Subgroups — C₂×#20253222 #27083840

Order 12032.

2234 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689751	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689597	C₂	1	1	yes	maximal, characteristic
3	#20253222	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689426	C₂	1	2	yes	maximal, complemented
5	C₂×#15689422	C₂	1	2	yes	maximal, complemented
6	C₂×#15689412	C₂	1	2	yes	maximal, complemented
7	C₂×#15689402	C₂	1	2	yes	maximal, complemented
8	C₂×#15689166	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689149	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15689127	C₂	1	1	yes	maximal, characteristic
11	C₂²×#13093946	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
14	C₂²×#10625329	C₂²	1	1	yes	characteristic
15	#15689751	—	2	4	no	—
16	#15689751	C₂²	1	8	yes	complemented
17	C₂×#13094024	—	2	1	no	—
18	C₂×#13094023	C₂²	1	2	yes	complemented
19	C₂×#13094016	—	2	1	no	—
20	C₂×#13094015	C₂²	1	2	yes	complemented
21	C₂×#13094001	—	2	2	no	—
22	#15689597	—	2	4	no	—
23	#15689597	C₂²	1	8	yes	—
24	C₂×C₄×D₁₈₈	—	2	1	no	—
25	C₂×C₄×D₁₈₈	—	2	1	no	—
26	C₂×#13093986	C₂²	1	2	yes	—
27	C₂×#13093986	C₂²	1	2	yes	—
28	C₂×#13093983	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×D₄₇	—	2	2	no	—
31	#15689426	C₂²	1	16	yes	complemented
32	#15689422	C₂²	1	16	yes	complemented
33	#15689412	C₂²	1	16	yes	complemented
34	#15689402	C₂²	1	16	yes	complemented
35	#15689166	C₂²	1	8	yes	complemented
36	C₂×#13093957	C₂²	1	2	yes	complemented
37	C₂×#13093955	C₂²	1	2	yes	complemented
38	#15689149	C₂²	1	8	yes	complemented
39	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	complemented
40	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	complemented
41	#15689127	C₂²	1	8	yes	—
42	C₂×#13093946	C₂²	1	8	yes	—
43	C₂×#13093946	C₂²	1	2	yes	—
44	C₂×#13093946	C₂²	1	2	yes	—
45	C₂×#13093944	C₂²	1	2	yes	—
46	C₂×#13093944	C₂²	1	2	yes	—
47	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
48	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
50	C₄₇×#427	C₂²	1	8	yes	complemented
51	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
52	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic, complemented
55	C₂⁴×D₄₇	—	2	1	no	—
56	C₂²×Dic₉₄	—	2	2	no	—
57	C₂²×D₁₈₈	—	2	1	no	—
58	C₂²×D₁₈₈	—	2	2	no	—
59	C₂²×D₁₈₈	—	2	4	no	—
60	C₂²×D₁₈₈	Q₈	1	8	yes	complemented
61	C₂²×D₁₈₈	C₂³	1	2	yes	—
62	C₂²×D₁₈₈	C₂³	1	4	yes	—
63	C₂³×Dic₄₇	—	2	1	no	—
64	C₂²×C₄×D₄₇	—	2	2	no	—
65	C₂²×C₄×D₄₇	—	2	2	no	—
66	C₂×#10625329	—	2	4	no	—
67	C₂×#10625329	C₂³	1	4	yes	—
68	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
69	#13094024	—	2	8	no	—
70	#13094023	—	2	4	no	—
71	#13094023	C₂³	1	8	yes	complemented
72	#13094016	—	2	8	no	—
73	#13094015	—	2	4	no	—
74	#13094015	C₂³	1	8	yes	complemented
75	#13094001	—	2	16	no	—
76	C₄×D₁₈₈	—	2	8	no	—
77	C₄×D₁₈₈	—	2	8	no	—
78	#13093986	—	2	4	no	—
79	#13093986	—	2	4	no	—
80	#13093986	C₂³	1	8	yes	—
81	#13093986	C₂³	1	8	yes	—
82	#13093983	D₄	1	4	yes	—
83	#13093983	C₂³	1	4	yes	—
84	C₂×C₄⋊Dic₄₇	—	2	2	no	—
85	C₂×C₄⋊Dic₄₇	—	2	1	no	—
86	C₂×C₄⋊Dic₄₇	—	2	2	no	—
87	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
88	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
90	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
91	C₂×Dic₄₇⋊C₄	—	2	2	no	—
92	C₂×Dic₄₇⋊C₄	—	2	2	no	—
93	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
94	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
95	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
96	C₂²⋊C₄×D₄₇	—	2	16	no	—
97	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
98	#13093957	C₂³	1	8	yes	complemented
99	#13093955	C₂³	1	8	yes	complemented
100	Dic₄₇⋊C₈	C₂³	1	8	yes	complemented
101	Dic₄₇⋊C₈	C₂³	1	8	yes	complemented
102	#13093946	C₂³	1	8	yes	—
103	#13093946	C₂³	1	8	yes	—
104	#13093944	C₂³	1	8	yes	—
105	#13093944	C₂³	1	8	yes	—
106	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₇	—	2	4	no	—
108	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
111	#117×C₄₇	—	2	2	no	—
112	#117×C₄₇	—	2	2	no	—
113	#117×C₄₇	C₂³	1	4	yes	—
114	#117×C₄₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
121	C₂×C₄²×C₄₇	—	2	1	no	—
122	C₂×C₄²×C₄₇	—	2	1	no	—
123	#107×C₄₇	C₂³	1	4	yes	complemented
124	#107×C₄₇	C₂³	1	4	yes	complemented
125	#106×C₄₇	C₂³	1	4	yes	complemented
126	#106×C₄₇	C₂³	1	4	yes	complemented
127	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂³×D₄₇	—	2	2	no	—
129	C₂³×D₄₇	—	2	8	no	—
130	C₂³×D₄₇	—	2	4	no	—
131	C₂³×D₄₇	—	8	2	no	—
132	C₂³×D₄₇	—	8	2	no	—
133	C₂²×C₄×C₄₇	—	2	1	no	—
134	C₂²×C₄×C₄₇	—	2	1	no	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	—	2	1	no	—
137	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
140	C₂²×C₄×C₄₇	#41	1	4	yes	—
141	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
143	C₂²×Dic₄₇	—	2	2	no	—
144	C₂²×Dic₄₇	—	2	4	no	—
145	C₂²×Dic₄₇	—	8	2	no	—
146	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
147	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
148	C₂×D₁₈₈	—	2	16	no	—
149	C₂×D₁₈₈	—	2	8	no	—
150	C₂×D₁₈₈	—	2	2	no	—
151	C₂×D₁₈₈	—	2	4	no	—
152	C₂×D₁₈₈	—	2	4	no	—
153	C₂×D₁₈₈	—	2	8	no	—
154	C₂×D₁₈₈	C₂×Q₈	1	8	yes	—
155	C₂×D₁₈₈	C₂×Q₈	1	16	yes	complemented
156	C₂×D₁₈₈	C₂⁴	1	4	yes	—
157	C₂×C₄×D₄₇	—	2	8	no	—
158	C₂×C₄×D₄₇	—	2	8	no	—
159	C₂×C₄×D₄₇	—	8	4	no	—
160	C₂×C₄×D₄₇	—	8	4	no	—
161	C₂×Dic₉₄	—	2	8	no	—
162	C₂×Dic₉₄	—	8	4	no	—
163	C₂×C₈×C₄₇	—	2	2	no	—
164	C₂×C₈×C₄₇	—	2	2	no	—
165	C₂×C₈×C₄₇	—	2	8	no	—
166	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
167	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
168	C₄⋊C₄×C₄₇	—	2	1	no	—
169	C₄⋊C₄×C₄₇	—	2	1	no	—
170	C₄⋊C₄×C₄₇	—	2	1	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
173	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
174	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
175	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
176	C₂²⋊C₄×C₄₇	—	2	4	no	—
177	C₂²⋊C₄×C₄₇	—	2	4	no	—
178	C₄²×C₄₇	—	2	4	no	—
179	C₄²×C₄₇	—	2	4	no	—
180	C₂²⋊Dic₄₇	C₂×D₄	1	8	yes	—
181	(C₂×D₄₇)⋊C₄	—	2	8	no	—
182	(C₂×D₄₇)⋊C₄	—	2	8	no	—
183	C₄⋊Dic₄₇	—	2	2	no	—
184	C₄⋊Dic₄₇	—	2	4	no	—
185	C₄⋊Dic₄₇	—	2	8	no	—
186	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
187	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
188	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
189	Dic₄₇⋊C₄	—	2	8	no	—
190	Dic₄₇⋊C₄	—	2	8	no	—
191	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
192	C₄×Dic₄₇	C₂⁴	1	4	yes	—
193	#10625329	—	2	8	no	—
194	C₂×C₄₇⋊C₈	—	2	4	no	—
195	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
196	C₂³×C₄₇	—	2	2	no	—
197	C₂³×C₄₇	—	2	2	no	—
198	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
199	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
200	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
201	C₂²×D₄₇	—	2	8	no	—
202	C₂²×D₄₇	—	2	4	no	—
203	C₂²×D₄₇	—	2	16	no	—
204	C₂²×D₄₇	—	4	4	no	—
205	C₂²×D₄₇	—	4	4	no	—
206	C₂²×D₄₇	—	8	16	no	—
207	C₂²×D₄₇	—	8	4	no	—
208	C₂²×D₄₇	—	8	4	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	2	2	no	—
212	C₂×C₄×C₄₇	—	2	2	no	—
213	C₂×C₄×C₄₇	—	4	2	no	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	2	no	—
217	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
218	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
219	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
222	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
223	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
224	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
225	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
226	C₂×Dic₄₇	—	2	4	no	—
227	C₂×Dic₄₇	—	2	4	no	—
228	C₂×Dic₄₇	—	2	4	no	—
229	C₂×Dic₄₇	—	4	4	no	—
230	C₂×Dic₄₇	—	8	4	no	—
231	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
232	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
233	D₁₈₈	—	2	8	no	—
234	D₁₈₈	—	2	16	no	—
235	D₁₈₈	—	2	4	no	—
236	D₁₈₈	C₂²×Q₈	1	8	yes	—
237	C₄×D₄₇	—	8	8	no	—
238	C₄×D₄₇	—	8	8	no	—
239	Dic₉₄	—	8	8	no	—
240	C₈×C₄₇	—	2	2	no	—
241	C₈×C₄₇	—	2	2	no	—
242	C₄₇⋊C₈	—	2	4	no	—
243	C₂×#3081	—	47	1	no	maximal, Sylow
244	C₂²×C₄₇	—	2	8	no	—
245	C₂²×C₄₇	—	2	2	no	—
246	C₂²×C₄₇	—	2	2	no	—
247	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	4	yes	—
248	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
249	C₂²×C₄₇	#576	1	2	yes	—
250	C₂²×C₄₇	#577	1	2	yes	—
251	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
252	C₂×D₄₇	—	2	8	no	—
253	C₂×D₄₇	—	4	16	no	—
254	C₂×D₄₇	—	4	4	no	—
255	C₂×D₄₇	—	4	4	no	—
256	C₂×D₄₇	—	8	16	no	—
257	C₄×C₄₇	—	4	2	no	—
258	C₄×C₄₇	—	4	2	no	—
259	C₄×C₄₇	—	4	2	no	—
260	C₄×C₄₇	—	4	2	no	—
261	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
262	C₄×C₄₇	C₂×C₂²⋊Q₈	1	4	yes	—
263	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
264	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
265	Dic₄₇	—	2	4	no	—
266	Dic₄₇	—	2	4	no	—
267	Dic₄₇	—	4	4	no	—
268	C₂×#544	—	47	1	no	—
269	C₂×#518	—	47	1	no	—
270	#3081	—	47	16	no	—
271	C₂×#478	—	47	2	no	—
272	C₂×#478	—	47	2	no	—
273	C₂×#476	—	47	2	no	—
274	C₂×#474	—	47	2	no	—
275	C₂×#428	—	47	1	no	—
276	C₂×#427	D₄₇	1	1	yes	characteristic, complemented
277	C₂×#424	—	47	1	no	—
278	C₂×#418	—	47	1	no	—
279	C₂²×#102	—	47	1	no	—
280	C₂×C₄₇	—	2	4	no	—
281	C₂×C₄₇	#3081	1	4	yes	complemented
282	C₂×C₄₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
283	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
284	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
285	D₄₇	—	4	8	no	—
286	C₂³×D₄	—	47	1	no	—
287	C₂²×M₁₆	—	47	1	no	—
288	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
289	#544	—	47	8	no	—
290	#544	—	94	4	no	—
291	C₂×C₄⋊Q₈	—	47	2	no	—
292	C₂×C₄⋊Q₈	—	94	1	no	—
293	C₂×#125	—	47	2	no	—
294	C₂×#125	—	94	1	no	—
295	C₂×C₂²⋊Q₈	—	94	2	no	—
296	#518	—	47	8	no	—
297	#518	—	94	4	no	—
298	C₂×C₄×D₄	—	47	2	no	—
299	C₂×C₄×D₄	—	47	2	no	—
300	C₂×C₄×D₄	—	94	1	no	—
301	C₂×C₄×D₄	—	94	1	no	—
302	C₂×#117	—	47	1	no	—
303	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
304	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	—	47	1	no	—
306	C₂²×C₂²⋊C₄	—	94	2	no	—
307	#478	—	47	16	no	—
308	#478	—	47	16	no	—
309	#476	—	47	16	no	—
310	#474	—	47	16	no	—
311	#428	—	47	8	no	—
312	#427	C₂×D₄₇	1	8	yes	complemented
313	C₂×#107	—	47	2	no	—
314	C₂×#107	C₂×D₄₇	1	1	yes	characteristic, complemented
315	C₂×#107	C₂×D₄₇	1	1	yes	characteristic, complemented
316	C₂×#106	—	47	2	no	—
317	C₂×#106	C₂×D₄₇	1	1	yes	characteristic, complemented
318	C₂×#106	C₂×D₄₇	1	1	yes	characteristic, complemented
319	#424	—	47	8	no	—
320	C₂×C₄⋊C₈	—	47	2	no	—
321	C₂×C₄⋊C₈	—	47	2	no	—
322	#418	—	47	8	no	—
323	C₂×#102	—	47	2	no	—
324	C₂×#102	—	47	2	no	—
325	C₂×#102	—	47	8	no	—
326	C₂×#102	—	47	2	no	—
327	C₂×#102	—	47	2	no	—
328	C₄₇	C₂×#3081	1	1	yes	characteristic, complemented, Sylow
329	C₂⁵	—	94	1	no	—
330	C₂²×Q₈	—	94	2	no	—
331	C₂²×D₄	—	47	8	no	—
332	C₂²×D₄	—	47	2	no	—
333	C₂²×D₄	—	47	4	no	—
334	C₂²×D₄	—	94	4	no	—
335	C₂²×D₄	—	94	1	no	—
336	C₂²×D₄	—	94	2	no	—
337	C₂³×C₄	—	94	2	no	—
338	C₂³×C₄	—	94	2	no	—
339	C₂³×C₄	—	94	1	no	—
340	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
341	C₂×M₁₆	—	47	4	no	—
342	C₂×M₁₆	—	94	4	no	—
343	C₂²×C₈	—	2	4	no	—
344	C₂²×C₈	—	47	2	no	—
345	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
347	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
348	C₄⋊Q₈	—	47	8	no	—
349	C₄⋊Q₈	—	94	8	no	—
350	C₄⋊Q₈	—	94	4	no	—
351	#125	—	47	8	no	—
352	#125	—	94	8	no	—
353	#125	—	94	4	no	—
354	C₂²⋊Q₈	—	94	16	no	—
355	C₄×D₄	—	47	8	no	—
356	C₄×D₄	—	47	8	no	—
357	C₄×D₄	—	94	8	no	—
358	C₄×D₄	—	94	8	no	—
359	C₄×D₄	—	94	4	no	—
360	C₄×D₄	—	94	4	no	—
361	#117	—	2	2	no	—
362	#117	—	2	2	no	—
363	#117	—	47	4	no	—
364	#117	—	47	4	no	—
365	#117	C₂²×D₄₇	1	4	yes	—
366	#117	C₂²×D₄₇	1	4	yes	—
367	C₂×C₄⋊C₄	—	47	1	no	—
368	C₂×C₄⋊C₄	—	47	1	no	—
369	C₂×C₄⋊C₄	—	47	2	no	—
370	C₂×C₄⋊C₄	—	47	4	no	—
371	C₂×C₄⋊C₄	—	94	2	no	—
372	C₂×C₄⋊C₄	—	94	2	no	—
373	C₂×C₄⋊C₄	—	94	2	no	—
374	C₂×C₄⋊C₄	—	94	1	no	—
375	C₂×C₄⋊C₄	—	94	2	no	—
376	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	47	2	no	—
383	C₂×C₂²⋊C₄	—	94	16	no	—
384	C₂×C₂²⋊C₄	—	94	2	no	—
385	C₂×C₂²⋊C₄	—	94	2	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	47	2	no	—
389	#107	—	47	8	no	—
390	#107	C₂²×D₄₇	1	4	yes	complemented
391	#107	C₂²×D₄₇	1	4	yes	complemented
392	#106	—	47	8	no	—
393	#106	C₂²×D₄₇	1	4	yes	complemented
394	#106	C₂²×D₄₇	1	4	yes	complemented
395	C₄⋊C₈	—	47	8	no	—
396	C₄⋊C₈	—	47	8	no	—
397	#102	—	47	8	no	—
398	#102	—	47	8	no	—
399	#102	—	47	8	no	—
400	#102	—	47	8	no	—
401	C₂⁴	—	94	8	no	—
402	C₂⁴	—	94	4	no	—
403	C₂⁴	—	94	2	no	—
404	C₂⁴	—	376	2	no	—
405	C₂⁴	—	376	2	no	—
406	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
407	C₂×Q₈	—	94	8	no	—
408	C₂×Q₈	—	376	4	no	—
409	C₂×D₄	—	47	8	no	—
410	C₂×D₄	—	47	16	no	—
411	C₂×D₄	—	47	4	no	—
412	C₂×D₄	—	94	16	no	—
413	C₂×D₄	—	94	8	no	—
414	C₂×D₄	—	94	4	no	—
415	C₂×D₄	—	94	2	no	—
416	C₂×D₄	—	94	4	no	—
417	C₂×D₄	—	94	8	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	47	2	no	—
423	C₂²×C₄	—	47	2	no	—
424	C₂²×C₄	—	94	8	no	—
425	C₂²×C₄	—	94	8	no	—
426	C₂²×C₄	—	94	4	no	—
427	C₂²×C₄	—	94	2	no	—
428	C₂²×C₄	—	376	4	no	—
429	C₂²×C₄	—	376	4	no	—
430	C₂²×C₄	—	376	2	no	—
431	C₂²×C₄	#10625350	1	4	yes	—
432	C₂²×C₄	D₄×D₄₇	1	2	yes	—
433	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
434	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
435	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
436	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
437	M₁₆	—	94	8	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	8	no	—
441	C₂×C₈	—	47	4	no	—
442	C₂×C₈	—	94	4	no	—
443	C₂×C₈	C₂³×D₄₇	1	2	yes	—
444	C₂×C₈	C₂³×D₄₇	1	2	yes	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	47	4	no	—
450	C₄⋊C₄	—	47	4	no	—
451	C₄⋊C₄	—	47	4	no	—
452	C₄⋊C₄	—	94	8	no	—
453	C₄⋊C₄	—	94	8	no	—
454	C₄⋊C₄	—	94	8	no	—
455	C₄⋊C₄	—	94	4	no	—
456	C₄⋊C₄	—	94	2	no	—
457	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
458	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
459	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
460	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	47	8	no	—
464	C₂²⋊C₄	—	94	8	no	—
465	C₂²⋊C₄	—	94	8	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	47	4	no	—
469	C₄²	—	47	4	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	94	16	no	—
473	C₂³	—	94	8	no	—
474	C₂³	—	94	4	no	—
475	C₂³	—	376	16	no	—
476	C₂³	—	376	4	no	—
477	C₂³	—	376	4	no	—
478	C₂³	—	188	4	no	—
479	C₂³	—	188	4	no	—
480	C₂³	#13094002	1	4	yes	—
481	C₂³	C₂×D₄×D₄₇	1	2	yes	—
482	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
483	Q₈	—	376	8	no	—
484	D₄	—	47	8	no	—
485	D₄	—	94	8	no	—
486	D₄	—	94	16	no	—
487	D₄	—	94	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	47	4	no	—
497	C₂×C₄	—	47	4	no	—
498	C₂×C₄	—	94	4	no	—
499	C₂×C₄	—	94	4	no	—
500	C₂×C₄	—	94	4	no	—
501	C₂×C₄	—	376	8	no	—
502	C₂×C₄	—	376	8	no	—
503	C₂×C₄	—	376	4	no	—
504	C₂×C₄	—	188	4	no	—
505	C₂×C₄	#13094002	1	8	yes	—
506	C₂×C₄	#13094002	1	4	yes	—
507	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
508	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
509	C₂×C₄	C₂×Q₈×D₄₇	1	4	yes	—
510	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
511	C₂×C₄	C₂×#10625350	1	2	yes	—
512	C₂×C₄	C₂×#10625350	1	4	yes	—
513	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
514	C₈	—	2	2	no	—
515	C₈	—	2	2	no	—
516	C₈	—	94	4	no	—
517	C₂²	—	2	8	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	94	8	no	—
521	C₂²	—	376	16	no	—
522	C₂²	—	188	16	no	—
523	C₂²	—	188	4	no	—
524	C₂²	—	188	4	no	—
525	C₂²	C₂×#13094002	1	4	yes	—
526	C₂²	C₂×#13094002	1	2	yes	—
527	C₂²	#15689925	1	2	yes	—
528	C₂²	#15689930	1	2	yes	—
529	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	94	4	no	—
535	C₄	—	94	4	no	—
536	C₄	—	188	4	no	—
537	C₄	C₂×#13094002	1	4	yes	—
538	C₄	C₂×#13094002	1	2	yes	—
539	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
540	C₄	C₂²×#10625350	1	1	yes	characteristic
541	C₂	—	2	4	no	—
542	C₂	—	188	8	no	—
543	C₂	#20253222	1	4	yes	direct product factor
544	C₂	C₂²×#13094002	1	1	yes	characteristic
545	C₂	C₂×#15689925	1	1	yes	characteristic
546	C₂	C₂×#15689930	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#427	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₁₈₈	C₂²
hypercenter	C₂×#427	D₄₇
hypocenter	C₄₇	C₂×#3081
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
1. C₂×#15689751	C₂	semidirect
3. #20253222	C₂	direct (N × H)
4. C₂×#15689426	C₂	semidirect
5. C₂×#15689422	C₂	semidirect
6. C₂×#15689412	C₂	semidirect
7. C₂×#15689402	C₂	semidirect
8. C₂×#15689166	C₂	semidirect
9. C₂×#15689149	C₂	semidirect
12. C₂×C₄₇×#427	C₂	semidirect
16. #15689751	C₂²	semidirect
18. C₂×#13094023	C₂²	semidirect
20. C₂×#13094015	C₂²	semidirect
31. #15689426	C₂²	semidirect
32. #15689422	C₂²	semidirect
33. #15689412	C₂²	semidirect
34. #15689402	C₂²	semidirect
35. #15689166	C₂²	semidirect
36. C₂×#13093957	C₂²	semidirect
37. C₂×#13093955	C₂²	semidirect
38. #15689149	C₂²	semidirect
39. C₂×Dic₄₇⋊C₈	C₂²	semidirect
40. C₂×Dic₄₇⋊C₈	C₂²	semidirect
50. C₄₇×#427	C₂²	semidirect
51. C₂×#107×C₄₇	C₂²	semidirect
52. C₂×#107×C₄₇	C₂²	semidirect
53. C₂×#106×C₄₇	C₂²	semidirect
54. C₂×#106×C₄₇	C₂²	semidirect
60. C₂²×D₁₈₈	Q₈	semidirect
71. #13094023	C₂³	semidirect
74. #13094015	C₂³	semidirect
98. #13093957	C₂³	semidirect
99. #13093955	C₂³	semidirect
100. Dic₄₇⋊C₈	C₂³	semidirect
101. Dic₄₇⋊C₈	C₂³	semidirect
123. #107×C₄₇	C₂³	semidirect
124. #107×C₄₇	C₂³	semidirect
125. #106×C₄₇	C₂³	semidirect
126. #106×C₄₇	C₂³	semidirect
155. C₂×D₁₈₈	C₂×Q₈	semidirect
276. C₂×#427	D₄₇	semidirect
281. C₂×C₄₇	#3081	semidirect
312. #427	C₂×D₄₇	semidirect
314. C₂×#107	C₂×D₄₇	semidirect
315. C₂×#107	C₂×D₄₇	semidirect
317. C₂×#106	C₂×D₄₇	semidirect
318. C₂×#106	C₂×D₄₇	semidirect
328. C₄₇	C₂×#3081	semidirect
390. #107	C₂²×D₄₇	semidirect
391. #107	C₂²×D₄₇	semidirect
393. #106	C₂²×D₄₇	semidirect
394. #106	C₂²×D₄₇	semidirect
543. C₂	#20253222	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×#15689751	2
C₂×#15689597	2
#20253222	2
C₂×#15689426	2
C₂×#15689422	2
C₂×#15689412	2
C₂×#15689402	2
C₂×#15689166	2
C₂×#15689149	2
C₂×#15689127	2
C₂²×#13093946	2
C₂×C₄₇×#427	2
C₂×#3081	47

Subgroups — C2×#20253222 #27083840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20253222 #27083840