Subgroups — #20257073

Order 6016.

1328 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689802	C₂	1	4	yes	maximal, complemented
2	#15689797	C₂	1	4	yes	maximal, complemented
3	#15689769	C₂	1	4	yes	maximal, complemented
4	#15689763	C₂	1	4	yes	maximal, complemented
5	#15689749	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689706	C₂	1	4	yes	maximal, complemented
7	#15689682	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689632	C₂	1	4	yes	maximal, complemented
9	C₂×#13093994	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13093992	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689596	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂²⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂⁴×D₄₇	C₂²	1	1	yes	characteristic
15	C₂×#10625350	C₂²	1	4	yes	complemented
16	C₂²×D₁₈₈	C₂²	1	2	yes	complemented
17	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
19	C₂²×C₄×D₄₇	C₂²	1	2	yes	complemented
20	#13094019	C₂²	1	4	yes	complemented
21	#13094018	C₂²	1	4	yes	complemented
22	#13094012	C₂²	1	4	yes	complemented
23	#13094010	C₂²	1	4	yes	complemented
24	#13094009	C₂²	1	4	yes	complemented
25	#13094009	C₂²	1	4	yes	complemented
26	#13094007	C₂²	1	4	yes	complemented
27	#13094007	C₂²	1	2	yes	complemented
28	#13094006	C₂²	1	4	yes	complemented
29	#13094005	C₂²	1	2	yes	complemented
30	#13094003	C₂²	1	4	yes	complemented
31	#13094002	C₂²	1	4	yes	complemented
32	#13094001	C₂²	1	4	yes	complemented
33	#13094001	C₂²	1	4	yes	complemented
34	#13093998	C₂²	1	4	yes	complemented
35	#13093997	C₂²	1	4	yes	complemented
36	#13093997	C₂²	1	4	yes	complemented
37	#13093996	C₂²	1	4	yes	complemented
38	#13093994	C₂²	1	4	yes	—
39	#13093994	C₂²	1	2	yes	complemented
40	#13093994	C₂²	1	2	yes	complemented
41	#13093993	C₂²	1	2	yes	complemented
42	#13093992	C₂²	1	4	yes	—
43	#13093992	C₂²	1	2	yes	complemented
44	#13093992	C₂²	1	2	yes	complemented
45	#13093992	C₂²	1	2	yes	complemented
46	C₄×D₁₈₈	C₂²	1	4	yes	complemented
47	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
48	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
49	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
50	#13093981	C₂²	1	4	yes	complemented
51	#13093980	C₂²	1	2	yes	complemented
52	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
54	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
55	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
56	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
57	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
58	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
59	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
60	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
61	C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
62	C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
63	#117×C₄₇	C₂²	1	2	yes	complemented
64	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
67	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
68	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
69	C₂³×D₄₇	—	2	4	no	—
70	C₂³×D₄₇	—	4	4	no	—
71	C₂³×D₄₇	C₂³	1	1	yes	characteristic
72	C₂³×D₄₇	C₂³	1	2	yes	—
73	C₂³×D₄₇	C₂³	1	2	yes	—
74	C₂³×D₄₇	C₂³	1	1	yes	characteristic
75	C₂³×D₄₇	C₂³	1	1	yes	characteristic
76	C₂×D₄×C₄₇	—	2	4	no	—
77	C₂×D₄×C₄₇	C₂³	1	2	yes	—
78	C₂×D₄×C₄₇	C₂³	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
81	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂³	1	4	yes	complemented
83	C₂×C₂²⋊D₄₇	—	2	4	no	—
84	C₂×C₂²⋊D₄₇	—	4	4	no	—
85	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
86	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	complemented
90	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
91	C₂²×Dic₄₇	C₂³	1	2	yes	—
92	C₂²×Dic₄₇	C₂³	1	2	yes	—
93	#10625350	—	4	8	no	—
94	C₂×D₁₈₈	—	4	4	no	—
95	C₂×D₁₈₈	C₂³	1	4	yes	—
96	C₂×D₁₈₈	C₂³	1	4	yes	—
97	C₂×C₄×D₄₇	—	4	4	no	—
98	C₂×C₄×D₄₇	C₂³	1	4	yes	—
99	C₂×C₄×D₄₇	C₂³	1	4	yes	—
100	C₂×C₄×D₄₇	C₂³	1	4	yes	complemented
101	C₂×Dic₉₄	C₂³	1	4	yes	complemented
102	C₄⋊C₄×C₄₇	C₂³	1	4	yes	complemented
103	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
104	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
105	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
106	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
107	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	complemented
108	C₄²×C₄₇	C₂³	1	4	yes	complemented
109	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
110	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
111	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
112	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
113	C₂²⋊Dic₄₇	C₂³	1	4	yes	complemented
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	complemented
121	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	complemented
122	C₄⋊Dic₄₇	C₂³	1	4	yes	complemented
123	Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
124	Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
125	Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
126	Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
127	C₄×Dic₄₇	C₂³	1	4	yes	complemented
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	4	2	no	—
130	C₂³×C₄₇	—	4	2	no	—
131	C₂³×C₄₇	#41	1	4	yes	complemented
132	C₂³×C₄₇	C₂⁴	1	2	yes	—
133	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
134	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
136	C₂²×D₄₇	—	2	2	no	—
137	C₂²×D₄₇	—	2	4	no	—
138	C₂²×D₄₇	—	2	4	no	—
139	C₂²×D₄₇	—	2	4	no	—
140	C₂²×D₄₇	—	2	2	no	—
141	C₂²×D₄₇	—	2	2	no	—
142	C₂²×D₄₇	—	2	4	no	—
143	C₂²×D₄₇	—	2	4	no	—
144	C₂²×D₄₇	—	4	2	no	—
145	C₂²×D₄₇	—	4	2	no	—
146	C₂²×D₄₇	—	4	2	no	—
147	C₂²×D₄₇	—	4	2	no	—
148	C₂²×D₄₇	—	4	16	no	—
149	C₂²×D₄₇	C₂⁴	1	2	yes	—
150	C₂²×D₄₇	C₂⁴	1	2	yes	—
151	C₂²×D₄₇	C₂⁴	1	2	yes	—
152	D₄×C₄₇	—	2	4	no	—
153	D₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
159	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
160	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
161	C₂²⋊D₄₇	—	2	4	no	—
162	C₂²⋊D₄₇	—	2	4	no	—
163	C₂²⋊D₄₇	—	2	8	no	—
164	C₂²⋊D₄₇	—	4	4	no	—
165	C₂²⋊D₄₇	—	4	4	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	C₂⁴	1	2	yes	—
170	C₂×Dic₄₇	C₂⁴	1	4	yes	—
171	C₂×Dic₄₇	C₂⁴	1	4	yes	—
172	D₁₈₈	—	2	8	no	—
173	D₁₈₈	—	4	4	no	—
174	C₄×D₄₇	—	2	8	no	—
175	C₄×D₄₇	—	4	4	no	—
176	C₄×D₄₇	—	4	4	no	—
177	Dic₉₄	—	4	4	no	—
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	4	no	—
183	C₂²×C₄₇	—	4	4	no	—
184	C₂²×C₄₇	—	8	2	no	—
185	C₂²×C₄₇	C₂×#41	1	2	yes	—
186	C₂²×C₄₇	C₂×#41	1	2	yes	—
187	C₂²×C₄₇	C₂×#41	1	2	yes	—
188	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
189	C₂×D₄₇	—	2	8	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	4	no	—
195	C₂×D₄₇	—	2	2	no	—
196	C₂×D₄₇	—	2	2	no	—
197	C₂×D₄₇	—	4	8	no	—
198	C₂×D₄₇	—	4	8	no	—
199	C₂×D₄₇	—	4	4	no	—
200	C₂×D₄₇	—	8	2	no	—
201	C₂×D₄₇	H(5,𝔽₂)	1	4	yes	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	2	4	no	—
204	C₄×C₄₇	—	2	4	no	—
205	Dic₄₇	—	2	2	no	—
206	Dic₄₇	—	2	4	no	—
207	Dic₄₇	—	2	4	no	—
208	#3490	—	47	1	no	maximal, Sylow
209	C₂×C₄₇	—	2	2	no	—
210	C₂×C₄₇	—	2	2	no	—
211	C₂×C₄₇	—	2	2	no	—
212	C₂×C₄₇	—	4	2	no	—
213	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
214	C₂×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
215	D₄₇	—	2	4	no	—
216	D₄₇	—	4	2	no	—
217	D₄₇	—	4	2	no	—
218	#551	—	47	4	no	—
219	#551	—	47	4	no	—
220	#546	—	47	4	no	—
221	#546	—	47	4	no	—
222	#543	—	47	1	no	—
223	#538	—	47	4	no	—
224	#534	—	47	1	no	—
225	#525	—	47	4	no	—
226	C₂×#120	—	47	1	no	—
227	C₂×#120	—	47	1	no	—
228	#518	—	47	1	no	—
229	#518	D₄₇	1	1	yes	characteristic, complemented
230	C₂²×C₂²⋊C₄	—	47	1	no	—
231	C₄₇	#3490	1	1	yes	characteristic, complemented, Sylow
232	C₂⁵	—	47	1	no	—
233	C₂×#41	—	47	4	no	—
234	C₂²×D₄	—	47	1	no	—
235	C₂²×D₄	—	47	2	no	—
236	C₂²×D₄	—	47	2	no	—
237	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
238	C₂³×C₄	—	47	2	no	—
239	#126	—	47	4	no	—
240	#126	—	47	4	no	—
241	#124	—	47	4	no	—
242	#124	—	47	4	no	—
243	#123	—	47	2	no	—
244	#123	—	47	2	no	—
245	#123	—	47	4	no	—
246	#123	—	47	4	no	—
247	#123	—	47	4	no	—
248	#123	—	47	4	no	—
249	C₂²⋊Q₈	—	47	4	no	—
250	C₂²⋊Q₈	—	47	4	no	—
251	C₂²⋊Q₈	—	47	4	no	—
252	C₂²⋊Q₈	—	47	4	no	—
253	#121	—	47	4	no	—
254	#121	—	47	4	no	—
255	#121	—	47	4	no	—
256	#121	—	47	4	no	—
257	#120	—	47	2	no	—
258	#120	—	47	2	no	—
259	#120	—	47	2	no	—
260	#120	—	47	4	no	—
261	#120	—	47	2	no	—
262	#120	—	47	2	no	—
263	#120	—	47	2	no	—
264	#120	—	47	4	no	—
265	C₄×D₄	—	47	4	no	—
266	C₄×D₄	—	47	4	no	—
267	C₄×D₄	—	47	4	no	—
268	C₄×D₄	—	47	4	no	—
269	C₄×D₄	C₂×D₄₇	1	4	yes	complemented
270	C₄×D₄	C₂×D₄₇	1	4	yes	complemented
271	#117	—	47	2	no	—
272	#117	—	47	4	no	—
273	#117	C₂×D₄₇	1	2	yes	complemented
274	C₂×C₂²⋊C₄	—	47	1	no	—
275	C₂×C₂²⋊C₄	—	47	1	no	—
276	C₂×C₂²⋊C₄	—	47	2	no	—
277	C₂×C₂²⋊C₄	—	47	2	no	—
278	C₂×C₂²⋊C₄	—	47	2	no	—
279	C₂×C₂²⋊C₄	—	47	4	no	—
280	C₂×C₂²⋊C₄	—	47	4	no	—
281	C₂×C₂²⋊C₄	—	47	2	no	—
282	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	complemented
285	C₂⁴	—	47	1	no	—
286	C₂⁴	—	47	2	no	—
287	C₂⁴	—	47	2	no	—
288	C₂⁴	—	47	1	no	—
289	C₂⁴	—	47	1	no	—
290	C₂⁴	—	94	4	no	—
291	C₂⁴	—	188	4	no	—
292	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
293	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
294	#41	—	188	8	no	—
295	C₂×Q₈	—	47	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	47	2	no	—
298	C₂×D₄	—	47	2	no	—
299	C₂×D₄	—	47	4	no	—
300	C₂×D₄	—	47	4	no	—
301	C₂×D₄	—	47	4	no	—
302	C₂×D₄	—	47	4	no	—
303	C₂×D₄	—	47	4	no	—
304	C₂×D₄	—	94	4	no	—
305	C₂×D₄	—	188	4	no	—
306	C₂×D₄	—	188	4	no	—
307	C₂×D₄	C₂²×D₄₇	1	2	yes	—
308	C₂×D₄	C₂²×D₄₇	1	2	yes	—
309	C₂²×C₄	—	47	1	no	—
310	C₂²×C₄	—	47	2	no	—
311	C₂²×C₄	—	47	2	no	—
312	C₂²×C₄	—	47	4	no	—
313	C₂²×C₄	—	47	4	no	—
314	C₂²×C₄	—	47	4	no	—
315	C₂²×C₄	—	188	4	no	—
316	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
317	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
318	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
319	C₂²×C₄	C₂²×D₄₇	1	4	yes	complemented
320	C₄⋊C₄	—	47	4	no	—
321	C₄⋊C₄	—	47	4	no	—
322	C₄⋊C₄	—	47	4	no	—
323	C₄⋊C₄	—	47	4	no	—
324	C₄⋊C₄	—	47	4	no	—
325	C₄⋊C₄	C₂²×D₄₇	1	4	yes	complemented
326	C₂²⋊C₄	—	47	2	no	—
327	C₂²⋊C₄	—	47	2	no	—
328	C₂²⋊C₄	—	47	2	no	—
329	C₂²⋊C₄	—	47	2	no	—
330	C₂²⋊C₄	—	47	4	no	—
331	C₂²⋊C₄	—	47	4	no	—
332	C₂²⋊C₄	—	47	4	no	—
333	C₂²⋊C₄	—	47	4	no	—
334	C₂²⋊C₄	—	47	4	no	—
335	C₂²⋊C₄	—	47	4	no	—
336	C₂²⋊C₄	—	47	4	no	—
337	C₂²⋊C₄	—	47	4	no	—
338	C₂²⋊C₄	—	47	4	no	—
339	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
340	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
341	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
342	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
343	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	complemented
344	C₄²	—	47	4	no	—
345	C₄²	C₂²×D₄₇	1	4	yes	complemented
346	C₂³	—	2	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	47	2	no	—
350	C₂³	—	47	2	no	—
351	C₂³	—	47	2	no	—
352	C₂³	—	94	4	no	—
353	C₂³	—	94	4	no	—
354	C₂³	—	94	4	no	—
355	C₂³	—	94	2	no	—
356	C₂³	—	94	2	no	—
357	C₂³	—	94	4	no	—
358	C₂³	—	94	4	no	—
359	C₂³	—	94	2	no	—
360	C₂³	—	188	2	no	—
361	C₂³	—	188	2	no	—
362	C₂³	—	188	2	no	—
363	C₂³	—	188	2	no	—
364	C₂³	—	188	16	no	—
365	C₂³	#10625350	1	4	yes	complemented
366	C₂³	C₂³×D₄₇	1	2	yes	—
367	C₂³	C₂³×D₄₇	1	1	yes	characteristic
368	C₂³	C₂³×D₄₇	1	1	yes	characteristic
369	C₂³	C₂³×D₄₇	1	1	yes	characteristic
370	Q₈	—	188	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	2	4	no	—
373	D₄	—	94	8	no	—
374	D₄	—	94	8	no	—
375	D₄	—	94	4	no	—
376	D₄	—	94	4	no	—
377	D₄	—	188	4	no	—
378	D₄	—	188	4	no	—
379	D₄	—	188	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	47	2	no	—
385	C₂×C₄	—	47	4	no	—
386	C₂×C₄	—	47	4	no	—
387	C₂×C₄	—	94	8	no	—
388	C₂×C₄	—	94	2	no	—
389	C₂×C₄	—	188	4	no	—
390	C₂×C₄	—	188	4	no	—
391	C₂×C₄	—	188	2	no	—
392	C₂×C₄	—	188	2	no	—
393	C₂×C₄	C₂³×D₄₇	1	4	yes	—
394	C₂×C₄	C₂³×D₄₇	1	2	yes	—
395	C₂×C₄	C₂³×D₄₇	1	4	yes	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	47	4	no	—
404	C₂²	—	94	8	no	—
405	C₂²	—	94	2	no	—
406	C₂²	—	94	2	no	—
407	C₂²	—	94	2	no	—
408	C₂²	—	94	2	no	—
409	C₂²	—	94	4	no	—
410	C₂²	—	94	2	no	—
411	C₂²	—	94	2	no	—
412	C₂²	—	376	2	no	—
413	C₂²	—	188	8	no	—
414	C₂²	—	188	8	no	—
415	C₂²	—	188	4	no	—
416	C₂²	C₂×#10625350	1	2	yes	—
417	C₂²	C₂×#10625350	1	2	yes	—
418	C₂²	C₂×#10625350	1	2	yes	—
419	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	4	no	—
422	C₄	—	2	4	no	—
423	C₄	—	94	2	no	—
424	C₄	—	94	4	no	—
425	C₄	—	94	4	no	—
426	C₂	—	2	2	no	—
427	C₂	—	2	2	no	—
428	C₂	—	2	2	no	—
429	C₂	—	4	2	no	—
430	C₂	—	94	4	no	—
431	C₂	—	188	2	no	—
432	C₂	—	188	2	no	—
433	C₂	C₂²×#10625350	1	1	yes	characteristic
434	C₂	H(5,𝔽₂)×D₄₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#518	C₂
hypercenter	#518	D₄₇
hypocenter	C₄₇	#3490
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. #15689802	C₂	semidirect
2. #15689797	C₂	semidirect
3. #15689769	C₂	semidirect
4. #15689763	C₂	semidirect
5. #15689749	C₂	semidirect
6. #15689706	C₂	semidirect
7. #15689682	C₂	semidirect
8. #15689632	C₂	semidirect
9. C₂×#13093994	C₂	semidirect
10. C₂×#13093992	C₂	semidirect
11. #15689596	C₂	semidirect
12. C₂×C₂²⋊C₄×D₄₇	C₂	semidirect
13. C₄₇×#518	C₂	semidirect
15. C₂×#10625350	C₂²	semidirect
16. C₂²×D₁₈₈	C₂²	semidirect
18. C₂²×C₂²⋊D₄₇	C₂²	semidirect
19. C₂²×C₄×D₄₇	C₂²	semidirect
20. #13094019	C₂²	semidirect
21. #13094018	C₂²	semidirect
22. #13094012	C₂²	semidirect
23. #13094010	C₂²	semidirect
24. #13094009	C₂²	semidirect
25. #13094009	C₂²	semidirect
26. #13094007	C₂²	semidirect
27. #13094007	C₂²	semidirect
28. #13094006	C₂²	semidirect
29. #13094005	C₂²	semidirect
30. #13094003	C₂²	semidirect
31. #13094002	C₂²	semidirect
32. #13094001	C₂²	semidirect
33. #13094001	C₂²	semidirect
34. #13093998	C₂²	semidirect
35. #13093997	C₂²	semidirect
36. #13093997	C₂²	semidirect
37. #13093996	C₂²	semidirect
39. #13093994	C₂²	semidirect
40. #13093994	C₂²	semidirect
41. #13093993	C₂²	semidirect
43. #13093992	C₂²	semidirect
44. #13093992	C₂²	semidirect
45. #13093992	C₂²	semidirect
46. C₄×D₁₈₈	C₂²	semidirect
47. C₄×C₂²⋊D₄₇	C₂²	semidirect
48. C₄×C₂²⋊D₄₇	C₂²	semidirect
49. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
50. #13093981	C₂²	semidirect
51. #13093980	C₂²	semidirect
54. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
55. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
56. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
57. C₂²⋊C₄×D₄₇	C₂²	semidirect
58. C₂²⋊C₄×D₄₇	C₂²	semidirect
59. C₂²⋊C₄×D₄₇	C₂²	semidirect
61. C₄×D₄×C₄₇	C₂²	semidirect
62. C₄×D₄×C₄₇	C₂²	semidirect
63. #117×C₄₇	C₂²	semidirect
66. C₂×C₂²⋊C₄×C₄₇	C₂²	semidirect
82. C₂²×C₄×C₄₇	C₂³	semidirect
89. C₂×C₂²⋊D₄₇	C₂³	semidirect
100. C₂×C₄×D₄₇	C₂³	semidirect
101. C₂×Dic₉₄	C₂³	semidirect
102. C₄⋊C₄×C₄₇	C₂³	semidirect
107. C₂²⋊C₄×C₄₇	C₂³	semidirect
108. C₄²×C₄₇	C₂³	semidirect
113. C₂²⋊Dic₄₇	C₂³	semidirect
120. (C₂×D₄₇)⋊C₄	C₂³	semidirect
121. (C₂×D₄₇)⋊C₄	C₂³	semidirect
122. C₄⋊Dic₄₇	C₂³	semidirect
123. Dic₄₇⋊C₄	C₂³	semidirect
124. Dic₄₇⋊C₄	C₂³	semidirect
125. Dic₄₇⋊C₄	C₂³	semidirect
126. Dic₄₇⋊C₄	C₂³	semidirect
127. C₄×Dic₄₇	C₂³	semidirect
131. C₂³×C₄₇	#41	semidirect
229. #518	D₄₇	semidirect
231. C₄₇	#3490	semidirect
269. C₄×D₄	C₂×D₄₇	semidirect
270. C₄×D₄	C₂×D₄₇	semidirect
273. #117	C₂×D₄₇	semidirect
284. C₂×C₂²⋊C₄	C₂×D₄₇	semidirect
319. C₂²×C₄	C₂²×D₄₇	semidirect
325. C₄⋊C₄	C₂²×D₄₇	semidirect
343. C₂²⋊C₄	C₂²×D₄₇	semidirect
345. C₄²	C₂²×D₄₇	semidirect
365. C₂³	#10625350	semidirect