Subgroups — #33241589

Order 18688.

532 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620582	C₂	1	1	yes	maximal, characteristic, complemented
2	#22620578	C₂	1	1	yes	maximal, characteristic, complemented
3	#22612207	C₂	1	1	yes	maximal, characteristic, complemented
4	#22612180	C₂	1	1	yes	maximal, characteristic, complemented
5	#22612173	C₂	1	1	yes	maximal, characteristic, complemented
6	#22612033	C₂	1	2	yes	maximal, complemented
7	#22612016	C₂	1	2	yes	maximal, complemented
8	#22611804	C₂	1	2	yes	maximal, complemented
9	#22611775	C₂	1	2	yes	maximal, complemented
10	#22611529	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2244	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989193	—	2	1	no	—
13	#17989191	—	2	1	no	—
14	C₂×#14556532	C₂²	1	2	yes	—
15	C₂×#14556532	C₂²	1	2	yes	—
16	C₂×#14556530	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
18	#17988989	C₂²	1	1	yes	characteristic
19	#17988964	C₂²	1	1	yes	characteristic
20	#17988953	—	2	1	no	—
21	#17988951	—	2	1	no	—
22	#17988841	—	2	1	no	—
23	#17988837	—	2	1	no	—
24	#17988824	C₂²	1	2	yes	—
25	#17988820	C₂²	1	2	yes	—
26	#17988699	—	2	1	no	—
27	#17988698	—	2	1	no	—
28	D₈×Dic₇₃	C₂²	1	2	yes	—
29	#17988669	C₂²	1	2	yes	—
30	#17988541	C₂²	1	1	yes	characteristic
31	#17988414	C₂²	1	2	yes	—
32	#17988412	C₂²	1	2	yes	—
33	#17988389	C₂²	1	2	yes	—
34	#17988389	C₂²	1	2	yes	—
35	#17988362	C₂²	1	1	yes	characteristic
36	C₄×#11924003	C₂²	1	1	yes	characteristic
37	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
38	#499×C₇₃	C₂²	1	1	yes	characteristic
39	#493×C₇₃	C₂²	1	1	yes	characteristic
40	#357×C₇₃	C₂²	1	2	yes	—
41	#357×C₇₃	C₂²	1	2	yes	—
42	#346×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×D₅₈₄	—	2	1	no	—
44	C₂×D₅₈₄	C₂³	1	2	yes	—
45	C₂×#11924011	D₄	1	1	yes	characteristic
46	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
47	#14556588	—	2	1	no	—
48	#14556583	—	2	1	no	—
49	#14556576	—	4	2	no	—
50	#14556572	—	4	2	no	—
51	#14556566	—	2	2	no	—
52	#14556566	—	4	2	no	—
53	#14556563	—	4	2	no	—
54	#14556562	—	2	2	no	—
55	D₄×Dic₇₃	—	2	2	no	—
56	#14556553	—	2	2	no	—
57	#14556548	D₄	1	1	yes	characteristic
58	#14556532	—	2	4	no	—
59	#14556532	—	2	4	no	—
60	#14556530	—	2	2	no	—
61	C₂×#11924003	C₂³	1	1	yes	characteristic
62	C₂×#11924003	C₂³	1	1	yes	characteristic
63	C₁₆×D₇₃	—	2	2	no	—
64	#14556525	C₂³	1	2	yes	—
65	#14556523	—	2	1	no	—
66	#14556512	—	2	2	no	—
67	#14556512	—	2	2	no	—
68	#14556511	—	2	2	no	—
69	#14556511	—	2	2	no	—
70	#14556502	D₄	1	1	yes	characteristic
71	#14556501	D₄	1	1	yes	characteristic
72	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
73	C₂×D₈×C₇₃	—	2	1	no	—
74	C₂×D₈×C₇₃	C₂³	1	2	yes	—
75	#127×C₇₃	—	2	1	no	—
76	#125×C₇₃	—	2	1	no	—
77	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
79	#107×C₇₃	C₂³	1	2	yes	—
80	#106×C₇₃	—	2	1	no	—
81	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×D₂₉₂	—	2	2	no	—
83	C₂×D₂₉₂	—	4	2	no	—
84	C₂×D₂₉₂	—	4	2	no	—
85	C₂×C₂²⋊D₇₃	—	4	2	no	—
86	C₂²×Dic₇₃	—	4	2	no	—
87	C₂×C₄×D₇₃	—	4	2	no	—
88	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
89	D₅₈₄	—	2	2	no	—
90	D₅₈₄	—	2	2	no	—
91	D₅₈₄	—	4	2	no	—
92	#11924011	—	2	2	no	—
93	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
94	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
95	C₈×D₇₃	—	2	1	no	—
96	C₈×D₇₃	—	2	1	no	—
97	C₄⋊Dic₇₃	—	2	2	no	—
98	#11924007	—	4	2	no	—
99	#11924007	D₈	1	2	yes	—
100	C₂²⋊Dic₇₃	—	4	2	no	—
101	C₂²⋊Dic₇₃	—	4	2	no	—
102	#11924005	—	4	2	no	—
103	#11924005	—	4	2	no	—
104	#11924005	D₈	1	2	yes	—
105	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
106	#11924003	#41	1	2	yes	—
107	#11924003	#41	1	2	yes	—
108	C₂×D₄×C₇₃	—	2	2	no	—
109	C₂×D₄×C₇₃	—	4	2	no	—
110	D₈×C₇₃	—	2	2	no	—
111	D₈×C₇₃	—	2	2	no	—
112	D₈×C₇₃	—	4	2	no	—
113	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
115	C₄⋊C₄×C₇₃	—	2	2	no	—
116	C₄⋊C₄×C₇₃	—	4	2	no	—
117	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
118	C₁₆×C₇₃	—	2	1	no	—
119	C₁₆×C₇₃	—	2	1	no	—
120	C₂³×C₇₃	—	4	2	no	—
121	C₂²×D₇₃	—	4	2	no	—
122	C₂²×D₇₃	C₂×D₈	1	1	yes	characteristic
123	D₄×C₇₃	—	4	2	no	—
124	D₄×C₇₃	—	4	2	no	—
125	D₄×C₇₃	—	16	2	no	—
126	C₂×C₄×C₇₃	—	4	2	no	—
127	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
128	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
129	C₂²⋊D₇₃	—	16	2	no	—
130	C₂×Dic₇₃	—	4	2	no	—
131	C₂×Dic₇₃	—	16	2	no	—
132	C₂×Dic₇₃	C₂×D₈	1	2	yes	—
133	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
134	D₂₉₂	—	4	2	no	—
135	D₂₉₂	—	4	2	no	—
136	D₂₉₂	—	16	2	no	—
137	D₂₉₂	—	16	2	no	—
138	C₄×D₇₃	—	2	1	no	—
139	C₄×D₇₃	—	2	1	no	—
140	C₄×D₇₃	—	16	2	no	—
141	C₈×C₇₃	#135	1	2	yes	—
142	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
143	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
144	#10596831	—	2	1	no	—
145	#10596831	—	2	1	no	—
146	C₂²×C₇₃	—	8	2	no	—
147	C₂²×C₇₃	—	8	2	no	—
148	C₂²×C₇₃	—	8	2	no	—
149	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
150	C₂×D₇₃	—	2	2	no	—
151	C₂×D₇₃	—	2	1	no	—
152	C₂×D₇₃	—	8	2	no	—
153	C₂×D₇₃	—	8	2	no	—
154	C₂×D₇₃	—	8	2	no	—
155	C₄×C₇₃	—	2	2	no	—
156	C₄×C₇₃	—	8	2	no	—
157	C₄×C₇₃	#532	1	1	yes	characteristic
158	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
159	Dic₇₃	—	2	2	no	—
160	Dic₇₃	—	2	1	no	—
161	Dic₇₃	—	8	2	no	—
162	#33740	—	73	1	no	maximal, Sylow
163	C₂×C₇₃	—	16	2	no	—
164	C₂×C₇₃	#3169	1	1	yes	characteristic
165	C₂×C₇₃	#3415	1	2	yes	—
166	D₇₃	—	4	1	no	—
167	D₇₃	—	16	2	no	—
168	#3176	—	73	1	no	—
169	#3176	—	73	1	no	—
170	#2253	—	73	1	no	—
171	#2246	—	73	1	no	—
172	#2244	—	73	1	no	—
173	#2244	D₇₃	1	1	yes	characteristic, complemented
174	#2218	—	73	2	no	—
175	#2215	—	73	2	no	—
176	#2177	—	73	2	no	—
177	C₄×D₁₆	—	73	2	no	—
178	#2108	—	73	1	no	—
179	C₇₃	#33740	1	1	yes	characteristic, complemented, Sylow
180	#540	—	146	1	no	—
181	#540	—	146	1	no	—
182	C₂×D₁₆	—	73	2	no	—
183	C₂×D₁₆	—	73	2	no	—
184	C₂×M₃₂	—	73	1	no	—
185	C₂²×C₁₆	—	73	1	no	—
186	#499	—	73	1	no	—
187	#499	C₂×D₇₃	1	1	yes	characteristic
188	#493	—	73	1	no	—
189	#493	C₂×D₇₃	1	1	yes	characteristic
190	#490	—	146	1	no	—
191	#490	—	146	1	no	—
192	#469	—	146	1	no	—
193	#469	—	146	1	no	—
194	#466	—	73	2	no	—
195	#466	—	73	2	no	—
196	#442	—	146	1	no	—
197	#442	—	146	1	no	—
198	C₄×D₈	—	73	2	no	—
199	C₄×D₈	—	73	2	no	—
200	#405	—	73	1	no	—
201	#367	—	73	2	no	—
202	#366	—	73	2	no	—
203	#357	—	73	2	no	—
204	#357	—	73	2	no	—
205	#357	C₂×D₇₃	1	2	yes	—
206	#357	C₂×D₇₃	1	2	yes	—
207	#346	—	73	1	no	—
208	#346	C₂×D₇₃	1	1	yes	characteristic
209	C₄×C₁₆	—	73	1	no	—
210	C₄×C₁₆	—	73	1	no	—
211	C₂×D₈	—	2	1	no	—
212	C₂×D₈	—	73	2	no	—
213	C₂×D₈	—	146	1	no	—
214	C₂×D₈	C₂²×D₇₃	1	2	yes	—
215	C₂×M₁₆	—	73	1	no	—
216	C₂²×C₈	—	73	1	no	—
217	#127	—	2	1	no	—
218	#127	—	146	1	no	—
219	#125	—	2	1	no	—
220	#125	—	146	1	no	—
221	#123	—	292	2	no	—
222	#123	—	292	2	no	—
223	#121	—	292	2	no	—
224	#121	—	292	2	no	—
225	#121	—	146	2	no	—
226	#121	—	146	2	no	—
227	C₄×D₄	—	146	2	no	—
228	C₄×D₄	—	146	2	no	—
229	#117	—	73	1	no	—
230	D₁₆	—	146	4	no	—
231	D₁₆	—	146	4	no	—
232	M₃₂	—	146	2	no	—
233	C₂×C₁₆	—	73	1	no	—
234	C₂×C₁₆	—	73	1	no	—
235	C₂×C₁₆	—	146	2	no	—
236	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
237	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
238	#107	—	73	2	no	—
239	#107	C₂²×D₇₃	1	2	yes	—
240	#106	—	2	1	no	—
241	#106	—	146	1	no	—
242	#102	—	146	2	no	—
243	#102	—	146	2	no	—
244	#102	—	146	2	no	—
245	#102	—	146	2	no	—
246	#97	—	73	1	no	—
247	#97	—	73	1	no	—
248	C₄×C₈	—	73	1	no	—
249	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	4	2	no	—
252	C₂×D₄	—	292	2	no	—
253	C₂×D₄	—	292	2	no	—
254	C₂×D₄	—	292	2	no	—
255	C₂×D₄	—	146	2	no	—
256	C₂²×C₄	—	292	2	no	—
257	C₂²×C₄	—	292	2	no	—
258	C₂²×C₄	—	73	1	no	—
259	D₈	—	2	2	no	—
260	D₈	—	2	2	no	—
261	D₈	—	4	2	no	—
262	D₈	—	292	2	no	—
263	D₈	—	146	2	no	—
264	D₈	—	146	2	no	—
265	M₁₆	—	146	2	no	—
266	C₂×C₈	—	73	1	no	—
267	C₂×C₈	—	73	1	no	—
268	C₂×C₈	—	146	1	no	—
269	C₂×C₈	—	146	1	no	—
270	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
271	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	4	2	no	—
274	C₄⋊C₄	—	292	2	no	—
275	C₄⋊C₄	—	73	2	no	—
276	C₄⋊C₄	—	146	2	no	—
277	C₂²⋊C₄	—	292	2	no	—
278	C₂²⋊C₄	—	292	2	no	—
279	C₂²⋊C₄	—	292	2	no	—
280	C₂²⋊C₄	—	292	2	no	—
281	C₂²⋊C₄	—	73	2	no	—
282	C₄²	—	73	1	no	—
283	C₄²	D₄×D₇₃	1	1	yes	characteristic
284	C₁₆	—	2	1	no	—
285	C₁₆	—	2	1	no	—
286	C₁₆	—	73	2	no	—
287	C₁₆	—	73	2	no	—
288	C₂³	—	4	2	no	—
289	C₂³	—	292	2	no	—
290	C₂³	—	73	1	no	—
291	D₄	—	4	2	no	—
292	D₄	—	4	2	no	—
293	D₄	—	16	2	no	—
294	D₄	—	292	2	no	—
295	D₄	—	292	2	no	—
296	D₄	—	1168	2	no	—
297	D₄	—	1168	2	no	—
298	D₄	—	1168	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	292	2	no	—
301	C₂×C₄	—	73	2	no	—
302	C₂×C₄	—	73	1	no	—
303	C₂×C₄	—	1168	2	no	—
304	C₂×C₄	—	1168	2	no	—
305	C₂×C₄	—	146	1	no	—
306	C₂×C₄	—	146	1	no	—
307	C₂×C₄	D₈×D₇₃	1	2	yes	—
308	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
309	C₈	—	146	1	no	—
310	C₈	—	146	1	no	—
311	C₈	#14556612	1	2	yes	—
312	C₈	#41×D₇₃	1	1	yes	characteristic
313	C₈	#41×D₇₃	1	1	yes	characteristic
314	C₂²	—	8	2	no	—
315	C₂²	—	8	2	no	—
316	C₂²	—	8	2	no	—
317	C₂²	—	584	2	no	—
318	C₂²	—	584	2	no	—
319	C₂²	—	584	2	no	—
320	C₂²	—	146	1	no	—
321	C₂²	—	146	2	no	—
322	C₂²	C₂×D₈×D₇₃	1	1	yes	characteristic
323	C₄	—	2	2	no	—
324	C₄	—	8	2	no	—
325	C₄	—	584	2	no	—
326	C₄	—	146	1	no	—
327	C₄	—	146	2	no	—
328	C₄	#17989136	1	1	yes	characteristic
329	C₄	C₂×#14556612	1	1	yes	characteristic
330	C₂	—	16	2	no	—
331	C₂	—	292	1	no	—
332	C₂	—	1168	2	no	—
333	C₂	#22620509	1	1	yes	characteristic
334	C₂	#22623071	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₃
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2244	C₂
socle	C₂²×C₇₃	C₂²×D₈
hypercenter	#2244	D₇₃
hypocenter	C₇₃	#33740
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2244

Complements

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

N	H ≅ G/N	type
1. #22620582	C₂	semidirect
2. #22620578	C₂	semidirect
3. #22612207	C₂	semidirect
4. #22612180	C₂	semidirect
5. #22612173	C₂	semidirect
6. #22612033	C₂	semidirect
7. #22612016	C₂	semidirect
8. #22611804	C₂	semidirect
9. #22611775	C₂	semidirect
10. #22611529	C₂	semidirect
11. C₇₃×#2244	C₂	semidirect
173. #2244	D₇₃	semidirect
179. C₇₃	#33740	semidirect

Maximal subgroups

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

subgroup	index
#22620582	2
#22620578	2
#22612207	2
#22612180	2
#22612173	2
#22612033	2
#22612016	2
#22611804	2
#22611775	2
#22611529	2
C₇₃×#2244	2
#33740	73