Subgroups — #26111052

Order 12032.

660 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689324	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244315	C₂	1	1	yes	maximal, characteristic
4	#20244194	C₂	1	1	yes	maximal, characteristic
5	C₂×#15688855	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241272	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625325	—	2	1	no	—
9	C₂×#13094021	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₉₄	—	2	1	no	—
11	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
12	#15689324	—	2	2	no	—
13	#15689324	C₄	1	4	yes	complemented
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#13093946	—	2	1	no	—
16	C₂×#13093946	—	2	2	no	—
17	C₂×#13093944	—	2	1	no	—
18	C₂×#13093944	—	2	1	no	—
19	#15689021	—	2	1	no	—
20	#15689020	—	2	2	no	—
21	#15688993	C₂²	1	1	yes	characteristic
22	#15688992	—	2	1	no	—
23	C₄⋊C₄×Dic₄₇	—	2	1	no	—
24	#15688855	—	2	2	no	—
25	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×Dic₉₄	D₄	1	1	yes	characteristic
29	C₂²×D₁₈₈	—	2	1	no	—
30	C₂²×D₁₈₈	—	2	1	no	—
31	C₂²×D₁₈₈	—	2	1	no	—
32	C₂×#10625325	—	2	4	no	—
33	C₂×#10625325	—	4	2	no	—
34	C₂×#10625325	—	4	2	no	—
35	C₂²×C₄₇⋊C₈	—	2	1	no	—
36	#13094021	—	2	1	no	—
37	#13094021	—	2	1	no	—
38	#13094021	—	2	1	no	—
39	#13094021	C₂×C₄	1	2	yes	—
40	C₄×Dic₉₄	—	2	1	no	—
41	C₄×Dic₉₄	—	2	1	no	—
42	C₄×Dic₉₄	—	4	2	no	—
43	C₄×Dic₉₄	—	4	2	no	—
44	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
45	C₄×Dic₉₄	D₄	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	—	2	1	no	—
47	C₂×C₄⋊Dic₄₇	—	2	1	no	—
48	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
50	C₂×Dic₄₇⋊C₄	—	2	1	no	—
51	C₂×Dic₄₇⋊C₄	—	2	2	no	—
52	C₂×Dic₄₇⋊C₄	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	2	1	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
57	#13093946	—	2	4	no	—
58	#13093946	—	4	4	no	—
59	#13093944	—	4	2	no	—
60	#13093944	—	4	2	no	—
61	C₄₇⋊#95	—	2	2	no	—
62	C₂²×C₈×C₄₇	—	2	1	no	—
63	C₂²×C₈×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	—	2	1	no	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₇	—	2	1	no	—
69	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
70	C₄×C₈×C₄₇	—	2	1	no	—
71	C₄×C₈×C₄₇	—	2	1	no	—
72	#95×C₄₇	—	2	1	no	—
73	C₂³×D₄₇	—	4	1	no	—
74	C₂²×C₄×C₄₇	—	2	1	no	—
75	C₂²×C₄×C₄₇	—	2	1	no	—
76	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×Dic₄₇	—	2	1	no	—
80	C₂²×Dic₄₇	—	2	1	no	—
81	C₂²×Dic₄₇	—	2	2	no	—
82	C₂×D₁₈₈	—	2	2	no	—
83	C₂×D₁₈₈	—	2	2	no	—
84	C₂×D₁₈₈	—	2	2	no	—
85	C₂×D₁₈₈	—	4	2	no	—
86	C₂×D₁₈₈	—	4	2	no	—
87	C₂×D₁₈₈	—	4	1	no	—
88	C₂×D₁₈₈	—	4	1	no	—
89	C₂×D₁₈₈	—	4	1	no	—
90	C₂×D₁₈₈	—	4	1	no	—
91	C₂×D₁₈₈	—	4	1	no	—
92	C₂×D₁₈₈	—	4	1	no	—
93	C₂×D₁₈₈	—	4	1	no	—
94	C₂×D₁₈₈	—	4	1	no	—
95	C₂×D₁₈₈	—	4	1	no	—
96	C₂×D₁₈₈	—	4	1	no	—
97	C₂×D₁₈₈	—	4	1	no	—
98	C₂×Dic₉₄	—	2	1	no	—
99	C₂×Dic₉₄	—	2	1	no	—
100	C₂×Dic₉₄	—	2	1	no	—
101	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
102	C₂×Dic₉₄	D₈	1	2	yes	—
103	C₂×Dic₉₄	SD₁₆	1	2	yes	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	4	1	no	—
107	C₂×C₈×C₄₇	—	4	1	no	—
108	C₂×C₈×C₄₇	—	4	1	no	—
109	C₂×C₈×C₄₇	—	4	1	no	—
110	C₄⋊C₄×C₄₇	—	2	1	no	—
111	C₄⋊C₄×C₄₇	—	2	1	no	—
112	C₄⋊C₄×C₄₇	—	2	1	no	—
113	C₄⋊C₄×C₄₇	SD₁₆	1	2	yes	complemented
114	C₄²×C₄₇	—	4	1	no	—
115	C₄²×C₄₇	—	4	1	no	—
116	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₄₇	#41	1	1	yes	characteristic
119	C₄²×C₄₇	#41	1	1	yes	characteristic
120	C₄⋊Dic₄₇	—	2	1	no	—
121	C₄⋊Dic₄₇	—	4	1	no	—
122	C₄⋊Dic₄₇	—	4	1	no	—
123	C₄⋊Dic₄₇	—	4	1	no	—
124	C₄⋊Dic₄₇	—	4	1	no	—
125	C₄⋊Dic₄₇	—	4	2	no	—
126	C₄⋊Dic₄₇	C₂²⋊C₄	1	2	yes	—
127	Dic₄₇⋊C₄	—	2	2	no	—
128	Dic₄₇⋊C₄	—	2	2	no	—
129	Dic₄₇⋊C₄	—	4	4	no	—
130	Dic₄₇⋊C₄	—	8	2	no	—
131	C₄×Dic₄₇	—	2	2	no	—
132	C₄×Dic₄₇	—	2	2	no	—
133	C₄×Dic₄₇	—	4	4	no	—
134	C₂×C₄₇⋊C₈	—	4	1	no	—
135	C₂×C₄₇⋊C₈	—	4	1	no	—
136	C₂×C₄₇⋊C₈	—	4	1	no	—
137	#10625325	—	4	8	no	—
138	C₂³×C₄₇	#120	1	1	yes	characteristic
139	C₂²×D₄₇	—	4	2	no	—
140	C₂²×D₄₇	—	8	1	no	—
141	C₂²×D₄₇	—	8	1	no	—
142	C₂²×D₄₇	—	8	1	no	—
143	C₂²×D₄₇	—	8	1	no	—
144	C₂²×D₄₇	—	8	1	no	—
145	C₂²×D₄₇	—	8	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	4	1	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	4	1	no	—
153	C₂×C₄×C₄₇	—	4	1	no	—
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
164	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	4	1	no	—
173	C₂×Dic₄₇	—	4	1	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	D₁₈₈	—	4	4	no	—
178	D₁₈₈	—	4	2	no	—
179	D₁₈₈	—	4	2	no	—
180	D₁₈₈	—	4	2	no	—
181	D₁₈₈	—	4	2	no	—
182	D₁₈₈	—	8	2	no	—
183	D₁₈₈	—	8	1	no	—
184	D₁₈₈	—	8	1	no	—
185	D₁₈₈	—	8	1	no	—
186	D₁₈₈	—	8	1	no	—
187	Dic₉₄	—	2	2	no	—
188	Dic₉₄	—	2	2	no	—
189	Dic₉₄	—	2	2	no	—
190	Dic₉₄	#102	1	4	yes	complemented
191	C₈×C₄₇	—	4	2	no	—
192	C₈×C₄₇	—	4	2	no	—
193	C₄₇⋊C₈	—	8	1	no	—
194	#8979	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	#386	1	1	yes	characteristic
196	C₂²×C₄₇	#447	1	1	yes	characteristic
197	C₂²×C₄₇	#448	1	1	yes	characteristic
198	C₂²×C₄₇	#448	1	1	yes	characteristic
199	C₂²×C₄₇	#449	1	1	yes	characteristic
200	C₂²×C₄₇	#453	1	1	yes	characteristic
201	C₂²×C₄₇	#454	1	1	yes	characteristic
202	C₂×D₄₇	—	8	2	no	—
203	C₂×D₄₇	—	8	2	no	—
204	C₂×D₄₇	—	8	2	no	—
205	C₂×D₄₇	—	16	1	no	—
206	C₂×D₄₇	—	16	1	no	—
207	C₂×D₄₇	—	16	1	no	—
208	C₂×D₄₇	—	16	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	—	8	1	no	—
213	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
214	C₄×C₄₇	#417	1	1	yes	characteristic
215	C₄×C₄₇	C₄×SD₁₆	1	1	yes	characteristic
216	C₄×C₄₇	#440	1	1	yes	characteristic
217	C₄×C₄₇	#460	1	1	yes	characteristic
218	C₄×C₄₇	#464	1	1	yes	characteristic
219	C₄×C₄₇	#480	1	1	yes	characteristic
220	C₄×C₄₇	#481	1	1	yes	characteristic
221	Dic₄₇	—	2	4	no	—
222	Dic₄₇	—	4	2	no	—
223	Dic₄₇	—	8	2	no	—
224	C₂×#460	—	47	1	no	—
225	Q₈×C₄⋊C₄	—	47	1	no	—
226	#1982	—	47	1	no	—
227	#1957	—	47	1	no	—
228	C₂×Q₈⋊C₈	—	47	1	no	—
229	#1296	—	47	1	no	—
230	#1279	D₄₇	1	1	yes	characteristic, complemented
231	C₂×C₄₇	#1621	1	1	yes	characteristic
232	C₂×C₄₇	#1623	1	1	yes	characteristic
233	C₂×C₄₇	#1626	1	1	yes	characteristic
234	C₂×C₄₇	#1627	1	1	yes	characteristic
235	C₂×C₄₇	#1874	1	1	yes	characteristic
236	C₂×C₄₇	#1880	1	1	yes	characteristic
237	C₂×C₄₇	#1883	1	1	yes	characteristic
238	D₄₇	—	16	2	no	—
239	C₂²×SD₁₆	—	94	1	no	—
240	C₂×#127	—	47	1	no	—
241	C₂×C₄×Q₈	—	47	1	no	—
242	C₂×C₄×Q₈	—	94	1	no	—
243	#460	—	47	4	no	—
244	#460	—	94	2	no	—
245	C₂×C₄⋊C₈	—	47	1	no	—
246	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
247	C₂×#102	—	94	1	no	—
248	C₂×#102	—	94	2	no	—
249	C₂×#102	—	94	1	no	—
250	C₂×#102	—	94	1	no	—
251	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
252	#389	—	94	2	no	—
253	#389	—	94	1	no	—
254	#384	—	47	1	no	—
255	#384	—	94	1	no	—
256	C₄×C₄⋊C₄	—	94	1	no	—
257	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
258	Q₈⋊C₈	—	94	2	no	—
259	C₄₇	#8979	1	1	yes	characteristic, complemented, Sylow
260	C₂²×Q₈	—	47	1	no	—
261	C₂²×D₄	—	94	1	no	—
262	C₂²×D₄	—	94	1	no	—
263	C₂²×D₄	—	94	1	no	—
264	C₂×SD₁₆	—	94	4	no	—
265	C₂×SD₁₆	—	188	2	no	—
266	C₂×SD₁₆	—	188	2	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	94	1	no	—
270	#127	—	47	2	no	—
271	#127	—	94	1	no	—
272	#127	—	94	1	no	—
273	#127	—	94	1	no	—
274	C₄×Q₈	—	47	2	no	—
275	C₄×Q₈	—	47	2	no	—
276	C₄×Q₈	—	94	1	no	—
277	C₄×Q₈	—	94	1	no	—
278	C₄×Q₈	—	188	2	no	—
279	C₄×Q₈	—	188	2	no	—
280	C₂×C₄⋊C₄	—	47	1	no	—
281	C₂×C₄⋊C₄	—	47	2	no	—
282	C₂×C₄⋊C₄	—	94	1	no	—
283	C₂×C₄⋊C₄	—	94	2	no	—
284	C₂×C₄⋊C₄	—	94	2	no	—
285	C₂×C₄⋊C₄	—	94	1	no	—
286	C₂×C₄⋊C₄	—	94	1	no	—
287	C₂×C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
288	C₂×C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	94	1	no	—
291	C₂×C₄²	—	94	2	no	—
292	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	94	1	no	—
295	C₄⋊C₈	—	94	1	no	—
296	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
297	#102	—	94	4	no	—
298	#102	—	188	2	no	—
299	#102	—	188	4	no	—
300	#102	—	188	2	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	2	1	no	—
303	#95	—	2	1	no	—
304	#95	—	94	2	no	—
305	C₂⁴	—	188	1	no	—
306	C₂×Q₈	—	47	2	no	—
307	C₂×Q₈	—	47	2	no	—
308	C₂×Q₈	—	47	2	no	—
309	C₂×Q₈	—	94	1	no	—
310	C₂×Q₈	—	94	1	no	—
311	C₂×Q₈	—	94	1	no	—
312	C₂×D₄	—	94	2	no	—
313	C₂×D₄	—	94	2	no	—
314	C₂×D₄	—	94	2	no	—
315	C₂×D₄	—	188	2	no	—
316	C₂×D₄	—	188	2	no	—
317	C₂×D₄	—	188	1	no	—
318	C₂×D₄	—	188	1	no	—
319	C₂×D₄	—	188	1	no	—
320	C₂×D₄	—	188	1	no	—
321	C₂×D₄	—	188	1	no	—
322	C₂×D₄	—	188	1	no	—
323	C₂×D₄	—	188	1	no	—
324	C₂×D₄	—	188	1	no	—
325	C₂×D₄	—	188	1	no	—
326	C₂×D₄	—	188	1	no	—
327	C₂×D₄	—	188	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	94	1	no	—
331	C₂²×C₄	—	94	1	no	—
332	C₂²×C₄	—	94	2	no	—
333	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
336	SD₁₆	—	188	8	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	188	1	no	—
344	C₂×C₈	—	188	1	no	—
345	C₂×C₈	—	188	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	47	2	no	—
350	C₄⋊C₄	—	94	2	no	—
351	C₄⋊C₄	—	94	2	no	—
352	C₄⋊C₄	—	94	1	no	—
353	C₄⋊C₄	—	376	2	no	—
354	C₄⋊C₄	—	188	2	no	—
355	C₄⋊C₄	—	188	4	no	—
356	C₄⋊C₄	—	188	1	no	—
357	C₄⋊C₄	—	188	1	no	—
358	C₄⋊C₄	—	188	1	no	—
359	C₄⋊C₄	—	188	1	no	—
360	C₄⋊C₄	#10625325	1	2	yes	complemented
361	C₄²	—	4	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	—	94	2	no	—
364	C₄²	—	94	2	no	—
365	C₄²	—	188	4	no	—
366	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₄²	#10625350	1	1	yes	characteristic
368	C₄²	D₄×D₄₇	1	1	yes	characteristic
369	C₄²	#10625354	1	1	yes	characteristic
370	C₂³	—	376	1	no	—
371	C₂³	—	376	1	no	—
372	C₂³	—	376	1	no	—
373	C₂³	—	376	1	no	—
374	C₂³	—	376	1	no	—
375	C₂³	—	376	1	no	—
376	C₂³	—	188	2	no	—
377	C₂³	#13093994	1	1	yes	characteristic
378	Q₈	—	47	4	no	—
379	Q₈	—	94	2	no	—
380	Q₈	—	94	2	no	—
381	Q₈	—	94	2	no	—
382	D₄	—	376	2	no	—
383	D₄	—	376	1	no	—
384	D₄	—	376	1	no	—
385	D₄	—	376	1	no	—
386	D₄	—	376	1	no	—
387	D₄	—	188	4	no	—
388	D₄	—	188	2	no	—
389	D₄	—	188	2	no	—
390	D₄	—	188	2	no	—
391	D₄	—	188	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	94	2	no	—
401	C₂×C₄	—	94	2	no	—
402	C₂×C₄	—	94	2	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	188	2	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	—	188	1	no	—
408	C₂×C₄	—	188	1	no	—
409	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
410	C₂×C₄	#13093986	1	1	yes	characteristic
411	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
412	C₂×C₄	#13093997	1	1	yes	characteristic
413	C₂×C₄	#13093999	1	1	yes	characteristic
414	C₂×C₄	#13094009	1	1	yes	characteristic
415	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
416	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
418	C₂×C₄	#13094046	1	1	yes	characteristic
419	C₂×C₄	#13094051	1	1	yes	characteristic
420	C₂×C₄	#13094052	1	1	yes	characteristic
421	C₂×C₄	#13094056	1	1	yes	characteristic
422	C₂×C₄	#13094057	1	1	yes	characteristic
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	376	1	no	—
426	C₂²	—	376	2	no	—
427	C₂²	—	376	2	no	—
428	C₂²	—	376	2	no	—
429	C₂²	—	752	1	no	—
430	C₂²	—	752	1	no	—
431	C₂²	—	752	1	no	—
432	C₂²	—	752	1	no	—
433	C₂²	#15689001	1	1	yes	characteristic
434	C₂²	#15689258	1	1	yes	characteristic
435	C₂²	#15689263	1	1	yes	characteristic
436	C₂²	#15689264	1	1	yes	characteristic
437	C₂²	#15689270	1	1	yes	characteristic
438	C₂²	#15689292	1	1	yes	characteristic
439	C₂²	#15689297	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	2	no	—
443	C₄	—	8	1	no	—
444	C₄	—	94	4	no	—
445	C₄	—	376	2	no	—
446	C₄	—	188	2	no	—
447	C₄	#102×D₄₇	1	1	yes	characteristic
448	C₄	#15689123	1	1	yes	characteristic
449	C₄	C₄×#10625325	1	1	yes	characteristic
450	C₄	#15689225	1	1	yes	characteristic
451	C₄	#15689324	1	1	yes	characteristic
452	C₄	#15689346	1	1	yes	characteristic
453	C₄	#15689438	1	1	yes	characteristic
454	C₄	#15689443	1	1	yes	characteristic
455	C₂	—	752	2	no	—
456	C₂	#20242456	1	1	yes	characteristic
457	C₂	#20242468	1	1	yes	characteristic
458	C₂	#20242486	1	1	yes	characteristic
459	C₂	#20242494	1	1	yes	characteristic
460	C₂	#20243704	1	1	yes	characteristic
461	C₂	#20243742	1	1	yes	characteristic
462	C₂	#20243765	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093994
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1279	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂×#13094021	C₂²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1279	D₄₇
hypocenter	C₄₇	#8979
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. C₄⋊C₄×Dic₉₄	C₂	semidirect
5. C₂×#15688855	C₂	semidirect
6. #20241272	C₂	semidirect
7. C₄₇×#1279	C₂	semidirect
13. #15689324	C₄	semidirect
113. C₄⋊C₄×C₄₇	SD₁₆	semidirect
190. Dic₉₄	#102	semidirect
230. #1279	D₄₇	semidirect
259. C₄₇	#8979	semidirect
360. C₄⋊C₄	#10625325	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689324	2
C₄⋊C₄×Dic₉₄	2
#20244315	2
#20244194	2
C₂×#15688855	2
#20241272	2
C₄₇×#1279	2
#8979	47