Subgroups — C₂×#23762152 #34257248

Order 20224.

834 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098616	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#23762152	C₂	1	8	yes	maximal, direct product factor
4	C₂×#19098316	C₂	1	2	yes	maximal, complemented
5	C₂×#19098314	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×M₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₇₉⋊C₈	—	2	1	no	—
8	#19098616	—	2	2	no	—
9	#19098616	C₂²	1	4	yes	—
10	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
11	C₂×C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
12	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
17	C₂×C₄×C₇₉⋊C₈	—	2	1	no	—
18	#19098316	C₂²	1	8	yes	complemented
19	#19098314	C₂²	1	8	yes	complemented
20	C₂²×M₁₆×C₇₉	C₄	1	1	yes	characteristic
21	C₂²×M₁₆×C₇₉	C₄	1	1	yes	characteristic
22	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
23	C₄×M₁₆×C₇₉	C₄	1	4	yes	—
24	C₄×M₁₆×C₇₉	C₂²	1	4	yes	—
25	C₂×#97×C₇₉	C₄	1	2	yes	—
26	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
27	C₂²×C₇₉⋊C₈	—	2	1	no	—
28	C₂²×C₇₉⋊C₈	—	2	1	no	—
29	C₂²×C₇₉⋊C₈	—	2	4	no	—
30	C₂²×C₇₉⋊C₈	—	2	2	no	—
31	C₂²×C₇₉⋊C₈	—	4	4	no	—
32	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
33	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
34	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
35	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
36	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
37	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
38	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
39	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
40	C₄×C₇₉⋊C₈	—	2	4	no	—
41	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₇₉	Q₈	1	1	yes	characteristic
44	C₂×M₁₆×C₇₉	—	2	4	no	—
45	C₂×M₁₆×C₇₉	C₈	1	8	yes	complemented
46	C₂×M₁₆×C₇₉	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₇₉	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₇₉	D₄	1	2	yes	—
54	C₂×C₄²×C₇₉	Q₈	1	1	yes	characteristic
55	C₂×C₄²×C₇₉	Q₈	1	2	yes	—
56	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
58	#97×C₇₉	C₂×C₄	1	8	yes	—
59	C₄×C₈×C₇₉	C₂×C₄	1	4	yes	—
60	C₄×C₈×C₇₉	C₂³	1	4	yes	—
61	C₂×C₇₉⋊C₈	—	2	2	no	—
62	C₂×C₇₉⋊C₈	—	2	2	no	—
63	C₂×C₇₉⋊C₈	—	2	4	no	—
64	C₂×C₇₉⋊C₈	—	4	8	no	—
65	C₂×C₇₉⋊C₈	—	4	2	no	—
66	C₂×C₇₉⋊C₈	—	4	4	no	—
67	C₂×C₇₉⋊C₈	—	4	2	no	—
68	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₇₉	—	2	2	no	—
70	C₂²×C₄×C₇₉	—	2	2	no	—
71	C₂²×C₄×C₇₉	—	4	2	no	—
72	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
75	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇₉	C₂×C₈	1	4	yes	—
79	C₂²×C₄×C₇₉	M₁₆	1	4	yes	—
80	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
86	M₁₆×C₇₉	—	2	8	no	—
87	M₁₆×C₇₉	C₂×C₈	1	16	yes	complemented
88	C₂×C₈×C₇₉	—	2	4	no	—
89	C₂×C₈×C₇₉	C₂×C₈	1	8	yes	complemented
90	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
91	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
92	C₄²×C₇₉	C₄⋊C₄	1	2	yes	—
93	C₄²×C₇₉	C₄⋊C₄	1	2	yes	—
94	C₄²×C₇₉	C₄⋊C₄	1	2	yes	—
95	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
96	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
97	C₄²×C₇₉	C₂×D₄	1	2	yes	—
98	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
99	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
100	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
101	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
102	C₂³×C₇₉	—	2	2	no	—
103	C₂³×C₇₉	—	2	2	no	—
104	C₂³×C₇₉	C₄⋊C₈	1	4	yes	—
105	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
106	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₇₉	—	2	2	no	—
108	C₂×C₄×C₇₉	—	2	2	no	—
109	C₂×C₄×C₇₉	—	2	2	no	—
110	C₂×C₄×C₇₉	—	2	2	no	—
111	C₂×C₄×C₇₉	—	2	2	no	—
112	C₂×C₄×C₇₉	—	2	4	no	—
113	C₂×C₄×C₇₉	—	4	2	no	—
114	C₂×C₄×C₇₉	—	4	2	no	—
115	C₂×C₄×C₇₉	C₄⋊C₈	1	8	yes	—
116	C₂×C₄×C₇₉	C₄⋊C₈	1	4	yes	—
117	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
119	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
120	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
121	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
124	C₂×C₄×C₇₉	C₂²×C₈	1	4	yes	—
125	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
126	C₂×C₄×C₇₉	C₂×M₁₆	1	4	yes	—
127	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
128	C₂×C₄×C₇₉	#137	1	2	yes	—
129	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
132	C₈×C₇₉	—	2	4	no	—
133	C₈×C₇₉	C₂²×C₈	1	8	yes	complemented
134	C₇₉⋊C₈	—	4	2	no	—
135	C₇₉⋊C₈	—	4	4	no	—
136	C₇₉⋊C₈	—	4	2	no	—
137	C₂²×C₇₉	—	2	8	no	—
138	C₂²×C₇₉	—	2	2	no	—
139	C₂²×C₇₉	—	2	2	no	—
140	C₂²×C₇₉	C₂×C₄⋊C₈	1	4	yes	—
141	C₂²×C₇₉	C₂×C₄⋊C₈	1	2	yes	—
142	C₂²×C₇₉	#428	1	2	yes	—
143	C₂²×C₇₉	#430	1	2	yes	—
144	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
145	C₄×C₇₉	—	2	2	no	—
146	C₄×C₇₉	—	2	2	no	—
147	C₄×C₇₉	—	2	1	no	—
148	C₄×C₇₉	—	2	1	no	—
149	C₄×C₇₉	C₂×C₄⋊C₈	1	2	yes	—
150	C₄×C₇₉	C₂×C₄⋊C₈	1	4	yes	—
151	C₄×C₇₉	#428	1	2	yes	—
152	C₄×C₇₉	C₂³×C₈	1	1	yes	characteristic
153	C₄×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
154	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
156	C₂×#1565	—	79	1	no	maximal, Sylow
157	C₂×C₇₉	—	2	4	no	—
158	C₂×C₇₉	#1565	1	4	yes	complemented
159	C₂×C₇₉	C₂²×C₄⋊C₈	1	1	yes	characteristic
160	C₂×C₇₉	C₂×#428	1	1	yes	characteristic
161	C₂×C₇₉	C₂×#430	1	1	yes	characteristic
162	C₂×#431	—	79	1	no	—
163	C₂²×C₄⋊C₈	—	79	1	no	—
164	C₂×C₄×M₁₆	D₇₉	1	1	yes	characteristic
165	#1565	—	79	8	no	—
166	C₂×#335	—	79	2	no	—
167	C₂×#334	—	79	2	no	—
168	C₇₉	C₂×#1565	1	1	yes	characteristic, complemented, Sylow
169	C₂²×M₁₆	Dic₇₉	1	1	yes	characteristic
170	C₂²×M₁₆	Dic₇₉	1	1	yes	characteristic
171	C₂³×C₈	—	158	1	no	—
172	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
173	#431	—	79	4	no	—
174	#431	—	158	2	no	—
175	C₂×C₄⋊C₈	—	79	1	no	—
176	C₂×C₄⋊C₈	—	79	2	no	—
177	C₂×C₄⋊C₈	—	79	1	no	—
178	C₂×C₄⋊C₈	—	79	4	no	—
179	C₂×C₄⋊C₈	—	158	2	no	—
180	C₂×C₄⋊C₈	—	158	1	no	—
181	C₂×C₂²⋊C₈	—	158	1	no	—
182	C₄×M₁₆	Dic₇₉	1	4	yes	—
183	C₄×M₁₆	C₂×D₇₉	1	4	yes	—
184	C₂×#97	Dic₇₉	1	2	yes	—
185	C₂×C₄×C₈	—	158	1	no	—
186	C₂×C₄×C₈	C₂×D₇₉	1	2	yes	—
187	#335	—	79	8	no	—
188	#334	—	79	8	no	—
189	C₂³×C₄	Dic₁₅₈	1	1	yes	characteristic
190	C₂³×C₄	D₃₁₆	1	1	yes	characteristic
191	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
192	C₂×M₁₆	—	2	4	no	—
193	C₂×M₁₆	C₇₉⋊C₈	1	8	yes	complemented
194	C₂×M₁₆	C₂×Dic₇₉	1	4	yes	—
195	C₂×M₁₆	C₂×Dic₇₉	1	4	yes	—
196	C₂²×C₈	—	316	4	no	—
197	C₂²×C₈	—	158	4	no	—
198	C₂²×C₈	—	158	2	no	—
199	C₂²×C₈	—	158	1	no	—
200	C₂²×C₈	—	158	1	no	—
201	C₂²×C₈	C₂×Dic₇₉	1	2	yes	—
202	C₂²×C₈	C₂×Dic₇₉	1	2	yes	—
203	C₂×C₄²	Dic₁₅₈	1	1	yes	characteristic
204	C₂×C₄²	Dic₁₅₈	1	2	yes	—
205	C₂×C₄²	D₃₁₆	1	2	yes	—
206	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
207	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
208	C₂×C₄²	C₂×Dic₇₉	1	2	yes	—
209	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
210	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
211	C₄⋊C₈	—	79	2	no	—
212	C₄⋊C₈	—	79	4	no	—
213	C₄⋊C₈	—	79	2	no	—
214	C₄⋊C₈	—	158	4	no	—
215	C₄⋊C₈	—	158	2	no	—
216	C₄⋊C₈	—	158	1	no	—
217	C₄⋊C₈	—	158	1	no	—
218	C₂²⋊C₈	—	158	4	no	—
219	#97	C₂×Dic₇₉	1	8	yes	—
220	C₄×C₈	—	158	4	no	—
221	C₄×C₈	C₂×Dic₇₉	1	4	yes	—
222	C₄×C₈	C₂²×D₇₉	1	4	yes	—
223	C₂⁴	C₄⋊Dic₇₉	1	1	yes	characteristic
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	4	2	no	—
227	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
228	C₂²×C₄	C₄⋊Dic₇₉	1	2	yes	—
229	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
230	C₂²×C₄	C₄⋊Dic₇₉	1	2	yes	—
231	C₂²×C₄	C₄⋊Dic₇₉	1	2	yes	—
232	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
233	C₂²×C₄	C₂×C₇₉⋊C₈	1	4	yes	—
234	C₂²×C₄	#11929608	1	4	yes	—
235	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
236	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
237	C₂²×C₄	C₂×D₃₁₆	1	2	yes	—
238	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
239	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
240	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
241	M₁₆	—	2	8	no	—
242	M₁₆	C₂×C₇₉⋊C₈	1	16	yes	complemented
243	C₂×C₈	—	2	4	no	—
244	C₂×C₈	—	316	8	no	—
245	C₂×C₈	—	316	4	no	—
246	C₂×C₈	—	316	2	no	—
247	C₂×C₈	—	316	2	no	—
248	C₂×C₈	—	158	2	no	—
249	C₂×C₈	—	158	2	no	—
250	C₂×C₈	—	158	4	no	—
251	C₂×C₈	C₂×C₇₉⋊C₈	1	8	yes	complemented
252	C₂×C₈	C₂²×Dic₇₉	1	4	yes	—
253	C₂×C₈	C₂²×Dic₇₉	1	4	yes	—
254	C₄²	C₄⋊Dic₇₉	1	2	yes	—
255	C₄²	C₄⋊Dic₇₉	1	2	yes	—
256	C₄²	C₄⋊Dic₇₉	1	2	yes	—
257	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
258	C₄²	C₂²×Dic₇₉	1	2	yes	—
259	C₄²	C₂×D₃₁₆	1	2	yes	—
260	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
261	C₄²	C₂×Dic₁₅₈	1	2	yes	—
262	C₄²	C₂×Dic₁₅₈	1	1	yes	characteristic
263	C₄²	C₂³×D₇₉	1	1	yes	characteristic
264	C₂³	—	2	2	no	—
265	C₂³	—	2	2	no	—
266	C₂³	C₄⋊(C₇₉⋊C₈)	1	4	yes	—
267	C₂³	C₂×C₄⋊Dic₇₉	1	2	yes	—
268	C₂³	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	4	no	—
275	C₂×C₄	—	4	2	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	C₄⋊(C₇₉⋊C₈)	1	8	yes	—
278	C₂×C₄	C₄⋊(C₇₉⋊C₈)	1	4	yes	—
279	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
280	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
281	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
282	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
283	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
284	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
285	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
286	C₂×C₄	C₂²×C₇₉⋊C₈	1	4	yes	—
287	C₂×C₄	C₂×#11929608	1	2	yes	—
288	C₂×C₄	C₂×#11929608	1	4	yes	—
289	C₂×C₄	#14579189	1	2	yes	—
290	C₂×C₄	#14579194	1	2	yes	—
291	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
292	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
293	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
294	C₈	—	2	4	no	—
295	C₈	—	316	4	no	—
296	C₈	—	316	2	no	—
297	C₈	—	316	2	no	—
298	C₈	C₂²×C₇₉⋊C₈	1	8	yes	complemented
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	8	no	—
302	C₂²	C₂×C₄⋊(C₇₉⋊C₈)	1	4	yes	—
303	C₂²	C₂×C₄⋊(C₇₉⋊C₈)	1	2	yes	—
304	C₂²	#19098605	1	2	yes	—
305	C₂²	#19098612	1	2	yes	—
306	C₂²	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
307	C₄	—	2	2	no	—
308	C₄	—	2	1	no	—
309	C₄	—	2	2	no	—
310	C₄	—	2	1	no	—
311	C₄	C₂×C₄⋊(C₇₉⋊C₈)	1	2	yes	—
312	C₄	C₂×C₄⋊(C₇₉⋊C₈)	1	4	yes	—
313	C₄	#19098605	1	2	yes	—
314	C₄	C₂³×C₇₉⋊C₈	1	1	yes	characteristic
315	C₄	C₂²×#11929608	1	1	yes	characteristic
316	C₄	C₂×#14579189	1	1	yes	characteristic
317	C₄	C₂×#14579194	1	1	yes	characteristic
318	C₂	—	2	4	no	—
319	C₂	#23762152	1	4	yes	direct product factor
320	C₂	C₂²×C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
321	C₂	C₂×#19098605	1	1	yes	characteristic
322	C₂	C₂×#19098612	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃₁₆
commutator	C₄×C₇₉	C₂³×C₈
Frattini	C₄²	C₂³×D₇₉
Fitting	C₂×C₄×M₁₆×C₇₉	C₂
socle	C₂³×C₇₉	C₂×C₄⋊C₄
prime radical	C₂⁴×C₇₉	C₄⋊C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₇₉
hypocenter	C₇₉	C₂×#1565
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #23762152	C₂	direct (N × H)
4. C₂×#19098316	C₂	semidirect
5. C₂×#19098314	C₂	semidirect
18. #19098316	C₂²	semidirect
19. #19098314	C₂²	semidirect
45. C₂×M₁₆×C₇₉	C₈	semidirect
87. M₁₆×C₇₉	C₂×C₈	semidirect
89. C₂×C₈×C₇₉	C₂×C₈	semidirect
133. C₈×C₇₉	C₂²×C₈	semidirect
158. C₂×C₇₉	#1565	semidirect
168. C₇₉	C₂×#1565	semidirect
193. C₂×M₁₆	C₇₉⋊C₈	semidirect
242. M₁₆	C₂×C₇₉⋊C₈	semidirect
251. C₂×C₈	C₂×C₇₉⋊C₈	semidirect
298. C₈	C₂²×C₇₉⋊C₈	semidirect
319. C₂	#23762152	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×#19098616	2
C₂²×C₄⋊(C₇₉⋊C₈)	2
#23762152	2
C₂×#19098316	2
C₂×#19098314	2
C₂×C₄×M₁₆×C₇₉	2
C₂×#1565	79

Subgroups — C2×#23762152 #34257248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23762152 #34257248