Subgroups — #26124989

Order 12032.

822 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689165	C₂	1	2	yes	maximal
2	#20246006	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688884	C₂	1	2	yes	maximal
4	#20241617	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#343	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093983	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	#15689165	—	2	4	no	—
10	#15689165	—	2	4	no	—
11	C₂×#13093958	—	2	2	no	—
12	C₂×#13093956	—	2	2	no	—
13	#15689022	—	2	2	no	—
14	#15689022	—	2	2	no	—
15	#15688983	—	2	2	no	—
16	C₂×C₄₇⋊#95	—	2	2	no	—
17	#15688884	—	2	4	no	—
18	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#343	C₄	1	4	yes	complemented
21	C₂³×Dic₄₇	—	2	1	no	—
22	C₂³×Dic₄₇	—	2	1	no	—
23	#13093983	—	2	2	no	—
24	#13093983	—	2	2	no	—
25	#13093983	—	2	2	no	—
26	#13093983	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	1	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
33	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
34	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
35	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	—	2	2	no	—
39	C₂×C₄×Dic₄₇	—	2	1	no	—
40	C₂×C₄×Dic₄₇	Q₈	1	2	yes	—
41	#13093958	—	2	8	no	—
42	#13093956	—	2	8	no	—
43	C₄₇⋊#95	—	2	4	no	—
44	C₄₇⋊#95	—	4	4	no	—
45	C₂³×C₄×C₄₇	D₄	1	2	yes	—
46	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₄₇	—	2	2	no	—
48	C₂×M₁₆×C₄₇	—	2	2	no	—
49	C₂×M₁₆×C₄₇	—	2	2	no	—
50	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
51	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
52	C₂×M₁₆×C₄₇	Q₈	1	4	yes	—
53	C₂²×C₈×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₇	Q₈	1	2	yes	—
58	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	2	no	—
61	C₂²×C₄×C₄₇	—	4	2	no	—
62	C₂²×C₄×C₄₇	—	4	2	no	—
63	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
64	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
68	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	#41	1	2	yes	—
72	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
74	C₂²×Dic₄₇	—	2	2	no	—
75	C₂²×Dic₄₇	—	2	2	no	—
76	C₂²×Dic₄₇	—	2	2	no	—
77	C₂²×Dic₄₇	—	2	2	no	—
78	C₂²×Dic₄₇	—	2	2	no	—
79	C₂²×Dic₄₇	—	2	2	no	—
80	C₂²×Dic₄₇	—	4	1	no	—
81	C₂²×Dic₄₇	—	4	1	no	—
82	C₂²×Dic₄₇	—	4	1	no	—
83	C₂²×Dic₄₇	—	4	1	no	—
84	C₂²×Dic₄₇	—	4	2	no	—
85	C₂²×Dic₄₇	—	4	2	no	—
86	C₂²×Dic₄₇	—	4	1	no	—
87	C₂²×Dic₄₇	—	4	1	no	—
88	M₁₆×C₄₇	—	2	4	no	—
89	M₁₆×C₄₇	—	2	4	no	—
90	M₁₆×C₄₇	—	2	4	no	—
91	M₁₆×C₄₇	C₄⋊C₄	1	8	yes	complemented
92	C₂×C₈×C₄₇	—	2	4	no	—
93	C₂×C₈×C₄₇	—	2	4	no	—
94	C₂×C₈×C₄₇	—	2	4	no	—
95	C₄⋊C₄×C₄₇	—	2	4	no	—
96	C₄⋊C₄×C₄₇	—	2	4	no	—
97	C₂²⋊Dic₄₇	—	4	2	no	—
98	C₂²⋊Dic₄₇	—	4	2	no	—
99	C₄⋊Dic₄₇	—	2	2	no	—
100	C₄⋊Dic₄₇	—	2	4	no	—
101	C₄⋊Dic₄₇	—	2	2	no	—
102	C₄⋊Dic₄₇	—	2	2	no	—
103	C₄⋊Dic₄₇	—	2	2	no	—
104	C₄⋊Dic₄₇	—	4	2	no	—
105	C₄⋊Dic₄₇	—	8	2	no	—
106	C₄⋊Dic₄₇	—	8	2	no	—
107	C₄×Dic₄₇	—	2	4	no	—
108	C₄×Dic₄₇	—	4	2	no	—
109	C₄×Dic₄₇	—	4	2	no	—
110	C₄×Dic₄₇	—	4	2	no	—
111	C₂³×C₄₇	—	2	1	no	—
112	C₂³×C₄₇	—	2	1	no	—
113	C₂³×C₄₇	—	2	1	no	—
114	C₂³×C₄₇	—	2	1	no	—
115	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
116	C₂³×C₄₇	#120	1	1	yes	characteristic
117	C₂³×C₄₇	#121	1	1	yes	characteristic
118	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
119	C₂³×C₄₇	#123	1	1	yes	characteristic
120	C₂³×C₄₇	#127	1	1	yes	characteristic
121	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
122	C₂×C₄×C₄₇	—	2	4	no	—
123	C₂×C₄×C₄₇	—	4	2	no	—
124	C₂×C₄×C₄₇	—	4	2	no	—
125	C₂×C₄×C₄₇	—	4	4	no	—
126	C₂×C₄×C₄₇	—	8	2	no	—
127	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
129	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
130	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
131	C₂×C₄×C₄₇	#120	1	2	yes	—
132	C₂×C₄×C₄₇	#121	1	2	yes	—
133	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
134	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
135	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
136	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
137	C₂×C₄×C₄₇	#123	1	2	yes	—
138	C₂×C₄×C₄₇	#125	1	2	yes	—
139	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
141	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
143	C₂×Dic₄₇	—	2	4	no	—
144	C₂×Dic₄₇	—	4	2	no	—
145	C₂×Dic₄₇	—	4	2	no	—
146	C₂×Dic₄₇	—	4	2	no	—
147	C₂×Dic₄₇	—	4	2	no	—
148	C₂×Dic₄₇	—	4	2	no	—
149	C₂×Dic₄₇	—	4	2	no	—
150	C₂×Dic₄₇	—	4	4	no	—
151	C₂×Dic₄₇	—	4	2	no	—
152	C₂×Dic₄₇	—	4	2	no	—
153	C₂×Dic₄₇	—	4	2	no	—
154	C₂×Dic₄₇	—	4	2	no	—
155	C₂×Dic₄₇	—	4	2	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	8	2	no	—
159	C₂×Dic₄₇	—	8	1	no	—
160	C₂×Dic₄₇	—	8	1	no	—
161	C₈×C₄₇	—	2	8	no	—
162	#11342	—	47	1	no	maximal, Sylow
163	C₂²×C₄₇	—	2	1	no	—
164	C₂²×C₄₇	—	2	1	no	—
165	C₂²×C₄₇	—	2	1	no	—
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	—	2	1	no	—
168	C₂²×C₄₇	—	2	1	no	—
169	C₂²×C₄₇	—	2	1	no	—
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	—	2	1	no	—
173	C₂²×C₄₇	—	2	1	no	—
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	#384	1	1	yes	characteristic
176	C₂²×C₄₇	#385	1	1	yes	characteristic
177	C₂²×C₄₇	#389	1	1	yes	characteristic
178	C₂²×C₄₇	#392	1	1	yes	characteristic
179	C₂²×C₄₇	#395	1	1	yes	characteristic
180	C₂²×C₄₇	#398	1	1	yes	characteristic
181	C₂²×C₄₇	#399	1	1	yes	characteristic
182	C₂²×C₄₇	#453	1	1	yes	characteristic
183	C₂²×C₄₇	#454	1	1	yes	characteristic
184	C₂²×C₄₇	#455	1	1	yes	characteristic
185	C₂²×C₄₇	#456	1	1	yes	characteristic
186	C₄×C₄₇	—	4	4	no	—
187	C₄×C₄₇	#385	1	2	yes	—
188	C₄×C₄₇	#389	1	2	yes	—
189	C₄×C₄₇	#395	1	2	yes	—
190	C₄×C₄₇	#398	1	2	yes	—
191	Dic₄₇	—	4	4	no	—
192	Dic₄₇	—	8	2	no	—
193	Dic₄₇	—	8	2	no	—
194	Dic₄₇	—	8	2	no	—
195	C₂×#428	—	47	2	no	—
196	#2316	—	47	1	no	—
197	C₂×#343	D₄₇	1	1	yes	characteristic
198	C₂×#339	—	47	2	no	—
199	C₄⋊#95	—	47	1	no	—
200	C₂×C₄₇	—	2	1	no	—
201	C₂×C₄₇	—	2	1	no	—
202	C₂×C₄₇	—	2	1	no	—
203	C₂×C₄₇	—	2	1	no	—
204	C₂×C₄₇	#1444	1	1	yes	characteristic
205	C₂×C₄₇	#1856	1	1	yes	characteristic
206	C₂×C₄₇	#1857	1	1	yes	characteristic
207	C₂×C₄₇	#2006	1	1	yes	characteristic
208	C₂×C₄₇	#2007	1	1	yes	characteristic
209	C₂×C₄₇	#2060	1	1	yes	characteristic
210	C₂×C₄₇	#2061	1	1	yes	characteristic
211	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
212	C₂×#117	—	47	2	no	—
213	C₂²×C₄⋊C₄	—	47	1	no	—
214	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
215	C₂²×C₄²	—	47	1	no	—
216	#428	—	94	4	no	—
217	#428	—	94	4	no	—
218	C₂×#107	—	94	2	no	—
219	C₂×#106	—	94	2	no	—
220	#389	—	94	2	no	—
221	#389	—	94	2	no	—
222	#380	—	94	2	no	—
223	C₂×#95	—	94	2	no	—
224	#343	Dic₄₇	1	4	yes	complemented
225	#339	—	94	4	no	—
226	C₄₇	#11342	1	1	yes	characteristic, complemented, Sylow
227	C₂³×C₄	—	94	1	no	—
228	C₂³×C₄	—	94	1	no	—
229	C₂³×C₄	D₁₈₈	1	2	yes	—
230	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	Dic₉₄	1	4	yes	—
235	C₂×M₁₆	D₁₈₈	1	4	yes	—
236	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
237	C₂²×C₈	—	2	2	no	—
238	#117	—	94	2	no	—
239	#117	—	94	2	no	—
240	#117	—	94	2	no	—
241	#117	—	94	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	47	2	no	—
245	C₂×C₄⋊C₄	—	47	2	no	—
246	C₂×C₄⋊C₄	—	47	2	no	—
247	C₂×C₄⋊C₄	—	94	2	no	—
248	C₂×C₄⋊C₄	—	94	2	no	—
249	C₂×C₄⋊C₄	—	94	2	no	—
250	C₂×C₄⋊C₄	—	94	2	no	—
251	C₂×C₄⋊C₄	—	94	1	no	—
252	C₂×C₄⋊C₄	Dic₉₄	1	2	yes	—
253	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
254	C₂×C₂²⋊C₄	—	94	2	no	—
255	C₂×C₄²	—	47	2	no	—
256	C₂×C₄²	—	94	2	no	—
257	C₂×C₄²	—	94	2	no	—
258	C₂×C₄²	—	94	2	no	—
259	C₂×C₄²	—	94	1	no	—
260	#107	—	94	8	no	—
261	#106	—	94	8	no	—
262	#95	—	94	4	no	—
263	#95	—	188	4	no	—
264	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	94	2	no	—
270	C₂²×C₄	—	94	2	no	—
271	C₂²×C₄	—	94	2	no	—
272	C₂²×C₄	—	94	2	no	—
273	C₂²×C₄	—	94	2	no	—
274	C₂²×C₄	—	94	2	no	—
275	C₂²×C₄	—	188	2	no	—
276	C₂²×C₄	—	188	2	no	—
277	C₂²×C₄	—	188	1	no	—
278	C₂²×C₄	—	188	1	no	—
279	C₂²×C₄	—	188	1	no	—
280	C₂²×C₄	—	188	1	no	—
281	C₂²×C₄	—	188	1	no	—
282	C₂²×C₄	—	188	1	no	—
283	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
284	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
285	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
287	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
288	C₂²×C₄	D₄×D₄₇	1	2	yes	—
289	C₂²×C₄	#10625352	1	2	yes	—
290	C₂²×C₄	#10625352	1	1	yes	characteristic
291	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
292	C₂²×C₄	#10625354	1	1	yes	characteristic
293	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
294	M₁₆	—	2	4	no	—
295	M₁₆	—	2	4	no	—
296	M₁₆	—	2	4	no	—
297	M₁₆	C₄⋊Dic₄₇	1	8	yes	complemented
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	4	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	94	2	no	—
304	C₄⋊C₄	—	94	4	no	—
305	C₄⋊C₄	—	94	2	no	—
306	C₄⋊C₄	—	94	2	no	—
307	C₄⋊C₄	—	94	2	no	—
308	C₄⋊C₄	—	376	2	no	—
309	C₄⋊C₄	—	376	2	no	—
310	C₄⋊C₄	—	188	2	no	—
311	C₂²⋊C₄	—	188	2	no	—
312	C₂²⋊C₄	—	188	2	no	—
313	C₄²	—	94	4	no	—
314	C₄²	—	188	2	no	—
315	C₄²	—	188	2	no	—
316	C₄²	—	188	2	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
322	C₂³	#13093994	1	1	yes	characteristic
323	C₂³	#13093999	1	1	yes	characteristic
324	C₂³	#13094004	1	1	yes	characteristic
325	C₂³	#13094008	1	1	yes	characteristic
326	C₂³	#13094021	1	1	yes	characteristic
327	C₂³	#13094024	1	1	yes	characteristic
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	8	2	no	—
333	C₂×C₄	—	94	4	no	—
334	C₂×C₄	—	376	2	no	—
335	C₂×C₄	—	376	1	no	—
336	C₂×C₄	—	376	1	no	—
337	C₂×C₄	—	188	4	no	—
338	C₂×C₄	—	188	2	no	—
339	C₂×C₄	—	188	2	no	—
340	C₂×C₄	—	188	2	no	—
341	C₂×C₄	—	188	2	no	—
342	C₂×C₄	—	188	2	no	—
343	C₂×C₄	—	188	2	no	—
344	C₂×C₄	—	188	2	no	—
345	C₂×C₄	—	188	2	no	—
346	C₂×C₄	—	188	2	no	—
347	C₂×C₄	—	188	2	no	—
348	C₂×C₄	—	188	2	no	—
349	C₂×C₄	—	188	2	no	—
350	C₂×C₄	—	188	2	no	—
351	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
352	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
353	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
354	C₂×C₄	Q₈×Dic₄₇	1	1	yes	characteristic
355	C₂×C₄	#13093994	1	2	yes	—
356	C₂×C₄	#13093999	1	2	yes	—
357	C₂×C₄	#13094001	1	2	yes	—
358	C₂×C₄	#13094001	1	2	yes	—
359	C₂×C₄	#13094001	1	2	yes	—
360	C₂×C₄	#13094004	1	2	yes	—
361	C₂×C₄	#13094008	1	2	yes	—
362	C₂×C₄	#13094015	1	2	yes	—
363	C₂×C₄	#13094015	1	1	yes	characteristic
364	C₂×C₄	#13094023	1	2	yes	—
365	C₂×C₄	#13094023	1	1	yes	characteristic
366	C₂×C₄	#13094024	1	2	yes	—
367	C₈	—	2	8	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	#15688993	1	1	yes	characteristic
381	C₂²	#15688998	1	1	yes	characteristic
382	C₂²	#15689022	1	1	yes	characteristic
383	C₂²	#15689033	1	1	yes	characteristic
384	C₂²	#15689044	1	1	yes	characteristic
385	C₂²	#15689055	1	1	yes	characteristic
386	C₂²	#15689060	1	1	yes	characteristic
387	C₂²	#15689293	1	1	yes	characteristic
388	C₂²	#15689298	1	1	yes	characteristic
389	C₂²	#15689303	1	1	yes	characteristic
390	C₂²	#15689308	1	1	yes	characteristic
391	C₄	—	4	4	no	—
392	C₄	—	376	2	no	—
393	C₄	—	376	2	no	—
394	C₄	—	376	2	no	—
395	C₄	—	188	4	no	—
396	C₄	#15688998	1	2	yes	—
397	C₄	#15689022	1	2	yes	—
398	C₄	#15689044	1	2	yes	—
399	C₄	#15689055	1	2	yes	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	#20241653	1	1	yes	characteristic
405	C₂	#20243600	1	1	yes	characteristic
406	C₂	#20243605	1	1	yes	characteristic
407	C₂	#20244432	1	1	yes	characteristic
408	C₂	#20244437	1	1	yes	characteristic
409	C₂	#20244734	1	1	yes	characteristic
410	C₂	#20244739	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093994
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#343	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#343	D₄₇
hypocenter	C₄₇	#11342
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#343

Complements

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

N	H ≅ G/N	type
20. C₄₇×#343	C₄	semidirect
91. M₁₆×C₄₇	C₄⋊C₄	semidirect
224. #343	Dic₄₇	semidirect
226. C₄₇	#11342	semidirect
297. M₁₆	C₄⋊Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689165	2
#20246006	2
C₂×#15688884	2
#20241617	2
C₂×C₄₇×#343	2
#11342	47