Subgroups — #33057161

Order 18688.

600 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619996	C₂	1	1	yes	maximal, characteristic
2	#22619052	C₂	1	1	yes	maximal, characteristic
3	#22608826	C₂	1	2	yes	maximal, complemented
4	#22608802	C₂	1	2	yes	maximal, complemented
5	#22608786	C₂	1	2	yes	maximal, complemented
6	C₈×#11924015	C₂	1	2	yes	maximal, complemented
7	#22608719	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608386	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608311	C₂	1	1	yes	maximal, characteristic
10	#22608215	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11924028	C₂²	1	1	yes	characteristic
13	#17988925	C₄	1	2	yes	—
14	#17988869	C₄	1	1	yes	characteristic
15	#17988864	C₄	1	1	yes	characteristic
16	#17988794	C₄	1	1	yes	characteristic
17	#17988789	C₄	1	1	yes	characteristic
18	#17988747	C₄	1	2	yes	—
19	#17988717	C₂²	1	2	yes	—
20	C₄×#11924018	C₂²	1	2	yes	—
21	C₄×#11924015	C₂²	1	2	yes	—
22	#17988661	—	2	2	no	—
23	C₈×D₂₉₂	C₂²	1	2	yes	—
24	#17988643	—	2	1	no	—
25	#17988640	C₂²	1	1	yes	characteristic
26	#17988611	C₂²	1	1	yes	characteristic
27	C₄⋊C₈×D₇₃	—	2	1	no	—
28	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
29	#17988339	C₂²	1	2	yes	—
30	#17988337	C₂²	1	2	yes	—
31	Q₈⋊#10596831	C₂²	1	2	yes	—
32	Q₈⋊#10596831	C₂²	1	2	yes	—
33	#17988317	C₂²	1	1	yes	characteristic
34	#17988317	C₂²	1	1	yes	characteristic
35	#17988314	C₂²	1	1	yes	characteristic
36	#17988314	C₂²	1	1	yes	characteristic
37	#17988309	C₂²	1	2	yes	—
38	C₈×#10596831	C₂²	1	2	yes	—
39	#533×C₇₃	C₂²	1	1	yes	characteristic
40	#446×C₇₃	—	2	1	no	—
41	#446×C₇₃	C₂²	1	2	yes	—
42	C₈×Q₈×C₇₃	—	2	1	no	—
43	C₈×Q₈×C₇₃	C₂²	1	2	yes	—
44	#433×C₇₃	—	2	2	no	—
45	#431×C₇₃	C₂²	1	1	yes	characteristic
46	#431×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
48	C₂×#11924018	C₂×C₄	1	2	yes	—
49	C₂×#11924015	C₂×C₄	1	2	yes	—
50	C₂×#11924012	—	2	1	no	—
51	C₂²×#10596831	—	2	1	no	—
52	C₂×C₈×D₇₃	—	2	2	no	—
53	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
54	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
55	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
56	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
57	C₄×C₂²⋊D₇₃	—	2	1	no	—
58	C₄×C₂²⋊D₇₃	—	2	1	no	—
59	#14556550	C₂×C₄	1	1	yes	characteristic
60	#14556548	—	2	1	no	—
61	C₄²×D₇₃	—	2	1	no	—
62	#14556524	C₂×C₄	1	2	yes	—
63	#14556522	C₂×C₄	1	2	yes	—
64	C₄⋊#10596831	—	2	1	no	—
65	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
66	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
67	C₄⋊#10596831	C₂³	1	2	yes	—
68	#14556520	—	2	2	no	—
69	#14556515	C₂×C₄	1	2	yes	—
70	#14556515	C₂×C₄	1	2	yes	—
71	#14556514	C₂×C₄	1	2	yes	—
72	#14556511	C₂×C₄	1	2	yes	—
73	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
74	#14556503	—	2	2	no	—
75	#14556501	—	2	2	no	—
76	C₄×#10596831	—	2	1	no	—
77	C₄×#10596831	C₂³	1	1	yes	characteristic
78	C₄×#10596831	C₂³	1	1	yes	characteristic
79	C₄×#10596831	C₂³	1	2	yes	—
80	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
81	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
82	#125×C₇₃	—	2	1	no	—
83	C₂²⋊Q₈×C₇₃	—	2	1	no	—
84	C₂²⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₇₃	—	2	1	no	—
86	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
87	#117×C₇₃	—	2	1	no	—
88	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₇₃	—	2	2	no	—
90	C₄⋊C₈×C₇₃	—	2	2	no	—
91	C₄⋊C₈×C₇₃	D₄	1	1	yes	characteristic
92	C₄⋊C₈×C₇₃	D₄	1	1	yes	characteristic
93	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
95	C₂²⋊C₈×C₇₃	—	2	1	no	—
96	C₂²⋊C₈×C₇₃	D₄	1	2	yes	—
97	#97×C₇₃	—	2	2	no	—
98	C₄×C₈×C₇₃	—	2	2	no	—
99	C₄×C₈×C₇₃	—	2	1	no	—
100	C₄×C₈×C₇₃	C₂³	1	2	yes	—
101	#11924028	—	2	2	no	—
102	#11924028	—	4	1	no	—
103	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
104	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊D₇₃	—	2	1	no	—
106	C₂×C₄×D₇₃	—	2	1	no	—
107	C₂×C₄×D₇₃	—	2	1	no	—
108	C₂×C₄×D₇₃	—	2	1	no	—
109	#11924018	—	4	2	no	—
110	#11924015	—	2	4	no	—
111	#11924012	—	8	1	no	—
112	C₂×#10596831	—	2	4	no	—
113	C₂×#10596831	—	2	1	no	—
114	C₂×#10596831	—	2	1	no	—
115	C₂×#10596831	—	2	2	no	—
116	C₂×#10596831	C₂²×C₄	1	2	yes	—
117	C₂×#10596831	C₂²×C₄	1	2	yes	—
118	C₈×D₇₃	—	8	2	no	—
119	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
121	#11924007	—	2	1	no	—
122	#11924007	—	2	1	no	—
123	C₂²⋊Dic₇₃	—	2	1	no	—
124	#11924005	—	2	1	no	—
125	#11924005	—	2	1	no	—
126	C₄×Dic₇₃	—	2	1	no	—
127	C₄×Dic₇₃	—	2	1	no	—
128	C₄×Dic₇₃	—	2	1	no	—
129	C₂×Q₈×C₇₃	—	2	1	no	—
130	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
134	C₂×C₈×C₇₃	—	2	1	no	—
135	C₂×C₈×C₇₃	—	2	1	no	—
136	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₇₃	—	2	1	no	—
139	C₄⋊C₄×C₇₃	—	2	1	no	—
140	C₄⋊C₄×C₇₃	—	2	1	no	—
141	C₄⋊C₄×C₇₃	—	2	2	no	—
142	C₄⋊C₄×C₇₃	—	2	2	no	—
143	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₇₃	—	2	2	no	—
145	C₄²×C₇₃	—	2	2	no	—
146	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₇₃	#41	1	1	yes	characteristic
149	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
150	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
151	C₂²×D₇₃	—	2	1	no	—
152	Q₈×C₇₃	—	2	2	no	—
153	Q₈×C₇₃	—	2	2	no	—
154	Q₈×C₇₃	—	4	2	no	—
155	C₂×C₄×C₇₃	—	2	1	no	—
156	C₂×C₄×C₇₃	—	2	1	no	—
157	C₂×C₄×C₇₃	—	2	1	no	—
158	C₂×C₄×C₇₃	—	2	1	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	—	2	2	no	—
161	C₂×C₄×C₇₃	—	2	2	no	—
162	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
168	C₂²⋊D₇₃	—	4	2	no	—
169	C₂×Dic₇₃	—	2	1	no	—
170	C₂×Dic₇₃	—	2	1	no	—
171	C₂×Dic₇₃	—	2	1	no	—
172	D₂₉₂	—	2	1	no	—
173	D₂₉₂	#131	1	2	yes	—
174	C₄×D₇₃	—	4	2	no	—
175	C₄×D₇₃	—	4	1	no	—
176	C₄×D₇₃	—	4	1	no	—
177	C₄×D₇₃	—	4	2	no	—
178	Dic₁₄₆	—	2	1	no	—
179	Dic₁₄₆	—	2	1	no	—
180	C₈×C₇₃	—	2	2	no	—
181	C₈×C₇₃	—	2	2	no	—
182	C₈×C₇₃	—	4	1	no	—
183	C₈×C₇₃	—	4	1	no	—
184	#10596831	—	2	2	no	—
185	#10596831	—	2	2	no	—
186	#10596831	—	2	2	no	—
187	#10596831	—	2	2	no	—
188	#10596831	—	4	2	no	—
189	C₂²×C₇₃	—	2	1	no	—
190	C₂²×C₇₃	—	2	1	no	—
191	C₂²×C₇₃	—	2	1	no	—
192	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂×D₇₃	—	2	2	no	—
194	C₂×D₇₃	—	4	1	no	—
195	C₂×D₇₃	—	4	1	no	—
196	C₄×C₇₃	—	2	1	no	—
197	C₄×C₇₃	—	2	1	no	—
198	C₄×C₇₃	—	2	1	no	—
199	C₄×C₇₃	—	4	2	no	—
200	C₄×C₇₃	—	4	2	no	—
201	C₄×C₇₃	#443	1	2	yes	—
202	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
203	C₄×C₇₃	#568	1	1	yes	characteristic
204	C₄×C₇₃	#577	1	1	yes	characteristic
205	C₄×C₇₃	#578	1	1	yes	characteristic
206	Dic₇₃	—	4	1	no	—
207	Dic₇₃	—	4	1	no	—
208	Dic₇₃	—	4	1	no	—
209	#18016	—	73	1	no	maximal, Sylow
210	C₂×C₇₃	—	4	1	no	—
211	C₂×C₇₃	#2933	1	1	yes	characteristic
212	C₂×C₇₃	#2947	1	1	yes	characteristic
213	C₂×C₇₃	C₂×#443	1	1	yes	characteristic
214	D₇₃	—	4	2	no	—
215	#3107	—	73	1	no	—
216	#2990	—	73	1	no	—
217	#2986	D₇₃	1	1	yes	characteristic, complemented
218	#1591	—	73	2	no	—
219	#1587	—	73	2	no	—
220	#1585	—	73	2	no	—
221	C₈×SD₁₆	—	73	2	no	—
222	#1574	—	73	1	no	—
223	#1493	—	73	1	no	—
224	#1476	—	73	1	no	—
225	#1450	—	73	1	no	—
226	C₇₃	#18016	1	1	yes	characteristic, complemented, Sylow
227	#533	C₂×D₇₃	1	1	yes	characteristic
228	C₄×#41	—	73	1	no	—
229	#485	—	73	2	no	—
230	#475	—	73	1	no	—
231	#474	—	73	1	no	—
232	#462	—	73	1	no	—
233	#461	—	73	1	no	—
234	#452	—	73	2	no	—
235	#446	—	2	1	no	—
236	#446	—	73	2	no	—
237	#446	C₂×D₇₃	1	2	yes	—
238	C₈×Q₈	—	2	1	no	—
239	C₈×Q₈	C₂×D₇₃	1	2	yes	—
240	C₄×Q₁₆	—	73	2	no	—
241	C₄×SD₁₆	—	73	2	no	—
242	#435	—	146	2	no	—
243	C₈×D₄	—	73	2	no	—
244	#433	—	2	2	no	—
245	#432	—	146	1	no	—
246	#431	—	73	1	no	—
247	#431	C₂×D₇₃	1	1	yes	characteristic
248	#431	C₂×D₇₃	1	1	yes	characteristic
249	#423	—	73	1	no	—
250	C₂×C₄⋊C₈	—	146	1	no	—
251	C₂×C₄×C₈	—	73	1	no	—
252	#335	—	73	2	no	—
253	#334	—	73	2	no	—
254	Q₈⋊C₈	—	73	2	no	—
255	Q₈⋊C₈	—	73	2	no	—
256	Q₈⋊C₈	—	73	1	no	—
257	Q₈⋊C₈	—	73	1	no	—
258	D₄⋊C₈	—	73	1	no	—
259	D₄⋊C₈	—	73	1	no	—
260	#322	—	73	2	no	—
261	C₈²	—	73	2	no	—
262	C₂×#41	—	73	1	no	—
263	C₂×Q₁₆	—	73	2	no	—
264	C₂×SD₁₆	—	73	2	no	—
265	C₂×M₁₆	—	146	1	no	—
266	C₂²×C₈	—	146	2	no	—
267	C₂²×C₈	—	146	1	no	—
268	C₄⋊Q₈	C₄×D₇₃	1	1	yes	characteristic
269	C₄⋊Q₈	C₄×D₇₃	1	1	yes	characteristic
270	#125	—	2	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	C₄×D₇₃	1	2	yes	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	—	73	1	no	—
275	C₄×Q₈	—	73	1	no	—
276	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
277	C₄×D₄	—	73	1	no	—
278	C₄×D₄	—	73	1	no	—
279	C₄×D₄	—	146	1	no	—
280	C₄×D₄	—	146	1	no	—
281	#117	—	2	1	no	—
282	#117	—	73	1	no	—
283	#117	—	146	1	no	—
284	C₂×C₄²	—	146	1	no	—
285	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
286	#107	—	73	2	no	—
287	#106	—	73	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	73	1	no	—
291	C₄⋊C₈	—	73	1	no	—
292	C₄⋊C₈	—	73	2	no	—
293	C₄⋊C₈	—	146	2	no	—
294	C₄⋊C₈	—	146	1	no	—
295	C₄⋊C₈	C₂²⋊D₇₃	1	1	yes	characteristic
296	C₄⋊C₈	C₂²⋊D₇₃	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
298	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
299	#103	—	73	2	no	—
300	#103	—	73	2	no	—
301	#103	—	73	2	no	—
302	#102	—	73	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	73	2	no	—
305	C₂²⋊C₈	—	146	2	no	—
306	C₂²⋊C₈	C₂²⋊D₇₃	1	2	yes	—
307	#97	—	2	2	no	—
308	#97	—	146	2	no	—
309	C₄×C₈	—	2	2	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	73	2	no	—
312	C₄×C₈	—	73	1	no	—
313	C₄×C₈	—	73	1	no	—
314	C₄×C₈	—	146	1	no	—
315	C₄×C₈	C₂²×D₇₃	1	2	yes	—
316	#41	—	292	1	no	—
317	#41	—	146	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	73	1	no	—
320	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
321	C₂×D₄	—	73	1	no	—
322	C₂×D₄	—	146	1	no	—
323	C₂²×C₄	—	146	1	no	—
324	C₂²×C₄	—	146	1	no	—
325	C₂²×C₄	—	146	1	no	—
326	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
328	C₂²×C₄	#11924028	1	1	yes	characteristic
329	Q₁₆	—	292	2	no	—
330	SD₁₆	—	146	4	no	—
331	M₁₆	—	584	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	584	2	no	—
335	C₂×C₈	—	73	2	no	—
336	C₂×C₈	—	73	2	no	—
337	C₂×C₈	—	146	2	no	—
338	C₂×C₈	—	146	4	no	—
339	C₂×C₈	—	146	1	no	—
340	C₂×C₈	—	146	1	no	—
341	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
342	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	73	1	no	—
349	C₄⋊C₄	—	73	1	no	—
350	C₄⋊C₄	—	146	1	no	—
351	C₄⋊C₄	—	146	1	no	—
352	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	146	1	no	—
355	C₂²⋊C₄	—	146	1	no	—
356	C₂²⋊C₄	—	146	1	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	146	1	no	—
359	C₄²	—	146	1	no	—
360	C₄²	—	146	1	no	—
361	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
362	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
363	C₄²	#11924028	1	1	yes	characteristic
364	C₄²	C₂³×D₇₃	1	1	yes	characteristic
365	C₂³	—	146	1	no	—
366	C₂³	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	146	1	no	—
371	Q₈	—	146	1	no	—
372	D₄	—	292	2	no	—
373	D₄	—	73	2	no	—
374	D₄	—	146	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	292	2	no	—
383	C₂×C₄	—	292	1	no	—
384	C₂×C₄	—	292	1	no	—
385	C₂×C₄	—	292	2	no	—
386	C₂×C₄	—	146	1	no	—
387	C₂×C₄	—	146	1	no	—
388	C₂×C₄	—	146	1	no	—
389	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
390	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
391	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
394	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	292	2	no	—
400	C₈	—	146	2	no	—
401	C₈	—	146	2	no	—
402	C₈	—	146	2	no	—
403	C₈	—	146	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	292	1	no	—
408	C₂²	—	292	1	no	—
409	C₂²	—	146	2	no	—
410	C₂²	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	292	1	no	—
417	C₄	—	292	1	no	—
418	C₄	—	292	1	no	—
419	C₄	#17988702	1	2	yes	—
420	C₄	#131×D₇₃	1	1	yes	characteristic
421	C₄	#17989352	1	1	yes	characteristic
422	C₄	#17989395	1	1	yes	characteristic
423	C₄	#17989402	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	292	2	no	—
426	C₂	#22618653	1	1	yes	characteristic
427	C₂	#22618774	1	1	yes	characteristic
428	C₂	C₂×#17988702	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#2986	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#11924028	C₂×C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#2986	D₇₃
hypocenter	C₇₃	#18016
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2986

Complements

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

N	H ≅ G/N	type
3. #22608826	C₂	semidirect
4. #22608802	C₂	semidirect
5. #22608786	C₂	semidirect
6. C₈×#11924015	C₂	semidirect
7. #22608719	C₂	semidirect
8. #22608386	C₂	semidirect
10. #22608215	C₂	semidirect
11. C₇₃×#2986	C₂	semidirect
217. #2986	D₇₃	semidirect
226. C₇₃	#18016	semidirect

Maximal subgroups

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

subgroup	index
#22619996	2
#22619052	2
#22608826	2
#22608802	2
#22608786	2
C₈×#11924015	2
#22608719	2
#22608386	2
#22608311	2
#22608215	2
C₇₃×#2986	2
#18016	73