Subgroups — #20254985

Order 6016.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094052	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13094051	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689775	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689757	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689494	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689370	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689327	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689317	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689275	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689273	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689271	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689266	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689205	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689199	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#468	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625354	C₂²	1	1	yes	characteristic, complemented
17	C₂×#10625350	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₄₇	—	2	1	no	—
20	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
21	#13094052	—	2	4	no	—
22	#13094051	—	2	4	no	—
23	C₂×#10625325	C₂²	1	1	yes	characteristic
24	C₂×#10625325	C₂²	1	1	yes	characteristic, complemented
25	C₂×#10625335	C₂²	1	1	yes	characteristic, complemented
26	C₂×#10625336	C₂²	1	1	yes	characteristic
27	C₂×#10625336	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
29	C₂×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×#10625334	C₂²	1	1	yes	characteristic, complemented
31	C₂×#10625324	C₂²	1	1	yes	characteristic, complemented
32	#13094022	C₂²	1	1	yes	characteristic, complemented
33	#13094020	C₂²	1	1	yes	characteristic
34	#13094009	—	2	1	no	—
35	#13094006	—	2	1	no	—
36	#13094004	C₂²	1	1	yes	characteristic, complemented
37	#13093999	C₂²	1	1	yes	characteristic
38	#13093997	—	2	1	no	—
39	#13093997	—	2	1	no	—
40	#13093994	—	2	1	no	—
41	#13093992	—	2	1	no	—
42	#13093986	C₂²	1	1	yes	characteristic
43	#13093986	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
45	C₄⋊C₄×D₄₇	—	2	1	no	—
46	Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	#13093947	C₂²	1	1	yes	characteristic, complemented
48	#13093944	C₂²	1	1	yes	characteristic
49	#13093944	C₂²	1	1	yes	characteristic, complemented
50	#13093944	C₂²	1	1	yes	characteristic, complemented
51	C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
57	#121×C₄₇	C₂²	1	1	yes	characteristic
58	#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
59	#103×C₄₇	C₂²	1	1	yes	characteristic, complemented
60	#102×C₄₇	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₄₇	—	2	1	no	—
62	C₂³×D₄₇	—	2	1	no	—
63	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₄₇	—	2	1	no	—
65	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₄₇	—	2	1	no	—
68	C₂×C₂²⋊D₄₇	—	2	1	no	—
69	C₂×C₂²⋊D₄₇	—	2	1	no	—
70	C₂×C₂²⋊D₄₇	—	2	1	no	—
71	C₂×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
72	#10625354	—	2	2	no	—
73	#10625354	—	4	1	no	—
74	D₄×D₄₇	—	2	2	no	—
75	D₄×D₄₇	—	4	1	no	—
76	D₄×D₄₇	—	4	4	no	—
77	#10625350	—	2	2	no	—
78	#10625350	—	4	1	no	—
79	C₂×D₁₈₈	—	2	2	no	—
80	C₂×D₁₈₈	—	2	1	no	—
81	C₂×D₁₈₈	—	2	1	no	—
82	C₂×D₁₈₈	—	2	1	no	—
83	C₂×D₁₈₈	—	4	1	no	—
84	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
85	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
86	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
87	C₂×C₄×D₄₇	—	2	1	no	—
88	C₂×C₄×D₄₇	—	2	1	no	—
89	C₂×C₄×D₄₇	—	2	1	no	—
90	C₂×C₄×D₄₇	—	2	1	no	—
91	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
92	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
93	SD₁₆×C₄₇	—	2	2	no	—
94	M₁₆×C₄₇	—	2	2	no	—
95	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₄₇	—	2	1	no	—
98	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
100	C₂²⋊C₄×C₄₇	—	2	1	no	—
101	C₂²⋊C₄×C₄₇	—	2	1	no	—
102	C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
103	#10625336	—	2	2	no	—
104	#10625336	—	4	1	no	—
105	#10625335	—	4	1	no	—
106	#10625334	—	2	2	no	—
107	(C₂×D₄₇)⋊C₄	—	2	1	no	—
108	(C₂×D₄₇)⋊C₄	—	2	1	no	—
109	(C₂×D₄₇)⋊C₄	—	2	1	no	—
110	(C₂×D₄₇)⋊C₄	—	2	1	no	—
111	(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
112	C₄⋊Dic₄₇	—	2	1	no	—
113	Dic₄₇⋊C₄	—	2	1	no	—
114	Dic₄₇⋊C₄	—	2	1	no	—
115	Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
116	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
117	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
118	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
119	D₃₇₆	—	2	2	no	—
120	D₃₇₆	D₄	1	4	yes	complemented
121	#10625325	—	2	2	no	—
122	#10625325	—	2	2	no	—
123	#10625324	—	2	2	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×D₄₇	—	2	1	no	—
127	C₂²×D₄₇	—	2	1	no	—
128	C₂²×D₄₇	—	2	1	no	—
129	C₂²×D₄₇	—	4	2	no	—
130	C₂²×D₄₇	—	4	2	no	—
131	C₂²×D₄₇	—	4	2	no	—
132	C₂²×D₄₇	—	4	2	no	—
133	C₂²×D₄₇	—	8	1	no	—
134	C₂²×D₄₇	—	8	1	no	—
135	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₄₇	—	2	1	no	—
137	Q₈×C₄₇	—	2	1	no	—
138	D₄×C₄₇	—	2	1	no	—
139	D₄×C₄₇	—	2	1	no	—
140	D₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₂²⋊D₄₇	—	2	2	no	—
149	C₂²⋊D₄₇	—	4	2	no	—
150	C₂²⋊D₄₇	—	4	2	no	—
151	C₂²⋊D₄₇	—	4	2	no	—
152	C₂²⋊D₄₇	—	8	1	no	—
153	C₂×Dic₄₇	—	2	1	no	—
154	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
155	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
156	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
157	D₁₈₈	—	2	1	no	—
158	D₁₈₈	—	2	1	no	—
159	D₁₈₈	—	2	1	no	—
160	D₁₈₈	—	2	1	no	—
161	D₁₈₈	—	4	2	no	—
162	D₁₈₈	—	4	2	no	—
163	D₁₈₈	—	4	2	no	—
164	D₁₈₈	C₂×D₄	1	2	yes	—
165	D₁₈₈	C₂×D₄	1	2	yes	complemented
166	C₄×D₄₇	—	2	1	no	—
167	C₄×D₄₇	—	2	1	no	—
168	C₄×D₄₇	—	4	2	no	—
169	C₄×D₄₇	—	4	2	no	—
170	C₄×D₄₇	—	4	2	no	—
171	C₄×D₄₇	—	4	2	no	—
172	Dic₉₄	—	2	1	no	—
173	Dic₉₄	—	2	1	no	—
174	C₈×C₄₇	—	2	1	no	—
175	C₈×C₄₇	C₂×D₄	1	2	yes	complemented
176	C₄₇⋊C₈	—	2	1	no	—
177	C₄₇⋊C₈	—	2	1	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	4	1	no	—
182	C₂²×C₄₇	—	4	1	no	—
183	C₂²×C₄₇	—	4	1	no	—
184	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×D₄₇	—	2	1	no	—
186	C₂×D₄₇	—	2	2	no	—
187	C₂×D₄₇	—	2	2	no	—
188	C₂×D₄₇	—	2	1	no	—
189	C₂×D₄₇	—	2	1	no	—
190	C₂×D₄₇	—	4	1	no	—
191	C₂×D₄₇	—	4	1	no	—
192	C₂×D₄₇	—	4	1	no	—
193	C₂×D₄₇	—	4	1	no	—
194	C₂×D₄₇	—	4	1	no	—
195	C₂×D₄₇	—	4	1	no	—
196	C₂×D₄₇	—	4	1	no	—
197	C₂×D₄₇	—	8	4	no	—
198	C₂×D₄₇	—	8	4	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	4	1	no	—
201	C₄×C₄₇	—	4	1	no	—
202	C₄×C₄₇	—	4	1	no	—
203	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
204	C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
205	Dic₄₇	—	2	1	no	—
206	Dic₄₇	—	2	1	no	—
207	Dic₄₇	—	4	1	no	—
208	Dic₄₇	AGL(1,ℤ/8)	1	2	yes	complemented
209	#3272	—	47	1	no	maximal, Sylow
210	C₂×C₄₇	—	4	1	no	—
211	C₂×C₄₇	—	8	1	no	—
212	C₂×C₄₇	D₄²	1	1	yes	characteristic
213	C₂×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂×C₄₇	#577	1	1	yes	characteristic
215	D₄₇	—	4	1	no	—
216	D₄₇	—	4	2	no	—
217	D₄₇	—	4	2	no	—
218	D₄₇	—	8	1	no	—
219	C₂×AGL(1,ℤ/8)	—	47	1	no	—
220	C₂×AGL(1,ℤ/8)	—	47	1	no	—
221	#547	—	47	1	no	—
222	D₄²	—	47	1	no	—
223	#492	—	47	1	no	—
224	#468	—	47	1	no	—
225	#468	D₄₇	1	1	yes	characteristic, complemented
226	#461	—	47	1	no	—
227	#459	—	47	1	no	—
228	#450	—	47	1	no	—
229	#450	—	47	1	no	—
230	#449	—	47	1	no	—
231	#449	—	47	1	no	—
232	C₄×D₈	—	47	1	no	—
233	#436	—	47	1	no	—
234	C₄₇	#3272	1	1	yes	characteristic, complemented, Sylow
235	C₂×#41	—	47	1	no	—
236	C₂×#41	—	47	1	no	—
237	C₂²×D₄	—	47	1	no	—
238	C₂²×D₄	—	47	1	no	—
239	C₂²×D₄	—	94	1	no	—
240	AGL(1,ℤ/8)	—	94	4	no	—
241	AGL(1,ℤ/8)	—	94	4	no	—
242	C₂×SD₁₆	—	47	1	no	—
243	C₂×SD₁₆	—	47	1	no	—
244	C₂×SD₁₆	—	47	1	no	—
245	C₂×SD₁₆	—	47	1	no	—
246	C₂×SD₁₆	—	47	1	no	—
247	C₂×SD₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
248	C₂×D₈	—	47	1	no	—
249	C₂×D₈	—	47	1	no	—
250	C₂×D₈	—	47	1	no	—
251	C₂×M₁₆	—	47	1	no	—
252	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
253	C₄⋊Q₈	—	47	1	no	—
254	#127	—	47	1	no	—
255	#123	—	94	1	no	—
256	#123	—	94	1	no	—
257	C₂²⋊Q₈	—	47	1	no	—
258	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
259	#121	—	47	1	no	—
260	#121	—	94	1	no	—
261	#121	—	94	1	no	—
262	#121	C₂×D₄₇	1	1	yes	characteristic
263	#120	—	94	1	no	—
264	#120	—	94	1	no	—
265	C₄×D₄	—	47	1	no	—
266	C₄×D₄	—	47	1	no	—
267	C₄×D₄	—	47	1	no	—
268	C₂×C₄⋊C₄	—	94	1	no	—
269	#107	C₂×D₄₇	1	1	yes	characteristic, complemented
270	C₄⋊C₈	—	47	1	no	—
271	#103	—	47	1	no	—
272	#103	C₂×D₄₇	1	1	yes	characteristic, complemented
273	#102	—	47	1	no	—
274	#102	—	47	1	no	—
275	#102	—	47	1	no	—
276	#102	C₂×D₄₇	1	1	yes	characteristic, complemented
277	C₂²⋊C₈	—	47	1	no	—
278	C₂²⋊C₈	—	47	1	no	—
279	C₄×C₈	—	47	1	no	—
280	C₂⁴	—	94	1	no	—
281	C₂⁴	—	94	1	no	—
282	#41	—	94	2	no	—
283	#41	—	94	2	no	—
284	#41	—	188	1	no	—
285	#41	—	188	1	no	—
286	C₂×Q₈	—	47	1	no	—
287	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	47	1	no	—
290	C₂×D₄	—	47	1	no	—
291	C₂×D₄	—	47	1	no	—
292	C₂×D₄	—	47	1	no	—
293	C₂×D₄	—	94	2	no	—
294	C₂×D₄	—	94	1	no	—
295	C₂×D₄	—	94	1	no	—
296	C₂×D₄	—	94	1	no	—
297	C₂×D₄	—	94	1	no	—
298	C₂×D₄	—	94	1	no	—
299	C₂×D₄	—	94	2	no	—
300	C₂×D₄	—	94	1	no	—
301	C₂×D₄	—	94	1	no	—
302	C₂×D₄	—	188	1	no	—
303	C₂×D₄	—	188	1	no	—
304	C₂×D₄	—	188	4	no	—
305	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	94	1	no	—
308	C₂²×C₄	—	94	1	no	—
309	C₂²×C₄	—	94	1	no	—
310	C₂²×C₄	—	94	1	no	—
311	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	94	2	no	—
314	SD₁₆	—	94	2	no	—
315	SD₁₆	—	94	2	no	—
316	SD₁₆	—	188	1	no	—
317	SD₁₆	—	188	1	no	—
318	D₈	—	47	4	no	—
319	D₈	—	94	2	no	—
320	D₈	—	94	2	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	94	2	no	—
323	C₂×C₈	—	47	1	no	—
324	C₂×C₈	—	47	1	no	—
325	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	47	1	no	—
329	C₄⋊C₄	—	94	1	no	—
330	C₄⋊C₄	—	94	1	no	—
331	C₄⋊C₄	—	94	1	no	—
332	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
333	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	47	1	no	—
337	C₂²⋊C₄	—	47	1	no	—
338	C₂²⋊C₄	—	94	1	no	—
339	C₂²⋊C₄	—	94	1	no	—
340	C₂²⋊C₄	—	94	1	no	—
341	C₂²⋊C₄	—	94	1	no	—
342	C₄²	—	47	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	47	1	no	—
345	C₂³	—	94	1	no	—
346	C₂³	—	94	1	no	—
347	C₂³	—	94	1	no	—
348	C₂³	—	376	1	no	—
349	C₂³	—	376	1	no	—
350	C₂³	—	188	2	no	—
351	C₂³	—	188	2	no	—
352	C₂³	—	188	2	no	—
353	C₂³	—	188	2	no	—
354	C₂³	D₄×D₄₇	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	94	1	no	—
358	Q₈	—	94	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	47	2	no	—
363	D₄	—	47	2	no	—
364	D₄	—	94	2	no	—
365	D₄	—	94	1	no	—
366	D₄	—	94	1	no	—
367	D₄	—	94	1	no	—
368	D₄	—	94	1	no	—
369	D₄	—	376	1	no	—
370	D₄	—	188	2	no	—
371	D₄	—	188	2	no	—
372	D₄	—	188	2	no	—
373	D₄	—	188	2	no	—
374	D₄	—	188	2	no	—
375	D₄	—	188	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	47	1	no	—
382	C₂×C₄	—	47	1	no	—
383	C₂×C₄	—	47	1	no	—
384	C₂×C₄	—	94	1	no	—
385	C₂×C₄	—	94	1	no	—
386	C₂×C₄	—	94	1	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	—	188	2	no	—
391	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	94	1	no	—
395	C₈	—	94	1	no	—
396	C₈	D₄×D₄₇	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	94	1	no	—
404	C₂²	—	94	2	no	—
405	C₂²	—	94	2	no	—
406	C₂²	—	94	1	no	—
407	C₂²	—	94	1	no	—
408	C₂²	—	376	4	no	—
409	C₂²	—	376	4	no	—
410	C₂²	—	188	1	no	—
411	C₂²	—	188	1	no	—
412	C₂²	—	188	1	no	—
413	C₂²	—	188	1	no	—
414	C₂²	—	188	1	no	—
415	C₂²	—	188	1	no	—
416	C₂²	—	188	1	no	—
417	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	47	2	no	—
423	C₄	—	94	1	no	—
424	C₄	—	94	1	no	—
425	C₄	—	188	1	no	—
426	C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
427	C₄	#13094070	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	8	1	no	—
430	C₂	—	376	1	no	—
431	C₂	—	188	1	no	—
432	C₂	—	188	2	no	—
433	C₂	—	188	2	no	—
434	C₂	#15689757	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
436	C₂	#15689932	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#468	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#468	D₄₇
hypocenter	C₄₇	#3272
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #468

Complements

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

N	H ≅ G/N	type
1. C₂×#13094052	C₂	semidirect
2. C₂×#13094051	C₂	semidirect
3. #15689775	C₂	semidirect
4. #15689757	C₂	semidirect
5. #15689494	C₂	semidirect
6. #15689370	C₂	semidirect
7. #15689327	C₂	semidirect
8. #15689317	C₂	semidirect
9. #15689275	C₂	semidirect
10. #15689273	C₂	semidirect
11. #15689271	C₂	semidirect
12. #15689266	C₂	semidirect
13. #15689205	C₂	semidirect
14. #15689199	C₂	semidirect
15. C₄₇×#468	C₂	semidirect
16. C₂×#10625354	C₂²	semidirect
17. C₂×#10625350	C₂²	semidirect
24. C₂×#10625325	C₂²	semidirect
25. C₂×#10625335	C₂²	semidirect
27. C₂×#10625336	C₂²	semidirect
29. C₂×D₃₇₆	C₂²	semidirect
30. C₂×#10625334	C₂²	semidirect
31. C₂×#10625324	C₂²	semidirect
32. #13094022	C₂²	semidirect
36. #13094004	C₂²	semidirect
43. #13093986	C₂²	semidirect
46. Dic₄₇⋊C₈	C₂²	semidirect
47. #13093947	C₂²	semidirect
49. #13093944	C₂²	semidirect
50. #13093944	C₂²	semidirect
51. C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
52. (C₂×D₄₇)⋊C₈	C₂²	semidirect
53. C₈×Dic₄₇	C₂²	semidirect
54. C₂×SD₁₆×C₄₇	C₂²	semidirect
55. C₂×M₁₆×C₄₇	C₂²	semidirect
56. C₂²⋊Q₈×C₄₇	C₂²	semidirect
58. #107×C₄₇	C₂²	semidirect
59. #103×C₄₇	C₂²	semidirect
60. #102×C₄₇	C₂²	semidirect
120. D₃₇₆	D₄	semidirect
165. D₁₈₈	C₂×D₄	semidirect
175. C₈×C₄₇	C₂×D₄	semidirect
208. Dic₄₇	AGL(1,ℤ/8)	semidirect
225. #468	D₄₇	semidirect
234. C₄₇	#3272	semidirect
247. C₂×SD₁₆	C₂×D₄₇	semidirect
252. C₂×M₁₆	C₂×D₄₇	semidirect
258. C₂²⋊Q₈	C₂×D₄₇	semidirect
269. #107	C₂×D₄₇	semidirect
272. #103	C₂×D₄₇	semidirect
276. #102	C₂×D₄₇	semidirect
396. C₈	D₄×D₄₇	semidirect