Subgroups — #26184133

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252429	C₂	1	1	yes	maximal, characteristic, complemented
2	#20246298	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241952	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241948	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241931	C₂	1	4	yes	maximal, complemented
6	#20241892	C₂	1	4	yes	maximal, complemented
7	#20241887	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241883	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#3506	C₂	1	1	yes	maximal, characteristic
10	C₂×D₄×Dic₄₇	—	2	1	no	—
11	#15689201	—	2	2	no	—
12	#15689201	—	2	2	no	—
13	#15689176	C₂²	1	1	yes	characteristic
14	#15689176	C₂²	1	1	yes	characteristic
15	#15689087	C₂²	1	4	yes	—
16	#15689022	—	2	1	no	—
17	#15688998	—	2	2	no	—
18	#15688989	C₂²	1	1	yes	characteristic
19	#15688983	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
22	#15688860	C₂²	1	2	yes	—
23	#15688860	C₂²	1	4	yes	—
24	#15688860	C₂²	1	2	yes	—
25	#15688857	C₂²	1	2	yes	—
26	#15688857	C₂²	1	4	yes	—
27	#15688857	C₂²	1	2	yes	—
28	C₄₇×#559	—	2	2	no	—
29	C₄₇×#556	C₄	1	2	yes	complemented
30	C₄₇×#555	C₄	1	2	yes	complemented
31	C₄₇×#553	—	2	2	no	—
32	C₄₇×#550	C₄	1	2	yes	complemented
33	C₄₇×#547	C₄	1	2	yes	complemented
34	C₄₇×#538	—	2	2	no	—
35	C₄₇×#535	—	2	1	no	—
36	C₄₇×#533	C₂²	1	1	yes	characteristic
37	C₄₇×#532	C₂²	1	1	yes	characteristic
38	C₄₇×#525	C₂²	1	4	yes	—
39	C₄₇×#520	—	2	1	no	—
40	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂³×Dic₄₇	—	2	2	no	—
42	C₂×#10625329	—	2	4	no	—
43	D₄×Dic₄₇	—	4	4	no	—
44	C₂×C₄⋊Dic₄₇	—	2	1	no	—
45	C₂×C₄⋊Dic₄₇	—	2	1	no	—
46	C₂×C₄⋊Dic₄₇	—	2	2	no	—
47	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
48	C₂×C₄×Dic₄₇	—	2	1	no	—
49	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
51	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
52	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
53	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
54	C₄×C₄₇⋊C₈	—	2	1	no	—
55	C₄×C₄₇⋊C₈	—	2	1	no	—
56	C₄₇⋊#95	—	2	2	no	—
57	C₄₇⋊#95	—	2	1	no	—
58	C₄₇⋊#95	C₂³	1	1	yes	characteristic
59	C₄₇⋊#95	C₂³	1	2	yes	—
60	C₄₇⋊#95	C₂³	1	1	yes	characteristic
61	C₂×#41×C₄₇	—	2	1	no	—
62	C₂×#41×C₄₇	C₂×C₄	1	4	yes	complemented
63	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
66	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
67	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
68	#127×C₄₇	—	2	2	no	—
69	#127×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
70	#126×C₄₇	—	2	4	no	—
71	#125×C₄₇	—	2	1	no	—
72	#124×C₄₇	—	2	2	no	—
73	#124×C₄₇	—	2	4	no	—
74	#124×C₄₇	—	2	1	no	—
75	#123×C₄₇	—	2	4	no	—
76	#123×C₄₇	—	2	4	no	—
77	C₂²⋊Q₈×C₄₇	—	2	1	no	—
78	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
79	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
80	#121×C₄₇	—	2	2	no	—
81	#121×C₄₇	—	2	2	no	—
82	#121×C₄₇	—	2	1	no	—
83	#121×C₄₇	—	2	4	no	—
84	#121×C₄₇	C₂×C₄	1	4	yes	complemented
85	#121×C₄₇	C₂³	1	2	yes	—
86	#120×C₄₇	—	2	4	no	—
87	C₄×Q₈×C₄₇	—	2	2	no	—
88	C₄×Q₈×C₄₇	—	2	1	no	—
89	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
90	C₄×D₄×C₄₇	—	2	4	no	—
91	C₄×D₄×C₄₇	—	2	4	no	—
92	C₄×D₄×C₄₇	—	2	2	no	—
93	C₄×D₄×C₄₇	—	2	1	no	—
94	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
95	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
96	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	complemented
97	C₄×D₄×C₄₇	D₄	1	2	yes	—
98	C₄×D₄×C₄₇	D₄	1	2	yes	—
99	#117×C₄₇	—	2	1	no	—
100	#117×C₄₇	—	2	2	no	—
101	#117×C₄₇	C₂×C₄	1	4	yes	complemented
102	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
105	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
106	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
107	#41×C₄₇	—	4	2	no	—
108	#41×C₄₇	—	4	2	no	—
109	#41×C₄₇	—	8	4	no	—
110	C₂×Q₈×C₄₇	—	2	1	no	—
111	C₂×Q₈×C₄₇	—	2	1	no	—
112	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	2	4	no	—
115	C₂×D₄×C₄₇	—	2	4	no	—
116	C₂×D₄×C₄₇	—	2	1	no	—
117	C₂×D₄×C₄₇	—	2	1	no	—
118	C₂×D₄×C₄₇	—	2	2	no	—
119	C₂×D₄×C₄₇	—	2	2	no	—
120	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
121	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
122	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	4	no	—
125	C₂²×C₄×C₄₇	—	8	2	no	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂²×Dic₄₇	—	2	1	no	—
133	C₂²×Dic₄₇	—	2	2	no	—
134	C₂²×Dic₄₇	—	2	1	no	—
135	C₂²×Dic₄₇	—	4	4	no	—
136	C₂²×Dic₄₇	—	4	4	no	—
137	C₂²×Dic₄₇	—	8	2	no	—
138	C₄⋊C₄×C₄₇	—	2	1	no	—
139	C₄⋊C₄×C₄₇	—	2	4	no	—
140	C₄⋊C₄×C₄₇	—	2	1	no	—
141	C₄⋊C₄×C₄₇	—	2	1	no	—
142	C₄⋊C₄×C₄₇	—	2	1	no	—
143	C₄⋊C₄×C₄₇	—	2	2	no	—
144	C₄⋊C₄×C₄₇	—	2	2	no	—
145	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
146	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
147	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
148	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
149	C₂²⋊C₄×C₄₇	—	2	4	no	—
150	C₂²⋊C₄×C₄₇	—	2	4	no	—
151	C₂²⋊C₄×C₄₇	—	2	2	no	—
152	C₂²⋊C₄×C₄₇	—	2	4	no	—
153	C₂²⋊C₄×C₄₇	—	2	2	no	—
154	C₂²⋊C₄×C₄₇	—	2	2	no	—
155	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
156	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
157	C₄²×C₄₇	—	2	4	no	—
158	C₄²×C₄₇	—	2	2	no	—
159	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂²⋊Dic₄₇	—	4	4	no	—
164	C₄⋊Dic₄₇	—	4	2	no	—
165	C₄⋊Dic₄₇	—	4	2	no	—
166	C₄⋊Dic₄₇	—	8	2	no	—
167	C₄×Dic₄₇	—	4	2	no	—
168	#10625329	—	8	4	no	—
169	C₂×C₄₇⋊C₈	—	2	2	no	—
170	C₂×C₄₇⋊C₈	—	2	2	no	—
171	C₂³×C₄₇	—	2	2	no	—
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	—	2	2	no	—
174	C₂³×C₄₇	—	4	2	no	—
175	C₂³×C₄₇	—	4	2	no	—
176	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₄₇	—	4	2	no	—
179	Q₈×C₄₇	—	4	2	no	—
180	Q₈×C₄₇	—	8	1	no	—
181	D₄×C₄₇	—	2	4	no	—
182	D₄×C₄₇	—	2	4	no	—
183	D₄×C₄₇	—	4	2	no	—
184	D₄×C₄₇	—	4	2	no	—
185	D₄×C₄₇	—	4	2	no	—
186	D₄×C₄₇	—	4	2	no	—
187	D₄×C₄₇	—	8	1	no	—
188	D₄×C₄₇	—	8	4	no	—
189	D₄×C₄₇	—	8	4	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	4	4	no	—
194	C₂×C₄×C₄₇	—	4	1	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	1	no	—
197	C₂×C₄×C₄₇	—	4	4	no	—
198	C₂×C₄×C₄₇	—	4	4	no	—
199	C₂×C₄×C₄₇	—	8	4	no	—
200	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
201	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₄₇	#137	1	2	yes	—
207	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
209	C₂×Dic₄₇	—	2	2	no	—
210	C₂×Dic₄₇	—	4	1	no	—
211	C₂×Dic₄₇	—	4	1	no	—
212	C₂×Dic₄₇	—	4	1	no	—
213	C₂×Dic₄₇	—	4	1	no	—
214	C₂×Dic₄₇	—	4	2	no	—
215	C₂×Dic₄₇	—	4	2	no	—
216	C₂×Dic₄₇	—	4	1	no	—
217	C₂×Dic₄₇	—	4	2	no	—
218	C₂×Dic₄₇	—	8	8	no	—
219	C₄₇⋊C₈	—	4	2	no	—
220	C₄₇⋊C₈	—	4	2	no	—
221	#17630	—	47	1	no	maximal, Sylow
222	C₂²×C₄₇	—	2	1	no	—
223	C₂²×C₄₇	—	2	1	no	—
224	C₂²×C₄₇	—	2	4	no	—
225	C₂²×C₄₇	—	2	4	no	—
226	C₂²×C₄₇	—	2	4	no	—
227	C₂²×C₄₇	—	4	4	no	—
228	C₂²×C₄₇	—	4	4	no	—
229	C₂²×C₄₇	—	4	2	no	—
230	C₂²×C₄₇	—	4	2	no	—
231	C₂²×C₄₇	—	4	2	no	—
232	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
233	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
235	C₄×C₄₇	—	2	1	no	—
236	C₄×C₄₇	—	2	1	no	—
237	C₄×C₄₇	—	2	4	no	—
238	C₄×C₄₇	—	2	1	no	—
239	C₄×C₄₇	—	2	1	no	—
240	C₄×C₄₇	—	4	2	no	—
241	C₄×C₄₇	—	4	2	no	—
242	C₄×C₄₇	—	4	2	no	—
243	C₄×C₄₇	#417	1	2	yes	—
244	C₄×C₄₇	#417	1	2	yes	—
245	Dic₄₇	—	4	2	no	—
246	Dic₄₇	—	8	1	no	—
247	Dic₄₇	—	8	2	no	—
248	#3506	D₄₇	1	1	yes	characteristic
249	#2975	—	47	1	no	—
250	#2349	—	47	1	no	—
251	#1518	—	47	1	no	—
252	#1517	—	47	1	no	—
253	#1513	—	47	4	no	—
254	#1504	—	47	4	no	—
255	#1503	—	47	1	no	—
256	#1502	—	47	1	no	—
257	C₂×C₄₇	—	2	1	no	—
258	C₂×C₄₇	—	2	1	no	—
259	C₂×C₄₇	—	4	4	no	—
260	C₂×C₄₇	—	8	2	no	—
261	C₂×C₄₇	#2883	1	1	yes	characteristic
262	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
263	C₂×C₄₇	#2901	1	1	yes	characteristic
264	#559	—	2	2	no	—
265	#556	Dic₄₇	1	2	yes	complemented
266	#555	Dic₄₇	1	2	yes	complemented
267	#553	—	2	2	no	—
268	#550	Dic₄₇	1	2	yes	complemented
269	#547	Dic₄₇	1	2	yes	complemented
270	#538	—	2	2	no	—
271	#535	—	2	1	no	—
272	#533	C₂×D₄₇	1	1	yes	characteristic
273	#532	C₂×D₄₇	1	1	yes	characteristic
274	#525	C₂×D₄₇	1	4	yes	—
275	#520	—	2	1	no	—
276	C₂×C₄×D₄	—	94	1	no	—
277	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
278	#436	—	94	2	no	—
279	#436	—	94	2	no	—
280	#431	—	47	1	no	—
281	#431	—	47	1	no	—
282	#407	—	47	4	no	—
283	#389	—	94	1	no	—
284	#385	—	94	2	no	—
285	#382	—	47	1	no	—
286	#380	—	47	2	no	—
287	C₄×C₄⋊C₄	—	47	1	no	—
288	C₂×#95	—	47	2	no	—
289	#328	—	47	2	no	—
290	#328	—	47	2	no	—
291	#328	—	47	4	no	—
292	#327	—	47	2	no	—
293	#327	—	47	2	no	—
294	#327	—	47	4	no	—
295	C₄₇	#17630	1	1	yes	characteristic, complemented, Sylow
296	C₂×#41	—	2	1	no	—
297	C₂×#41	C₂×Dic₄₇	1	4	yes	complemented
298	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
299	C₂³×C₄	—	94	2	no	—
300	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
301	C₂×M₁₆	—	94	4	no	—
302	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
303	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
304	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
305	#127	—	2	2	no	—
306	#127	C₂×Dic₄₇	1	1	yes	characteristic, complemented
307	#126	—	2	4	no	—
308	#125	—	2	1	no	—
309	#124	—	2	2	no	—
310	#124	—	2	4	no	—
311	#124	—	2	1	no	—
312	#123	—	2	4	no	—
313	#123	—	2	4	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
316	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
317	#121	—	2	2	no	—
318	#121	—	2	2	no	—
319	#121	—	2	1	no	—
320	#121	—	2	4	no	—
321	#121	C₂×Dic₄₇	1	4	yes	complemented
322	#121	C₂²×D₄₇	1	2	yes	—
323	#120	—	2	4	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×Q₈	C₂×Dic₄₇	1	2	yes	complemented
327	C₄×D₄	—	2	4	no	—
328	C₄×D₄	—	2	4	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	—	188	4	no	—
332	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
333	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
334	C₄×D₄	C₂×Dic₄₇	1	2	yes	complemented
335	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
336	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
337	#117	—	2	1	no	—
338	#117	—	2	2	no	—
339	#117	C₂×Dic₄₇	1	4	yes	complemented
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	94	2	no	—
342	C₂×C₄⋊C₄	—	94	1	no	—
343	C₂×C₄⋊C₄	—	94	1	no	—
344	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	94	2	no	—
346	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
347	C₂×C₄²	—	94	1	no	—
348	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
349	C₄⋊C₈	—	94	1	no	—
350	C₄⋊C₈	—	94	1	no	—
351	C₂²⋊C₈	—	47	2	no	—
352	C₂²⋊C₈	—	47	2	no	—
353	C₂²⋊C₈	—	94	4	no	—
354	C₄×C₈	—	94	1	no	—
355	C₄×C₈	—	94	1	no	—
356	#95	—	47	1	no	—
357	#95	—	47	2	no	—
358	#95	—	47	1	no	—
359	#95	—	94	2	no	—
360	#95	—	94	1	no	—
361	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
362	#41	—	4	2	no	—
363	#41	—	4	2	no	—
364	#41	—	8	4	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
376	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
377	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	8	2	no	—
381	C₂²×C₄	—	94	1	no	—
382	C₂²×C₄	—	94	2	no	—
383	C₂²×C₄	—	94	1	no	—
384	C₂²×C₄	—	376	2	no	—
385	C₂²×C₄	—	188	4	no	—
386	C₂²×C₄	—	188	4	no	—
387	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
388	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
390	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
391	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
392	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
393	M₁₆	—	376	4	no	—
394	C₂×C₈	—	94	2	no	—
395	C₂×C₈	—	94	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	376	2	no	—
404	C₄⋊C₄	—	188	2	no	—
405	C₄⋊C₄	—	188	2	no	—
406	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
407	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
408	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
409	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	188	4	no	—
417	C₂²⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
418	C₂²⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
419	C₄²	—	2	4	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	188	2	no	—
422	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
423	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
424	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
425	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
432	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
433	Q₈	—	4	2	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	8	1	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	8	1	no	—
443	D₄	—	8	4	no	—
444	D₄	—	8	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	8	4	no	—
455	C₂×C₄	—	94	2	no	—
456	C₂×C₄	—	376	8	no	—
457	C₂×C₄	—	188	1	no	—
458	C₂×C₄	—	188	2	no	—
459	C₂×C₄	—	188	1	no	—
460	C₂×C₄	—	188	2	no	—
461	C₂×C₄	—	188	1	no	—
462	C₂×C₄	—	188	2	no	—
463	C₂×C₄	—	188	1	no	—
464	C₂×C₄	—	188	1	no	—
465	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
466	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
467	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
468	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
469	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
470	C₂×C₄	#13094049	1	2	yes	—
471	C₂×C₄	#13094054	1	2	yes	—
472	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
474	C₈	—	188	2	no	—
475	C₈	—	188	2	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
487	C₂²	C₂×#13094049	1	1	yes	characteristic
488	C₂²	C₂×#13094054	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	376	2	no	—
498	C₄	—	376	1	no	—
499	C₄	—	188	2	no	—
500	C₄	#15689124	1	2	yes	—
501	C₄	#15689124	1	2	yes	—
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	4	4	no	—
505	C₂	—	8	2	no	—
506	C₂	#20251849	1	1	yes	characteristic
507	C₂	C₂×#15689124	1	1	yes	characteristic
508	C₂	#20251935	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3506	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3506	D₄₇
hypocenter	C₄₇	#17630
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ #3506

Complements

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

N	H ≅ G/N	type
1. #20252429	C₂	semidirect
2. #20246298	C₂	semidirect
3. #20241952	C₂	semidirect
4. #20241948	C₂	semidirect
5. #20241931	C₂	semidirect
6. #20241892	C₂	semidirect
7. #20241887	C₂	semidirect
8. #20241883	C₂	semidirect
29. C₄₇×#556	C₄	semidirect
30. C₄₇×#555	C₄	semidirect
32. C₄₇×#550	C₄	semidirect
33. C₄₇×#547	C₄	semidirect
62. C₂×#41×C₄₇	C₂×C₄	semidirect
65. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
66. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
67. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
69. #127×C₄₇	C₂×C₄	semidirect
78. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
84. #121×C₄₇	C₂×C₄	semidirect
89. C₄×Q₈×C₄₇	C₂×C₄	semidirect
96. C₄×D₄×C₄₇	C₂×C₄	semidirect
101. #117×C₄₇	C₂×C₄	semidirect
265. #556	Dic₄₇	semidirect
266. #555	Dic₄₇	semidirect
268. #550	Dic₄₇	semidirect
269. #547	Dic₄₇	semidirect
295. C₄₇	#17630	semidirect
297. C₂×#41	C₂×Dic₄₇	semidirect
302. C₄⋊Q₈	C₂×Dic₄₇	semidirect
303. C₄⋊Q₈	C₂×Dic₄₇	semidirect
304. C₄⋊Q₈	C₂×Dic₄₇	semidirect
306. #127	C₂×Dic₄₇	semidirect
315. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
321. #121	C₂×Dic₄₇	semidirect
326. C₄×Q₈	C₂×Dic₄₇	semidirect
334. C₄×D₄	C₂×Dic₄₇	semidirect
339. #117	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252429	2
#20246298	2
#20241952	2
#20241948	2
#20241931	2
#20241892	2
#20241887	2
#20241883	2
C₄₇×#3506	2
#17630	47