Subgroups — #34444938

Order 20224.

738 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₃₂×D₇₉	C₂	1	2	yes	maximal, complemented
2	Q₁₆×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#23775075	C₂	1	1	yes	maximal, characteristic
4	#23765655	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765495	C₂	1	2	yes	maximal, complemented
6	#23765446	C₂	1	1	yes	maximal, characteristic, complemented
7	#23765330	C₂	1	2	yes	maximal, complemented
8	#23765315	C₂	1	2	yes	maximal, complemented
9	C₄×#14579104	C₂	1	1	yes	maximal, characteristic, complemented
10	#23765219	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₇₉	C₂²	1	2	yes	complemented
13	C₂×D₈×D₇₉	C₂²	1	2	yes	—
14	Q₈×D₃₁₆	—	2	1	no	—
15	#19099198	—	2	1	no	—
16	C₂×#14579106	C₂²	1	2	yes	—
17	C₂×#14579105	C₂²	1	2	yes	complemented
18	C₂×#14579105	C₂²	1	2	yes	complemented
19	C₂×#14579104	C₂²	1	1	yes	characteristic
20	SD₃₂×D₇₉	—	2	8	no	—
21	C₂×C₁₆×D₇₉	C₂²	1	2	yes	complemented
22	#19098943	C₂²	1	1	yes	characteristic, complemented
23	#19098805	C₂²	1	2	yes	complemented
24	#19098796	C₂²	1	2	yes	—
25	#19098773	—	2	1	no	—
26	#19098755	—	2	1	no	—
27	#19098720	—	2	2	no	—
28	#19098695	—	2	2	no	—
29	C₄×D₆₃₂	C₂²	1	1	yes	characteristic
30	C₈×D₃₁₆	C₂²	1	1	yes	characteristic
31	#19098390	C₂²	1	1	yes	characteristic, complemented
32	#19098368	C₂²	1	2	yes	complemented
33	#19098367	C₂²	1	1	yes	characteristic, complemented
34	#19098363	C₂²	1	1	yes	characteristic
35	(C₂×D₇₉)⋊C₁₆	C₂²	1	2	yes	complemented
36	C₄×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
37	C₂×SD₃₂×C₇₉	C₂²	1	2	yes	complemented
38	#493×C₇₉	C₂²	1	1	yes	characteristic
39	C₄×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	C₄⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
41	#357×C₇₉	C₂²	1	2	yes	complemented
42	C₂×Q₈×D₇₉	—	2	2	no	—
43	C₂×D₄×D₇₉	—	2	2	no	—
44	C₂×D₄×D₇₉	—	4	1	no	—
45	C₂×Dic₃₁₆	—	2	1	no	—
46	C₂×Dic₃₁₆	C₂³	1	2	yes	—
47	C₂×#11929614	—	2	2	no	—
48	Q₁₆×D₇₉	—	2	4	no	—
49	Q₁₆×D₇₉	—	4	2	no	—
50	C₂×D₆₃₂	C₂³	1	1	yes	characteristic
51	C₂×#11929609	—	2	2	no	—
52	D₈×D₇₉	—	2	4	no	—
53	D₈×D₇₉	—	4	2	no	—
54	C₂×C₈×D₇₉	C₂³	1	2	yes	—
55	#14579161	—	2	1	no	—
56	#14579161	—	4	1	no	—
57	#14579141	—	2	2	no	—
58	#14579141	—	4	2	no	—
59	#14579132	—	2	2	no	—
60	#14579132	—	4	1	no	—
61	#14579129	—	4	2	no	—
62	C₄×D₃₁₆	—	2	1	no	—
63	C₄×D₃₁₆	—	4	1	no	—
64	C₄×D₃₁₆	D₄	1	1	yes	characteristic
65	#14579106	—	2	4	no	—
66	#14579105	—	2	4	no	—
67	#14579105	—	4	2	no	—
68	#14579104	D₄	1	4	yes	complemented
69	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
71	C₁₆×D₇₉	—	2	4	no	—
72	#14579095	C₂³	1	1	yes	characteristic
73	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
74	#14579084	—	2	2	no	—
75	#14579083	—	2	1	no	—
76	#14579082	—	2	2	no	—
77	(C₂×D₇₉)⋊C₈	D₄	1	2	yes	—
78	C₂×Q₁₆×C₇₉	C₂³	1	1	yes	characteristic
79	C₂×D₈×C₇₉	—	2	1	no	—
80	C₂×D₈×C₇₉	C₂³	1	2	yes	—
81	#127×C₇₉	—	2	1	no	—
82	C₄×Q₈×C₇₉	—	2	1	no	—
83	SD₃₂×C₇₉	—	2	4	no	—
84	C₂×C₁₆×C₇₉	C₂³	1	2	yes	—
85	#107×C₇₉	C₂³	1	1	yes	characteristic
86	#103×C₇₉	—	2	1	no	—
87	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
88	C₂³×D₇₉	—	4	2	no	—
89	C₂×Dic₁₅₈	—	2	2	no	—
90	C₂×Dic₁₅₈	—	4	2	no	—
91	Q₈×D₇₉	—	4	4	no	—
92	Q₈×D₇₉	—	8	2	no	—
93	C₂×D₃₁₆	—	2	1	no	—
94	C₂×D₃₁₆	D₈	1	1	yes	characteristic
95	C₂×C₂²⋊D₇₉	—	4	2	no	—
96	C₂×C₂²⋊D₇₉	—	4	2	no	—
97	D₄×D₇₉	—	4	4	no	—
98	D₄×D₇₉	—	8	2	no	—
99	D₄×D₇₉	—	8	4	no	—
100	C₂×C₄×D₇₉	—	4	2	no	—
101	C₂×C₄×D₇₉	—	4	1	no	—
102	C₂×C₄×D₇₉	C₂×D₄	1	2	yes	—
103	Dic₃₁₆	—	2	2	no	—
104	Dic₃₁₆	—	2	2	no	—
105	Dic₃₁₆	—	8	1	no	—
106	#11929614	—	4	4	no	—
107	D₆₃₂	—	2	1	no	—
108	D₆₃₂	C₂×D₄	1	2	yes	—
109	#11929609	—	4	4	no	—
110	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
111	C₈×D₇₉	—	2	2	no	—
112	C₈×D₇₉	—	2	2	no	—
113	C₄⋊Dic₇₉	—	2	1	no	—
114	C₄⋊Dic₇₉	—	4	2	no	—
115	C₄⋊Dic₇₉	—	4	1	no	—
116	C₄⋊Dic₇₉	—	4	1	no	—
117	C₄⋊Dic₇₉	D₈	1	1	yes	characteristic
118	C₂²⋊Dic₇₉	—	4	2	no	—
119	(C₂×D₇₉)⋊C₄	—	4	2	no	—
120	(C₂×D₇₉)⋊C₄	—	4	1	no	—
121	(C₂×D₇₉)⋊C₄	D₈	1	2	yes	—
122	C₇₉⋊C₁₆	—	2	1	no	—
123	C₇₉⋊C₁₆	C₂×D₄	1	2	yes	complemented
124	C₂×Q₈×C₇₉	—	2	1	no	—
125	C₂×D₄×C₇₉	—	2	2	no	—
126	C₂×D₄×C₇₉	—	4	1	no	—
127	C₂×D₄×C₇₉	—	4	1	no	—
128	Q₁₆×C₇₉	—	2	1	no	—
129	Q₁₆×C₇₉	C₂×D₄	1	2	yes	complemented
130	D₈×C₇₉	—	2	2	no	—
131	D₈×C₇₉	—	2	2	no	—
132	D₈×C₇₉	—	8	1	no	—
133	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
135	C₄⋊C₄×C₇₉	—	2	1	no	—
136	C₄⋊C₄×C₇₉	—	4	1	no	—
137	C₄²×C₇₉	—	4	1	no	—
138	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₁₆×C₇₉	—	2	2	no	—
140	C₂³×C₇₉	—	4	2	no	—
141	C₂²×D₇₉	—	4	1	no	—
142	C₂²×D₇₉	—	8	4	no	—
143	C₂²×D₇₉	—	8	4	no	—
144	C₂²×D₇₉	—	16	2	no	—
145	C₂²×D₇₉	C₂×D₈	1	2	yes	—
146	Q₈×C₇₉	—	2	2	no	—
147	Q₈×C₇₉	—	4	1	no	—
148	D₄×C₇₉	—	4	2	no	—
149	D₄×C₇₉	—	4	2	no	—
150	D₄×C₇₉	—	8	2	no	—
151	D₄×C₇₉	—	16	1	no	—
152	C₂×C₄×C₇₉	—	4	1	no	—
153	C₂×C₄×C₇₉	—	4	1	no	—
154	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
157	C₂²⋊D₇₉	—	8	4	no	—
158	C₂²⋊D₇₉	—	8	4	no	—
159	C₂×Dic₇₉	—	4	1	no	—
160	C₂×Dic₇₉	—	4	2	no	—
161	C₂×Dic₇₉	C₂×D₈	1	2	yes	—
162	D₃₁₆	—	2	2	no	—
163	D₃₁₆	—	4	1	no	—
164	D₃₁₆	SD₃₂	1	4	yes	complemented
165	C₄×D₇₉	—	2	2	no	—
166	C₄×D₇₉	—	2	2	no	—
167	C₄×D₇₉	—	8	4	no	—
168	C₄×D₇₉	—	8	2	no	—
169	Dic₁₅₈	—	4	2	no	—
170	Dic₁₅₈	—	4	2	no	—
171	Dic₁₅₈	—	8	4	no	—
172	C₈×C₇₉	—	2	1	no	—
173	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
174	C₈×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
175	C₇₉⋊C₈	—	2	2	no	—
176	C₂²×C₇₉	—	8	2	no	—
177	C₂²×C₇₉	—	8	2	no	—
178	C₂²×C₇₉	—	8	2	no	—
179	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
180	C₂×D₇₉	—	2	2	no	—
181	C₂×D₇₉	—	2	2	no	—
182	C₂×D₇₉	—	4	2	no	—
183	C₂×D₇₉	—	8	1	no	—
184	C₂×D₇₉	—	8	1	no	—
185	C₂×D₇₉	—	16	8	no	—
186	C₂×D₇₉	C₂×SD₃₂	1	4	yes	complemented
187	C₄×C₇₉	—	2	1	no	—
188	C₄×C₇₉	—	4	2	no	—
189	C₄×C₇₉	—	8	1	no	—
190	C₄×C₇₉	C₂×SD₃₂	1	2	yes	complemented
191	C₄×C₇₉	D₄²	1	1	yes	characteristic
192	C₄×C₇₉	#576	1	1	yes	characteristic
193	Dic₇₉	—	2	2	no	—
194	Dic₇₉	—	8	1	no	—
195	Dic₇₉	—	8	2	no	—
196	D₄×SD₃₂	—	79	1	no	maximal, Sylow
197	C₂×C₇₉	—	16	2	no	—
198	C₂×C₇₉	D₄×D₈	1	1	yes	characteristic
199	C₂×C₇₉	C₂²×SD₃₂	1	1	yes	characteristic
200	C₂×C₇₉	#3416	1	1	yes	characteristic
201	D₇₉	—	2	4	no	—
202	D₇₉	—	8	2	no	—
203	C₂²×SD₃₂	—	79	2	no	—
204	D₄×Q₁₆	—	79	1	no	—
205	D₄×D₈	—	79	1	no	—
206	#2248	—	79	1	no	—
207	#2217	—	79	2	no	—
208	#2208	—	79	1	no	—
209	#2207	D₇₉	1	1	yes	characteristic, complemented
210	#2187	—	79	2	no	—
211	#2185	—	79	2	no	—
212	C₄×SD₃₂	—	79	1	no	—
213	D₄×C₁₆	—	79	1	no	—
214	C₇₉	D₄×SD₃₂	1	1	yes	characteristic, complemented, Sylow
215	C₂²×Q₁₆	—	79	2	no	—
216	C₂²×D₈	—	79	2	no	—
217	D₄×Q₈	—	158	1	no	—
218	D₄²	—	158	1	no	—
219	C₂×SD₃₂	—	79	2	no	—
220	C₂×SD₃₂	—	79	1	no	—
221	C₂×SD₃₂	—	79	2	no	—
222	C₂×SD₃₂	—	79	2	no	—
223	C₂×SD₃₂	—	158	8	no	—
224	C₂×SD₃₂	C₂×D₇₉	1	2	yes	complemented
225	C₂²×C₁₆	—	79	2	no	—
226	#494	—	79	1	no	—
227	#493	C₂×D₇₉	1	1	yes	characteristic
228	#467	—	79	2	no	—
229	#466	—	79	2	no	—
230	#462	—	158	1	no	—
231	#459	—	158	1	no	—
232	#451	—	158	2	no	—
233	#447	—	158	2	no	—
234	C₄×Q₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
235	C₄×D₈	—	79	1	no	—
236	C₈×D₄	—	79	1	no	—
237	#367	—	79	1	no	—
238	C₄⋊C₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
239	#358	—	79	1	no	—
240	#358	—	79	2	no	—
241	#357	—	79	1	no	—
242	#357	C₂×D₇₉	1	2	yes	complemented
243	C₂²⋊C₁₆	—	79	2	no	—
244	C₄×C₁₆	—	79	1	no	—
245	C₂²×Q₈	—	158	2	no	—
246	C₂²×D₄	—	316	1	no	—
247	C₂²×D₄	—	158	2	no	—
248	C₂×Q₁₆	—	316	2	no	—
249	C₂×Q₁₆	—	79	2	no	—
250	C₂×Q₁₆	—	158	2	no	—
251	C₂×Q₁₆	—	158	4	no	—
252	C₂×Q₁₆	—	158	1	no	—
253	C₂×Q₁₆	C₂²×D₇₉	1	1	yes	characteristic
254	C₂×D₈	—	2	1	no	—
255	C₂×D₈	—	316	2	no	—
256	C₂×D₈	—	79	1	no	—
257	C₂×D₈	—	158	2	no	—
258	C₂×D₈	—	158	4	no	—
259	C₂×D₈	C₂²×D₇₉	1	2	yes	—
260	C₂²×C₈	—	79	2	no	—
261	C₄⋊Q₈	—	316	1	no	—
262	C₄⋊Q₈	—	158	1	no	—
263	#127	—	2	1	no	—
264	C₂²⋊Q₈	—	316	2	no	—
265	C₂²⋊Q₈	—	158	2	no	—
266	#121	—	316	1	no	—
267	#121	—	158	2	no	—
268	#120	—	316	2	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×D₄	—	316	1	no	—
271	C₄×D₄	—	79	1	no	—
272	C₄×D₄	—	158	1	no	—
273	SD₃₂	—	2	4	no	—
274	SD₃₂	—	316	2	no	—
275	SD₃₂	—	79	4	no	—
276	SD₃₂	—	158	4	no	—
277	SD₃₂	—	158	4	no	—
278	C₂×C₁₆	—	79	1	no	—
279	C₂×C₁₆	—	79	1	no	—
280	C₂×C₁₆	—	158	4	no	—
281	C₂×C₁₆	C₂²×D₇₉	1	2	yes	—
282	#107	—	79	1	no	—
283	#107	C₂²×D₇₉	1	1	yes	characteristic
284	C₄⋊C₈	—	79	1	no	—
285	#103	—	2	1	no	—
286	#103	—	158	2	no	—
287	#102	—	158	2	no	—
288	#102	—	158	1	no	—
289	C₂²⋊C₈	—	79	2	no	—
290	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
291	C₂⁴	—	316	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	316	2	no	—
294	C₂×Q₈	—	316	4	no	—
295	C₂×Q₈	—	632	2	no	—
296	C₂×Q₈	—	158	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	316	2	no	—
301	C₂×D₄	—	316	2	no	—
302	C₂×D₄	—	316	4	no	—
303	C₂×D₄	—	79	1	no	—
304	C₂×D₄	—	632	4	no	—
305	C₂×D₄	—	632	2	no	—
306	C₂×D₄	—	158	1	no	—
307	C₂²×C₄	—	316	2	no	—
308	C₂²×C₄	—	316	1	no	—
309	C₂²×C₄	—	79	2	no	—
310	Q₁₆	—	2	1	no	—
311	Q₁₆	—	316	4	no	—
312	Q₁₆	—	632	1	no	—
313	Q₁₆	—	158	2	no	—
314	Q₁₆	—	158	2	no	—
315	Q₁₆	D₄×D₇₉	1	2	yes	complemented
316	D₈	—	2	2	no	—
317	D₈	—	2	2	no	—
318	D₈	—	8	1	no	—
319	D₈	—	316	4	no	—
320	D₈	—	79	2	no	—
321	D₈	—	158	1	no	—
322	C₂×C₈	—	79	2	no	—
323	C₂×C₈	—	158	2	no	—
324	C₂×C₈	—	158	2	no	—
325	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
326	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	316	2	no	—
330	C₄⋊C₄	—	316	1	no	—
331	C₄⋊C₄	—	316	1	no	—
332	C₄⋊C₄	—	79	1	no	—
333	C₄⋊C₄	—	158	1	no	—
334	C₂²⋊C₄	—	316	2	no	—
335	C₂²⋊C₄	—	316	2	no	—
336	C₂²⋊C₄	—	316	1	no	—
337	C₂²⋊C₄	—	79	2	no	—
338	C₄²	—	4	1	no	—
339	C₄²	D₄×D₇₉	1	1	yes	characteristic
340	C₁₆	—	2	2	no	—
341	C₁₆	—	79	2	no	—
342	C₁₆	—	158	1	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	316	1	no	—
345	C₂³	—	79	2	no	—
346	C₂³	—	632	4	no	—
347	C₂³	—	632	4	no	—
348	C₂³	—	1264	2	no	—
349	Q₈	—	2	2	no	—
350	Q₈	—	4	1	no	—
351	Q₈	—	316	2	no	—
352	Q₈	—	316	2	no	—
353	Q₈	—	632	4	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	8	2	no	—
357	D₄	—	16	1	no	—
358	D₄	—	316	1	no	—
359	D₄	—	79	4	no	—
360	D₄	—	632	4	no	—
361	D₄	—	632	4	no	—
362	D₄	—	158	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	316	1	no	—
366	C₂×C₄	—	316	2	no	—
367	C₂×C₄	—	79	2	no	—
368	C₂×C₄	—	632	4	no	—
369	C₂×C₄	—	632	2	no	—
370	C₂×C₄	—	158	2	no	—
371	C₂×C₄	—	158	2	no	—
372	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
373	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	158	2	no	—
377	C₈	C₂×D₄×D₇₉	1	1	yes	characteristic
378	C₈	#14579207	1	1	yes	characteristic
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	316	2	no	—
383	C₂²	—	79	4	no	—
384	C₂²	—	632	1	no	—
385	C₂²	—	632	1	no	—
386	C₂²	—	158	2	no	—
387	C₂²	—	158	2	no	—
388	C₂²	—	1264	8	no	—
389	C₂²	C₂×D₈×D₇₉	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	8	1	no	—
393	C₄	—	632	2	no	—
394	C₄	—	632	1	no	—
395	C₄	—	158	2	no	—
396	C₄	SD₃₂×D₇₉	1	2	yes	complemented
397	C₄	#19099197	1	1	yes	characteristic
398	C₄	#19099367	1	1	yes	characteristic
399	C₂	—	16	2	no	—
400	C₂	—	632	2	no	—
401	C₂	—	158	4	no	—
402	C₂	#23775072	1	1	yes	characteristic
403	C₂	C₂×SD₃₂×D₇₉	1	1	yes	characteristic
404	C₂	#23776546	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₇₉×#2207	C₂
socle	C₂²×C₇₉	C₂²×D₈
prime radical	#23775075	C₂
hypercenter	#2207	D₇₉
hypocenter	C₇₉	D₄×SD₃₂
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2207

Complements

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

N	H ≅ G/N	type
1. C₂×SD₃₂×D₇₉	C₂	semidirect
2. Q₁₆×D₃₁₆	C₂	semidirect
4. #23765655	C₂	semidirect
5. #23765495	C₂	semidirect
6. #23765446	C₂	semidirect
7. #23765330	C₂	semidirect
8. #23765315	C₂	semidirect
9. C₄×#14579104	C₂	semidirect
10. #23765219	C₂	semidirect
11. C₇₉×#2207	C₂	semidirect
12. C₂×Q₁₆×D₇₉	C₂²	semidirect
17. C₂×#14579105	C₂²	semidirect
18. C₂×#14579105	C₂²	semidirect
21. C₂×C₁₆×D₇₉	C₂²	semidirect
22. #19098943	C₂²	semidirect
23. #19098805	C₂²	semidirect
31. #19098390	C₂²	semidirect
32. #19098368	C₂²	semidirect
33. #19098367	C₂²	semidirect
35. (C₂×D₇₉)⋊C₁₆	C₂²	semidirect
36. C₄×C₇₉⋊C₁₆	C₂²	semidirect
37. C₂×SD₃₂×C₇₉	C₂²	semidirect
39. C₄×Q₁₆×C₇₉	C₂²	semidirect
40. C₄⋊C₁₆×C₇₉	C₂²	semidirect
41. #357×C₇₉	C₂²	semidirect
68. #14579104	D₄	semidirect
123. C₇₉⋊C₁₆	C₂×D₄	semidirect
129. Q₁₆×C₇₉	C₂×D₄	semidirect
164. D₃₁₆	SD₃₂	semidirect
186. C₂×D₇₉	C₂×SD₃₂	semidirect
190. C₄×C₇₉	C₂×SD₃₂	semidirect
209. #2207	D₇₉	semidirect
214. C₇₉	D₄×SD₃₂	semidirect
224. C₂×SD₃₂	C₂×D₇₉	semidirect
234. C₄×Q₁₆	C₂×D₇₉	semidirect
238. C₄⋊C₁₆	C₂×D₇₉	semidirect
242. #357	C₂×D₇₉	semidirect
315. Q₁₆	D₄×D₇₉	semidirect
396. C₄	SD₃₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₃₂×D₇₉	2
Q₁₆×D₃₁₆	2
#23775075	2
#23765655	2
#23765495	2
#23765446	2
#23765330	2
#23765315	2
C₄×#14579104	2
#23765219	2
C₇₉×#2207	2
D₄×SD₃₂	79