Subgroups — #26199482

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 440 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×#15689499	C₂	1	1	yes	maximal, characteristic
3	#20252323	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242870	C₂	1	4	yes	maximal, complemented
5	#20242746	C₂	1	4	yes	maximal, complemented
6	#20242134	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242056	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#10625334	—	2	1	no	—
11	C₂²×#10625334	—	2	1	no	—
12	C₂×#13094021	C₂²	1	1	yes	characteristic
13	#15689499	—	2	1	no	—
14	#15689499	—	2	1	no	—
15	#15689499	C₂²	1	2	yes	—
16	#15689499	C₂²	1	2	yes	—
17	#15689497	—	2	1	no	—
18	#15689471	—	2	1	no	—
19	#15689323	C₂²	1	4	yes	complemented
20	#15689273	—	2	2	no	—
21	#15689254	—	2	1	no	—
22	#15689254	C₂²	1	2	yes	complemented
23	Q₈×C₄₇⋊C₈	—	2	1	no	—
24	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
25	#15689176	C₂²	1	1	yes	characteristic
26	#15689150	—	2	1	no	—
27	#15689147	C₂²	1	1	yes	characteristic
28	#15689079	—	2	1	no	—
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	#15688875	C₂²	1	2	yes	complemented
31	#15688873	C₂²	1	2	yes	complemented
32	#15688867	C₂²	1	4	yes	complemented
33	#15688866	C₂²	1	4	yes	complemented
34	C₄₇×#533	C₂²	1	1	yes	characteristic
35	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#492	—	2	1	no	—
37	C₄₇×#486	—	2	1	no	—
38	C₄₇×#460	C₂²	1	4	yes	complemented
39	C₄₇×#450	—	2	2	no	—
40	C₄₇×#431	C₂²	1	1	yes	characteristic
41	C₂²×D₁₈₈	—	2	1	no	—
42	C₂²×D₁₈₈	—	2	1	no	—
43	C₂²×D₁₈₈	—	2	1	no	—
44	C₂×#10625336	—	2	4	no	—
45	C₂×#10625334	—	2	2	no	—
46	C₂×#10625334	—	2	2	no	—
47	C₂×#10625334	—	2	2	no	—
48	C₂×#10625334	—	2	2	no	—
49	C₂×#10625334	—	4	4	no	—
50	C₂×#10625334	—	4	4	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
54	#13094021	—	2	1	no	—
55	#13094021	—	2	1	no	—
56	#13094021	—	2	1	no	—
57	#13094021	C₂³	1	2	yes	—
58	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
63	#13093944	—	2	4	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
65	#13093935	—	2	2	no	—
66	C₄×C₄₇⋊C₈	—	2	1	no	—
67	C₄×C₄₇⋊C₈	—	2	2	no	—
68	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
69	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
70	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₄₇	—	2	1	no	—
73	C₂²×D₄×C₄₇	—	2	1	no	—
74	C₂²×D₄×C₄₇	—	2	1	no	—
75	C₂×SD₁₆×C₄₇	—	2	4	no	—
76	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
77	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
78	#127×C₄₇	—	2	1	no	—
79	#127×C₄₇	—	2	1	no	—
80	#127×C₄₇	—	2	1	no	—
81	#127×C₄₇	C₂³	1	2	yes	—
82	#125×C₄₇	—	2	1	no	—
83	C₂²⋊Q₈×C₄₇	—	2	1	no	—
84	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
85	C₄×Q₈×C₄₇	—	2	1	no	—
86	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
87	#117×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
90	#102×C₄₇	—	2	4	no	—
91	C₂²⋊C₈×C₄₇	—	2	1	no	—
92	C₄×C₈×C₄₇	—	2	1	no	—
93	C₂⁴×C₄₇	—	4	1	no	—
94	C₂³×D₄₇	—	4	1	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	4	1	no	—
101	C₂×D₄×C₄₇	—	4	1	no	—
102	C₂×D₄×C₄₇	—	4	1	no	—
103	C₂×D₄×C₄₇	—	4	2	no	—
104	C₂×D₄×C₄₇	—	4	2	no	—
105	C₂×D₄×C₄₇	—	8	2	no	—
106	C₂×D₄×C₄₇	—	8	2	no	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
110	C₂×D₁₈₈	—	2	2	no	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	—	2	2	no	—
113	C₂×D₁₈₈	—	4	2	no	—
114	C₂×D₁₈₈	—	4	2	no	—
115	C₂×D₁₈₈	—	4	1	no	—
116	C₂×D₁₈₈	—	4	1	no	—
117	C₂×D₁₈₈	—	4	1	no	—
118	C₂×D₁₈₈	—	8	2	no	—
119	C₂×D₁₈₈	—	8	2	no	—
120	SD₁₆×C₄₇	—	8	4	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	—	2	1	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₂²⋊C₄×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₇	#41	1	1	yes	characteristic
133	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
134	#10625336	—	8	4	no	—
135	#10625334	—	4	4	no	—
136	#10625334	—	4	4	no	—
137	#10625334	—	4	4	no	—
138	#10625334	—	4	4	no	—
139	#10625329	—	4	2	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	SD₁₆	1	4	yes	complemented
144	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
148	C₂³×C₄₇	—	4	2	no	—
149	C₂³×C₄₇	—	8	2	no	—
150	C₂³×C₄₇	—	8	2	no	—
151	C₂³×C₄₇	—	8	2	no	—
152	C₂³×C₄₇	#121	1	1	yes	characteristic
153	C₂²×D₄₇	—	4	2	no	—
154	C₂²×D₄₇	—	8	2	no	—
155	C₂²×D₄₇	—	8	2	no	—
156	C₂²×D₄₇	—	8	2	no	—
157	Q₈×C₄₇	—	2	4	no	—
158	Q₈×C₄₇	—	4	2	no	—
159	D₄×C₄₇	—	4	2	no	—
160	D₄×C₄₇	—	4	2	no	—
161	D₄×C₄₇	—	4	4	no	—
162	D₄×C₄₇	—	8	2	no	—
163	D₄×C₄₇	—	8	2	no	—
164	D₄×C₄₇	—	8	2	no	—
165	D₄×C₄₇	—	8	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
174	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
178	D₁₈₈	—	4	2	no	—
179	D₁₈₈	—	4	2	no	—
180	D₁₈₈	—	4	4	no	—
181	D₁₈₈	—	8	2	no	—
182	D₁₈₈	—	8	2	no	—
183	D₁₈₈	—	8	2	no	—
184	D₁₈₈	—	8	2	no	—
185	C₈×C₄₇	—	4	2	no	—
186	C₄₇⋊C₈	—	2	1	no	—
187	C₄₇⋊C₈	—	2	1	no	—
188	C₄₇⋊C₈	—	4	2	no	—
189	C₄₇⋊C₈	—	4	2	no	—
190	C₄₇⋊C₈	C₂×SD₁₆	1	2	yes	—
191	C₄₇⋊C₈	C₂×SD₁₆	1	2	yes	—
192	#19203	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	8	2	no	—
196	C₂²×C₄₇	—	8	2	no	—
197	C₂²×C₄₇	—	8	2	no	—
198	C₂²×C₄₇	—	16	4	no	—
199	C₂²×C₄₇	#460	1	2	yes	—
200	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
201	C₂×D₄₇	—	8	2	no	—
202	C₂×D₄₇	—	8	2	no	—
203	C₂×D₄₇	—	8	2	no	—
204	C₂×D₄₇	—	16	4	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	4	2	no	—
208	C₄×C₄₇	—	4	2	no	—
209	C₄×C₄₇	#460	1	2	yes	—
210	C₄×C₄₇	#472	1	2	yes	—
211	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
212	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₄×C₄₇	#576	1	2	yes	—
214	#3208	—	47	1	no	—
215	#3208	D₄₇	1	1	yes	characteristic, complemented
216	C₂×#493	—	47	1	no	—
217	#2960	—	47	1	no	—
218	#1688	—	47	4	no	—
219	#1668	—	47	4	no	—
220	#1564	—	47	1	no	—
221	#1545	—	47	1	no	—
222	#1545	—	47	1	no	—
223	C₂×C₄₇	—	2	2	no	—
224	C₂×C₄₇	—	16	2	no	—
225	C₂×C₄₇	C₂×#460	1	1	yes	characteristic
226	C₂×C₄₇	#3058	1	1	yes	characteristic
227	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
228	D₄₇	—	16	2	no	—
229	C₂²×D₈	—	94	1	no	—
230	C₂²×D₈	—	94	1	no	—
231	#533	C₂×D₄₇	1	1	yes	characteristic
232	C₂×#127	—	47	1	no	—
233	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
234	#493	—	47	2	no	—
235	#493	—	47	2	no	—
236	#493	—	94	1	no	—
237	#493	—	94	1	no	—
238	#492	—	2	1	no	—
239	#492	—	94	1	no	—
240	#486	—	2	1	no	—
241	#486	—	94	1	no	—
242	#460	—	47	4	no	—
243	#460	C₂×D₄₇	1	4	yes	complemented
244	#450	—	2	2	no	—
245	#450	—	94	2	no	—
246	#446	—	47	2	no	—
247	#446	—	94	1	no	—
248	C₈×Q₈	—	47	2	no	—
249	C₈×Q₈	—	94	1	no	—
250	#431	—	47	1	no	—
251	#431	C₂×D₄₇	1	1	yes	characteristic
252	#424	—	94	1	no	—
253	#423	—	47	1	no	—
254	#405	—	94	1	no	—
255	C₂×C₄×C₈	—	47	1	no	—
256	#335	—	47	2	no	—
257	#334	—	47	2	no	—
258	#331	—	47	4	no	—
259	#331	—	47	4	no	—
260	C₄₇	#19203	1	1	yes	characteristic, complemented, Sylow
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	94	1	no	—
265	C₂²×D₄	—	94	1	no	—
266	C₂²×D₄	—	94	1	no	—
267	C₂×SD₁₆	—	2	4	no	—
268	C₂×SD₁₆	—	94	4	no	—
269	C₂×D₈	—	94	2	no	—
270	C₂×D₈	—	94	2	no	—
271	C₂×D₈	—	94	2	no	—
272	C₂×D₈	—	94	2	no	—
273	C₂×D₈	—	188	4	no	—
274	C₂×D₈	—	188	4	no	—
275	C₂×M₁₆	—	94	1	no	—
276	C₂²×C₈	—	47	1	no	—
277	C₂²×C₈	—	47	1	no	—
278	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
279	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
280	#127	—	2	1	no	—
281	#127	—	2	1	no	—
282	#127	—	2	1	no	—
283	#127	—	47	2	no	—
284	#127	—	94	1	no	—
285	#127	—	94	1	no	—
286	#127	—	94	1	no	—
287	#127	C₂²×D₄₇	1	2	yes	—
288	#125	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
293	#117	—	2	1	no	—
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	C₄⋊C₈	—	47	2	no	—
296	C₄⋊C₈	—	47	2	no	—
297	C₄⋊C₈	—	94	2	no	—
298	C₄⋊C₈	—	94	2	no	—
299	C₄⋊C₈	—	94	1	no	—
300	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
301	#102	—	2	4	no	—
302	#102	—	94	4	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	94	1	no	—
305	#97	—	94	2	no	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	—	47	1	no	—
308	C₄×C₈	—	47	1	no	—
309	C₄×C₈	—	47	1	no	—
310	C₄×C₈	—	47	1	no	—
311	C₄×C₈	—	94	2	no	—
312	C₄×C₈	—	94	1	no	—
313	C₂⁴	—	4	1	no	—
314	C₂⁴	—	188	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	8	2	no	—
326	C₂×D₄	—	8	2	no	—
327	C₂×D₄	—	94	2	no	—
328	C₂×D₄	—	94	2	no	—
329	C₂×D₄	—	94	2	no	—
330	C₂×D₄	—	376	2	no	—
331	C₂×D₄	—	376	2	no	—
332	C₂×D₄	—	188	1	no	—
333	C₂×D₄	—	188	1	no	—
334	C₂×D₄	—	188	1	no	—
335	C₂×D₄	—	188	2	no	—
336	C₂×D₄	—	188	2	no	—
337	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
338	C₂²×C₄	#10625352	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
340	SD₁₆	—	8	4	no	—
341	SD₁₆	—	376	4	no	—
342	D₈	—	188	4	no	—
343	D₈	—	188	4	no	—
344	D₈	—	188	4	no	—
345	D₈	—	188	4	no	—
346	M₁₆	—	188	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	47	4	no	—
349	C₂×C₈	—	47	1	no	—
350	C₂×C₈	—	47	1	no	—
351	C₂×C₈	—	47	1	no	—
352	C₂×C₈	—	47	1	no	—
353	C₂×C₈	—	94	2	no	—
354	C₂×C₈	—	94	2	no	—
355	C₂×C₈	—	94	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	D₄×D₄₇	1	1	yes	characteristic
365	C₄²	#10625352	1	1	yes	characteristic
366	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
367	C₄²	C₂³×D₄₇	1	1	yes	characteristic
368	C₂³	—	4	2	no	—
369	C₂³	—	8	2	no	—
370	C₂³	—	8	2	no	—
371	C₂³	—	8	2	no	—
372	C₂³	—	376	2	no	—
373	C₂³	—	376	2	no	—
374	C₂³	—	376	2	no	—
375	C₂³	—	188	2	no	—
376	C₂³	#13093996	1	1	yes	characteristic
377	Q₈	—	2	4	no	—
378	Q₈	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	4	no	—
382	D₄	—	8	2	no	—
383	D₄	—	8	2	no	—
384	D₄	—	8	2	no	—
385	D₄	—	8	2	no	—
386	D₄	—	376	2	no	—
387	D₄	—	376	2	no	—
388	D₄	—	376	2	no	—
389	D₄	—	376	2	no	—
390	D₄	—	188	2	no	—
391	D₄	—	188	2	no	—
392	D₄	—	188	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	#13093996	1	1	yes	characteristic
398	C₂×C₄	#13093996	1	1	yes	characteristic
399	C₂×C₄	#13093996	1	1	yes	characteristic
400	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
401	C₂×C₄	#13094051	1	2	yes	—
402	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
405	C₈	—	4	2	no	—
406	C₈	—	47	2	no	—
407	C₈	—	47	2	no	—
408	C₈	—	94	1	no	—
409	C₈	—	94	1	no	—
410	C₈	—	188	2	no	—
411	C₈	—	188	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	16	4	no	—
418	C₂²	—	376	2	no	—
419	C₂²	—	376	2	no	—
420	C₂²	—	376	2	no	—
421	C₂²	—	752	4	no	—
422	C₂²	#15689321	1	2	yes	—
423	C₂²	C₂×#13093996	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	#15689321	1	2	yes	—
429	C₄	#15689391	1	2	yes	—
430	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
431	C₄	C₂×#13094051	1	1	yes	characteristic
432	C₄	#15689926	1	2	yes	—
433	C₂	—	2	2	no	—
434	C₂	—	16	2	no	—
435	C₂	—	752	2	no	—
436	C₂	C₂×#15689321	1	1	yes	characteristic
437	C₂	#20253033	1	1	yes	characteristic
438	C₂	C₂×#15689391	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3208	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#15689499	C₂
hypercenter	#3208	D₄₇
hypocenter	C₄₇	#19203
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3208

Complements

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

N	H ≅ G/N	type
1. #20254326	C₂	semidirect
3. #20252323	C₂	semidirect
4. #20242870	C₂	semidirect
5. #20242746	C₂	semidirect
6. #20242134	C₂	semidirect
7. #20242056	C₂	semidirect
8. #20242055	C₂	semidirect
9. C₄₇×#3208	C₂	semidirect
19. #15689323	C₂²	semidirect
22. #15689254	C₂²	semidirect
24. Q₈×C₄₇⋊C₈	C₂²	semidirect
30. #15688875	C₂²	semidirect
31. #15688873	C₂²	semidirect
32. #15688867	C₂²	semidirect
33. #15688866	C₂²	semidirect
38. C₄₇×#460	C₂²	semidirect
143. C₂×C₄₇⋊C₈	SD₁₆	semidirect
215. #3208	D₄₇	semidirect
243. #460	C₂×D₄₇	semidirect
260. C₄₇	#19203	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×#15689499	2
#20252323	2
#20242870	2
#20242746	2
#20242134	2
#20242056	2
#20242055	2
C₄₇×#3208	2
#19203	47