Subgroups — #26221614

Order 12032.

1122 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252026	C₂	1	1	yes	maximal, characteristic, complemented
2	#117×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244370	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244366	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244221	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244217	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243837	C₂	1	2	yes	maximal, complemented
8	#20243832	C₂	1	2	yes	maximal, complemented
9	#20243198	C₂	1	2	yes	maximal, complemented
10	C₄×#13093951	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3455	C₂	1	1	yes	maximal, characteristic
12	C₂×#13093983	C₂²	1	1	yes	characteristic
13	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
14	#15689184	—	2	4	no	—
15	#15689147	C₂²	1	1	yes	characteristic
16	#15689147	C₂²	1	1	yes	characteristic
17	C₂×#13093951	C₂²	1	2	yes	—
18	C₂×#13093951	C₂²	1	2	yes	—
19	C₂×#13093951	C₂²	1	2	yes	—
20	C₂×#13093951	C₂²	1	2	yes	—
21	#15689087	C₂²	1	2	yes	—
22	C₄×#10625329	C₂²	1	2	yes	—
23	C₄⋊C₄×Dic₄₇	—	2	2	no	—
24	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
25	#15688969	C₂²	1	1	yes	characteristic
26	#15688969	C₂²	1	1	yes	characteristic
27	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
29	#15688882	C₂²	1	2	yes	—
30	#15688882	C₂²	1	2	yes	—
31	#15688882	C₂²	1	2	yes	—
32	#15688882	C₂²	1	2	yes	—
33	C₄₇×#542	C₄	1	4	yes	complemented
34	C₄₇×#541	C₄	1	2	yes	complemented
35	C₄₇×#540	C₄	1	2	yes	complemented
36	C₄₇×#539	—	2	2	no	—
37	C₄₇×#538	—	2	2	no	—
38	C₄₇×#533	C₂²	1	1	yes	characteristic
39	C₄₇×#532	C₂²	1	1	yes	characteristic
40	C₄₇×#529	—	2	4	no	—
41	C₄₇×#525	C₂²	1	2	yes	—
42	C₄×#41×C₄₇	C₂²	1	2	yes	—
43	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
44	C₂³×Dic₄₇	—	2	1	no	—
45	C₂×#10625329	C₂³	1	2	yes	—
46	C₂×#10625329	C₂³	1	2	yes	—
47	#13093983	—	2	2	no	—
48	#13093983	—	2	2	no	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
51	C₂×C₄×Dic₄₇	—	2	1	no	—
52	C₂×C₄×Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	2	2	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
62	#13093951	—	2	4	no	—
63	#13093951	—	2	4	no	—
64	#13093951	—	2	4	no	—
65	#13093951	—	2	4	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
67	#13093935	—	2	2	no	—
68	C₄×C₄₇⋊C₈	—	2	2	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₂×#41×C₄₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
74	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
75	#127×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
76	#126×C₄₇	—	2	4	no	—
77	#126×C₄₇	—	2	4	no	—
78	#125×C₄₇	—	2	4	no	—
79	#125×C₄₇	C₂×C₄	1	2	yes	complemented
80	#124×C₄₇	—	2	4	no	—
81	#124×C₄₇	C₂×C₄	1	2	yes	complemented
82	#123×C₄₇	—	2	2	no	—
83	#123×C₄₇	—	2	4	no	—
84	#123×C₄₇	—	2	4	no	—
85	C₂²⋊Q₈×C₄₇	—	2	2	no	—
86	C₂²⋊Q₈×C₄₇	—	2	4	no	—
87	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
88	#121×C₄₇	—	2	2	no	—
89	#121×C₄₇	—	2	4	no	—
90	#121×C₄₇	C₂×C₄	1	4	yes	—
91	#120×C₄₇	—	2	2	no	—
92	C₄×Q₈×C₄₇	—	2	2	no	—
93	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
94	C₄×D₄×C₄₇	—	2	4	no	—
95	C₄×D₄×C₄₇	—	2	4	no	—
96	C₄×D₄×C₄₇	—	2	2	no	—
97	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
98	#117×C₄₇	—	2	2	no	—
99	#117×C₄₇	C₂×C₄	1	2	yes	—
100	#117×C₄₇	C₂×C₄	1	2	yes	—
101	#117×C₄₇	D₄	1	4	yes	—
102	#117×C₄₇	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
104	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
105	C₂×C₄²×C₄₇	—	2	2	no	—
106	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
109	#41×C₄₇	—	2	2	no	—
110	#41×C₄₇	—	2	2	no	—
111	#41×C₄₇	—	2	2	no	—
112	#41×C₄₇	—	2	2	no	—
113	C₂×Q₈×C₄₇	—	2	2	no	—
114	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	4	no	—
117	C₂×D₄×C₄₇	—	2	2	no	—
118	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	4	no	—
125	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
131	C₂²×Dic₄₇	—	2	1	no	—
132	C₂²×Dic₄₇	—	2	4	no	—
133	C₂²×Dic₄₇	—	2	1	no	—
134	C₂²×Dic₄₇	—	2	1	no	—
135	C₂²×Dic₄₇	—	2	1	no	—
136	C₂²×Dic₄₇	—	4	4	no	—
137	C₄⋊C₄×C₄₇	—	2	4	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	4	no	—
140	C₄⋊C₄×C₄₇	—	2	4	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
143	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
144	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
145	C₂²⋊C₄×C₄₇	—	2	4	no	—
146	C₂²⋊C₄×C₄₇	—	2	2	no	—
147	C₂²⋊C₄×C₄₇	—	2	4	no	—
148	C₂²⋊C₄×C₄₇	—	2	4	no	—
149	C₂²⋊C₄×C₄₇	—	2	4	no	—
150	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
151	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
152	C₄²×C₄₇	—	2	4	no	—
153	C₄²×C₄₇	—	2	2	no	—
154	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
155	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₄₇	C₂×D₄	1	2	yes	—
158	C₄²×C₄₇	C₂×D₄	1	2	yes	—
159	C₂²⋊Dic₄₇	—	2	4	no	—
160	C₄⋊Dic₄₇	—	2	4	no	—
161	C₄×Dic₄₇	—	2	4	no	—
162	C₄×Dic₄₇	—	2	1	no	—
163	C₄×Dic₄₇	—	2	1	no	—
164	C₄×Dic₄₇	—	2	1	no	—
165	C₄×Dic₄₇	—	2	1	no	—
166	C₄×Dic₄₇	—	4	4	no	—
167	C₄×Dic₄₇	—	4	4	no	—
168	C₄×Dic₄₇	#41	1	2	yes	—
169	C₄×Dic₄₇	#41	1	2	yes	—
170	C₄×Dic₄₇	#41	1	2	yes	—
171	C₄×Dic₄₇	#41	1	2	yes	—
172	#10625329	—	2	2	no	—
173	#10625329	—	2	2	no	—
174	#10625329	—	2	2	no	—
175	#10625329	—	2	2	no	—
176	C₂×C₄₇⋊C₈	—	2	2	no	—
177	C₂×C₄₇⋊C₈	—	2	2	no	—
178	C₂³×C₄₇	—	2	1	no	—
179	C₂³×C₄₇	—	2	1	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	4	2	no	—
182	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₄₇	—	2	2	no	—
185	Q₈×C₄₇	—	2	2	no	—
186	Q₈×C₄₇	—	8	2	no	—
187	D₄×C₄₇	—	2	2	no	—
188	D₄×C₄₇	—	2	2	no	—
189	D₄×C₄₇	—	4	2	no	—
190	D₄×C₄₇	—	4	2	no	—
191	D₄×C₄₇	—	8	2	no	—
192	D₄×C₄₇	—	8	4	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	4	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	8	4	no	—
206	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
207	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
216	C₂×Dic₄₇	—	2	4	no	—
217	C₂×Dic₄₇	—	2	2	no	—
218	C₂×Dic₄₇	—	2	2	no	—
219	C₂×Dic₄₇	—	2	2	no	—
220	C₂×Dic₄₇	—	2	2	no	—
221	C₂×Dic₄₇	—	4	8	no	—
222	C₂×Dic₄₇	—	4	2	no	—
223	C₂×Dic₄₇	—	4	2	no	—
224	C₂×Dic₄₇	—	4	2	no	—
225	C₄₇⋊C₈	—	4	2	no	—
226	C₄₇⋊C₈	—	4	2	no	—
227	#21419	—	47	1	no	maximal, Sylow
228	C₂²×C₄₇	—	2	2	no	—
229	C₂²×C₄₇	—	2	4	no	—
230	C₂²×C₄₇	—	2	2	no	—
231	C₂²×C₄₇	—	4	2	no	—
232	C₂²×C₄₇	—	4	2	no	—
233	C₂²×C₄₇	—	4	4	no	—
234	C₂²×C₄₇	—	4	2	no	—
235	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₄₇	#525	1	1	yes	characteristic
237	C₂²×C₄₇	#525	1	1	yes	characteristic
238	C₄×C₄₇	—	2	4	no	—
239	C₄×C₄₇	—	2	2	no	—
240	C₄×C₄₇	—	2	2	no	—
241	C₄×C₄₇	—	2	2	no	—
242	C₄×C₄₇	—	4	4	no	—
243	C₄×C₄₇	—	4	2	no	—
244	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
245	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
246	C₄×C₄₇	#532	1	1	yes	characteristic
247	C₄×C₄₇	#532	1	1	yes	characteristic
248	Dic₄₇	—	2	4	no	—
249	Dic₄₇	—	4	2	no	—
250	Dic₄₇	—	4	2	no	—
251	Dic₄₇	—	4	2	no	—
252	#3455	D₄₇	1	1	yes	characteristic
253	#2921	—	47	1	no	—
254	C₄×#117	—	47	1	no	—
255	#1995	—	47	1	no	—
256	#1994	—	47	1	no	—
257	#1963	—	47	1	no	—
258	#1962	—	47	1	no	—
259	#1897	—	47	2	no	—
260	#1896	—	47	2	no	—
261	#1759	—	47	2	no	—
262	C₄×#104	—	47	2	no	—
263	C₂×C₄₇	—	2	1	no	—
264	C₂×C₄₇	—	2	1	no	—
265	C₂×C₄₇	—	4	2	no	—
266	C₂×C₄₇	—	8	2	no	—
267	C₂×C₄₇	#2297	1	1	yes	characteristic
268	C₂×C₄₇	#2901	1	2	yes	—
269	#542	Dic₄₇	1	4	yes	complemented
270	#541	Dic₄₇	1	2	yes	complemented
271	#540	Dic₄₇	1	2	yes	complemented
272	#539	—	2	2	no	—
273	#538	—	2	2	no	—
274	#533	C₂×D₄₇	1	1	yes	characteristic
275	#532	C₂×D₄₇	1	1	yes	characteristic
276	#529	—	2	4	no	—
277	#525	C₂×D₄₇	1	2	yes	—
278	C₄×#41	C₂×D₄₇	1	2	yes	—
279	C₂×#117	—	47	1	no	—
280	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
281	C₂²×C₄²	—	47	1	no	—
282	#433	—	94	4	no	—
283	#423	—	47	1	no	—
284	#423	—	47	1	no	—
285	C₂×#104	—	47	2	no	—
286	C₂×#104	—	47	2	no	—
287	C₂×#104	—	47	2	no	—
288	C₂×#104	—	47	2	no	—
289	#407	—	47	2	no	—
290	C₄×M₁₆	—	47	2	no	—
291	C₄×C₄⋊C₄	—	94	2	no	—
292	C₄×C₂²⋊C₄	—	94	2	no	—
293	#376	—	47	1	no	—
294	#376	—	47	1	no	—
295	C₄³	—	47	1	no	—
296	C₄³	—	47	1	no	—
297	#339	—	47	2	no	—
298	#339	—	47	2	no	—
299	#339	—	47	2	no	—
300	#339	—	47	2	no	—
301	C₄₇	#21419	1	1	yes	characteristic, complemented, Sylow
302	C₂×#41	C₂²×D₄₇	1	2	yes	—
303	C₂³×C₄	—	94	1	no	—
304	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
305	C₂×M₁₆	—	47	2	no	—
306	C₂×M₁₆	—	47	2	no	—
307	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
308	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
309	#127	C₂×Dic₄₇	1	1	yes	characteristic, complemented
310	#126	—	2	4	no	—
311	#126	—	2	4	no	—
312	#125	—	2	4	no	—
313	#125	C₂×Dic₄₇	1	2	yes	complemented
314	#124	—	2	4	no	—
315	#124	C₂×Dic₄₇	1	2	yes	complemented
316	#123	—	2	2	no	—
317	#123	—	2	4	no	—
318	#123	—	2	4	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
322	#121	—	2	2	no	—
323	#121	—	2	4	no	—
324	#121	C₂×Dic₄₇	1	4	yes	—
325	#120	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
328	C₄×D₄	—	2	4	no	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
332	#117	—	2	2	no	—
333	#117	—	94	2	no	—
334	#117	—	94	2	no	—
335	#117	C₂×Dic₄₇	1	2	yes	—
336	#117	C₂×Dic₄₇	1	2	yes	—
337	#117	C₂²⋊D₄₇	1	4	yes	—
338	#117	C₂²×D₄₇	1	2	yes	—
339	C₂×C₄⋊C₄	—	94	1	no	—
340	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
341	C₂×C₂²⋊C₄	—	94	1	no	—
342	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	47	1	no	—
345	C₂×C₄²	—	47	1	no	—
346	C₂×C₄²	—	47	1	no	—
347	C₂×C₄²	—	47	1	no	—
348	C₂×C₄²	—	94	2	no	—
349	C₂×C₄²	—	94	2	no	—
350	C₂×C₄²	—	94	1	no	—
351	C₂×C₄²	—	94	2	no	—
352	C₂×C₄²	—	94	2	no	—
353	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
354	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
355	C₄⋊C₈	—	94	2	no	—
356	C₄⋊C₈	—	94	2	no	—
357	#104	—	94	4	no	—
358	#104	—	94	4	no	—
359	#104	—	94	4	no	—
360	#104	—	94	4	no	—
361	C₂²⋊C₈	—	94	4	no	—
362	#97	—	94	2	no	—
363	C₄×C₈	—	94	2	no	—
364	#95	—	94	2	no	—
365	#95	—	94	2	no	—
366	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	94	1	no	—
384	C₂²×C₄	—	94	4	no	—
385	C₂²×C₄	—	94	1	no	—
386	C₂²×C₄	—	94	1	no	—
387	C₂²×C₄	—	94	1	no	—
388	C₂²×C₄	—	188	4	no	—
389	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
390	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
392	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
393	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
394	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
395	M₁₆	—	94	2	no	—
396	M₁₆	—	94	2	no	—
397	M₁₆	—	94	2	no	—
398	M₁₆	—	94	2	no	—
399	C₂×C₈	—	94	2	no	—
400	C₂×C₈	—	94	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	94	4	no	—
407	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
408	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
409	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	94	4	no	—
416	C₂²⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
417	C₂²⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	47	2	no	—
421	C₄²	—	47	2	no	—
422	C₄²	—	47	2	no	—
423	C₄²	—	47	2	no	—
424	C₄²	—	94	4	no	—
425	C₄²	—	94	1	no	—
426	C₄²	—	94	1	no	—
427	C₄²	—	94	1	no	—
428	C₄²	—	94	1	no	—
429	C₄²	—	188	4	no	—
430	C₄²	—	188	4	no	—
431	C₄²	C₂²×Dic₄₇	1	2	yes	—
432	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
433	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
434	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
435	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
441	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
442	Q₈	—	2	2	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	8	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	8	2	no	—
450	D₄	—	8	4	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	8	4	no	—
464	C₂×C₄	—	94	4	no	—
465	C₂×C₄	—	94	2	no	—
466	C₂×C₄	—	94	2	no	—
467	C₂×C₄	—	94	2	no	—
468	C₂×C₄	—	94	2	no	—
469	C₂×C₄	—	188	8	no	—
470	C₂×C₄	—	188	2	no	—
471	C₂×C₄	—	188	2	no	—
472	C₂×C₄	—	188	2	no	—
473	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
474	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
475	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
476	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
477	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
478	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
479	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
480	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
481	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
482	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
483	C₈	—	188	2	no	—
484	C₈	—	188	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	2	no	—
492	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
493	C₂²	#15689630	1	1	yes	characteristic
494	C₂²	#15689630	1	1	yes	characteristic
495	C₄	—	2	4	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	2	no	—
501	C₄	—	94	4	no	—
502	C₄	—	188	2	no	—
503	C₄	—	188	2	no	—
504	C₄	—	188	2	no	—
505	C₄	#41×Dic₄₇	1	1	yes	characteristic
506	C₄	#41×Dic₄₇	1	1	yes	characteristic
507	C₄	#15689669	1	1	yes	characteristic
508	C₄	#15689669	1	1	yes	characteristic
509	C₂	—	2	1	no	—
510	C₂	—	2	1	no	—
511	C₂	—	4	2	no	—
512	C₂	—	8	2	no	—
513	C₂	#20245879	1	1	yes	characteristic
514	C₂	#20251935	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3455	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3455	D₄₇
hypocenter	C₄₇	#21419
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ #3455

Complements

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

N	H ≅ G/N	type
1. #20252026	C₂	semidirect
2. #117×Dic₄₇	C₂	semidirect
3. #20244370	C₂	semidirect
4. #20244366	C₂	semidirect
5. #20244221	C₂	semidirect
6. #20244217	C₂	semidirect
7. #20243837	C₂	semidirect
8. #20243832	C₂	semidirect
9. #20243198	C₂	semidirect
10. C₄×#13093951	C₂	semidirect
33. C₄₇×#542	C₄	semidirect
34. C₄₇×#541	C₄	semidirect
35. C₄₇×#540	C₄	semidirect
73. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
74. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
75. #127×C₄₇	C₂×C₄	semidirect
79. #125×C₄₇	C₂×C₄	semidirect
81. #124×C₄₇	C₂×C₄	semidirect
93. C₄×Q₈×C₄₇	C₂×C₄	semidirect
97. C₄×D₄×C₄₇	C₂×C₄	semidirect
269. #542	Dic₄₇	semidirect
270. #541	Dic₄₇	semidirect
271. #540	Dic₄₇	semidirect
301. C₄₇	#21419	semidirect
307. C₄⋊Q₈	C₂×Dic₄₇	semidirect
308. C₄⋊Q₈	C₂×Dic₄₇	semidirect
309. #127	C₂×Dic₄₇	semidirect
313. #125	C₂×Dic₄₇	semidirect
315. #124	C₂×Dic₄₇	semidirect
327. C₄×Q₈	C₂×Dic₄₇	semidirect
331. C₄×D₄	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252026	2
#117×Dic₄₇	2
#20244370	2
#20244366	2
#20244221	2
#20244217	2
#20243837	2
#20243832	2
#20243198	2
C₄×#13093951	2
C₄₇×#3455	2
#21419	47