Subgroups — #33077250

Order 18688.

798 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22622278	C₂	1	1	yes	maximal, characteristic, complemented
2	#22621606	C₂	1	1	yes	maximal, characteristic, complemented
3	#22621530	C₂	1	2	yes	maximal, complemented
4	#22609393	C₂	1	2	yes	maximal, complemented
5	#22609317	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609283	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609107	C₂	1	2	yes	maximal, complemented
8	#22609017	C₂	1	2	yes	maximal, complemented
9	#22608817	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×D₅₈₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1706	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556618	—	2	2	no	—
13	C₂×D₈×D₇₃	—	2	1	no	—
14	#17989240	C₂²	1	2	yes	complemented
15	#17989222	C₂²	1	2	yes	—
16	#17988902	—	2	2	no	—
17	#17988864	C₂²	1	2	yes	complemented
18	#17988830	—	2	2	no	—
19	#17988824	—	2	1	no	—
20	#17988820	—	2	1	no	—
21	#17988789	C₂²	1	2	yes	—
22	#17988779	C₂²	1	2	yes	—
23	#17988779	C₂²	1	2	yes	complemented
24	#17988736	—	2	2	no	—
25	#17988731	—	2	2	no	—
26	#17988719	—	2	2	no	—
27	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
28	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
29	#17988666	C₂²	1	2	yes	complemented
30	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
31	C₈×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
32	#107×D₇₃	—	2	1	no	—
33	#17988340	C₂²	1	1	yes	characteristic, complemented
34	#17988340	C₂²	1	1	yes	characteristic, complemented
35	#17988333	C₂²	1	2	yes	complemented
36	#17988331	C₂²	1	2	yes	complemented
37	#17988316	C₂²	1	1	yes	characteristic
38	#17988316	C₂²	1	1	yes	characteristic, complemented
39	#17988316	C₂²	1	2	yes	complemented
40	#500×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	#493×C₇₃	C₂²	1	1	yes	characteristic
42	#492×C₇₃	C₂²	1	2	yes	complemented
43	#486×C₇₃	C₂²	1	2	yes	complemented
44	C₈²×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#11924029	—	2	2	no	—
46	C₂×D₄×D₇₃	—	2	2	no	—
47	C₂×D₄×D₇₃	—	2	2	no	—
48	#14556618	—	4	8	no	—
49	C₂×#11924015	—	2	2	no	—
50	C₂×D₅₈₄	D₄	1	1	yes	characteristic
51	C₂×D₅₈₄	D₄	1	1	yes	characteristic
52	C₂×#11924013	—	2	2	no	—
53	C₂×#11924013	—	2	2	no	—
54	D₈×D₇₃	—	4	4	no	—
55	C₂×#11924011	—	2	2	no	—
56	C₂×C₈×D₇₃	—	2	1	no	—
57	C₂×C₈×D₇₃	—	2	1	no	—
58	#14556576	—	4	2	no	—
59	#14556567	—	2	2	no	—
60	#14556566	—	2	2	no	—
61	#14556562	—	2	2	no	—
62	#14556562	—	2	2	no	—
63	#14556559	—	4	2	no	—
64	C₄×D₂₉₂	C₂³	1	2	yes	—
65	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
66	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
67	C₄⋊C₄×D₇₃	—	2	2	no	—
68	#14556525	D₄	1	1	yes	characteristic
69	#14556525	D₄	1	1	yes	characteristic
70	#14556524	—	2	2	no	—
71	C₄⋊#10596831	C₂³	1	1	yes	characteristic
72	C₄⋊#10596831	C₂³	1	1	yes	characteristic
73	C₄⋊#10596831	C₂³	1	2	yes	—
74	#14556515	—	2	2	no	—
75	#14556513	D₄	1	2	yes	—
76	#14556513	D₄	1	1	yes	characteristic
77	#14556513	D₄	1	1	yes	characteristic
78	#14556512	—	2	2	no	—
79	#14556512	—	2	2	no	—
80	#14556511	—	2	2	no	—
81	#14556503	—	2	1	no	—
82	#14556503	—	2	1	no	—
83	#14556503	—	2	2	no	—
84	C₂×SD₁₆×C₇₃	—	2	2	no	—
85	C₂×SD₁₆×C₇₃	—	2	2	no	—
86	C₂×D₈×C₇₃	—	2	1	no	—
87	C₂×D₈×C₇₃	—	2	1	no	—
88	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
89	#127×C₇₃	C₂³	1	2	yes	—
90	#107×C₇₃	—	2	1	no	—
91	#107×C₇₃	—	2	1	no	—
92	#102×C₇₃	—	4	2	no	—
93	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
96	C₂³×D₇₃	—	4	2	no	—
97	#11924029	—	4	4	no	—
98	#11924029	—	8	2	no	—
99	C₂×D₂₉₂	—	4	2	no	—
100	C₂×D₂₉₂	C₂×D₄	1	2	yes	—
101	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
102	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
103	C₂×C₂²⋊D₇₃	—	4	2	no	—
104	C₂×C₂²⋊D₇₃	—	4	2	no	—
105	D₄×D₇₃	—	4	4	no	—
106	D₄×D₇₃	—	4	4	no	—
107	D₄×D₇₃	—	8	2	no	—
108	D₄×D₇₃	—	8	2	no	—
109	C₂×C₄×D₇₃	—	2	1	no	—
110	C₂×C₄×D₇₃	—	2	1	no	—
111	C₂×C₄×D₇₃	—	2	2	no	—
112	C₂×C₄×D₇₃	—	4	2	no	—
113	#11924015	—	4	4	no	—
114	D₅₈₄	—	2	2	no	—
115	D₅₈₄	D₈	1	4	yes	complemented
116	#11924013	—	4	4	no	—
117	#11924013	—	4	4	no	—
118	#11924011	—	4	4	no	—
119	C₂×#10596831	—	2	1	no	—
120	C₂×#10596831	—	2	1	no	—
121	C₂×#10596831	—	2	2	no	—
122	C₈×D₇₃	—	4	2	no	—
123	C₈×D₇₃	—	4	2	no	—
124	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
125	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
126	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
127	#11924007	—	4	2	no	—
128	C₂²⋊Dic₇₃	—	4	2	no	—
129	#11924005	—	2	1	no	—
130	#11924005	—	2	2	no	—
131	#11924005	—	2	1	no	—
132	#11924005	—	4	2	no	—
133	C₂×Q₈×C₇₃	—	2	2	no	—
134	C₂×D₄×C₇₃	—	2	2	no	—
135	C₂×D₄×C₇₃	—	2	2	no	—
136	C₂×D₄×C₇₃	—	2	2	no	—
137	SD₁₆×C₇₃	—	4	4	no	—
138	SD₁₆×C₇₃	—	8	2	no	—
139	D₈×C₇₃	—	4	2	no	—
140	D₈×C₇₃	—	8	1	no	—
141	C₂×C₈×C₇₃	—	2	1	no	—
142	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₄⋊C₄×C₇₃	—	2	2	no	—
147	C₄⋊C₄×C₇₃	—	2	2	no	—
148	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
149	C₂³×C₇₃	—	4	2	no	—
150	C₂²×D₇₃	—	2	1	no	—
151	C₂²×D₇₃	—	2	1	no	—
152	C₂²×D₇₃	—	2	2	no	—
153	C₂²×D₇₃	—	8	4	no	—
154	C₂²×D₇₃	—	8	4	no	—
155	C₂²×D₇₃	—	16	2	no	—
156	Q₈×C₇₃	—	4	2	no	—
157	Q₈×C₇₃	—	4	2	no	—
158	D₄×C₇₃	—	4	2	no	—
159	D₄×C₇₃	—	4	2	no	—
160	D₄×C₇₃	—	4	2	no	—
161	D₄×C₇₃	—	4	2	no	—
162	D₄×C₇₃	—	8	2	no	—
163	C₂×C₄×C₇₃	—	4	2	no	—
164	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²⋊D₇₃	—	8	4	no	—
168	C₂²⋊D₇₃	—	8	4	no	—
169	C₂×Dic₇₃	—	2	1	no	—
170	C₂×Dic₇₃	—	2	1	no	—
171	C₂×Dic₇₃	—	2	2	no	—
172	D₂₉₂	—	2	2	no	—
173	D₂₉₂	—	2	1	no	—
174	D₂₉₂	—	2	1	no	—
175	D₂₉₂	—	2	2	no	—
176	D₂₉₂	—	8	4	no	—
177	D₂₉₂	C₂×D₈	1	2	yes	—
178	D₂₉₂	C₂×D₈	1	2	yes	complemented
179	C₄×D₇₃	—	4	2	no	—
180	C₄×D₇₃	—	4	1	no	—
181	C₄×D₇₃	—	4	1	no	—
182	C₄×D₇₃	—	4	2	no	—
183	C₄×D₇₃	—	4	1	no	—
184	C₄×D₇₃	—	4	1	no	—
185	C₄×D₇₃	—	8	4	no	—
186	C₈×C₇₃	—	2	1	no	—
187	C₈×C₇₃	—	2	1	no	—
188	C₈×C₇₃	—	4	1	no	—
189	C₈×C₇₃	C₂×D₈	1	2	yes	complemented
190	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	complemented
191	#10596831	—	4	2	no	—
192	#10596831	—	4	1	no	—
193	#10596831	—	4	1	no	—
194	C₂²×C₇₃	—	8	2	no	—
195	C₂²×C₇₃	—	8	2	no	—
196	C₂²×C₇₃	—	8	2	no	—
197	C₂²×C₇₃	D₄²	1	1	yes	characteristic
198	C₂×D₇₃	—	2	2	no	—
199	C₂×D₇₃	—	2	2	no	—
200	C₂×D₇₃	—	4	1	no	—
201	C₂×D₇₃	—	4	1	no	—
202	C₂×D₇₃	—	4	1	no	—
203	C₂×D₇₃	—	4	1	no	—
204	C₂×D₇₃	—	4	2	no	—
205	C₂×D₇₃	—	4	2	no	—
206	C₂×D₇₃	—	4	2	no	—
207	C₂×D₇₃	—	16	8	no	—
208	C₄×C₇₃	—	2	1	no	—
209	C₄×C₇₃	—	8	2	no	—
210	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
211	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₄×C₇₃	#576	1	1	yes	characteristic
213	C₄×C₇₃	#577	1	1	yes	characteristic
214	Dic₇₃	—	4	1	no	—
215	Dic₇₃	—	4	1	no	—
216	Dic₇₃	—	4	2	no	—
217	#19883	—	73	1	no	maximal, Sylow
218	C₂×C₇₃	—	16	2	no	—
219	C₂×C₇₃	#3272	1	1	yes	characteristic
220	C₂×C₇₃	D₄×D₈	1	1	yes	characteristic
221	C₂×C₇₃	#3290	1	1	yes	characteristic
222	D₇₃	—	4	2	no	—
223	D₇₃	—	4	2	no	—
224	D₇₃	—	8	2	no	—
225	#3334	—	73	1	no	—
226	D₄×D₈	—	73	1	no	—
227	#3272	—	73	2	no	—
228	#1706	D₇₃	1	1	yes	characteristic, complemented
229	#1685	—	73	2	no	—
230	#1673	—	73	1	no	—
231	#1667	—	73	1	no	—
232	#1639	—	73	2	no	—
233	#1625	—	73	2	no	—
234	#1589	—	73	1	no	—
235	C₈×D₈	—	73	1	no	—
236	C₇₃	#19883	1	1	yes	characteristic, complemented, Sylow
237	C₂×AGL(1,ℤ/8)	—	146	2	no	—
238	C₂²×D₈	—	146	1	no	—
239	#547	—	73	2	no	—
240	D₄²	—	73	2	no	—
241	#500	C₂×D₇₃	1	1	yes	characteristic, complemented
242	#493	C₂×D₇₃	1	1	yes	characteristic
243	#492	C₂×D₇₃	1	2	yes	complemented
244	#486	C₂×D₇₃	1	2	yes	complemented
245	#480	—	146	2	no	—
246	#474	—	73	2	no	—
247	#468	—	146	2	no	—
248	#466	—	146	1	no	—
249	#466	—	146	1	no	—
250	#461	—	73	2	no	—
251	#459	—	73	2	no	—
252	#459	—	73	2	no	—
253	#450	—	146	2	no	—
254	#449	—	146	2	no	—
255	#447	—	146	2	no	—
256	C₄×D₈	—	73	1	no	—
257	C₄×D₈	—	73	1	no	—
258	#436	—	73	2	no	—
259	C₈×D₄	—	73	1	no	—
260	C₈×D₄	—	73	1	no	—
261	C₂×#107	—	146	1	no	—
262	#335	—	73	1	no	—
263	#335	—	73	1	no	—
264	#332	—	73	2	no	—
265	#331	—	73	2	no	—
266	D₄⋊C₈	—	73	1	no	—
267	D₄⋊C₈	—	73	1	no	—
268	D₄⋊C₈	—	73	2	no	—
269	C₈²	C₂×D₇₃	1	1	yes	characteristic, complemented
270	C₂×#41	—	146	2	no	—
271	C₂²×D₄	—	146	2	no	—
272	C₂²×D₄	—	146	2	no	—
273	AGL(1,ℤ/8)	—	292	8	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	146	2	no	—
277	C₂×D₈	—	2	1	no	—
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	—	292	4	no	—
280	C₂×D₈	—	73	1	no	—
281	C₂×D₈	—	73	1	no	—
282	C₂×D₈	—	146	2	no	—
283	C₂×D₈	—	146	2	no	—
284	C₂×M₁₆	—	146	2	no	—
285	C₂²×C₈	—	146	1	no	—
286	C₂²×C₈	—	146	1	no	—
287	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
288	#127	C₂²×D₇₃	1	2	yes	—
289	#123	—	292	2	no	—
290	C₂²⋊Q₈	—	146	2	no	—
291	#121	—	146	2	no	—
292	#121	—	146	2	no	—
293	#121	—	146	2	no	—
294	#120	—	292	2	no	—
295	C₄×D₄	—	73	1	no	—
296	C₄×D₄	—	73	2	no	—
297	C₄×D₄	—	73	1	no	—
298	C₂×C₄⋊C₄	—	146	2	no	—
299	#107	—	2	1	no	—
300	#107	—	2	1	no	—
301	#107	—	73	1	no	—
302	#107	—	73	1	no	—
303	#107	—	146	2	no	—
304	C₄⋊C₈	—	73	1	no	—
305	C₄⋊C₈	—	73	2	no	—
306	C₄⋊C₈	—	73	1	no	—
307	#103	—	146	2	no	—
308	#102	—	4	2	no	—
309	#102	—	73	2	no	—
310	#102	—	73	1	no	—
311	#102	—	73	1	no	—
312	#102	—	146	2	no	—
313	#102	—	146	2	no	—
314	#102	—	146	2	no	—
315	C₂²⋊C₈	—	146	1	no	—
316	C₂²⋊C₈	—	146	1	no	—
317	C₂²⋊C₈	—	146	2	no	—
318	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
321	C₂⁴	—	292	2	no	—
322	#41	—	292	4	no	—
323	#41	—	584	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	292	2	no	—
329	C₂×D₄	—	292	4	no	—
330	C₂×D₄	—	292	4	no	—
331	C₂×D₄	—	292	2	no	—
332	C₂×D₄	—	292	2	no	—
333	C₂×D₄	—	584	2	no	—
334	C₂×D₄	—	584	2	no	—
335	C₂×D₄	—	73	1	no	—
336	C₂×D₄	—	73	1	no	—
337	C₂×D₄	—	73	2	no	—
338	C₂²×C₄	—	292	2	no	—
339	C₂²×C₄	—	146	1	no	—
340	C₂²×C₄	—	146	1	no	—
341	C₂²×C₄	—	146	2	no	—
342	SD₁₆	—	4	4	no	—
343	SD₁₆	—	8	2	no	—
344	SD₁₆	—	292	4	no	—
345	D₈	—	4	2	no	—
346	D₈	—	8	1	no	—
347	D₈	—	292	4	no	—
348	D₈	—	292	4	no	—
349	D₈	—	73	4	no	—
350	D₈	—	146	2	no	—
351	M₁₆	—	292	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	292	2	no	—
354	C₂×C₈	—	292	2	no	—
355	C₂×C₈	—	146	1	no	—
356	C₂×C₈	—	146	1	no	—
357	C₂×C₈	—	146	2	no	—
358	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
359	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
360	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
361	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	292	2	no	—
365	C₄⋊C₄	—	73	1	no	—
366	C₄⋊C₄	—	73	2	no	—
367	C₄⋊C₄	—	73	1	no	—
368	C₂²⋊C₄	—	292	2	no	—
369	C₂²⋊C₄	—	292	2	no	—
370	C₂²⋊C₄	—	146	1	no	—
371	C₂²⋊C₄	—	146	2	no	—
372	C₂²⋊C₄	—	146	1	no	—
373	C₄²	C₂³×D₇₃	1	1	yes	characteristic
374	C₂³	—	4	2	no	—
375	C₂³	—	584	4	no	—
376	C₂³	—	584	4	no	—
377	C₂³	—	1168	2	no	—
378	C₂³	—	146	2	no	—
379	C₂³	—	146	1	no	—
380	C₂³	—	146	1	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	584	4	no	—
389	D₄	—	584	4	no	—
390	D₄	—	584	4	no	—
391	D₄	—	73	2	no	—
392	D₄	—	73	2	no	—
393	D₄	—	146	1	no	—
394	D₄	—	146	1	no	—
395	D₄	—	146	2	no	—
396	D₄	—	146	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	292	2	no	—
399	C₂×C₄	—	292	1	no	—
400	C₂×C₄	—	292	1	no	—
401	C₂×C₄	—	292	2	no	—
402	C₂×C₄	—	292	1	no	—
403	C₂×C₄	—	292	1	no	—
404	C₂×C₄	—	584	4	no	—
405	C₂×C₄	—	146	1	no	—
406	C₂×C₄	—	146	1	no	—
407	C₂×C₄	—	146	2	no	—
408	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
409	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
410	C₂×C₄	#14556636	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	4	1	no	—
414	C₈	—	292	2	no	—
415	C₈	—	292	1	no	—
416	C₈	—	292	1	no	—
417	C₈	D₈×D₇₃	1	2	yes	complemented
418	C₈	#14556618	1	2	yes	complemented
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	292	1	no	—
423	C₂²	—	292	1	no	—
424	C₂²	—	292	1	no	—
425	C₂²	—	292	1	no	—
426	C₂²	—	292	2	no	—
427	C₂²	—	292	2	no	—
428	C₂²	—	292	2	no	—
429	C₂²	—	1168	8	no	—
430	C₂²	—	146	2	no	—
431	C₂²	—	146	2	no	—
432	C₂²	#17989222	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	8	2	no	—
435	C₄	—	292	1	no	—
436	C₄	—	292	1	no	—
437	C₄	—	292	2	no	—
438	C₄	C₂×D₈×D₇₃	1	1	yes	characteristic
439	C₄	C₂×#14556618	1	1	yes	characteristic
440	C₄	#17989388	1	1	yes	characteristic
441	C₄	#17989393	1	1	yes	characteristic
442	C₂	—	16	2	no	—
443	C₂	—	292	2	no	—
444	C₂	—	292	2	no	—
445	C₂	—	584	2	no	—
446	C₂	#22621530	1	1	yes	characteristic
447	C₂	#22621606	1	1	yes	characteristic
448	C₂	#22621716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17989222
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1706	C₂
socle	C₂²×C₇₃	D₄²
hypercenter	#1706	D₇₃
hypocenter	C₇₃	#19883
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1706

Complements

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

N	H ≅ G/N	type
1. #22622278	C₂	semidirect
2. #22621606	C₂	semidirect
3. #22621530	C₂	semidirect
4. #22609393	C₂	semidirect
5. #22609317	C₂	semidirect
6. #22609283	C₂	semidirect
7. #22609107	C₂	semidirect
8. #22609017	C₂	semidirect
9. #22608817	C₂	semidirect
10. C₈×D₅₈₄	C₂	semidirect
11. C₇₃×#1706	C₂	semidirect
14. #17989240	C₂²	semidirect
17. #17988864	C₂²	semidirect
23. #17988779	C₂²	semidirect
29. #17988666	C₂²	semidirect
31. C₈×D₂₉₂	C₂²	semidirect
33. #17988340	C₂²	semidirect
34. #17988340	C₂²	semidirect
35. #17988333	C₂²	semidirect
36. #17988331	C₂²	semidirect
38. #17988316	C₂²	semidirect
39. #17988316	C₂²	semidirect
40. #500×C₇₃	C₂²	semidirect
42. #492×C₇₃	C₂²	semidirect
43. #486×C₇₃	C₂²	semidirect
44. C₈²×C₇₃	C₂²	semidirect
115. D₅₈₄	D₈	semidirect
178. D₂₉₂	C₂×D₈	semidirect
189. C₈×C₇₃	C₂×D₈	semidirect
190. C₈×C₇₃	AGL(1,ℤ/8)	semidirect
228. #1706	D₇₃	semidirect
236. C₇₃	#19883	semidirect
241. #500	C₂×D₇₃	semidirect
243. #492	C₂×D₇₃	semidirect
244. #486	C₂×D₇₃	semidirect
269. C₈²	C₂×D₇₃	semidirect
417. C₈	D₈×D₇₃	semidirect
418. C₈	#14556618	semidirect

Maximal subgroups

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

subgroup	index
#22622278	2
#22621606	2
#22621530	2
#22609393	2
#22609317	2
#22609283	2
#22609107	2
#22609017	2
#22608817	2
C₈×D₅₈₄	2
C₇₃×#1706	2
#19883	73