Subgroups — #20257229

Order 6016.

1152 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689821	C₂	1	4	yes	maximal, complemented
2	#15689821	C₂	1	2	yes	maximal, complemented
3	#15689815	C₂	1	2	yes	maximal, complemented
4	#15689800	C₂	1	4	yes	maximal, complemented
5	#15689784	C₂	1	2	yes	maximal, complemented
6	#15689764	C₂	1	2	yes	maximal, complemented
7	#15689722	C₂	1	2	yes	maximal, complemented
8	#15689713	C₂	1	2	yes	maximal, complemented
9	#15689685	C₂	1	2	yes	maximal, complemented
10	#15689659	C₂	1	2	yes	maximal, complemented
11	#15689636	C₂	1	2	yes	maximal, complemented
12	C₂×#13093998	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689596	C₂	1	2	yes	maximal, complemented
14	C₂×C₄×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625354	C₂²	1	2	yes	complemented
17	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₄₇	C₂²	1	2	yes	—
20	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
21	#13094019	C₂²	1	4	yes	complemented
22	#13094019	C₂²	1	4	yes	complemented
23	#13094019	C₂²	1	4	yes	complemented
24	#13094015	C₂²	1	2	yes	complemented
25	#13094015	C₂²	1	4	yes	complemented
26	#13094013	C₂²	1	2	yes	complemented
27	#13094013	C₂²	1	4	yes	complemented
28	#13094009	C₂²	1	4	yes	complemented
29	#13094009	C₂²	1	4	yes	complemented
30	#13094009	C₂²	1	4	yes	complemented
31	#13094008	C₂²	1	4	yes	—
32	#13094008	C₂²	1	4	yes	complemented
33	#13094000	C₂²	1	4	yes	complemented
34	#13094000	C₂²	1	2	yes	complemented
35	#13093999	C₂²	1	2	yes	complemented
36	#13093999	C₂²	1	4	yes	complemented
37	#13093998	C₂²	1	2	yes	—
38	#13093998	C₂²	1	2	yes	—
39	#13093998	C₂²	1	2	yes	complemented
40	#13093998	C₂²	1	4	yes	complemented
41	#13093998	C₂²	1	2	yes	complemented
42	#13093998	C₂²	1	4	yes	complemented
43	#13093994	C₂²	1	4	yes	—
44	#13093994	C₂²	1	4	yes	complemented
45	Q₈×Dic₄₇	C₂²	1	2	yes	complemented
46	#13093986	C₂²	1	2	yes	complemented
47	#13093986	C₂²	1	4	yes	complemented
48	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
52	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
53	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
54	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
55	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
56	#13093982	C₂²	1	4	yes	complemented
57	#13093982	C₂²	1	2	yes	complemented
58	#13093980	C₂²	1	4	yes	complemented
59	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
62	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
63	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
64	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
65	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
66	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
67	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
68	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
69	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
70	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
71	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
72	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
74	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
75	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
76	C₂³×D₄₇	C₂³	1	2	yes	—
77	C₂³×D₄₇	C₂³	1	1	yes	characteristic
78	C₂×Q₈×C₄₇	—	4	2	no	—
79	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
80	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
81	C₂²×C₄×C₄₇	—	4	2	no	—
82	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊D₄₇	—	2	4	no	—
91	C₂×C₂²⋊D₄₇	—	2	8	no	—
92	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
96	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
97	C₂²×Dic₄₇	C₂³	1	2	yes	—
98	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
100	#10625354	—	4	4	no	—
101	C₂×D₁₈₈	—	4	2	no	—
102	C₂×D₁₈₈	C₂³	1	2	yes	—
103	C₂×D₁₈₈	C₂³	1	4	yes	—
104	C₂×D₁₈₈	C₂³	1	4	yes	—
105	C₂×D₁₈₈	C₂³	1	2	yes	—
106	C₂×C₄×D₄₇	—	4	2	no	—
107	C₂×C₄×D₄₇	C₂³	1	2	yes	—
108	C₂×C₄×D₄₇	C₂³	1	4	yes	—
109	C₂×C₄×D₄₇	C₂³	1	4	yes	—
110	C₂×C₄×D₄₇	C₂³	1	2	yes	—
111	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
113	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
114	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
116	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
117	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
118	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
119	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
123	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
124	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
129	C₄⋊Dic₄₇	C₂³	1	2	yes	—
130	C₄⋊Dic₄₇	C₂³	1	2	yes	—
131	C₄⋊Dic₄₇	C₂³	1	4	yes	—
132	C₄⋊Dic₄₇	C₂³	1	4	yes	—
133	Dic₄₇⋊C₄	C₂³	1	2	yes	—
134	Dic₄₇⋊C₄	C₂³	1	2	yes	—
135	Dic₄₇⋊C₄	C₂³	1	4	yes	—
136	Dic₄₇⋊C₄	C₂³	1	4	yes	—
137	C₄×Dic₄₇	C₂³	1	2	yes	—
138	C₄×Dic₄₇	C₂³	1	2	yes	—
139	C₄×Dic₄₇	C₂³	1	4	yes	—
140	C₄×Dic₄₇	C₂³	1	4	yes	—
141	C₂³×C₄₇	—	4	1	no	—
142	C₂³×C₄₇	—	4	1	no	—
143	C₂³×C₄₇	#41	1	4	yes	complemented
144	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
147	C₂²×D₄₇	—	2	2	no	—
148	C₂²×D₄₇	—	2	4	no	—
149	C₂²×D₄₇	—	4	1	no	—
150	C₂²×D₄₇	—	4	1	no	—
151	C₂²×D₄₇	—	4	2	no	—
152	C₂²×D₄₇	—	4	2	no	—
153	C₂²×D₄₇	C₂⁴	1	2	yes	—
154	C₂²×D₄₇	C₂⁴	1	4	yes	—
155	Q₈×C₄₇	—	2	4	no	—
156	Q₈×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
167	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
168	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₄₇	—	2	4	no	—
172	C₂²⋊D₄₇	—	2	8	no	—
173	C₂²⋊D₄₇	—	2	4	no	—
174	C₂²⋊D₄₇	—	2	8	no	—
175	C₂×Dic₄₇	—	2	4	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	4	1	no	—
178	C₂×Dic₄₇	—	4	1	no	—
179	C₂×Dic₄₇	C₂⁴	1	2	yes	—
180	C₂×Dic₄₇	C₂⁴	1	2	yes	—
181	C₂×Dic₄₇	C₂⁴	1	2	yes	—
182	C₂×Dic₄₇	C₂⁴	1	4	yes	—
183	D₁₈₈	—	2	4	no	—
184	D₁₈₈	—	4	2	no	—
185	D₁₈₈	—	4	4	no	—
186	D₁₈₈	—	4	4	no	—
187	C₄×D₄₇	—	2	4	no	—
188	C₄×D₄₇	—	4	2	no	—
189	C₄×D₄₇	—	4	4	no	—
190	C₄×D₄₇	—	4	4	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	4	4	no	—
198	C₂²×C₄₇	C₂×#41	1	2	yes	—
199	C₂²×C₄₇	C₂×#41	1	2	yes	—
200	C₂²×C₄₇	C₂×#41	1	2	yes	—
201	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
202	C₂×D₄₇	—	2	2	no	—
203	C₂×D₄₇	—	2	4	no	—
204	C₂×D₄₇	—	2	2	no	—
205	C₂×D₄₇	—	2	4	no	—
206	C₂×D₄₇	—	2	4	no	—
207	C₂×D₄₇	—	2	2	no	—
208	C₂×D₄₇	—	4	4	no	—
209	C₂×D₄₇	—	8	4	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	4	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	2	1	no	—
214	C₄×C₄₇	—	2	4	no	—
215	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
216	Dic₄₇	—	2	4	no	—
217	Dic₄₇	—	2	2	no	—
218	Dic₄₇	—	2	2	no	—
219	Dic₄₇	—	2	2	no	—
220	#3505	—	47	1	no	maximal, Sylow
221	C₂×C₄₇	—	2	2	no	—
222	C₂×C₄₇	—	2	2	no	—
223	C₂×C₄₇	—	2	2	no	—
224	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
225	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄₇	#585	1	1	yes	characteristic
227	D₄₇	—	4	2	no	—
228	D₄₇	—	4	4	no	—
229	#553	—	47	2	no	—
230	#553	—	47	4	no	—
231	#552	—	47	2	no	—
232	#551	—	47	4	no	—
233	#548	—	47	2	no	—
234	#546	—	47	2	no	—
235	#539	—	47	2	no	—
236	#538	—	47	2	no	—
237	#534	—	47	2	no	—
238	#529	—	47	2	no	—
239	#525	—	47	2	no	—
240	C₂×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
241	C₂×#121	—	47	1	no	—
242	#518	—	47	2	no	—
243	C₂×C₄×D₄	—	47	1	no	—
244	C₄₇	#3505	1	1	yes	characteristic, complemented, Sylow
245	C₂×#41	—	47	2	no	—
246	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
247	C₂²×D₄	—	47	1	no	—
248	C₂²×D₄	—	47	2	no	—
249	C₂²×D₄	—	47	1	no	—
250	C₂³×C₄	—	47	1	no	—
251	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
252	#126	—	47	4	no	—
253	#126	—	47	4	no	—
254	#126	—	47	4	no	—
255	#125	—	47	2	no	—
256	#125	—	47	4	no	—
257	#124	—	47	2	no	—
258	#124	—	47	4	no	—
259	#123	—	47	4	no	—
260	#123	—	47	4	no	—
261	#123	—	47	4	no	—
262	#123	—	47	4	no	—
263	#123	—	47	4	no	—
264	C₂²⋊Q₈	—	47	2	no	—
265	C₂²⋊Q₈	—	47	4	no	—
266	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
267	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
268	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
269	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
270	#121	—	47	2	no	—
271	#121	—	47	2	no	—
272	#121	—	47	2	no	—
273	#121	—	47	2	no	—
274	#121	—	47	4	no	—
275	#121	—	47	4	no	—
276	#121	—	47	2	no	—
277	#121	—	47	4	no	—
278	#120	—	47	4	no	—
279	#120	—	47	4	no	—
280	C₄×Q₈	—	47	2	no	—
281	C₄×D₄	—	47	2	no	—
282	C₄×D₄	—	47	2	no	—
283	C₄×D₄	—	47	2	no	—
284	C₄×D₄	—	47	2	no	—
285	C₄×D₄	—	47	4	no	—
286	C₄×D₄	—	47	4	no	—
287	C₄×D₄	—	47	4	no	—
288	C₄×D₄	—	47	2	no	—
289	C₄×D₄	—	47	4	no	—
290	C₄×D₄	—	47	4	no	—
291	#117	—	47	2	no	—
292	#117	—	47	4	no	—
293	#117	—	47	4	no	—
294	C₂×C₄⋊C₄	—	47	1	no	—
295	C₂×C₄⋊C₄	—	47	1	no	—
296	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
297	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
298	C₂×C₂²⋊C₄	—	47	1	no	—
299	C₂×C₂²⋊C₄	—	47	1	no	—
300	C₂×C₂²⋊C₄	—	47	2	no	—
301	C₂×C₂²⋊C₄	—	47	4	no	—
302	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
303	C₂×C₄²	—	47	1	no	—
304	C₂⁴	—	47	2	no	—
305	C₂⁴	—	47	1	no	—
306	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
307	#41	—	188	4	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
310	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
311	C₂×D₄	—	47	2	no	—
312	C₂×D₄	—	47	4	no	—
313	C₂×D₄	—	47	2	no	—
314	C₂×D₄	—	47	4	no	—
315	C₂×D₄	—	47	2	no	—
316	C₂×D₄	—	47	4	no	—
317	C₂×D₄	—	47	4	no	—
318	C₂×D₄	—	47	2	no	—
319	C₂×D₄	—	94	8	no	—
320	C₂×D₄	—	94	4	no	—
321	C₂×D₄	—	188	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	47	1	no	—
324	C₂²×C₄	—	47	2	no	—
325	C₂²×C₄	—	47	1	no	—
326	C₂²×C₄	—	47	1	no	—
327	C₂²×C₄	—	47	2	no	—
328	C₂²×C₄	—	47	4	no	—
329	C₂²×C₄	—	47	4	no	—
330	C₂²×C₄	—	47	2	no	—
331	C₂²×C₄	—	188	2	no	—
332	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
335	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
337	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
338	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
339	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
340	C₄⋊C₄	—	47	2	no	—
341	C₄⋊C₄	—	47	2	no	—
342	C₄⋊C₄	—	47	4	no	—
343	C₄⋊C₄	—	47	4	no	—
344	C₄⋊C₄	—	47	2	no	—
345	C₄⋊C₄	—	47	2	no	—
346	C₄⋊C₄	—	47	4	no	—
347	C₄⋊C₄	—	47	4	no	—
348	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
349	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
350	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
351	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
352	C₂²⋊C₄	—	47	2	no	—
353	C₂²⋊C₄	—	47	2	no	—
354	C₂²⋊C₄	—	47	4	no	—
355	C₂²⋊C₄	—	47	2	no	—
356	C₂²⋊C₄	—	47	4	no	—
357	C₂²⋊C₄	—	47	4	no	—
358	C₂²⋊C₄	—	47	2	no	—
359	C₂²⋊C₄	—	47	4	no	—
360	C₂²⋊C₄	—	47	4	no	—
361	C₂²⋊C₄	—	47	4	no	—
362	C₂²⋊C₄	—	47	4	no	—
363	C₂²⋊C₄	—	47	4	no	—
364	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
365	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
366	C₄²	—	47	2	no	—
367	C₄²	—	47	2	no	—
368	C₄²	—	47	4	no	—
369	C₄²	—	47	4	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	47	2	no	—
373	C₂³	—	47	4	no	—
374	C₂³	—	94	4	no	—
375	C₂³	—	94	2	no	—
376	C₂³	—	188	2	no	—
377	C₂³	—	188	2	no	—
378	C₂³	—	188	1	no	—
379	C₂³	—	188	1	no	—
380	C₂³	#10625354	1	4	yes	complemented
381	C₂³	C₂³×D₄₇	1	1	yes	characteristic
382	C₂³	C₂³×D₄₇	1	1	yes	characteristic
383	C₂³	C₂³×D₄₇	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	4	2	no	—
386	D₄	—	94	4	no	—
387	D₄	—	94	8	no	—
388	D₄	—	94	8	no	—
389	D₄	—	94	4	no	—
390	D₄	—	94	4	no	—
391	D₄	—	188	4	no	—
392	D₄	—	188	2	no	—
393	D₄	—	188	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	47	2	no	—
403	C₂×C₄	—	47	2	no	—
404	C₂×C₄	—	47	4	no	—
405	C₂×C₄	—	47	2	no	—
406	C₂×C₄	—	94	4	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	4	no	—
409	C₂×C₄	—	188	4	no	—
410	C₂×C₄	—	188	2	no	—
411	C₂×C₄	—	188	4	no	—
412	C₂×C₄	—	188	1	no	—
413	C₂×C₄	—	188	1	no	—
414	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₄₇	1	4	yes	—
416	C₂×C₄	C₂³×D₄₇	1	4	yes	—
417	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
418	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	94	4	no	—
428	C₂²	—	94	2	no	—
429	C₂²	—	94	2	no	—
430	C₂²	—	94	4	no	—
431	C₂²	—	94	4	no	—
432	C₂²	—	94	2	no	—
433	C₂²	—	376	4	no	—
434	C₂²	—	188	4	no	—
435	C₂²	C₂×#10625354	1	2	yes	—
436	C₂²	C₂×#10625354	1	2	yes	—
437	C₂²	C₂×#10625354	1	2	yes	—
438	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	4	no	—
444	C₄	—	94	2	no	—
445	C₄	—	94	4	no	—
446	C₄	—	94	2	no	—
447	C₄	—	94	2	no	—
448	C₄	#13094069	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	2	2	no	—
451	C₂	—	2	2	no	—
452	C₂	—	188	4	no	—
453	C₂	—	188	2	no	—
454	C₂	C₂²×#10625354	1	1	yes	characteristic
455	C₂	C₂×#13094069	1	1	yes	characteristic
456	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₂×C₂²⋊Q₈×C₄₇	C₂
hypercenter	C₂×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	#3505
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #15689821	C₂	semidirect
2. #15689821	C₂	semidirect
3. #15689815	C₂	semidirect
4. #15689800	C₂	semidirect
5. #15689784	C₂	semidirect
6. #15689764	C₂	semidirect
7. #15689722	C₂	semidirect
8. #15689713	C₂	semidirect
9. #15689685	C₂	semidirect
10. #15689659	C₂	semidirect
11. #15689636	C₂	semidirect
12. C₂×#13093998	C₂	semidirect
13. #15689596	C₂	semidirect
14. C₂×C₄×C₂²⋊D₄₇	C₂	semidirect
15. C₂×C₂²⋊Q₈×C₄₇	C₂	semidirect
16. C₂×#10625354	C₂²	semidirect
17. C₂²×D₁₈₈	C₂²	semidirect
20. C₂²×C₄×D₄₇	C₂²	semidirect
21. #13094019	C₂²	semidirect
22. #13094019	C₂²	semidirect
23. #13094019	C₂²	semidirect
24. #13094015	C₂²	semidirect
25. #13094015	C₂²	semidirect
26. #13094013	C₂²	semidirect
27. #13094013	C₂²	semidirect
28. #13094009	C₂²	semidirect
29. #13094009	C₂²	semidirect
30. #13094009	C₂²	semidirect
32. #13094008	C₂²	semidirect
33. #13094000	C₂²	semidirect
34. #13094000	C₂²	semidirect
35. #13093999	C₂²	semidirect
36. #13093999	C₂²	semidirect
39. #13093998	C₂²	semidirect
40. #13093998	C₂²	semidirect
41. #13093998	C₂²	semidirect
42. #13093998	C₂²	semidirect
44. #13093994	C₂²	semidirect
45. Q₈×Dic₄₇	C₂²	semidirect
46. #13093986	C₂²	semidirect
47. #13093986	C₂²	semidirect
50. C₄×C₂²⋊D₄₇	C₂²	semidirect
51. C₄×C₂²⋊D₄₇	C₂²	semidirect
52. C₄×C₂²⋊D₄₇	C₂²	semidirect
53. C₄×C₂²⋊D₄₇	C₂²	semidirect
54. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
55. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
56. #13093982	C₂²	semidirect
57. #13093982	C₂²	semidirect
58. #13093980	C₂²	semidirect
59. C₂×C₄⋊Dic₄₇	C₂²	semidirect
60. C₂×Dic₄₇⋊C₄	C₂²	semidirect
62. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
63. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
64. C₂²⋊C₄×D₄₇	C₂²	semidirect
65. C₂×C₄×Dic₄₇	C₂²	semidirect
66. C₂²×Q₈×C₄₇	C₂²	semidirect
68. C₂²⋊Q₈×C₄₇	C₂²	semidirect
69. C₂²⋊Q₈×C₄₇	C₂²	semidirect
70. C₂²⋊Q₈×C₄₇	C₂²	semidirect
71. C₂²⋊Q₈×C₄₇	C₂²	semidirect
72. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
73. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
143. C₂³×C₄₇	#41	semidirect
240. C₂×C₂²⋊Q₈	D₄₇	semidirect
244. C₄₇	#3505	semidirect
246. C₂²×Q₈	C₂×D₄₇	semidirect
266. C₂²⋊Q₈	C₂×D₄₇	semidirect
267. C₂²⋊Q₈	C₂×D₄₇	semidirect
268. C₂²⋊Q₈	C₂×D₄₇	semidirect
269. C₂²⋊Q₈	C₂×D₄₇	semidirect
296. C₂×C₄⋊C₄	C₂×D₄₇	semidirect
297. C₂×C₄⋊C₄	C₂×D₄₇	semidirect
380. C₂³	#10625354	semidirect