Subgroups — C₂×#15689869 #20257513

Order 6016.

1152 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689869	C₂	1	16	yes	maximal, direct product factor
2	C₂×#13094014	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13094013	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13094010	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13094009	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13094009	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13094007	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13094006	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13094004	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13094002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#13094000	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13093999	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13093998	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13093997	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#13093997	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
18	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
19	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
20	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
27	#13094014	C₂²	1	8	yes	complemented
28	#13094013	C₂²	1	8	yes	complemented
29	#13094010	C₂²	1	8	yes	complemented
30	#13094009	C₂²	1	8	yes	complemented
31	#13094009	C₂²	1	8	yes	complemented
32	#13094007	C₂²	1	8	yes	complemented
33	#13094006	C₂²	1	8	yes	complemented
34	#13094004	C₂²	1	8	yes	complemented
35	#13094002	C₂²	1	8	yes	complemented
36	#13094000	C₂²	1	8	yes	complemented
37	#13093999	C₂²	1	8	yes	complemented
38	#13093998	C₂²	1	8	yes	complemented
39	#13093997	C₂²	1	8	yes	complemented
40	#13093997	C₂²	1	8	yes	complemented
41	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
43	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
49	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
54	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
56	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
61	C₂²⋊Q₈×C₄₇	C₂²	1	8	yes	complemented
62	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
67	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
68	C₂³×D₄₇	C₂³	1	1	yes	characteristic
69	C₂³×D₄₇	C₂³	1	1	yes	characteristic
70	C₂³×D₄₇	C₂³	1	1	yes	characteristic
71	C₂×Q₈×C₄₇	—	4	2	no	—
72	C₂×Q₈×C₄₇	C₂³	1	4	yes	—
73	C₂²×C₄×C₄₇	—	4	2	no	—
74	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
81	C₂×C₂²⋊D₄₇	—	4	2	no	—
82	C₂×C₂²⋊D₄₇	—	4	2	no	—
83	C₂×C₂²⋊D₄₇	—	4	2	no	—
84	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
87	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
88	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
89	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
90	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
91	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
92	C₂×D₁₈₈	—	4	2	no	—
93	C₂×D₁₈₈	—	4	2	no	—
94	C₂×D₁₈₈	—	4	2	no	—
95	C₂×D₁₈₈	C₂³	1	4	yes	—
96	C₂×D₁₈₈	C₂³	1	4	yes	—
97	C₂×D₁₈₈	C₂³	1	4	yes	—
98	C₂×C₄×D₄₇	—	4	2	no	—
99	C₂×C₄×D₄₇	—	4	2	no	—
100	C₂×C₄×D₄₇	—	4	2	no	—
101	C₂×C₄×D₄₇	C₂³	1	4	yes	—
102	C₂×C₄×D₄₇	C₂³	1	4	yes	—
103	C₂×C₄×D₄₇	C₂³	1	4	yes	—
104	C₂×Dic₉₄	—	4	2	no	—
105	C₂×Dic₉₄	C₂³	1	4	yes	—
106	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
107	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
108	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
110	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
111	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
112	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
113	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
114	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
115	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
116	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
121	C₄⋊Dic₄₇	C₂³	1	4	yes	—
122	C₄⋊Dic₄₇	C₂³	1	4	yes	—
123	Dic₄₇⋊C₄	C₂³	1	4	yes	—
124	Dic₄₇⋊C₄	C₂³	1	4	yes	—
125	Dic₄₇⋊C₄	C₂³	1	4	yes	—
126	Dic₄₇⋊C₄	C₂³	1	4	yes	—
127	Dic₄₇⋊C₄	C₂³	1	4	yes	—
128	C₄×Dic₄₇	C₂³	1	4	yes	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	C₂⁴	1	2	yes	—
133	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
134	C₂²×D₄₇	—	2	2	no	—
135	C₂²×D₄₇	—	2	2	no	—
136	C₂²×D₄₇	—	2	2	no	—
137	C₂²×D₄₇	—	2	2	no	—
138	C₂²×D₄₇	—	2	2	no	—
139	C₂²×D₄₇	—	2	2	no	—
140	C₂²×D₄₇	—	2	2	no	—
141	C₂²×D₄₇	—	2	2	no	—
142	C₂²×D₄₇	—	2	2	no	—
143	C₂²×D₄₇	C₂⁴	1	2	yes	—
144	C₂²×D₄₇	C₂⁴	1	2	yes	—
145	C₂²×D₄₇	C₂⁴	1	2	yes	—
146	Q₈×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	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	2	no	—
153	C₂×C₄×C₄₇	—	4	4	no	—
154	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
155	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
156	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
157	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
158	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
159	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
160	C₂²⋊D₄₇	—	4	4	no	—
161	C₂²⋊D₄₇	—	4	4	no	—
162	C₂²⋊D₄₇	—	4	4	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	C₂⁴	1	2	yes	—
169	C₂×Dic₄₇	C₂⁴	1	2	yes	—
170	C₂×Dic₄₇	C₂⁴	1	2	yes	—
171	C₂×Dic₄₇	C₂⁴	1	2	yes	—
172	C₂×Dic₄₇	C₂⁴	1	2	yes	—
173	D₁₈₈	—	4	4	no	—
174	D₁₈₈	—	4	4	no	—
175	D₁₈₈	—	4	4	no	—
176	C₄×D₄₇	—	4	4	no	—
177	C₄×D₄₇	—	4	4	no	—
178	C₄×D₄₇	—	4	4	no	—
179	Dic₉₄	—	4	4	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	4	4	no	—
184	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
185	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
186	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
187	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
188	C₂×D₄₇	—	2	2	no	—
189	C₂×D₄₇	—	2	2	no	—
190	C₂×D₄₇	—	2	2	no	—
191	C₂×D₄₇	—	2	2	no	—
192	C₂×D₄₇	—	2	2	no	—
193	C₂×D₄₇	—	2	2	no	—
194	C₂×D₄₇	—	2	2	no	—
195	C₂×D₄₇	—	2	2	no	—
196	C₂×D₄₇	—	2	2	no	—
197	C₂×D₄₇	—	4	4	no	—
198	C₂×D₄₇	—	4	4	no	—
199	C₂×D₄₇	—	4	4	no	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	2	2	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	2	2	no	—
206	Dic₄₇	—	2	2	no	—
207	Dic₄₇	—	2	2	no	—
208	Dic₄₇	—	2	2	no	—
209	Dic₄₇	—	2	2	no	—
210	Dic₄₇	—	2	2	no	—
211	C₂×#562	—	47	1	no	maximal, Sylow
212	C₂×C₄₇	—	4	2	no	—
213	C₂×C₄₇	#562	1	4	yes	complemented
214	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
217	D₄₇	—	4	2	no	—
218	D₄₇	—	4	2	no	—
219	D₄₇	—	4	2	no	—
220	#562	—	47	16	no	—
221	C₂×#125	—	47	1	no	—
222	C₂×#124	—	47	1	no	—
223	C₂×#124	—	47	1	no	—
224	C₂×#123	—	47	1	no	—
225	C₂×#123	—	47	1	no	—
226	C₂×#123	—	47	1	no	—
227	C₂×#123	—	47	1	no	—
228	C₂×C₂²⋊Q₈	—	47	1	no	—
229	C₂×C₂²⋊Q₈	—	47	1	no	—
230	C₂×C₂²⋊Q₈	—	47	1	no	—
231	C₂×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
232	C₂×#121	—	47	1	no	—
233	C₂×#121	—	47	1	no	—
234	C₂×#121	—	47	1	no	—
235	C₂×#121	—	47	1	no	—
236	C₄₇	C₂×#562	1	1	yes	characteristic, complemented, Sylow
237	C₂²×Q₈	—	47	1	no	—
238	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
239	C₂²×D₄	—	47	1	no	—
240	C₂²×D₄	—	47	1	no	—
241	C₂²×D₄	—	47	1	no	—
242	C₂²×D₄	—	47	1	no	—
243	C₂²×D₄	—	47	1	no	—
244	C₂²×D₄	—	47	1	no	—
245	C₂³×C₄	—	47	1	no	—
246	C₂³×C₄	—	47	1	no	—
247	C₂³×C₄	—	47	1	no	—
248	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
249	#125	—	47	8	no	—
250	#124	—	47	8	no	—
251	#124	—	47	8	no	—
252	#123	—	47	8	no	—
253	#123	—	47	8	no	—
254	#123	—	47	8	no	—
255	#123	—	47	8	no	—
256	C₂²⋊Q₈	—	47	8	no	—
257	C₂²⋊Q₈	—	47	8	no	—
258	C₂²⋊Q₈	—	47	8	no	—
259	C₂²⋊Q₈	C₂×D₄₇	1	8	yes	complemented
260	#121	—	47	8	no	—
261	#121	—	47	8	no	—
262	#121	—	47	8	no	—
263	#121	—	47	8	no	—
264	C₂×C₄⋊C₄	—	47	1	no	—
265	C₂×C₄⋊C₄	—	47	1	no	—
266	C₂×C₄⋊C₄	—	47	1	no	—
267	C₂×C₄⋊C₄	—	47	1	no	—
268	C₂×C₄⋊C₄	—	47	1	no	—
269	C₂×C₄⋊C₄	—	47	1	no	—
270	C₂×C₄⋊C₄	—	47	1	no	—
271	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	47	1	no	—
275	C₂×C₂²⋊C₄	—	47	1	no	—
276	C₂×C₂²⋊C₄	—	47	1	no	—
277	C₂×C₂²⋊C₄	—	47	1	no	—
278	C₂×C₂²⋊C₄	—	47	1	no	—
279	C₂×C₂²⋊C₄	—	47	1	no	—
280	C₂×C₂²⋊C₄	—	47	1	no	—
281	C₂×C₂²⋊C₄	—	47	1	no	—
282	C₂×C₂²⋊C₄	—	47	1	no	—
283	C₂×C₂²⋊C₄	—	47	1	no	—
284	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
286	C₂×C₄²	—	47	1	no	—
287	C₂⁴	—	47	1	no	—
288	C₂⁴	—	47	1	no	—
289	C₂⁴	—	47	1	no	—
290	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	47	4	no	—
293	C₂×Q₈	—	188	2	no	—
294	C₂×Q₈	C₂²×D₄₇	1	4	yes	—
295	C₂×D₄	—	47	4	no	—
296	C₂×D₄	—	47	4	no	—
297	C₂×D₄	—	47	4	no	—
298	C₂×D₄	—	47	4	no	—
299	C₂×D₄	—	47	4	no	—
300	C₂×D₄	—	47	4	no	—
301	C₂×D₄	—	188	2	no	—
302	C₂×D₄	—	188	2	no	—
303	C₂×D₄	—	188	2	no	—
304	C₂×D₄	—	188	2	no	—
305	C₂×D₄	—	188	2	no	—
306	C₂×D₄	—	188	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	47	1	no	—
309	C₂²×C₄	—	47	1	no	—
310	C₂²×C₄	—	47	1	no	—
311	C₂²×C₄	—	47	1	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	47	4	no	—
314	C₂²×C₄	—	47	4	no	—
315	C₂²×C₄	—	47	4	no	—
316	C₂²×C₄	—	188	2	no	—
317	C₂²×C₄	—	188	2	no	—
318	C₂²×C₄	—	188	2	no	—
319	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
326	C₄⋊C₄	—	47	4	no	—
327	C₄⋊C₄	—	47	4	no	—
328	C₄⋊C₄	—	47	4	no	—
329	C₄⋊C₄	—	47	4	no	—
330	C₄⋊C₄	—	47	4	no	—
331	C₄⋊C₄	—	47	4	no	—
332	C₄⋊C₄	—	47	4	no	—
333	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
334	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
335	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
336	C₂²⋊C₄	—	47	4	no	—
337	C₂²⋊C₄	—	47	4	no	—
338	C₂²⋊C₄	—	47	4	no	—
339	C₂²⋊C₄	—	47	4	no	—
340	C₂²⋊C₄	—	47	4	no	—
341	C₂²⋊C₄	—	47	4	no	—
342	C₂²⋊C₄	—	47	4	no	—
343	C₂²⋊C₄	—	47	4	no	—
344	C₂²⋊C₄	—	47	4	no	—
345	C₂²⋊C₄	—	47	4	no	—
346	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
348	C₄²	—	47	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	47	2	no	—
353	C₂³	—	47	2	no	—
354	C₂³	—	47	2	no	—
355	C₂³	—	94	2	no	—
356	C₂³	—	94	2	no	—
357	C₂³	—	94	2	no	—
358	C₂³	—	94	2	no	—
359	C₂³	—	94	2	no	—
360	C₂³	—	94	2	no	—
361	C₂³	—	94	2	no	—
362	C₂³	—	94	2	no	—
363	C₂³	—	94	2	no	—
364	C₂³	C₂³×D₄₇	1	2	yes	—
365	C₂³	C₂³×D₄₇	1	1	yes	characteristic
366	Q₈	—	4	4	no	—
367	Q₈	—	188	4	no	—
368	D₄	—	188	4	no	—
369	D₄	—	188	4	no	—
370	D₄	—	188	4	no	—
371	D₄	—	188	4	no	—
372	D₄	—	188	4	no	—
373	D₄	—	188	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	47	2	no	—
382	C₂×C₄	—	47	2	no	—
383	C₂×C₄	—	47	2	no	—
384	C₂×C₄	—	47	2	no	—
385	C₂×C₄	—	47	2	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	94	2	no	—
389	C₂×C₄	—	94	2	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	188	4	no	—
392	C₂×C₄	—	188	4	no	—
393	C₂×C₄	—	188	4	no	—
394	C₂×C₄	C₂³×D₄₇	1	2	yes	—
395	C₂×C₄	C₂³×D₄₇	1	2	yes	—
396	C₂×C₄	C₂³×D₄₇	1	2	yes	—
397	C₂×C₄	C₂³×D₄₇	1	2	yes	—
398	C₂×C₄	C₂³×D₄₇	1	2	yes	—
399	C₂×C₄	C₂³×D₄₇	1	2	yes	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	94	2	no	—
405	C₂²	—	94	2	no	—
406	C₂²	—	94	2	no	—
407	C₂²	—	94	2	no	—
408	C₂²	—	94	2	no	—
409	C₂²	—	94	2	no	—
410	C₂²	—	94	2	no	—
411	C₂²	—	94	2	no	—
412	C₂²	—	94	2	no	—
413	C₂²	—	188	4	no	—
414	C₂²	—	188	4	no	—
415	C₂²	—	188	4	no	—
416	C₂²	#13094069	1	2	yes	—
417	C₂²	#13094070	1	2	yes	—
418	C₂²	#13094072	1	2	yes	—
419	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	94	2	no	—
427	C₄	—	94	2	no	—
428	C₄	—	94	2	no	—
429	C₄	—	94	2	no	—
430	C₄	—	94	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	188	2	no	—
433	C₂	—	188	2	no	—
434	C₂	—	188	2	no	—
435	C₂	#15689869	1	4	yes	direct product factor
436	C₂	C₂×#13094069	1	1	yes	characteristic
437	C₂	C₂×#13094070	1	1	yes	characteristic
438	C₂	C₂×#13094072	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₂×C₂²⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	C₂×#562
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #15689869	C₂	direct (N × H)
2. C₂×#13094014	C₂	semidirect
3. C₂×#13094013	C₂	semidirect
4. C₂×#13094010	C₂	semidirect
5. C₂×#13094009	C₂	semidirect
6. C₂×#13094009	C₂	semidirect
7. C₂×#13094007	C₂	semidirect
8. C₂×#13094006	C₂	semidirect
9. C₂×#13094004	C₂	semidirect
10. C₂×#13094002	C₂	semidirect
11. C₂×#13094000	C₂	semidirect
12. C₂×#13093999	C₂	semidirect
13. C₂×#13093998	C₂	semidirect
14. C₂×#13093997	C₂	semidirect
15. C₂×#13093997	C₂	semidirect
16. C₂×C₂²⋊Q₈×C₄₇	C₂	semidirect
27. #13094014	C₂²	semidirect
28. #13094013	C₂²	semidirect
29. #13094010	C₂²	semidirect
30. #13094009	C₂²	semidirect
31. #13094009	C₂²	semidirect
32. #13094007	C₂²	semidirect
33. #13094006	C₂²	semidirect
34. #13094004	C₂²	semidirect
35. #13094002	C₂²	semidirect
36. #13094000	C₂²	semidirect
37. #13093999	C₂²	semidirect
38. #13093998	C₂²	semidirect
39. #13093997	C₂²	semidirect
40. #13093997	C₂²	semidirect
61. C₂²⋊Q₈×C₄₇	C₂²	semidirect
213. C₂×C₄₇	#562	semidirect
231. C₂×C₂²⋊Q₈	D₄₇	semidirect
236. C₄₇	C₂×#562	semidirect
259. C₂²⋊Q₈	C₂×D₄₇	semidirect
435. C₂	#15689869	direct (N × H)

Subgroups — C2×#15689869 #20257513

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689869 #20257513