Subgroups — C₂×#20243492 #26216122

Order 12032.

1354 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689107	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689097	C₂	1	1	yes	maximal, characteristic
3	#20243492	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688883	C₂	1	2	yes	maximal, complemented
5	C₂×#15688879	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂×#13093983	C₂²	1	2	yes	—
9	#15689107	—	2	2	no	—
10	#15689107	C₂²	1	4	yes	—
11	C₂×#13093943	—	2	1	no	—
12	C₂×#13093941	—	2	1	no	—
13	#15689097	—	2	2	no	—
14	#15689097	C₂²	1	4	yes	—
15	C₂×#13093939	—	2	2	no	—
16	#15688883	C₂²	1	8	yes	complemented
17	#15688879	C₂²	1	8	yes	complemented
18	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
19	C₄×#41×C₄₇	—	2	2	no	—
20	C₄×#41×C₄₇	—	2	2	no	—
21	C₄×#41×C₄₇	C₄	1	4	yes	complemented
22	C₄×#41×C₄₇	C₂²	1	4	yes	—
23	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
24	C₂×C₄×D₄×C₄₇	—	2	2	no	—
25	C₂×C₄×D₄×C₄₇	—	2	1	no	—
26	C₂×#117×C₄₇	C₄	1	2	yes	complemented
27	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₄₇	C₄	1	2	yes	complemented
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	2	no	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	C₂³	1	4	yes	—
36	C₂²×C₄₇⋊C₈	—	2	2	no	—
37	#13093983	—	2	2	no	—
38	#13093983	—	2	2	no	—
39	#13093983	—	2	2	no	—
40	#13093983	C₂³	1	4	yes	—
41	C₂×C₄⋊Dic₄₇	—	2	2	no	—
42	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
43	C₂×C₄×Dic₄₇	—	2	2	no	—
44	#13093943	—	2	4	no	—
45	#13093941	—	2	4	no	—
46	#13093939	—	2	8	no	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	—	2	2	no	—
49	C₂×#41×C₄₇	—	2	2	no	—
50	C₂×#41×C₄₇	—	2	2	no	—
51	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×#41×C₄₇	D₄	1	2	yes	—
53	C₂×#41×C₄₇	D₄	1	2	yes	—
54	C₂×#41×C₄₇	C₂³	1	2	yes	—
55	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₄₇	D₄	1	2	yes	—
57	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	—	2	2	no	—
59	C₂³×C₄×C₄₇	—	2	1	no	—
60	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₄×Q₈×C₄₇	—	2	4	no	—
63	C₄×Q₈×C₄₇	—	2	4	no	—
64	C₄×D₄×C₄₇	—	2	4	no	—
65	C₄×D₄×C₄₇	—	2	8	no	—
66	C₄×D₄×C₄₇	—	2	8	no	—
67	C₄×D₄×C₄₇	—	2	4	no	—
68	#117×C₄₇	—	2	4	no	—
69	#117×C₄₇	—	2	1	no	—
70	#117×C₄₇	—	2	1	no	—
71	#117×C₄₇	C₂×C₄	1	2	yes	—
72	#117×C₄₇	C₂×C₄	1	8	yes	complemented
73	#117×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	—	2	4	no	—
80	C₂×C₄²×C₄₇	—	2	1	no	—
81	C₂×C₄²×C₄₇	—	2	1	no	—
82	C₂×C₄²×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
87	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
88	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
89	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
90	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
91	#41×C₄₇	—	2	4	no	—
92	#41×C₄₇	—	2	4	no	—
93	#41×C₄₇	—	2	4	no	—
94	#41×C₄₇	—	2	4	no	—
95	#41×C₄₇	—	2	4	no	—
96	#41×C₄₇	—	2	4	no	—
97	#41×C₄₇	—	2	4	no	—
98	#41×C₄₇	—	2	4	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
102	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
103	C₂×D₄×C₄₇	—	2	4	no	—
104	C₂×D₄×C₄₇	—	2	4	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
108	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
109	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
110	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	8	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	4	4	no	—
122	C₂²×C₄×C₄₇	—	4	8	no	—
123	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
125	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	#41	1	2	yes	—
132	C₂²×C₄×C₄₇	#41	1	2	yes	—
133	C₂²×C₄×C₄₇	#41	1	2	yes	—
134	C₂²×C₄×C₄₇	#41	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
136	C₂²×Dic₄₇	—	4	2	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	8	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₂²⋊C₄×C₄₇	—	2	2	no	—
141	C₂²⋊C₄×C₄₇	—	2	8	no	—
142	C₂²⋊C₄×C₄₇	—	2	2	no	—
143	C₄²×C₄₇	—	2	1	no	—
144	C₄²×C₄₇	—	2	2	no	—
145	C₄²×C₄₇	—	2	1	no	—
146	C₄²×C₄₇	—	2	2	no	—
147	C₄²×C₄₇	—	2	8	no	—
148	C₄²×C₄₇	—	2	2	no	—
149	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
150	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
151	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
152	C₂²⋊Dic₄₇	—	2	4	no	—
153	C₂²⋊Dic₄₇	—	4	2	no	—
154	C₄⋊Dic₄₇	—	2	4	no	—
155	C₄⋊Dic₄₇	—	4	2	no	—
156	C₄×Dic₄₇	—	2	4	no	—
157	C₄×Dic₄₇	—	4	2	no	—
158	#10625329	—	2	4	no	—
159	#10625329	—	2	4	no	—
160	#10625329	—	4	2	no	—
161	#10625329	—	4	2	no	—
162	C₂×C₄₇⋊C₈	—	2	4	no	—
163	C₂×C₄₇⋊C₈	—	4	2	no	—
164	C₂×C₄₇⋊C₈	—	4	2	no	—
165	C₂³×C₄₇	—	2	2	no	—
166	C₂³×C₄₇	—	2	2	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	—	4	4	no	—
169	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
171	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂³×C₄₇	#123	1	2	yes	—
173	C₂³×C₄₇	#123	1	2	yes	—
174	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₄₇	—	2	4	no	—
176	Q₈×C₄₇	—	2	4	no	—
177	D₄×C₄₇	—	2	8	no	—
178	D₄×C₄₇	—	2	8	no	—
179	D₄×C₄₇	—	2	4	no	—
180	D₄×C₄₇	—	2	4	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	4	no	—
186	C₂×C₄×C₄₇	—	2	4	no	—
187	C₂×C₄×C₄₇	—	2	4	no	—
188	C₂×C₄×C₄₇	—	2	4	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	4	no	—
191	C₂×C₄×C₄₇	—	4	4	no	—
192	C₂×C₄×C₄₇	—	4	4	no	—
193	C₂×C₄×C₄₇	—	4	16	no	—
194	C₂×C₄×C₄₇	—	4	4	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
197	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
200	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
201	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
202	C₂×C₄×C₄₇	#117	1	2	yes	—
203	C₂×C₄×C₄₇	#117	1	2	yes	—
204	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
205	C₂×C₄×C₄₇	#123	1	2	yes	—
206	C₂×C₄×C₄₇	#123	1	2	yes	—
207	C₂×C₄×C₄₇	#123	1	2	yes	—
208	C₂×C₄×C₄₇	#123	1	2	yes	—
209	C₂×C₄×C₄₇	#123	1	2	yes	—
210	C₂×C₄×C₄₇	#123	1	2	yes	—
211	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
214	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
215	C₂×Dic₄₇	—	4	4	no	—
216	C₂×Dic₄₇	—	8	4	no	—
217	C₄₇⋊C₈	—	4	4	no	—
218	C₂×#1827	—	47	1	no	maximal, Sylow
219	C₂²×C₄₇	—	2	4	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	4	no	—
222	C₂²×C₄₇	—	4	1	no	—
223	C₂²×C₄₇	—	4	1	no	—
224	C₂²×C₄₇	—	4	2	no	—
225	C₂²×C₄₇	—	4	4	no	—
226	C₂²×C₄₇	—	4	4	no	—
227	C₂²×C₄₇	—	4	4	no	—
228	C₂²×C₄₇	#381	1	1	yes	characteristic
229	C₂²×C₄₇	#381	1	2	yes	—
230	C₂²×C₄₇	#381	1	1	yes	characteristic
231	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₂²×C₄₇	C₂×#123	1	2	yes	—
233	C₄×C₄₇	—	2	4	no	—
234	C₄×C₄₇	—	2	4	no	—
235	C₄×C₄₇	—	4	2	no	—
236	C₄×C₄₇	—	4	4	no	—
237	C₄×C₄₇	#381	1	1	yes	characteristic
238	C₄×C₄₇	#381	1	1	yes	characteristic
239	C₄×C₄₇	#381	1	2	yes	—
240	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
241	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
242	C₄×C₄₇	C₂×#123	1	2	yes	—
243	Dic₄₇	—	8	4	no	—
244	C₂×C₄×#41	D₄₇	1	1	yes	characteristic
245	C₂×#413	—	47	1	no	—
246	C₂×#410	—	47	1	no	—
247	#1827	—	47	8	no	—
248	C₂×#339	—	47	2	no	—
249	C₂×H(3,ℤ/4)	—	47	2	no	—
250	C₂×C₄₇	—	2	2	no	—
251	C₂×C₄₇	—	2	1	no	—
252	C₂×C₄₇	—	2	1	no	—
253	C₂×C₄₇	—	2	2	no	—
254	C₂×C₄₇	—	4	4	no	—
255	C₂×C₄₇	#1827	1	2	yes	complemented
256	C₂×C₄₇	C₂×#381	1	1	yes	characteristic
257	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
258	C₂²×M₁₆	—	47	2	no	—
259	C₄×#41	—	2	2	no	—
260	C₄×#41	—	2	2	no	—
261	C₄×#41	Dic₄₇	1	4	yes	complemented
262	C₄×#41	C₂×D₄₇	1	4	yes	—
263	C₂×C₄×Q₈	—	2	1	no	—
264	C₂×C₄×D₄	—	2	2	no	—
265	C₂×C₄×D₄	—	2	1	no	—
266	C₂×#117	—	47	2	no	—
267	C₂×#117	Dic₄₇	1	2	yes	complemented
268	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
269	C₂²×C₄²	Dic₄₇	1	2	yes	complemented
270	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
271	#413	—	47	4	no	—
272	#413	—	94	2	no	—
273	C₂×#101	—	94	1	no	—
274	C₂×#100	—	94	1	no	—
275	#410	—	47	4	no	—
276	#410	—	94	2	no	—
277	C₂×#99	—	94	2	no	—
278	#339	—	47	8	no	—
279	H(3,ℤ/4)	—	47	8	no	—
280	C₄₇	C₂×#1827	1	1	yes	characteristic, complemented, Sylow
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	C₂×Dic₄₇	1	2	yes	—
286	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
287	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
288	C₂×#41	C₂²×D₄₇	1	2	yes	—
289	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
290	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
291	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
292	C₂³×C₄	—	2	2	no	—
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
295	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
296	C₂×M₁₆	—	47	4	no	—
297	C₂×M₁₆	—	94	2	no	—
298	C₂×M₁₆	—	94	2	no	—
299	C₂×M₁₆	—	94	2	no	—
300	C₂×M₁₆	—	94	2	no	—
301	C₂×M₁₆	—	94	2	no	—
302	C₂²×C₈	—	94	2	no	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	8	no	—
307	C₄×D₄	—	2	8	no	—
308	C₄×D₄	—	2	4	no	—
309	#117	—	2	4	no	—
310	#117	—	2	1	no	—
311	#117	—	2	1	no	—
312	#117	—	47	4	no	—
313	#117	—	94	2	no	—
314	#117	—	94	2	no	—
315	#117	—	94	2	no	—
316	#117	C₂×Dic₄₇	1	2	yes	—
317	#117	C₂×Dic₄₇	1	8	yes	complemented
318	#117	C₂²×D₄₇	1	2	yes	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	94	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	94	2	no	—
325	C₂×C₄²	—	2	2	no	—
326	C₂×C₄²	—	2	4	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	94	2	no	—
331	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
332	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
333	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
334	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
335	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
336	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
337	#101	—	94	4	no	—
338	#100	—	94	4	no	—
339	#99	—	94	8	no	—
340	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
341	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	#41	—	2	4	no	—
345	#41	—	2	4	no	—
346	#41	—	2	4	no	—
347	#41	—	2	4	no	—
348	#41	—	2	4	no	—
349	#41	—	2	4	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
353	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
359	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
360	C₂×D₄	C₂×C₂²⋊D₄₇	1	4	yes	—
361	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	—	4	8	no	—
374	C₂²×C₄	—	188	2	no	—
375	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
376	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
377	C₂²×C₄	#10625350	1	2	yes	—
378	C₂²×C₄	#10625350	1	2	yes	—
379	C₂²×C₄	#10625350	1	2	yes	—
380	C₂²×C₄	#10625350	1	2	yes	—
381	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
382	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
387	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
388	M₁₆	—	94	4	no	—
389	M₁₆	—	94	4	no	—
390	M₁₆	—	188	2	no	—
391	M₁₆	—	188	2	no	—
392	C₂×C₈	—	94	4	no	—
393	C₂×C₈	—	188	2	no	—
394	C₂×C₈	—	188	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	94	4	no	—
399	C₄⋊C₄	—	188	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	94	4	no	—
404	C₂²⋊C₄	—	188	2	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	8	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	94	4	no	—
412	C₄²	—	188	2	no	—
413	C₄²	C₂²×Dic₄₇	1	2	yes	—
414	C₄²	C₂²×Dic₄₇	1	2	yes	—
415	C₄²	C₂²×Dic₄₇	1	4	yes	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	4	no	—
420	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
421	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
422	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
423	C₂³	#13094007	1	2	yes	—
424	C₂³	#13094007	1	2	yes	—
425	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
426	Q₈	—	2	4	no	—
427	Q₈	—	2	4	no	—
428	D₄	—	2	8	no	—
429	D₄	—	2	8	no	—
430	D₄	—	2	4	no	—
431	D₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	16	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	376	4	no	—
448	C₂×C₄	—	188	4	no	—
449	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
450	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
451	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
452	C₂×C₄	#13093983	1	1	yes	characteristic
453	C₂×C₄	#13093983	1	1	yes	characteristic
454	C₂×C₄	#13093983	1	1	yes	characteristic
455	C₂×C₄	#13093983	1	2	yes	—
456	C₂×C₄	#13093983	1	2	yes	—
457	C₂×C₄	#13093983	1	1	yes	characteristic
458	C₂×C₄	#13094007	1	2	yes	—
459	C₂×C₄	#13094007	1	2	yes	—
460	C₂×C₄	#13094007	1	2	yes	—
461	C₂×C₄	#13094007	1	2	yes	—
462	C₂×C₄	#13094007	1	2	yes	—
463	C₂×C₄	#13094007	1	2	yes	—
464	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
466	C₂×C₄	C₂×#10625350	1	2	yes	—
467	C₂×C₄	C₂×#10625350	1	2	yes	—
468	C₈	—	188	4	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	#15688986	1	1	yes	characteristic
479	C₂²	#15688986	1	2	yes	—
480	C₂²	#15688986	1	1	yes	characteristic
481	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
482	C₂²	C₂×#13094007	1	2	yes	—
483	C₄	—	2	4	no	—
484	C₄	—	2	4	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	376	4	no	—
488	C₄	#15688986	1	1	yes	characteristic
489	C₄	#15688986	1	1	yes	characteristic
490	C₄	#15688986	1	2	yes	—
491	C₄	C₂×#13093983	1	1	yes	characteristic
492	C₄	C₂×#13093983	1	1	yes	characteristic
493	C₄	C₂×#13094007	1	2	yes	—
494	C₂	—	2	1	no	—
495	C₂	—	2	2	no	—
496	C₂	—	2	1	no	—
497	C₂	—	2	2	no	—
498	C₂	—	4	4	no	—
499	C₂	#20243492	1	2	yes	direct product factor
500	C₂	C₂×#15688986	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093983
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×#41×C₄₇	C₂
socle	C₂²×C₄₇	#381
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×#41	D₄₇
hypocenter	C₄₇	C₂×#1827
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
3. #20243492	C₂	direct (N × H)
4. C₂×#15688883	C₂	semidirect
5. C₂×#15688879	C₂	semidirect
16. #15688883	C₂²	semidirect
17. #15688879	C₂²	semidirect
21. C₄×#41×C₄₇	C₄	semidirect
26. C₂×#117×C₄₇	C₄	semidirect
28. C₂²×C₄²×C₄₇	C₄	semidirect
72. #117×C₄₇	C₂×C₄	semidirect
87. C₂×C₄²×C₄₇	C₂×C₄	semidirect
255. C₂×C₄₇	#1827	semidirect
261. C₄×#41	Dic₄₇	semidirect
267. C₂×#117	Dic₄₇	semidirect
269. C₂²×C₄²	Dic₄₇	semidirect
280. C₄₇	C₂×#1827	semidirect
317. #117	C₂×Dic₄₇	semidirect
335. C₂×C₄²	C₂×Dic₄₇	semidirect
499. C₂	#20243492	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×#15689107	2
C₂×#15689097	2
#20243492	2
C₂×#15688883	2
C₂×#15688879	2
C₂×C₄×#41×C₄₇	2
C₂×#1827	47

Subgroups — C2×#20243492 #26216122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243492 #26216122