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
119	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
120	C₂²⋊C₄×C₄₇	—	2	4	no	—
121	C₂²⋊C₄×C₄₇	—	2	4	no	—
122	C₄²×C₄₇	—	2	4	no	—
123	C₄²×C₄₇	—	2	4	no	—
124	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
125	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
126	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
129	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
130	C₄²×C₄₇	C₂×D₄	1	2	yes	—
131	C₄²×C₄₇	C₂×D₄	1	2	yes	—
132	C₄⋊Dic₄₇	—	2	16	no	—
133	C₄×Dic₄₇	—	2	8	no	—
134	C₄×Dic₄₇	—	4	4	no	—
135	#10625329	—	2	8	no	—
136	#10625329	—	2	4	no	—
137	#10625329	C₂×Q₈	1	8	yes	complemented
138	C₂×C₄₇⋊C₈	—	2	8	no	—
139	C₂×C₄₇⋊C₈	—	2	4	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₄₇	#124	1	2	yes	—
145	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
146	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₄₇	—	4	8	no	—
148	Q₈×C₄₇	—	4	8	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	4	no	—
159	C₂×C₄×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	#104	1	4	yes	—
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
168	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
169	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
170	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
171	C₂×C₄×C₄₇	#124	1	2	yes	—
172	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
173	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
176	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
177	C₂×Dic₄₇	—	2	8	no	—
178	C₂×Dic₄₇	—	4	4	no	—
179	C₂×Dic₄₇	—	4	16	no	—
180	C₂×Dic₄₇	—	4	4	no	—
181	C₄₇⋊C₈	—	2	8	no	—
182	C₂×#1986	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	1	no	—
186	C₂²×C₄₇	—	2	1	no	—
187	C₂²×C₄₇	—	2	4	no	—
188	C₂²×C₄₇	—	2	4	no	—
189	C₂²×C₄₇	#391	1	2	yes	—
190	C₂²×C₄₇	#391	1	2	yes	—
191	C₂²×C₄₇	C₂×#104	1	2	yes	—
192	C₂²×C₄₇	#421	1	2	yes	—
193	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
196	C₄×C₄₇	—	2	2	no	—
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	4	4	no	—
200	C₄×C₄₇	—	4	4	no	—
201	C₄×C₄₇	#391	1	2	yes	—
202	C₄×C₄₇	#391	1	2	yes	—
203	C₄×C₄₇	C₂×#104	1	4	yes	—
204	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
205	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
206	Dic₄₇	—	4	8	no	—
207	C₂×#533	D₄₇	1	1	yes	characteristic
208	C₂×C₄×M₁₆	—	47	1	no	—
209	C₂×C₄×C₄⋊C₄	—	47	1	no	—
210	#1986	—	47	8	no	—
211	C₂×#339	—	47	4	no	—
212	C₂×C₄₇	—	2	1	no	—
213	C₂×C₄₇	—	2	1	no	—
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	#1986	1	4	yes	complemented
216	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
217	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
219	C₂²×M₁₆	—	47	2	no	—
220	#533	—	2	2	no	—
221	#533	—	2	2	no	—
222	#533	Dic₄₇	1	4	yes	complemented
223	#533	C₂×D₄₇	1	4	yes	—
224	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
225	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
226	C₂×#125	Dic₄₇	1	2	yes	complemented
227	C₂×C₂²⋊Q₈	—	2	1	no	—
228	C₂×C₂²⋊Q₈	—	2	1	no	—
229	C₂×C₄×Q₈	—	2	1	no	—
230	C₂×C₄×Q₈	—	2	1	no	—
231	C₂×#117	C₂×D₄₇	1	2	yes	—
232	C₂²×C₄⋊C₄	—	94	1	no	—
233	C₂²×C₄²	—	47	2	no	—
234	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
235	C₄×M₁₆	—	47	4	no	—
236	C₄×M₁₆	—	94	2	no	—
237	C₂×#97	—	94	1	no	—
238	C₂×C₄×C₈	—	94	1	no	—
239	C₄×C₄⋊C₄	—	47	4	no	—
240	C₄×C₄⋊C₄	—	94	2	no	—
241	C₂×#95	—	94	1	no	—
242	#339	—	47	16	no	—
243	C₄₇	C₂×#1986	1	1	yes	characteristic, complemented, Sylow
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	—	2	1	no	—
246	C₂³×C₄	—	94	2	no	—
247	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
248	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
249	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
250	C₂×M₁₆	—	47	8	no	—
251	C₂×M₁₆	—	47	4	no	—
252	C₂×M₁₆	—	94	4	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂²×C₈	—	94	2	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
258	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
259	#125	—	2	4	no	—
260	#125	C₂×Dic₄₇	1	8	yes	complemented
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	—	2	4	no	—
264	C₂²⋊Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	2	4	no	—
268	C₄×Q₈	—	2	4	no	—
269	#117	—	2	2	no	—
270	#117	—	2	2	no	—
271	#117	C₂×Dic₄₇	1	4	yes	—
272	#117	C₂²×D₄₇	1	4	yes	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	94	8	no	—
278	C₂×C₄⋊C₄	—	94	4	no	—
279	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
280	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	—	47	4	no	—
284	C₂×C₄²	—	94	8	no	—
285	C₂×C₄²	—	94	2	no	—
286	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
287	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
288	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
289	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
290	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
291	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
292	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
293	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
294	#97	—	94	4	no	—
295	C₄×C₈	—	94	4	no	—
296	#95	—	94	4	no	—
297	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	4	4	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	94	8	no	—
307	C₂²×C₄	—	94	4	no	—
308	C₂²×C₄	—	188	4	no	—
309	C₂²×C₄	—	188	4	no	—
310	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
312	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
314	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
315	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
316	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
317	C₂²×C₄	#10625354	1	4	yes	—
318	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
321	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
326	M₁₆	—	47	8	no	—
327	M₁₆	—	94	8	no	—
328	M₁₆	—	94	4	no	—
329	C₂×C₈	—	94	8	no	—
330	C₂×C₈	—	94	4	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	94	16	no	—
338	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
339	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	94	8	no	—
345	C₄²	—	188	4	no	—
346	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
347	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
348	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
349	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
350	C₄²	C₂²×Dic₄₇	1	2	yes	—
351	C₄²	C₂²×Dic₄₇	1	2	yes	—
352	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
353	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
357	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
358	C₂³	#13094013	1	2	yes	—
359	C₂³	#13094022	1	2	yes	—
360	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
361	Q₈	—	4	8	no	—
362	Q₈	—	4	8	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	94	8	no	—
375	C₂×C₄	—	188	4	no	—
376	C₂×C₄	—	188	16	no	—
377	C₂×C₄	—	188	4	no	—
378	C₂×C₄	#13093951	1	4	yes	—
379	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
381	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
382	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
383	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
384	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
385	C₂×C₄	Q₈×Dic₄₇	1	4	yes	—
386	C₂×C₄	Q₈×Dic₄₇	1	4	yes	—
387	C₂×C₄	#13094000	1	4	yes	—
388	C₂×C₄	#13094000	1	4	yes	—
389	C₂×C₄	#13094013	1	2	yes	—
390	C₂×C₄	#13094022	1	2	yes	—
391	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
394	C₂×C₄	C₂×#10625354	1	2	yes	—
395	C₈	—	94	8	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	#15689030	1	2	yes	—
403	C₂²	#15689030	1	2	yes	—
404	C₂²	C₂×#13093951	1	2	yes	—
405	C₂²	#15689140	1	2	yes	—
406	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
407	C₂²	C₂×#13094013	1	1	yes	characteristic
408	C₂²	C₂×#13094022	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	4	no	—
414	C₄	—	188	8	no	—
415	C₄	#15689030	1	2	yes	—
416	C₄	#15689030	1	2	yes	—
417	C₄	C₂×#13093951	1	4	yes	—
418	C₄	C₂×Q₈×Dic₄₇	1	2	yes	—
419	C₄	C₂×#13094000	1	2	yes	—
420	C₂	—	2	1	no	—
421	C₂	—	2	2	no	—
422	C₂	—	2	1	no	—
423	C₂	#20244333	1	4	yes	direct product factor
424	C₂	C₂×#15689030	1	1	yes	characteristic
425	C₂	C₂²×#13093951	1	1	yes	characteristic
426	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	C₂×#1986
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #20244333	C₂	direct (N × H)
19. C₄₇×#533	C₄	semidirect
21. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
22. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
23. C₂×#125×C₄₇	C₄	semidirect
33. C₂×#10625329	Q₈	semidirect
51. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
52. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
54. #125×C₄₇	C₂×C₄	semidirect
137. #10625329	C₂×Q₈	semidirect
215. C₂×C₄₇	#1986	semidirect
222. #533	Dic₄₇	semidirect
224. C₂×C₄⋊Q₈	Dic₄₇	semidirect
225. C₂×C₄⋊Q₈	Dic₄₇	semidirect
226. C₂×#125	Dic₄₇	semidirect
243. C₄₇	C₂×#1986	semidirect
257. C₄⋊Q₈	C₂×Dic₄₇	semidirect
258. C₄⋊Q₈	C₂×Dic₄₇	semidirect
260. #125	C₂×Dic₄₇	semidirect
423. C₂	#20244333	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×#10625329	2
C₂×C₄×C₄⋊Dic₄₇	2
#20244333	2
C₂×#15688882	2
C₂×C₄₇×#533	2
C₂×#1986	47

Subgroups — C2×#20244333 #26220761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244333 #26220761