Subgroups — #34347187

Order 20224.

690 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773940	C₂	1	1	yes	maximal, characteristic, complemented
2	#23773253	C₂	1	2	yes	maximal
3	#23771997	C₂	1	1	yes	maximal, characteristic
4	#23764905	C₂	1	2	yes	maximal, complemented
5	#23764744	C₂	1	2	yes	maximal, complemented
6	#23764186	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763627	C₂	1	2	yes	maximal
8	#23763560	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763461	C₂	1	1	yes	maximal, characteristic
10	#23763237	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579167	C₂²	1	1	yes	characteristic
13	#19099191	C₂²	1	2	yes	—
14	#19099043	C₂²	1	2	yes	—
15	#19098970	—	2	2	no	—
16	#19098967	—	2	1	no	—
17	#19098964	—	2	1	no	—
18	#19098871	—	2	2	no	—
19	#19098864	—	2	2	no	—
20	#19098859	—	2	2	no	—
21	#19098844	—	2	2	no	—
22	#19098606	C₂²	1	2	yes	—
23	#19098606	C₂²	1	2	yes	—
24	#19098605	C₂²	1	2	yes	—
25	#19098602	—	2	2	no	—
26	#19098600	—	2	1	no	—
27	C₂×#14579095	C₂²	1	1	yes	characteristic
28	C₂×#14579095	C₂²	1	2	yes	—
29	C₂×#14579095	C₂²	1	1	yes	characteristic
30	#107×D₇₉	—	2	1	no	—
31	C₂×#14579089	C₂²	1	1	yes	characteristic
32	#19098565	C₂²	1	2	yes	—
33	#19098560	C₂²	1	1	yes	characteristic
34	#19098518	C₂²	1	1	yes	characteristic
35	#19098433	C₂²	1	2	yes	—
36	#19098331	C₂²	1	2	yes	—
37	#19098331	C₂²	1	2	yes	—
38	#19098328	C₂²	1	1	yes	characteristic
39	#19098323	C₂²	1	1	yes	characteristic
40	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
41	#427×C₇₉	C₂²	1	1	yes	characteristic
42	#424×C₇₉	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
44	#339×C₇₉	C₂²	1	2	yes	—
45	C₂×#11929624	C₂³	1	1	yes	characteristic
46	#14579167	—	2	2	no	—
47	#14579167	Q₈	1	4	yes	complemented
48	C₂×#11929608	C₂³	1	1	yes	characteristic
49	C₂×#11929608	C₂³	1	1	yes	characteristic
50	C₂×#11929607	—	2	1	no	—
51	C₂×C₈×D₇₉	—	2	1	no	—
52	#14579161	—	2	2	no	—
53	#14579160	—	2	2	no	—
54	#14579153	—	2	2	no	—
55	#14579152	—	2	2	no	—
56	#14579138	—	4	2	no	—
57	C₄×Dic₁₅₈	—	2	2	no	—
58	C₄×D₃₁₆	—	2	2	no	—
59	(C₂²⋊D₇₉)⋊C₄	—	4	2	no	—
60	#14579120	C₂³	1	1	yes	characteristic
61	#14579119	—	2	2	no	—
62	C₂×C₄⋊Dic₇₉	—	4	2	no	—
63	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
65	C₄⋊C₄×D₇₉	—	2	2	no	—
66	#14579095	—	2	1	no	—
67	#14579095	—	2	1	no	—
68	#14579095	—	2	2	no	—
69	#14579095	—	2	1	no	—
70	#14579095	—	2	1	no	—
71	#14579095	—	2	2	no	—
72	#14579095	—	2	2	no	—
73	#14579094	—	2	2	no	—
74	#14579094	—	2	2	no	—
75	#14579093	—	2	2	no	—
76	#14579092	—	2	2	no	—
77	#14579092	—	2	2	no	—
78	#14579089	Q₈	1	4	yes	complemented
79	#14579086	—	2	2	no	—
80	#14579086	D₄	1	1	yes	characteristic
81	#14579086	D₄	1	1	yes	characteristic
82	#14579083	—	2	2	no	—
83	#14579083	D₄	1	1	yes	characteristic
84	#14579083	D₄	1	1	yes	characteristic
85	#14579071	—	2	1	no	—
86	C₈×Dic₇₉	—	2	1	no	—
87	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
88	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
90	#117×C₇₉	C₂³	1	2	yes	—
91	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
92	#108×C₇₉	—	2	2	no	—
93	#107×C₇₉	D₄	1	1	yes	characteristic
94	#107×C₇₉	D₄	1	1	yes	characteristic
95	#106×C₇₉	D₄	1	2	yes	—
96	C₄⋊C₈×C₇₉	—	2	2	no	—
97	C₄⋊C₈×C₇₉	—	2	2	no	—
98	C₄×C₈×C₇₉	—	2	2	no	—
99	#11929624	—	2	1	no	—
100	#11929624	—	2	1	no	—
101	#11929624	C₂×Q₈	1	2	yes	—
102	#11929624	C₂×Q₈	1	2	yes	—
103	C₂×Dic₁₅₈	—	4	2	no	—
104	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
105	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₇₉	—	2	1	no	—
107	C₂²×Dic₇₉	—	2	2	no	—
108	C₂²×Dic₇₉	—	2	2	no	—
109	C₂×C₄×D₇₉	—	2	1	no	—
110	C₂×C₄×D₇₉	—	4	2	no	—
111	#11929608	—	2	1	no	—
112	#11929608	—	2	1	no	—
113	#11929608	C₂×Q₈	1	2	yes	—
114	#11929608	C₂×Q₈	1	2	yes	—
115	#11929607	—	2	4	no	—
116	C₂×C₇₉⋊C₈	—	2	1	no	—
117	C₂×C₇₉⋊C₈	—	2	1	no	—
118	C₈×D₇₉	—	2	4	no	—
119	C₄⋊Dic₇₉	—	2	2	no	—
120	C₄⋊Dic₇₉	—	2	2	no	—
121	C₄⋊Dic₇₉	—	2	2	no	—
122	C₄⋊Dic₇₉	—	2	2	no	—
123	C₄⋊Dic₇₉	—	4	2	no	—
124	C₄⋊Dic₇₉	—	8	4	no	—
125	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
126	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
127	Dic₇₉⋊C₄	—	4	2	no	—
128	Dic₇₉⋊C₄	—	4	2	no	—
129	Dic₇₉⋊C₄	—	4	2	no	—
130	C₂²⋊Dic₇₉	—	2	1	no	—
131	(C₂×D₇₉)⋊C₄	—	4	2	no	—
132	C₄×Dic₇₉	—	2	1	no	—
133	C₄×Dic₇₉	—	4	2	no	—
134	C₂²×C₄×C₇₉	—	2	1	no	—
135	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
136	M₁₆×C₇₉	—	2	2	no	—
137	M₁₆×C₇₉	—	2	2	no	—
138	C₂×C₈×C₇₉	—	2	2	no	—
139	C₂×C₈×C₇₉	—	2	1	no	—
140	C₂×C₈×C₇₉	—	2	1	no	—
141	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
146	C₂×C₈×C₇₉	#41	1	2	yes	—
147	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₇₉	—	2	2	no	—
150	C₄²×C₇₉	—	2	2	no	—
151	C₄²×C₇₉	—	2	1	no	—
152	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
153	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂²×D₇₉	—	2	1	no	—
155	C₂×C₄×C₇₉	—	2	2	no	—
156	C₂×C₄×C₇₉	—	2	2	no	—
157	C₂×C₄×C₇₉	—	2	2	no	—
158	C₂×C₄×C₇₉	—	2	2	no	—
159	C₂×C₄×C₇₉	—	2	2	no	—
160	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
166	C₂²⋊D₇₉	—	2	2	no	—
167	C₂²⋊D₇₉	—	2	2	no	—
168	C₂×Dic₇₉	—	2	1	no	—
169	C₂×Dic₇₉	—	2	1	no	—
170	C₂×Dic₇₉	—	2	1	no	—
171	C₂×Dic₇₉	—	4	2	no	—
172	C₂×Dic₇₉	—	4	2	no	—
173	C₂×Dic₇₉	—	8	2	no	—
174	C₂×Dic₇₉	—	8	2	no	—
175	D₃₁₆	—	2	1	no	—
176	D₃₁₆	C₄⋊Q₈	1	2	yes	—
177	C₄×D₇₉	—	2	2	no	—
178	C₄×D₇₉	—	2	2	no	—
179	C₄×D₇₉	—	16	2	no	—
180	Dic₁₅₈	—	2	1	no	—
181	Dic₁₅₈	—	16	2	no	—
182	Dic₁₅₈	C₄⋊Q₈	1	2	yes	—
183	C₈×C₇₉	—	2	1	no	—
184	C₈×C₇₉	—	2	1	no	—
185	C₈×C₇₉	—	4	2	no	—
186	C₈×C₇₉	C₂²⋊Q₈	1	2	yes	—
187	C₈×C₇₉	C₂²⋊Q₈	1	2	yes	—
188	C₇₉⋊C₈	—	2	2	no	—
189	C₇₉⋊C₈	—	2	2	no	—
190	C₂²×C₇₉	—	2	1	no	—
191	C₂²×C₇₉	—	2	1	no	—
192	C₂²×C₇₉	#544	1	1	yes	characteristic
193	C₂²×C₇₉	D₄²	1	1	yes	characteristic
194	C₂²×C₇₉	#554	1	1	yes	characteristic
195	C₂×D₇₉	—	2	2	no	—
196	C₂×D₇₉	—	4	1	no	—
197	C₂×D₇₉	—	4	1	no	—
198	C₄×C₇₉	—	2	4	no	—
199	C₄×C₇₉	—	4	2	no	—
200	C₄×C₇₉	—	4	2	no	—
201	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₄×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
203	C₄×C₇₉	#547	1	1	yes	characteristic
204	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
205	Dic₇₉	—	2	2	no	—
206	Dic₇₉	—	4	1	no	—
207	Dic₇₉	—	4	1	no	—
208	Dic₇₉	—	8	2	no	—
209	Dic₇₉	—	8	2	no	—
210	#26083	—	79	1	no	maximal, Sylow
211	C₂×C₇₉	—	2	1	no	—
212	C₂×C₇₉	—	2	1	no	—
213	C₂×C₇₉	#2440	1	1	yes	characteristic
214	C₂×C₇₉	#3292	1	1	yes	characteristic
215	C₂×C₇₉	#3293	1	1	yes	characteristic
216	D₇₉	—	4	2	no	—
217	#3164	—	79	1	no	—
218	#3083	—	79	2	no	—
219	#2913	—	79	1	no	—
220	#2089	—	79	2	no	—
221	#2060	—	79	2	no	—
222	#1952	—	79	1	no	—
223	#1945	D₇₉	1	1	yes	characteristic, complemented
224	#1859	—	79	2	no	—
225	#1845	—	79	1	no	—
226	#1816	—	79	1	no	—
227	#1764	—	79	1	no	—
228	C₇₉	#26083	1	1	yes	characteristic, complemented, Sylow
229	C₂×#131	—	79	1	no	—
230	#544	—	79	2	no	—
231	#520	—	79	2	no	—
232	#501	—	158	2	no	—
233	#500	—	158	1	no	—
234	#499	—	158	1	no	—
235	#479	—	158	2	no	—
236	#478	—	158	2	no	—
237	#477	—	158	2	no	—
238	#474	—	158	2	no	—
239	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
240	#428	—	79	2	no	—
241	#428	—	79	2	no	—
242	#428	—	79	2	no	—
243	#428	—	158	2	no	—
244	#427	—	158	1	no	—
245	#427	C₂×D₇₉	1	1	yes	characteristic
246	C₂×#107	—	79	2	no	—
247	C₂×#107	—	79	1	no	—
248	C₂×#107	—	79	1	no	—
249	C₂×#107	—	158	1	no	—
250	#424	C₂×D₇₉	1	2	yes	—
251	C₂×#104	—	79	1	no	—
252	#417	—	79	2	no	—
253	#416	—	79	1	no	—
254	#405	—	79	1	no	—
255	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
256	#384	—	79	2	no	—
257	#343	—	79	2	no	—
258	#343	—	79	2	no	—
259	#341	—	79	1	no	—
260	#339	—	79	1	no	—
261	#339	C₂×D₇₉	1	2	yes	—
262	C₂×#41	—	79	1	no	—
263	#131	—	79	4	no	—
264	#131	—	158	2	no	—
265	C₂×M₁₆	—	79	1	no	—
266	C₂×M₁₆	—	79	1	no	—
267	C₂×M₁₆	—	158	1	no	—
268	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
269	C₂²×C₈	—	158	1	no	—
270	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
272	C₄⋊Q₈	—	158	2	no	—
273	C₄⋊Q₈	—	158	2	no	—
274	#125	—	158	2	no	—
275	#125	—	158	2	no	—
276	C₂²⋊Q₈	—	316	2	no	—
277	C₄×Q₈	—	158	2	no	—
278	C₄×D₄	—	316	2	no	—
279	C₄×D₄	—	158	2	no	—
280	#117	—	79	1	no	—
281	#117	—	158	2	no	—
282	#117	C₂²×D₇₉	1	2	yes	—
283	C₂×C₄⋊C₄	—	316	2	no	—
284	C₂×C₄⋊C₄	—	79	2	no	—
285	C₂×C₄⋊C₄	—	79	2	no	—
286	C₂×C₄⋊C₄	—	158	2	no	—
287	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
288	#108	—	2	2	no	—
289	#107	—	158	2	no	—
290	#107	—	158	2	no	—
291	#107	—	158	2	no	—
292	#107	—	158	1	no	—
293	#107	—	158	1	no	—
294	#107	—	158	1	no	—
295	#107	—	158	1	no	—
296	#107	—	158	2	no	—
297	#107	—	158	2	no	—
298	#107	D₃₁₆	1	1	yes	characteristic
299	#107	D₃₁₆	1	1	yes	characteristic
300	#106	—	158	2	no	—
301	#106	—	158	2	no	—
302	#106	—	158	2	no	—
303	#106	D₃₁₆	1	2	yes	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	#104	—	79	4	no	—
307	#103	—	79	1	no	—
308	#103	—	79	1	no	—
309	#103	—	158	2	no	—
310	#102	—	79	1	no	—
311	#102	—	79	1	no	—
312	#102	—	158	2	no	—
313	#97	—	158	1	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	158	1	no	—
316	#41	—	79	2	no	—
317	#41	—	79	2	no	—
318	#41	—	158	1	no	—
319	#41	—	158	1	no	—
320	C₂×Q₈	—	316	2	no	—
321	C₂×Q₈	—	79	1	no	—
322	C₂×D₄	—	79	1	no	—
323	C₂×D₄	—	158	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	316	2	no	—
326	C₂²×C₄	—	158	2	no	—
327	C₂²×C₄	—	158	2	no	—
328	C₂²×C₄	—	158	1	no	—
329	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	79	2	no	—
333	M₁₆	—	79	2	no	—
334	M₁₆	—	158	1	no	—
335	M₁₆	—	158	1	no	—
336	M₁₆	—	158	4	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	158	1	no	—
341	C₂×C₈	—	158	1	no	—
342	C₂×C₈	—	158	4	no	—
343	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
344	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
345	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
346	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
347	C₂×C₈	Q₈×D₇₉	1	2	yes	—
348	C₂×C₈	#11929623	1	2	yes	—
349	C₄⋊C₄	—	316	2	no	—
350	C₄⋊C₄	—	316	2	no	—
351	C₄⋊C₄	—	316	2	no	—
352	C₄⋊C₄	—	316	2	no	—
353	C₄⋊C₄	—	79	1	no	—
354	C₄⋊C₄	—	79	1	no	—
355	C₄⋊C₄	—	632	4	no	—
356	C₄⋊C₄	—	158	2	no	—
357	C₄⋊C₄	—	158	2	no	—
358	C₄⋊C₄	—	158	2	no	—
359	C₄⋊C₄	—	158	2	no	—
360	C₄⋊C₄	C₂×D₃₁₆	1	2	yes	—
361	C₄⋊C₄	C₂×D₃₁₆	1	2	yes	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	316	2	no	—
364	C₂²⋊C₄	—	158	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	316	2	no	—
368	C₄²	—	158	1	no	—
369	C₄²	Q₈×D₇₉	1	2	yes	—
370	C₂³	—	158	1	no	—
371	C₂³	#14579207	1	1	yes	characteristic
372	Q₈	—	79	2	no	—
373	Q₈	—	158	1	no	—
374	Q₈	—	1264	2	no	—
375	D₄	—	79	2	no	—
376	D₄	—	158	2	no	—
377	D₄	—	158	2	no	—
378	D₄	—	158	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	316	2	no	—
385	C₂×C₄	—	316	2	no	—
386	C₂×C₄	—	632	2	no	—
387	C₂×C₄	—	632	2	no	—
388	C₂×C₄	—	158	1	no	—
389	C₂×C₄	—	158	1	no	—
390	C₂×C₄	—	158	1	no	—
391	C₂×C₄	—	158	2	no	—
392	C₂×C₄	—	158	2	no	—
393	C₂×C₄	—	1264	2	no	—
394	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
396	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
397	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
398	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
399	C₂×C₄	#14579208	1	1	yes	characteristic
400	C₈	—	2	1	no	—
401	C₈	—	2	1	no	—
402	C₈	—	4	2	no	—
403	C₈	—	158	2	no	—
404	C₈	—	158	2	no	—
405	C₈	#14579141	1	2	yes	—
406	C₈	#14579141	1	2	yes	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	316	1	no	—
410	C₂²	—	316	1	no	—
411	C₂²	—	158	2	no	—
412	C₂²	#19099193	1	1	yes	characteristic
413	C₂²	D₄×D₃₁₆	1	1	yes	characteristic
414	C₂²	#19099271	1	1	yes	characteristic
415	C₄	—	2	4	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	316	1	no	—
419	C₄	—	316	1	no	—
420	C₄	—	632	2	no	—
421	C₄	—	632	2	no	—
422	C₄	—	158	2	no	—
423	C₄	C₂×#14579141	1	1	yes	characteristic
424	C₄	C₄⋊Q₈×D₇₉	1	1	yes	characteristic
425	C₄	#19099213	1	1	yes	characteristic
426	C₄	Q₈×D₃₁₆	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	316	2	no	—
430	C₂	#23767100	1	1	yes	characteristic
431	C₂	#23775200	1	1	yes	characteristic
432	C₂	#23775205	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₁₆
commutator, cosocle	C₂²×C₄×C₇₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1945	C₂
socle	C₂²×C₇₉	D₄²
prime radical	C₂×#11929624	C₂³
hypercenter	#1945	D₇₉
hypocenter	C₇₉	#26083
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1945

Complements

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

N	H ≅ G/N	type
1. #23773940	C₂	semidirect
4. #23764905	C₂	semidirect
5. #23764744	C₂	semidirect
6. #23764186	C₂	semidirect
8. #23763560	C₂	semidirect
11. C₇₉×#1945	C₂	semidirect
47. #14579167	Q₈	semidirect
78. #14579089	Q₈	semidirect
223. #1945	D₇₉	semidirect
228. C₇₉	#26083	semidirect

Maximal subgroups

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

subgroup	index
#23773940	2
#23773253	2
#23771997	2
#23764905	2
#23764744	2
#23764186	2
#23763627	2
#23763560	2
#23763461	2
#23763237	2
C₇₉×#1945	2
#26083	79