Subgroups — #20257829

Order 6016.

1004 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	#15689872	C₂	1	4	yes	maximal, complemented
2	#15689848	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689847	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689828	C₂	1	2	yes	maximal, complemented
5	#15689821	C₂	1	2	yes	maximal, complemented
6	#15689788	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₈×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
8	#15689784	C₂	1	2	yes	maximal, complemented
9	#15689776	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689750	C₂	1	2	yes	maximal, complemented
11	#15689747	C₂	1	2	yes	maximal, complemented
12	#15689734	C₂	1	2	yes	maximal, complemented
13	#15689720	C₂	1	4	yes	maximal, complemented
14	#15689698	C₂	1	2	yes	maximal, complemented
15	#15689657	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689657	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625354	C₂²	1	2	yes	—
19	C₂×Q₈×D₄₇	C₂²	1	2	yes	—
20	#13094023	C₂²	1	2	yes	—
21	#13094022	C₂²	1	4	yes	—
22	#13094022	C₂²	1	2	yes	—
23	#13094019	C₂²	1	4	yes	—
24	#13094019	C₂²	1	4	yes	—
25	#13094019	C₂²	1	4	yes	—
26	#13094018	C₂²	1	2	yes	—
27	#13094018	C₂²	1	2	yes	—
28	#13094016	C₂²	1	1	yes	characteristic
29	#13094016	C₂²	1	1	yes	characteristic
30	#13094015	C₂²	1	2	yes	—
31	#13094014	C₂²	1	4	yes	—
32	#13094014	C₂²	1	4	yes	—
33	#13094014	C₂²	1	4	yes	—
34	#13094013	C₂²	1	4	yes	—
35	#13094013	C₂²	1	2	yes	—
36	#13094012	C₂²	1	1	yes	characteristic
37	#13094012	C₂²	1	1	yes	characteristic
38	#13094009	C₂²	1	4	yes	—
39	#13094009	C₂²	1	4	yes	—
40	#13094009	C₂²	1	4	yes	—
41	#13094007	C₂²	1	2	yes	—
42	#13094007	C₂²	1	2	yes	—
43	#13094004	C₂²	1	2	yes	—
44	#13094003	C₂²	1	1	yes	characteristic
45	#13094003	C₂²	1	4	yes	—
46	#13094003	C₂²	1	1	yes	characteristic
47	#13094002	C₂²	1	4	yes	—
48	#13094002	C₂²	1	4	yes	—
49	#13094002	C₂²	1	4	yes	—
50	#13094000	C₂²	1	2	yes	—
51	#13094000	C₂²	1	2	yes	—
52	#13094000	C₂²	1	4	yes	—
53	#13094000	C₂²	1	4	yes	—
54	#13093999	C₂²	1	2	yes	—
55	#13093998	C₂²	1	1	yes	characteristic
56	#13093998	C₂²	1	4	yes	—
57	#13093998	C₂²	1	1	yes	characteristic
58	Q₈×Dic₄₇	C₂²	1	2	yes	—
59	Q₈×Dic₄₇	C₂²	1	2	yes	—
60	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
61	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
62	#13093989	C₂²	1	2	yes	—
63	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
64	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
65	#13093986	C₂²	1	2	yes	—
66	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
67	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
68	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
69	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
70	#13093982	C₂²	1	2	yes	—
71	#13093981	C₂²	1	2	yes	—
72	#13093981	C₂²	1	2	yes	—
73	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
74	C₂²×Q₈×C₄₇	C₂²	1	2	yes	—
75	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
76	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
77	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
78	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
79	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
83	C₂×Q₈×C₄₇	—	4	4	no	—
84	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
85	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
86	C₂×Q₈×C₄₇	C₂³	1	4	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	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
93	#10625354	—	4	4	no	—
94	Q₈×D₄₇	—	4	4	no	—
95	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
96	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
97	C₂×D₁₈₈	C₂³	1	4	yes	—
98	C₂×C₄×D₄₇	C₂³	1	2	yes	—
99	C₂×C₄×D₄₇	C₂³	1	2	yes	—
100	C₂×C₄×D₄₇	C₂³	1	4	yes	—
101	C₂×C₄×D₄₇	C₂³	1	4	yes	—
102	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
103	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
104	C₂×Dic₉₄	C₂³	1	4	yes	—
105	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
106	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
107	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
110	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₄²×C₄₇	C₂³	1	1	yes	characteristic
112	C₄²×C₄₇	C₂³	1	1	yes	characteristic
113	C₄²×C₄₇	C₂³	1	1	yes	characteristic
114	C₄²×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
116	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
117	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
118	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
119	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
120	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
121	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
124	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
125	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
129	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
131	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
132	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₄₇	C₂³	1	4	yes	—
134	C₄⋊Dic₄₇	C₂³	1	4	yes	—
135	Dic₄₇⋊C₄	C₂³	1	4	yes	—
136	Dic₄₇⋊C₄	C₂³	1	2	yes	—
137	Dic₄₇⋊C₄	C₂³	1	2	yes	—
138	Dic₄₇⋊C₄	C₂³	1	2	yes	—
139	Dic₄₇⋊C₄	C₂³	1	2	yes	—
140	Dic₄₇⋊C₄	C₂³	1	4	yes	—
141	Dic₄₇⋊C₄	C₂³	1	2	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	2	yes	—
146	Dic₄₇⋊C₄	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	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
152	C₂²×D₄₇	C₂⁴	1	2	yes	—
153	C₂²×D₄₇	C₂⁴	1	2	yes	—
154	Q₈×C₄₇	—	2	4	no	—
155	Q₈×C₄₇	—	2	4	no	—
156	Q₈×C₄₇	—	4	4	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	4	no	—
161	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
162	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
163	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂²⋊D₄₇	—	2	4	no	—
170	C₂²⋊D₄₇	—	2	4	no	—
171	C₂×Dic₄₇	C₂⁴	1	2	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	D₁₈₈	—	2	2	no	—
178	D₁₈₈	—	2	2	no	—
179	D₁₈₈	—	4	4	no	—
180	C₄×D₄₇	—	2	4	no	—
181	C₄×D₄₇	—	2	4	no	—
182	C₄×D₄₇	—	4	4	no	—
183	C₄×D₄₇	—	4	4	no	—
184	Dic₉₄	—	2	2	no	—
185	Dic₉₄	—	2	2	no	—
186	Dic₉₄	—	4	4	no	—
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
190	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
191	C₂×D₄₇	—	2	2	no	—
192	C₂×D₄₇	—	2	2	no	—
193	C₂×D₄₇	—	2	2	no	—
194	C₂×D₄₇	—	2	2	no	—
195	C₂×D₄₇	—	2	2	no	—
196	C₂×D₄₇	—	2	2	no	—
197	C₄×C₄₇	—	2	4	no	—
198	C₄×C₄₇	—	2	4	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	2	1	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
204	C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
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	—	2	2	no	—
211	#3552	—	47	1	no	maximal, Sylow
212	C₂×C₄₇	—	2	2	no	—
213	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
215	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
216	D₄₇	—	4	2	no	—
217	D₄₇	—	4	2	no	—
218	#563	—	47	4	no	—
219	#557	—	47	1	no	—
220	#556	—	47	1	no	—
221	#554	—	47	2	no	—
222	#553	—	47	2	no	—
223	D₄×Q₈	—	47	2	no	—
224	D₄×Q₈	—	47	1	no	—
225	#548	—	47	2	no	—
226	#547	—	47	1	no	—
227	#544	—	47	2	no	—
228	#542	—	47	2	no	—
229	#541	—	47	2	no	—
230	#539	—	47	4	no	—
231	#536	—	47	2	no	—
232	C₂×C₄⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
233	#529	—	47	1	no	—
234	#529	—	47	1	no	—
235	C₄₇	#3552	1	1	yes	characteristic, complemented, Sylow
236	C₂×#41	—	47	2	no	—
237	C₂²×Q₈	—	47	2	no	—
238	C₂²×Q₈	C₂×D₄₇	1	2	yes	—
239	C₄⋊Q₈	—	47	2	no	—
240	C₄⋊Q₈	—	47	4	no	—
241	C₄⋊Q₈	—	47	2	no	—
242	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
243	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
244	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
245	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
246	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
247	#126	—	47	4	no	—
248	#126	—	47	4	no	—
249	#126	—	47	4	no	—
250	#126	—	47	2	no	—
251	#126	—	47	2	no	—
252	#125	—	47	4	no	—
253	#125	—	47	4	no	—
254	#125	—	47	4	no	—
255	#125	—	47	2	no	—
256	#125	—	47	1	no	—
257	#125	—	47	1	no	—
258	#124	—	47	2	no	—
259	#124	—	47	4	no	—
260	#124	—	47	1	no	—
261	#124	—	47	1	no	—
262	#123	—	47	2	no	—
263	#123	—	47	2	no	—
264	#123	—	47	4	no	—
265	#123	—	47	4	no	—
266	#123	—	47	4	no	—
267	C₂²⋊Q₈	—	47	2	no	—
268	C₂²⋊Q₈	—	47	2	no	—
269	C₂²⋊Q₈	—	47	4	no	—
270	C₂²⋊Q₈	—	47	4	no	—
271	C₂²⋊Q₈	—	47	1	no	—
272	C₂²⋊Q₈	—	47	1	no	—
273	C₂²⋊Q₈	—	47	4	no	—
274	C₂²⋊Q₈	—	47	4	no	—
275	C₂²⋊Q₈	—	47	4	no	—
276	C₂²⋊Q₈	—	47	4	no	—
277	C₂²⋊Q₈	—	47	2	no	—
278	#121	—	47	1	no	—
279	#121	—	47	1	no	—
280	#121	—	47	4	no	—
281	#121	—	47	2	no	—
282	C₄×Q₈	—	47	2	no	—
283	C₄×Q₈	—	47	2	no	—
284	C₄×Q₈	—	47	2	no	—
285	C₄×Q₈	—	47	1	no	—
286	C₄×Q₈	—	47	1	no	—
287	C₄×D₄	—	47	2	no	—
288	C₄×D₄	—	47	2	no	—
289	C₄×D₄	—	47	4	no	—
290	C₄×D₄	—	47	4	no	—
291	C₄×D₄	—	47	2	no	—
292	C₄×D₄	—	47	1	no	—
293	C₄×D₄	—	47	1	no	—
294	#117	—	47	2	no	—
295	#117	—	47	2	no	—
296	#117	—	47	2	no	—
297	C₂×C₄⋊C₄	—	47	2	no	—
298	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
299	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
300	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
301	#41	—	188	4	no	—
302	C₂×Q₈	—	4	4	no	—
303	C₂×Q₈	—	47	1	no	—
304	C₂×Q₈	—	47	1	no	—
305	C₂×Q₈	—	47	4	no	—
306	C₂×Q₈	—	188	4	no	—
307	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
308	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
309	C₂×Q₈	C₂²×D₄₇	1	4	yes	—
310	C₂×D₄	—	47	2	no	—
311	C₂×D₄	—	47	2	no	—
312	C₂×D₄	—	47	1	no	—
313	C₂×D₄	—	47	1	no	—
314	C₂×D₄	—	47	4	no	—
315	C₂²×C₄	—	47	2	no	—
316	C₂²×C₄	—	47	2	no	—
317	C₂²×C₄	—	47	4	no	—
318	C₂²×C₄	—	47	4	no	—
319	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
323	C₄⋊C₄	—	47	4	no	—
324	C₄⋊C₄	—	47	2	no	—
325	C₄⋊C₄	—	47	2	no	—
326	C₄⋊C₄	—	47	2	no	—
327	C₄⋊C₄	—	47	2	no	—
328	C₄⋊C₄	—	47	4	no	—
329	C₄⋊C₄	—	47	2	no	—
330	C₄⋊C₄	—	47	4	no	—
331	C₄⋊C₄	—	47	2	no	—
332	C₄⋊C₄	—	47	4	no	—
333	C₄⋊C₄	—	47	2	no	—
334	C₄⋊C₄	—	47	2	no	—
335	C₄⋊C₄	—	47	1	no	—
336	C₄⋊C₄	—	47	1	no	—
337	C₄⋊C₄	—	47	1	no	—
338	C₄⋊C₄	—	47	1	no	—
339	C₄⋊C₄	—	47	4	no	—
340	C₄⋊C₄	—	47	4	no	—
341	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
342	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
343	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
344	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
345	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
346	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
347	C₂²⋊C₄	—	47	2	no	—
348	C₂²⋊C₄	—	47	2	no	—
349	C₂²⋊C₄	—	47	4	no	—
350	C₂²⋊C₄	—	47	2	no	—
351	C₂²⋊C₄	—	47	2	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	2	no	—
357	C₂²⋊C₄	—	47	2	no	—
358	C₂²⋊C₄	—	47	4	no	—
359	C₂²⋊C₄	—	47	2	no	—
360	C₂²⋊C₄	—	47	2	no	—
361	C₄²	—	47	2	no	—
362	C₄²	—	47	2	no	—
363	C₄²	—	47	4	no	—
364	C₄²	—	47	4	no	—
365	C₄²	C₂²×D₄₇	1	1	yes	characteristic
366	C₄²	C₂²×D₄₇	1	1	yes	characteristic
367	C₄²	C₂²×D₄₇	1	1	yes	characteristic
368	C₄²	C₂²×D₄₇	1	1	yes	characteristic
369	C₂³	—	47	2	no	—
370	C₂³	—	47	2	no	—
371	C₂³	C₂³×D₄₇	1	1	yes	characteristic
372	Q₈	—	2	4	no	—
373	Q₈	—	2	4	no	—
374	Q₈	—	4	4	no	—
375	Q₈	—	94	2	no	—
376	Q₈	—	94	2	no	—
377	Q₈	—	188	4	no	—
378	D₄	—	94	4	no	—
379	D₄	—	94	4	no	—
380	D₄	—	94	2	no	—
381	D₄	—	94	2	no	—
382	D₄	—	188	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	47	2	no	—
388	C₂×C₄	—	47	2	no	—
389	C₂×C₄	—	47	2	no	—
390	C₂×C₄	—	47	2	no	—
391	C₂×C₄	—	47	2	no	—
392	C₂×C₄	—	47	2	no	—
393	C₂×C₄	—	94	4	no	—
394	C₂×C₄	—	94	4	no	—
395	C₂×C₄	—	188	4	no	—
396	C₂×C₄	—	188	4	no	—
397	C₂×C₄	C₂³×D₄₇	1	4	yes	—
398	C₂×C₄	C₂³×D₄₇	1	4	yes	—
399	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	94	2	no	—
408	C₂²	—	94	2	no	—
409	C₂²	—	94	2	no	—
410	C₂²	—	94	2	no	—
411	C₂²	—	94	2	no	—
412	C₂²	—	94	2	no	—
413	C₂²	#13094072	1	2	yes	—
414	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	4	no	—
417	C₄	—	2	4	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	94	2	no	—
422	C₄	—	94	2	no	—
423	C₄	—	94	2	no	—
424	C₄	—	94	2	no	—
425	C₄	—	94	2	no	—
426	C₄	—	94	2	no	—
427	C₄	#13094069	1	2	yes	—
428	C₄	#13094072	1	2	yes	—
429	C₂	—	2	2	no	—
430	C₂	—	188	2	no	—
431	C₂	—	188	2	no	—
432	C₂	C₂×#13094069	1	1	yes	characteristic
433	C₂	C₂×#13094072	1	1	yes	characteristic
434	C₂	C₂×#13094072	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₂×C₄⋊Q₈×C₄₇	C₂
hypercenter	C₂×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	#3552
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #15689872	C₂	semidirect
2. #15689848	C₂	semidirect
3. #15689847	C₂	semidirect
4. #15689828	C₂	semidirect
5. #15689821	C₂	semidirect
6. #15689788	C₂	semidirect
7. Q₈×C₂²⋊D₄₇	C₂	semidirect
8. #15689784	C₂	semidirect
9. #15689776	C₂	semidirect
10. #15689750	C₂	semidirect
11. #15689747	C₂	semidirect
12. #15689734	C₂	semidirect
13. #15689720	C₂	semidirect
14. #15689698	C₂	semidirect
15. #15689657	C₂	semidirect
16. #15689657	C₂	semidirect
17. C₂×C₄⋊Q₈×C₄₇	C₂	semidirect
232. C₂×C₄⋊Q₈	D₄₇	semidirect
235. C₄₇	#3552	semidirect