Subgroups — C₂×#20274087 #27366338

Order 13568.

758 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810910	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810825	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₂₁₂	C₂	1	1	yes	maximal, characteristic
4	#20274087	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16810374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16810372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16810369	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#11719924	—	2	1	no	—
10	C₂²×C₈×D₅₃	—	2	1	no	—
11	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
12	#16810910	—	2	2	no	—
13	#16810910	C₂²	1	4	yes	—
14	#16810825	—	2	2	no	—
15	#16810825	C₂²	1	4	yes	—
16	C₈×D₂₁₂	—	2	2	no	—
17	C₈×D₂₁₂	C₂²	1	4	yes	—
18	C₂×#13133148	—	2	1	no	—
19	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
22	C₂×#13133141	—	2	1	no	—
23	C₂×#13133137	—	2	1	no	—
24	C₂×#13133129	—	2	1	no	—
25	#16810374	C₂²	1	4	yes	complemented
26	#16810372	C₂²	1	4	yes	complemented
27	#16810369	C₂²	1	4	yes	complemented
28	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₅₃×#498	—	2	2	no	—
31	C₅₃×#498	C₂²	1	4	yes	complemented
32	C₂×#106×C₅₃	—	2	1	no	—
33	C₂×#106×C₅₃	—	2	1	no	—
34	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₂²×D₂₁₂	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₅₃	—	2	1	no	—
37	C₂×#11719924	—	2	4	no	—
38	C₂×#11719924	—	4	4	no	—
39	C₂²×#88322	—	2	1	no	—
40	C₂²×#88322	—	2	1	no	—
41	C₂²×#88322	—	2	1	no	—
42	C₂×C₈×D₅₃	—	2	4	no	—
43	C₂×C₈×D₅₃	—	4	4	no	—
44	C₄×D₂₁₂	—	2	1	no	—
45	C₄×D₂₁₂	—	2	1	no	—
46	C₄×D₂₁₂	D₄	1	2	yes	—
47	C₄×D₂₁₂	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₅₃	D₄	1	1	yes	characteristic
49	C₂×#11719921	—	2	1	no	—
50	#13133148	—	2	4	no	—
51	C₄⋊#88322	—	2	1	no	—
52	C₄⋊#88322	—	2	1	no	—
53	C₄⋊#88322	—	2	1	no	—
54	C₄⋊#88322	C₂³	1	2	yes	—
55	C₄⋊#88322	C₂³	1	2	yes	—
56	C₄⋊#88322	C₂³	1	2	yes	—
57	#13133141	—	2	4	no	—
58	#13133137	—	2	4	no	—
59	#13133129	—	2	4	no	—
60	C₂²×Q₈×C₅₃	—	2	1	no	—
61	C₂²×Q₈×C₅₃	—	2	1	no	—
62	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₅₃	—	2	1	no	—
65	C₄⋊Q₈×C₅₃	—	2	1	no	—
66	C₄⋊Q₈×C₅₃	—	2	1	no	—
67	C₄⋊Q₈×C₅₃	—	2	1	no	—
68	C₄⋊Q₈×C₅₃	—	2	1	no	—
69	C₄⋊Q₈×C₅₃	—	2	1	no	—
70	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
71	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
76	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
77	#106×C₅₃	—	2	4	no	—
78	#106×C₅₃	—	2	4	no	—
79	C₄×C₈×C₅₃	D₄	1	2	yes	—
80	C₄×C₈×C₅₃	C₂³	1	2	yes	—
81	C₂³×D₅₃	—	2	1	no	—
82	C₂×Q₈×C₅₃	—	2	2	no	—
83	C₂×Q₈×C₅₃	—	2	2	no	—
84	C₂×Q₈×C₅₃	—	4	1	no	—
85	C₂×Q₈×C₅₃	—	4	1	no	—
86	C₂×Q₈×C₅₃	—	4	2	no	—
87	C₂×Q₈×C₅₃	—	4	2	no	—
88	C₂×Q₈×C₅₃	—	8	2	no	—
89	C₂²×C₄×C₅₃	—	4	1	no	—
90	C₂²×C₄×C₅₃	—	4	1	no	—
91	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
94	C₂²×Dic₅₃	—	2	1	no	—
95	C₂×D₂₁₂	—	2	1	no	—
96	C₂×D₂₁₂	—	2	2	no	—
97	C₂×D₂₁₂	SD₁₆	1	4	yes	—
98	C₂×D₂₁₂	C₂×D₄	1	2	yes	—
99	C₂×C₄×D₅₃	—	2	2	no	—
100	C₂×C₄×D₅₃	—	2	2	no	—
101	C₂×C₄×D₅₃	—	4	2	no	—
102	C₂×C₄×D₅₃	—	4	2	no	—
103	C₂×C₈×C₅₃	—	2	2	no	—
104	C₂×C₈×C₅₃	SD₁₆	1	4	yes	complemented
105	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
107	C₄⋊C₄×C₅₃	—	2	2	no	—
108	C₄⋊C₄×C₅₃	—	2	2	no	—
109	C₄⋊C₄×C₅₃	—	2	2	no	—
110	C₄⋊C₄×C₅₃	—	2	2	no	—
111	C₄⋊C₄×C₅₃	—	4	1	no	—
112	C₄⋊C₄×C₅₃	—	4	1	no	—
113	C₄⋊C₄×C₅₃	—	4	1	no	—
114	C₄⋊C₄×C₅₃	—	4	1	no	—
115	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₅₃	#41	1	1	yes	characteristic
118	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
119	#11719924	—	4	8	no	—
120	#11719921	—	2	2	no	—
121	#11719921	—	2	2	no	—
122	C₄⋊Dic₅₃	—	2	1	no	—
123	C₄⋊Dic₅₃	C₂×D₄	1	2	yes	—
124	C₂×#88322	—	2	2	no	—
125	C₂×#88322	—	2	2	no	—
126	C₂×#88322	—	2	2	no	—
127	C₂×#88322	—	4	2	no	—
128	C₂×#88322	—	4	2	no	—
129	C₂×#88322	—	4	2	no	—
130	C₈×D₅₃	—	4	8	no	—
131	C₂³×C₅₃	#121	1	1	yes	characteristic
132	C₂²×D₅₃	—	2	2	no	—
133	C₂²×D₅₃	—	2	4	no	—
134	C₂²×D₅₃	—	4	2	no	—
135	C₂²×D₅₃	—	4	2	no	—
136	Q₈×C₅₃	—	4	2	no	—
137	Q₈×C₅₃	—	4	2	no	—
138	Q₈×C₅₃	—	8	2	no	—
139	Q₈×C₅₃	—	8	2	no	—
140	Q₈×C₅₃	—	8	2	no	—
141	C₂×C₄×C₅₃	—	2	2	no	—
142	C₂×C₄×C₅₃	—	4	2	no	—
143	C₂×C₄×C₅₃	—	4	2	no	—
144	C₂×C₄×C₅₃	—	8	2	no	—
145	C₂×C₄×C₅₃	—	8	2	no	—
146	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
147	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
148	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
150	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
151	C₂×C₄×C₅₃	#135	1	2	yes	—
152	C₂×C₄×C₅₃	#137	1	2	yes	—
153	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
156	C₂×Dic₅₃	—	2	2	no	—
157	C₂×Dic₅₃	—	4	2	no	—
158	D₂₁₂	—	2	2	no	—
159	D₂₁₂	—	2	4	no	—
160	D₂₁₂	C₂×SD₁₆	1	4	yes	—
161	C₄×D₅₃	—	4	2	no	—
162	C₄×D₅₃	—	4	2	no	—
163	C₄×D₅₃	—	4	4	no	—
164	C₈×C₅₃	—	2	2	no	—
165	C₈×C₅₃	C₂×SD₁₆	1	4	yes	complemented
166	#88322	—	4	2	no	—
167	#88322	—	4	2	no	—
168	#88322	—	4	2	no	—
169	C₂×#1671	—	53	1	no	maximal, Sylow
170	C₂²×C₅₃	#461	1	2	yes	—
171	C₂²×C₅₃	#465	1	2	yes	—
172	C₂²×C₅₃	#471	1	2	yes	—
173	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
174	C₂×D₅₃	—	2	4	no	—
175	C₂×D₅₃	—	4	8	no	—
176	C₂×D₅₃	—	4	2	no	—
177	C₂×D₅₃	—	4	2	no	—
178	C₄×C₅₃	—	2	1	no	—
179	C₄×C₅₃	—	2	1	no	—
180	C₄×C₅₃	—	8	2	no	—
181	C₄×C₅₃	—	8	2	no	—
182	C₄×C₅₃	#461	1	2	yes	—
183	C₄×C₅₃	#465	1	2	yes	—
184	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
185	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
186	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
187	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
188	Dic₅₃	—	4	2	no	—
189	C₂×#498	D₅₃	1	1	yes	characteristic, complemented
190	C₂×#476	—	53	1	no	—
191	C₂×#461	—	53	1	no	—
192	C₂×C₈×D₄	—	53	1	no	—
193	#1671	—	53	8	no	—
194	C₂×#334	—	53	1	no	—
195	C₂×#333	—	53	1	no	—
196	C₂×#332	—	53	1	no	—
197	C₂×C₅₃	#1671	1	4	yes	complemented
198	C₂×C₅₃	C₂×#461	1	1	yes	characteristic
199	C₂×C₅₃	C₂×#465	1	1	yes	characteristic
200	C₂×C₅₃	C₂×#471	1	1	yes	characteristic
201	D₅₃	—	4	4	no	—
202	C₂²×SD₁₆	—	106	1	no	—
203	C₂³×C₈	—	106	1	no	—
204	C₂×C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
206	C₂×C₄×D₄	—	53	1	no	—
207	#498	—	2	2	no	—
208	#498	C₂×D₅₃	1	4	yes	complemented
209	#476	—	53	4	no	—
210	#476	—	106	2	no	—
211	#461	—	53	4	no	—
212	#461	—	106	2	no	—
213	C₈×D₄	—	53	4	no	—
214	C₈×D₄	—	106	2	no	—
215	C₂×#106	—	2	1	no	—
216	C₂×#106	—	2	1	no	—
217	C₂×#106	—	106	1	no	—
218	C₂×C₄⋊C₈	—	53	1	no	—
219	C₂×C₄⋊C₈	—	53	1	no	—
220	C₂×C₄⋊C₈	—	53	1	no	—
221	C₂×#103	—	106	1	no	—
222	C₂×#102	—	106	1	no	—
223	C₂×C₂²⋊C₈	—	106	1	no	—
224	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
225	#334	—	53	4	no	—
226	#333	—	53	4	no	—
227	#332	—	53	4	no	—
228	C₅₃	C₂×#1671	1	1	yes	characteristic, complemented, Sylow
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×D₄	—	53	1	no	—
232	C₂³×C₄	—	106	1	no	—
233	C₂×SD₁₆	—	106	4	no	—
234	C₂×SD₁₆	—	212	4	no	—
235	C₂²×C₈	—	106	1	no	—
236	C₂²×C₈	—	106	1	no	—
237	C₂²×C₈	—	106	1	no	—
238	C₂²×C₈	—	106	4	no	—
239	C₂²×C₈	—	212	4	no	—
240	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
241	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
249	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
250	C₄×D₄	—	53	2	no	—
251	C₄×D₄	—	53	2	no	—
252	C₄×D₄	—	106	1	no	—
253	C₄×D₄	—	106	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	53	1	no	—
259	C₂×C₂²⋊C₄	—	106	1	no	—
260	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
261	#106	—	2	4	no	—
262	#106	—	2	4	no	—
263	#106	—	106	4	no	—
264	C₄⋊C₈	—	53	2	no	—
265	C₄⋊C₈	—	53	2	no	—
266	C₄⋊C₈	—	53	2	no	—
267	C₄⋊C₈	—	106	1	no	—
268	C₄⋊C₈	—	106	1	no	—
269	C₄⋊C₈	—	106	1	no	—
270	#103	—	106	4	no	—
271	#102	—	106	4	no	—
272	C₂²⋊C₈	—	106	4	no	—
273	C₄×C₈	C₂²⋊D₅₃	1	2	yes	—
274	C₄×C₈	C₂²×D₅₃	1	2	yes	—
275	C₂⁴	—	106	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	—	8	2	no	—
283	C₂×D₄	—	53	4	no	—
284	C₂×D₄	—	53	2	no	—
285	C₂×D₄	—	106	1	no	—
286	C₂×D₄	—	106	2	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	106	1	no	—
290	C₂²×C₄	—	106	2	no	—
291	C₂²×C₄	—	106	2	no	—
292	C₂²×C₄	—	212	2	no	—
293	C₂²×C₄	—	212	2	no	—
294	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
295	C₂²×C₄	#11719947	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
297	SD₁₆	—	212	8	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	106	2	no	—
300	C₂×C₈	—	106	2	no	—
301	C₂×C₈	—	106	2	no	—
302	C₂×C₈	—	212	2	no	—
303	C₂×C₈	—	212	2	no	—
304	C₂×C₈	—	212	2	no	—
305	C₂×C₈	—	212	8	no	—
306	C₂×C₈	#11719924	1	4	yes	complemented
307	C₂×C₈	C₂×C₂²⋊D₅₃	1	2	yes	—
308	C₂×C₈	C₂×C₂²⋊D₅₃	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	53	2	no	—
318	C₄⋊C₄	—	106	1	no	—
319	C₂²⋊C₄	—	106	2	no	—
320	C₂²⋊C₄	—	106	2	no	—
321	C₄²	D₄×D₅₃	1	1	yes	characteristic
322	C₄²	#11719947	1	1	yes	characteristic
323	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
324	C₄²	C₂³×D₅₃	1	1	yes	characteristic
325	C₂³	—	106	4	no	—
326	C₂³	—	106	2	no	—
327	C₂³	—	212	2	no	—
328	C₂³	—	212	2	no	—
329	C₂³	#13133188	1	1	yes	characteristic
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	8	2	no	—
333	Q₈	—	8	2	no	—
334	Q₈	—	8	2	no	—
335	D₄	—	53	4	no	—
336	D₄	—	106	4	no	—
337	D₄	—	106	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	8	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	106	2	no	—
344	C₂×C₄	—	212	2	no	—
345	C₂×C₄	—	212	4	no	—
346	C₂×C₄	—	212	2	no	—
347	C₂×C₄	—	212	2	no	—
348	C₂×C₄	#13133188	1	1	yes	characteristic
349	C₂×C₄	#13133188	1	1	yes	characteristic
350	C₂×C₄	#13133188	1	1	yes	characteristic
351	C₂×C₄	SD₁₆×D₅₃	1	2	yes	—
352	C₂×C₄	C₂×#11719924	1	2	yes	—
353	C₂×C₄	#13133238	1	2	yes	—
354	C₂×C₄	#13133248	1	2	yes	—
355	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
357	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
358	C₈	—	2	2	no	—
359	C₈	—	212	2	no	—
360	C₈	—	212	2	no	—
361	C₈	—	212	2	no	—
362	C₈	C₂×#11719924	1	4	yes	complemented
363	C₂²	—	106	4	no	—
364	C₂²	—	212	8	no	—
365	C₂²	—	212	2	no	—
366	C₂²	—	212	2	no	—
367	C₂²	#16810825	1	2	yes	—
368	C₂²	#16810849	1	2	yes	—
369	C₂²	#16810883	1	2	yes	—
370	C₂²	C₂×#13133188	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	212	2	no	—
376	C₄	#16810825	1	2	yes	—
377	C₄	#16810849	1	2	yes	—
378	C₄	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
379	C₄	C₂²×#11719924	1	1	yes	characteristic
380	C₄	C₂×#13133238	1	1	yes	characteristic
381	C₄	C₂×#13133248	1	1	yes	characteristic
382	C₂	—	212	4	no	—
383	C₂	#20274087	1	4	yes	direct product factor
384	C₂	C₂×#16810825	1	1	yes	characteristic
385	C₂	C₂×#16810849	1	1	yes	characteristic
386	C₂	C₂×#16810883	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13133188
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₂×C₅₃×#498	C₂
socle	C₂³×C₅₃	#121
prime radical	C₂²×D₂₁₂	D₄
hypercenter	C₂×#498	D₅₃
hypocenter	C₅₃	C₂×#1671
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#498

Complements

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

N	H ≅ G/N	type
4. #20274087	C₂	direct (N × H)
5. C₂×#16810374	C₂	semidirect
6. C₂×#16810372	C₂	semidirect
7. C₂×#16810369	C₂	semidirect
8. C₂×C₅₃×#498	C₂	semidirect
25. #16810374	C₂²	semidirect
26. #16810372	C₂²	semidirect
27. #16810369	C₂²	semidirect
31. C₅₃×#498	C₂²	semidirect
104. C₂×C₈×C₅₃	SD₁₆	semidirect
165. C₈×C₅₃	C₂×SD₁₆	semidirect
189. C₂×#498	D₅₃	semidirect
197. C₂×C₅₃	#1671	semidirect
208. #498	C₂×D₅₃	semidirect
228. C₅₃	C₂×#1671	semidirect
306. C₂×C₈	#11719924	semidirect
362. C₈	C₂×#11719924	semidirect
383. C₂	#20274087	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×#16810910	2
C₂×#16810825	2
C₂×C₈×D₂₁₂	2
#20274087	2
C₂×#16810374	2
C₂×#16810372	2
C₂×#16810369	2
C₂×C₅₃×#498	2
C₂×#1671	53

Subgroups — C2×#20274087 #27366338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20274087 #27366338