Subgroups — #26238099

Order 12032.

822 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689408	C₂	1	1	yes	maximal, characteristic
2	#20246446	C₂	1	1	yes	maximal, characteristic
3	#20244348	C₂	1	1	yes	maximal, characteristic
4	#20244149	C₂	1	1	yes	maximal, characteristic
5	#20244113	C₂	1	2	yes	maximal
6	#20243970	C₂	1	2	yes	maximal
7	#20243656	C₂	1	2	yes	maximal
8	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₄×#13093948	C₂	1	2	yes	maximal
10	C₄×#13093948	C₂	1	1	yes	maximal, characteristic
11	Q₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094024	C₂²	1	1	yes	characteristic
13	C₂×#13093989	—	2	1	no	—
14	#15689408	C₄	1	8	yes	complemented
15	C₂×#13093955	C₂²	1	2	yes	—
16	C₂×#13093955	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×#13093948	C₂²	1	1	yes	characteristic
19	C₂×#13093948	C₂²	1	2	yes	—
20	C₂×#13093948	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
23	#15689028	—	2	1	no	—
24	#15689021	C₂²	1	2	yes	—
25	#15689008	—	2	2	no	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
27	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
28	#15688885	C₂²	1	1	yes	characteristic
29	#15688885	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	1	yes	characteristic
33	#15688878	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#389	—	2	2	no	—
37	C₄₇×#389	C₂²	1	2	yes	—
38	C₄₇×#384	—	2	1	no	—
39	C₄₇×#384	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×Dic₉₄	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	#13094024	—	2	2	no	—
47	#13094024	C₂×C₄	1	4	yes	—
48	#13093989	—	4	4	no	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×Dic₄₇⋊C₄	—	2	2	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	C₂×C₄×Dic₄₇	—	2	1	no	—
56	#13093955	—	4	2	no	—
57	#13093955	C₂×C₄	1	8	yes	—
58	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
59	#13093948	—	2	2	no	—
60	#13093948	C₂×C₄	1	8	yes	—
61	#13093948	Q₈	1	4	yes	complemented
62	C₄×C₄₇⋊C₈	—	2	2	no	—
63	C₄×C₄₇⋊C₈	—	4	2	no	—
64	C₄₇⋊#95	—	2	1	no	—
65	C₄₇⋊#95	—	2	2	no	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
68	C₄×Q₈×C₄₇	—	2	2	no	—
69	C₄×Q₈×C₄₇	—	2	4	no	—
70	C₄×Q₈×C₄₇	—	4	2	no	—
71	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	—	2	1	no	—
82	C₂×C₄²×C₄₇	—	2	2	no	—
83	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	#95×C₄₇	—	2	2	no	—
86	#95×C₄₇	D₄	1	2	yes	—
87	C₂×Q₈×C₄₇	—	2	1	no	—
88	C₂×Q₈×C₄₇	—	2	1	no	—
89	C₂×Q₈×C₄₇	—	2	1	no	—
90	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
92	C₂×Q₈×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₄₇	—	2	1	no	—
102	C₂²×Dic₄₇	—	2	2	no	—
103	C₂²×Dic₄₇	—	2	1	no	—
104	C₂×Dic₉₄	—	2	4	no	—
105	C₂×Dic₉₄	—	4	2	no	—
106	C₂×Dic₉₄	—	4	2	no	—
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	1	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	4	4	no	—
113	C₄⋊C₄×C₄₇	—	4	2	no	—
114	C₄⋊C₄×C₄₇	—	8	1	no	—
115	C₄⋊C₄×C₄₇	—	8	2	no	—
116	C₄⋊C₄×C₄₇	SD₁₆	1	4	yes	—
117	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₄₇	—	2	4	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	4	4	no	—
122	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₄₇	#41	1	2	yes	—
124	C₄⋊Dic₄₇	—	2	4	no	—
125	C₄⋊Dic₄₇	—	2	2	no	—
126	C₄⋊Dic₄₇	—	2	1	no	—
127	C₄⋊Dic₄₇	—	2	1	no	—
128	C₄⋊Dic₄₇	—	2	1	no	—
129	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
130	C₄⋊Dic₄₇	C₂×Q₈	1	2	yes	—
131	Dic₄₇⋊C₄	—	4	4	no	—
132	C₄×Dic₄₇	—	4	4	no	—
133	C₄×Dic₄₇	—	4	2	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
142	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
143	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₄₇	—	2	2	no	—
145	Q₈×C₄₇	—	2	2	no	—
146	Q₈×C₄₇	—	2	2	no	—
147	Q₈×C₄₇	C₄×Q₈	1	4	yes	complemented
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
167	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
168	C₂×C₄×C₄₇	#135	1	2	yes	—
169	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
175	C₂×Dic₄₇	—	2	4	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	4	1	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	C₂×Dic₄₇	—	4	2	no	—
180	C₂×Dic₄₇	—	4	1	no	—
181	C₂×Dic₄₇	—	4	1	no	—
182	C₂×Dic₄₇	—	4	1	no	—
183	C₂×Dic₄₇	—	4	1	no	—
184	Dic₉₄	—	4	8	no	—
185	C₄₇⋊C₈	—	2	4	no	—
186	C₄₇⋊C₈	—	2	2	no	—
187	C₄₇⋊C₈	—	4	1	no	—
188	#22964	—	47	1	no	maximal, Sylow
189	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂²×C₄₇	#546	1	1	yes	characteristic
191	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
192	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
194	C₂²×C₄₇	#577	1	1	yes	characteristic
195	C₂²×C₄₇	#578	1	1	yes	characteristic
196	C₄×C₄₇	—	2	4	no	—
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	2	4	no	—
199	C₄×C₄₇	—	4	2	no	—
200	C₄×C₄₇	—	4	2	no	—
201	C₄×C₄₇	—	8	2	no	—
202	C₄×C₄₇	C₄×SD₁₆	1	4	yes	—
203	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
204	C₄×C₄₇	#520	1	1	yes	characteristic
205	C₄×C₄₇	#552	1	1	yes	characteristic
206	C₄×C₄₇	#554	1	1	yes	characteristic
207	Dic₄₇	—	4	2	no	—
208	Dic₄₇	—	4	4	no	—
209	Dic₄₇	—	8	1	no	—
210	C₂×#475	—	47	1	no	—
211	#2365	—	47	1	no	—
212	Q₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic
213	#1990	—	47	1	no	—
214	#1948	—	47	1	no	—
215	#1941	—	47	2	no	—
216	#1920	—	47	2	no	—
217	#1865	—	47	2	no	—
218	C₈×C₄⋊C₄	—	47	1	no	—
219	C₄×#103	—	47	2	no	—
220	C₄×#103	—	47	1	no	—
221	C₂×C₄₇	#2360	1	1	yes	characteristic
222	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
223	C₂×C₄₇	#2947	1	1	yes	characteristic
224	C₂×C₄₇	#3298	1	1	yes	characteristic
225	C₂×C₄₇	#3304	1	1	yes	characteristic
226	C₂×C₄₇	Q₈×SD₁₆	1	1	yes	characteristic
227	C₂×C₄₇	#3383	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	—	47	1	no	—
229	C₂×C₄×Q₈	—	94	1	no	—
230	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
231	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
232	#475	—	47	8	no	—
233	C₂×#106	—	47	2	no	—
234	C₂×#106	—	47	2	no	—
235	C₂×C₄⋊C₈	—	47	1	no	—
236	C₂×#103	—	47	2	no	—
237	C₂×#103	—	47	1	no	—
238	C₂×#103	—	47	1	no	—
239	C₂×C₄×C₈	—	47	1	no	—
240	C₂×C₄×C₈	—	47	2	no	—
241	#391	—	94	1	no	—
242	#389	—	2	2	no	—
243	#389	—	47	2	no	—
244	#389	C₂×D₄₇	1	2	yes	—
245	#387	—	94	2	no	—
246	#384	—	2	1	no	—
247	#384	C₂×D₄₇	1	1	yes	characteristic
248	C₄×C₄⋊C₄	—	2	1	no	—
249	C₄×C₄⋊C₄	—	47	2	no	—
250	C₄×C₄⋊C₄	—	47	1	no	—
251	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
252	#340	—	47	2	no	—
253	#340	—	47	1	no	—
254	#340	—	47	2	no	—
255	#340	—	47	1	no	—
256	#340	—	47	2	no	—
257	#336	—	47	2	no	—
258	C₄₇	#22964	1	1	yes	characteristic, complemented, Sylow
259	C₂²×Q₈	—	94	1	no	—
260	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
261	C₂²×C₈	—	47	2	no	—
262	C₂²×C₈	—	47	1	no	—
263	C₂²×C₈	—	47	1	no	—
264	C₄⋊Q₈	—	47	4	no	—
265	C₄⋊Q₈	—	94	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	—	2	4	no	—
268	C₄×Q₈	—	4	2	no	—
269	C₄×Q₈	—	188	4	no	—
270	C₄×Q₈	C₄×D₄₇	1	4	yes	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	47	2	no	—
277	C₂×C₄⋊C₄	—	47	1	no	—
278	C₂×C₄⋊C₄	—	47	1	no	—
279	C₂×C₄⋊C₄	—	94	1	no	—
280	C₂×C₄⋊C₄	—	94	2	no	—
281	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	94	2	no	—
288	C₂×C₄²	—	94	1	no	—
289	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
290	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
291	#106	—	47	8	no	—
292	#106	—	188	2	no	—
293	C₄⋊C₈	—	47	4	no	—
294	#103	—	47	8	no	—
295	#103	—	47	4	no	—
296	#103	—	94	2	no	—
297	C₄×C₈	—	94	2	no	—
298	C₄×C₈	—	188	2	no	—
299	#95	—	2	2	no	—
300	#95	—	94	1	no	—
301	#95	—	94	2	no	—
302	#95	—	94	2	no	—
303	#95	C₂²⋊D₄₇	1	2	yes	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	94	4	no	—
308	C₂×Q₈	—	188	2	no	—
309	C₂×Q₈	—	188	2	no	—
310	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
311	C₂×Q₈	#10625352	1	2	yes	—
312	C₂×Q₈	Q₈×D₄₇	1	2	yes	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	94	1	no	—
317	C₂²×C₄	—	94	2	no	—
318	C₂²×C₄	—	94	1	no	—
319	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
320	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
324	C₂×C₈	—	47	4	no	—
325	C₂×C₈	—	47	2	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	—	94	1	no	—
328	C₂×C₈	—	94	2	no	—
329	C₂×C₈	—	94	2	no	—
330	C₂×C₈	—	94	1	no	—
331	C₂×C₈	—	94	1	no	—
332	C₂×C₈	—	94	1	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	8	1	no	—
341	C₄⋊C₄	—	8	2	no	—
342	C₄⋊C₄	—	47	4	no	—
343	C₄⋊C₄	—	47	2	no	—
344	C₄⋊C₄	—	94	4	no	—
345	C₄⋊C₄	—	94	2	no	—
346	C₄⋊C₄	—	94	1	no	—
347	C₄⋊C₄	—	94	1	no	—
348	C₄⋊C₄	—	94	1	no	—
349	C₄⋊C₄	—	188	4	no	—
350	C₄⋊C₄	#10625336	1	4	yes	—
351	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
352	C₄²	—	2	4	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	4	4	no	—
356	C₄²	—	188	2	no	—
357	C₄²	—	188	4	no	—
358	C₄²	C₂×C₄×D₄₇	1	2	yes	—
359	C₄²	#10625350	1	2	yes	—
360	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	188	8	no	—
365	Q₈	#13093989	1	4	yes	complemented
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	94	2	no	—
383	C₂×C₄	—	94	4	no	—
384	C₂×C₄	—	188	1	no	—
385	C₂×C₄	—	188	1	no	—
386	C₂×C₄	—	188	1	no	—
387	C₂×C₄	—	188	1	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	—	188	1	no	—
391	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
392	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
393	C₂×C₄	C₂×#10625336	1	4	yes	—
394	C₂×C₄	C₂×#10625336	1	2	yes	—
395	C₂×C₄	#13094044	1	2	yes	—
396	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
398	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
399	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
400	C₂×C₄	#13094069	1	1	yes	characteristic
401	C₂×C₄	#13094072	1	1	yes	characteristic
402	C₈	—	94	2	no	—
403	C₈	—	94	4	no	—
404	C₈	—	188	1	no	—
405	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₂²	#15689767	1	1	yes	characteristic
407	C₂²	Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
408	C₂²	C₂²×#10625336	1	1	yes	characteristic
409	C₂²	C₂×#13094044	1	1	yes	characteristic
410	C₂²	#15689934	1	1	yes	characteristic
411	C₂²	#15689938	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	4	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	376	1	no	—
419	C₄	—	188	4	no	—
420	C₄	—	188	2	no	—
421	C₄	C₄×#10625336	1	4	yes	—
422	C₄	C₂×#13093989	1	1	yes	characteristic
423	C₄	#15689604	1	1	yes	characteristic
424	C₄	#15689808	1	1	yes	characteristic
425	C₄	#15689828	1	1	yes	characteristic
426	C₂	#20246393	1	1	yes	characteristic
427	C₂	C₂×C₄×#10625336	1	1	yes	characteristic
428	C₂	#20252227	1	1	yes	characteristic
429	C₂	#20255253	1	1	yes	characteristic
430	C₂	#20255327	1	1	yes	characteristic
431	C₂	Q₈×#10625336	1	1	yes	characteristic
432	C₂	#20256275	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	Q₈×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	Q₈×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#22964
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ Q₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
14. #15689408	C₄	semidirect
61. #13093948	Q₈	semidirect
147. Q₈×C₄₇	C₄×Q₈	semidirect
258. C₄₇	#22964	semidirect
365. Q₈	#13093989	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689408	2
#20246446	2
#20244348	2
#20244149	2
#20244113	2
#20243970	2
#20243656	2
C₄⋊C₄×C₄₇⋊C₈	2
C₄×#13093948	2
Q₈×C₄⋊C₄×C₄₇	2
#22964	47