Subgroups — C₂×#20245283 #26369716

Order 12032.

710 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689558	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689234	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245283	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688945	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688937	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688900	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#360	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
10	C₂×#13094031	—	2	1	no	—
11	C₂×#13093986	—	2	1	no	—
12	#15689558	C₄	1	4	yes	complemented
13	#15689558	C₂²	1	4	yes	—
14	C₂×#13093967	C₄	1	2	yes	complemented
15	C₂×#13093965	C₄	1	2	yes	complemented
16	C₂×#13093964	C₂²	1	1	yes	characteristic
17	#15689245	—	2	2	no	—
18	#15689245	C₂²	1	4	yes	complemented
19	#15689234	—	2	2	no	—
20	#15689234	C₂²	1	4	yes	complemented
21	C₂×#13093960	C₂²	1	1	yes	characteristic
22	C₂×#13093951	—	2	1	no	—
23	C₂×#13093944	—	2	1	no	—
24	C₂×#13093934	C₂²	1	1	yes	characteristic
25	#15688945	C₂²	1	4	yes	complemented
26	#15688937	C₂²	1	4	yes	complemented
27	#15688900	C₂²	1	4	yes	complemented
28	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#360	C₂²	1	4	yes	complemented
32	C₂²×D₁₈₈	—	2	1	no	—
33	C₂²×C₄×D₄₇	—	4	1	no	—
34	C₂×D₃₇₆	—	2	1	no	—
35	C₂×D₃₇₆	—	2	1	no	—
36	C₂×D₃₇₆	—	2	1	no	—
37	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
38	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
39	C₂×D₃₇₆	C₂³	1	2	yes	—
40	#13094031	—	2	4	no	—
41	#13094031	—	4	2	no	—
42	C₂×#10625329	—	2	1	no	—
43	C₂×#10625329	—	4	1	no	—
44	C₂²×C₄₇⋊C₈	—	4	1	no	—
45	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
46	#13093986	—	2	4	no	—
47	#13093986	—	4	2	no	—
48	C₂×(C₂×D₄₇)⋊C₄	—	4	1	no	—
49	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
50	#13093967	C₂×C₄	1	8	yes	complemented
51	#13093965	C₂×C₄	1	8	yes	complemented
52	#13093964	C₂×C₄	1	2	yes	complemented
53	#13093964	C₂³	1	2	yes	—
54	C₂×C₄₇⋊C₁₆	C₂×C₄	1	2	yes	complemented
55	#13093960	—	2	1	no	—
56	#13093960	C₂³	1	2	yes	—
57	#13093951	—	2	4	no	—
58	#13093944	—	2	4	no	—
59	#13093934	D₄	1	2	yes	—
60	#13093934	C₂³	1	2	yes	—
61	C₂×#41×C₄₇	—	2	1	no	—
62	#135×C₄₇	—	2	1	no	—
63	#135×C₄₇	—	2	1	no	—
64	#135×C₄₇	C₂×C₄	1	2	yes	complemented
65	#135×C₄₇	C₂³	1	2	yes	—
66	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×SD₁₆×C₄₇	—	2	1	no	—
68	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	M₃₂×C₄₇	—	2	1	no	—
72	M₃₂×C₄₇	C₂³	1	2	yes	—
73	C₂×C₁₆×C₄₇	—	2	1	no	—
74	#106×C₄₇	—	2	1	no	—
75	#106×C₄₇	C₂³	1	2	yes	—
76	C₂³×D₄₇	—	4	1	no	—
77	#41×C₄₇	—	2	2	no	—
78	#41×C₄₇	—	2	2	no	—
79	#41×C₄₇	—	4	1	no	—
80	#41×C₄₇	—	4	1	no	—
81	C₂×Q₈×C₄₇	—	2	1	no	—
82	C₂×D₄×C₄₇	—	2	1	no	—
83	C₂×D₄×C₄₇	—	4	1	no	—
84	C₂²×C₄×C₄₇	—	4	1	no	—
85	C₂²×C₄×C₄₇	—	4	1	no	—
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×Dic₄₇	—	2	1	no	—
88	C₂×D₁₈₈	—	2	2	no	—
89	C₂×D₁₈₈	—	2	2	no	—
90	C₂×D₁₈₈	—	2	2	no	—
91	C₂×D₁₈₈	—	4	1	no	—
92	C₂×D₁₈₈	—	4	1	no	—
93	C₂×D₁₈₈	—	4	1	no	—
94	C₂×C₄×D₄₇	—	4	4	no	—
95	C₂×C₄×D₄₇	—	8	4	no	—
96	Q₁₆×C₄₇	—	2	1	no	—
97	Q₁₆×C₄₇	C₂²×C₄	1	2	yes	complemented
98	SD₁₆×C₄₇	—	2	2	no	—
99	SD₁₆×C₄₇	—	2	2	no	—
100	D₈×C₄₇	—	2	1	no	—
101	D₈×C₄₇	C₂²×C₄	1	2	yes	complemented
102	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
106	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
107	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	4	1	no	—
110	(C₂×D₄₇)⋊C₄	—	4	4	no	—
111	C₄×Dic₄₇	—	2	1	no	—
112	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
113	#10625329	—	2	2	no	—
114	#10625329	—	4	4	no	—
115	#10625329	—	4	1	no	—
116	C₂×C₄₇⋊C₈	—	2	1	no	—
117	C₂×C₄₇⋊C₈	—	2	1	no	—
118	C₂×C₄₇⋊C₈	—	4	4	no	—
119	C₂×C₄₇⋊C₈	—	4	1	no	—
120	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
121	D₃₇₆	—	2	2	no	—
122	D₃₇₆	—	2	2	no	—
123	D₃₇₆	—	2	2	no	—
124	D₃₇₆	C₂²×C₄	1	4	yes	—
125	C₁₆×C₄₇	—	2	2	no	—
126	C₄₇⋊C₁₆	C₂²×C₄	1	4	yes	complemented
127	C₂³×C₄₇	—	4	1	no	—
128	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
129	C₂²×D₄₇	—	4	2	no	—
130	C₂²×D₄₇	—	4	2	no	—
131	C₂²×D₄₇	—	4	2	no	—
132	C₂²×D₄₇	—	8	2	no	—
133	C₂²×D₄₇	—	8	2	no	—
134	Q₈×C₄₇	—	2	2	no	—
135	Q₈×C₄₇	—	4	1	no	—
136	D₄×C₄₇	—	2	2	no	—
137	D₄×C₄₇	—	4	2	no	—
138	D₄×C₄₇	—	4	2	no	—
139	D₄×C₄₇	—	4	1	no	—
140	C₂×C₄×C₄₇	—	4	1	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	8	2	no	—
145	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	4	2	no	—
153	D₁₈₈	—	2	4	no	—
154	D₁₈₈	—	4	2	no	—
155	D₁₈₈	—	4	2	no	—
156	D₁₈₈	—	4	2	no	—
157	C₄×D₄₇	—	8	8	no	—
158	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
159	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
161	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₄₇⋊C₈	—	2	2	no	—
163	C₄₇⋊C₈	—	4	2	no	—
164	C₂×AGL(1,ℤ/16)	—	47	1	no	maximal, Sylow
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	4	2	no	—
167	C₂²×C₄₇	—	8	2	no	—
168	C₂²×C₄₇	#442	1	1	yes	characteristic
169	C₂²×C₄₇	#442	1	1	yes	characteristic
170	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×D₄₇	—	4	4	no	—
172	C₂×D₄₇	—	8	2	no	—
173	C₂×D₄₇	—	8	2	no	—
174	C₂×D₄₇	—	8	4	no	—
175	C₂×D₄₇	—	8	4	no	—
176	C₄×C₄₇	—	4	2	no	—
177	C₄×C₄₇	—	8	2	no	—
178	C₄×C₄₇	#442	1	1	yes	characteristic
179	C₄×C₄₇	#442	1	1	yes	characteristic
180	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
181	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
182	Dic₄₇	—	4	2	no	—
183	C₂×#509	—	47	1	no	—
184	C₂×#444	—	47	1	no	—
185	C₂×#442	—	47	1	no	—
186	AGL(1,ℤ/16)	—	47	8	no	—
187	C₂×#365	—	47	1	no	—
188	C₂×#361	—	47	1	no	—
189	C₂×#360	D₄₇	1	1	yes	characteristic, complemented
190	C₂×#347	—	47	1	no	—
191	C₂×C₄₇	—	2	1	no	—
192	C₂×C₄₇	—	2	1	no	—
193	C₂×C₄₇	—	8	2	no	—
194	C₂×C₄₇	AGL(1,ℤ/16)	1	2	yes	complemented
195	C₂×C₄₇	C₂×#442	1	1	yes	characteristic
196	D₄₇	—	8	4	no	—
197	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
198	C₂²×D₈	—	47	1	no	—
199	C₂×#131	—	94	1	no	—
200	C₂×C₄×D₄	—	94	1	no	—
201	#509	—	47	4	no	—
202	#509	—	47	4	no	—
203	C₂×SD₃₂	—	47	2	no	—
204	C₂×D₁₆	—	47	2	no	—
205	C₂×M₃₂	—	47	1	no	—
206	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
207	#444	—	47	4	no	—
208	#444	—	94	2	no	—
209	#442	—	47	4	no	—
210	#442	—	94	2	no	—
211	C₂×#108	—	47	1	no	—
212	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
213	C₂×#104	—	94	1	no	—
214	C₂×#102	—	94	1	no	—
215	C₂×#97	—	47	1	no	—
216	#365	—	47	4	no	—
217	#361	—	47	4	no	—
218	#360	C₂×D₄₇	1	4	yes	complemented
219	#347	—	47	4	no	—
220	C₄₇	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic, complemented, Sylow
221	C₂×#41	—	2	1	no	—
222	C₂²×D₄	—	94	1	no	—
223	C₂³×C₄	—	188	1	no	—
224	#135	—	2	1	no	—
225	#135	—	2	1	no	—
226	#135	C₄×D₄₇	1	2	yes	complemented
227	#135	C₂²×D₄₇	1	2	yes	—
228	C₂×Q₁₆	C₄×D₄₇	1	1	yes	characteristic, complemented
229	C₂×SD₁₆	—	2	1	no	—
230	C₂×D₈	—	47	2	no	—
231	C₂×D₈	—	47	2	no	—
232	C₂×D₈	—	47	2	no	—
233	C₂×D₈	—	94	1	no	—
234	C₂×D₈	—	94	1	no	—
235	C₂×D₈	—	94	1	no	—
236	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic, complemented
237	#131	—	94	4	no	—
238	#131	—	188	2	no	—
239	C₂×M₁₆	—	94	1	no	—
240	C₂×M₁₆	—	188	1	no	—
241	C₂²×C₈	—	47	1	no	—
242	C₂²×C₈	—	188	1	no	—
243	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
244	C₄×D₄	—	94	4	no	—
245	C₄×D₄	—	188	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₂²⋊C₄	—	188	1	no	—
248	C₂×C₄²	—	47	1	no	—
249	SD₃₂	—	47	8	no	—
250	D₁₆	—	47	8	no	—
251	M₃₂	—	2	1	no	—
252	M₃₂	—	47	2	no	—
253	M₃₂	—	47	2	no	—
254	M₃₂	C₂²×D₄₇	1	2	yes	—
255	C₂×C₁₆	—	2	1	no	—
256	C₂×C₁₆	—	47	2	no	—
257	#108	—	47	2	no	—
258	#108	—	94	1	no	—
259	#106	—	2	1	no	—
260	#106	C₂²×D₄₇	1	2	yes	—
261	#104	—	94	4	no	—
262	#102	—	94	4	no	—
263	#97	—	47	2	no	—
264	#97	—	47	2	no	—
265	C₂⁴	—	188	1	no	—
266	#41	—	2	2	no	—
267	#41	—	2	2	no	—
268	#41	—	4	1	no	—
269	#41	—	4	1	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂×D₄	—	94	2	no	—
274	C₂×D₄	—	94	2	no	—
275	C₂×D₄	—	94	2	no	—
276	C₂×D₄	—	188	1	no	—
277	C₂×D₄	—	188	1	no	—
278	C₂×D₄	—	188	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	94	1	no	—
282	C₂²×C₄	—	376	4	no	—
283	C₂²×C₄	—	188	4	no	—
284	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
285	Q₁₆	—	2	1	no	—
286	Q₁₆	C₂×C₄×D₄₇	1	2	yes	complemented
287	SD₁₆	—	2	2	no	—
288	SD₁₆	—	2	2	no	—
289	D₈	—	2	1	no	—
290	D₈	—	47	4	no	—
291	D₈	—	94	2	no	—
292	D₈	—	94	2	no	—
293	D₈	—	94	2	no	—
294	D₈	C₂×C₄×D₄₇	1	2	yes	complemented
295	M₁₆	—	94	2	no	—
296	M₁₆	—	188	4	no	—
297	M₁₆	—	188	1	no	—
298	C₂×C₈	—	47	2	no	—
299	C₂×C₈	—	94	1	no	—
300	C₂×C₈	—	94	1	no	—
301	C₂×C₈	—	188	4	no	—
302	C₂×C₈	—	188	1	no	—
303	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
304	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
305	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
306	C₂×C₈	#10625352	1	1	yes	characteristic
307	C₂×C₈	#10625352	1	1	yes	characteristic
308	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	188	4	no	—
312	C₄²	—	47	2	no	—
313	C₄²	—	94	1	no	—
314	C₁₆	—	2	2	no	—
315	C₁₆	—	47	4	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	376	2	no	—
318	C₂³	—	376	2	no	—
319	C₂³	—	188	2	no	—
320	C₂³	—	188	2	no	—
321	C₂³	—	188	2	no	—
322	C₂³	#13094048	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	4	1	no	—
325	D₄	—	2	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	94	4	no	—
330	D₄	—	188	2	no	—
331	D₄	—	188	2	no	—
332	D₄	—	188	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	—	94	2	no	—
339	C₂×C₄	—	376	8	no	—
340	C₂×C₄	—	188	2	no	—
341	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
342	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
343	C₂×C₄	#13094048	1	1	yes	characteristic
344	C₂×C₄	#13094051	1	1	yes	characteristic
345	C₂×C₄	#13094051	1	1	yes	characteristic
346	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
347	C₈	—	94	2	no	—
348	C₈	—	188	2	no	—
349	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
350	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
351	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
352	C₈	C₂×#10625352	1	1	yes	characteristic
353	C₂²	—	2	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	376	2	no	—
357	C₂²	—	376	2	no	—
358	C₂²	—	376	4	no	—
359	C₂²	—	376	4	no	—
360	C₂²	—	188	4	no	—
361	C₂²	#15689232	1	1	yes	characteristic
362	C₂²	#15689232	1	1	yes	characteristic
363	C₂²	C₂×#13094048	1	1	yes	characteristic
364	C₄	—	4	2	no	—
365	C₄	—	8	2	no	—
366	C₄	—	188	2	no	—
367	C₄	#15689232	1	1	yes	characteristic
368	C₄	#15689232	1	1	yes	characteristic
369	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
370	C₄	C₂×#13094051	1	1	yes	characteristic
371	C₂	—	2	1	no	—
372	C₂	—	2	1	no	—
373	C₂	—	8	2	no	—
374	C₂	—	376	4	no	—
375	C₂	#20245283	1	2	yes	direct product factor
376	C₂	C₂×#15689232	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689232
commutator	C₈×C₄₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₂×C₄₇×#360	C₂
socle	C₂²×C₄₇	#442
prime radical	C₂×#15689558	C₂
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	C₂×#360	D₄₇
hypocenter	C₄₇	C₂×AGL(1,ℤ/16)
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#360

Complements

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

N	H ≅ G/N	type
2. C₂×#15689245	C₂	semidirect
3. C₂×#15689234	C₂	semidirect
4. #20245283	C₂	direct (N × H)
5. C₂×#15688945	C₂	semidirect
6. C₂×#15688937	C₂	semidirect
7. C₂×#15688900	C₂	semidirect
8. C₂×C₄₇×#360	C₂	semidirect
12. #15689558	C₄	semidirect
14. C₂×#13093967	C₄	semidirect
15. C₂×#13093965	C₄	semidirect
18. #15689245	C₂²	semidirect
20. #15689234	C₂²	semidirect
25. #15688945	C₂²	semidirect
26. #15688937	C₂²	semidirect
27. #15688900	C₂²	semidirect
31. C₄₇×#360	C₂²	semidirect
50. #13093967	C₂×C₄	semidirect
51. #13093965	C₂×C₄	semidirect
52. #13093964	C₂×C₄	semidirect
54. C₂×C₄₇⋊C₁₆	C₂×C₄	semidirect
64. #135×C₄₇	C₂×C₄	semidirect
66. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
68. C₂×D₈×C₄₇	C₂×C₄	semidirect
97. Q₁₆×C₄₇	C₂²×C₄	semidirect
101. D₈×C₄₇	C₂²×C₄	semidirect
126. C₄₇⋊C₁₆	C₂²×C₄	semidirect
189. C₂×#360	D₄₇	semidirect
194. C₂×C₄₇	AGL(1,ℤ/16)	semidirect
218. #360	C₂×D₄₇	semidirect
220. C₄₇	C₂×AGL(1,ℤ/16)	semidirect
226. #135	C₄×D₄₇	semidirect
228. C₂×Q₁₆	C₄×D₄₇	semidirect
236. C₂×D₈	C₄×D₄₇	semidirect
286. Q₁₆	C₂×C₄×D₄₇	semidirect
294. D₈	C₂×C₄×D₄₇	semidirect
375. C₂	#20245283	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689558	2
C₂×#15689245	2
C₂×#15689234	2
#20245283	2
C₂×#15688945	2
C₂×#15688937	2
C₂×#15688900	2
C₂×C₄₇×#360	2
C₂×AGL(1,ℤ/16)	47

Subgroups — C2×#20245283 #26369716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245283 #26369716