Subgroups — #26232894

Order 12032.

1010 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689851	C₂	1	1	yes	maximal, characteristic
2	#20246345	C₂	1	1	yes	maximal, characteristic
3	#20244353	C₂	1	2	yes	maximal
4	#20244349	C₂	1	1	yes	maximal, characteristic
5	#20244343	C₂	1	2	yes	maximal
6	#20244339	C₂	1	1	yes	maximal, characteristic
7	#20243404	C₂	1	2	yes	maximal
8	#20243394	C₂	1	1	yes	maximal, characteristic
9	C₄×#13093949	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093949	C₂	1	2	yes	maximal
11	C₂×C₈×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	#15689851	—	2	4	no	—
13	#15689851	C₄	1	8	yes	complemented
14	C₂×#13094024	C₂²	1	1	yes	characteristic
15	C₂×#13094022	—	2	1	no	—
16	C₂×#13094016	C₂²	1	2	yes	—
17	C₂×#13094014	—	2	2	no	—
18	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
20	C₂×#13093989	—	2	1	no	—
21	C₂×#13093949	C₂²	1	2	yes	—
22	C₂×#13093949	C₂²	1	1	yes	characteristic
23	C₂×#13093949	C₂²	1	1	yes	characteristic
24	#15689030	—	2	1	no	—
25	#15689009	—	2	2	no	—
26	#15688993	C₂²	1	1	yes	characteristic
27	#15688989	C₂²	1	2	yes	—
28	C₄⋊C₄×Dic₄₇	—	2	1	no	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
31	#15688886	C₂²	1	2	yes	—
32	#15688886	C₂²	1	1	yes	characteristic
33	#15688886	C₂²	1	2	yes	—
34	#15688886	C₂²	1	1	yes	characteristic
35	#15688886	C₂²	1	2	yes	—
36	#15688886	C₂²	1	2	yes	—
37	#15688886	C₂²	1	2	yes	—
38	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₈×Q₈×C₄₇	—	2	4	no	—
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
44	C₂²×Dic₉₄	—	2	1	no	—
45	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
46	#13094024	—	2	2	no	—
47	#13094024	C₂×C₄	1	4	yes	—
48	#13094022	—	2	8	no	—
49	#13094016	—	2	4	no	—
50	#13094016	C₂×C₄	1	8	yes	—
51	#13094014	—	2	16	no	—
52	C₄×Dic₉₄	—	2	4	no	—
53	C₄×Dic₉₄	—	2	2	no	—
54	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
55	C₄×Dic₉₄	C₂×C₄	1	4	yes	—
56	#13093989	—	2	8	no	—
57	C₂×C₄⋊Dic₄₇	—	2	1	no	—
58	C₂×C₄⋊Dic₄₇	—	2	1	no	—
59	C₂×C₄⋊Dic₄₇	—	2	1	no	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
62	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×Dic₄₇⋊C₄	—	2	2	no	—
66	C₂×Dic₄₇⋊C₄	—	2	1	no	—
67	C₂×Dic₄₇⋊C₄	—	2	2	no	—
68	C₂×Dic₄₇⋊C₄	—	2	2	no	—
69	C₂×C₄×Dic₄₇	—	2	2	no	—
70	C₂×C₄×Dic₄₇	—	2	1	no	—
71	C₂×C₄×Dic₄₇	—	2	1	no	—
72	C₂×C₄×Dic₄₇	—	2	2	no	—
73	#13093949	—	2	4	no	—
74	#13093949	—	2	2	no	—
75	#13093949	Q₈	1	4	yes	complemented
76	C₄₇⋊#95	—	2	1	no	—
77	C₄₇⋊#95	—	2	2	no	—
78	C₄₇⋊#95	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
85	C₄×Q₈×C₄₇	D₄	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
88	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₇	—	2	4	no	—
91	C₄⋊C₈×C₄₇	—	2	2	no	—
92	C₄×C₈×C₄₇	—	2	4	no	—
93	C₄×C₈×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	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₇	—	2	1	no	—
103	C₂²×Dic₄₇	—	2	1	no	—
104	C₂²×Dic₄₇	—	2	1	no	—
105	C₂²×Dic₄₇	—	2	2	no	—
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	—	2	2	no	—
108	C₂×Dic₉₄	—	2	1	no	—
109	C₂×Dic₉₄	—	2	1	no	—
110	C₂×Dic₉₄	—	2	1	no	—
111	C₂×Dic₉₄	—	2	4	no	—
112	C₂×Dic₉₄	—	4	2	no	—
113	C₂×Dic₉₄	—	4	2	no	—
114	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
115	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
116	C₂×Dic₉₄	#41	1	2	yes	—
117	C₂×C₈×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
127	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
128	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
129	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
130	C₄²×C₄₇	C₂×D₄	1	4	yes	—
131	C₄²×C₄₇	C₂×D₄	1	2	yes	—
132	C₄⋊Dic₄₇	—	2	4	no	—
133	C₄⋊Dic₄₇	—	2	1	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	1	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	1	no	—
139	C₄⋊Dic₄₇	—	2	2	no	—
140	C₄⋊Dic₄₇	—	4	2	no	—
141	C₄⋊Dic₄₇	—	8	1	no	—
142	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
143	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
144	C₄⋊Dic₄₇	C₂×Q₈	1	2	yes	—
145	Dic₄₇⋊C₄	—	2	8	no	—
146	Dic₄₇⋊C₄	—	2	4	no	—
147	Dic₄₇⋊C₄	—	2	8	no	—
148	Dic₄₇⋊C₄	—	2	8	no	—
149	C₄×Dic₄₇	—	2	8	no	—
150	C₄×Dic₄₇	—	2	4	no	—
151	C₄×Dic₄₇	—	4	2	no	—
152	C₄×Dic₄₇	—	8	2	no	—
153	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₄₇	—	2	8	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	1	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	#135	1	2	yes	—
166	C₂×C₄×C₄₇	#135	1	2	yes	—
167	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	4	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	4	1	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	1	no	—
183	C₂×Dic₄₇	—	4	1	no	—
184	C₂×Dic₄₇	—	4	1	no	—
185	C₂×Dic₄₇	—	4	1	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	4	1	no	—
188	C₂×Dic₄₇	—	4	2	no	—
189	C₂×Dic₄₇	—	4	2	no	—
190	C₂×Dic₄₇	—	4	1	no	—
191	Dic₉₄	—	2	2	no	—
192	Dic₉₄	—	2	2	no	—
193	Dic₉₄	—	2	2	no	—
194	Dic₉₄	—	4	8	no	—
195	Dic₉₄	C₄×Q₈	1	4	yes	—
196	C₈×C₄₇	—	2	2	no	—
197	C₈×C₄₇	—	4	1	no	—
198	C₈×C₄₇	—	4	2	no	—
199	#22521	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₄₇	#548	1	1	yes	characteristic
202	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
203	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
205	C₂²×C₄₇	#577	1	1	yes	characteristic
206	C₂²×C₄₇	#578	1	1	yes	characteristic
207	C₄×C₄₇	—	2	4	no	—
208	C₄×C₄₇	—	2	4	no	—
209	C₄×C₄₇	—	2	2	no	—
210	C₄×C₄₇	#416	1	4	yes	—
211	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
212	C₄×C₄₇	#519	1	1	yes	characteristic
213	C₄×C₄₇	#548	1	1	yes	characteristic
214	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
215	Dic₄₇	—	2	4	no	—
216	Dic₄₇	—	4	2	no	—
217	Dic₄₇	—	4	4	no	—
218	Dic₄₇	—	4	2	no	—
219	Dic₄₇	—	8	1	no	—
220	Dic₄₇	—	8	2	no	—
221	C₂×#557	—	47	1	no	—
222	C₂×C₈×Q₈	D₄₇	1	1	yes	characteristic
223	#2355	—	47	1	no	—
224	#1991	—	47	2	no	—
225	#1990	—	47	1	no	—
226	#1989	—	47	2	no	—
227	#1988	—	47	1	no	—
228	#1805	—	47	2	no	—
229	#1803	—	47	1	no	—
230	C₄×#103	—	47	1	no	—
231	C₄×#103	—	47	2	no	—
232	C₂×C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
234	C₂×C₄₇	#2898	1	1	yes	characteristic
235	C₂×C₄₇	#3364	1	1	yes	characteristic
236	C₂×C₄₇	#3365	1	1	yes	characteristic
237	C₂×C₄₇	#3381	1	1	yes	characteristic
238	C₂×C₄₇	#3383	1	1	yes	characteristic
239	#557	—	47	8	no	—
240	#557	—	94	4	no	—
241	C₂×C₄⋊Q₈	—	47	1	no	—
242	C₂×C₄⋊Q₈	—	94	1	no	—
243	C₂×#125	—	47	2	no	—
244	C₂×#125	—	94	2	no	—
245	C₂×C₄×Q₈	—	47	1	no	—
246	C₂×C₄×Q₈	—	47	2	no	—
247	C₂×C₄×Q₈	—	94	1	no	—
248	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
249	C₈×Q₈	—	2	4	no	—
250	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
252	C₂×#103	—	47	1	no	—
253	C₂×#103	—	47	2	no	—
254	C₂×#103	—	47	1	no	—
255	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
256	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
257	#391	—	94	1	no	—
258	#387	—	94	2	no	—
259	#384	—	47	1	no	—
260	#382	—	47	2	no	—
261	C₄×C₄⋊C₄	—	47	1	no	—
262	C₄×C₄⋊C₄	—	47	2	no	—
263	C₄×C₄⋊C₄	—	94	1	no	—
264	#340	—	47	2	no	—
265	#340	—	47	2	no	—
266	#340	—	47	2	no	—
267	#340	—	47	2	no	—
268	#340	—	47	1	no	—
269	#340	—	47	2	no	—
270	#340	—	47	1	no	—
271	C₄₇	#22521	1	1	yes	characteristic, complemented, Sylow
272	C₂²×Q₈	—	47	1	no	—
273	C₂²×Q₈	—	94	1	no	—
274	C₂²×Q₈	D₁₈₈	1	1	yes	characteristic
275	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
276	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
277	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
278	C₄⋊Q₈	—	47	4	no	—
279	C₄⋊Q₈	—	94	8	no	—
280	C₄⋊Q₈	—	94	2	no	—
281	#125	—	47	8	no	—
282	#125	—	94	16	no	—
283	#125	—	94	4	no	—
284	C₄×Q₈	—	47	8	no	—
285	C₄×Q₈	—	47	4	no	—
286	C₄×Q₈	—	94	8	no	—
287	C₄×Q₈	—	94	4	no	—
288	C₄×Q₈	—	94	2	no	—
289	C₄×Q₈	C₄×D₄₇	1	4	yes	—
290	C₄×Q₈	C₂²⋊D₄₇	1	4	yes	—
291	C₂×C₄⋊C₄	—	47	1	no	—
292	C₂×C₄⋊C₄	—	47	2	no	—
293	C₂×C₄⋊C₄	—	47	1	no	—
294	C₂×C₄⋊C₄	—	47	1	no	—
295	C₂×C₄⋊C₄	—	47	2	no	—
296	C₂×C₄⋊C₄	—	94	1	no	—
297	C₂×C₄⋊C₄	—	94	2	no	—
298	C₂×C₄⋊C₄	—	94	2	no	—
299	C₂×C₄⋊C₄	—	94	2	no	—
300	C₂×C₄⋊C₄	—	94	1	no	—
301	C₂×C₄⋊C₄	—	94	1	no	—
302	C₂×C₄⋊C₄	—	94	1	no	—
303	C₂×C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
304	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
305	C₂×C₄²	—	94	2	no	—
306	C₂×C₄²	—	94	1	no	—
307	C₂×C₄²	—	94	2	no	—
308	C₂×C₄²	—	94	1	no	—
309	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
310	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
311	C₄⋊C₈	—	2	4	no	—
312	C₄⋊C₈	—	2	2	no	—
313	#103	—	47	4	no	—
314	#103	—	94	4	no	—
315	#103	—	94	2	no	—
316	C₄×C₈	—	2	4	no	—
317	C₄×C₈	—	2	2	no	—
318	#95	—	94	1	no	—
319	#95	—	94	2	no	—
320	#95	—	94	2	no	—
321	#95	—	94	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	47	2	no	—
325	C₂×Q₈	—	47	2	no	—
326	C₂×Q₈	—	47	2	no	—
327	C₂×Q₈	—	94	4	no	—
328	C₂×Q₈	—	94	1	no	—
329	C₂×Q₈	—	94	1	no	—
330	C₂×Q₈	—	94	1	no	—
331	C₂×Q₈	—	188	2	no	—
332	C₂×Q₈	—	188	2	no	—
333	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	4	yes	—
334	C₂²×C₄	—	94	1	no	—
335	C₂²×C₄	—	94	1	no	—
336	C₂²×C₄	—	94	1	no	—
337	C₂²×C₄	—	94	2	no	—
338	C₂²×C₄	—	94	1	no	—
339	C₂²×C₄	—	94	2	no	—
340	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
341	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
342	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	Q₈×D₄₇	1	2	yes	—
354	C₄⋊C₄	—	47	2	no	—
355	C₄⋊C₄	—	47	4	no	—
356	C₄⋊C₄	—	47	2	no	—
357	C₄⋊C₄	—	94	4	no	—
358	C₄⋊C₄	—	94	8	no	—
359	C₄⋊C₄	—	94	8	no	—
360	C₄⋊C₄	—	94	8	no	—
361	C₄⋊C₄	—	94	4	no	—
362	C₄⋊C₄	—	94	1	no	—
363	C₄⋊C₄	—	94	2	no	—
364	C₄⋊C₄	—	94	1	no	—
365	C₄⋊C₄	—	94	1	no	—
366	C₄⋊C₄	—	94	2	no	—
367	C₄⋊C₄	—	94	1	no	—
368	C₄⋊C₄	—	94	2	no	—
369	C₄⋊C₄	—	376	1	no	—
370	C₄⋊C₄	—	188	2	no	—
371	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
372	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	8	yes	—
373	C₄²	—	94	8	no	—
374	C₄²	—	94	4	no	—
375	C₄²	—	376	2	no	—
376	C₄²	—	188	2	no	—
377	C₄²	C₂×C₄×D₄₇	1	4	yes	—
378	C₄²	C₂×C₄×D₄₇	1	2	yes	—
379	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
380	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
381	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
382	Q₈	—	2	8	no	—
383	Q₈	—	47	4	no	—
384	Q₈	—	94	2	no	—
385	Q₈	—	94	2	no	—
386	Q₈	—	94	2	no	—
387	Q₈	—	188	8	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	94	2	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	94	2	no	—
398	C₂×C₄	—	94	2	no	—
399	C₂×C₄	—	94	4	no	—
400	C₂×C₄	—	188	1	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	—	188	1	no	—
403	C₂×C₄	—	188	2	no	—
404	C₂×C₄	—	188	2	no	—
405	C₂×C₄	—	188	1	no	—
406	C₂×C₄	—	188	1	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	—	188	1	no	—
410	C₂×C₄	—	188	1	no	—
411	C₂×C₄	—	188	1	no	—
412	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
413	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
414	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
415	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
416	C₂×C₄	#13094046	1	2	yes	—
417	C₂×C₄	#13094046	1	2	yes	—
418	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
420	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
421	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
422	C₂×C₄	#13094071	1	1	yes	characteristic
423	C₂×C₄	#13094072	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	1	no	—
427	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
428	C₂²	#15689785	1	1	yes	characteristic
429	C₂²	Q₈×D₁₈₈	1	1	yes	characteristic
430	C₂²	C₂×#13094046	1	1	yes	characteristic
431	C₂²	C₂×#13094046	1	1	yes	characteristic
432	C₂²	#15689935	1	1	yes	characteristic
433	C₂²	#15689940	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	4	no	—
437	C₄	—	94	4	no	—
438	C₄	—	376	1	no	—
439	C₄	—	376	2	no	—
440	C₄	—	188	2	no	—
441	C₄	—	188	2	no	—
442	C₄	—	188	4	no	—
443	C₄	#15689120	1	4	yes	—
444	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
445	C₄	#15689599	1	1	yes	characteristic
446	C₄	#15689780	1	1	yes	characteristic
447	C₄	Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
448	C₂	Q₈×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
449	C₂	C₂×#15689120	1	1	yes	characteristic
450	C₂	#20251922	1	1	yes	characteristic
451	C₂	#20256075	1	1	yes	characteristic
452	C₂	#20256086	1	1	yes	characteristic
453	C₂	#20256265	1	1	yes	characteristic
454	C₂	#20256280	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₈×Q₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₈×Q₈	D₄₇
hypocenter	C₄₇	#22521
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
13. #15689851	C₄	semidirect
75. #13093949	Q₈	semidirect
271. C₄₇	#22521	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689851	2
#20246345	2
#20244353	2
#20244349	2
#20244343	2
#20244339	2
#20243404	2
#20243394	2
C₄×#13093949	2
C₂×C₈×Q₈×C₄₇	2
#22521	47