Subgroups — #26216835

Order 12032.

810 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689079	C₂	1	1	yes	maximal, characteristic
2	#20245997	C₂	1	1	yes	maximal, characteristic
3	#20243550	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243544	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243523	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243521	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243419	C₂	1	2	yes	maximal
8	#20243411	C₂	1	2	yes	maximal
9	#20243286	C₂	1	2	yes	maximal, complemented
10	C₄×#13093955	C₂	1	2	yes	maximal, complemented
11	C₄₇×#2314	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×#13093957	C₂²	1	2	yes	—
15	C₂×#13093955	C₂²	1	2	yes	—
16	C₂×#13093955	C₂²	1	2	yes	—
17	C₂×#13093955	C₂²	1	2	yes	—
18	#15689079	C₄	1	8	yes	complemented
19	C₂×#13093935	C₂²	1	1	yes	characteristic
20	C₂×#13093935	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	#15689016	—	2	2	no	—
24	#15689009	—	2	2	no	—
25	#15688993	C₂²	1	1	yes	characteristic
26	#15688989	C₂²	1	1	yes	characteristic
27	#15688983	C₂²	1	2	yes	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
29	#15688885	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#388	—	2	2	no	—
35	C₄₇×#387	—	2	2	no	—
36	C₄₇×#384	C₂²	1	1	yes	characteristic
37	C₄₇×#382	C₂²	1	1	yes	characteristic
38	C₄₇×#380	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
40	C₂×#10625329	—	2	2	no	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	C₂×C₄	1	4	yes	—
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₇	—	2	2	no	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
53	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	#13093957	—	2	4	no	—
56	#13093955	—	2	4	no	—
57	#13093955	—	2	4	no	—
58	#13093955	—	2	4	no	—
59	#13093935	C₂×C₄	1	4	yes	—
60	#13093935	C₂×C₄	1	4	yes	—
61	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
62	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
63	C₄₇⋊#95	—	2	2	no	—
64	C₄₇⋊#95	—	2	2	no	—
65	C₄₇⋊#95	—	2	2	no	—
66	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	#117×C₄₇	C₂×C₄	1	4	yes	—
68	#117×C₄₇	Q₈	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
75	C₂×C₄²×C₄₇	—	2	2	no	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	#95×C₄₇	—	2	2	no	—
79	#95×C₄₇	—	2	2	no	—
80	#95×C₄₇	—	2	2	no	—
81	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	—	2	1	no	—
83	C₂²×C₄×C₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	1	no	—
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₄⋊C₄×C₄₇	—	2	2	no	—
97	C₄⋊C₄×C₄₇	—	2	2	no	—
98	C₄⋊C₄×C₄₇	—	2	2	no	—
99	C₄⋊C₄×C₄₇	—	2	2	no	—
100	C₄⋊C₄×C₄₇	—	8	2	no	—
101	C₄⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	—
102	C₂²⋊C₄×C₄₇	—	8	2	no	—
103	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	—
104	C₄²×C₄₇	—	8	2	no	—
105	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
106	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
107	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
108	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
109	C₂²⋊Dic₄₇	—	8	2	no	—
110	C₄⋊Dic₄₇	—	2	2	no	—
111	C₄⋊Dic₄₇	—	2	2	no	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	—	8	2	no	—
115	C₄×Dic₄₇	—	8	2	no	—
116	#10625329	—	2	8	no	—
117	C₂×C₄₇⋊C₈	—	2	1	no	—
118	C₂×C₄₇⋊C₈	—	2	1	no	—
119	C₂×C₄₇⋊C₈	—	2	1	no	—
120	C₂×C₄₇⋊C₈	—	2	1	no	—
121	C₂×C₄₇⋊C₈	—	2	8	no	—
122	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
123	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
124	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
125	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₄₇⋊C₈	#41	1	2	yes	—
127	C₂×C₄₇⋊C₈	#41	1	2	yes	—
128	C₂×C₄₇⋊C₈	#41	1	2	yes	—
129	C₂×C₄₇⋊C₈	#41	1	2	yes	—
130	C₂³×C₄₇	—	2	1	no	—
131	C₂³×C₄₇	—	2	1	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
135	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
154	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₄₇⋊C₈	—	2	2	no	—
168	C₄₇⋊C₈	—	2	2	no	—
169	C₄₇⋊C₈	#117	1	4	yes	—
170	C₄₇⋊C₈	#117	1	4	yes	—
171	#20820	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	2	4	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	4	2	no	—
175	C₂²×C₄₇	—	4	1	no	—
176	C₂²×C₄₇	—	4	1	no	—
177	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×C₄₇	#532	1	1	yes	characteristic
179	C₂²×C₄₇	#532	1	1	yes	characteristic
180	C₂²×C₄₇	#577	1	2	yes	—
181	C₂²×C₄₇	#577	1	2	yes	—
182	C₄×C₄₇	—	2	4	no	—
183	C₄×C₄₇	—	2	4	no	—
184	C₄×C₄₇	—	2	2	no	—
185	C₄×C₄₇	—	8	2	no	—
186	C₄×C₄₇	—	8	2	no	—
187	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
188	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
189	C₄×C₄₇	#533	1	1	yes	characteristic
190	C₄×C₄₇	#533	1	1	yes	characteristic
191	Dic₄₇	—	8	2	no	—
192	Dic₄₇	—	8	2	no	—
193	C₂×#405	—	47	1	no	—
194	#2314	—	47	1	no	—
195	#2314	D₄₇	1	1	yes	characteristic
196	#1846	—	47	1	no	—
197	#1844	—	47	1	no	—
198	#1836	—	47	1	no	—
199	#1836	—	47	1	no	—
200	#1809	—	47	2	no	—
201	#1807	—	47	2	no	—
202	#1776	—	47	2	no	—
203	C₄×#106	—	47	2	no	—
204	C₂×C₄₇	—	4	2	no	—
205	C₂×C₄₇	#2285	1	1	yes	characteristic
206	C₂×C₄₇	#2912	1	2	yes	—
207	C₂×C₄₇	#3173	1	2	yes	—
208	C₂×C₄₇	#3174	1	1	yes	characteristic
209	C₂×C₄₇	#3174	1	1	yes	characteristic
210	C₂²×M₁₆	—	47	1	no	—
211	C₂³×C₈	—	47	1	no	—
212	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
213	C₂×#107	—	47	2	no	—
214	C₂×#106	—	47	2	no	—
215	C₂×#106	—	47	2	no	—
216	C₂×#106	—	47	2	no	—
217	#405	—	47	8	no	—
218	C₂×#97	—	47	1	no	—
219	C₂×#97	—	47	1	no	—
220	C₂×C₄×C₈	—	47	1	no	—
221	C₂×C₄×C₈	—	47	1	no	—
222	#388	—	2	2	no	—
223	#388	—	94	2	no	—
224	#387	—	2	2	no	—
225	#387	—	94	2	no	—
226	#384	—	47	1	no	—
227	#384	C₂×D₄₇	1	1	yes	characteristic
228	#382	—	47	1	no	—
229	#382	C₂×D₄₇	1	1	yes	characteristic
230	#380	—	47	2	no	—
231	#380	C₂×D₄₇	1	2	yes	—
232	C₄×C₄⋊C₄	—	47	2	no	—
233	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
234	#340	—	47	2	no	—
235	#340	—	47	2	no	—
236	#340	—	47	2	no	—
237	#340	—	47	2	no	—
238	C₄₇	#20820	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
240	C₂×M₁₆	—	47	4	no	—
241	C₂×M₁₆	—	94	2	no	—
242	C₂×M₁₆	—	94	2	no	—
243	C₂²×C₈	—	47	1	no	—
244	C₂²×C₈	—	47	1	no	—
245	C₂²×C₈	—	47	4	no	—
246	C₂²×C₈	—	47	1	no	—
247	C₂²×C₈	—	47	1	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₂²×C₈	—	94	2	no	—
250	#117	Dic₉₄	1	4	yes	—
251	#117	C₄×D₄₇	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	47	2	no	—
254	C₂×C₄⋊C₄	—	47	2	no	—
255	C₂×C₄⋊C₄	—	94	2	no	—
256	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
257	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	94	2	no	—
261	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	94	2	no	—
264	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
265	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
266	#107	—	94	4	no	—
267	#106	—	94	4	no	—
268	#106	—	94	4	no	—
269	#106	—	94	4	no	—
270	#97	—	47	4	no	—
271	#97	—	47	4	no	—
272	C₄×C₈	—	47	4	no	—
273	C₄×C₈	—	47	4	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	94	2	no	—
278	#95	—	94	2	no	—
279	#95	—	94	2	no	—
280	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
290	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
291	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
293	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
294	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
295	M₁₆	—	94	8	no	—
296	C₂×C₈	—	47	2	no	—
297	C₂×C₈	—	47	2	no	—
298	C₂×C₈	—	47	2	no	—
299	C₂×C₈	—	47	2	no	—
300	C₂×C₈	—	47	2	no	—
301	C₂×C₈	—	47	2	no	—
302	C₂×C₈	—	47	2	no	—
303	C₂×C₈	—	47	2	no	—
304	C₂×C₈	—	94	8	no	—
305	C₂×C₈	—	94	1	no	—
306	C₂×C₈	—	94	1	no	—
307	C₂×C₈	—	94	1	no	—
308	C₂×C₈	—	94	1	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	8	2	no	—
314	C₄⋊C₄	—	94	2	no	—
315	C₄⋊C₄	—	94	2	no	—
316	C₄⋊C₄	—	94	2	no	—
317	C₄⋊C₄	—	94	2	no	—
318	C₄⋊C₄	—	376	2	no	—
319	C₄⋊C₄	Dic₄₇⋊C₄	1	8	yes	—
320	C₂²⋊C₄	—	8	2	no	—
321	C₂²⋊C₄	—	376	2	no	—
322	C₂²⋊C₄	Dic₄₇⋊C₄	1	8	yes	—
323	C₄²	—	8	2	no	—
324	C₄²	—	376	2	no	—
325	C₄²	C₂×Dic₉₄	1	2	yes	—
326	C₄²	C₂×Dic₉₄	1	2	yes	—
327	C₄²	C₂×C₄×D₄₇	1	2	yes	—
328	C₄²	C₂×C₄×D₄₇	1	2	yes	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
334	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	188	2	no	—
352	C₂×C₄	—	188	2	no	—
353	C₂×C₄	—	188	2	no	—
354	C₂×C₄	—	188	2	no	—
355	C₂×C₄	—	188	2	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
358	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
359	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
360	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
362	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
363	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
364	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
365	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
366	C₈	—	47	4	no	—
367	C₈	—	47	4	no	—
368	C₈	—	94	2	no	—
369	C₈	—	94	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
376	C₂²	#15689669	1	1	yes	characteristic
377	C₂²	#15689669	1	1	yes	characteristic
378	C₂²	#15689931	1	2	yes	—
379	C₂²	#15689934	1	2	yes	—
380	C₄	—	2	2	no	—
381	C₄	—	2	4	no	—
382	C₄	—	2	4	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	376	2	no	—
386	C₄	—	376	2	no	—
387	C₄	#117×D₄₇	1	1	yes	characteristic
388	C₄	#117×D₄₇	1	1	yes	characteristic
389	C₄	#15689676	1	1	yes	characteristic
390	C₄	#15689676	1	1	yes	characteristic
391	C₂	—	4	2	no	—
392	C₂	#20245791	1	1	yes	characteristic
393	C₂	#20251981	1	2	yes	—
394	C₂	#20253999	1	2	yes	—
395	C₂	#20254010	1	1	yes	characteristic
396	C₂	#20254017	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2314	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2314	D₄₇
hypocenter	C₄₇	#20820
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#117 ◁ #2314

Complements

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

N	H ≅ G/N	type
3. #20243550	C₂	semidirect
4. #20243544	C₂	semidirect
5. #20243523	C₂	semidirect
6. #20243521	C₂	semidirect
9. #20243286	C₂	semidirect
10. C₄×#13093955	C₂	semidirect
18. #15689079	C₄	semidirect
238. C₄₇	#20820	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689079	2
#20245997	2
#20243550	2
#20243544	2
#20243523	2
#20243521	2
#20243419	2
#20243411	2
#20243286	2
C₄×#13093955	2
C₄₇×#2314	2
#20820	47