Subgroups — #32980229

Order 18688.

602 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	#22612831	C₂	1	1	yes	maximal, characteristic
2	#22610695	C₂	1	1	yes	maximal, characteristic, complemented
3	#22610058	C₂	1	1	yes	maximal, characteristic, complemented
4	#22609932	C₂	1	1	yes	maximal, characteristic
5	C₂×#17988314	C₂	1	1	yes	maximal, characteristic
6	#22607770	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
9	C₂×#14556553	—	2	1	no	—
10	C₂×C₄⋊C₄×D₇₃	—	2	1	no	—
11	C₂×#14556523	—	2	1	no	—
12	C₂×#14556513	—	2	1	no	—
13	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
14	#17988483	—	2	1	no	—
15	#17988458	—	2	2	no	—
16	#17988457	C₂²	1	1	yes	characteristic
17	#17988444	—	2	1	no	—
18	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
19	#17988350	—	2	1	no	—
20	#17988350	—	2	1	no	—
21	#17988349	—	2	2	no	—
22	#17988314	C₄	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
25	#384×C₇₃	C₂²	1	1	yes	characteristic
26	C₂²×D₂₉₂	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₇₃	—	2	2	no	—
28	C₂²×C₄×D₇₃	—	2	1	no	—
29	C₂²×#10596831	—	2	1	no	—
30	C₄×D₂₉₂	—	2	1	no	—
31	C₄×D₂₉₂	—	2	1	no	—
32	C₄×D₂₉₂	C₂×C₄	1	2	yes	—
33	C₄×D₂₉₂	Q₈	1	2	yes	—
34	#14556553	—	4	2	no	—
35	#14556553	—	4	2	no	—
36	C₂×C₄⋊Dic₇₃	—	2	1	no	—
37	C₂×C₄⋊Dic₇₃	—	2	1	no	—
38	C₂×C₄⋊Dic₇₃	—	2	1	no	—
39	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
42	C₂×#11924007	—	2	2	no	—
43	C₄⋊C₄×D₇₃	—	4	2	no	—
44	C₄⋊C₄×D₇₃	—	4	2	no	—
45	C₂×#11924005	—	2	2	no	—
46	C₂×#11924005	—	2	1	no	—
47	C₂×C₄×Dic₇₃	—	2	1	no	—
48	#14556523	—	4	2	no	—
49	#14556513	—	4	2	no	—
50	C₄×#10596831	—	2	1	no	—
51	C₄×#10596831	C₂×C₄	1	2	yes	complemented
52	#14556498	—	2	2	no	—
53	#14556498	—	2	1	no	—
54	C₂²×C₈×C₇₃	—	2	1	no	—
55	C₂²×C₈×C₇₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
59	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
60	C₄⋊C₈×C₇₃	—	2	1	no	—
61	C₄⋊C₈×C₇₃	—	2	1	no	—
62	C₄⋊C₈×C₇₃	—	2	1	no	—
63	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	complemented
64	C₂³×D₇₃	—	2	1	no	—
65	C₂×D₂₉₂	—	2	1	no	—
66	C₂×D₂₉₂	—	2	1	no	—
67	C₂×D₂₉₂	—	2	1	no	—
68	C₂×D₂₉₂	C₄⋊C₄	1	2	yes	—
69	C₂×D₂₉₂	SD₁₆	1	2	yes	—
70	C₂×D₂₉₂	SD₁₆	1	2	yes	—
71	C₂²×Dic₇₃	—	2	1	no	—
72	C₂²×Dic₇₃	—	2	1	no	—
73	C₂²×Dic₇₃	—	2	1	no	—
74	C₂²×Dic₇₃	—	4	1	no	—
75	C₂×C₄×D₇₃	—	2	2	no	—
76	C₂×C₄×D₇₃	—	2	2	no	—
77	C₂×C₄×D₇₃	—	4	1	no	—
78	C₂×C₄×D₇₃	—	4	1	no	—
79	C₂×C₄×D₇₃	—	4	1	no	—
80	C₂×C₄×D₇₃	—	4	1	no	—
81	C₂×C₄×D₇₃	—	4	4	no	—
82	C₂×C₄×D₇₃	—	4	4	no	—
83	C₂×C₄×D₇₃	—	8	2	no	—
84	C₂×#10596831	—	2	2	no	—
85	C₂×#10596831	—	4	1	no	—
86	C₂×#10596831	—	4	1	no	—
87	C₄⋊Dic₇₃	—	2	1	no	—
88	C₄⋊Dic₇₃	—	2	1	no	—
89	C₄⋊Dic₇₃	—	2	1	no	—
90	C₄⋊Dic₇₃	—	2	1	no	—
91	C₄⋊Dic₇₃	—	4	2	no	—
92	C₄⋊Dic₇₃	—	4	1	no	—
93	C₄⋊Dic₇₃	—	4	1	no	—
94	C₄⋊Dic₇₃	—	4	1	no	—
95	C₄⋊Dic₇₃	—	4	1	no	—
96	C₄⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
97	C₄⋊Dic₇₃	D₈	1	2	yes	—
98	#11924007	—	4	4	no	—
99	#11924005	—	2	2	no	—
100	#11924005	—	2	2	no	—
101	#11924005	—	4	4	no	—
102	C₄×Dic₇₃	—	4	1	no	—
103	C₄×Dic₇₃	—	4	1	no	—
104	C₂²×C₄×C₇₃	—	2	2	no	—
105	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₇₃	—	2	2	no	—
109	C₂×C₈×C₇₃	—	4	1	no	—
110	C₂×C₈×C₇₃	—	4	1	no	—
111	C₂×C₈×C₇₃	—	4	1	no	—
112	C₂×C₈×C₇₃	—	4	1	no	—
113	C₂×C₈×C₇₃	—	4	1	no	—
114	C₄⋊C₄×C₇₃	—	4	2	no	—
115	C₄⋊C₄×C₇₃	—	4	1	no	—
116	C₄⋊C₄×C₇₃	—	4	1	no	—
117	C₄⋊C₄×C₇₃	—	4	1	no	—
118	C₄⋊C₄×C₇₃	—	4	1	no	—
119	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
121	C₄²×C₇₃	#41	1	1	yes	characteristic
122	C₄²×C₇₃	#41	1	1	yes	characteristic
123	C₂³×C₇₃	#120	1	1	yes	characteristic
124	C₂²×D₇₃	—	2	2	no	—
125	C₂²×D₇₃	—	2	2	no	—
126	C₂²×D₇₃	—	2	2	no	—
127	C₂²×D₇₃	—	4	1	no	—
128	C₂²×D₇₃	—	4	1	no	—
129	C₂²×D₇₃	—	4	1	no	—
130	C₂²×D₇₃	—	4	1	no	—
131	C₂×C₄×C₇₃	—	2	1	no	—
132	C₂×C₄×C₇₃	—	2	1	no	—
133	C₂×C₄×C₇₃	—	4	2	no	—
134	C₂×C₄×C₇₃	—	4	2	no	—
135	C₂×C₄×C₇₃	—	4	2	no	—
136	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
142	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
143	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
144	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
146	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
149	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
150	C₂×Dic₇₃	—	2	2	no	—
151	C₂×Dic₇₃	—	2	2	no	—
152	C₂×Dic₇₃	—	4	1	no	—
153	C₂×Dic₇₃	—	4	1	no	—
154	C₂×Dic₇₃	—	4	1	no	—
155	C₂×Dic₇₃	—	4	1	no	—
156	C₂×Dic₇₃	—	4	1	no	—
157	C₂×Dic₇₃	—	4	1	no	—
158	C₂×Dic₇₃	—	4	1	no	—
159	C₂×Dic₇₃	—	8	1	no	—
160	C₂×Dic₇₃	—	8	1	no	—
161	C₂×Dic₇₃	—	8	1	no	—
162	D₂₉₂	—	2	2	no	—
163	D₂₉₂	—	2	2	no	—
164	D₂₉₂	—	2	2	no	—
165	D₂₉₂	#106	1	4	yes	complemented
166	C₄×D₇₃	—	4	2	no	—
167	C₄×D₇₃	—	4	2	no	—
168	C₄×D₇₃	—	4	2	no	—
169	C₄×D₇₃	—	4	2	no	—
170	C₄×D₇₃	—	8	8	no	—
171	C₈×C₇₃	—	4	2	no	—
172	C₈×C₇₃	—	8	1	no	—
173	#10596831	—	4	2	no	—
174	C₂²×C₇₃	#385	1	1	yes	characteristic
175	C₂²×C₇₃	#447	1	1	yes	characteristic
176	C₂²×C₇₃	#448	1	1	yes	characteristic
177	C₂²×C₇₃	#450	1	1	yes	characteristic
178	C₂²×C₇₃	#452	1	1	yes	characteristic
179	C₂²×C₇₃	#454	1	1	yes	characteristic
180	C₂²×C₇₃	#455	1	1	yes	characteristic
181	C₂×D₇₃	—	2	4	no	—
182	C₂×D₇₃	—	4	2	no	—
183	C₂×D₇₃	—	4	2	no	—
184	C₂×D₇₃	—	4	2	no	—
185	C₂×D₇₃	—	4	2	no	—
186	C₂×D₇₃	—	4	2	no	—
187	C₂×D₇₃	—	4	2	no	—
188	C₄×C₇₃	—	2	1	no	—
189	C₄×C₇₃	—	2	1	no	—
190	C₄×C₇₃	—	8	2	no	—
191	C₄×C₇₃	C₂×#106	1	1	yes	characteristic
192	C₄×C₇₃	#428	1	1	yes	characteristic
193	C₄×C₇₃	C₄×D₈	1	1	yes	characteristic
194	C₄×C₇₃	#440	1	1	yes	characteristic
195	C₄×C₇₃	#474	1	1	yes	characteristic
196	C₄×C₇₃	#478	1	1	yes	characteristic
197	C₄×C₇₃	#481	1	1	yes	characteristic
198	C₄×C₇₃	#483	1	1	yes	characteristic
199	Dic₇₃	—	4	2	no	—
200	Dic₇₃	—	4	2	no	—
201	Dic₇₃	—	8	1	no	—
202	Dic₇₃	—	16	1	no	—
203	#8894	—	73	1	no	maximal, Sylow
204	C₂×C₇₃	#1627	1	1	yes	characteristic
205	C₂×C₇₃	#1635	1	1	yes	characteristic
206	C₂×C₇₃	#1639	1	1	yes	characteristic
207	C₂×C₇₃	#1643	1	1	yes	characteristic
208	C₂×C₇₃	#1853	1	1	yes	characteristic
209	C₂×C₇₃	#1860	1	1	yes	characteristic
210	C₂×C₇₃	#1862	1	1	yes	characteristic
211	D₇₃	—	4	4	no	—
212	D₄×C₄⋊C₄	—	73	1	no	—
213	#1948	—	73	1	no	—
214	#1834	—	73	1	no	—
215	#1802	—	73	1	no	—
216	C₂×D₄⋊C₈	—	73	1	no	—
217	#1296	D₇₃	1	1	yes	characteristic, complemented
218	#1279	—	73	1	no	—
219	C₇₃	#8894	1	1	yes	characteristic, complemented, Sylow
220	C₂×C₄×D₄	—	73	1	no	—
221	C₂×C₄×D₄	—	146	1	no	—
222	C₂²×C₄⋊C₄	—	146	1	no	—
223	C₂×#106	—	146	1	no	—
224	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
226	C₂×#102	—	146	1	no	—
227	C₂×C₄×C₈	—	73	1	no	—
228	#389	—	146	1	no	—
229	#385	—	146	2	no	—
230	#384	—	73	1	no	—
231	#384	C₂×D₇₃	1	1	yes	characteristic
232	#380	—	146	1	no	—
233	C₄×C₄⋊C₄	—	73	1	no	—
234	#340	—	146	1	no	—
235	#340	—	146	1	no	—
236	#340	—	146	2	no	—
237	D₄⋊C₈	—	73	4	no	—
238	C₂²×D₄	—	73	1	no	—
239	C₂³×C₄	—	146	2	no	—
240	C₂³×C₄	—	146	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	146	1	no	—
244	C₄×D₄	—	292	2	no	—
245	C₄×D₄	—	292	2	no	—
246	C₄×D₄	—	73	2	no	—
247	C₄×D₄	—	73	2	no	—
248	C₄×D₄	—	146	1	no	—
249	C₄×D₄	—	146	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	292	2	no	—
253	C₂×C₄⋊C₄	—	292	2	no	—
254	C₂×C₄⋊C₄	—	73	1	no	—
255	C₂×C₄⋊C₄	—	73	1	no	—
256	C₂×C₄⋊C₄	—	73	1	no	—
257	C₂×C₄⋊C₄	—	146	2	no	—
258	C₂×C₄⋊C₄	—	146	1	no	—
259	C₂×C₄⋊C₄	—	146	1	no	—
260	C₂×C₄⋊C₄	—	146	1	no	—
261	C₂×C₄⋊C₄	D₂₉₂	1	2	yes	—
262	C₂×C₂²⋊C₄	—	146	2	no	—
263	C₂×C₂²⋊C₄	—	146	1	no	—
264	C₂×C₄²	—	146	1	no	—
265	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
266	#106	—	292	2	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	C₄×D₇₃	1	2	yes	complemented
271	#102	—	292	2	no	—
272	C₄×C₈	—	73	2	no	—
273	C₄×C₈	—	146	1	no	—
274	#95	—	146	2	no	—
275	#95	—	146	1	no	—
276	C₂⁴	—	146	1	no	—
277	C₂×D₄	—	73	2	no	—
278	C₂×D₄	—	73	2	no	—
279	C₂×D₄	—	73	2	no	—
280	C₂×D₄	—	146	1	no	—
281	C₂×D₄	—	146	1	no	—
282	C₂×D₄	—	146	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	292	4	no	—
285	C₂²×C₄	—	292	4	no	—
286	C₂²×C₄	—	292	1	no	—
287	C₂²×C₄	—	292	1	no	—
288	C₂²×C₄	—	292	1	no	—
289	C₂²×C₄	—	292	1	no	—
290	C₂²×C₄	—	292	1	no	—
291	C₂²×C₄	—	584	2	no	—
292	C₂²×C₄	—	146	1	no	—
293	C₂²×C₄	—	146	1	no	—
294	C₂²×C₄	—	146	1	no	—
295	C₂²×C₄	—	146	2	no	—
296	C₂²×C₄	—	146	2	no	—
297	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	292	1	no	—
307	C₂×C₈	—	292	1	no	—
308	C₂×C₈	—	146	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	292	2	no	—
315	C₄⋊C₄	—	292	4	no	—
316	C₄⋊C₄	—	292	1	no	—
317	C₄⋊C₄	—	292	1	no	—
318	C₄⋊C₄	—	292	1	no	—
319	C₄⋊C₄	—	292	1	no	—
320	C₄⋊C₄	—	73	2	no	—
321	C₄⋊C₄	—	73	2	no	—
322	C₄⋊C₄	—	146	1	no	—
323	C₄⋊C₄	—	146	1	no	—
324	C₄⋊C₄	—	146	1	no	—
325	C₄⋊C₄	—	146	1	no	—
326	C₂²⋊C₄	—	292	4	no	—
327	C₂²⋊C₄	—	146	2	no	—
328	C₂²⋊C₄	—	146	2	no	—
329	C₄²	—	292	1	no	—
330	C₄²	—	292	1	no	—
331	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
332	C₄²	Q₈×D₇₃	1	1	yes	characteristic
333	C₄²	#11924027	1	1	yes	characteristic
334	C₄²	#11924028	1	1	yes	characteristic
335	C₂³	—	292	1	no	—
336	C₂³	—	292	1	no	—
337	C₂³	—	292	1	no	—
338	C₂³	—	292	1	no	—
339	C₂³	—	146	2	no	—
340	C₂³	—	146	2	no	—
341	C₂³	—	146	2	no	—
342	C₂³	#14556561	1	1	yes	characteristic
343	D₄	—	73	4	no	—
344	D₄	—	146	2	no	—
345	D₄	—	146	2	no	—
346	D₄	—	146	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	292	1	no	—
353	C₂×C₄	—	292	1	no	—
354	C₂×C₄	—	292	1	no	—
355	C₂×C₄	—	292	1	no	—
356	C₂×C₄	—	292	2	no	—
357	C₂×C₄	—	292	2	no	—
358	C₂×C₄	—	292	2	no	—
359	C₂×C₄	—	292	2	no	—
360	C₂×C₄	—	292	1	no	—
361	C₂×C₄	—	292	1	no	—
362	C₂×C₄	—	292	1	no	—
363	C₂×C₄	—	584	8	no	—
364	C₂×C₄	—	584	1	no	—
365	C₂×C₄	—	584	1	no	—
366	C₂×C₄	—	584	1	no	—
367	C₂×C₄	—	146	2	no	—
368	C₂×C₄	—	146	2	no	—
369	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
370	C₂×C₄	#14556551	1	1	yes	characteristic
371	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
372	C₂×C₄	#14556569	1	1	yes	characteristic
373	C₂×C₄	#14556571	1	1	yes	characteristic
374	C₂×C₄	#14556573	1	1	yes	characteristic
375	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
376	C₂×C₄	SD₁₆×D₇₃	1	1	yes	characteristic
377	C₂×C₄	SD₁₆×D₇₃	1	1	yes	characteristic
378	C₂×C₄	#14556612	1	1	yes	characteristic
379	C₂×C₄	#14556615	1	1	yes	characteristic
380	C₂×C₄	#14556618	1	1	yes	characteristic
381	C₂×C₄	#14556623	1	1	yes	characteristic
382	C₂×C₄	#14556623	1	1	yes	characteristic
383	C₈	—	4	2	no	—
384	C₈	—	8	1	no	—
385	C₈	—	292	2	no	—
386	C₂²	—	292	2	no	—
387	C₂²	—	292	2	no	—
388	C₂²	—	292	2	no	—
389	C₂²	—	292	2	no	—
390	C₂²	—	292	2	no	—
391	C₂²	—	292	2	no	—
392	C₂²	—	146	4	no	—
393	C₂²	#17988461	1	1	yes	characteristic
394	C₂²	#17988722	1	1	yes	characteristic
395	C₂²	#17988727	1	1	yes	characteristic
396	C₂²	#17988739	1	1	yes	characteristic
397	C₂²	#17988752	1	1	yes	characteristic
398	C₂²	#17988762	1	1	yes	characteristic
399	C₂²	#17988767	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	292	2	no	—
404	C₄	—	292	2	no	—
405	C₄	—	584	1	no	—
406	C₄	—	1168	1	no	—
407	C₄	#106×D₇₃	1	1	yes	characteristic
408	C₄	#17988628	1	1	yes	characteristic
409	C₄	#17988667	1	1	yes	characteristic
410	C₄	#17988690	1	1	yes	characteristic
411	C₄	#17988866	1	1	yes	characteristic
412	C₄	#17988886	1	1	yes	characteristic
413	C₄	#17988904	1	1	yes	characteristic
414	C₄	#17988916	1	1	yes	characteristic
415	C₂	—	292	4	no	—
416	C₂	#22609035	1	1	yes	characteristic
417	C₂	#22609083	1	1	yes	characteristic
418	C₂	#22609111	1	1	yes	characteristic
419	C₂	#22609139	1	1	yes	characteristic
420	C₂	#22610125	1	1	yes	characteristic
421	C₂	#22610167	1	1	yes	characteristic
422	C₂	#22610179	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14556561
commutator	C₄²×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1296	C₂
socle	C₂³×C₇₃	#120
prime radical	C₂²×D₂₉₂	D₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1296	D₇₃
hypocenter	C₇₃	#8894
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
2. #22610695	C₂	semidirect
3. #22610058	C₂	semidirect
6. #22607770	C₂	semidirect
7. C₇₃×#1296	C₂	semidirect
22. #17988314	C₄	semidirect
51. C₄×#10596831	C₂×C₄	semidirect
63. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
165. D₂₉₂	#106	semidirect
217. #1296	D₇₃	semidirect
219. C₇₃	#8894	semidirect
270. C₄⋊C₈	C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22612831	2
#22610695	2
#22610058	2
#22609932	2
C₂×#17988314	2
#22607770	2
C₇₃×#1296	2
#8894	73