Subgroups — #26234143

Order 12032.

828 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
2	#20244106	C₂	1	2	yes	maximal, complemented
3	#20243991	C₂	1	4	yes	maximal
4	#20243503	C₂	1	2	yes	maximal, complemented
5	#20243368	C₂	1	1	yes	maximal, characteristic
6	C₈×C₄⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
7	#20243132	C₂	1	2	yes	maximal, complemented
8	C₄×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#13093983	C₄	1	1	yes	characteristic
10	C₂×#13093983	C₄	1	1	yes	characteristic
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
13	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₈×Dic₄₇	C₂²	1	4	yes	—
15	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
16	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
17	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
19	C₄×C₂²⋊Dic₄₇	C₄	1	2	yes	—
20	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
21	#15688969	C₄	1	2	yes	—
22	C₄²×Dic₄₇	C₂²	1	2	yes	—
23	#15688878	C₂²	1	2	yes	—
24	#15688877	C₂²	1	4	yes	—
25	#15688877	C₂²	1	4	yes	—
26	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#336	C₂²	1	1	yes	characteristic
30	C₄₇×#336	C₂²	1	1	yes	characteristic
31	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
32	#13093983	—	2	4	no	—
33	#13093983	C₈	1	8	yes	complemented
34	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
39	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
40	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
41	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
42	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
43	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
44	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
45	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
46	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
47	Dic₄₇⋊C₈	—	4	4	no	—
48	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
49	C₈×Dic₄₇	—	2	8	no	—
50	C₄₇⋊#95	C₂×C₄	1	2	yes	—
51	C₄₇⋊#95	C₂×C₄	1	2	yes	—
52	C₄₇⋊#95	C₂×C₄	1	2	yes	—
53	C₄₇⋊#95	C₂×C₄	1	2	yes	—
54	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
58	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
59	C₂×C₄²×C₄₇	—	2	4	no	—
60	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
64	C₂²⋊C₈×C₄₇	—	2	4	no	—
65	C₄×C₈×C₄₇	—	2	4	no	—
66	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	1	no	—
74	C₂²×C₄×C₄₇	—	2	1	no	—
75	C₂²×C₄×C₄₇	—	4	1	no	—
76	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
77	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
83	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
84	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
85	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
86	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
87	C₂×C₈×C₄₇	—	2	2	no	—
88	C₂×C₈×C₄₇	—	2	2	no	—
89	C₂×C₈×C₄₇	—	2	2	no	—
90	C₂×C₈×C₄₇	—	2	2	no	—
91	C₂×C₈×C₄₇	—	2	2	no	—
92	C₂×C₈×C₄₇	#41	1	4	yes	—
93	C₄²×C₄₇	—	2	2	no	—
94	C₄²×C₄₇	—	2	2	no	—
95	C₄²×C₄₇	—	2	2	no	—
96	C₄²×C₄₇	#41	1	4	yes	—
97	C₂²⋊Dic₄₇	—	2	4	no	—
98	C₂²⋊Dic₄₇	C₂×C₈	1	8	yes	—
99	C₄⋊Dic₄₇	—	2	2	no	—
100	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	—
101	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	—
102	C₄⋊Dic₄₇	M₁₆	1	4	yes	—
103	C₄×Dic₄₇	—	2	4	no	—
104	C₄×Dic₄₇	—	2	4	no	—
105	C₄×Dic₄₇	—	2	2	no	—
106	C₄×Dic₄₇	—	2	2	no	—
107	C₄×Dic₄₇	—	2	4	no	—
108	C₄×Dic₄₇	—	4	2	no	—
109	C₄×Dic₄₇	C₂×C₈	1	8	yes	—
110	C₂×C₄₇⋊C₈	—	2	4	no	—
111	C₂×C₄₇⋊C₈	—	2	4	no	—
112	C₂×C₄₇⋊C₈	—	2	4	no	—
113	C₂³×C₄₇	—	2	1	no	—
114	C₂³×C₄₇	—	2	1	no	—
115	C₂³×C₄₇	—	2	1	no	—
116	C₂³×C₄₇	—	2	1	no	—
117	C₂³×C₄₇	—	2	1	no	—
118	C₂³×C₄₇	—	2	1	no	—
119	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
120	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
121	C₂×C₄×C₄₇	—	2	1	no	—
122	C₂×C₄×C₄₇	—	2	1	no	—
123	C₂×C₄×C₄₇	—	2	1	no	—
124	C₂×C₄×C₄₇	—	2	1	no	—
125	C₂×C₄×C₄₇	—	2	1	no	—
126	C₂×C₄×C₄₇	—	2	1	no	—
127	C₂×C₄×C₄₇	—	2	8	no	—
128	C₂×C₄×C₄₇	—	2	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	4	4	no	—
132	C₂×C₄×C₄₇	—	4	2	no	—
133	C₂×C₄×C₄₇	—	4	2	no	—
134	C₂×C₄×C₄₇	#117	1	2	yes	—
135	C₂×C₄×C₄₇	#117	1	2	yes	—
136	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
137	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
139	C₂×C₄×C₄₇	#131	1	2	yes	—
140	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
142	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
143	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
144	C₂×Dic₄₇	—	2	2	no	—
145	C₂×Dic₄₇	—	2	2	no	—
146	C₂×Dic₄₇	—	2	2	no	—
147	C₂×Dic₄₇	—	2	2	no	—
148	C₂×Dic₄₇	—	2	2	no	—
149	C₂×Dic₄₇	—	2	2	no	—
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
154	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
155	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
156	C₈×C₄₇	—	2	4	no	—
157	C₈×C₄₇	—	4	2	no	—
158	C₄₇⋊C₈	—	4	4	no	—
159	#22632	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	2	no	—
163	C₂²×C₄₇	—	4	1	no	—
164	C₂²×C₄₇	—	4	1	no	—
165	C₂²×C₄₇	—	4	1	no	—
166	C₂²×C₄₇	—	4	1	no	—
167	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
168	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
169	C₂²×C₄₇	#520	1	1	yes	characteristic
170	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
171	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
173	C₂²×C₄₇	#568	1	1	yes	characteristic
174	C₄×C₄₇	—	2	2	no	—
175	C₄×C₄₇	—	2	2	no	—
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	4	1	no	—
178	C₄×C₄₇	#431	1	4	yes	—
179	C₄×C₄₇	#552	1	2	yes	—
180	C₄×C₄₇	#555	1	2	yes	—
181	Dic₄₇	—	2	4	no	—
182	Dic₄₇	—	2	4	no	—
183	Dic₄₇	—	2	4	no	—
184	Dic₄₇	—	4	2	no	—
185	C₄×#117	—	47	1	no	—
186	#1939	—	47	2	no	—
187	#1923	—	47	4	no	—
188	#1831	—	47	2	no	—
189	#1797	—	47	1	no	—
190	C₈×C₄⋊C₄	—	47	2	no	—
191	C₄×C₂²⋊C₈	D₄₇	1	1	yes	characteristic
192	#1744	—	47	2	no	—
193	C₂×C₄₇	—	4	2	no	—
194	C₂×C₄₇	#2346	1	1	yes	characteristic
195	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
196	C₂×C₄₇	#2924	1	1	yes	characteristic
197	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
198	C₂×C₄₇	#2970	1	1	yes	characteristic
199	C₂×C₄₇	#2988	1	1	yes	characteristic
200	C₂×C₄₇	#2991	1	1	yes	characteristic
201	C₂×#117	—	47	1	no	—
202	C₂×#117	—	47	1	no	—
203	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
204	C₂×C₄⋊C₈	—	47	2	no	—
205	C₂×C₄⋊C₈	—	47	4	no	—
206	C₂×C₂²⋊C₈	—	47	2	no	—
207	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
208	C₂×C₄×C₈	—	47	4	no	—
209	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
210	C₄×C₄⋊C₄	—	47	1	no	—
211	C₄×C₄⋊C₄	—	47	1	no	—
212	C₄×C₄⋊C₄	—	47	1	no	—
213	C₄×C₄⋊C₄	—	47	1	no	—
214	C₄×C₂²⋊C₄	—	47	2	no	—
215	C₄×C₂²⋊C₄	—	47	2	no	—
216	#376	—	47	2	no	—
217	C₄³	—	47	2	no	—
218	#336	—	47	4	no	—
219	#336	—	47	4	no	—
220	#336	—	47	2	no	—
221	#336	C₂×D₄₇	1	1	yes	characteristic
222	#336	C₂×D₄₇	1	1	yes	characteristic
223	C₄₇	#22632	1	1	yes	characteristic, complemented, Sylow
224	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
225	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
226	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
227	C₂²×C₈	—	47	4	no	—
228	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
229	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
230	#117	—	47	8	no	—
231	#117	—	94	4	no	—
232	C₂×C₄⋊C₄	—	47	1	no	—
233	C₂×C₄⋊C₄	—	47	1	no	—
234	C₂×C₄⋊C₄	—	47	1	no	—
235	C₂×C₄⋊C₄	—	47	1	no	—
236	C₂×C₂²⋊C₄	—	47	2	no	—
237	C₂×C₂²⋊C₄	—	47	2	no	—
238	C₂×C₄²	—	2	4	no	—
239	C₂×C₄²	—	47	2	no	—
240	C₂×C₄²	—	47	2	no	—
241	C₂×C₄²	—	47	2	no	—
242	C₂×C₄²	—	47	2	no	—
243	C₂×C₄²	—	47	2	no	—
244	C₂×C₄²	—	47	2	no	—
245	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
247	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
248	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
249	C₄⋊C₈	—	94	4	no	—
250	C₄⋊C₈	—	188	4	no	—
251	C₂²⋊C₈	—	2	4	no	—
252	C₂²⋊C₈	—	188	2	no	—
253	C₄×C₈	—	2	4	no	—
254	C₄×C₈	—	94	8	no	—
255	#95	—	47	2	no	—
256	#95	—	47	2	no	—
257	#95	—	47	2	no	—
258	#95	—	47	2	no	—
259	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	47	2	no	—
270	C₂²×C₄	—	47	2	no	—
271	C₂²×C₄	—	47	2	no	—
272	C₂²×C₄	—	47	2	no	—
273	C₂²×C₄	C₈×D₄₇	1	4	yes	—
274	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
279	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	94	4	no	—
286	C₂×C₈	—	94	4	no	—
287	C₂×C₈	—	94	4	no	—
288	C₂×C₈	#10625350	1	4	yes	—
289	C₄⋊C₄	—	47	4	no	—
290	C₄⋊C₄	—	47	4	no	—
291	C₄⋊C₄	—	47	4	no	—
292	C₄⋊C₄	—	94	2	no	—
293	C₂²⋊C₄	—	47	8	no	—
294	C₂²⋊C₄	—	94	4	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	47	8	no	—
299	C₄²	—	94	4	no	—
300	C₄²	—	94	4	no	—
301	C₄²	—	94	4	no	—
302	C₄²	—	94	2	no	—
303	C₄²	—	94	2	no	—
304	C₄²	—	188	2	no	—
305	C₄²	#10625352	1	4	yes	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	C₂×C₈×D₄₇	1	2	yes	—
313	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	47	4	no	—
328	C₂×C₄	—	47	4	no	—
329	C₂×C₄	—	47	4	no	—
330	C₂×C₄	—	94	2	no	—
331	C₂×C₄	—	94	2	no	—
332	C₂×C₄	—	94	2	no	—
333	C₂×C₄	—	94	2	no	—
334	C₂×C₄	—	94	2	no	—
335	C₂×C₄	—	94	2	no	—
336	C₂×C₄	—	94	2	no	—
337	C₂×C₄	—	94	2	no	—
338	C₂×C₄	—	94	2	no	—
339	C₂×C₄	#13093980	1	2	yes	—
340	C₂×C₄	#13093980	1	2	yes	—
341	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
342	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
343	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
344	C₂×C₄	#13094030	1	2	yes	—
345	C₂×C₄	C₂×#10625352	1	2	yes	—
346	C₂×C₄	C₂×#10625350	1	2	yes	—
347	C₂×C₄	#13094070	1	1	yes	characteristic
348	C₂×C₄	#13094071	1	1	yes	characteristic
349	C₈	—	2	4	no	—
350	C₈	—	4	2	no	—
351	C₈	—	188	4	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	C₂×#13093980	1	1	yes	characteristic
360	C₂²	C₄×#10625350	1	1	yes	characteristic
361	C₂²	#15689603	1	1	yes	characteristic
362	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
363	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
364	C₂²	C₂×#13094030	1	1	yes	characteristic
365	C₂²	#15689889	1	1	yes	characteristic
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	1	no	—
370	C₄	—	94	4	no	—
371	C₄	—	94	4	no	—
372	C₄	—	94	4	no	—
373	C₄	—	188	2	no	—
374	C₄	#15689173	1	4	yes	—
375	C₄	#15689813	1	2	yes	—
376	C₄	#15689838	1	2	yes	—
377	C₂	—	4	2	no	—
378	C₂	#20246271	1	1	yes	characteristic
379	C₂	C₂×#15689173	1	1	yes	characteristic
380	C₂	#20252042	1	1	yes	characteristic
381	C₂	C₈×#10625350	1	1	yes	characteristic
382	C₂	#20252403	1	1	yes	characteristic
383	C₂	#20252496	1	1	yes	characteristic
384	C₂	#20252517	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄×C₂²⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₂²⋊C₈	D₄₇
hypocenter	C₄₇	#22632
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. #20244106	C₂	semidirect
4. #20243503	C₂	semidirect
6. C₈×C₄⋊Dic₄₇	C₂	semidirect
7. #20243132	C₂	semidirect
33. #13093983	C₈	semidirect
223. C₄₇	#22632	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13093983	2
#20244106	2
#20243991	2
#20243503	2
#20243368	2
C₈×C₄⋊Dic₄₇	2
#20243132	2
C₄×C₂²⋊C₈×C₄₇	2
#22632	47