Subgroups — #33068460

Order 18688.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620510	C₂	1	1	yes	maximal, characteristic, complemented
2	#22619992	C₂	1	2	yes	maximal, complemented
3	C₈×#11924028	C₂	1	1	yes	maximal, characteristic, complemented
4	#22609348	C₂	1	2	yes	maximal, complemented
5	#22609341	C₂	1	2	yes	maximal, complemented
6	#22609336	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609331	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609292	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609287	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608591	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989137	C₂²	1	2	yes	—
13	C₄×#11924028	C₂²	1	1	yes	characteristic
14	#17988992	C₂²	1	1	yes	characteristic
15	#17988964	C₂²	1	1	yes	characteristic
16	#17988934	C₂²	1	2	yes	—
17	#17988912	—	2	2	no	—
18	#17988883	C₂²	1	2	yes	—
19	#17988878	C₂²	1	2	yes	—
20	#17988823	—	2	1	no	—
21	#17988823	—	2	1	no	—
22	#17988788	C₂²	1	2	yes	—
23	#17988783	C₂²	1	2	yes	—
24	#17988734	—	2	2	no	—
25	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
27	C₄×#11924017	—	2	2	no	—
28	C₄×D₅₈₄	—	2	2	no	—
29	C₄×D₅₈₄	—	2	1	no	—
30	C₄×D₅₈₄	—	2	1	no	—
31	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
32	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
33	C₈×C₂²⋊D₇₃	—	2	1	no	—
34	C₈×C₂²⋊D₇₃	—	2	1	no	—
35	#17988640	C₂²	1	1	yes	characteristic
36	#17988638	—	2	1	no	—
37	C₄×C₈×D₇₃	—	2	1	no	—
38	#17988335	C₂²	1	2	yes	—
39	#17988335	C₂²	1	2	yes	—
40	#17988330	C₂²	1	2	yes	—
41	#17988330	C₂²	1	2	yes	—
42	#431×C₇₃	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
44	#335×C₇₃	C₂²	1	1	yes	characteristic
45	#335×C₇₃	C₂²	1	1	yes	characteristic
46	#334×C₇₃	C₂²	1	2	yes	—
47	C₂×#11924028	—	2	2	no	—
48	C₂×#11924028	D₄	1	1	yes	characteristic
49	C₂×#11924017	—	2	2	no	—
50	C₂×D₅₈₄	—	2	2	no	—
51	C₂×D₅₈₄	—	2	1	no	—
52	C₂×D₅₈₄	—	2	1	no	—
53	C₂×C₈×D₇₃	—	2	1	no	—
54	C₂×C₈×D₇₃	—	2	1	no	—
55	#14556591	C₂³	1	2	yes	—
56	#14556588	C₂³	1	2	yes	—
57	#14556579	—	2	2	no	—
58	#14556565	—	2	2	no	—
59	#14556565	—	2	2	no	—
60	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
61	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
62	C₄×D₂₉₂	—	2	2	no	—
63	C₄×D₂₉₂	—	2	2	no	—
64	C₄×D₂₉₂	D₄	1	1	yes	characteristic
65	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
66	C₄×C₂²⋊D₇₃	—	2	1	no	—
67	C₄×C₂²⋊D₇₃	—	2	1	no	—
68	#14556550	D₄	1	1	yes	characteristic
69	#14556548	—	2	1	no	—
70	C₄²×D₇₃	—	2	1	no	—
71	#14556525	—	2	2	no	—
72	#14556525	—	2	1	no	—
73	#14556525	—	2	1	no	—
74	#14556523	—	2	2	no	—
75	C₄⋊#10596831	C₂³	1	1	yes	characteristic
76	C₄⋊#10596831	C₂³	1	1	yes	characteristic
77	#14556520	—	2	1	no	—
78	#14556520	—	2	1	no	—
79	#14556516	—	2	2	no	—
80	#14556513	—	2	2	no	—
81	#14556513	—	2	2	no	—
82	#14556513	—	2	2	no	—
83	#14556513	—	2	2	no	—
84	#14556513	—	2	2	no	—
85	C₂²⋊#10596831	—	2	1	no	—
86	#14556503	—	2	1	no	—
87	#14556503	—	2	1	no	—
88	C₄×#10596831	—	2	1	no	—
89	C₈×Dic₇₃	—	2	1	no	—
90	C₈×Dic₇₃	—	2	1	no	—
91	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
95	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
96	C₂²⋊C₈×C₇₃	—	2	2	no	—
97	C₄×C₈×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	—	2	2	no	—
104	#11924028	—	8	4	no	—
105	C₂×Dic₁₄₆	—	2	2	no	—
106	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
107	C₂×D₂₉₂	—	2	2	no	—
108	C₂×D₂₉₂	—	2	2	no	—
109	C₂×D₂₉₂	—	2	2	no	—
110	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
111	C₂×C₂²⋊D₇₃	—	2	1	no	—
112	C₂×C₂²⋊D₇₃	—	4	2	no	—
113	C₂×C₄×D₇₃	—	2	1	no	—
114	C₂×C₄×D₇₃	—	2	1	no	—
115	C₂×C₄×D₇₃	—	2	1	no	—
116	C₂×C₄×D₇₃	—	4	2	no	—
117	#11924017	—	4	4	no	—
118	D₅₈₄	—	4	2	no	—
119	D₅₈₄	—	4	4	no	—
120	D₅₈₄	—	4	2	no	—
121	C₂×#10596831	—	2	1	no	—
122	C₂×#10596831	—	2	1	no	—
123	C₈×D₇₃	—	4	2	no	—
124	C₈×D₇₃	—	4	2	no	—
125	C₄⋊Dic₇₃	—	2	2	no	—
126	C₄⋊Dic₇₃	—	2	2	no	—
127	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
128	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
129	#11924007	—	2	1	no	—
130	#11924007	—	2	1	no	—
131	C₂²⋊Dic₇₃	—	2	1	no	—
132	#11924005	—	2	1	no	—
133	#11924005	—	2	1	no	—
134	#11924005	—	4	2	no	—
135	#11924005	—	4	2	no	—
136	C₄×Dic₇₃	—	2	1	no	—
137	C₄×Dic₇₃	—	2	1	no	—
138	C₄×Dic₇₃	—	2	1	no	—
139	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	2	no	—
144	C₂×C₈×C₇₃	—	2	2	no	—
145	C₂×C₈×C₇₃	—	4	1	no	—
146	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₇₃	#41	1	1	yes	characteristic
153	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
154	C₂³×C₇₃	#121	1	1	yes	characteristic
155	C₂²×D₇₃	—	2	1	no	—
156	C₂²×D₇₃	—	4	2	no	—
157	C₂×C₄×C₇₃	—	2	1	no	—
158	C₂×C₄×C₇₃	—	2	1	no	—
159	C₂×C₄×C₇₃	—	2	1	no	—
160	C₂×C₄×C₇₃	—	2	1	no	—
161	C₂×C₄×C₇₃	—	2	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	C₂²×D₄	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	—	2	4	no	—
169	C₂²⋊D₇₃	—	8	4	no	—
170	C₂×Dic₇₃	—	2	1	no	—
171	C₂×Dic₇₃	—	2	1	no	—
172	C₂×Dic₇₃	—	2	1	no	—
173	C₂×Dic₇₃	—	4	2	no	—
174	D₂₉₂	—	2	1	no	—
175	D₂₉₂	—	4	2	no	—
176	D₂₉₂	—	4	2	no	—
177	D₂₉₂	—	4	2	no	—
178	D₂₉₂	—	4	2	no	—
179	D₂₉₂	—	8	2	no	—
180	D₂₉₂	#135	1	2	yes	—
181	C₄×D₇₃	—	2	4	no	—
182	C₄×D₇₃	—	4	1	no	—
183	C₄×D₇₃	—	4	1	no	—
184	C₄×D₇₃	—	4	2	no	—
185	C₄×D₇₃	—	8	4	no	—
186	Dic₁₄₆	—	2	1	no	—
187	Dic₁₄₆	—	8	2	no	—
188	Dic₁₄₆	#135	1	2	yes	—
189	C₈×C₇₃	—	2	1	no	—
190	C₈×C₇₃	—	2	1	no	—
191	C₈×C₇₃	—	2	1	no	—
192	C₈×C₇₃	—	4	2	no	—
193	C₈×C₇₃	—	4	2	no	—
194	C₈×C₇₃	#135	1	2	yes	—
195	#10596831	—	4	1	no	—
196	#10596831	—	4	1	no	—
197	C₂²×C₇₃	—	2	1	no	—
198	C₂²×C₇₃	—	2	1	no	—
199	C₂²×C₇₃	—	2	1	no	—
200	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
201	C₂×D₇₃	—	2	2	no	—
202	C₂×D₇₃	—	4	1	no	—
203	C₂×D₇₃	—	4	1	no	—
204	C₂×D₇₃	—	8	2	no	—
205	C₂×D₇₃	—	8	2	no	—
206	C₂×D₇₃	—	8	2	no	—
207	C₄×C₇₃	—	2	1	no	—
208	C₄×C₇₃	—	2	1	no	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	#472	1	2	yes	—
211	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
212	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
213	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
214	C₄×C₇₃	#575	1	1	yes	characteristic
215	Dic₇₃	—	2	2	no	—
216	Dic₇₃	—	4	1	no	—
217	Dic₇₃	—	4	1	no	—
218	Dic₇₃	—	8	2	no	—
219	#19128	—	73	1	no	maximal, Sylow
220	C₂×C₇₃	—	4	1	no	—
221	C₂×C₇₃	#3035	1	1	yes	characteristic
222	C₂×C₇₃	#3050	1	1	yes	characteristic
223	C₂×C₇₃	C₂×#472	1	1	yes	characteristic
224	D₇₃	—	4	2	no	—
225	D₇₃	—	16	2	no	—
226	#3169	—	73	1	no	—
227	#3106	—	73	2	no	—
228	C₈×#41	—	73	1	no	—
229	#1678	—	73	2	no	—
230	#1677	—	73	2	no	—
231	#1676	—	73	1	no	—
232	#1675	—	73	1	no	—
233	#1668	—	73	1	no	—
234	#1667	—	73	1	no	—
235	#1564	D₇₃	1	1	yes	characteristic, complemented
236	#1543	—	73	2	no	—
237	C₇₃	#19128	1	1	yes	characteristic, complemented, Sylow
238	#532	—	73	2	no	—
239	C₄×#41	—	73	1	no	—
240	#500	—	73	1	no	—
241	#493	—	73	1	no	—
242	#486	—	73	2	no	—
243	#482	—	146	2	no	—
244	#477	—	73	2	no	—
245	#476	—	73	2	no	—
246	#466	—	146	1	no	—
247	#466	—	146	1	no	—
248	#460	—	73	2	no	—
249	#459	—	73	2	no	—
250	#449	—	146	2	no	—
251	C₈×Q₈	—	73	1	no	—
252	C₈×Q₈	—	73	1	no	—
253	C₄×SD₁₆	—	146	2	no	—
254	C₄×D₈	—	146	2	no	—
255	C₄×D₈	—	146	1	no	—
256	C₄×D₈	—	146	1	no	—
257	C₈×D₄	—	73	1	no	—
258	C₈×D₄	—	73	1	no	—
259	C₈×D₄	—	146	1	no	—
260	C₈×D₄	—	146	1	no	—
261	#431	—	73	1	no	—
262	#431	—	146	1	no	—
263	#431	C₂×D₇₃	1	2	yes	—
264	C₂×C₄×C₈	—	146	1	no	—
265	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
266	#335	C₂×D₇₃	1	1	yes	characteristic
267	#335	C₂×D₇₃	1	1	yes	characteristic
268	#334	C₂×D₇₃	1	2	yes	—
269	#333	—	73	2	no	—
270	#333	—	73	2	no	—
271	#331	—	73	2	no	—
272	#331	—	73	2	no	—
273	C₂×#41	—	73	1	no	—
274	C₂×#41	—	146	2	no	—
275	C₂×SD₁₆	—	146	2	no	—
276	C₂×D₈	—	146	2	no	—
277	C₂×D₈	—	146	1	no	—
278	C₂×D₈	—	146	1	no	—
279	C₂²×C₈	—	146	1	no	—
280	C₂²×C₈	—	146	1	no	—
281	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
282	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
283	C₄⋊Q₈	—	73	2	no	—
284	#127	—	73	2	no	—
285	#124	—	146	2	no	—
286	#121	—	146	2	no	—
287	#121	—	146	2	no	—
288	C₄×Q₈	—	73	1	no	—
289	C₄×Q₈	—	73	1	no	—
290	C₄×D₄	—	73	1	no	—
291	C₄×D₄	—	73	1	no	—
292	C₄×D₄	—	146	1	no	—
293	C₄×D₄	—	146	1	no	—
294	C₄×D₄	—	146	2	no	—
295	C₄×D₄	—	146	2	no	—
296	#117	—	73	1	no	—
297	#117	—	146	1	no	—
298	C₂×C₄²	—	146	1	no	—
299	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
300	#107	—	146	2	no	—
301	#107	—	146	1	no	—
302	#107	—	146	1	no	—
303	#106	—	146	2	no	—
304	C₄⋊C₈	—	73	1	no	—
305	C₄⋊C₈	—	73	1	no	—
306	C₄⋊C₈	—	146	1	no	—
307	C₄⋊C₈	—	146	1	no	—
308	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
309	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
310	#103	—	146	2	no	—
311	#102	—	146	2	no	—
312	#102	—	146	2	no	—
313	#102	—	146	2	no	—
314	#102	—	146	2	no	—
315	#102	—	146	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	146	1	no	—
318	C₂²⋊C₈	—	146	1	no	—
319	C₂²⋊C₈	—	146	1	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	146	1	no	—
322	C₄×C₈	—	146	1	no	—
323	C₄×C₈	—	146	1	no	—
324	C₄×C₈	D₂₉₂	1	1	yes	characteristic
325	C₄×C₈	D₂₉₂	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
327	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
328	#41	—	584	4	no	—
329	#41	—	146	2	no	—
330	#41	—	146	2	no	—
331	C₂×Q₈	—	73	1	no	—
332	C₂×Q₈	—	146	2	no	—
333	C₂×D₄	—	292	2	no	—
334	C₂×D₄	—	73	1	no	—
335	C₂×D₄	—	146	1	no	—
336	C₂×D₄	—	146	2	no	—
337	C₂×D₄	—	146	2	no	—
338	C₂×D₄	—	146	2	no	—
339	C₂²×C₄	—	292	2	no	—
340	C₂²×C₄	—	146	1	no	—
341	C₂²×C₄	—	146	1	no	—
342	C₂²×C₄	—	146	1	no	—
343	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
345	C₂²×C₄	#11924029	1	1	yes	characteristic
346	SD₁₆	—	292	4	no	—
347	D₈	—	292	2	no	—
348	D₈	—	292	4	no	—
349	D₈	—	292	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	292	2	no	—
355	C₂×C₈	—	292	2	no	—
356	C₂×C₈	—	146	1	no	—
357	C₂×C₈	—	146	1	no	—
358	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
359	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
360	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
361	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
362	C₄⋊C₄	—	73	1	no	—
363	C₄⋊C₄	—	73	1	no	—
364	C₄⋊C₄	—	146	2	no	—
365	C₄⋊C₄	—	146	2	no	—
366	C₄⋊C₄	—	146	1	no	—
367	C₄⋊C₄	—	146	1	no	—
368	C₂²⋊C₄	—	292	2	no	—
369	C₂²⋊C₄	—	292	2	no	—
370	C₂²⋊C₄	—	146	1	no	—
371	C₂²⋊C₄	—	146	1	no	—
372	C₂²⋊C₄	—	146	1	no	—
373	C₄²	—	146	1	no	—
374	C₄²	—	146	1	no	—
375	C₄²	—	146	1	no	—
376	C₄²	D₄×D₇₃	1	1	yes	characteristic
377	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
378	C₄²	#11924029	1	1	yes	characteristic
379	C₄²	C₂³×D₇₃	1	1	yes	characteristic
380	C₂³	—	292	2	no	—
381	C₂³	—	146	1	no	—
382	C₂³	#14556566	1	1	yes	characteristic
383	Q₈	—	584	2	no	—
384	Q₈	—	73	2	no	—
385	Q₈	—	146	1	no	—
386	D₄	—	292	2	no	—
387	D₄	—	292	2	no	—
388	D₄	—	292	2	no	—
389	D₄	—	292	2	no	—
390	D₄	—	584	2	no	—
391	D₄	—	584	4	no	—
392	D₄	—	73	2	no	—
393	D₄	—	146	4	no	—
394	D₄	—	146	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	292	1	no	—
401	C₂×C₄	—	292	1	no	—
402	C₂×C₄	—	292	2	no	—
403	C₂×C₄	—	292	2	no	—
404	C₂×C₄	—	584	4	no	—
405	C₂×C₄	—	146	4	no	—
406	C₂×C₄	—	146	1	no	—
407	C₂×C₄	—	146	1	no	—
408	C₂×C₄	—	146	1	no	—
409	C₂×C₄	#14556566	1	1	yes	characteristic
410	C₂×C₄	#14556566	1	1	yes	characteristic
411	C₂×C₄	#14556566	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
414	C₂×C₄	C₂×#11924029	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	292	1	no	—
421	C₈	—	292	1	no	—
422	C₈	#14556613	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	292	1	no	—
427	C₂²	—	292	1	no	—
428	C₂²	—	584	2	no	—
429	C₂²	—	584	2	no	—
430	C₂²	—	584	2	no	—
431	C₂²	—	146	2	no	—
432	C₂²	C₂×#14556566	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	292	1	no	—
437	C₄	—	292	1	no	—
438	C₄	—	584	2	no	—
439	C₄	—	146	2	no	—
440	C₄	#17988858	1	2	yes	—
441	C₄	#135×D₇₃	1	1	yes	characteristic
442	C₄	#135×D₇₃	1	1	yes	characteristic
443	C₄	C₂×#14556613	1	1	yes	characteristic
444	C₄	#17989387	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	292	2	no	—
447	C₂	—	1168	2	no	—
448	C₂	#22619388	1	1	yes	characteristic
449	C₂	#22619513	1	1	yes	characteristic
450	C₂	C₂×#17988858	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14556566
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1564	C₂
socle	C₂²×C₇₃	C₂×#121
hypercenter	#1564	D₇₃
hypocenter	C₇₃	#19128
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #22620510	C₂	semidirect
2. #22619992	C₂	semidirect
3. C₈×#11924028	C₂	semidirect
4. #22609348	C₂	semidirect
5. #22609341	C₂	semidirect
6. #22609336	C₂	semidirect
7. #22609331	C₂	semidirect
8. #22609292	C₂	semidirect
9. #22609287	C₂	semidirect
10. #22608591	C₂	semidirect
11. C₇₃×#1564	C₂	semidirect
235. #1564	D₇₃	semidirect
237. C₇₃	#19128	semidirect

Maximal subgroups

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

subgroup	index
#22620510	2
#22619992	2
C₈×#11924028	2
#22609348	2
#22609341	2
#22609336	2
#22609331	2
#22609292	2
#22609287	2
#22608591	2
C₇₃×#1564	2
#19128	73