Subgroups — #26221597

Order 12032.

1214 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252021	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15688969	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244370	C₂	1	2	yes	maximal, complemented
4	#20244221	C₂	1	2	yes	maximal, complemented
5	#20243832	C₂	1	4	yes	maximal, complemented
6	#20243198	C₂	1	4	yes	maximal, complemented
7	C₄₇×#3444	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
9	#15689180	—	2	2	no	—
10	#15689176	—	2	2	no	—
11	#15689147	C₂²	1	2	yes	—
12	C₂×#13093951	C₂²	1	8	yes	—
13	#15689087	C₂²	1	2	yes	—
14	C₄×#10625329	C₂²	1	2	yes	—
15	#15688969	—	2	2	no	—
16	#15688969	C₂²	1	2	yes	—
17	#15688969	C₂²	1	2	yes	—
18	C₂×C₄₇⋊#95	—	2	2	no	—
19	#15688882	C₂²	1	8	yes	—
20	C₄₇×#533	C₄	1	2	yes	complemented
21	C₄₇×#533	C₂²	1	1	yes	characteristic
22	C₄₇×#532	C₄	1	2	yes	complemented
23	C₄₇×#532	C₂²	1	1	yes	characteristic
24	C₄₇×#529	—	2	2	no	—
25	C₄₇×#529	—	2	2	no	—
26	C₄₇×#529	C₄	1	4	yes	complemented
27	C₄₇×#525	—	2	2	no	—
28	C₄₇×#525	C₂²	1	2	yes	—
29	C₄×#41×C₄₇	—	2	2	no	—
30	C₄×#41×C₄₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂³×Dic₄₇	—	2	2	no	—
33	C₂×#10625329	C₂³	1	4	yes	—
34	C₂×C₄×Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	8	no	—
36	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
37	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
38	#13093951	—	2	16	no	—
39	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
40	#13093935	—	2	2	no	—
41	C₄×C₄₇⋊C₈	—	2	2	no	—
42	C₄₇⋊#95	—	2	4	no	—
43	C₄₇⋊#95	—	2	4	no	—
44	C₂×#41×C₄₇	—	2	2	no	—
45	C₂×#41×C₄₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₇	D₄	1	2	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
49	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
50	#127×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
51	#126×C₄₇	—	2	4	no	—
52	#125×C₄₇	—	2	2	no	—
53	#125×C₄₇	C₂×C₄	1	2	yes	complemented
54	#124×C₄₇	—	2	2	no	—
55	#124×C₄₇	C₂×C₄	1	2	yes	complemented
56	#123×C₄₇	—	2	4	no	—
57	#123×C₄₇	—	2	2	no	—
58	C₂²⋊Q₈×C₄₇	—	2	2	no	—
59	C₂²⋊Q₈×C₄₇	—	2	2	no	—
60	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
61	#121×C₄₇	—	2	2	no	—
62	#121×C₄₇	—	2	2	no	—
63	#121×C₄₇	C₂×C₄	1	4	yes	—
64	#120×C₄₇	—	2	2	no	—
65	C₄×Q₈×C₄₇	—	2	2	no	—
66	C₄×Q₈×C₄₇	—	2	2	no	—
67	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
68	C₄×D₄×C₄₇	—	2	4	no	—
69	C₄×D₄×C₄₇	—	2	4	no	—
70	C₄×D₄×C₄₇	—	2	4	no	—
71	C₄×D₄×C₄₇	—	2	2	no	—
72	C₄×D₄×C₄₇	—	2	2	no	—
73	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
74	#117×C₄₇	—	2	2	no	—
75	#117×C₄₇	—	2	4	no	—
76	#117×C₄₇	—	2	2	no	—
77	#117×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₄₇	D₄	1	2	yes	—
82	C₂×C₄²×C₄₇	D₄	1	2	yes	—
83	C₂×C₄²×C₄₇	D₄	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
87	#41×C₄₇	—	2	8	no	—
88	#41×C₄₇	—	4	8	no	—
89	C₂×Q₈×C₄₇	—	2	2	no	—
90	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂×D₄×C₄₇	—	2	4	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	4	4	no	—
99	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	8	no	—
110	C₂²×Dic₄₇	—	2	4	no	—
111	C₂²×Dic₄₇	—	4	8	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	4	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
118	C₂²⋊C₄×C₄₇	—	2	4	no	—
119	C₂²⋊C₄×C₄₇	—	2	2	no	—
120	C₂²⋊C₄×C₄₇	—	2	4	no	—
121	C₂²⋊C₄×C₄₇	—	2	4	no	—
122	C₂²⋊C₄×C₄₇	—	2	4	no	—
123	C₄²×C₄₇	—	2	4	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
126	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
130	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂×D₄	1	2	yes	—
135	C₄×Dic₄₇	—	2	8	no	—
136	C₄×Dic₄₇	—	2	4	no	—
137	C₄×Dic₄₇	#41	1	8	yes	complemented
138	#10625329	—	2	8	no	—
139	C₂×C₄₇⋊C₈	—	2	4	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	4	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₄₇	—	2	4	no	—
146	Q₈×C₄₇	—	4	4	no	—
147	D₄×C₄₇	—	2	4	no	—
148	D₄×C₄₇	—	4	4	no	—
149	D₄×C₄₇	—	4	4	no	—
150	D₄×C₄₇	—	4	8	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	8	no	—
163	C₂×C₄×C₄₇	—	4	4	no	—
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
172	C₂×Dic₄₇	—	2	8	no	—
173	C₂×Dic₄₇	—	4	16	no	—
174	C₂×Dic₄₇	—	4	8	no	—
175	C₄₇⋊C₈	—	4	4	no	—
176	#21417	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	—	2	8	no	—
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	#421	1	4	yes	—
184	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₄₇	#525	1	2	yes	—
186	C₄×C₄₇	—	2	2	no	—
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	—	4	4	no	—
192	C₄×C₄₇	—	4	2	no	—
193	C₄×C₄₇	C₄×#41	1	2	yes	—
194	C₄×C₄₇	#532	1	2	yes	—
195	Dic₄₇	—	4	8	no	—
196	#3444	D₄₇	1	1	yes	characteristic
197	#2920	—	47	1	no	—
198	C₂×#376	—	47	1	no	—
199	#1995	—	47	2	no	—
200	#1963	—	47	2	no	—
201	#1896	—	47	4	no	—
202	#1759	—	47	4	no	—
203	C₂×C₄₇	—	2	2	no	—
204	C₂×C₄₇	—	2	4	no	—
205	C₂×C₄₇	—	8	2	no	—
206	C₂×C₄₇	#2297	1	1	yes	characteristic
207	C₂×C₄₇	C₂×#421	1	2	yes	—
208	#533	Dic₄₇	1	2	yes	complemented
209	#533	C₂×D₄₇	1	1	yes	characteristic
210	#532	Dic₄₇	1	2	yes	complemented
211	#532	C₂×D₄₇	1	1	yes	characteristic
212	#529	—	2	2	no	—
213	#529	—	2	2	no	—
214	#529	Dic₄₇	1	4	yes	complemented
215	#525	—	2	2	no	—
216	#525	C₂×D₄₇	1	2	yes	—
217	C₄×#41	—	2	2	no	—
218	C₄×#41	C₂×D₄₇	1	2	yes	—
219	C₂²×C₄²	—	47	2	no	—
220	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
221	#432	—	94	2	no	—
222	#431	—	94	2	no	—
223	#423	—	47	2	no	—
224	C₂×#104	—	47	8	no	—
225	#407	—	47	2	no	—
226	C₄×M₁₆	—	47	2	no	—
227	#376	—	47	2	no	—
228	#376	—	47	2	no	—
229	#376	—	94	2	no	—
230	C₂×#95	—	94	2	no	—
231	#339	—	47	8	no	—
232	C₄₇	#21417	1	1	yes	characteristic, complemented, Sylow
233	C₂×#41	—	2	2	no	—
234	C₂×#41	C₂²×D₄₇	1	2	yes	—
235	C₂³×C₄	—	94	2	no	—
236	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
237	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
238	C₂×M₁₆	—	47	4	no	—
239	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
240	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
241	#127	C₂×Dic₄₇	1	1	yes	characteristic, complemented
242	#126	—	2	4	no	—
243	#125	—	2	2	no	—
244	#125	C₂×Dic₄₇	1	2	yes	complemented
245	#124	—	2	2	no	—
246	#124	C₂×Dic₄₇	1	2	yes	complemented
247	#123	—	2	4	no	—
248	#123	—	2	2	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	C₂²⋊Q₈	—	2	2	no	—
251	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
252	#121	—	2	2	no	—
253	#121	—	2	2	no	—
254	#121	C₂×Dic₄₇	1	4	yes	—
255	#120	—	2	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
259	C₄×D₄	—	2	4	no	—
260	C₄×D₄	—	2	4	no	—
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
265	#117	—	2	2	no	—
266	#117	—	2	4	no	—
267	#117	—	2	2	no	—
268	#117	C₂²×D₄₇	1	2	yes	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	47	4	no	—
271	C₂×C₄²	—	94	8	no	—
272	C₂×C₄²	—	94	2	no	—
273	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
274	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
275	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
276	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
277	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
278	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
279	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
280	C₄⋊C₈	—	94	4	no	—
281	#104	—	94	16	no	—
282	C₂²⋊C₈	—	94	4	no	—
283	#97	—	94	2	no	—
284	C₄×C₈	—	94	2	no	—
285	#95	—	94	4	no	—
286	#95	—	94	4	no	—
287	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
288	#41	—	2	8	no	—
289	#41	—	4	8	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	—	94	8	no	—
301	C₂²×C₄	—	94	4	no	—
302	C₂²×C₄	—	188	8	no	—
303	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
304	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
305	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
306	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
307	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
308	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
310	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
311	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
312	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
313	M₁₆	—	94	8	no	—
314	C₂×C₈	—	94	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	47	8	no	—
329	C₄²	—	94	8	no	—
330	C₄²	—	94	4	no	—
331	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
332	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
333	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
334	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
335	C₄²	C₂²×Dic₄₇	1	2	yes	—
336	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
337	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
338	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
339	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	2	no	—
344	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
345	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
346	Q₈	—	2	4	no	—
347	Q₈	—	4	4	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	8	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	94	8	no	—
366	C₂×C₄	—	188	16	no	—
367	C₂×C₄	—	188	8	no	—
368	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
371	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
373	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
375	C₂×C₄	#41×D₄₇	1	4	yes	—
376	C₈	—	188	4	no	—
377	C₂²	—	2	8	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	2	no	—
383	C₂²	#15689140	1	4	yes	—
384	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
385	C₂²	#15689630	1	2	yes	—
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	4	no	—
392	C₄	—	4	2	no	—
393	C₄	—	188	8	no	—
394	C₄	#41×Dic₄₇	1	2	yes	—
395	C₄	#15689669	1	2	yes	—
396	C₂	—	2	2	no	—
397	C₂	—	2	4	no	—
398	C₂	—	8	2	no	—
399	C₂	#20245879	1	1	yes	characteristic
400	C₂	C₂×#15689140	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×#3444	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3444	D₄₇
hypocenter	C₄₇	#21417
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. #20252021	C₂	semidirect
2. C₂×#15688969	C₂	semidirect
3. #20244370	C₂	semidirect
4. #20244221	C₂	semidirect
5. #20243832	C₂	semidirect
6. #20243198	C₂	semidirect
20. C₄₇×#533	C₄	semidirect
22. C₄₇×#532	C₄	semidirect
26. C₄₇×#529	C₄	semidirect
48. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
49. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
50. #127×C₄₇	C₂×C₄	semidirect
53. #125×C₄₇	C₂×C₄	semidirect
55. #124×C₄₇	C₂×C₄	semidirect
67. C₄×Q₈×C₄₇	C₂×C₄	semidirect
73. C₄×D₄×C₄₇	C₂×C₄	semidirect
137. C₄×Dic₄₇	#41	semidirect
208. #533	Dic₄₇	semidirect
210. #532	Dic₄₇	semidirect
214. #529	Dic₄₇	semidirect
232. C₄₇	#21417	semidirect
239. C₄⋊Q₈	C₂×Dic₄₇	semidirect
240. C₄⋊Q₈	C₂×Dic₄₇	semidirect
241. #127	C₂×Dic₄₇	semidirect
244. #125	C₂×Dic₄₇	semidirect
246. #124	C₂×Dic₄₇	semidirect
258. C₄×Q₈	C₂×Dic₄₇	semidirect
264. 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
#20252021	2
C₂×#15688969	2
#20244370	2
#20244221	2
#20243832	2
#20243198	2
C₄₇×#3444	2
#21417	47