Subgroups — #33068426

Order 18688.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619713	C₂	1	2	yes	maximal
2	C₈×#11924028	C₂	1	1	yes	maximal, characteristic
3	#22609386	C₂	1	2	yes	maximal, complemented
4	#22609379	C₂	1	2	yes	maximal, complemented
5	#22609332	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609327	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609298	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609293	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#17988340	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608588	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11924028	C₂²	1	1	yes	characteristic
13	#17988891	—	2	2	no	—
14	#17988884	—	2	2	no	—
15	#17988879	C₂²	1	2	yes	—
16	#17988874	C₂²	1	2	yes	—
17	#17988869	C₂²	1	2	yes	—
18	#17988864	C₂²	1	2	yes	—
19	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
21	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
22	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₇₃	—	2	1	no	—
24	C₈×C₂²⋊D₇₃	—	2	1	no	—
25	#17988640	C₂²	1	1	yes	characteristic
26	#17988638	—	2	1	no	—
27	#17988623	—	2	2	no	—
28	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
29	#17988581	—	2	2	no	—
30	C₄×C₈×D₇₃	—	2	1	no	—
31	#17988340	C₂²	1	1	yes	characteristic
32	#17988340	C₂²	1	1	yes	characteristic
33	#17988340	C₂²	1	2	yes	—
34	#17988336	C₂²	1	2	yes	—
35	#17988336	C₂²	1	2	yes	—
36	#17988333	C₂²	1	2	yes	—
37	#17988333	C₂²	1	2	yes	—
38	#533×C₇₃	C₂²	1	2	yes	—
39	#500×C₇₃	C₂²	1	1	yes	characteristic
40	#494×C₇₃	C₂²	1	1	yes	characteristic
41	#487×C₇₃	C₂²	1	2	yes	—
42	#467×C₇₃	—	2	1	no	—
43	#467×C₇₃	—	2	1	no	—
44	C₄×Q₁₆×C₇₃	—	2	1	no	—
45	C₄×Q₁₆×C₇₃	—	2	1	no	—
46	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#11924028	D₄	1	1	yes	characteristic
48	C₂²×#10596831	—	2	2	no	—
49	C₂×C₈×D₇₃	—	2	1	no	—
50	C₂×C₈×D₇₃	—	2	1	no	—
51	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
52	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
53	C₄×D₂₉₂	D₄	1	1	yes	characteristic
54	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₇₃	—	2	1	no	—
56	C₄×C₂²⋊D₇₃	—	2	1	no	—
57	#14556550	D₄	1	1	yes	characteristic
58	#14556548	—	2	1	no	—
59	C₄²×D₇₃	—	2	1	no	—
60	#14556524	—	2	2	no	—
61	#14556524	—	2	2	no	—
62	#14556522	—	2	2	no	—
63	#14556522	—	2	2	no	—
64	C₄⋊#10596831	—	2	2	no	—
65	C₄⋊#10596831	C₂³	1	2	yes	—
66	C₄⋊#10596831	C₂³	1	2	yes	—
67	C₄⋊#10596831	C₂³	1	1	yes	characteristic
68	C₄⋊#10596831	C₂³	1	1	yes	characteristic
69	#14556520	—	2	1	no	—
70	#14556520	—	2	1	no	—
71	#14556514	—	2	2	no	—
72	#14556514	—	2	2	no	—
73	#14556511	—	2	2	no	—
74	#14556511	—	2	2	no	—
75	C₂²⋊#10596831	—	2	1	no	—
76	#14556503	—	2	1	no	—
77	#14556503	—	2	1	no	—
78	C₄×#10596831	—	2	1	no	—
79	C₈×Dic₇₃	—	2	1	no	—
80	C₈×Dic₇₃	—	2	1	no	—
81	C₂×Q₁₆×C₇₃	—	2	1	no	—
82	C₂×Q₁₆×C₇₃	—	2	1	no	—
83	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
86	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
87	#125×C₇₃	—	2	2	no	—
88	C₂²⋊Q₈×C₇₃	—	2	2	no	—
89	C₂²⋊Q₈×C₇₃	—	2	2	no	—
90	C₄×Q₈×C₇₃	—	2	2	no	—
91	C₄×Q₈×C₇₃	—	2	2	no	—
92	#117×C₇₃	—	2	2	no	—
93	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
94	#107×C₇₃	—	2	1	no	—
95	#107×C₇₃	—	2	1	no	—
96	#103×C₇₃	—	2	2	no	—
97	#103×C₇₃	—	2	2	no	—
98	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
102	#11924028	—	2	2	no	—
103	#11924028	Q₁₆	1	4	yes	complemented
104	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
105	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₇₃	—	2	1	no	—
107	C₂×C₄×D₇₃	—	2	1	no	—
108	C₂×C₄×D₇₃	—	2	1	no	—
109	C₂×C₄×D₇₃	—	2	1	no	—
110	C₂×#10596831	—	2	1	no	—
111	C₂×#10596831	—	2	1	no	—
112	C₂×#10596831	—	2	2	no	—
113	C₂×#10596831	—	2	2	no	—
114	C₂×#10596831	—	4	4	no	—
115	C₈×D₇₃	—	4	2	no	—
116	C₈×D₇₃	—	4	2	no	—
117	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
118	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
119	#11924007	—	2	1	no	—
120	#11924007	—	2	1	no	—
121	C₂²⋊Dic₇₃	—	2	1	no	—
122	#11924005	—	2	1	no	—
123	#11924005	—	2	1	no	—
124	C₄×Dic₇₃	—	2	1	no	—
125	C₄×Dic₇₃	—	2	1	no	—
126	C₄×Dic₇₃	—	2	1	no	—
127	C₂×Q₈×C₇₃	—	2	2	no	—
128	C₂×Q₈×C₇₃	—	2	2	no	—
129	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
132	Q₁₆×C₇₃	—	4	2	no	—
133	Q₁₆×C₇₃	—	4	2	no	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	4	1	no	—
136	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₇₃	—	2	2	no	—
141	C₄⋊C₄×C₇₃	—	2	2	no	—
142	C₄⋊C₄×C₇₃	—	2	2	no	—
143	C₄⋊C₄×C₇₃	—	2	2	no	—
144	C₄⋊C₄×C₇₃	—	4	2	no	—
145	C₄⋊C₄×C₇₃	—	4	2	no	—
146	C₂²⋊C₄×C₇₃	—	4	2	no	—
147	C₄²×C₇₃	—	4	2	no	—
148	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₇₃	#41	1	1	yes	characteristic
151	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
152	C₂³×C₇₃	#121	1	1	yes	characteristic
153	C₂²×D₇₃	—	2	1	no	—
154	Q₈×C₇₃	—	4	2	no	—
155	Q₈×C₇₃	—	4	2	no	—
156	Q₈×C₇₃	—	8	2	no	—
157	C₂×C₄×C₇₃	—	2	1	no	—
158	C₂×C₄×C₇₃	—	2	1	no	—
159	C₂×C₄×C₇₃	—	4	1	no	—
160	C₂×C₄×C₇₃	—	4	2	no	—
161	C₂×C₄×C₇₃	—	4	2	no	—
162	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
165	C₂×C₄×C₇₃	C₂×Q₁₆	1	2	yes	—
166	C₂×C₄×C₇₃	#135	1	2	yes	—
167	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
170	C₂²⋊D₇₃	—	2	4	no	—
171	C₂×Dic₇₃	—	2	1	no	—
172	C₂×Dic₇₃	—	2	1	no	—
173	C₂×Dic₇₃	—	2	1	no	—
174	D₂₉₂	—	2	1	no	—
175	D₂₉₂	C₂×Q₁₆	1	2	yes	—
176	C₄×D₇₃	—	2	4	no	—
177	C₄×D₇₃	—	4	2	no	—
178	C₄×D₇₃	—	4	1	no	—
179	C₄×D₇₃	—	4	1	no	—
180	Dic₁₄₆	—	2	1	no	—
181	Dic₁₄₆	C₂×Q₁₆	1	2	yes	—
182	C₈×C₇₃	—	2	1	no	—
183	C₈×C₇₃	—	2	1	no	—
184	C₈×C₇₃	—	2	1	no	—
185	C₈×C₇₃	#135	1	2	yes	—
186	#10596831	—	4	1	no	—
187	#10596831	—	4	2	no	—
188	#10596831	—	4	2	no	—
189	#10596831	—	4	1	no	—
190	C₂²×C₇₃	—	2	1	no	—
191	C₂²×C₇₃	—	2	1	no	—
192	C₂²×C₇₃	#467	1	2	yes	—
193	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
194	C₂×D₇₃	—	2	2	no	—
195	C₂×D₇₃	—	4	1	no	—
196	C₂×D₇₃	—	4	1	no	—
197	C₄×C₇₃	—	2	1	no	—
198	C₄×C₇₃	—	2	1	no	—
199	C₄×C₇₃	—	2	1	no	—
200	C₄×C₇₃	—	8	2	no	—
201	C₄×C₇₃	—	8	2	no	—
202	C₄×C₇₃	#467	1	2	yes	—
203	C₄×C₇₃	C₂²×Q₁₆	1	1	yes	characteristic
204	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
205	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
206	C₄×C₇₃	#575	1	1	yes	characteristic
207	Dic₇₃	—	2	2	no	—
208	Dic₇₃	—	4	1	no	—
209	Dic₇₃	—	4	1	no	—
210	#19126	—	73	1	no	maximal, Sylow
211	C₂×C₇₃	—	2	2	no	—
212	C₂×C₇₃	#3035	1	1	yes	characteristic
213	C₂×C₇₃	C₂×#467	1	1	yes	characteristic
214	C₂×C₇₃	#3067	1	1	yes	characteristic
215	D₇₃	—	4	2	no	—
216	#3170	D₇₃	1	1	yes	characteristic, complemented
217	#3076	—	73	2	no	—
218	C₈×#41	—	73	1	no	—
219	#1684	—	73	2	no	—
220	#1683	—	73	2	no	—
221	#1676	—	73	1	no	—
222	#1675	—	73	1	no	—
223	#1670	—	73	1	no	—
224	#1669	—	73	1	no	—
225	C₂×#335	—	73	1	no	—
226	#1542	—	73	2	no	—
227	C₇₃	#19126	1	1	yes	characteristic, complemented, Sylow
228	#533	C₂×D₇₃	1	2	yes	—
229	C₄×#41	—	73	1	no	—
230	#500	C₂×D₇₃	1	1	yes	characteristic
231	#494	C₂×D₇₃	1	1	yes	characteristic
232	#487	C₂×D₇₃	1	2	yes	—
233	#479	—	146	2	no	—
234	#478	—	146	2	no	—
235	#477	—	73	2	no	—
236	#476	—	73	2	no	—
237	#475	—	73	2	no	—
238	#474	—	73	2	no	—
239	#467	—	2	1	no	—
240	#467	—	2	1	no	—
241	C₈×Q₈	—	73	1	no	—
242	C₈×Q₈	—	73	1	no	—
243	C₄×Q₁₆	—	2	1	no	—
244	C₄×Q₁₆	—	2	1	no	—
245	C₈×D₄	—	73	1	no	—
246	C₈×D₄	—	73	1	no	—
247	C₈×D₄	—	146	1	no	—
248	C₈×D₄	—	146	1	no	—
249	#431	—	73	1	no	—
250	#431	—	146	1	no	—
251	#427	—	146	2	no	—
252	C₂×C₄⋊C₈	—	73	2	no	—
253	#416	—	146	2	no	—
254	C₂×C₄×C₈	—	146	1	no	—
255	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
256	#335	—	73	1	no	—
257	#335	—	73	1	no	—
258	#335	—	73	2	no	—
259	#333	—	73	2	no	—
260	#333	—	73	2	no	—
261	#332	—	73	2	no	—
262	#332	—	73	2	no	—
263	C₂×#41	—	73	1	no	—
264	C₂×Q₁₆	—	2	1	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂²×C₈	—	146	2	no	—
267	C₂²×C₈	—	146	1	no	—
268	C₂²×C₈	—	146	1	no	—
269	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
271	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
272	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
273	#125	—	2	2	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	—	73	1	no	—
279	C₄×Q₈	—	73	1	no	—
280	C₄×D₄	—	73	1	no	—
281	C₄×D₄	—	73	1	no	—
282	C₄×D₄	—	146	1	no	—
283	C₄×D₄	—	146	1	no	—
284	#117	—	2	2	no	—
285	#117	—	73	1	no	—
286	#117	—	146	1	no	—
287	C₂×C₄²	—	146	1	no	—
288	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
289	#107	—	2	1	no	—
290	#107	—	2	1	no	—
291	#107	—	146	2	no	—
292	#107	—	146	2	no	—
293	#106	—	146	2	no	—
294	#106	—	146	2	no	—
295	C₄⋊C₈	—	73	1	no	—
296	C₄⋊C₈	—	73	1	no	—
297	C₄⋊C₈	—	73	2	no	—
298	C₄⋊C₈	—	73	2	no	—
299	C₄⋊C₈	—	146	1	no	—
300	C₄⋊C₈	—	146	1	no	—
301	C₄⋊C₈	—	146	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	—	146	2	no	—
305	#103	—	146	2	no	—
306	#102	—	146	2	no	—
307	#102	—	146	2	no	—
308	C₂²⋊C₈	—	146	1	no	—
309	C₂²⋊C₈	—	146	1	no	—
310	C₂²⋊C₈	—	146	1	no	—
311	C₄×C₈	—	146	1	no	—
312	C₄×C₈	—	146	1	no	—
313	C₄×C₈	—	146	1	no	—
314	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
315	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
318	#41	—	73	4	no	—
319	#41	—	146	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	73	1	no	—
323	C₂×D₄	—	73	1	no	—
324	C₂×D₄	—	146	1	no	—
325	C₂²×C₄	—	146	1	no	—
326	C₂²×C₄	—	146	1	no	—
327	C₂²×C₄	—	146	1	no	—
328	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
330	C₂²×C₄	#11924027	1	1	yes	characteristic
331	Q₁₆	—	4	2	no	—
332	Q₁₆	—	4	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	292	2	no	—
336	C₂×C₈	—	292	4	no	—
337	C₂×C₈	—	292	2	no	—
338	C₂×C₈	—	146	2	no	—
339	C₂×C₈	—	146	2	no	—
340	C₂×C₈	—	146	1	no	—
341	C₂×C₈	—	146	1	no	—
342	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	73	1	no	—
353	C₄⋊C₄	—	73	1	no	—
354	C₄⋊C₄	—	146	1	no	—
355	C₄⋊C₄	—	146	1	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	146	1	no	—
358	C₂²⋊C₄	—	146	1	no	—
359	C₂²⋊C₄	—	146	1	no	—
360	C₄²	—	4	2	no	—
361	C₄²	—	146	1	no	—
362	C₄²	—	146	1	no	—
363	C₄²	—	146	1	no	—
364	C₄²	D₄×D₇₃	1	1	yes	characteristic
365	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
366	C₄²	#11924027	1	1	yes	characteristic
367	C₄²	C₂³×D₇₃	1	1	yes	characteristic
368	C₂³	—	146	1	no	—
369	C₂³	#14556562	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	8	2	no	—
373	Q₈	—	73	2	no	—
374	Q₈	—	146	1	no	—
375	D₄	—	73	2	no	—
376	D₄	—	146	4	no	—
377	D₄	—	146	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	292	2	no	—
384	C₂×C₄	—	292	1	no	—
385	C₂×C₄	—	292	1	no	—
386	C₂×C₄	—	146	1	no	—
387	C₂×C₄	—	146	1	no	—
388	C₂×C₄	—	146	1	no	—
389	C₂×C₄	—	146	4	no	—
390	C₂×C₄	#14556562	1	1	yes	characteristic
391	C₂×C₄	#14556562	1	1	yes	characteristic
392	C₂×C₄	#14556562	1	1	yes	characteristic
393	C₂×C₄	Q₁₆×D₇₃	1	2	yes	—
394	C₂×C₄	#14556614	1	2	yes	—
395	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
397	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	292	1	no	—
402	C₈	—	292	1	no	—
403	C₈	—	292	2	no	—
404	C₈	—	292	2	no	—
405	C₈	#14556611	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	292	1	no	—
409	C₂²	—	292	1	no	—
410	C₂²	—	146	2	no	—
411	C₂²	#17988825	1	2	yes	—
412	C₂²	C₂×#14556562	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	292	1	no	—
419	C₄	—	292	1	no	—
420	C₄	—	146	2	no	—
421	C₄	#17988825	1	2	yes	—
422	C₄	C₂×Q₁₆×D₇₃	1	1	yes	characteristic
423	C₄	C₂×#14556611	1	1	yes	characteristic
424	C₄	C₂×#14556614	1	1	yes	characteristic
425	C₄	#17989385	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	292	2	no	—
428	C₂	#22619380	1	1	yes	characteristic
429	C₂	C₂×#17988825	1	1	yes	characteristic
430	C₂	#22619647	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14556562
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#3170	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	C₂×#11924028	D₄
hypercenter	#3170	D₇₃
hypocenter	C₇₃	#19126
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

Complements

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

N	H ≅ G/N	type
3. #22609386	C₂	semidirect
4. #22609379	C₂	semidirect
5. #22609332	C₂	semidirect
6. #22609327	C₂	semidirect
7. #22609298	C₂	semidirect
8. #22609293	C₂	semidirect
9. C₂×#17988340	C₂	semidirect
10. #22608588	C₂	semidirect
11. C₇₃×#3170	C₂	semidirect
103. #11924028	Q₁₆	semidirect
216. #3170	D₇₃	semidirect
227. C₇₃	#19126	semidirect

Maximal subgroups

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

subgroup	index
#22619713	2
C₈×#11924028	2
#22609386	2
#22609379	2
#22609332	2
#22609327	2
#22609298	2
#22609293	2
C₂×#17988340	2
#22608588	2
C₇₃×#3170	2
#19126	73