Subgroups — C₂×#20242515 #26192141

Order 12032.

1322 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689418	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689413	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242515	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688867	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#550	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625335	—	2	2	no	—
10	C₂×#13094024	C₂²	1	1	yes	characteristic
11	#15689495	—	2	2	no	—
12	#15689495	C₂²	1	4	yes	complemented
13	#15689418	—	2	2	no	—
14	#15689418	C₂²	1	4	yes	complemented
15	#15689413	—	2	2	no	—
16	#15689413	C₂²	1	4	yes	complemented
17	C₂×#13093957	—	2	1	no	—
18	C₂×#13093955	—	2	1	no	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#13093948	—	2	1	no	—
22	C₂×#13093945	—	2	1	no	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	#15688867	C₂²	1	4	yes	complemented
25	Q₈⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
26	D₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
27	C₂²×#41×C₄₇	—	2	1	no	—
28	C₄₇×#550	—	2	2	no	—
29	C₄₇×#550	—	2	2	no	—
30	C₄₇×#550	—	2	2	no	—
31	C₄₇×#550	C₂²	1	4	yes	—
32	C₂×#127×C₄₇	—	2	1	no	—
33	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#121×C₄₇	—	2	2	no	—
35	C₂×#121×C₄₇	—	2	1	no	—
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₄₇	—	2	1	no	—
38	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×Dic₉₄	—	2	1	no	—
40	C₂×#10625335	—	2	8	no	—
41	C₂×#10625335	—	4	8	no	—
42	C₂²×C₄₇⋊C₈	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	—	2	1	no	—
44	C₂²×C₄₇⋊C₈	—	2	1	no	—
45	#13094024	—	2	1	no	—
46	#13094024	—	2	1	no	—
47	#13094024	—	2	1	no	—
48	#13094024	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	#13093957	—	2	4	no	—
52	#13093955	—	2	4	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	#13093948	—	2	4	no	—
58	#13093945	—	2	4	no	—
59	C₄×C₄₇⋊C₈	—	2	1	no	—
60	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
61	C₂×#41×C₄₇	—	2	4	no	—
62	C₂×#41×C₄₇	—	2	4	no	—
63	C₂×#41×C₄₇	—	4	4	no	—
64	C₂×#41×C₄₇	—	4	4	no	—
65	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
66	C₂²×D₄×C₄₇	—	2	2	no	—
67	C₂²×D₄×C₄₇	—	2	2	no	—
68	C₂²×D₄×C₄₇	—	2	1	no	—
69	C₂²×D₄×C₄₇	—	2	1	no	—
70	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₄₇	D₄	1	2	yes	—
72	C₂³×C₄×C₄₇	—	2	2	no	—
73	C₂³×C₄×C₄₇	—	2	1	no	—
74	#127×C₄₇	—	2	4	no	—
75	#127×C₄₇	—	2	4	no	—
76	#127×C₄₇	—	2	1	no	—
77	#127×C₄₇	—	2	1	no	—
78	#127×C₄₇	D₄	1	2	yes	—
79	#127×C₄₇	C₂³	1	2	yes	—
80	#121×C₄₇	—	2	4	no	—
81	#121×C₄₇	—	2	8	no	—
82	#121×C₄₇	—	2	8	no	—
83	#121×C₄₇	—	2	4	no	—
84	C₄×Q₈×C₄₇	—	2	1	no	—
85	C₄×Q₈×C₄₇	—	2	1	no	—
86	C₄×Q₈×C₄₇	D₄	1	2	yes	—
87	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
88	C₄×D₄×C₄₇	—	2	4	no	—
89	C₄×D₄×C₄₇	—	2	4	no	—
90	C₄×D₄×C₄₇	—	2	1	no	—
91	C₄×D₄×C₄₇	—	2	1	no	—
92	C₄×D₄×C₄₇	D₄	1	2	yes	—
93	C₄×D₄×C₄₇	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
99	C₂×C₄²×C₄₇	—	2	1	no	—
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₂⁴×C₄₇	—	2	1	no	—
102	C₂⁴×C₄₇	—	2	2	no	—
103	#41×C₄₇	—	4	8	no	—
104	#41×C₄₇	—	4	16	no	—
105	#41×C₄₇	—	4	8	no	—
106	C₂×Q₈×C₄₇	—	2	1	no	—
107	C₂×Q₈×C₄₇	—	2	2	no	—
108	C₂×Q₈×C₄₇	SD₁₆	1	4	yes	complemented
109	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₄₇	—	2	8	no	—
111	C₂×D₄×C₄₇	—	2	8	no	—
112	C₂×D₄×C₄₇	—	2	1	no	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	2	2	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	2	no	—
117	C₂×D₄×C₄₇	—	2	2	no	—
118	C₂×D₄×C₄₇	—	2	2	no	—
119	C₂×D₄×C₄₇	—	2	2	no	—
120	C₂×D₄×C₄₇	—	4	8	no	—
121	C₂×D₄×C₄₇	—	4	4	no	—
122	C₂×D₄×C₄₇	—	4	2	no	—
123	C₂×D₄×C₄₇	—	4	2	no	—
124	C₂×D₄×C₄₇	—	4	2	no	—
125	C₂×D₄×C₄₇	—	4	2	no	—
126	C₂×D₄×C₄₇	—	8	4	no	—
127	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₄₇	—	2	1	no	—
130	C₂²×C₄×C₄₇	—	2	8	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	1	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	4	8	no	—
136	C₂²×C₄×C₄₇	—	4	2	no	—
137	C₂²×C₄×C₄₇	—	4	2	no	—
138	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×Dic₄₇	—	4	1	no	—
142	C₂×Dic₉₄	—	2	2	no	—
143	C₂×Dic₉₄	—	4	4	no	—
144	C₂×Dic₉₄	—	4	1	no	—
145	C₄⋊C₄×C₄₇	—	2	2	no	—
146	C₄⋊C₄×C₄₇	—	2	1	no	—
147	C₄⋊C₄×C₄₇	—	2	1	no	—
148	C₄⋊C₄×C₄₇	—	2	2	no	—
149	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₄₇	—	2	8	no	—
152	C₂²⋊C₄×C₄₇	—	2	2	no	—
153	C₂²⋊C₄×C₄₇	—	2	2	no	—
154	C₄²×C₄₇	—	2	2	no	—
155	C₄²×C₄₇	—	2	2	no	—
156	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
160	#10625335	—	4	16	no	—
161	C₄⋊Dic₄₇	—	2	2	no	—
162	C₄⋊Dic₄₇	—	2	2	no	—
163	C₄⋊Dic₄₇	—	4	1	no	—
164	C₄⋊Dic₄₇	—	4	1	no	—
165	C₂×C₄₇⋊C₈	—	2	4	no	—
166	C₂×C₄₇⋊C₈	—	2	2	no	—
167	C₂×C₄₇⋊C₈	—	2	2	no	—
168	C₂×C₄₇⋊C₈	—	2	2	no	—
169	C₂×C₄₇⋊C₈	—	4	2	no	—
170	C₂×C₄₇⋊C₈	—	4	2	no	—
171	C₂³×C₄₇	—	2	2	no	—
172	C₂³×C₄₇	—	2	4	no	—
173	C₂³×C₄₇	—	4	4	no	—
174	C₂³×C₄₇	—	4	2	no	—
175	C₂³×C₄₇	—	4	2	no	—
176	C₂³×C₄₇	—	4	4	no	—
177	C₂³×C₄₇	—	4	4	no	—
178	C₂³×C₄₇	—	4	2	no	—
179	C₂³×C₄₇	#120	1	1	yes	characteristic
180	Q₈×C₄₇	—	2	2	no	—
181	Q₈×C₄₇	—	2	4	no	—
182	Q₈×C₄₇	C₂×SD₁₆	1	4	yes	complemented
183	D₄×C₄₇	—	2	2	no	—
184	D₄×C₄₇	—	2	2	no	—
185	D₄×C₄₇	—	4	4	no	—
186	D₄×C₄₇	—	4	16	no	—
187	D₄×C₄₇	—	4	2	no	—
188	D₄×C₄₇	—	4	2	no	—
189	D₄×C₄₇	—	4	2	no	—
190	D₄×C₄₇	—	4	2	no	—
191	D₄×C₄₇	—	4	4	no	—
192	D₄×C₄₇	—	4	2	no	—
193	D₄×C₄₇	—	4	4	no	—
194	D₄×C₄₇	—	8	2	no	—
195	D₄×C₄₇	—	8	8	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	4	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	4	16	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	—	4	4	no	—
207	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
208	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
209	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
211	C₂×C₄×C₄₇	#135	1	2	yes	—
212	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
213	C₂×C₄×C₄₇	#137	1	2	yes	—
214	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×Dic₄₇	—	4	2	no	—
218	C₂×Dic₄₇	—	8	2	no	—
219	Dic₉₄	—	4	4	no	—
220	Dic₉₄	—	8	2	no	—
221	C₄₇⋊C₈	—	2	4	no	—
222	C₄₇⋊C₈	—	4	2	no	—
223	C₄₇⋊C₈	—	4	2	no	—
224	C₂×#1631	—	47	1	no	maximal, Sylow
225	C₂²×C₄₇	—	4	4	no	—
226	C₂²×C₄₇	—	4	2	no	—
227	C₂²×C₄₇	—	4	2	no	—
228	C₂²×C₄₇	—	4	4	no	—
229	C₂²×C₄₇	—	4	4	no	—
230	C₂²×C₄₇	—	4	2	no	—
231	C₂²×C₄₇	—	8	4	no	—
232	C₂²×C₄₇	—	8	8	no	—
233	C₂²×C₄₇	#450	1	2	yes	—
234	C₂²×C₄₇	#452	1	2	yes	—
235	C₂²×C₄₇	#453	1	2	yes	—
236	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
237	C₄×C₄₇	—	2	4	no	—
238	C₄×C₄₇	—	2	1	no	—
239	C₄×C₄₇	—	2	1	no	—
240	C₄×C₄₇	—	4	2	no	—
241	C₄×C₄₇	—	4	2	no	—
242	C₄×C₄₇	#450	1	2	yes	—
243	C₄×C₄₇	#452	1	2	yes	—
244	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
245	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
246	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
247	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
248	Dic₄₇	—	8	2	no	—
249	C₂×#550	D₄₇	1	1	yes	characteristic
250	C₂×#492	—	47	1	no	—
251	C₂×#477	—	47	1	no	—
252	C₂×#476	—	47	1	no	—
253	#1631	—	47	8	no	—
254	C₂×#331	—	47	1	no	—
255	C₂×Q₈⋊C₈	—	47	1	no	—
256	C₂×D₄⋊C₈	—	47	1	no	—
257	C₂×C₄₇	—	8	2	no	—
258	C₂×C₄₇	—	8	4	no	—
259	C₂×C₄₇	#1631	1	4	yes	complemented
260	C₂×C₄₇	C₂×#450	1	1	yes	characteristic
261	C₂×C₄₇	C₂×#452	1	1	yes	characteristic
262	C₂×C₄₇	C₂×#453	1	1	yes	characteristic
263	C₂²×#41	—	2	1	no	—
264	C₂²×SD₁₆	—	94	2	no	—
265	#550	—	2	2	no	—
266	#550	—	2	2	no	—
267	#550	—	2	2	no	—
268	#550	C₂×D₄₇	1	4	yes	—
269	C₂×C₄⋊Q₈	—	47	1	no	—
270	C₂×#127	—	2	1	no	—
271	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
272	C₂×#121	—	2	2	no	—
273	C₂×#121	—	2	1	no	—
274	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
275	C₂×C₄×D₄	—	2	1	no	—
276	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
277	#492	—	47	4	no	—
278	#492	—	94	2	no	—
279	#477	—	47	4	no	—
280	#477	—	94	2	no	—
281	#476	—	47	4	no	—
282	#476	—	94	2	no	—
283	C₂×#107	—	94	1	no	—
284	C₂×#106	—	94	1	no	—
285	C₂×C₄⋊C₈	—	47	1	no	—
286	C₂×C₄⋊C₈	—	47	1	no	—
287	C₂×#103	—	94	1	no	—
288	C₂×#102	—	94	1	no	—
289	C₂×C₄×C₈	—	47	1	no	—
290	#331	—	47	4	no	—
291	Q₈⋊C₈	—	47	4	no	—
292	D₄⋊C₈	—	47	4	no	—
293	C₄₇	C₂×#1631	1	1	yes	characteristic, complemented, Sylow
294	C₂×#41	—	2	4	no	—
295	C₂×#41	—	2	4	no	—
296	C₂×#41	—	4	4	no	—
297	C₂×#41	—	4	4	no	—
298	C₂²×Q₈	—	94	1	no	—
299	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
305	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
306	C₂³×C₄	—	2	2	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂×SD₁₆	—	94	8	no	—
309	C₂×SD₁₆	—	188	8	no	—
310	C₂²×C₈	—	94	1	no	—
311	C₂²×C₈	—	94	1	no	—
312	C₂²×C₈	—	94	1	no	—
313	C₄⋊Q₈	—	47	2	no	—
314	C₄⋊Q₈	—	94	1	no	—
315	C₄⋊Q₈	—	94	1	no	—
316	C₄⋊Q₈	—	94	1	no	—
317	#127	—	2	4	no	—
318	#127	—	2	4	no	—
319	#127	—	2	1	no	—
320	#127	—	2	1	no	—
321	#127	C₂²⋊D₄₇	1	2	yes	—
322	#127	C₂²×D₄₇	1	2	yes	—
323	#121	—	2	4	no	—
324	#121	—	2	8	no	—
325	#121	—	2	8	no	—
326	#121	—	2	4	no	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
330	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
336	C₄×D₄	C₂²×D₄₇	1	2	yes	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	94	1	no	—
339	C₂×C₄⋊C₄	—	94	1	no	—
340	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
346	#107	—	94	4	no	—
347	#106	—	94	4	no	—
348	C₄⋊C₈	—	47	2	no	—
349	C₄⋊C₈	—	47	2	no	—
350	C₄⋊C₈	—	94	1	no	—
351	C₄⋊C₈	—	94	1	no	—
352	#103	—	94	4	no	—
353	#102	—	94	4	no	—
354	C₄×C₈	—	47	2	no	—
355	C₄×C₈	—	94	1	no	—
356	C₂⁴	—	2	1	no	—
357	C₂⁴	—	2	2	no	—
358	#41	—	4	16	no	—
359	#41	—	4	8	no	—
360	#41	—	4	8	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	94	2	no	—
364	C₂×Q₈	—	188	4	no	—
365	C₂×Q₈	—	188	1	no	—
366	C₂×Q₈	#10625335	1	4	yes	complemented
367	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	4	8	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	8	4	no	—
385	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
386	C₂×D₄	C₂×C₂²⋊D₄₇	1	4	yes	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	4	8	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	188	1	no	—
397	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
398	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
400	SD₁₆	—	188	16	no	—
401	C₂×C₈	—	94	4	no	—
402	C₂×C₈	—	94	2	no	—
403	C₂×C₈	—	94	2	no	—
404	C₂×C₈	—	94	2	no	—
405	C₂×C₈	—	188	2	no	—
406	C₂×C₈	—	188	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	94	2	no	—
412	C₄⋊C₄	—	94	2	no	—
413	C₄⋊C₄	—	188	1	no	—
414	C₄⋊C₄	—	188	1	no	—
415	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
416	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
423	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
424	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
425	C₄²	C₂³×D₄₇	1	1	yes	characteristic
426	C₂³	—	2	4	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	4	no	—
432	C₂³	—	4	4	no	—
433	C₂³	—	4	2	no	—
434	C₂³	#13093993	1	1	yes	characteristic
435	Q₈	—	2	4	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	376	2	no	—
438	Q₈	—	188	4	no	—
439	Q₈	C₂×#10625335	1	4	yes	complemented
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	4	4	no	—
443	D₄	—	4	16	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	4	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	8	2	no	—
452	D₄	—	8	8	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	16	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	376	2	no	—
465	C₂×C₄	—	188	2	no	—
466	C₂×C₄	#13093993	1	1	yes	characteristic
467	C₂×C₄	#13093993	1	1	yes	characteristic
468	C₂×C₄	#13093993	1	1	yes	characteristic
469	C₂×C₄	C₂×#10625335	1	2	yes	—
470	C₂×C₄	#13094044	1	2	yes	—
471	C₂×C₄	#13094050	1	2	yes	—
472	C₂×C₄	#13094054	1	2	yes	—
473	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
474	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
475	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
476	C₈	—	94	4	no	—
477	C₈	—	188	2	no	—
478	C₈	—	188	2	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	8	4	no	—
486	C₂²	—	8	8	no	—
487	C₂²	#15689274	1	2	yes	—
488	C₂²	#15689285	1	2	yes	—
489	C₂²	#15689291	1	2	yes	—
490	C₂²	C₂×#13093993	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	376	2	no	—
497	C₄	#15689274	1	2	yes	—
498	C₄	#15689285	1	2	yes	—
499	C₄	C₂²×#10625335	1	1	yes	characteristic
500	C₄	C₂×#13094044	1	1	yes	characteristic
501	C₄	C₂×#13094050	1	1	yes	characteristic
502	C₄	C₂×#13094054	1	1	yes	characteristic
503	C₂	—	8	4	no	—
504	C₂	—	8	2	no	—
505	C₂	#20242515	1	4	yes	direct product factor
506	C₂	C₂×#15689274	1	1	yes	characteristic
507	C₂	C₂×#15689285	1	1	yes	characteristic
508	C₂	C₂×#15689291	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093993
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#550	C₂
socle	C₂³×C₄₇	#120
hypercenter	C₂×#550	D₄₇
hypocenter	C₄₇	C₂×#1631
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#550

Complements

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

N	H ≅ G/N	type
1. C₂×#15689495	C₂	semidirect
2. C₂×#15689418	C₂	semidirect
3. C₂×#15689413	C₂	semidirect
4. #20242515	C₂	direct (N × H)
5. C₂×#15688867	C₂	semidirect
6. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
7. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
12. #15689495	C₂²	semidirect
14. #15689418	C₂²	semidirect
16. #15689413	C₂²	semidirect
24. #15688867	C₂²	semidirect
25. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
26. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
108. C₂×Q₈×C₄₇	SD₁₆	semidirect
182. Q₈×C₄₇	C₂×SD₁₆	semidirect
259. C₂×C₄₇	#1631	semidirect
293. C₄₇	C₂×#1631	semidirect
366. C₂×Q₈	#10625335	semidirect
439. Q₈	C₂×#10625335	semidirect
505. C₂	#20242515	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×#15689495	2
C₂×#15689418	2
C₂×#15689413	2
#20242515	2
C₂×#15688867	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₂×D₄⋊(C₄₇⋊C₈)	2
C₂×C₄₇×#550	2
C₂×#1631	47

Subgroups — C2×#20242515 #26192141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242515 #26192141