Subgroups — C₂×#20242746 #26198604

Order 12032.

870 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689499	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689323	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242746	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688867	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688866	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625336	—	2	1	no	—
10	C₂²×#10625334	—	2	1	no	—
11	C₂²×#10625334	—	2	1	no	—
12	C₂×#13094021	C₂²	1	1	yes	characteristic
13	#15689499	—	2	2	no	—
14	#15689499	C₂²	1	4	yes	—
15	#15689323	—	2	2	no	—
16	#15689323	C₂²	1	4	yes	complemented
17	Q₈×C₄₇⋊C₈	—	2	2	no	—
18	Q₈×C₄₇⋊C₈	C₂²	1	4	yes	complemented
19	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#13093944	—	2	1	no	—
23	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15688875	C₂²	1	4	yes	complemented
26	#15688867	C₂²	1	4	yes	complemented
27	#15688866	C₂²	1	4	yes	complemented
28	C₂²×SD₁₆×C₄₇	—	2	1	no	—
29	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#460	—	2	2	no	—
32	C₄₇×#460	C₂²	1	4	yes	complemented
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₇	—	2	1	no	—
35	C₂²×D₁₈₈	—	2	1	no	—
36	C₂²×D₁₈₈	—	2	1	no	—
37	C₂²×D₁₈₈	—	2	1	no	—
38	C₂×#10625336	—	2	4	no	—
39	C₂×#10625336	—	4	4	no	—
40	C₂×#10625334	—	2	4	no	—
41	C₂×#10625334	—	2	4	no	—
42	C₂×#10625334	—	4	4	no	—
43	C₂×#10625334	—	4	4	no	—
44	C₂²×C₄₇⋊C₈	—	2	1	no	—
45	C₂²×C₄₇⋊C₈	—	2	1	no	—
46	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
48	#13094021	—	2	1	no	—
49	#13094021	—	2	1	no	—
50	#13094021	—	2	1	no	—
51	#13094021	C₂³	1	2	yes	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	#13093944	—	2	4	no	—
58	C₄×C₄₇⋊C₈	—	2	4	no	—
59	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
60	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
61	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₄₇	—	2	1	no	—
63	C₂²×D₄×C₄₇	—	2	1	no	—
64	C₂²×D₄×C₄₇	—	2	1	no	—
65	C₂×SD₁₆×C₄₇	—	2	4	no	—
66	C₂×SD₁₆×C₄₇	—	4	4	no	—
67	C₂²×C₈×C₄₇	—	2	1	no	—
68	#127×C₄₇	—	2	1	no	—
69	#127×C₄₇	—	2	1	no	—
70	#127×C₄₇	—	2	1	no	—
71	#127×C₄₇	C₂³	1	2	yes	—
72	C₄×Q₈×C₄₇	—	2	1	no	—
73	C₄×Q₈×C₄₇	—	2	1	no	—
74	C₄×Q₈×C₄₇	D₄	1	2	yes	—
75	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₄₇	—	2	1	no	—
81	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
82	#102×C₄₇	—	2	4	no	—
83	C₂⁴×C₄₇	—	4	1	no	—
84	C₂³×D₄₇	—	4	1	no	—
85	C₂×Q₈×C₄₇	—	2	1	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	D₈	1	4	yes	complemented
88	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	4	1	no	—
93	C₂×D₄×C₄₇	—	4	1	no	—
94	C₂×D₄×C₄₇	—	4	1	no	—
95	C₂×D₄×C₄₇	—	4	2	no	—
96	C₂×D₄×C₄₇	—	4	2	no	—
97	C₂×D₄×C₄₇	—	4	2	no	—
98	C₂×D₄×C₄₇	—	4	2	no	—
99	C₂×D₄×C₄₇	—	8	2	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂×D₁₈₈	—	2	2	no	—
106	C₂×D₁₈₈	—	2	2	no	—
107	C₂×D₁₈₈	—	2	2	no	—
108	C₂×D₁₈₈	—	4	2	no	—
109	C₂×D₁₈₈	—	4	2	no	—
110	C₂×D₁₈₈	—	4	2	no	—
111	C₂×D₁₈₈	—	4	2	no	—
112	C₂×D₁₈₈	—	4	1	no	—
113	C₂×D₁₈₈	—	4	1	no	—
114	C₂×D₁₈₈	—	4	1	no	—
115	C₂×D₁₈₈	—	8	2	no	—
116	SD₁₆×C₄₇	—	4	8	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	4	2	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₇	#41	1	1	yes	characteristic
128	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
129	#10625336	—	4	8	no	—
130	#10625334	—	4	8	no	—
131	#10625334	—	4	8	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	4	2	no	—
136	C₂×C₄₇⋊C₈	—	4	2	no	—
137	C₂×C₄₇⋊C₈	SD₁₆	1	4	yes	complemented
138	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
139	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	8	2	no	—
142	C₂³×C₄₇	—	8	2	no	—
143	C₂³×C₄₇	—	8	2	no	—
144	C₂³×C₄₇	#121	1	1	yes	characteristic
145	C₂²×D₄₇	—	4	2	no	—
146	C₂²×D₄₇	—	8	2	no	—
147	C₂²×D₄₇	—	8	2	no	—
148	C₂²×D₄₇	—	8	2	no	—
149	Q₈×C₄₇	—	2	2	no	—
150	Q₈×C₄₇	—	2	4	no	—
151	Q₈×C₄₇	C₂×D₈	1	4	yes	complemented
152	D₄×C₄₇	—	4	2	no	—
153	D₄×C₄₇	—	4	2	no	—
154	D₄×C₄₇	—	4	2	no	—
155	D₄×C₄₇	—	4	2	no	—
156	D₄×C₄₇	—	8	2	no	—
157	D₄×C₄₇	—	8	2	no	—
158	D₄×C₄₇	—	8	2	no	—
159	D₄×C₄₇	—	8	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
169	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
170	C₂×C₄×C₄₇	#135	1	2	yes	—
171	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	D₁₈₈	—	4	2	no	—
176	D₁₈₈	—	4	2	no	—
177	D₁₈₈	—	4	2	no	—
178	D₁₈₈	—	4	2	no	—
179	D₁₈₈	—	8	2	no	—
180	D₁₈₈	—	8	2	no	—
181	D₁₈₈	—	8	2	no	—
182	D₁₈₈	—	8	2	no	—
183	C₈×C₄₇	—	4	2	no	—
184	C₄₇⋊C₈	—	2	2	no	—
185	C₄₇⋊C₈	—	4	2	no	—
186	C₄₇⋊C₈	—	4	2	no	—
187	C₄₇⋊C₈	C₂×SD₁₆	1	4	yes	complemented
188	C₂×#1668	—	47	1	no	maximal, Sylow
189	C₂²×C₄₇	—	8	2	no	—
190	C₂²×C₄₇	—	8	2	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	—	16	4	no	—
193	C₂²×C₄₇	#460	1	2	yes	—
194	C₂²×C₄₇	#466	1	2	yes	—
195	C₂²×C₄₇	#472	1	2	yes	—
196	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
197	C₂×D₄₇	—	8	2	no	—
198	C₂×D₄₇	—	8	2	no	—
199	C₂×D₄₇	—	8	2	no	—
200	C₂×D₄₇	—	16	4	no	—
201	C₄×C₄₇	—	2	4	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	—	2	1	no	—
204	C₄×C₄₇	—	4	2	no	—
205	C₄×C₄₇	#460	1	2	yes	—
206	C₄×C₄₇	#466	1	2	yes	—
207	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
208	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
209	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
210	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂×#493	—	47	1	no	—
212	C₂×#460	—	47	1	no	—
213	C₂×#460	D₄₇	1	1	yes	characteristic, complemented
214	C₂×C₈×Q₈	—	47	1	no	—
215	#1668	—	47	8	no	—
216	C₂×#335	—	47	1	no	—
217	C₂×#331	—	47	1	no	—
218	C₂×#331	—	47	1	no	—
219	C₂×C₄₇	—	16	2	no	—
220	C₂×C₄₇	#1668	1	4	yes	complemented
221	C₂×C₄₇	C₂×#460	1	1	yes	characteristic
222	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
223	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
224	D₄₇	—	16	2	no	—
225	C₂²×SD₁₆	—	2	1	no	—
226	C₂²×SD₁₆	—	94	1	no	—
227	C₂²×D₈	—	94	1	no	—
228	C₂²×D₈	—	94	1	no	—
229	C₂×#127	—	47	1	no	—
230	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
232	#493	—	47	4	no	—
233	#493	—	94	2	no	—
234	#460	—	2	2	no	—
235	#460	—	47	4	no	—
236	#460	—	94	2	no	—
237	#460	C₂×D₄₇	1	4	yes	complemented
238	C₈×Q₈	—	47	4	no	—
239	C₈×Q₈	—	94	2	no	—
240	C₂×C₄⋊C₈	—	47	1	no	—
241	C₂×C₄⋊C₈	—	47	1	no	—
242	C₂×C₄⋊C₈	—	94	1	no	—
243	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
244	C₂×#102	—	2	1	no	—
245	C₂×#102	—	94	1	no	—
246	C₂×C₄×C₈	—	47	1	no	—
247	C₂×C₄×C₈	—	94	1	no	—
248	#335	—	47	4	no	—
249	#331	—	47	4	no	—
250	#331	—	47	4	no	—
251	C₄₇	C₂×#1668	1	1	yes	characteristic, complemented, Sylow
252	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	94	1	no	—
257	C₂²×D₄	—	94	1	no	—
258	C₂²×D₄	—	94	1	no	—
259	C₂×SD₁₆	—	2	4	no	—
260	C₂×SD₁₆	—	4	4	no	—
261	C₂×SD₁₆	—	94	4	no	—
262	C₂×SD₁₆	—	188	4	no	—
263	C₂×D₈	—	94	4	no	—
264	C₂×D₈	—	94	4	no	—
265	C₂×D₈	—	188	4	no	—
266	C₂×D₈	—	188	4	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	47	1	no	—
269	C₂²×C₈	—	47	1	no	—
270	C₂²×C₈	—	94	1	no	—
271	C₂²×C₈	—	94	1	no	—
272	#127	—	2	1	no	—
273	#127	—	2	1	no	—
274	#127	—	2	1	no	—
275	#127	—	47	2	no	—
276	#127	—	94	1	no	—
277	#127	—	94	1	no	—
278	#127	—	94	1	no	—
279	#127	C₂²×D₄₇	1	2	yes	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
283	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	47	2	no	—
290	C₄⋊C₈	—	47	2	no	—
291	C₄⋊C₈	—	94	4	no	—
292	C₄⋊C₈	—	94	1	no	—
293	C₄⋊C₈	—	94	1	no	—
294	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
295	#102	—	2	4	no	—
296	#102	—	94	4	no	—
297	C₄×C₈	—	47	2	no	—
298	C₄×C₈	—	47	2	no	—
299	C₄×C₈	—	94	4	no	—
300	C₂⁴	—	4	1	no	—
301	C₂⁴	—	188	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	#10625334	1	4	yes	complemented
305	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	8	2	no	—
317	C₂×D₄	—	94	2	no	—
318	C₂×D₄	—	94	2	no	—
319	C₂×D₄	—	94	2	no	—
320	C₂×D₄	—	376	2	no	—
321	C₂×D₄	—	188	1	no	—
322	C₂×D₄	—	188	1	no	—
323	C₂×D₄	—	188	1	no	—
324	C₂×D₄	—	188	2	no	—
325	C₂×D₄	—	188	2	no	—
326	C₂×D₄	—	188	2	no	—
327	C₂×D₄	—	188	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
331	C₂²×C₄	#10625352	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
333	SD₁₆	—	4	8	no	—
334	SD₁₆	—	188	8	no	—
335	D₈	—	188	8	no	—
336	D₈	—	188	8	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	47	4	no	—
340	C₂×C₈	—	47	2	no	—
341	C₂×C₈	—	47	2	no	—
342	C₂×C₈	—	94	2	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	188	2	no	—
346	C₂×C₈	—	188	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	D₄×D₄₇	1	1	yes	characteristic
354	C₄²	#10625352	1	1	yes	characteristic
355	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
356	C₄²	C₂³×D₄₇	1	1	yes	characteristic
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	—	376	2	no	—
362	C₂³	—	376	2	no	—
363	C₂³	—	376	2	no	—
364	C₂³	—	188	2	no	—
365	C₂³	#13093996	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	2	2	no	—
368	Q₈	C₂×#10625334	1	4	yes	complemented
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	2	no	—
376	D₄	—	8	2	no	—
377	D₄	—	376	2	no	—
378	D₄	—	376	2	no	—
379	D₄	—	376	2	no	—
380	D₄	—	376	2	no	—
381	D₄	—	188	2	no	—
382	D₄	—	188	2	no	—
383	D₄	—	188	2	no	—
384	D₄	—	188	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	#13093996	1	1	yes	characteristic
391	C₂×C₄	#13093996	1	1	yes	characteristic
392	C₂×C₄	#13093996	1	1	yes	characteristic
393	C₂×C₄	C₂×#10625334	1	2	yes	—
394	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
395	C₂×C₄	#13094044	1	2	yes	—
396	C₂×C₄	#13094051	1	2	yes	—
397	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
399	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
400	C₈	—	4	2	no	—
401	C₈	—	47	4	no	—
402	C₈	—	94	2	no	—
403	C₈	—	188	2	no	—
404	C₈	—	188	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	16	4	no	—
409	C₂²	—	376	2	no	—
410	C₂²	—	376	2	no	—
411	C₂²	—	376	2	no	—
412	C₂²	—	752	4	no	—
413	C₂²	#15689321	1	2	yes	—
414	C₂²	#15689357	1	2	yes	—
415	C₂²	#15689391	1	2	yes	—
416	C₂²	C₂×#13093996	1	1	yes	characteristic
417	C₄	—	2	4	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	4	2	no	—
421	C₄	#15689321	1	2	yes	—
422	C₄	#15689357	1	2	yes	—
423	C₄	C₂²×#10625334	1	1	yes	characteristic
424	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
425	C₄	C₂×#13094044	1	1	yes	characteristic
426	C₄	C₂×#13094051	1	1	yes	characteristic
427	C₂	—	16	2	no	—
428	C₂	—	752	2	no	—
429	C₂	#20242746	1	4	yes	direct product factor
430	C₂	C₂×#15689321	1	1	yes	characteristic
431	C₂	C₂×#15689357	1	1	yes	characteristic
432	C₂	C₂×#15689391	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#460	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂×#15689499	C₂
hypercenter	C₂×#460	D₄₇
hypocenter	C₄₇	C₂×#1668
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#460

Complements

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

N	H ≅ G/N	type
2. C₂×#15689323	C₂	semidirect
3. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
4. #20242746	C₂	direct (N × H)
5. C₂×#15688875	C₂	semidirect
6. C₂×#15688867	C₂	semidirect
7. C₂×#15688866	C₂	semidirect
8. C₂×C₄₇×#460	C₂	semidirect
16. #15689323	C₂²	semidirect
18. Q₈×C₄₇⋊C₈	C₂²	semidirect
25. #15688875	C₂²	semidirect
26. #15688867	C₂²	semidirect
27. #15688866	C₂²	semidirect
32. C₄₇×#460	C₂²	semidirect
87. C₂×Q₈×C₄₇	D₈	semidirect
137. C₂×C₄₇⋊C₈	SD₁₆	semidirect
151. Q₈×C₄₇	C₂×D₈	semidirect
187. C₄₇⋊C₈	C₂×SD₁₆	semidirect
213. C₂×#460	D₄₇	semidirect
220. C₂×C₄₇	#1668	semidirect
237. #460	C₂×D₄₇	semidirect
251. C₄₇	C₂×#1668	semidirect
304. C₂×Q₈	#10625334	semidirect
368. Q₈	C₂×#10625334	semidirect
429. C₂	#20242746	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×#15689499	2
C₂×#15689323	2
C₂×Q₈×C₄₇⋊C₈	2
#20242746	2
C₂×#15688875	2
C₂×#15688867	2
C₂×#15688866	2
C₂×C₄₇×#460	2
C₂×#1668	47

Subgroups — C2×#20242746 #26198604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242746 #26198604