Subgroups — C₄×#15689470 #26224245

Order 12032.

1046 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×#15689470	C₂	1	1	yes	maximal, characteristic
2	C₄×#13094024	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094021	C₂	1	1	yes	maximal, characteristic
4	#20244349	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244194	C₂	1	1	yes	maximal, characteristic
6	#20244071	C₂	1	4	yes	maximal, complemented
7	#20243516	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13093946	C₂	1	4	yes	maximal, complemented
9	C₄²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13094024	C₂²	1	1	yes	characteristic
11	C₂×#13094021	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₉₄	—	2	1	no	—
13	C₂×C₄×D₁₈₈	—	2	1	no	—
14	C₂×C₄×D₁₈₈	—	2	1	no	—
15	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
16	#15689470	C₄	1	8	yes	direct product factor
17	C₂×#13093946	C₂²	1	4	yes	—
18	C₂×#13093946	C₂²	1	4	yes	—
19	#15689029	—	2	1	no	—
20	#15689025	—	2	1	no	—
21	#15689025	—	2	1	no	—
22	#15689025	C₂²	1	2	yes	—
23	#15689021	—	2	1	no	—
24	#15689021	C₂²	1	2	yes	—
25	#15688993	C₂²	1	1	yes	characteristic
26	#15688993	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊Dic₄₇	—	2	1	no	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
29	#15688886	C₂²	1	4	yes	—
30	#15688886	C₂²	1	4	yes	—
31	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₄³×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×Dic₉₄	—	2	1	no	—
37	C₂²×D₁₈₈	—	2	1	no	—
38	C₂²×D₁₈₈	—	2	1	no	—
39	C₂²×D₁₈₈	C₂³	1	2	yes	—
40	C₂²×C₄×D₄₇	—	2	2	no	—
41	#13094024	—	2	2	no	—
42	#13094024	C₂×C₄	1	4	yes	complemented
43	#13094021	—	2	2	no	—
44	#13094021	C₂×C₄	1	4	yes	—
45	C₄×Dic₉₄	—	4	4	no	—
46	C₄×D₁₈₈	—	2	8	no	—
47	C₄×D₁₈₈	—	4	4	no	—
48	C₄×D₁₈₈	—	4	4	no	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	C₂×C₄⋊Dic₄₇	—	2	1	no	—
52	C₂×C₄⋊Dic₄₇	—	2	1	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×Dic₄₇⋊C₄	—	2	2	no	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
59	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
60	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	2	no	—
62	#13093946	—	2	8	no	—
63	#13093946	C₂×C₄	1	16	yes	complemented
64	C₄₇⋊#95	—	2	2	no	—
65	C₄₇⋊#95	—	2	2	no	—
66	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₄₇	—	2	4	no	—
76	C₄×C₈×C₄₇	—	2	2	no	—
77	C₄×C₈×C₄₇	—	2	4	no	—
78	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
79	C₂³×D₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	—	2	2	no	—
89	C₂²×Dic₄₇	—	2	2	no	—
90	C₂×D₁₈₈	—	2	4	no	—
91	C₂×D₁₈₈	—	2	4	no	—
92	C₂×D₁₈₈	—	2	4	no	—
93	C₂×D₁₈₈	—	2	4	no	—
94	C₂×D₁₈₈	—	2	2	no	—
95	C₂×D₁₈₈	—	4	2	no	—
96	C₂×D₁₈₈	—	4	2	no	—
97	C₂×D₁₈₈	—	4	2	no	—
98	C₂×D₁₈₈	—	4	2	no	—
99	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
100	C₂×C₄×D₄₇	—	4	4	no	—
101	C₂×C₄×D₄₇	—	4	4	no	—
102	C₂×C₄×D₄₇	—	4	4	no	—
103	C₂×Dic₉₄	—	2	4	no	—
104	C₂×Dic₉₄	—	4	2	no	—
105	C₂×Dic₉₄	—	4	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
111	C₂×C₈×C₄₇	#41	1	4	yes	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	—	2	2	no	—
114	C₄²×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	D₈	1	4	yes	—
116	C₄²×C₄₇	SD₁₆	1	4	yes	—
117	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₄₇	#41	1	2	yes	—
119	C₄²×C₄₇	#41	1	4	yes	—
120	(C₂×D₄₇)⋊C₄	—	4	4	no	—
121	(C₂×D₄₇)⋊C₄	—	4	4	no	—
122	(C₂×D₄₇)⋊C₄	—	4	4	no	—
123	C₄⋊Dic₄₇	—	2	4	no	—
124	C₄⋊Dic₄₇	—	2	2	no	—
125	C₄⋊Dic₄₇	—	2	4	no	—
126	C₄⋊Dic₄₇	—	2	4	no	—
127	C₄⋊Dic₄₇	—	4	2	no	—
128	C₄⋊Dic₄₇	—	4	2	no	—
129	C₄⋊Dic₄₇	—	4	2	no	—
130	C₄⋊Dic₄₇	—	4	2	no	—
131	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
132	Dic₄₇⋊C₄	—	4	4	no	—
133	C₄×Dic₄₇	—	4	4	no	—
134	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
135	C₂²×D₄₇	—	2	4	no	—
136	C₂²×D₄₇	—	4	2	no	—
137	C₂²×D₄₇	—	4	2	no	—
138	C₂²×D₄₇	—	4	2	no	—
139	C₂²×D₄₇	—	4	2	no	—
140	C₂²×D₄₇	—	4	2	no	—
141	C₂²×D₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₄₇	#124	1	2	yes	—
151	C₂×C₄×C₄₇	#124	1	2	yes	—
152	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
156	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
157	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₄₇	#135	1	2	yes	—
159	C₂×C₄×C₄₇	#135	1	2	yes	—
160	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₄₇	—	2	4	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	D₁₈₈	—	2	8	no	—
174	D₁₈₈	—	4	4	no	—
175	D₁₈₈	—	4	8	no	—
176	D₁₈₈	—	4	8	no	—
177	C₄×D₄₇	—	8	8	no	—
178	Dic₉₄	—	4	8	no	—
179	C₈×C₄₇	—	2	4	no	—
180	C₈×C₄₇	—	2	4	no	—
181	C₄×#486	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
184	C₂²×C₄₇	#532	1	1	yes	characteristic
185	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
186	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
189	C₂×D₄₇	—	4	4	no	—
190	C₂×D₄₇	—	4	4	no	—
191	C₂×D₄₇	—	4	4	no	—
192	C₂×D₄₇	—	8	2	no	—
193	C₂×D₄₇	—	8	2	no	—
194	C₂×D₄₇	—	8	2	no	—
195	C₂×D₄₇	—	8	2	no	—
196	C₄×C₄₇	—	2	2	no	—
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	C₄×D₈	1	4	yes	—
200	C₄×C₄₇	C₄×SD₁₆	1	4	yes	—
201	C₄×C₄₇	#486	1	4	yes	complemented
202	C₄×C₄₇	C₄×#41	1	2	yes	—
203	C₄×C₄₇	#529	1	2	yes	—
204	Dic₄₇	—	4	4	no	—
205	Dic₄₇	—	8	2	no	—
206	Dic₄₇	—	8	2	no	—
207	C₂×#486	—	47	1	no	—
208	C₄×C₄⋊Q₈	—	47	1	no	—
209	C₄×#127	—	47	1	no	—
210	#1990	—	47	1	no	—
211	#1957	—	47	1	no	—
212	#1934	—	47	4	no	—
213	#1834	—	47	1	no	—
214	C₄×#102	—	47	4	no	—
215	C₄²×C₈	D₄₇	1	1	yes	characteristic, complemented
216	C₂×C₄₇	C₄×#124	1	1	yes	characteristic
217	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
218	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#486	1	1	yes	characteristic
220	C₂×C₄₇	#3131	1	1	yes	characteristic
221	C₂×C₄₇	#3167	1	1	yes	characteristic
222	C₂×C₄₇	#3169	1	1	yes	characteristic
223	D₄₇	—	8	4	no	—
224	C₂×C₄⋊Q₈	—	47	1	no	—
225	C₂×#127	—	47	1	no	—
226	C₂×C₄×Q₈	—	94	1	no	—
227	C₂×C₄×D₄	—	47	2	no	—
228	C₂×C₄×D₄	—	94	1	no	—
229	C₂×C₄×D₄	—	94	1	no	—
230	#486	—	47	8	no	—
231	C₂×#102	—	47	4	no	—
232	C₂×#102	—	47	4	no	—
233	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
234	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
236	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
237	#391	—	94	1	no	—
238	#390	—	47	2	no	—
239	#390	—	94	1	no	—
240	#390	—	94	1	no	—
241	#389	—	47	2	no	—
242	#389	—	94	1	no	—
243	#384	—	47	1	no	—
244	#384	—	47	1	no	—
245	C₄×C₄⋊C₄	—	47	2	no	—
246	C₄×C₄⋊C₄	—	94	1	no	—
247	C₄³	C₂×D₄₇	1	1	yes	characteristic
248	#340	—	47	4	no	—
249	#340	—	47	4	no	—
250	C₄₇	C₄×#486	1	1	yes	characteristic, complemented, Sylow
251	C₂²×Q₈	—	94	1	no	—
252	C₂²×D₄	—	47	2	no	—
253	C₂²×D₄	—	94	1	no	—
254	C₂²×D₄	—	94	1	no	—
255	C₂³×C₄	—	94	2	no	—
256	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
257	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
258	C₄⋊Q₈	—	47	4	no	—
259	C₄⋊Q₈	—	94	2	no	—
260	#127	—	47	4	no	—
261	#127	—	94	2	no	—
262	C₄×Q₈	—	188	4	no	—
263	C₄×D₄	—	94	8	no	—
264	C₄×D₄	—	188	4	no	—
265	C₄×D₄	—	188	4	no	—
266	C₂×C₄⋊C₄	—	47	2	no	—
267	C₂×C₄⋊C₄	—	47	2	no	—
268	C₂×C₄⋊C₄	—	47	2	no	—
269	C₂×C₄⋊C₄	—	94	1	no	—
270	C₂×C₄⋊C₄	—	94	1	no	—
271	C₂×C₄⋊C₄	—	94	1	no	—
272	C₂×C₄⋊C₄	—	94	2	no	—
273	C₂×C₄⋊C₄	—	94	1	no	—
274	C₂×C₄⋊C₄	—	94	1	no	—
275	C₂×C₂²⋊C₄	—	94	2	no	—
276	C₂×C₂²⋊C₄	—	94	2	no	—
277	C₂×C₂²⋊C₄	—	94	2	no	—
278	C₂×C₄²	—	94	2	no	—
279	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
280	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
281	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
282	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
283	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
284	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
285	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
286	#102	—	47	16	no	—
287	#102	—	94	8	no	—
288	C₄×C₈	—	2	4	no	—
289	C₄×C₈	—	2	2	no	—
290	C₄×C₈	—	2	4	no	—
291	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
292	#95	—	94	2	no	—
293	#95	—	94	2	no	—
294	C₂⁴	—	94	2	no	—
295	C₂×Q₈	—	94	4	no	—
296	C₂×Q₈	—	188	2	no	—
297	C₂×Q₈	—	188	2	no	—
298	C₂×D₄	—	47	4	no	—
299	C₂×D₄	—	94	4	no	—
300	C₂×D₄	—	94	4	no	—
301	C₂×D₄	—	94	4	no	—
302	C₂×D₄	—	94	4	no	—
303	C₂×D₄	—	94	2	no	—
304	C₂×D₄	—	188	2	no	—
305	C₂×D₄	—	188	2	no	—
306	C₂×D₄	—	188	2	no	—
307	C₂×D₄	—	188	2	no	—
308	C₂²×C₄	—	94	2	no	—
309	C₂²×C₄	—	94	2	no	—
310	C₂²×C₄	—	94	2	no	—
311	C₂²×C₄	—	188	4	no	—
312	C₂²×C₄	—	188	4	no	—
313	C₂²×C₄	—	188	4	no	—
314	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
320	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
326	C₂×C₈	#10625350	1	4	yes	—
327	C₄⋊C₄	—	47	4	no	—
328	C₄⋊C₄	—	94	4	no	—
329	C₄⋊C₄	—	94	2	no	—
330	C₄⋊C₄	—	94	4	no	—
331	C₄⋊C₄	—	94	4	no	—
332	C₄⋊C₄	—	188	4	no	—
333	C₄⋊C₄	—	188	2	no	—
334	C₄⋊C₄	—	188	2	no	—
335	C₄⋊C₄	—	188	2	no	—
336	C₄⋊C₄	—	188	2	no	—
337	C₂²⋊C₄	—	188	4	no	—
338	C₂²⋊C₄	—	188	4	no	—
339	C₂²⋊C₄	—	188	4	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	188	4	no	—
344	C₄²	#10625325	1	4	yes	—
345	C₄²	D₃₇₆	1	4	yes	—
346	C₄²	C₂×C₄×D₄₇	1	2	yes	—
347	C₄²	#10625350	1	2	yes	—
348	C₄²	#10625350	1	4	yes	—
349	C₂³	—	94	4	no	—
350	C₂³	—	188	2	no	—
351	C₂³	—	188	2	no	—
352	C₂³	—	188	2	no	—
353	C₂³	—	188	2	no	—
354	C₂³	—	188	2	no	—
355	C₂³	—	188	2	no	—
356	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
357	Q₈	—	188	8	no	—
358	D₄	—	94	8	no	—
359	D₄	—	188	4	no	—
360	D₄	—	188	8	no	—
361	D₄	—	188	8	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	94	4	no	—
369	C₂×C₄	—	376	8	no	—
370	C₂×C₄	—	188	2	no	—
371	C₂×C₄	—	188	2	no	—
372	C₂×C₄	—	188	2	no	—
373	C₂×C₄	—	188	2	no	—
374	C₂×C₄	—	188	2	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	—	188	2	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
379	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
380	C₂×C₄	#13094012	1	2	yes	—
381	C₂×C₄	#13094012	1	2	yes	—
382	C₂×C₄	C₂×D₃₇₆	1	2	yes	—
383	C₂×C₄	C₂×D₃₇₆	1	2	yes	—
384	C₂×C₄	C₂×D₃₇₆	1	2	yes	—
385	C₂×C₄	C₂×#10625325	1	2	yes	—
386	C₂×C₄	C₂×#10625325	1	2	yes	—
387	C₂×C₄	C₂×#10625325	1	2	yes	—
388	C₂×C₄	#13094046	1	2	yes	—
389	C₂×C₄	#13094046	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂×#10625350	1	2	yes	—
392	C₂×C₄	C₂×#10625350	1	2	yes	—
393	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
394	C₈	—	2	4	no	—
395	C₈	—	2	4	no	—
396	C₂²	—	376	2	no	—
397	C₂²	—	376	2	no	—
398	C₂²	—	376	2	no	—
399	C₂²	—	376	2	no	—
400	C₂²	—	188	4	no	—
401	C₂²	—	188	4	no	—
402	C₂²	—	188	4	no	—
403	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
404	C₂²	C₂×#13094012	1	1	yes	characteristic
405	C₂²	#15689673	1	1	yes	characteristic
406	C₂²	C₂²×D₃₇₆	1	1	yes	characteristic
407	C₂²	C₂²×#10625325	1	1	yes	characteristic
408	C₂²	C₂×#13094046	1	1	yes	characteristic
409	C₂²	C₂×#13094046	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	376	2	no	—
414	C₄	—	376	2	no	—
415	C₄	—	188	4	no	—
416	C₄	C₄×D₃₇₆	1	4	yes	—
417	C₄	C₄×#10625325	1	4	yes	—
418	C₄	#15689470	1	4	yes	direct product factor
419	C₄	C₄×#10625350	1	2	yes	—
420	C₄	#15689657	1	2	yes	—
421	C₂	—	376	4	no	—
422	C₂	C₄×#13094012	1	1	yes	characteristic
423	C₂	C₂×C₄×D₃₇₆	1	1	yes	characteristic
424	C₂	C₂×C₄×#10625325	1	1	yes	characteristic
425	C₂	C₂×#15689470	1	1	yes	characteristic
426	C₂	#20253711	1	1	yes	characteristic
427	C₂	#20253947	1	1	yes	characteristic
428	C₂	#20253967	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄²×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#13094021	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄²×C₈	D₄₇
hypocenter	C₄₇	C₄×#486
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×#13094024	C₂	semidirect
4. #20244349	C₂	semidirect
6. #20244071	C₂	semidirect
7. #20243516	C₂	semidirect
8. C₄×#13093946	C₂	semidirect
9. C₄²×C₈×C₄₇	C₂	semidirect
16. #15689470	C₄	direct (N × H)
42. #13094024	C₂×C₄	semidirect
63. #13093946	C₂×C₄	semidirect
78. C₄×C₈×C₄₇	C₂×C₄	semidirect
201. C₄×C₄₇	#486	semidirect
215. C₄²×C₈	D₄₇	semidirect
250. C₄₇	C₄×#486	semidirect
291. C₄×C₈	C₄×D₄₇	semidirect
418. C₄	#15689470	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×#15689470	2
C₄×#13094024	2
C₄×#13094021	2
#20244349	2
#20244194	2
#20244071	2
#20243516	2
C₄×#13093946	2
C₄²×C₈×C₄₇	2
C₄×#486	47

Subgroups — C4×#15689470 #26224245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689470 #26224245