Subgroups — #20257597

Order 6016.

1038 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689874	C₂	1	2	yes	maximal, complemented
2	#15689869	C₂	1	2	yes	maximal, complemented
3	#15689827	C₂	1	2	yes	maximal, complemented
4	#15689808	C₂	1	2	yes	maximal, complemented
5	#15689800	C₂	1	2	yes	maximal, complemented
6	#15689799	C₂	1	2	yes	maximal, complemented
7	#15689774	C₂	1	2	yes	maximal, complemented
8	#15689763	C₂	1	2	yes	maximal, complemented
9	#15689752	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689748	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689743	C₂	1	2	yes	maximal, complemented
12	#15689722	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689720	C₂	1	2	yes	maximal, complemented
14	#15689719	C₂	1	2	yes	maximal, complemented
15	#15689713	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689697	C₂	1	2	yes	maximal, complemented
17	#15689634	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13094007	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10625350	C₂²	1	2	yes	—
21	C₂×#10625350	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
23	#13094023	C₂²	1	2	yes	complemented
24	#13094022	C₂²	1	2	yes	complemented
25	#13094022	C₂²	1	2	yes	complemented
26	#13094019	C₂²	1	2	yes	complemented
27	#13094019	C₂²	1	2	yes	complemented
28	#13094019	C₂²	1	2	yes	complemented
29	#13094019	C₂²	1	2	yes	complemented
30	#13094017	C₂²	1	2	yes	complemented
31	#13094017	C₂²	1	2	yes	complemented
32	#13094015	C₂²	1	2	yes	complemented
33	#13094014	C₂²	1	2	yes	complemented
34	#13094014	C₂²	1	2	yes	complemented
35	#13094014	C₂²	1	2	yes	complemented
36	#13094014	C₂²	1	2	yes	complemented
37	#13094013	C₂²	1	2	yes	complemented
38	#13094013	C₂²	1	2	yes	complemented
39	#13094010	C₂²	1	2	yes	—
40	#13094010	C₂²	1	2	yes	complemented
41	#13094009	C₂²	1	2	yes	complemented
42	#13094009	C₂²	1	2	yes	complemented
43	#13094009	C₂²	1	2	yes	complemented
44	#13094009	C₂²	1	2	yes	complemented
45	#13094008	C₂²	1	2	yes	—
46	#13094007	C₂²	1	2	yes	—
47	#13094007	C₂²	1	2	yes	—
48	#13094007	C₂²	1	2	yes	—
49	#13094007	C₂²	1	2	yes	—
50	#13094007	C₂²	1	2	yes	—
51	#13094007	C₂²	1	2	yes	complemented
52	#13094007	C₂²	1	2	yes	complemented
53	#13094006	C₂²	1	2	yes	—
54	#13094006	C₂²	1	2	yes	complemented
55	#13094004	C₂²	1	2	yes	complemented
56	#13094003	C₂²	1	1	yes	characteristic
57	#13094003	C₂²	1	2	yes	complemented
58	#13094003	C₂²	1	1	yes	characteristic, complemented
59	#13094002	C₂²	1	2	yes	complemented
60	#13094002	C₂²	1	2	yes	complemented
61	#13094002	C₂²	1	2	yes	complemented
62	#13094002	C₂²	1	2	yes	complemented
63	#13094001	C₂²	1	2	yes	—
64	#13094001	C₂²	1	2	yes	—
65	#13094000	C₂²	1	2	yes	complemented
66	#13094000	C₂²	1	2	yes	complemented
67	#13094000	C₂²	1	2	yes	complemented
68	#13094000	C₂²	1	2	yes	complemented
69	#13093999	C₂²	1	2	yes	complemented
70	#13093998	C₂²	1	2	yes	—
71	#13093998	C₂²	1	1	yes	characteristic
72	#13093998	C₂²	1	1	yes	characteristic, complemented
73	#13093997	C₂²	1	2	yes	—
74	#13093997	C₂²	1	2	yes	—
75	#13093994	C₂²	1	2	yes	—
76	#13093993	C₂²	1	2	yes	—
77	#13093989	C₂²	1	2	yes	complemented
78	#13093986	C₂²	1	2	yes	complemented
79	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
80	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
81	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
83	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
84	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
85	#13093983	C₂²	1	2	yes	complemented
86	#13093983	C₂²	1	1	yes	characteristic, complemented
87	#13093982	C₂²	1	2	yes	complemented
88	#13093980	C₂²	1	2	yes	—
89	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
90	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
91	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
92	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
93	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
94	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
95	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
96	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
98	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
99	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
100	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
101	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
102	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
105	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
107	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
108	C₂³×D₄₇	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₄₇	—	4	2	no	—
110	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
112	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	—	4	2	no	—
114	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊D₄₇	—	4	2	no	—
123	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
128	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
129	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
130	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
131	#10625350	—	4	4	no	—
132	#10625350	—	4	2	no	—
133	C₂×D₁₈₈	C₂³	1	2	yes	—
134	C₂×D₁₈₈	C₂³	1	2	yes	—
135	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₄₇	C₂³	1	2	yes	—
137	C₂×C₄×D₄₇	C₂³	1	2	yes	—
138	C₂×C₄×D₄₇	C₂³	1	2	yes	—
139	C₂×C₄×D₄₇	C₂³	1	2	yes	—
140	C₂×C₄×D₄₇	C₂³	1	2	yes	—
141	C₂×Dic₉₄	C₂³	1	2	yes	—
142	C₂×Dic₉₄	C₂³	1	2	yes	—
143	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
145	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
146	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
147	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
149	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
150	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
151	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
155	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
156	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
157	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
158	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
159	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
160	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
174	C₄⋊Dic₄₇	C₂³	1	2	yes	—
175	C₄⋊Dic₄₇	C₂³	1	2	yes	—
176	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
177	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
178	C₄⋊Dic₄₇	C₂³	1	2	yes	—
179	C₄⋊Dic₄₇	C₂³	1	2	yes	—
180	Dic₄₇⋊C₄	C₂³	1	2	yes	—
181	Dic₄₇⋊C₄	C₂³	1	2	yes	—
182	Dic₄₇⋊C₄	C₂³	1	2	yes	—
183	Dic₄₇⋊C₄	C₂³	1	2	yes	—
184	Dic₄₇⋊C₄	C₂³	1	2	yes	—
185	Dic₄₇⋊C₄	C₂³	1	2	yes	—
186	Dic₄₇⋊C₄	C₂³	1	2	yes	—
187	Dic₄₇⋊C₄	C₂³	1	2	yes	—
188	Dic₄₇⋊C₄	C₂³	1	2	yes	—
189	Dic₄₇⋊C₄	C₂³	1	2	yes	—
190	Dic₄₇⋊C₄	C₂³	1	2	yes	—
191	Dic₄₇⋊C₄	C₂³	1	2	yes	—
192	Dic₄₇⋊C₄	C₂³	1	2	yes	—
193	Dic₄₇⋊C₄	C₂³	1	2	yes	—
194	C₄×Dic₄₇	C₂³	1	2	yes	—
195	C₄×Dic₄₇	C₂³	1	2	yes	—
196	C₄×Dic₄₇	C₂³	1	2	yes	—
197	C₄×Dic₄₇	C₂³	1	2	yes	—
198	C₄×Dic₄₇	C₂³	1	2	yes	—
199	C₂³×C₄₇	—	2	2	no	—
200	C₂³×C₄₇	—	2	2	no	—
201	C₂³×C₄₇	—	4	1	no	—
202	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
203	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
204	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
205	C₂²×D₄₇	—	2	2	no	—
206	C₂²×D₄₇	—	4	1	no	—
207	C₂²×D₄₇	—	4	1	no	—
208	C₂²×D₄₇	C₂⁴	1	2	yes	—
209	C₂²×D₄₇	C₂⁴	1	2	yes	—
210	Q₈×C₄₇	—	4	1	no	—
211	Q₈×C₄₇	—	4	2	no	—
212	Q₈×C₄₇	—	4	1	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	2	4	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	4	1	no	—
217	C₂×C₄×C₄₇	—	4	1	no	—
218	C₂×C₄×C₄₇	—	4	1	no	—
219	C₂×C₄×C₄₇	—	4	1	no	—
220	C₂×C₄×C₄₇	—	4	2	no	—
221	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
222	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
224	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
225	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
228	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
229	C₂²⋊D₄₇	—	2	4	no	—
230	C₂²⋊D₄₇	—	2	4	no	—
231	C₂²⋊D₄₇	—	2	4	no	—
232	C₂²⋊D₄₇	—	4	2	no	—
233	C₂²⋊D₄₇	—	4	2	no	—
234	C₂×Dic₄₇	—	2	2	no	—
235	C₂×Dic₄₇	—	4	1	no	—
236	C₂×Dic₄₇	—	4	1	no	—
237	C₂×Dic₄₇	C₂⁴	1	2	yes	—
238	C₂×Dic₄₇	C₂⁴	1	2	yes	—
239	C₂×Dic₄₇	C₂⁴	1	2	yes	—
240	C₂×Dic₄₇	C₂⁴	1	2	yes	—
241	C₂×Dic₄₇	C₂⁴	1	2	yes	—
242	C₂×Dic₄₇	C₂⁴	1	2	yes	—
243	D₁₈₈	—	4	2	no	—
244	D₁₈₈	—	4	1	no	—
245	D₁₈₈	—	4	2	no	—
246	C₄×D₄₇	—	4	2	no	—
247	C₄×D₄₇	—	4	2	no	—
248	C₄×D₄₇	—	4	2	no	—
249	C₄×D₄₇	—	4	2	no	—
250	C₄×D₄₇	—	4	2	no	—
251	Dic₉₄	—	4	2	no	—
252	Dic₉₄	—	4	1	no	—
253	Dic₉₄	—	4	2	no	—
254	C₂²×C₄₇	—	2	1	no	—
255	C₂²×C₄₇	—	2	1	no	—
256	C₂²×C₄₇	—	2	1	no	—
257	C₂²×C₄₇	—	2	1	no	—
258	C₂²×C₄₇	—	2	1	no	—
259	C₂²×C₄₇	—	2	1	no	—
260	C₂²×C₄₇	—	2	1	no	—
261	C₂²×C₄₇	—	4	4	no	—
262	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
263	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
264	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
265	C₂×D₄₇	—	2	2	no	—
266	C₂×D₄₇	—	2	2	no	—
267	C₂×D₄₇	—	2	2	no	—
268	C₂×D₄₇	—	2	2	no	—
269	C₂×D₄₇	—	2	2	no	—
270	C₂×D₄₇	—	2	2	no	—
271	C₂×D₄₇	—	8	2	no	—
272	C₄×C₄₇	—	2	1	no	—
273	C₄×C₄₇	—	2	2	no	—
274	C₄×C₄₇	—	2	1	no	—
275	C₄×C₄₇	—	2	2	no	—
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	2	1	no	—
278	C₄×C₄₇	—	2	2	no	—
279	C₄×C₄₇	—	2	2	no	—
280	Dic₄₇	—	2	2	no	—
281	Dic₄₇	—	2	2	no	—
282	Dic₄₇	—	2	2	no	—
283	Dic₄₇	—	2	2	no	—
284	Dic₄₇	—	2	2	no	—
285	Dic₄₇	—	2	2	no	—
286	#3535	—	47	1	no	maximal, Sylow
287	C₂×C₄₇	—	2	2	no	—
288	C₂×C₄₇	—	2	2	no	—
289	C₂×C₄₇	—	4	1	no	—
290	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
292	C₂×C₄₇	#585	1	1	yes	characteristic
293	D₄₇	—	4	2	no	—
294	D₄₇	—	4	2	no	—
295	#563	—	47	2	no	—
296	#562	—	47	2	no	—
297	#554	—	47	2	no	—
298	#552	—	47	2	no	—
299	#551	—	47	2	no	—
300	#551	—	47	2	no	—
301	#547	—	47	2	no	—
302	#546	—	47	2	no	—
303	#544	—	47	1	no	—
304	#543	—	47	1	no	—
305	#542	—	47	2	no	—
306	#539	—	47	1	no	—
307	#539	—	47	2	no	—
308	#539	—	47	2	no	—
309	#538	—	47	1	no	—
310	#536	—	47	2	no	—
311	#525	—	47	1	no	—
312	C₂×#123	—	47	1	no	—
313	C₂×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
314	C₄₇	#3535	1	1	yes	characteristic, complemented, Sylow
315	C₂×#41	—	47	1	no	—
316	C₂×#41	—	47	2	no	—
317	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
318	C₂²×D₄	—	47	1	no	—
319	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
320	C₄⋊Q₈	—	47	2	no	—
321	C₄⋊Q₈	—	47	2	no	—
322	C₄⋊Q₈	—	47	2	no	—
323	#126	—	47	2	no	—
324	#126	—	47	2	no	—
325	#126	—	47	2	no	—
326	#126	—	47	2	no	—
327	#126	—	47	2	no	—
328	#126	—	47	2	no	—
329	#125	—	47	2	no	—
330	#125	—	47	2	no	—
331	#125	—	47	2	no	—
332	#125	—	47	2	no	—
333	#125	—	47	2	no	—
334	#124	—	47	2	no	—
335	#124	—	47	2	no	—
336	#124	—	47	2	no	—
337	#124	—	47	2	no	—
338	#123	—	47	2	no	—
339	#123	—	47	2	no	—
340	#123	—	47	2	no	—
341	#123	—	47	2	no	—
342	#123	—	47	2	no	—
343	#123	—	47	2	no	—
344	#123	—	47	2	no	—
345	#123	—	47	2	no	—
346	#123	—	47	2	no	—
347	#123	—	47	2	no	—
348	#123	—	47	2	no	—
349	#123	—	47	2	no	—
350	#123	—	47	2	no	—
351	#123	—	47	2	no	—
352	C₂²⋊Q₈	—	47	2	no	—
353	C₂²⋊Q₈	—	47	2	no	—
354	C₂²⋊Q₈	—	47	2	no	—
355	C₂²⋊Q₈	—	47	2	no	—
356	C₂²⋊Q₈	—	47	1	no	—
357	C₂²⋊Q₈	—	47	1	no	—
358	C₂²⋊Q₈	—	47	2	no	—
359	C₂²⋊Q₈	—	47	2	no	—
360	C₂²⋊Q₈	—	47	2	no	—
361	C₂²⋊Q₈	—	47	2	no	—
362	C₂²⋊Q₈	—	47	2	no	—
363	C₂²⋊Q₈	—	47	2	no	—
364	C₂²⋊Q₈	—	47	2	no	—
365	C₂²⋊Q₈	—	47	2	no	—
366	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
367	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
368	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
369	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
370	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
371	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
372	#121	—	47	1	no	—
373	#121	—	47	1	no	—
374	#121	—	47	2	no	—
375	#121	—	47	2	no	—
376	#121	—	47	2	no	—
377	#121	—	47	2	no	—
378	#120	—	47	2	no	—
379	#120	—	47	2	no	—
380	C₄×Q₈	—	47	2	no	—
381	C₄×D₄	—	47	2	no	—
382	C₄×D₄	—	47	2	no	—
383	C₄×D₄	—	47	2	no	—
384	C₄×D₄	—	47	2	no	—
385	C₄×D₄	—	47	2	no	—
386	C₄×D₄	—	47	2	no	—
387	C₄×D₄	—	47	2	no	—
388	#117	—	47	1	no	—
389	#117	—	47	2	no	—
390	#117	—	47	2	no	—
391	#117	—	47	2	no	—
392	C₂×C₄⋊C₄	—	47	1	no	—
393	C₂×C₄⋊C₄	—	47	1	no	—
394	C₂×C₄⋊C₄	—	47	2	no	—
395	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
396	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
397	C₂×C₂²⋊C₄	—	47	1	no	—
398	C₂×C₂²⋊C₄	—	47	1	no	—
399	C₂×C₂²⋊C₄	—	47	1	no	—
400	C₂×C₂²⋊C₄	—	47	2	no	—
401	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
402	C₂⁴	—	47	1	no	—
403	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
404	#41	—	188	2	no	—
405	#41	—	188	4	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	—	47	2	no	—
408	C₂×Q₈	—	47	1	no	—
409	C₂×Q₈	—	47	2	no	—
410	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
411	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
412	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
413	C₂×D₄	—	47	2	no	—
414	C₂×D₄	—	47	2	no	—
415	C₂×D₄	—	47	2	no	—
416	C₂×D₄	—	47	2	no	—
417	C₂×D₄	—	47	2	no	—
418	C₂×D₄	—	47	2	no	—
419	C₂×D₄	—	47	2	no	—
420	C₂×D₄	—	47	1	no	—
421	C₂×D₄	—	188	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	47	1	no	—
424	C₂²×C₄	—	47	1	no	—
425	C₂²×C₄	—	47	1	no	—
426	C₂²×C₄	—	47	2	no	—
427	C₂²×C₄	—	47	2	no	—
428	C₂²×C₄	—	47	2	no	—
429	C₂²×C₄	—	47	2	no	—
430	C₂²×C₄	—	47	2	no	—
431	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
432	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
433	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
434	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
435	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
436	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
437	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
438	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
439	C₄⋊C₄	—	47	2	no	—
440	C₄⋊C₄	—	47	2	no	—
441	C₄⋊C₄	—	47	2	no	—
442	C₄⋊C₄	—	47	2	no	—
443	C₄⋊C₄	—	47	2	no	—
444	C₄⋊C₄	—	47	2	no	—
445	C₄⋊C₄	—	47	2	no	—
446	C₄⋊C₄	—	47	2	no	—
447	C₄⋊C₄	—	47	2	no	—
448	C₄⋊C₄	—	47	2	no	—
449	C₄⋊C₄	—	47	2	no	—
450	C₄⋊C₄	—	47	2	no	—
451	C₄⋊C₄	—	47	2	no	—
452	C₄⋊C₄	—	47	2	no	—
453	C₄⋊C₄	—	47	2	no	—
454	C₄⋊C₄	—	47	1	no	—
455	C₄⋊C₄	—	47	1	no	—
456	C₄⋊C₄	—	47	2	no	—
457	C₄⋊C₄	—	47	2	no	—
458	C₄⋊C₄	—	47	2	no	—
459	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
460	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
461	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
462	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
463	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
464	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
465	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
466	C₂²⋊C₄	—	47	2	no	—
467	C₂²⋊C₄	—	47	2	no	—
468	C₂²⋊C₄	—	47	2	no	—
469	C₂²⋊C₄	—	47	2	no	—
470	C₂²⋊C₄	—	47	2	no	—
471	C₂²⋊C₄	—	47	2	no	—
472	C₂²⋊C₄	—	47	2	no	—
473	C₂²⋊C₄	—	47	2	no	—
474	C₂²⋊C₄	—	47	2	no	—
475	C₂²⋊C₄	—	47	2	no	—
476	C₂²⋊C₄	—	47	2	no	—
477	C₂²⋊C₄	—	47	2	no	—
478	C₂²⋊C₄	—	47	2	no	—
479	C₂²⋊C₄	—	47	2	no	—
480	C₂²⋊C₄	—	47	2	no	—
481	C₂²⋊C₄	—	47	2	no	—
482	C₂²⋊C₄	—	47	2	no	—
483	C₂²⋊C₄	—	47	2	no	—
484	C₂²⋊C₄	—	47	2	no	—
485	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
487	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
489	C₄²	—	47	2	no	—
490	C₄²	—	47	2	no	—
491	C₄²	—	47	2	no	—
492	C₄²	—	47	2	no	—
493	C₄²	—	47	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	47	2	no	—
498	C₂³	—	47	2	no	—
499	C₂³	—	94	2	no	—
500	C₂³	—	188	1	no	—
501	C₂³	—	188	1	no	—
502	C₂³	C₂³×D₄₇	1	1	yes	characteristic
503	C₂³	C₂³×D₄₇	1	1	yes	characteristic
504	C₂³	C₂³×D₄₇	1	1	yes	characteristic
505	Q₈	—	4	1	no	—
506	Q₈	—	4	2	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	188	2	no	—
509	Q₈	—	188	1	no	—
510	Q₈	—	188	2	no	—
511	D₄	—	94	4	no	—
512	D₄	—	94	4	no	—
513	D₄	—	94	4	no	—
514	D₄	—	188	2	no	—
515	D₄	—	188	1	no	—
516	D₄	—	188	2	no	—
517	D₄	—	188	2	no	—
518	D₄	—	188	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	47	2	no	—
528	C₂×C₄	—	47	2	no	—
529	C₂×C₄	—	47	2	no	—
530	C₂×C₄	—	47	2	no	—
531	C₂×C₄	—	47	2	no	—
532	C₂×C₄	—	47	2	no	—
533	C₂×C₄	—	94	2	no	—
534	C₂×C₄	—	188	2	no	—
535	C₂×C₄	—	188	2	no	—
536	C₂×C₄	—	188	2	no	—
537	C₂×C₄	—	188	2	no	—
538	C₂×C₄	—	188	2	no	—
539	C₂×C₄	—	188	1	no	—
540	C₂×C₄	—	188	1	no	—
541	C₂×C₄	C₂³×D₄₇	1	2	yes	—
542	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
543	C₂×C₄	C₂³×D₄₇	1	2	yes	—
544	C₂×C₄	C₂³×D₄₇	1	2	yes	—
545	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₄₇	1	2	yes	—
548	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	94	2	no	—
558	C₂²	—	94	2	no	—
559	C₂²	—	94	2	no	—
560	C₂²	—	94	2	no	—
561	C₂²	—	94	2	no	—
562	C₂²	—	94	2	no	—
563	C₂²	—	376	2	no	—
564	C₂²	#13094069	1	2	yes	—
565	C₂²	#13094072	1	2	yes	—
566	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	94	2	no	—
576	C₄	—	94	2	no	—
577	C₄	—	94	2	no	—
578	C₄	—	94	2	no	—
579	C₄	—	94	2	no	—
580	C₄	—	94	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	2	2	no	—
583	C₂	—	4	1	no	—
584	C₂	—	188	2	no	—
585	C₂	—	188	2	no	—
586	C₂	C₂×#13094069	1	1	yes	characteristic
587	C₂	C₂×#13094072	1	1	yes	characteristic
588	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	#3535
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. #15689874	C₂	semidirect
2. #15689869	C₂	semidirect
3. #15689827	C₂	semidirect
4. #15689808	C₂	semidirect
5. #15689800	C₂	semidirect
6. #15689799	C₂	semidirect
7. #15689774	C₂	semidirect
8. #15689763	C₂	semidirect
9. #15689752	C₂	semidirect
10. #15689748	C₂	semidirect
11. #15689743	C₂	semidirect
12. #15689722	C₂	semidirect
13. #15689720	C₂	semidirect
14. #15689719	C₂	semidirect
15. #15689713	C₂	semidirect
16. #15689697	C₂	semidirect
17. #15689634	C₂	semidirect
18. C₂×#13094007	C₂	semidirect
19. C₂×C₂²⋊Q₈×C₄₇	C₂	semidirect
21. C₂×#10625350	C₂²	semidirect
23. #13094023	C₂²	semidirect
24. #13094022	C₂²	semidirect
25. #13094022	C₂²	semidirect
26. #13094019	C₂²	semidirect
27. #13094019	C₂²	semidirect
28. #13094019	C₂²	semidirect
29. #13094019	C₂²	semidirect
30. #13094017	C₂²	semidirect
31. #13094017	C₂²	semidirect
32. #13094015	C₂²	semidirect
33. #13094014	C₂²	semidirect
34. #13094014	C₂²	semidirect
35. #13094014	C₂²	semidirect
36. #13094014	C₂²	semidirect
37. #13094013	C₂²	semidirect
38. #13094013	C₂²	semidirect
40. #13094010	C₂²	semidirect
41. #13094009	C₂²	semidirect
42. #13094009	C₂²	semidirect
43. #13094009	C₂²	semidirect
44. #13094009	C₂²	semidirect
51. #13094007	C₂²	semidirect
52. #13094007	C₂²	semidirect
54. #13094006	C₂²	semidirect
55. #13094004	C₂²	semidirect
57. #13094003	C₂²	semidirect
58. #13094003	C₂²	semidirect
59. #13094002	C₂²	semidirect
60. #13094002	C₂²	semidirect
61. #13094002	C₂²	semidirect
62. #13094002	C₂²	semidirect
65. #13094000	C₂²	semidirect
66. #13094000	C₂²	semidirect
67. #13094000	C₂²	semidirect
68. #13094000	C₂²	semidirect
69. #13093999	C₂²	semidirect
72. #13093998	C₂²	semidirect
77. #13093989	C₂²	semidirect
78. #13093986	C₂²	semidirect
81. C₄×C₂²⋊D₄₇	C₂²	semidirect
82. C₄×C₂²⋊D₄₇	C₂²	semidirect
85. #13093983	C₂²	semidirect
86. #13093983	C₂²	semidirect
87. #13093982	C₂²	semidirect
91. C₄⋊C₄×D₄₇	C₂²	semidirect
96. C₂²×Q₈×C₄₇	C₂²	semidirect
101. C₂²⋊Q₈×C₄₇	C₂²	semidirect
102. C₂²⋊Q₈×C₄₇	C₂²	semidirect
103. C₂²⋊Q₈×C₄₇	C₂²	semidirect
104. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
105. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
313. C₂×C₂²⋊Q₈	D₄₇	semidirect
314. C₄₇	#3535	semidirect
317. C₂²×Q₈	C₂×D₄₇	semidirect
369. C₂²⋊Q₈	C₂×D₄₇	semidirect
370. C₂²⋊Q₈	C₂×D₄₇	semidirect
371. C₂²⋊Q₈	C₂×D₄₇	semidirect
395. C₂×C₄⋊C₄	C₂×D₄₇	semidirect
396. C₂×C₄⋊C₄	C₂×D₄₇	semidirect