Subgroups — #26234746

Order 12032.

870 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×#15689241	C₂	1	2	yes	maximal
2	C₄×#13094046	C₂	1	1	yes	maximal, characteristic
3	#20251953	C₂	1	2	yes	maximal, complemented
4	#20244136	C₂	1	2	yes	maximal, complemented
5	#20243666	C₂	1	4	yes	maximal, complemented
6	#20243560	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243409	C₂	1	2	yes	maximal, complemented
8	C₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13094046	C₂²	1	1	yes	characteristic
10	C₂×#13094030	C₂²	1	4	yes	—
11	C₄×#10625350	C₂²	1	2	yes	—
12	#15689241	—	2	8	no	—
13	C₄×Dic₁₈₈	C₄	1	1	yes	characteristic, complemented
14	C₄×Dic₁₈₈	C₄	1	1	yes	characteristic, complemented
15	C₄×#10625325	C₄	1	2	yes	complemented
16	C₄×#10625325	C₄	1	2	yes	complemented
17	C₄×D₃₇₆	C₄	1	1	yes	characteristic, complemented
18	C₄×D₃₇₆	C₄	1	1	yes	characteristic, complemented
19	C₂×#13093960	C₂²	1	2	yes	—
20	C₂×#13093960	C₂²	1	2	yes	—
21	#15689161	C₂²	1	1	yes	characteristic
22	#15689149	C₂²	1	4	yes	—
23	#15689148	—	2	4	no	—
24	#15689147	C₂²	1	2	yes	—
25	#15689145	—	2	2	no	—
26	C₄⋊C₈×D₄₇	—	2	2	no	—
27	C₂×#13093952	C₂²	1	4	yes	—
28	#15689120	C₂²	1	2	yes	—
29	#15688883	C₂²	1	4	yes	—
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#336	C₂²	1	2	yes	—
35	C₂×#10625350	C₂³	1	2	yes	—
36	#13094046	D₄	1	4	yes	—
37	#13094046	Q₈	1	4	yes	—
38	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
39	C₂×#10625325	C₂×C₄	1	2	yes	—
40	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
41	#13094030	—	2	8	no	—
42	#13094030	—	4	4	no	—
43	C₂×#10625329	C₂³	1	4	yes	—
44	C₂×#10625324	—	2	4	no	—
45	C₂×C₈×D₄₇	—	2	4	no	—
46	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
47	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
48	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
49	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
50	C₄×C₂²⋊D₄₇	—	2	2	no	—
51	C₄×C₂²⋊D₄₇	—	2	2	no	—
52	#13093983	C₂³	1	2	yes	—
53	#13093981	—	2	2	no	—
54	C₄²×D₄₇	—	2	2	no	—
55	#13093960	—	2	4	no	—
56	#13093960	—	4	2	no	—
57	#13093958	C₂×C₄	1	1	yes	characteristic
58	#13093958	C₂×C₄	1	1	yes	characteristic
59	#13093956	C₂×C₄	1	2	yes	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
62	Dic₄₇⋊C₈	—	2	4	no	—
63	Dic₄₇⋊C₈	—	2	4	no	—
64	#13093952	—	2	8	no	—
65	#13093949	C₂×C₄	1	2	yes	—
66	#13093949	C₂×C₄	1	2	yes	—
67	#13093946	C₂×C₄	1	2	yes	—
68	#13093946	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
71	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
76	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
77	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
78	C₄×C₈×C₄₇	—	2	4	no	—
79	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
83	#95×C₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
88	C₂×C₂²⋊D₄₇	—	2	2	no	—
89	#10625350	—	2	2	no	—
90	#10625350	—	2	2	no	—
91	#10625350	C₂×D₄	1	4	yes	—
92	#10625350	C₂×Q₈	1	4	yes	—
93	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
94	C₂×C₄×D₄₇	—	2	2	no	—
95	C₂×C₄×D₄₇	—	2	2	no	—
96	C₂×C₄×D₄₇	—	2	2	no	—
97	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	—	2	1	no	—
102	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
110	C₄⋊C₄×C₄₇	—	2	4	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²⋊Dic₄₇	—	2	2	no	—
118	(C₂×D₄₇)⋊C₄	—	2	2	no	—
119	(C₂×D₄₇)⋊C₄	—	2	2	no	—
120	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
121	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
122	Dic₄₇⋊C₄	—	2	2	no	—
123	Dic₄₇⋊C₄	—	2	2	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	—	2	2	no	—
126	C₄×Dic₄₇	—	2	2	no	—
127	#10625329	—	2	4	no	—
128	#10625329	—	2	4	no	—
129	C₂×C₄₇⋊C₈	—	2	4	no	—
130	Dic₁₈₈	C₄⋊C₄	1	4	yes	complemented
131	D₃₇₆	C₄⋊C₄	1	4	yes	complemented
132	#10625325	C₄⋊C₄	1	8	yes	complemented
133	#10625324	—	4	8	no	—
134	C₈×D₄₇	—	4	8	no	—
135	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
136	C₂²×D₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	4	1	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
152	C₂²⋊D₄₇	—	2	4	no	—
153	C₂²⋊D₄₇	—	2	4	no	—
154	C₂×Dic₄₇	—	2	2	no	—
155	C₂×Dic₄₇	—	2	2	no	—
156	C₂×Dic₄₇	—	2	2	no	—
157	D₁₈₈	—	2	2	no	—
158	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
159	C₄×D₄₇	—	2	4	no	—
160	C₄×D₄₇	—	2	4	no	—
161	C₄×D₄₇	—	4	4	no	—
162	C₄×D₄₇	—	8	2	no	—
163	Dic₉₄	—	2	2	no	—
164	Dic₉₄	C₂×C₄⋊C₄	1	4	yes	—
165	C₈×C₄₇	—	2	1	no	—
166	C₈×C₄₇	—	2	1	no	—
167	C₈×C₄₇	—	2	2	no	—
168	C₈×C₄₇	—	2	2	no	—
169	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
170	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
171	C₄₇⋊C₈	—	4	4	no	—
172	#22688	—	47	1	no	maximal, Sylow
173	C₂²×C₄₇	—	2	1	no	—
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
176	C₂²×C₄₇	#547	1	1	yes	characteristic
177	C₂²×C₄₇	#554	1	1	yes	characteristic
178	C₂×D₄₇	—	2	4	no	—
179	C₂×D₄₇	—	4	2	no	—
180	C₂×D₄₇	—	4	2	no	—
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	2	1	no	—
183	C₄×C₄₇	—	2	1	no	—
184	C₄×C₄₇	—	4	4	no	—
185	C₄×C₄₇	#443	1	2	yes	complemented
186	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₄×C₄₇	#520	1	1	yes	characteristic
188	C₄×C₄₇	D₄²	1	1	yes	characteristic
189	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
190	Dic₄₇	—	2	4	no	—
191	Dic₄₇	—	4	2	no	—
192	Dic₄₇	—	4	2	no	—
193	C₂×#443	—	47	2	no	—
194	C₄×#135	—	47	1	no	—
195	#2906	—	47	2	no	—
196	#1945	—	47	2	no	—
197	#1866	—	47	4	no	—
198	#1848	—	47	1	no	—
199	#1806	—	47	2	no	—
200	C₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
201	C₂×C₄₇	—	2	1	no	—
202	C₂×C₄₇	—	2	1	no	—
203	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
205	C₂×C₄₇	#2957	1	1	yes	characteristic
206	D₄₇	—	4	4	no	—
207	C₂×#135	—	47	1	no	—
208	C₂×#131	—	47	4	no	—
209	C₄×#41	—	47	2	no	—
210	#443	—	94	8	no	—
211	C₄×Q₁₆	—	47	1	no	—
212	C₄×Q₁₆	—	47	1	no	—
213	C₄×SD₁₆	—	47	2	no	—
214	C₄×SD₁₆	—	47	2	no	—
215	C₄×D₈	—	47	1	no	—
216	C₄×D₈	—	47	1	no	—
217	C₂×#108	—	47	2	no	—
218	C₂×#108	—	47	2	no	—
219	#427	—	47	1	no	—
220	#424	—	47	4	no	—
221	#424	—	94	4	no	—
222	#423	—	47	2	no	—
223	#423	—	94	2	no	—
224	C₂×C₄⋊C₈	—	94	2	no	—
225	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
226	C₂×#104	—	47	4	no	—
227	#416	—	47	2	no	—
228	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
229	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
230	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
231	#339	—	47	4	no	—
232	#336	C₂×D₄₇	1	2	yes	—
233	C₄₇	#22688	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	—	47	2	no	—
235	#135	—	47	4	no	—
236	#135	—	47	4	no	—
237	C₂×Q₁₆	—	47	1	no	—
238	C₂×SD₁₆	—	47	2	no	—
239	C₂×D₈	—	47	1	no	—
240	#131	—	94	8	no	—
241	#131	—	188	4	no	—
242	C₂×M₁₆	—	47	4	no	—
243	C₂×M₁₆	—	94	4	no	—
244	C₂²×C₈	—	94	4	no	—
245	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
246	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
247	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
248	C₄×Q₈	—	47	2	no	—
249	C₄×Q₈	—	47	2	no	—
250	C₄×D₄	—	47	2	no	—
251	C₄×D₄	—	47	2	no	—
252	C₄×D₄	—	94	2	no	—
253	C₄×D₄	—	94	2	no	—
254	#117	—	47	2	no	—
255	#117	—	94	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄²	—	94	2	no	—
258	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
259	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
260	#108	—	94	4	no	—
261	#108	—	188	2	no	—
262	#107	—	47	1	no	—
263	#107	—	47	1	no	—
264	#106	—	47	2	no	—
265	C₄⋊C₈	—	94	4	no	—
266	C₄⋊C₈	—	94	4	no	—
267	C₄⋊C₈	—	94	2	no	—
268	C₄⋊C₈	—	94	2	no	—
269	C₄⋊C₈	D₁₈₈	1	1	yes	characteristic
270	C₄⋊C₈	D₁₈₈	1	1	yes	characteristic
271	C₄⋊C₈	D₁₈₈	1	2	yes	—
272	#104	—	94	8	no	—
273	#103	—	47	2	no	—
274	#103	—	47	2	no	—
275	#102	—	47	2	no	—
276	#102	—	47	2	no	—
277	C₄×C₈	—	2	4	no	—
278	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
279	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
280	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
281	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
282	#95	—	2	1	no	—
283	#41	—	47	4	no	—
284	#41	—	47	4	no	—
285	#41	—	94	2	no	—
286	#41	—	94	2	no	—
287	C₂×Q₈	—	47	2	no	—
288	C₂×D₄	—	47	2	no	—
289	C₂×D₄	—	94	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	94	2	no	—
292	C₂²×C₄	—	94	2	no	—
293	C₂²×C₄	—	94	2	no	—
294	C₂²×C₄	#10625350	1	1	yes	characteristic
295	C₂²×C₄	#10625350	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
297	Q₁₆	—	47	4	no	—
298	SD₁₆	—	47	8	no	—
299	D₈	—	47	4	no	—
300	M₁₆	—	94	4	no	—
301	M₁₆	—	94	4	no	—
302	M₁₆	—	188	8	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	94	4	no	—
308	C₂×C₈	—	188	8	no	—
309	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
310	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
311	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
312	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
313	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
314	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
315	C₂×C₈	D₄×D₄₇	1	2	yes	—
316	C₂×C₈	Q₈×D₄₇	1	2	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	47	2	no	—
319	C₄⋊C₄	—	47	2	no	—
320	C₄⋊C₄	—	94	2	no	—
321	C₄⋊C₄	—	94	2	no	—
322	C₂²⋊C₄	—	94	2	no	—
323	C₂²⋊C₄	—	94	2	no	—
324	C₂²⋊C₄	—	94	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	94	2	no	—
328	C₄²	—	94	2	no	—
329	C₄²	—	94	2	no	—
330	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
331	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
332	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
333	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
334	C₂³	—	94	2	no	—
335	C₂³	C₂×#10625350	1	1	yes	characteristic
336	Q₈	—	47	4	no	—
337	Q₈	—	94	2	no	—
338	D₄	—	47	4	no	—
339	D₄	—	94	4	no	—
340	D₄	—	94	4	no	—
341	D₄	—	94	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	94	4	no	—
349	C₂×C₄	—	94	4	no	—
350	C₂×C₄	—	94	2	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	376	2	no	—
353	C₂×C₄	—	188	4	no	—
354	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
355	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
356	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
357	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
361	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
362	C₂×C₄	#13094070	1	1	yes	characteristic
363	C₂×C₄	#13094071	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	2	2	no	—
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	188	4	no	—
369	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
370	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	94	4	no	—
374	C₂²	—	188	2	no	—
375	C₂²	—	188	2	no	—
376	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
377	C₂²	#15689778	1	1	yes	characteristic
378	C₂²	#15689833	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	4	no	—
383	C₄	—	94	4	no	—
384	C₄	—	188	2	no	—
385	C₄	—	188	2	no	—
386	C₄	#15689241	1	2	yes	complemented
387	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
388	C₄	#15689603	1	1	yes	characteristic
389	C₄	D₄×D₁₈₈	1	1	yes	characteristic
390	C₄	Q₈×D₁₈₈	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	188	4	no	—
394	C₂	C₄⋊C₄×D₁₈₈	1	1	yes	characteristic
395	C₂	C₂×#15689241	1	1	yes	characteristic
396	C₂	#20252306	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₈×C₄⋊C₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094046	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#22688
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #20251953	C₂	semidirect
4. #20244136	C₂	semidirect
5. #20243666	C₂	semidirect
6. #20243560	C₂	semidirect
7. #20243409	C₂	semidirect
8. C₈×C₄⋊C₄×C₄₇	C₂	semidirect
13. C₄×Dic₁₈₈	C₄	semidirect
14. C₄×Dic₁₈₈	C₄	semidirect
15. C₄×#10625325	C₄	semidirect
16. C₄×#10625325	C₄	semidirect
17. C₄×D₃₇₆	C₄	semidirect
18. C₄×D₃₇₆	C₄	semidirect
130. Dic₁₈₈	C₄⋊C₄	semidirect
131. D₃₇₆	C₄⋊C₄	semidirect
132. #10625325	C₄⋊C₄	semidirect
185. C₄×C₄₇	#443	semidirect
200. C₈×C₄⋊C₄	D₄₇	semidirect
233. C₄₇	#22688	semidirect
386. C₄	#15689241	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689241	2
C₄×#13094046	2
#20251953	2
#20244136	2
#20243666	2
#20243560	2
#20243409	2
C₈×C₄⋊C₄×C₄₇	2
#22688	47