Subgroups — #34271405

Order 20224.

714 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23774528	C₂	1	1	yes	maximal, characteristic, complemented
2	#23774318	C₂	1	1	yes	maximal, characteristic
3	#23772113	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762930	C₂	1	4	yes	maximal, complemented
5	#23762806	C₂	1	4	yes	maximal, complemented
6	#23762148	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762081	C₂	1	1	yes	maximal, characteristic, complemented
8	#23762068	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#486×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14579167	—	2	1	no	—
11	#19099113	C₂²	1	1	yes	characteristic
12	#19098959	—	2	1	no	—
13	#19098939	—	2	1	no	—
14	#19098911	—	2	1	no	—
15	#19098909	—	2	1	no	—
16	#19098881	—	2	2	no	—
17	#19098850	C₂²	1	4	yes	complemented
18	#19098755	C₂²	1	4	yes	—
19	#19098697	—	2	2	no	—
20	#19098642	—	2	1	no	—
21	#19098642	C₂²	1	2	yes	complemented
22	C₈×D₃₁₆	—	2	1	no	—
23	C₈×D₃₁₆	C₂²	1	2	yes	complemented
24	#19098616	C₂²	1	1	yes	characteristic
25	#19098616	C₂²	1	1	yes	characteristic
26	#19098587	C₂²	1	1	yes	characteristic
27	#19098529	—	2	1	no	—
28	#19098316	C₂²	1	2	yes	complemented
29	#19098314	C₂²	1	2	yes	complemented
30	#19098312	C₂²	1	4	yes	complemented
31	#19098307	C₂²	1	4	yes	—
32	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
34	#486×C₇₉	—	2	1	no	—
35	#486×C₇₉	—	2	1	no	—
36	#486×C₇₉	C₂²	1	2	yes	—
37	#486×C₇₉	C₂²	1	2	yes	—
38	C₂×#102×C₇₉	—	2	1	no	—
39	C₂×#102×C₇₉	—	2	1	no	—
40	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#11929624	—	2	1	no	—
42	C₂×#11929609	—	2	4	no	—
43	#14579167	—	4	4	no	—
44	C₂×#11929608	—	2	1	no	—
45	C₂×#11929607	—	2	2	no	—
46	C₂×C₈×D₇₉	—	2	2	no	—
47	#14579161	D₄	1	1	yes	characteristic
48	#14579158	D₄	1	1	yes	characteristic
49	#14579149	—	2	1	no	—
50	#14579135	—	2	1	no	—
51	#14579135	D₄	1	2	yes	—
52	C₄×D₃₁₆	—	2	1	no	—
53	C₄×D₃₁₆	C₂³	1	2	yes	—
54	#14579092	—	2	4	no	—
55	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
56	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
57	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
58	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
59	#14579082	—	2	4	no	—
60	#14579081	—	2	4	no	—
61	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
62	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
63	(C₂×D₇₉)⋊C₈	—	2	2	no	—
64	(C₂×D₇₉)⋊C₈	—	2	2	no	—
65	C₄×C₇₉⋊C₈	—	2	1	no	—
66	C₄×C₇₉⋊C₈	—	2	1	no	—
67	C₂²×Q₈×C₇₉	—	2	1	no	—
68	C₂²×D₄×C₇₉	—	2	1	no	—
69	C₂²×D₄×C₇₉	—	2	1	no	—
70	C₂²×D₄×C₇₉	—	2	1	no	—
71	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
73	C₄⋊Q₈×C₇₉	—	2	1	no	—
74	C₄⋊Q₈×C₇₉	—	2	1	no	—
75	C₄⋊Q₈×C₇₉	—	2	1	no	—
76	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
77	#127×C₇₉	—	2	1	no	—
78	#127×C₇₉	—	2	1	no	—
79	#127×C₇₉	—	2	1	no	—
80	#127×C₇₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
83	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
84	#102×C₇₉	—	2	2	no	—
85	#102×C₇₉	—	2	2	no	—
86	#102×C₇₉	—	2	2	no	—
87	#102×C₇₉	—	2	2	no	—
88	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
89	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
90	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
92	#11929624	—	4	2	no	—
93	#11929624	—	4	2	no	—
94	C₂×Dic₁₅₈	—	2	1	no	—
95	C₂×D₃₁₆	—	2	1	no	—
96	C₂×D₃₁₆	—	2	1	no	—
97	C₂×D₃₁₆	C₂×D₄	1	2	yes	—
98	C₂×C₂²⋊D₇₉	—	2	2	no	—
99	C₂×C₄×D₇₉	—	2	2	no	—
100	#11929609	—	8	4	no	—
101	#11929608	—	4	2	no	—
102	#11929607	—	4	4	no	—
103	C₂×C₇₉⋊C₈	—	2	2	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	—	2	2	no	—
106	C₈×D₇₉	—	4	4	no	—
107	C₄⋊Dic₇₉	—	2	1	no	—
108	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
109	(C₂×D₇₉)⋊C₄	—	2	2	no	—
110	(C₂×D₇₉)⋊C₄	—	2	2	no	—
111	C₂⁴×C₇₉	—	4	1	no	—
112	C₂×Q₈×C₇₉	—	2	2	no	—
113	C₂×Q₈×C₇₉	—	4	1	no	—
114	C₂×Q₈×C₇₉	—	8	2	no	—
115	C₂×D₄×C₇₉	—	2	2	no	—
116	C₂×D₄×C₇₉	—	2	2	no	—
117	C₂×D₄×C₇₉	—	2	2	no	—
118	C₂×D₄×C₇₉	—	4	1	no	—
119	C₂×D₄×C₇₉	—	4	1	no	—
120	C₂×D₄×C₇₉	—	4	1	no	—
121	C₂×D₄×C₇₉	—	4	2	no	—
122	C₂×D₄×C₇₉	—	4	2	no	—
123	C₂×D₄×C₇₉	—	8	2	no	—
124	C₂×D₄×C₇₉	—	8	2	no	—
125	C₂²×C₄×C₇₉	—	4	1	no	—
126	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
129	C₂×C₈×C₇₉	—	2	2	no	—
130	C₂×C₈×C₇₉	—	2	2	no	—
131	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₇₉	—	2	2	no	—
136	C₄⋊C₄×C₇₉	—	2	2	no	—
137	C₄⋊C₄×C₇₉	—	4	1	no	—
138	C₄⋊C₄×C₇₉	—	4	1	no	—
139	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₇₉	#41	1	1	yes	characteristic
142	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
143	C₂³×C₇₉	—	4	2	no	—
144	C₂³×C₇₉	—	8	2	no	—
145	C₂³×C₇₉	—	8	2	no	—
146	C₂³×C₇₉	—	8	2	no	—
147	C₂³×C₇₉	#121	1	1	yes	characteristic
148	C₂²×D₇₉	—	2	2	no	—
149	Q₈×C₇₉	—	8	2	no	—
150	Q₈×C₇₉	—	8	2	no	—
151	D₄×C₇₉	—	4	2	no	—
152	D₄×C₇₉	—	4	2	no	—
153	D₄×C₇₉	—	4	4	no	—
154	D₄×C₇₉	—	8	2	no	—
155	D₄×C₇₉	—	8	2	no	—
156	D₄×C₇₉	—	8	2	no	—
157	D₄×C₇₉	—	8	2	no	—
158	C₂×C₄×C₇₉	—	2	2	no	—
159	C₂×C₄×C₇₉	—	2	2	no	—
160	C₂×C₄×C₇₉	—	4	2	no	—
161	C₂×C₄×C₇₉	—	8	2	no	—
162	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₇₉	#135	1	2	yes	—
166	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
170	C₂²⋊D₇₉	—	4	4	no	—
171	C₂×Dic₇₉	—	2	2	no	—
172	D₃₁₆	—	2	4	no	—
173	D₃₁₆	—	4	2	no	—
174	D₃₁₆	—	4	2	no	—
175	C₄×D₇₉	—	4	2	no	—
176	C₄×D₇₉	—	4	2	no	—
177	Dic₁₅₈	—	4	2	no	—
178	C₈×C₇₉	—	2	1	no	—
179	C₈×C₇₉	—	2	1	no	—
180	C₈×C₇₉	—	2	1	no	—
181	C₈×C₇₉	—	2	1	no	—
182	C₇₉⋊C₈	—	4	2	no	—
183	C₇₉⋊C₈	—	4	2	no	—
184	C₇₉⋊C₈	—	4	2	no	—
185	C₂²×C₇₉	—	2	1	no	—
186	C₂²×C₇₉	—	2	1	no	—
187	C₂²×C₇₉	—	8	2	no	—
188	C₂²×C₇₉	—	8	2	no	—
189	C₂²×C₇₉	—	8	2	no	—
190	C₂²×C₇₉	—	16	4	no	—
191	C₂²×C₇₉	#463	1	2	yes	—
192	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
193	C₂×D₇₉	—	4	2	no	—
194	C₂×D₇₉	—	4	2	no	—
195	C₂×D₇₉	—	4	2	no	—
196	C₄×C₇₉	—	2	1	no	—
197	C₄×C₇₉	—	2	1	no	—
198	C₄×C₇₉	—	8	2	no	—
199	C₄×C₇₉	#463	1	2	yes	—
200	C₄×C₇₉	#472	1	2	yes	—
201	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
202	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₄×C₇₉	#577	1	2	yes	—
204	Dic₇₉	—	4	2	no	—
205	#19196	—	79	1	no	maximal, Sylow
206	C₂×C₇₉	—	2	2	no	—
207	C₂×C₇₉	—	16	2	no	—
208	C₂×C₇₉	C₂×#463	1	1	yes	characteristic
209	C₂×C₇₉	#3057	1	1	yes	characteristic
210	C₂×C₇₉	C₂×#472	1	1	yes	characteristic
211	D₇₉	—	8	2	no	—
212	#3227	—	79	1	no	—
213	#3205	—	79	1	no	—
214	C₂×#486	D₇₉	1	1	yes	characteristic, complemented
215	#2931	—	79	1	no	—
216	#1697	—	79	4	no	—
217	#1677	—	79	4	no	—
218	#1564	—	79	1	no	—
219	#1548	—	79	1	no	—
220	#1545	—	79	1	no	—
221	C₇₉	#19196	1	1	yes	characteristic, complemented, Sylow
222	C₂×#131	—	158	1	no	—
223	#532	—	79	1	no	—
224	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
225	C₂×#127	C₂×D₇₉	1	1	yes	characteristic
226	#498	—	158	1	no	—
227	#493	—	158	1	no	—
228	#486	—	2	1	no	—
229	#486	—	2	1	no	—
230	#486	—	158	1	no	—
231	#486	—	158	1	no	—
232	#486	C₂×D₇₉	1	2	yes	—
233	#486	C₂×D₇₉	1	2	yes	—
234	#481	—	158	2	no	—
235	#476	—	79	4	no	—
236	#459	—	79	4	no	—
237	#447	—	158	2	no	—
238	#436	—	79	2	no	—
239	#436	—	158	1	no	—
240	C₈×D₄	—	79	2	no	—
241	C₈×D₄	—	158	1	no	—
242	#431	—	79	1	no	—
243	#431	—	79	1	no	—
244	#423	—	79	1	no	—
245	C₂×#102	—	2	1	no	—
246	C₂×#102	—	2	1	no	—
247	#408	—	158	1	no	—
248	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
249	#335	—	79	2	no	—
250	#334	—	79	2	no	—
251	#333	—	79	4	no	—
252	#331	—	79	4	no	—
253	C₂×#41	—	158	1	no	—
254	C₂²×Q₈	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂×D₈	—	158	4	no	—
259	#131	—	316	4	no	—
260	C₂×M₁₆	—	158	1	no	—
261	C₂×M₁₆	—	158	2	no	—
262	C₂²×C₈	—	158	2	no	—
263	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
264	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	79	1	no	—
269	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	—	79	1	no	—
274	#127	C₂²×D₇₉	1	2	yes	—
275	#124	—	158	1	no	—
276	#121	—	79	2	no	—
277	#121	—	158	1	no	—
278	C₄×D₄	—	79	2	no	—
279	C₄×D₄	—	158	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
283	#106	—	158	4	no	—
284	C₄⋊C₈	—	79	2	no	—
285	C₄⋊C₈	—	79	2	no	—
286	C₄⋊C₈	—	79	2	no	—
287	C₄⋊C₈	—	158	1	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	#102	—	158	4	no	—
293	#102	—	158	4	no	—
294	C₂²⋊C₈	—	158	1	no	—
295	C₂²⋊C₈	—	158	1	no	—
296	C₂²⋊C₈	—	158	2	no	—
297	C₂²⋊C₈	—	158	2	no	—
298	C₄×C₈	—	158	1	no	—
299	C₄×C₈	—	158	1	no	—
300	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
301	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
304	C₂⁴	—	4	1	no	—
305	#41	—	316	2	no	—
306	#41	—	316	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×Q₈	—	8	2	no	—
310	C₂×Q₈	—	158	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	8	2	no	—
320	C₂×D₄	—	8	2	no	—
321	C₂×D₄	—	79	2	no	—
322	C₂×D₄	—	158	2	no	—
323	C₂×D₄	—	158	1	no	—
324	C₂×D₄	—	158	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	158	2	no	—
327	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
329	C₂²×C₄	#11929623	1	1	yes	characteristic
330	D₈	—	632	4	no	—
331	M₁₆	—	316	4	no	—
332	M₁₆	—	316	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	316	4	no	—
336	C₂×C₈	—	158	2	no	—
337	C₂×C₈	—	158	2	no	—
338	C₂×C₈	—	158	2	no	—
339	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
340	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	79	2	no	—
348	C₄⋊C₄	—	158	1	no	—
349	C₂²⋊C₄	—	158	2	no	—
350	C₂²⋊C₄	—	158	2	no	—
351	C₄²	D₄×D₇₉	1	1	yes	characteristic
352	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
353	C₄²	#11929623	1	1	yes	characteristic
354	C₄²	C₂³×D₇₉	1	1	yes	characteristic
355	C₂³	—	4	2	no	—
356	C₂³	—	8	2	no	—
357	C₂³	—	8	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	158	2	no	—
360	C₂³	#14579132	1	1	yes	characteristic
361	Q₈	—	8	2	no	—
362	Q₈	—	8	2	no	—
363	Q₈	—	316	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	4	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	2	no	—
371	D₄	—	316	4	no	—
372	D₄	—	316	2	no	—
373	D₄	—	316	2	no	—
374	D₄	—	158	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	—	316	2	no	—
380	C₂×C₄	—	316	2	no	—
381	C₂×C₄	—	158	2	no	—
382	C₂×C₄	#14579132	1	1	yes	characteristic
383	C₂×C₄	#14579132	1	1	yes	characteristic
384	C₂×C₄	#14579132	1	1	yes	characteristic
385	C₂×C₄	#14579181	1	2	yes	—
386	C₂×C₄	#14579186	1	2	yes	—
387	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
388	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
389	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	2	1	no	—
393	C₈	—	2	1	no	—
394	C₈	—	316	2	no	—
395	C₈	—	316	2	no	—
396	C₈	—	316	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	16	4	no	—
403	C₂²	—	316	2	no	—
404	C₂²	—	316	2	no	—
405	C₂²	—	316	2	no	—
406	C₂²	#19098775	1	2	yes	—
407	C₂²	C₂×#14579132	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	8	2	no	—
411	C₄	—	316	2	no	—
412	C₄	#19098775	1	2	yes	—
413	C₄	#19098830	1	2	yes	—
414	C₄	C₂×#14579181	1	1	yes	characteristic
415	C₄	C₂×#14579186	1	1	yes	characteristic
416	C₄	#19099369	1	2	yes	—
417	C₂	—	2	2	no	—
418	C₂	—	16	2	no	—
419	C₂	—	632	2	no	—
420	C₂	C₂×#19098775	1	1	yes	characteristic
421	C₂	#23773035	1	1	yes	characteristic
422	C₂	C₂×#19098830	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14579132
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₂×#486×C₇₉	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	#23774318	C₂
hypercenter	C₂×#486	D₇₉
hypocenter	C₇₉	#19196
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#486

Complements

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

N	H ≅ G/N	type
1. #23774528	C₂	semidirect
3. #23772113	C₂	semidirect
4. #23762930	C₂	semidirect
5. #23762806	C₂	semidirect
6. #23762148	C₂	semidirect
7. #23762081	C₂	semidirect
8. #23762068	C₂	semidirect
9. C₂×#486×C₇₉	C₂	semidirect
17. #19098850	C₂²	semidirect
21. #19098642	C₂²	semidirect
23. C₈×D₃₁₆	C₂²	semidirect
28. #19098316	C₂²	semidirect
29. #19098314	C₂²	semidirect
30. #19098312	C₂²	semidirect
214. C₂×#486	D₇₉	semidirect
221. C₇₉	#19196	semidirect

Maximal subgroups

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

subgroup	index
#23774528	2
#23774318	2
#23772113	2
#23762930	2
#23762806	2
#23762148	2
#23762081	2
#23762068	2
C₂×#486×C₇₉	2
#19196	79