Subgroups — #20257003

Order 6016.

1094 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689851	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689846	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689841	C₂	1	2	yes	maximal, complemented
4	#15689813	C₂	1	2	yes	maximal, complemented
5	#15689806	C₂	1	4	yes	maximal, complemented
6	D₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689782	C₂	1	2	yes	maximal, complemented
8	#15689777	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689772	C₂	1	2	yes	maximal, complemented
10	#15689680	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689677	C₂	1	2	yes	maximal, complemented
12	#15689657	C₂	1	2	yes	maximal, complemented
13	#15689653	C₂	1	4	yes	maximal, complemented
14	C₄×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#10625352	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×Dic₉₄	C₂	1	2	yes	maximal, complemented
17	C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625350	C₂²	1	1	yes	characteristic
19	C₂×#10625352	C₂²	1	2	yes	—
20	C₂²×Dic₉₄	C₂²	1	2	yes	—
21	#13094024	C₂²	1	1	yes	characteristic
22	#13094024	C₂²	1	1	yes	characteristic
23	#13094023	C₂²	1	2	yes	—
24	#13094022	C₂²	1	2	yes	—
25	#13094019	C₂²	1	4	yes	—
26	#13094018	C₂²	1	4	yes	—
27	#13094017	C₂²	1	4	yes	—
28	#13094016	C₂²	1	2	yes	—
29	#13094016	C₂²	1	2	yes	—
30	#13094014	C₂²	1	4	yes	—
31	#13094014	C₂²	1	4	yes	—
32	#13094012	C₂²	1	2	yes	—
33	#13094010	C₂²	1	4	yes	—
34	#13094008	C₂²	1	4	yes	—
35	#13094007	C₂²	1	4	yes	—
36	#13094005	C₂²	1	4	yes	—
37	#13094004	C₂²	1	2	yes	—
38	#13094003	C₂²	1	2	yes	—
39	#13094003	C₂²	1	2	yes	—
40	#13094003	C₂²	1	2	yes	—
41	#13094002	C₂²	1	4	yes	—
42	#13094001	C₂²	1	4	yes	—
43	#13094000	C₂²	1	2	yes	—
44	#13093998	C₂²	1	2	yes	—
45	#13093996	C₂²	1	4	yes	—
46	C₄×Dic₉₄	C₂²	1	2	yes	—
47	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
48	C₄×Dic₉₄	C₂²	1	4	yes	—
49	C₄×Dic₉₄	C₂²	1	2	yes	—
50	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
51	C₄×Dic₉₄	C₂²	1	4	yes	—
52	C₄×Dic₉₄	C₂²	1	2	yes	—
53	C₄×Dic₉₄	C₂²	1	2	yes	—
54	#13093989	C₂²	1	2	yes	—
55	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
56	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
57	D₄×Dic₄₇	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
59	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
60	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
61	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
62	#13093983	C₂²	1	1	yes	characteristic
63	#13093983	C₂²	1	2	yes	—
64	#13093982	C₂²	1	2	yes	—
65	#13093981	C₂²	1	2	yes	—
66	#13093981	C₂²	1	4	yes	—
67	#13093980	C₂²	1	4	yes	—
68	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
69	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
70	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
71	C₄²×D₄₇	C₂²	1	2	yes	—
72	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
73	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
74	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
75	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₄₇	C₂²	1	2	yes	—
77	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
78	C₄×D₄×C₄₇	C₂²	1	2	yes	—
79	#117×C₄₇	C₂²	1	2	yes	—
80	#117×C₄₇	C₂²	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂²	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
83	#41×C₄₇	—	2	4	no	—
84	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₄₇	C₂³	1	2	yes	—
86	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
95	C₂²×Dic₄₇	C₂³	1	4	yes	—
96	C₂²×Dic₄₇	C₂³	1	4	yes	—
97	#10625352	—	2	8	no	—
98	#10625350	—	2	4	no	—
99	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₄₇	C₂³	1	2	yes	—
101	C₂×C₄×D₄₇	C₂³	1	2	yes	—
102	C₂×C₄×D₄₇	C₂³	1	2	yes	—
103	C₂×Dic₉₄	—	2	8	no	—
104	C₂×Dic₉₄	C₂³	1	2	yes	—
105	C₂×Dic₉₄	C₂³	1	4	yes	—
106	C₂×Dic₉₄	C₂³	1	2	yes	—
107	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
109	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
110	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
113	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
114	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
115	C₄²×C₄₇	C₂³	1	1	yes	characteristic
116	C₄²×C₄₇	C₂³	1	1	yes	characteristic
117	C₄²×C₄₇	C₂³	1	2	yes	—
118	C₄²×C₄₇	C₂³	1	1	yes	characteristic
119	C₄²×C₄₇	C₂³	1	2	yes	—
120	C₄²×C₄₇	C₂³	1	1	yes	characteristic
121	C₄²×C₄₇	C₂³	1	2	yes	—
122	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
123	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
124	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
125	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
130	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
131	C₄⋊Dic₄₇	C₂³	1	2	yes	—
132	C₄⋊Dic₄₇	C₂³	1	4	yes	—
133	C₄⋊Dic₄₇	C₂³	1	2	yes	—
134	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₄₇	C₂³	1	2	yes	—
136	C₄⋊Dic₄₇	C₂³	1	2	yes	—
137	Dic₄₇⋊C₄	C₂³	1	2	yes	—
138	Dic₄₇⋊C₄	C₂³	1	4	yes	—
139	Dic₄₇⋊C₄	C₂³	1	4	yes	—
140	Dic₄₇⋊C₄	C₂³	1	4	yes	—
141	Dic₄₇⋊C₄	C₂³	1	4	yes	—
142	Dic₄₇⋊C₄	C₂³	1	4	yes	—
143	Dic₄₇⋊C₄	C₂³	1	2	yes	—
144	Dic₄₇⋊C₄	C₂³	1	4	yes	—
145	Dic₄₇⋊C₄	C₂³	1	4	yes	—
146	C₄×Dic₄₇	C₂³	1	2	yes	—
147	C₄×Dic₄₇	C₂³	1	2	yes	—
148	C₄×Dic₄₇	C₂³	1	2	yes	—
149	C₄×Dic₄₇	C₂³	1	4	yes	—
150	C₄×Dic₄₇	C₂³	1	4	yes	—
151	C₄×Dic₄₇	C₂³	1	4	yes	—
152	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
153	C₂³×C₄₇	C₂⁴	1	2	yes	—
154	C₂²×D₄₇	C₂⁴	1	2	yes	—
155	Q₈×C₄₇	—	2	2	no	—
156	D₄×C₄₇	—	2	4	no	—
157	D₄×C₄₇	#41	1	4	yes	complemented
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
165	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
168	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
170	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₄₇	—	2	8	no	—
174	C₂²⋊D₄₇	—	2	4	no	—
175	C₂×Dic₄₇	—	2	8	no	—
176	C₂×Dic₄₇	—	2	8	no	—
177	C₂×Dic₄₇	C₂⁴	1	2	yes	—
178	C₂×Dic₄₇	C₂⁴	1	2	yes	—
179	C₂×Dic₄₇	C₂⁴	1	4	yes	—
180	C₂×Dic₄₇	C₂⁴	1	4	yes	—
181	C₂×Dic₄₇	C₂⁴	1	2	yes	—
182	D₁₈₈	—	2	2	no	—
183	C₄×D₄₇	—	2	4	no	—
184	C₄×D₄₇	—	2	4	no	—
185	C₄×D₄₇	—	2	4	no	—
186	Dic₉₄	—	2	4	no	—
187	Dic₉₄	—	2	4	no	—
188	Dic₉₄	—	2	8	no	—
189	Dic₉₄	#41	1	4	yes	complemented
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	2	2	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	C₂×#41	1	4	yes	—
196	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
197	C₂×D₄₇	—	2	2	no	—
198	C₂×D₄₇	—	2	2	no	—
199	C₂×D₄₇	—	2	2	no	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	2	1	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	C₂×#41	1	2	yes	—
207	C₄×C₄₇	C₂×#41	1	2	yes	—
208	C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
209	Dic₄₇	—	2	4	no	—
210	Dic₄₇	—	2	4	no	—
211	Dic₄₇	—	2	2	no	—
212	Dic₄₇	—	2	2	no	—
213	Dic₄₇	C₂×#41	1	4	yes	—
214	#3482	—	47	1	no	maximal, Sylow
215	C₂×C₄₇	—	2	4	no	—
216	C₂×C₄₇	—	4	1	no	—
217	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
218	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
219	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
220	D₄₇	—	4	2	no	—
221	#557	—	47	1	no	—
222	#556	—	47	1	no	—
223	#556	—	47	2	no	—
224	#552	—	47	2	no	—
225	#552	—	47	4	no	—
226	D₄×Q₈	—	47	1	no	—
227	#548	—	47	2	no	—
228	#547	—	47	2	no	—
229	#547	—	47	1	no	—
230	#533	—	47	2	no	—
231	#533	—	47	1	no	—
232	#529	—	47	4	no	—
233	#529	—	47	2	no	—
234	C₄×#41	—	47	2	no	—
235	C₄×#41	—	47	1	no	—
236	C₄×#41	D₄₇	1	1	yes	characteristic, complemented
237	C₂×C₄×Q₈	—	47	2	no	—
238	C₄₇	#3482	1	1	yes	characteristic, complemented, Sylow
239	C₂×#41	—	47	2	no	—
240	C₂×#41	—	47	1	no	—
241	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
242	C₂²×Q₈	—	47	2	no	—
243	C₄⋊Q₈	—	47	2	no	—
244	C₄⋊Q₈	—	47	2	no	—
245	C₄⋊Q₈	—	47	1	no	—
246	C₄⋊Q₈	—	47	1	no	—
247	#126	—	47	4	no	—
248	#126	—	47	4	no	—
249	#126	—	47	4	no	—
250	#125	—	47	4	no	—
251	#125	—	47	4	no	—
252	#125	—	47	2	no	—
253	#125	—	47	2	no	—
254	#124	—	47	4	no	—
255	#124	—	47	2	no	—
256	#123	—	47	4	no	—
257	#123	—	47	4	no	—
258	#123	—	47	4	no	—
259	C₂²⋊Q₈	—	47	2	no	—
260	C₂²⋊Q₈	—	47	2	no	—
261	C₂²⋊Q₈	—	47	2	no	—
262	C₂²⋊Q₈	—	47	2	no	—
263	C₂²⋊Q₈	—	47	2	no	—
264	C₂²⋊Q₈	—	47	4	no	—
265	C₂²⋊Q₈	—	47	4	no	—
266	#121	—	47	4	no	—
267	#121	—	47	2	no	—
268	C₄×Q₈	—	47	2	no	—
269	C₄×Q₈	—	47	1	no	—
270	C₄×Q₈	—	47	4	no	—
271	C₄×Q₈	—	47	2	no	—
272	C₄×Q₈	—	47	2	no	—
273	C₄×Q₈	—	47	2	no	—
274	C₄×Q₈	—	47	4	no	—
275	C₄×Q₈	—	47	2	no	—
276	C₄×Q₈	—	47	1	no	—
277	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
278	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
279	C₄×D₄	—	47	2	no	—
280	C₄×D₄	—	47	2	no	—
281	C₄×D₄	—	47	4	no	—
282	C₄×D₄	—	47	2	no	—
283	C₄×D₄	—	47	4	no	—
284	C₄×D₄	—	47	1	no	—
285	C₄×D₄	—	47	1	no	—
286	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
287	C₄×D₄	C₂×D₄₇	1	2	yes	—
288	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
289	C₄×D₄	C₂×D₄₇	1	2	yes	—
290	#117	—	47	1	no	—
291	#117	—	47	2	no	—
292	#117	—	47	2	no	—
293	#117	—	47	4	no	—
294	#117	—	47	2	no	—
295	#117	—	47	4	no	—
296	#117	C₂×D₄₇	1	2	yes	—
297	#117	C₂×D₄₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	—	47	4	no	—
299	C₂×C₄⋊C₄	—	47	2	no	—
300	C₂×C₄²	—	47	4	no	—
301	C₂×C₄²	—	47	2	no	—
302	C₂×C₄²	C₂×D₄₇	1	2	yes	—
303	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
304	#41	—	2	4	no	—
305	#41	—	94	4	no	—
306	#41	—	94	8	no	—
307	C₂×Q₈	—	47	1	no	—
308	C₂×Q₈	—	47	4	no	—
309	C₂×Q₈	—	47	2	no	—
310	C₂×Q₈	—	47	2	no	—
311	C₂×Q₈	—	94	8	no	—
312	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
313	C₂×D₄	—	47	4	no	—
314	C₂×D₄	—	47	2	no	—
315	C₂×D₄	—	47	1	no	—
316	C₂×D₄	C₂²×D₄₇	1	2	yes	—
317	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
318	C₂²×C₄	—	47	4	no	—
319	C₂²×C₄	—	47	4	no	—
320	C₂²×C₄	—	47	2	no	—
321	C₂²×C₄	—	47	2	no	—
322	C₂²×C₄	—	47	2	no	—
323	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
324	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
325	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
328	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
329	C₄⋊C₄	—	47	2	no	—
330	C₄⋊C₄	—	47	4	no	—
331	C₄⋊C₄	—	47	4	no	—
332	C₄⋊C₄	—	47	4	no	—
333	C₄⋊C₄	—	47	2	no	—
334	C₄⋊C₄	—	47	4	no	—
335	C₄⋊C₄	—	47	4	no	—
336	C₄⋊C₄	—	47	4	no	—
337	C₄⋊C₄	—	47	4	no	—
338	C₄⋊C₄	—	47	1	no	—
339	C₄⋊C₄	—	47	2	no	—
340	C₄⋊C₄	—	47	4	no	—
341	C₄⋊C₄	—	47	1	no	—
342	C₄⋊C₄	—	47	2	no	—
343	C₄⋊C₄	—	47	2	no	—
344	C₄⋊C₄	—	47	2	no	—
345	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
346	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
347	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
348	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
349	C₂²⋊C₄	—	47	4	no	—
350	C₂²⋊C₄	—	47	2	no	—
351	C₂²⋊C₄	—	47	4	no	—
352	C₂²⋊C₄	—	47	2	no	—
353	C₂²⋊C₄	—	47	2	no	—
354	C₂²⋊C₄	—	47	4	no	—
355	C₂²⋊C₄	—	47	4	no	—
356	C₂²⋊C₄	—	47	4	no	—
357	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
358	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
359	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
360	C₄²	—	47	2	no	—
361	C₄²	—	47	4	no	—
362	C₄²	—	47	2	no	—
363	C₄²	—	47	4	no	—
364	C₄²	—	47	2	no	—
365	C₄²	—	47	4	no	—
366	C₄²	C₂²×D₄₇	1	1	yes	characteristic
367	C₄²	C₂²×D₄₇	1	2	yes	—
368	C₄²	C₂²×D₄₇	1	1	yes	characteristic
369	C₄²	C₂²×D₄₇	1	2	yes	—
370	C₄²	C₂²×D₄₇	1	1	yes	characteristic
371	C₄²	C₂²×D₄₇	1	1	yes	characteristic
372	C₄²	C₂²×D₄₇	1	2	yes	—
373	C₂³	—	47	2	no	—
374	C₂³	C₂³×D₄₇	1	1	yes	characteristic
375	C₂³	C₂³×D₄₇	1	2	yes	—
376	Q₈	—	2	2	no	—
377	Q₈	—	47	4	no	—
378	Q₈	—	94	8	no	—
379	Q₈	—	94	4	no	—
380	Q₈	—	94	4	no	—
381	D₄	—	2	4	no	—
382	D₄	—	94	4	no	—
383	D₄	—	94	8	no	—
384	D₄	—	94	2	no	—
385	D₄	#10625350	1	4	yes	complemented
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	47	2	no	—
393	C₂×C₄	—	47	2	no	—
394	C₂×C₄	—	47	2	no	—
395	C₂×C₄	—	47	4	no	—
396	C₂×C₄	—	47	4	no	—
397	C₂×C₄	—	94	4	no	—
398	C₂×C₄	—	94	8	no	—
399	C₂×C₄	—	94	8	no	—
400	C₂×C₄	—	94	4	no	—
401	C₂×C₄	—	94	4	no	—
402	C₂×C₄	C₂³×D₄₇	1	2	yes	—
403	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂³×D₄₇	1	2	yes	—
407	C₂×C₄	C₂³×D₄₇	1	2	yes	—
408	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
410	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	94	2	no	—
417	C₂²	—	94	2	no	—
418	C₂²	—	94	2	no	—
419	C₂²	C₂×#10625350	1	4	yes	—
420	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	47	4	no	—
428	C₄	—	94	4	no	—
429	C₄	—	94	2	no	—
430	C₄	—	94	4	no	—
431	C₄	—	94	2	no	—
432	C₄	#41×D₄₇	1	2	yes	—
433	C₄	C₂×#10625350	1	2	yes	—
434	C₄	#13094071	1	2	yes	—
435	C₂	—	2	4	no	—
436	C₂	—	4	1	no	—
437	C₂	—	188	2	no	—
438	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
439	C₂	C₂²×#10625350	1	1	yes	characteristic
440	C₂	C₂×#13094071	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₄×#41×C₄₇	C₂
hypercenter	C₄×#41	D₄₇
hypocenter	C₄₇	#3482
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #15689851	C₂	semidirect
2. #15689846	C₂	semidirect
3. #15689841	C₂	semidirect
4. #15689813	C₂	semidirect
5. #15689806	C₂	semidirect
6. D₄×Dic₉₄	C₂	semidirect
7. #15689782	C₂	semidirect
8. #15689777	C₂	semidirect
9. #15689772	C₂	semidirect
10. #15689680	C₂	semidirect
11. #15689677	C₂	semidirect
12. #15689657	C₂	semidirect
13. #15689653	C₂	semidirect
14. C₄×#10625350	C₂	semidirect
15. C₄×#10625352	C₂	semidirect
16. C₂×C₄×Dic₉₄	C₂	semidirect
17. C₄×#41×C₄₇	C₂	semidirect
157. D₄×C₄₇	#41	semidirect
189. Dic₉₄	#41	semidirect
236. C₄×#41	D₄₇	semidirect
238. C₄₇	#3482	semidirect
385. D₄	#10625350	semidirect