Subgroups — C₄×#15689508 #26224726

Order 12032.

1150 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689508	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625336	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic
4	C₄×#13094013	C₂	1	2	yes	maximal, complemented
5	#20244252	C₂	1	1	yes	maximal, characteristic
6	#20244250	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244239	C₂	1	2	yes	maximal, complemented
8	#20244196	C₂	1	2	yes	maximal, complemented
9	#20243551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	2	yes	—
13	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
14	C₂×#13094013	C₂²	1	2	yes	—
15	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
16	#15689508	C₄	1	8	yes	direct product factor
17	C₄×#10625336	—	2	8	no	—
18	C₄×D₃₇₆	—	2	4	no	—
19	C₂×#13093958	C₂²	1	1	yes	characteristic
20	C₂×#13093955	C₂²	1	2	yes	—
21	C₂×#13093948	C₂²	1	2	yes	—
22	C₂×#13093946	C₂²	1	2	yes	—
23	C₂×#13093944	C₂²	1	2	yes	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
29	#15689030	C₂²	1	2	yes	—
30	#15689024	C₂²	1	2	yes	—
31	#15689013	—	2	4	no	—
32	#15688988	C₂²	1	2	yes	—
33	C₄×(C₂×D₄₇)⋊C₄	—	2	4	no	—
34	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
37	C₄×Q₁₆×C₄₇	—	2	4	no	—
38	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂²×D₁₈₈	C₂³	1	2	yes	—
42	C₂²×C₄×D₄₇	—	2	2	no	—
43	C₂×#10625336	—	2	4	no	—
44	C₂×#10625336	—	2	4	no	—
45	C₂×#10625336	C₂×C₄	1	8	yes	complemented
46	C₂×D₃₇₆	—	2	2	no	—
47	C₂×D₃₇₆	—	2	2	no	—
48	C₂×D₃₇₆	C₂×C₄	1	4	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	#13094013	—	2	4	no	—
52	#13094013	C₂×C₄	1	8	yes	complemented
53	C₄×D₁₈₈	—	2	4	no	—
54	C₄×D₁₈₈	—	2	4	no	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
57	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
59	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
60	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
61	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	#13093958	—	2	2	no	—
64	#13093955	—	2	4	no	—
65	#13093948	—	2	4	no	—
66	#13093946	—	2	4	no	—
67	#13093944	—	2	4	no	—
68	C₄×C₄₇⋊C₈	D₄	1	4	yes	—
69	C₈×Dic₄₇	—	2	2	no	—
70	C₈×Dic₄₇	—	2	2	no	—
71	C₈×Dic₄₇	—	2	2	no	—
72	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
73	C₄₇⋊#95	—	2	4	no	—
74	C₄₇⋊#95	—	2	4	no	—
75	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
76	C₂×Q₁₆×C₄₇	—	2	2	no	—
77	C₂×Q₁₆×C₄₇	—	2	2	no	—
78	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₄×Q₈×C₄₇	—	2	4	no	—
82	C₄×Q₈×C₄₇	—	2	4	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₇	—	2	2	no	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	#107×C₄₇	—	2	2	no	—
88	#103×C₄₇	—	2	4	no	—
89	C₄×C₈×C₄₇	D₄	1	4	yes	—
90	C₂³×D₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₇	—	2	2	no	—
103	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
104	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
105	C₂×D₁₈₈	—	2	2	no	—
106	C₂×D₁₈₈	—	2	2	no	—
107	C₂×D₁₈₈	—	2	2	no	—
108	C₂×D₁₈₈	—	2	2	no	—
109	C₂×D₁₈₈	—	2	2	no	—
110	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
111	C₂×C₄×D₄₇	—	4	4	no	—
112	C₂×C₄×D₄₇	—	4	8	no	—
113	Q₁₆×C₄₇	—	2	8	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₄₇	#41	1	2	yes	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	4	4	no	—
123	C₄²×C₄₇	—	4	4	no	—
124	C₄²×C₄₇	C₂×D₄	1	2	yes	—
125	C₄²×C₄₇	C₂×D₄	1	2	yes	—
126	#10625336	—	2	16	no	—
127	(C₂×D₄₇)⋊C₄	—	2	16	no	—
128	(C₂×D₄₇)⋊C₄	—	4	4	no	—
129	(C₂×D₄₇)⋊C₄	—	4	8	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄×Dic₄₇	—	2	4	no	—
133	C₄×Dic₄₇	—	2	1	no	—
134	C₄×Dic₄₇	—	2	1	no	—
135	C₄×Dic₄₇	—	2	4	no	—
136	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
137	C₄×Dic₄₇	#41	1	2	yes	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
142	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
143	C₂×C₄₇⋊C₈	#41	1	2	yes	—
144	D₃₇₆	—	2	8	no	—
145	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
146	C₂²×D₄₇	—	2	4	no	—
147	C₂²×D₄₇	—	4	2	no	—
148	C₂²×D₄₇	—	4	2	no	—
149	C₂²×D₄₇	—	4	4	no	—
150	C₂²×D₄₇	—	4	4	no	—
151	Q₈×C₄₇	—	2	4	no	—
152	Q₈×C₄₇	—	2	4	no	—
153	Q₈×C₄₇	—	4	2	no	—
154	Q₈×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	#127	1	2	yes	—
162	C₂×C₄×C₄₇	#127	1	2	yes	—
163	C₂×C₄×C₄₇	#135	1	4	yes	—
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	4	4	no	—
176	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
177	C₂×Dic₄₇	#135	1	4	yes	—
178	D₁₈₈	—	2	4	no	—
179	D₁₈₈	—	2	4	no	—
180	D₁₈₈	—	4	2	no	—
181	D₁₈₈	—	4	2	no	—
182	C₄×D₄₇	—	8	8	no	—
183	C₈×C₄₇	—	2	2	no	—
184	C₈×C₄₇	C₄×D₄	1	4	yes	—
185	C₄₇⋊C₈	—	2	2	no	—
186	C₄₇⋊C₈	C₄×D₄	1	4	yes	—
187	C₄×#495	—	47	1	no	maximal, Sylow
188	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
190	C₂²×C₄₇	#532	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#135	1	2	yes	—
192	C₂²×C₄₇	C₂×#135	1	2	yes	—
193	C₂×D₄₇	—	4	4	no	—
194	C₂×D₄₇	—	4	8	no	—
195	C₂×D₄₇	—	8	2	no	—
196	C₂×D₄₇	—	8	2	no	—
197	C₂×D₄₇	—	8	4	no	—
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	4	4	no	—
200	C₄×C₄₇	—	8	2	no	—
201	C₄×C₄₇	#495	1	4	yes	complemented
202	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
203	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₇	#532	1	1	yes	characteristic
205	C₄×C₄₇	#532	1	1	yes	characteristic
206	Dic₄₇	—	2	4	no	—
207	Dic₄₇	—	2	4	no	—
208	Dic₄₇	—	8	2	no	—
209	C₂×#495	—	47	1	no	—
210	C₂×C₄×Q₁₆	D₄₇	1	1	yes	characteristic, complemented
211	C₂×C₄×SD₁₆	—	47	2	no	—
212	C₂×C₄×D₈	—	47	1	no	—
213	C₄×#124	—	47	2	no	—
214	#1970	—	47	1	no	—
215	#1969	—	47	1	no	—
216	#1968	—	47	2	no	—
217	#1958	—	47	2	no	—
218	#1846	—	47	1	no	—
219	C₄²×C₈	—	47	1	no	—
220	C₂×C₄₇	C₄×#127	1	1	yes	characteristic
221	C₂×C₄₇	C₄×#135	1	2	yes	—
222	C₂×C₄₇	C₂×#495	1	1	yes	characteristic
223	C₂×C₄₇	#3147	1	1	yes	characteristic
224	C₂×C₄₇	#3168	1	2	yes	—
225	D₄₇	—	8	4	no	—
226	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
227	C₂²×SD₁₆	—	47	2	no	—
228	C₂²×D₈	—	47	1	no	—
229	C₂×#124	—	47	2	no	—
230	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
231	C₂×C₄×D₄	—	47	2	no	—
232	#495	—	47	8	no	—
233	C₄×Q₁₆	—	2	4	no	—
234	C₄×SD₁₆	—	94	8	no	—
235	C₄×D₈	—	94	4	no	—
236	C₂×#107	—	47	1	no	—
237	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
238	C₂×#106	—	47	2	no	—
239	C₂×#103	—	47	2	no	—
240	C₂×#103	C₂×D₄₇	1	2	yes	—
241	C₂×#102	—	47	2	no	—
242	C₂×#102	—	47	2	no	—
243	C₂×C₄×C₈	—	47	1	no	—
244	C₂×C₄×C₈	—	47	1	no	—
245	C₂×C₄×C₈	—	47	1	no	—
246	C₂×C₄×C₈	—	47	1	no	—
247	C₂×C₄×C₈	—	47	1	no	—
248	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
249	#391	—	47	2	no	—
250	#390	—	47	2	no	—
251	#388	—	94	4	no	—
252	#382	—	47	2	no	—
253	C₄×C₂²⋊C₄	—	94	4	no	—
254	C₄³	—	47	1	no	—
255	C₄₇	C₄×#495	1	1	yes	characteristic, complemented, Sylow
256	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
257	C₂²×D₄	—	47	2	no	—
258	C₂³×C₄	—	94	2	no	—
259	C₂×Q₁₆	—	2	2	no	—
260	C₂×Q₁₆	—	2	2	no	—
261	C₂×Q₁₆	C₄×D₄₇	1	4	yes	complemented
262	C₂×SD₁₆	—	47	8	no	—
263	C₂×SD₁₆	—	94	4	no	—
264	C₂×SD₁₆	—	94	4	no	—
265	C₂×D₈	—	47	4	no	—
266	C₂×D₈	—	94	2	no	—
267	C₂×D₈	—	94	2	no	—
268	C₂²×C₈	—	47	1	no	—
269	C₂²×C₈	—	47	1	no	—
270	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
272	#124	—	47	8	no	—
273	#124	—	94	4	no	—
274	C₄×Q₈	—	2	4	no	—
275	C₄×Q₈	—	2	4	no	—
276	C₄×D₄	—	94	4	no	—
277	C₄×D₄	—	94	4	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	47	2	no	—
280	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
281	C₂×C₂²⋊C₄	—	94	4	no	—
282	C₂×C₂²⋊C₄	—	94	4	no	—
283	C₂×C₂²⋊C₄	—	94	2	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	47	1	no	—
286	C₂×C₄²	—	47	2	no	—
287	C₂×C₄²	—	47	2	no	—
288	C₂×C₄²	—	47	1	no	—
289	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
290	#107	—	2	2	no	—
291	#107	—	94	2	no	—
292	#106	—	94	4	no	—
293	#103	—	2	4	no	—
294	#103	—	94	4	no	—
295	#102	—	94	4	no	—
296	#102	—	94	4	no	—
297	C₄×C₈	—	47	4	no	—
298	C₄×C₈	—	47	4	no	—
299	C₄×C₈	—	94	2	no	—
300	C₄×C₈	—	94	2	no	—
301	C₄×C₈	—	94	2	no	—
302	C₄×C₈	C₂²⋊D₄₇	1	4	yes	—
303	#95	—	94	4	no	—
304	#95	—	94	4	no	—
305	C₂⁴	—	94	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
312	C₂×D₄	—	47	4	no	—
313	C₂×D₄	—	94	2	no	—
314	C₂×D₄	—	94	2	no	—
315	C₂×D₄	—	94	2	no	—
316	C₂×D₄	—	94	2	no	—
317	C₂×D₄	—	94	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	47	2	no	—
321	C₂²×C₄	—	47	2	no	—
322	C₂²×C₄	—	94	2	no	—
323	C₂²×C₄	—	188	4	no	—
324	C₂²×C₄	—	188	8	no	—
325	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
326	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
328	Q₁₆	—	2	8	no	—
329	SD₁₆	—	94	16	no	—
330	D₈	—	94	8	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	47	2	no	—
334	C₂×C₈	—	47	2	no	—
335	C₂×C₈	—	47	2	no	—
336	C₂×C₈	—	47	2	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
340	C₂×C₈	#10625350	1	2	yes	—
341	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
342	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	94	2	no	—
347	C₄⋊C₄	—	94	2	no	—
348	C₂²⋊C₄	—	94	16	no	—
349	C₂²⋊C₄	—	188	8	no	—
350	C₂²⋊C₄	—	188	4	no	—
351	C₄²	—	4	4	no	—
352	C₄²	—	47	2	no	—
353	C₄²	—	47	2	no	—
354	C₄²	—	94	4	no	—
355	C₄²	—	94	4	no	—
356	C₄²	—	94	1	no	—
357	C₄²	—	94	1	no	—
358	C₄²	D₄×D₄₇	1	2	yes	—
359	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
360	C₂³	—	94	4	no	—
361	C₂³	—	188	4	no	—
362	C₂³	—	188	4	no	—
363	C₂³	—	188	2	no	—
364	C₂³	—	188	2	no	—
365	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	D₄	—	94	4	no	—
371	D₄	—	94	4	no	—
372	D₄	—	188	2	no	—
373	D₄	—	188	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	47	4	no	—
381	C₂×C₄	—	47	4	no	—
382	C₂×C₄	—	94	2	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	94	2	no	—
385	C₂×C₄	—	94	2	no	—
386	C₂×C₄	—	376	8	no	—
387	C₂×C₄	—	188	4	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	#13094020	1	2	yes	—
390	C₂×C₄	#13094020	1	2	yes	—
391	C₂×C₄	#13094047	1	4	yes	—
392	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
395	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
396	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	47	4	no	—
400	C₈	—	94	2	no	—
401	C₈	C₄×C₂²⋊D₄₇	1	4	yes	—
402	C₂²	—	376	4	no	—
403	C₂²	—	376	2	no	—
404	C₂²	—	376	2	no	—
405	C₂²	—	188	8	no	—
406	C₂²	—	188	4	no	—
407	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
408	C₂²	C₂×#13094020	1	1	yes	characteristic
409	C₂²	#15689670	1	1	yes	characteristic
410	C₂²	#135×D₄₇	1	2	yes	—
411	C₂²	C₂×#13094047	1	2	yes	—
412	C₄	—	2	2	no	—
413	C₄	—	4	4	no	—
414	C₄	—	8	2	no	—
415	C₄	—	94	4	no	—
416	C₄	—	94	4	no	—
417	C₄	—	376	2	no	—
418	C₄	#15689508	1	4	yes	direct product factor
419	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
420	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
421	C₄	#15689669	1	1	yes	characteristic
422	C₄	#15689670	1	1	yes	characteristic
423	C₂	—	376	4	no	—
424	C₂	C₄×#13094020	1	1	yes	characteristic
425	C₂	C₄×#13094047	1	2	yes	—
426	C₂	C₂×#15689508	1	1	yes	characteristic
427	C₂	#20253812	1	1	yes	characteristic
428	C₂	#20253961	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×Q₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₃₇₆	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₄₇
hypocenter	C₄₇	C₄×#495
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#10625336	C₂	semidirect
4. C₄×#13094013	C₂	semidirect
6. #20244250	C₂	semidirect
7. #20244239	C₂	semidirect
8. #20244196	C₂	semidirect
9. #20243551	C₂	semidirect
10. C₄×C₈×Dic₄₇	C₂	semidirect
11. C₂×C₄×Q₁₆×C₄₇	C₂	semidirect
16. #15689508	C₄	direct (N × H)
45. C₂×#10625336	C₂×C₄	semidirect
52. #13094013	C₂×C₄	semidirect
72. C₈×Dic₄₇	C₂×C₄	semidirect
78. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
201. C₄×C₄₇	#495	semidirect
210. C₂×C₄×Q₁₆	D₄₇	semidirect
255. C₄₇	C₄×#495	semidirect
261. C₂×Q₁₆	C₄×D₄₇	semidirect
418. C₄	#15689508	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#15689508	2
C₂×C₄×#10625336	2
C₂×C₄×D₃₇₆	2
C₄×#13094013	2
#20244252	2
#20244250	2
#20244239	2
#20244196	2
#20243551	2
C₄×C₈×Dic₄₇	2
C₂×C₄×Q₁₆×C₄₇	2
C₄×#495	47

Subgroups — C4×#15689508 #26224726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689508 #26224726