Subgroups — M₁₆×#11929609 #34259689

Order 20224.

794 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11929609	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762283	C₂	1	2	yes	maximal, complemented
4	#23762229	C₂	1	2	yes	maximal, complemented
5	#23762227	C₂	1	2	yes	maximal, complemented
6	C₈×#11929609	C₂	1	2	yes	maximal, complemented
7	#23762158	C₂	1	1	yes	maximal, characteristic, complemented
8	#23761825	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761824	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×M₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11929609	C₄	1	1	yes	characteristic
13	C₂×M₁₆×D₇₉	—	2	1	no	—
14	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
15	C₄×#11929609	C₄	1	1	yes	characteristic
16	C₄×#11929609	C₄	1	1	yes	characteristic
17	C₄×#11929609	C₄	1	1	yes	characteristic
18	C₄×#11929609	C₄	1	1	yes	characteristic
19	C₄×#11929609	C₂²	1	1	yes	characteristic
20	C₄×#11929609	C₂²	1	1	yes	characteristic
21	C₄×#11929609	C₂²	1	1	yes	characteristic
22	C₄×#11929609	C₂²	1	1	yes	characteristic
23	#19098642	C₂²	1	2	yes	complemented
24	#19098636	—	2	2	no	—
25	C₈×D₃₁₆	C₂²	1	2	yes	complemented
26	#19098616	C₂²	1	1	yes	characteristic
27	C₂×#14579094	C₄	1	1	yes	characteristic
28	#19098587	C₂²	1	1	yes	characteristic
29	C₂×#14579082	C₄	1	1	yes	characteristic
30	C₂×#14579081	C₄	1	1	yes	characteristic
31	#19098526	—	2	1	no	—
32	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
33	#19098315	C₂²	1	2	yes	complemented
34	#19098315	C₂²	1	2	yes	complemented
35	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	complemented
36	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	complemented
37	#19098290	C₂²	1	2	yes	complemented
38	#19098290	C₂²	1	2	yes	complemented
39	#19098284	C₂²	1	2	yes	complemented
40	C₈×C₇₉⋊C₈	C₂²	1	2	yes	complemented
41	C₂²×M₁₆×C₇₉	—	2	1	no	—
42	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
43	#436×C₇₉	C₂²	1	2	yes	complemented
44	#435×C₇₉	—	2	2	no	—
45	C₈×D₄×C₇₉	C₂²	1	2	yes	complemented
46	#423×C₇₉	C₂²	1	1	yes	characteristic
47	#407×C₇₉	—	2	1	no	—
48	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
49	C₂²×D₃₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₇₉	—	2	1	no	—
51	C₂×#11929609	—	2	4	no	—
52	C₂×#11929609	C₂×C₄	1	1	yes	characteristic
53	C₂×#11929609	C₂×C₄	1	1	yes	characteristic
54	C₂×#11929609	C₂×C₄	1	1	yes	characteristic
55	C₂×#11929609	C₂×C₄	1	1	yes	characteristic
56	C₂×#11929608	—	2	1	no	—
57	C₂×#11929607	—	2	2	no	—
58	M₁₆×D₇₉	—	4	4	no	—
59	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₇₉	—	2	2	no	—
62	C₄×D₃₁₆	—	2	1	no	—
63	C₄×D₃₁₆	—	2	1	no	—
64	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
65	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
66	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
67	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
69	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
70	#14579094	C₂×C₄	1	1	yes	characteristic
71	#14579094	C₂×C₄	1	1	yes	characteristic
72	#14579094	C₂×C₄	1	1	yes	characteristic
73	#14579094	C₂×C₄	1	1	yes	characteristic
74	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
77	#14579082	C₂×C₄	1	1	yes	characteristic
78	#14579082	C₂×C₄	1	1	yes	characteristic
79	#14579082	C₂×C₄	1	1	yes	characteristic
80	#14579082	C₂×C₄	1	1	yes	characteristic
81	#14579081	C₂×C₄	1	1	yes	characteristic
82	#14579081	C₂×C₄	1	1	yes	characteristic
83	#14579081	C₂×C₄	1	1	yes	characteristic
84	#14579081	C₂×C₄	1	1	yes	characteristic
85	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
86	(C₂×D₇₉)⋊C₈	—	2	2	no	—
87	(C₂×D₇₉)⋊C₈	—	2	2	no	—
88	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
91	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
94	C₂³×C₄×C₇₉	—	2	1	no	—
95	C₂×M₁₆×C₇₉	—	2	1	no	—
96	C₂×M₁₆×C₇₉	—	2	2	no	—
97	C₂×M₁₆×C₇₉	—	4	4	no	—
98	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
99	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₇₉	—	2	2	no	—
101	C₄×D₄×C₇₉	—	2	1	no	—
102	C₄×D₄×C₇₉	—	2	1	no	—
103	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
109	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₇₉	—	2	1	no	—
111	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
112	C₂²⋊C₈×C₇₉	—	2	2	no	—
113	C₂²⋊C₈×C₇₉	—	2	2	no	—
114	#97×C₇₉	D₄	1	2	yes	—
115	C₄×C₈×C₇₉	C₂³	1	2	yes	—
116	C₂³×D₇₉	—	2	1	no	—
117	C₂×D₃₁₆	—	2	2	no	—
118	C₂×D₃₁₆	—	2	1	no	—
119	C₂×D₃₁₆	—	4	1	no	—
120	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
122	C₂²×Dic₇₉	—	2	1	no	—
123	C₂×C₄×D₇₉	—	2	1	no	—
124	C₂×C₄×D₇₉	—	2	1	no	—
125	C₂×C₄×D₇₉	—	2	1	no	—
126	C₂×C₄×D₇₉	—	2	1	no	—
127	C₂×C₄×D₇₉	—	4	2	no	—
128	C₂×C₄×D₇₉	—	4	2	no	—
129	#11929609	—	2	2	no	—
130	#11929609	—	2	2	no	—
131	#11929609	—	2	2	no	—
132	#11929609	M₁₆	1	4	yes	direct product factor
133	#11929608	—	4	2	no	—
134	#11929607	—	4	4	no	—
135	C₂×C₇₉⋊C₈	—	2	2	no	—
136	C₂×C₇₉⋊C₈	—	2	2	no	—
137	C₂×C₇₉⋊C₈	—	2	2	no	—
138	C₂×C₇₉⋊C₈	—	4	1	no	—
139	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	C₈×D₇₉	—	4	4	no	—
144	C₄⋊Dic₇₉	—	2	1	no	—
145	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
147	(C₂×D₇₉)⋊C₄	—	2	1	no	—
148	(C₂×D₇₉)⋊C₄	—	2	1	no	—
149	(C₂×D₇₉)⋊C₄	—	2	1	no	—
150	(C₂×D₇₉)⋊C₄	—	2	1	no	—
151	C₂⁴×C₇₉	—	2	1	no	—
152	C₂×D₄×C₇₉	—	2	2	no	—
153	C₂×D₄×C₇₉	—	2	1	no	—
154	C₂×D₄×C₇₉	—	4	1	no	—
155	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₉	—	2	1	no	—
158	C₂²×C₄×C₇₉	—	2	1	no	—
159	C₂²×C₄×C₇₉	—	2	1	no	—
160	C₂²×C₄×C₇₉	—	2	1	no	—
161	C₂²×C₄×C₇₉	—	2	1	no	—
162	C₂²×C₄×C₇₉	—	4	2	no	—
163	C₂²×C₄×C₇₉	—	4	2	no	—
164	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
167	M₁₆×C₇₉	—	2	2	no	—
168	M₁₆×C₇₉	—	4	4	no	—
169	M₁₆×C₇₉	—	4	2	no	—
170	M₁₆×C₇₉	D₈	1	4	yes	complemented
171	C₂×C₈×C₇₉	—	2	2	no	—
172	C₂×C₈×C₇₉	—	4	4	no	—
173	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₇₉	—	2	1	no	—
176	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
177	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
178	C₂²⋊C₄×C₇₉	—	2	1	no	—
179	C₂²⋊C₄×C₇₉	—	2	1	no	—
180	C₂²⋊C₄×C₇₉	—	2	1	no	—
181	C₂²⋊C₄×C₇₉	—	2	1	no	—
182	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₇₉	#41	1	1	yes	characteristic
185	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
186	C₂³×C₇₉	—	2	1	no	—
187	C₂³×C₇₉	—	2	1	no	—
188	C₂³×C₇₉	—	4	2	no	—
189	C₂³×C₇₉	—	4	2	no	—
190	C₂³×C₇₉	—	8	1	no	—
191	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
192	C₂²×D₇₉	—	2	1	no	—
193	C₂²×D₇₉	—	2	1	no	—
194	C₂²×D₇₉	—	4	2	no	—
195	C₂²×D₇₉	—	4	2	no	—
196	C₂²×D₇₉	—	8	1	no	—
197	D₄×C₇₉	—	2	1	no	—
198	D₄×C₇₉	—	2	1	no	—
199	D₄×C₇₉	—	2	1	no	—
200	D₄×C₇₉	—	4	2	no	—
201	D₄×C₇₉	C₂×M₁₆	1	2	yes	complemented
202	C₂×C₄×C₇₉	—	2	1	no	—
203	C₂×C₄×C₇₉	—	2	1	no	—
204	C₂×C₄×C₇₉	—	2	1	no	—
205	C₂×C₄×C₇₉	—	2	1	no	—
206	C₂×C₄×C₇₉	—	4	1	no	—
207	C₂×C₄×C₇₉	—	4	2	no	—
208	C₂×C₄×C₇₉	—	4	1	no	—
209	C₂×C₄×C₇₉	—	4	1	no	—
210	C₂×C₄×C₇₉	—	4	1	no	—
211	C₂×C₄×C₇₉	—	4	1	no	—
212	C₂×C₄×C₇₉	—	4	2	no	—
213	C₂×C₄×C₇₉	—	4	2	no	—
214	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
218	C₂×C₄×C₇₉	#135	1	2	yes	—
219	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
222	C₂×Dic₇₉	—	2	1	no	—
223	C₂×Dic₇₉	—	2	1	no	—
224	C₂×Dic₇₉	—	4	2	no	—
225	D₃₁₆	—	2	1	no	—
226	D₃₁₆	—	2	1	no	—
227	D₃₁₆	—	2	1	no	—
228	D₃₁₆	—	4	2	no	—
229	D₃₁₆	C₂×M₁₆	1	2	yes	complemented
230	C₄×D₇₉	—	4	1	no	—
231	C₄×D₇₉	—	4	1	no	—
232	C₄×D₇₉	—	4	1	no	—
233	C₄×D₇₉	—	4	1	no	—
234	C₄×D₇₉	—	4	2	no	—
235	C₄×D₇₉	—	4	2	no	—
236	C₈×C₇₉	—	2	2	no	—
237	C₈×C₇₉	—	4	2	no	—
238	C₈×C₇₉	C₂×D₈	1	4	yes	complemented
239	C₇₉⋊C₈	—	2	1	no	—
240	C₇₉⋊C₈	—	2	1	no	—
241	C₇₉⋊C₈	—	2	1	no	—
242	C₇₉⋊C₈	—	4	2	no	—
243	C₇₉⋊C₈	—	4	2	no	—
244	C₇₉⋊C₈	C₂×M₁₆	1	2	yes	complemented
245	C₂²×C₇₉	—	2	1	no	—
246	C₂²×C₇₉	—	2	1	no	—
247	C₂²×C₇₉	—	2	2	no	—
248	C₂²×C₇₉	—	4	1	no	—
249	C₂²×C₇₉	—	4	1	no	—
250	C₂²×C₇₉	—	4	1	no	—
251	C₂²×C₇₉	—	4	1	no	—
252	C₂²×C₇₉	—	4	1	no	—
253	C₂²×C₇₉	—	8	4	no	—
254	C₂²×C₇₉	C₄×D₈	1	2	yes	—
255	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂×D₇₉	—	2	2	no	—
257	C₂×D₇₉	—	4	1	no	—
258	C₂×D₇₉	—	4	1	no	—
259	C₂×D₇₉	—	4	1	no	—
260	C₂×D₇₉	—	4	1	no	—
261	C₂×D₇₉	—	4	1	no	—
262	C₂×D₇₉	—	8	4	no	—
263	C₄×C₇₉	—	2	1	no	—
264	C₄×C₇₉	—	2	1	no	—
265	C₄×C₇₉	—	2	1	no	—
266	C₄×C₇₉	—	4	1	no	—
267	C₄×C₇₉	—	4	1	no	—
268	C₄×C₇₉	C₄×D₈	1	2	yes	—
269	C₄×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
270	C₄×C₇₉	#568	1	1	yes	characteristic
271	C₄×C₇₉	C₂²×D₈	1	1	yes	characteristic
272	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
273	Dic₇₉	—	4	1	no	—
274	Dic₇₉	—	4	1	no	—
275	M₁₆×D₈	—	79	1	no	maximal, Sylow
276	C₂×C₇₉	—	2	2	no	—
277	C₂×C₇₉	—	4	2	no	—
278	C₂×C₇₉	—	8	1	no	—
279	C₂×C₇₉	D₄×M₁₆	1	1	yes	characteristic
280	C₂×C₇₉	C₂×C₄×D₈	1	1	yes	characteristic
281	C₂×C₇₉	#2957	1	1	yes	characteristic
282	D₇₉	—	4	2	no	—
283	D₇₉	—	8	1	no	—
284	C₂×C₄×D₈	—	79	1	no	—
285	D₄×M₁₆	—	79	1	no	—
286	D₄×M₁₆	D₇₉	1	1	yes	characteristic, complemented
287	#1589	—	79	2	no	—
288	#1581	—	79	2	no	—
289	#1581	—	79	2	no	—
290	C₈×D₈	—	79	2	no	—
291	#1567	—	79	1	no	—
292	#1486	—	79	1	no	—
293	#1486	—	79	1	no	—
294	C₈×M₁₆	—	79	1	no	—
295	C₇₉	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
296	C₂²×D₈	—	79	1	no	—
297	C₂²×M₁₆	—	2	1	no	—
298	C₂²×M₁₆	—	158	1	no	—
299	C₂×C₄×D₄	—	79	1	no	—
300	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
301	C₄×D₈	—	79	1	no	—
302	C₄×D₈	—	79	1	no	—
303	C₄×D₈	—	79	1	no	—
304	C₄×D₈	—	79	1	no	—
305	C₄×D₈	—	79	1	no	—
306	C₄×D₈	—	79	1	no	—
307	C₄×D₈	—	79	1	no	—
308	C₄×D₈	—	79	1	no	—
309	#436	—	79	2	no	—
310	#436	C₂×D₇₉	1	2	yes	complemented
311	#435	—	2	2	no	—
312	#435	—	158	2	no	—
313	C₈×D₄	—	79	2	no	—
314	C₈×D₄	C₂×D₇₉	1	2	yes	complemented
315	#431	—	79	1	no	—
316	C₂×#107	—	79	1	no	—
317	#423	—	79	1	no	—
318	#423	C₂×D₇₉	1	1	yes	characteristic
319	C₂×#102	—	79	1	no	—
320	C₂×#102	—	79	1	no	—
321	#407	—	2	1	no	—
322	#407	—	158	1	no	—
323	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
324	C₂×C₄×C₈	—	79	1	no	—
325	#335	—	79	2	no	—
326	#335	—	79	2	no	—
327	D₄⋊C₈	—	79	2	no	—
328	D₄⋊C₈	—	79	2	no	—
329	D₄⋊C₈	—	79	2	no	—
330	D₄⋊C₈	—	79	2	no	—
331	#322	—	79	2	no	—
332	C₈²	—	79	2	no	—
333	C₂²×D₄	—	79	1	no	—
334	C₂²×D₄	C₄×D₇₉	1	1	yes	characteristic
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	158	1	no	—
337	C₂×D₈	—	79	1	no	—
338	C₂×D₈	—	79	1	no	—
339	C₂×D₈	—	79	1	no	—
340	C₂×D₈	—	79	1	no	—
341	C₂×D₈	—	158	4	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	2	no	—
344	C₂×M₁₆	—	4	4	no	—
345	C₂×M₁₆	—	316	4	no	—
346	C₂×M₁₆	—	158	1	no	—
347	C₂×M₁₆	—	158	2	no	—
348	C₂×M₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
349	C₂×M₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
350	C₂²×C₈	—	2	2	no	—
351	C₂²×C₈	—	79	1	no	—
352	C₂²×C₈	—	79	1	no	—
353	C₂²×C₈	—	158	2	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	79	1	no	—
357	C₄×D₄	—	79	1	no	—
358	C₄×D₄	—	79	1	no	—
359	C₄×D₄	—	79	1	no	—
360	C₄×D₄	—	158	1	no	—
361	C₄×D₄	—	158	1	no	—
362	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
363	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
364	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
365	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	79	1	no	—
367	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	158	1	no	—
370	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
371	#107	—	79	1	no	—
372	#107	—	79	1	no	—
373	#107	—	79	1	no	—
374	#107	—	79	1	no	—
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	79	2	no	—
377	C₄⋊C₈	—	158	1	no	—
378	C₄⋊C₈	—	158	1	no	—
379	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
380	#102	—	79	1	no	—
381	#102	—	79	1	no	—
382	#102	—	79	1	no	—
383	#102	—	79	1	no	—
384	#102	—	79	1	no	—
385	#102	—	79	1	no	—
386	#102	—	79	1	no	—
387	#102	—	79	1	no	—
388	C₂²⋊C₈	—	2	2	no	—
389	C₂²⋊C₈	—	2	2	no	—
390	C₂²⋊C₈	—	158	1	no	—
391	C₂²⋊C₈	—	158	2	no	—
392	C₂²⋊C₈	—	158	2	no	—
393	#97	C₂²⋊D₇₉	1	2	yes	—
394	C₄×C₈	—	79	1	no	—
395	C₄×C₈	—	79	1	no	—
396	C₄×C₈	—	79	1	no	—
397	C₄×C₈	—	79	1	no	—
398	C₄×C₈	—	79	2	no	—
399	C₄×C₈	C₂²×D₇₉	1	2	yes	—
400	C₂⁴	—	2	1	no	—
401	C₂⁴	—	158	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	316	1	no	—
406	C₂×D₄	—	79	1	no	—
407	C₂×D₄	—	79	1	no	—
408	C₂×D₄	—	158	2	no	—
409	C₂×D₄	—	158	1	no	—
410	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
411	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	316	2	no	—
420	C₂²×C₄	—	316	2	no	—
421	C₂²×C₄	—	158	1	no	—
422	C₂²×C₄	—	158	1	no	—
423	C₂²×C₄	—	158	1	no	—
424	C₂²×C₄	—	158	1	no	—
425	C₂²×C₄	—	158	1	no	—
426	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
428	C₂²×C₄	#11929624	1	1	yes	characteristic
429	D₈	—	79	4	no	—
430	D₈	—	158	2	no	—
431	D₈	—	158	2	no	—
432	D₈	—	158	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	4	2	no	—
435	M₁₆	—	4	4	no	—
436	M₁₆	—	316	2	no	—
437	M₁₆	—	316	4	no	—
438	M₁₆	#11929609	1	4	yes	direct product factor
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	4	no	—
441	C₂×C₈	—	316	4	no	—
442	C₂×C₈	—	316	1	no	—
443	C₂×C₈	—	79	1	no	—
444	C₂×C₈	—	79	1	no	—
445	C₂×C₈	—	79	1	no	—
446	C₂×C₈	—	79	1	no	—
447	C₂×C₈	—	158	2	no	—
448	C₂×C₈	—	158	2	no	—
449	C₂×C₈	—	158	2	no	—
450	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
451	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	79	1	no	—
454	C₄⋊C₄	—	79	1	no	—
455	C₄⋊C₄	—	158	1	no	—
456	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
457	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	158	1	no	—
463	C₂²⋊C₄	—	158	1	no	—
464	C₂²⋊C₄	—	158	1	no	—
465	C₂²⋊C₄	—	158	1	no	—
466	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
467	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
468	C₄²	#11929624	1	1	yes	characteristic
469	C₄²	C₂³×D₇₉	1	1	yes	characteristic
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	8	1	no	—
475	C₂³	—	316	2	no	—
476	C₂³	—	316	2	no	—
477	C₂³	—	632	1	no	—
478	C₂³	—	158	1	no	—
479	C₂³	—	158	1	no	—
480	C₂³	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
481	D₄	—	2	1	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	1	no	—
484	D₄	—	4	2	no	—
485	D₄	—	316	2	no	—
486	D₄	—	79	2	no	—
487	D₄	—	158	1	no	—
488	D₄	—	158	1	no	—
489	D₄	—	158	1	no	—
490	D₄	M₁₆×D₇₉	1	2	yes	complemented
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	316	2	no	—
504	C₂×C₄	—	316	2	no	—
505	C₂×C₄	—	316	2	no	—
506	C₂×C₄	—	316	1	no	—
507	C₂×C₄	—	316	1	no	—
508	C₂×C₄	—	316	1	no	—
509	C₂×C₄	—	316	1	no	—
510	C₂×C₄	—	158	1	no	—
511	C₂×C₄	—	158	1	no	—
512	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
513	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
514	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
515	C₂×C₄	C₂×#11929609	1	2	yes	—
516	C₂×C₄	#14579181	1	2	yes	—
517	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
518	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
519	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	4	2	no	—
522	C₈	—	316	2	no	—
523	C₈	—	316	2	no	—
524	C₈	—	79	2	no	—
525	C₈	—	158	1	no	—
526	C₈	—	158	1	no	—
527	C₈	—	158	1	no	—
528	C₈	C₂×#11929609	1	4	yes	complemented
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	8	4	no	—
538	C₂²	—	316	1	no	—
539	C₂²	—	316	1	no	—
540	C₂²	—	316	1	no	—
541	C₂²	—	316	1	no	—
542	C₂²	—	316	1	no	—
543	C₂²	—	632	4	no	—
544	C₂²	—	158	2	no	—
545	C₂²	C₄×#11929609	1	2	yes	—
546	C₂²	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	316	1	no	—
553	C₄	—	316	1	no	—
554	C₄	C₄×#11929609	1	2	yes	—
555	C₄	C₂×M₁₆×D₇₉	1	1	yes	characteristic
556	C₄	#19099329	1	1	yes	characteristic
557	C₄	C₂²×#11929609	1	1	yes	characteristic
558	C₄	C₂×#14579181	1	1	yes	characteristic
559	C₂	—	2	2	no	—
560	C₂	—	4	2	no	—
561	C₂	—	8	1	no	—
562	C₂	—	316	2	no	—
563	C₂	—	632	1	no	—
564	C₂	M₁₆×C₂²⋊D₇₉	1	1	yes	characteristic
565	C₂	C₂×C₄×#11929609	1	1	yes	characteristic
566	C₂	#23772315	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	D₄×M₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂²×#11929609	C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	D₄×M₁₆	D₇₉
hypocenter	C₇₉	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. M₁₆×D₃₁₆	C₂	semidirect
3. #23762283	C₂	semidirect
4. #23762229	C₂	semidirect
5. #23762227	C₂	semidirect
6. C₈×#11929609	C₂	semidirect
7. #23762158	C₂	semidirect
8. #23761825	C₂	semidirect
9. #23761824	C₂	semidirect
10. M₁₆×C₇₉⋊C₈	C₂	semidirect
11. D₄×M₁₆×C₇₉	C₂	semidirect
23. #19098642	C₂²	semidirect
25. C₈×D₃₁₆	C₂²	semidirect
33. #19098315	C₂²	semidirect
34. #19098315	C₂²	semidirect
35. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
36. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
37. #19098290	C₂²	semidirect
38. #19098290	C₂²	semidirect
39. #19098284	C₂²	semidirect
40. C₈×C₇₉⋊C₈	C₂²	semidirect
43. #436×C₇₉	C₂²	semidirect
45. C₈×D₄×C₇₉	C₂²	semidirect
132. #11929609	M₁₆	direct (N × H)
170. M₁₆×C₇₉	D₈	semidirect
201. D₄×C₇₉	C₂×M₁₆	semidirect
229. D₃₁₆	C₂×M₁₆	semidirect
238. C₈×C₇₉	C₂×D₈	semidirect
244. C₇₉⋊C₈	C₂×M₁₆	semidirect
286. D₄×M₁₆	D₇₉	semidirect
295. C₇₉	M₁₆×D₈	semidirect
310. #436	C₂×D₇₉	semidirect
314. C₈×D₄	C₂×D₇₉	semidirect
438. M₁₆	#11929609	direct (N × H)
490. D₄	M₁₆×D₇₉	semidirect
528. C₈	C₂×#11929609	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#11929609	2
M₁₆×D₃₁₆	2
#23762283	2
#23762229	2
#23762227	2
C₈×#11929609	2
#23762158	2
#23761825	2
#23761824	2
M₁₆×C₇₉⋊C₈	2
D₄×M₁₆×C₇₉	2
M₁₆×D₈	79

Subgroups — M16×#11929609 #34259689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×#11929609 #34259689