Subgroups — C₂×#15689816 #20256904

Order 6016.

1252 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	#15689816	C₂	1	16	yes	maximal, direct product factor
2	C₂×#13094019	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13094017	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13094014	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13094006	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13094005	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13093996	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13093996	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13093996	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×(C₂²⋊D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13093980	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#121×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
20	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
21	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
25	#13094019	C₂²	1	8	yes	complemented
26	#13094017	C₂²	1	8	yes	complemented
27	#13094014	C₂²	1	8	yes	complemented
28	#13094006	C₂²	1	8	yes	complemented
29	#13094005	C₂²	1	8	yes	complemented
30	#13093996	C₂²	1	8	yes	complemented
31	#13093996	C₂²	1	8	yes	complemented
32	#13093996	C₂²	1	8	yes	complemented
33	D₄×Dic₄₇	C₂²	1	8	yes	complemented
34	D₄×Dic₄₇	C₂²	1	8	yes	complemented
35	C₄×C₂²⋊D₄₇	C₂²	1	8	yes	complemented
36	(C₂²⋊D₄₇)⋊C₄	C₂²	1	8	yes	complemented
37	#13093980	C₂²	1	8	yes	complemented
38	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
40	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×Dic₄₇⋊C₄	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	8	yes	complemented
48	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₄₇	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×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
63	#121×C₄₇	C₂²	1	8	yes	complemented
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	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
69	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
70	C₂³×D₄₇	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₄₇	—	2	4	no	—
72	C₂×D₄×C₄₇	—	2	4	no	—
73	C₂×D₄×C₄₇	—	4	2	no	—
74	C₂×D₄×C₄₇	C₂³	1	4	yes	—
75	C₂×D₄×C₄₇	C₂³	1	4	yes	—
76	C₂×D₄×C₄₇	C₂³	1	4	yes	—
77	C₂²×C₄×C₄₇	—	4	2	no	—
78	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
83	C₂×C₂²⋊D₄₇	—	2	4	no	—
84	C₂×C₂²⋊D₄₇	—	2	4	no	—
85	C₂×C₂²⋊D₄₇	—	4	2	no	—
86	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
89	C₂²×Dic₄₇	—	2	4	no	—
90	C₂²×Dic₄₇	—	2	4	no	—
91	C₂²×Dic₄₇	—	4	2	no	—
92	C₂²×Dic₄₇	—	4	2	no	—
93	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
94	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
95	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
96	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
97	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
98	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₂³	1	4	yes	—
100	C₂²×Dic₄₇	C₂³	1	4	yes	—
101	C₂²×Dic₄₇	C₂³	1	4	yes	—
102	C₂²×Dic₄₇	C₂³	1	4	yes	—
103	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
104	C₂×C₄×D₄₇	—	4	2	no	—
105	C₂×C₄×D₄₇	C₂³	1	4	yes	—
106	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
107	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
108	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
110	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
111	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
112	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
113	C₂²⋊Dic₄₇	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	C₄⋊Dic₄₇	C₂³	1	4	yes	—
118	C₄⋊Dic₄₇	C₂³	1	4	yes	—
119	Dic₄₇⋊C₄	C₂³	1	4	yes	—
120	Dic₄₇⋊C₄	C₂³	1	4	yes	—
121	Dic₄₇⋊C₄	C₂³	1	4	yes	—
122	Dic₄₇⋊C₄	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	C₄×Dic₄₇	C₂³	1	4	yes	—
127	C₄×Dic₄₇	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	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	#41	1	4	yes	—
138	C₂³×C₄₇	C₂⁴	1	2	yes	—
139	C₂³×C₄₇	C₂⁴	1	2	yes	—
140	C₂³×C₄₇	C₂⁴	1	2	yes	—
141	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂²×D₄₇	—	2	2	no	—
143	C₂²×D₄₇	—	2	2	no	—
144	C₂²×D₄₇	—	2	2	no	—
145	C₂²×D₄₇	C₂⁴	1	2	yes	—
146	D₄×C₄₇	—	2	8	no	—
147	D₄×C₄₇	—	2	8	no	—
148	D₄×C₄₇	—	4	4	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	C₂²⋊D₄₇	—	2	8	no	—
159	C₂²⋊D₄₇	—	2	8	no	—
160	C₂²⋊D₄₇	—	4	4	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	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	8	no	—
168	C₂×Dic₄₇	—	2	8	no	—
169	C₂×Dic₄₇	—	4	4	no	—
170	C₂×Dic₄₇	—	4	4	no	—
171	C₂×Dic₄₇	#41	1	4	yes	—
172	C₂×Dic₄₇	C₂⁴	1	2	yes	—
173	C₂×Dic₄₇	C₂⁴	1	2	yes	—
174	C₂×Dic₄₇	C₂⁴	1	2	yes	—
175	C₂×Dic₄₇	C₂⁴	1	2	yes	—
176	C₂×Dic₄₇	C₂⁴	1	2	yes	—
177	C₂×Dic₄₇	C₂⁴	1	2	yes	—
178	C₂×Dic₄₇	C₂⁴	1	2	yes	—
179	C₄×D₄₇	—	4	4	no	—
180	C₂²×C₄₇	—	2	8	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	2	no	—
189	C₂²×C₄₇	—	4	4	no	—
190	C₂²×C₄₇	—	4	4	no	—
191	C₂²×C₄₇	C₂×#41	1	2	yes	—
192	C₂²×C₄₇	C₂×#41	1	4	yes	—
193	C₂²×C₄₇	C₂×#41	1	2	yes	—
194	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
195	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
196	C₂×D₄₇	—	2	2	no	—
197	C₂×D₄₇	—	2	2	no	—
198	C₂×D₄₇	—	2	2	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	Dic₄₇	—	2	2	no	—
205	Dic₄₇	—	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	C₂×#41	1	4	yes	—
211	C₂×#553	—	47	1	no	maximal, Sylow
212	C₂×C₄₇	—	2	4	no	—
213	C₂×C₄₇	—	4	2	no	—
214	C₂×C₄₇	—	4	2	no	—
215	C₂×C₄₇	#553	1	4	yes	complemented
216	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
217	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
218	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
219	D₄₇	—	4	2	no	—
220	#553	—	47	16	no	—
221	C₂×#126	—	47	1	no	—
222	C₂×#126	—	47	1	no	—
223	C₂×#125	—	47	1	no	—
224	C₂×#123	—	47	1	no	—
225	C₂×#123	—	47	1	no	—
226	C₂×#121	—	47	1	no	—
227	C₂×#121	—	47	1	no	—
228	C₂×#121	—	47	1	no	—
229	C₂×#121	D₄₇	1	1	yes	characteristic, complemented
230	C₂×C₄×D₄	—	47	1	no	—
231	C₂×C₄×D₄	—	47	1	no	—
232	C₂×C₄×D₄	—	47	1	no	—
233	C₂×C₄×D₄	—	47	1	no	—
234	C₂×#117	—	47	1	no	—
235	C₂²×C₄⋊C₄	—	47	1	no	—
236	C₄₇	C₂×#553	1	1	yes	characteristic, complemented, Sylow
237	C₂²×D₄	—	47	1	no	—
238	C₂²×D₄	—	47	1	no	—
239	C₂²×D₄	—	47	1	no	—
240	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
241	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
242	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
243	C₂³×C₄	—	47	1	no	—
244	C₂³×C₄	—	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	#126	—	47	8	no	—
250	#126	—	47	8	no	—
251	#125	—	47	8	no	—
252	#123	—	47	8	no	—
253	#123	—	47	8	no	—
254	#121	—	47	8	no	—
255	#121	—	47	8	no	—
256	#121	—	47	8	no	—
257	#121	C₂×D₄₇	1	8	yes	complemented
258	C₄×D₄	—	47	8	no	—
259	C₄×D₄	—	47	8	no	—
260	C₄×D₄	—	47	8	no	—
261	C₄×D₄	—	47	8	no	—
262	#117	—	47	8	no	—
263	C₂×C₄⋊C₄	—	47	1	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	8	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	—	47	1	no	—
272	C₂×C₄⋊C₄	—	47	1	no	—
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	C₂×D₄₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
284	C₂×C₄²	—	47	1	no	—
285	C₂×C₄²	—	47	1	no	—
286	C₂×C₄²	—	47	1	no	—
287	C₂⁴	—	47	1	no	—
288	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
289	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
290	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	47	4	no	—
295	C₂×D₄	—	47	4	no	—
296	C₂×D₄	—	47	4	no	—
297	C₂×D₄	—	94	4	no	—
298	C₂×D₄	—	94	4	no	—
299	C₂×D₄	—	188	2	no	—
300	C₂×D₄	C₂²×D₄₇	1	4	yes	—
301	C₂×D₄	C₂²×D₄₇	1	4	yes	—
302	C₂×D₄	C₂²×D₄₇	1	4	yes	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	47	4	no	—
306	C₂²×C₄	—	47	4	no	—
307	C₂²×C₄	—	47	1	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	—	94	4	no	—
317	C₂²×C₄	—	94	4	no	—
318	C₂²×C₄	—	188	2	no	—
319	C₂²×C₄	—	188	2	no	—
320	C₂²×C₄	—	188	2	no	—
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	—	47	4	no	—
334	C₄⋊C₄	—	47	4	no	—
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	C₂²×D₄₇	1	4	yes	—
345	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
346	C₄²	—	47	4	no	—
347	C₄²	—	47	4	no	—
348	C₄²	—	47	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	47	2	no	—
358	C₂³	—	94	2	no	—
359	C₂³	—	94	2	no	—
360	C₂³	—	94	2	no	—
361	C₂³	#10625352	1	4	yes	—
362	C₂³	C₂³×D₄₇	1	2	yes	—
363	C₂³	C₂³×D₄₇	1	2	yes	—
364	C₂³	C₂³×D₄₇	1	2	yes	—
365	C₂³	C₂³×D₄₇	1	1	yes	characteristic
366	D₄	—	2	8	no	—
367	D₄	—	2	8	no	—
368	D₄	—	4	4	no	—
369	D₄	—	94	8	no	—
370	D₄	—	94	8	no	—
371	D₄	—	188	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	47	4	no	—
378	C₂×C₄	—	47	2	no	—
379	C₂×C₄	—	47	2	no	—
380	C₂×C₄	—	47	2	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	—	94	8	no	—
386	C₂×C₄	—	94	8	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	—	94	2	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	188	4	no	—
394	C₂×C₄	—	188	4	no	—
395	C₂×C₄	—	188	4	no	—
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	8	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	94	2	no	—
412	C₂²	—	94	2	no	—
413	C₂²	—	94	2	no	—
414	C₂²	—	188	4	no	—
415	C₂²	#41×D₄₇	1	2	yes	—
416	C₂²	C₂×#10625352	1	4	yes	—
417	C₂²	C₂×#10625352	1	2	yes	—
418	C₂²	#13094069	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	—	47	4	no	—
425	C₄	—	94	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	—	2	4	no	—
432	C₂	—	4	2	no	—
433	C₂	—	4	2	no	—
434	C₂	—	188	2	no	—
435	C₂	#15689816	1	4	yes	direct product factor
436	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
437	C₂	C₂²×#10625352	1	1	yes	characteristic
438	C₂	C₂×#13094069	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₂×#121×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×#121	D₄₇
hypocenter	C₄₇	C₂×#553
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. #15689816	C₂	direct (N × H)
2. C₂×#13094019	C₂	semidirect
3. C₂×#13094017	C₂	semidirect
4. C₂×#13094014	C₂	semidirect
5. C₂×#13094006	C₂	semidirect
6. C₂×#13094005	C₂	semidirect
7. C₂×#13093996	C₂	semidirect
8. C₂×#13093996	C₂	semidirect
9. C₂×#13093996	C₂	semidirect
10. C₂×D₄×Dic₄₇	C₂	semidirect
11. C₂×D₄×Dic₄₇	C₂	semidirect
12. C₂×C₄×C₂²⋊D₄₇	C₂	semidirect
13. C₂×(C₂²⋊D₄₇)⋊C₄	C₂	semidirect
14. C₂×#13093980	C₂	semidirect
15. C₂²×Dic₄₇⋊C₄	C₂	semidirect
16. C₂×#121×C₄₇	C₂	semidirect
25. #13094019	C₂²	semidirect
26. #13094017	C₂²	semidirect
27. #13094014	C₂²	semidirect
28. #13094006	C₂²	semidirect
29. #13094005	C₂²	semidirect
30. #13093996	C₂²	semidirect
31. #13093996	C₂²	semidirect
32. #13093996	C₂²	semidirect
33. D₄×Dic₄₇	C₂²	semidirect
34. D₄×Dic₄₇	C₂²	semidirect
35. C₄×C₂²⋊D₄₇	C₂²	semidirect
36. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
37. #13093980	C₂²	semidirect
47. C₂×Dic₄₇⋊C₄	C₂²	semidirect
63. #121×C₄₇	C₂²	semidirect
215. C₂×C₄₇	#553	semidirect
229. C₂×#121	D₄₇	semidirect
236. C₄₇	C₂×#553	semidirect
257. #121	C₂×D₄₇	semidirect
435. C₂	#15689816	direct (N × H)

Subgroups — C2×#15689816 #20256904

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689816 #20256904