Subgroups — #26193420

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254326	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689497	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252868	C₂	1	1	yes	maximal, characteristic
4	#20242466	C₂	1	4	yes	maximal, complemented
5	#20242460	C₂	1	4	yes	maximal, complemented
6	#20242069	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241843	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13094049	—	2	1	no	—
11	C₂²×#10625336	—	2	2	no	—
12	C₂×#13094021	C₂²	1	1	yes	characteristic
13	#15689497	—	2	2	no	—
14	#15689497	—	2	1	no	—
15	#15689497	C₂²	1	4	yes	—
16	#15689471	—	2	1	no	—
17	#15689323	—	2	1	no	—
18	#15689323	C₂²	1	4	yes	—
19	#15689323	C₂²	1	2	yes	—
20	#15689318	—	2	1	no	—
21	#15689318	C₂²	1	2	yes	—
22	#15689273	—	2	2	no	—
23	#15689176	C₂²	1	1	yes	characteristic
24	#15689147	C₂²	1	1	yes	characteristic
25	#15689127	—	2	1	no	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	#15688872	C₂²	1	4	yes	complemented
28	Q₈⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
29	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
30	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
31	Q₈²×C₄₇	C₂²	1	2	yes	complemented
32	C₄₇×#557	—	2	1	no	—
33	C₄₇×#554	—	2	2	no	—
34	C₄₇×#554	C₂²	1	2	yes	complemented
35	D₄×Q₈×C₄₇	—	2	2	no	—
36	D₄×Q₈×C₄₇	—	2	1	no	—
37	C₄₇×#544	—	2	2	no	—
38	C₄₇×#544	—	2	1	no	—
39	C₄₇×#533	—	2	1	no	—
40	C₄₇×#533	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
42	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#520	—	2	1	no	—
44	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×D₁₈₈	—	2	1	no	—
46	C₂²×D₁₈₈	—	2	1	no	—
47	C₂²×D₁₈₈	—	2	1	no	—
48	#13094049	—	4	4	no	—
49	C₂×#10625336	—	2	8	no	—
50	C₂×#10625336	—	2	2	no	—
51	C₂×#10625336	—	2	4	no	—
52	C₂×#10625336	—	4	8	no	—
53	C₂×#10625334	—	2	2	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	#13094021	—	2	1	no	—
57	#13094021	—	2	1	no	—
58	#13094021	—	2	1	no	—
59	#13094021	C₂³	1	2	yes	—
60	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
63	#13093944	—	2	4	no	—
64	#13093944	—	2	2	no	—
65	#13093944	—	2	2	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
67	C₄×C₄₇⋊C₈	—	2	1	no	—
68	C₄×C₄₇⋊C₈	—	2	1	no	—
69	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
70	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
71	C₂²×Q₈×C₄₇	—	2	2	no	—
72	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
73	C₄⋊Q₈×C₄₇	—	2	2	no	—
74	C₄⋊Q₈×C₄₇	—	2	2	no	—
75	C₄⋊Q₈×C₄₇	—	2	4	no	—
76	C₄⋊Q₈×C₄₇	—	2	2	no	—
77	C₄⋊Q₈×C₄₇	—	2	2	no	—
78	C₄⋊Q₈×C₄₇	—	2	1	no	—
79	C₄⋊Q₈×C₄₇	—	2	1	no	—
80	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
81	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
82	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
83	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
84	#125×C₄₇	—	2	2	no	—
85	#125×C₄₇	—	2	4	no	—
86	#125×C₄₇	—	2	2	no	—
87	#125×C₄₇	—	2	1	no	—
88	C₂²⋊Q₈×C₄₇	—	2	2	no	—
89	C₂²⋊Q₈×C₄₇	—	2	4	no	—
90	C₂²⋊Q₈×C₄₇	—	2	4	no	—
91	C₂²⋊Q₈×C₄₇	—	2	2	no	—
92	C₂²⋊Q₈×C₄₇	—	2	4	no	—
93	C₂²⋊Q₈×C₄₇	—	2	1	no	—
94	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
95	C₄×Q₈×C₄₇	—	2	2	no	—
96	C₄×Q₈×C₄₇	—	2	2	no	—
97	C₄×Q₈×C₄₇	—	2	2	no	—
98	C₄×Q₈×C₄₇	—	2	1	no	—
99	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
102	C₄×D₄×C₄₇	—	2	4	no	—
103	C₄×D₄×C₄₇	—	2	2	no	—
104	C₄×D₄×C₄₇	—	2	1	no	—
105	C₄×D₄×C₄₇	—	2	1	no	—
106	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
107	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
108	#117×C₄₇	—	2	2	no	—
109	#117×C₄₇	—	2	1	no	—
110	#117×C₄₇	—	2	1	no	—
111	#117×C₄₇	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
114	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
115	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₂×C₄²×C₄₇	—	2	1	no	—
117	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
118	C₂³×D₄₇	—	4	1	no	—
119	#41×C₄₇	—	2	2	no	—
120	#41×C₄₇	SD₁₆	1	4	yes	complemented
121	C₂×Q₈×C₄₇	—	2	4	no	—
122	C₂×Q₈×C₄₇	—	2	2	no	—
123	C₂×Q₈×C₄₇	—	2	1	no	—
124	C₂×Q₈×C₄₇	—	4	4	no	—
125	C₂×Q₈×C₄₇	—	8	4	no	—
126	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
127	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
129	C₂×D₄×C₄₇	—	2	1	no	—
130	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	1	no	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂×D₁₈₈	—	2	2	no	—
140	C₂×D₁₈₈	—	2	2	no	—
141	C₂×D₁₈₈	—	2	2	no	—
142	C₂×D₁₈₈	—	4	4	no	—
143	C₂×D₁₈₈	—	4	2	no	—
144	C₂×D₁₈₈	—	4	2	no	—
145	C₂×D₁₈₈	—	4	1	no	—
146	C₂×D₁₈₈	—	4	1	no	—
147	C₂×D₁₈₈	—	4	1	no	—
148	C₂×D₁₈₈	—	8	2	no	—
149	C₄⋊C₄×C₄₇	—	2	4	no	—
150	C₄⋊C₄×C₄₇	—	2	4	no	—
151	C₄⋊C₄×C₄₇	—	2	4	no	—
152	C₄⋊C₄×C₄₇	—	2	4	no	—
153	C₄⋊C₄×C₄₇	—	2	2	no	—
154	C₄⋊C₄×C₄₇	—	2	1	no	—
155	C₄⋊C₄×C₄₇	—	2	2	no	—
156	C₄⋊C₄×C₄₇	—	2	1	no	—
157	C₄⋊C₄×C₄₇	—	2	1	no	—
158	C₄⋊C₄×C₄₇	—	2	1	no	—
159	C₄⋊C₄×C₄₇	—	2	2	no	—
160	C₄⋊C₄×C₄₇	—	2	2	no	—
161	C₄⋊C₄×C₄₇	—	2	2	no	—
162	C₄⋊C₄×C₄₇	—	2	1	no	—
163	C₄⋊C₄×C₄₇	—	2	2	no	—
164	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
167	C₂²⋊C₄×C₄₇	—	2	4	no	—
168	C₂²⋊C₄×C₄₇	—	2	2	no	—
169	C₂²⋊C₄×C₄₇	—	2	1	no	—
170	C₂²⋊C₄×C₄₇	—	2	1	no	—
171	C₂²⋊C₄×C₄₇	—	2	1	no	—
172	C₄²×C₄₇	—	2	4	no	—
173	C₄²×C₄₇	—	2	1	no	—
174	C₄²×C₄₇	—	2	1	no	—
175	C₄²×C₄₇	—	2	1	no	—
176	C₄²×C₄₇	—	2	2	no	—
177	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
181	#10625336	—	4	16	no	—
182	#10625336	—	4	4	no	—
183	#10625336	—	8	4	no	—
184	#10625334	—	4	4	no	—
185	#10625329	—	4	2	no	—
186	C₂×C₄₇⋊C₈	—	2	4	no	—
187	C₂×C₄₇⋊C₈	—	2	2	no	—
188	C₂×C₄₇⋊C₈	—	2	2	no	—
189	C₂×C₄₇⋊C₈	—	2	2	no	—
190	C₂³×C₄₇	—	2	1	no	—
191	C₂³×C₄₇	#120	1	1	yes	characteristic
192	C₂²×D₄₇	—	4	2	no	—
193	C₂²×D₄₇	—	8	2	no	—
194	C₂²×D₄₇	—	8	2	no	—
195	C₂²×D₄₇	—	8	2	no	—
196	Q₈×C₄₇	—	2	1	no	—
197	Q₈×C₄₇	—	2	4	no	—
198	Q₈×C₄₇	—	4	4	no	—
199	Q₈×C₄₇	—	4	4	no	—
200	Q₈×C₄₇	—	4	2	no	—
201	Q₈×C₄₇	—	8	4	no	—
202	Q₈×C₄₇	C₂×SD₁₆	1	2	yes	complemented
203	D₄×C₄₇	—	2	4	no	—
204	D₄×C₄₇	—	2	1	no	—
205	D₄×C₄₇	C₂×SD₁₆	1	2	yes	complemented
206	C₂×C₄×C₄₇	—	2	1	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	2	1	no	—
212	C₂×C₄×C₄₇	—	2	1	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	2	no	—
217	C₂×C₄×C₄₇	—	8	2	no	—
218	C₂×C₄×C₄₇	—	8	4	no	—
219	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
220	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
221	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
223	C₂×C₄×C₄₇	#137	1	2	yes	—
224	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
227	D₁₈₈	—	4	4	no	—
228	D₁₈₈	—	4	2	no	—
229	D₁₈₈	—	4	2	no	—
230	D₁₈₈	—	4	4	no	—
231	D₁₈₈	—	8	2	no	—
232	D₁₈₈	—	8	2	no	—
233	D₁₈₈	—	8	2	no	—
234	C₄₇⋊C₈	—	2	4	no	—
235	C₄₇⋊C₈	—	4	2	no	—
236	C₄₇⋊C₈	—	4	2	no	—
237	#18622	—	47	1	no	maximal, Sylow
238	C₂²×C₄₇	—	2	1	no	—
239	C₂²×C₄₇	—	2	1	no	—
240	C₂²×C₄₇	—	2	2	no	—
241	C₂²×C₄₇	—	4	1	no	—
242	C₂²×C₄₇	—	4	1	no	—
243	C₂²×C₄₇	#448	1	2	yes	—
244	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
245	C₂×D₄₇	—	8	2	no	—
246	C₂×D₄₇	—	8	2	no	—
247	C₂×D₄₇	—	8	2	no	—
248	C₂×D₄₇	—	16	4	no	—
249	C₄×C₄₇	—	2	2	no	—
250	C₄×C₄₇	—	2	1	no	—
251	C₄×C₄₇	—	2	1	no	—
252	C₄×C₄₇	—	4	1	no	—
253	C₄×C₄₇	—	4	2	no	—
254	C₄×C₄₇	—	4	1	no	—
255	C₄×C₄₇	—	4	4	no	—
256	C₄×C₄₇	—	4	2	no	—
257	C₄×C₄₇	#448	1	2	yes	—
258	C₄×C₄₇	#453	1	2	yes	—
259	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
260	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
261	C₄×C₄₇	#577	1	2	yes	—
262	#3503	D₄₇	1	1	yes	characteristic, complemented
263	#3208	—	47	1	no	—
264	C₂×#492	—	47	1	no	—
265	#3038	—	47	1	no	—
266	#1623	—	47	4	no	—
267	#1622	—	47	4	no	—
268	#1548	—	47	1	no	—
269	#1493	—	47	1	no	—
270	#1476	—	47	1	no	—
271	C₂×C₄₇	—	2	2	no	—
272	C₂×C₄₇	—	4	2	no	—
273	C₂×C₄₇	C₂×#448	1	1	yes	characteristic
274	C₂×C₄₇	#3010	1	1	yes	characteristic
275	C₂×C₄₇	C₂×#453	1	1	yes	characteristic
276	D₄₇	—	16	2	no	—
277	C₂×AGL(1,ℤ/8)	—	94	1	no	—
278	C₂²×SD₁₆	—	94	2	no	—
279	Q₈²	C₂×D₄₇	1	2	yes	complemented
280	#557	—	2	1	no	—
281	#554	—	2	2	no	—
282	#554	C₂×D₄₇	1	2	yes	complemented
283	D₄×Q₈	—	2	2	no	—
284	D₄×Q₈	—	2	1	no	—
285	#544	—	2	2	no	—
286	#544	—	2	1	no	—
287	#533	—	2	1	no	—
288	#533	C₂×D₄₇	1	1	yes	characteristic
289	C₂×C₄⋊Q₈	—	2	1	no	—
290	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
291	C₂×#127	—	47	1	no	—
292	#520	—	2	1	no	—
293	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
294	#492	—	47	4	no	—
295	#492	—	94	2	no	—
296	#492	—	94	1	no	—
297	#486	—	94	1	no	—
298	#460	—	47	4	no	—
299	#460	—	47	2	no	—
300	#460	—	94	1	no	—
301	#459	—	47	2	no	—
302	#459	—	94	1	no	—
303	#450	—	94	2	no	—
304	#431	—	47	1	no	—
305	#423	—	47	1	no	—
306	#418	—	94	1	no	—
307	C₂×C₄×C₈	—	47	1	no	—
308	#333	—	47	4	no	—
309	Q₈⋊C₈	—	47	4	no	—
310	Q₈⋊C₈	—	47	2	no	—
311	D₄⋊C₈	—	47	2	no	—
312	C₄₇	#18622	1	1	yes	characteristic, complemented, Sylow
313	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	C₂²⋊D₄₇	1	2	yes	—
316	C₂²×D₄	—	94	1	no	—
317	C₂²×D₄	—	94	1	no	—
318	C₂²×D₄	—	94	1	no	—
319	AGL(1,ℤ/8)	—	188	4	no	—
320	C₂×SD₁₆	—	94	4	no	—
321	C₂×SD₁₆	—	94	8	no	—
322	C₂×SD₁₆	—	94	2	no	—
323	C₂×SD₁₆	—	188	8	no	—
324	C₂×D₈	—	94	2	no	—
325	C₂×M₁₆	—	94	1	no	—
326	C₂²×C₈	—	94	1	no	—
327	C₄⋊Q₈	—	2	2	no	—
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	—	2	4	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	—	2	2	no	—
332	C₄⋊Q₈	—	2	1	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
335	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
336	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
337	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
338	#127	—	47	2	no	—
339	#127	—	94	1	no	—
340	#127	—	94	1	no	—
341	#127	—	94	1	no	—
342	#125	—	2	2	no	—
343	#125	—	2	4	no	—
344	#125	—	2	2	no	—
345	#125	—	2	1	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	4	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	—	2	2	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
358	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
359	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
360	C₄×D₄	—	2	4	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
365	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
366	#117	—	2	2	no	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	C₂²⋊D₄₇	1	1	yes	characteristic
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
376	C₄⋊C₈	—	47	2	no	—
377	C₄⋊C₈	—	47	2	no	—
378	C₄⋊C₈	—	94	1	no	—
379	#102	—	94	2	no	—
380	#102	—	94	2	no	—
381	#102	—	94	4	no	—
382	C₂²⋊C₈	—	94	1	no	—
383	C₄×C₈	—	47	2	no	—
384	C₄×C₈	—	94	1	no	—
385	C₄×C₈	—	94	1	no	—
386	C₂⁴	—	188	1	no	—
387	#41	—	2	2	no	—
388	#41	#10625336	1	4	yes	complemented
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	4	4	no	—
393	C₂×Q₈	—	8	4	no	—
394	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
395	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
396	C₂×Q₈	C₂×C₂²⋊D₄₇	1	4	yes	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	94	2	no	—
399	C₂×D₄	—	94	2	no	—
400	C₂×D₄	—	94	2	no	—
401	C₂×D₄	—	376	2	no	—
402	C₂×D₄	—	188	4	no	—
403	C₂×D₄	—	188	1	no	—
404	C₂×D₄	—	188	1	no	—
405	C₂×D₄	—	188	1	no	—
406	C₂×D₄	—	188	2	no	—
407	C₂×D₄	—	188	2	no	—
408	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
415	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
416	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
417	SD₁₆	—	376	4	no	—
418	SD₁₆	—	188	16	no	—
419	SD₁₆	—	188	4	no	—
420	D₈	—	188	4	no	—
421	M₁₆	—	188	2	no	—
422	C₂×C₈	—	94	4	no	—
423	C₂×C₈	—	94	2	no	—
424	C₂×C₈	—	94	2	no	—
425	C₂×C₈	—	94	2	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
442	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
443	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	2	no	—
454	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
455	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
456	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
457	C₄²	C₂³×D₄₇	1	1	yes	characteristic
458	C₂³	—	2	1	no	—
459	C₂³	—	376	2	no	—
460	C₂³	—	376	2	no	—
461	C₂³	—	376	2	no	—
462	C₂³	—	188	2	no	—
463	C₂³	#13093993	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	2	4	no	—
466	Q₈	—	4	4	no	—
467	Q₈	—	4	4	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	8	4	no	—
470	Q₈	C₂×#10625336	1	2	yes	complemented
471	D₄	—	2	4	no	—
472	D₄	—	2	1	no	—
473	D₄	—	376	2	no	—
474	D₄	—	376	2	no	—
475	D₄	—	376	2	no	—
476	D₄	—	188	4	no	—
477	D₄	—	188	2	no	—
478	D₄	—	188	2	no	—
479	D₄	—	188	4	no	—
480	D₄	C₂×#10625336	1	2	yes	complemented
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	8	2	no	—
493	C₂×C₄	—	8	4	no	—
494	C₂×C₄	#13093993	1	1	yes	characteristic
495	C₂×C₄	#13093993	1	1	yes	characteristic
496	C₂×C₄	#13093993	1	1	yes	characteristic
497	C₂×C₄	C₂×#10625336	1	2	yes	—
498	C₂×C₄	#13094055	1	2	yes	—
499	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
500	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
501	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
502	C₈	—	94	4	no	—
503	C₈	—	188	2	no	—
504	C₈	—	188	2	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	376	2	no	—
511	C₂²	—	376	2	no	—
512	C₂²	—	376	2	no	—
513	C₂²	—	752	4	no	—
514	C₂²	#15689262	1	2	yes	—
515	C₂²	C₂×#13093993	1	1	yes	characteristic
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	2	no	—
524	C₄	#15689262	1	2	yes	—
525	C₄	#15689291	1	2	yes	—
526	C₄	C₂²×#10625336	1	1	yes	characteristic
527	C₄	C₂×#13094055	1	1	yes	characteristic
528	C₄	#15689931	1	2	yes	—
529	C₂	—	2	2	no	—
530	C₂	—	4	2	no	—
531	C₂	—	752	2	no	—
532	C₂	C₂×#15689262	1	1	yes	characteristic
533	C₂	#20252674	1	1	yes	characteristic
534	C₂	C₂×#15689291	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093993
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3503	C₂
socle	C₂²×C₄₇	C₂×#120
prime radical	#20252868	C₂
hypercenter	#3503	D₄₇
hypocenter	C₄₇	#18622
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3503

Complements

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

N	H ≅ G/N	type
1. #20254326	C₂	semidirect
2. C₂×#15689497	C₂	semidirect
4. #20242466	C₂	semidirect
5. #20242460	C₂	semidirect
6. #20242069	C₂	semidirect
7. #20241843	C₂	semidirect
8. #20241770	C₂	semidirect
9. C₄₇×#3503	C₂	semidirect
27. #15688872	C₂²	semidirect
28. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
29. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
30. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
31. Q₈²×C₄₇	C₂²	semidirect
34. C₄₇×#554	C₂²	semidirect
120. #41×C₄₇	SD₁₆	semidirect
202. Q₈×C₄₇	C₂×SD₁₆	semidirect
205. D₄×C₄₇	C₂×SD₁₆	semidirect
262. #3503	D₄₇	semidirect
279. Q₈²	C₂×D₄₇	semidirect
282. #554	C₂×D₄₇	semidirect
312. C₄₇	#18622	semidirect
388. #41	#10625336	semidirect
470. Q₈	C₂×#10625336	semidirect
480. D₄	C₂×#10625336	semidirect

Maximal subgroups

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

subgroup	index
#20254326	2
C₂×#15689497	2
#20252868	2
#20242466	2
#20242460	2
#20242069	2
#20241843	2
#20241770	2
C₄₇×#3503	2
#18622	47