Subgroups — #34020241

Order 18688.

1018 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃⋊#430	C₂	1	1	yes	maximal, characteristic
2	#22626584	C₂	1	1	yes	maximal, characteristic
3	C₂×#17989550	C₂	1	2	yes	maximal
4	#22625737	C₂	1	4	yes	maximal, complemented
5	#22625733	C₂	1	4	yes	maximal, complemented
6	#22625612	C₂	1	2	yes	maximal
7	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×D₇₃⋊M₁₆	C₂²	1	2	yes	—
9	C₂×#14556670	C₂²	1	2	yes	—
10	#17989602	C₄	1	8	yes	complemented
11	D₇₃⋊#108	C₂²	1	4	yes	—
12	#17989598	C₄	1	8	yes	complemented
13	#17989597	C₂²	1	4	yes	—
14	#17989550	—	2	2	no	—
15	#17989550	—	2	2	no	—
16	#17989550	C₂²	1	4	yes	—
17	#17989550	C₂²	1	4	yes	—
18	C₂×#14556645	—	2	2	no	—
19	C₂×C₈×#64408	—	2	2	no	—
20	#17989458	C₂²	1	8	yes	—
21	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
22	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
23	#117×D₇₃	C₂²	1	1	yes	characteristic
24	#17988545	C₄	1	1	yes	characteristic, complemented
25	#17988544	C₄	1	2	yes	complemented
26	#17988543	C₄	1	1	yes	characteristic, complemented
27	#17988542	C₄	1	1	yes	characteristic, complemented
28	#17988541	C₄	1	2	yes	complemented
29	#97×D₇₃	C₂²	1	2	yes	—
30	C₄×C₈×D₇₃	C₂²	1	2	yes	—
31	#405×C₇₃	C₄	1	1	yes	characteristic, complemented
32	C₂×#11924038	C₂×C₄	1	4	yes	—
33	D₇₃⋊M₁₆	—	2	2	no	—
34	D₇₃⋊M₁₆	—	2	2	no	—
35	D₇₃⋊M₁₆	C₂×C₄	1	4	yes	—
36	D₇₃⋊M₁₆	C₂³	1	4	yes	—
37	C₂×#11924037	—	2	2	no	—
38	C₂×#11924036	—	2	2	no	—
39	#14556670	—	2	2	no	—
40	#14556670	—	2	2	no	—
41	#14556670	C₂×C₄	1	4	yes	—
42	#14556670	C₂³	1	4	yes	—
43	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
44	C₂×C₂²⋊#64408	—	2	2	no	—
45	C₂×C₄×#64408	—	2	2	no	—
46	#14556662	C₂×C₄	1	8	yes	complemented
47	#14556661	C₂×C₄	1	8	yes	complemented
48	#14556660	C₂×C₄	1	8	yes	—
49	#14556659	C₂×C₄	1	8	yes	—
50	#14556645	—	2	4	no	—
51	#14556645	—	2	4	no	—
52	C₈×#64408	—	2	4	no	—
53	C₈×#64408	—	2	4	no	—
54	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
55	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
56	C₂×#11924011	C₂×C₄	1	2	yes	—
57	M₁₆×D₇₃	C₂×C₄	1	4	yes	—
58	M₁₆×D₇₃	C₂×C₄	1	4	yes	—
59	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₇₃	D₄	1	2	yes	—
63	C₂×C₈×D₇₃	D₄	1	2	yes	—
64	C₂×C₈×D₇₃	Q₈	1	2	yes	—
65	C₂×C₈×D₇₃	Q₈	1	2	yes	—
66	C₂×C₈×D₇₃	C₂³	1	2	yes	—
67	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
69	#14556550	C₂×C₄	1	1	yes	characteristic
70	#14556549	—	2	1	no	—
71	#14556548	C₂×C₄	1	2	yes	—
72	#14556547	—	2	1	no	—
73	C₄⋊C₄×D₇₃	—	2	1	no	—
74	C₂²⋊C₄×D₇₃	—	2	1	no	—
75	C₄²×D₇₃	C₂³	1	2	yes	—
76	#14556502	C₂×C₄	1	2	yes	complemented
77	#14556501	C₂×C₄	1	2	yes	complemented
78	#14556501	C₂×C₄	1	2	yes	complemented
79	C₄×#10596831	C₂×C₄	1	2	yes	complemented
80	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
81	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
82	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
84	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
85	#97×C₇₃	C₂×C₄	1	2	yes	complemented
86	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
87	C₂²×#64408	—	2	4	no	—
88	#11924038	—	2	4	no	—
89	#11924038	C₂²×C₄	1	8	yes	—
90	#11924037	—	2	4	no	—
91	#11924037	—	2	4	no	—
92	#11924036	—	2	4	no	—
93	#11924036	—	2	4	no	—
94	C₂×#10596833	—	2	4	no	—
95	C₄⋊#64408	—	2	4	no	—
96	C₄⋊#64408	C₂²×C₄	1	8	yes	—
97	C₂²⋊#64408	—	2	4	no	—
98	C₂²⋊#64408	—	2	4	no	—
99	C₄×#64408	—	2	4	no	—
100	C₄×#64408	—	2	4	no	—
101	C₂³×D₇₃	#41	1	1	yes	characteristic
102	C₂²×Dic₇₃	#41	1	1	yes	characteristic
103	C₂×C₄×D₇₃	—	2	2	no	—
104	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
108	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
109	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
110	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
111	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
112	#11924012	C₄²	1	4	yes	—
113	#11924011	C₄²	1	8	yes	—
114	C₂×#10596831	C₄⋊C₄	1	2	yes	—
115	C₂×#10596831	C₄⋊C₄	1	2	yes	—
116	C₂×#10596831	C₂²×C₄	1	2	yes	—
117	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
118	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
119	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
120	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
121	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
122	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
123	C₈×D₇₃	C₂²×C₄	1	4	yes	—
124	C₈×D₇₃	C₂²×C₄	1	4	yes	—
125	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
126	C₈×D₇₃	C₂×D₄	1	2	yes	—
127	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
128	C₈×D₇₃	C₂×Q₈	1	1	yes	characteristic
129	C₈×D₇₃	C₂×Q₈	1	2	yes	—
130	C₈×D₇₃	C₂×Q₈	1	1	yes	characteristic
131	C₄⋊Dic₇₃	—	2	1	no	—
132	#11924007	—	2	2	no	—
133	C₂²⋊Dic₇₃	—	2	1	no	—
134	#11924005	—	2	2	no	—
135	C₄×Dic₇₃	—	2	2	no	—
136	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
138	M₁₆×C₇₃	C₄²	1	4	yes	—
139	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
140	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
141	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₂²⋊C₄×C₇₃	—	2	1	no	—
146	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
147	C₂³×C₇₃	#117	1	1	yes	characteristic
148	C₂²×D₇₃	—	4	2	no	—
149	C₂²×D₇₃	#117	1	1	yes	characteristic
150	C₂²×D₇₃	C₄×D₄	1	2	yes	—
151	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
152	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
153	C₂×#64408	—	2	8	no	—
154	C₂×#64408	—	4	8	no	—
155	C₂×C₄×C₇₃	—	2	2	no	—
156	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
157	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×Dic₇₃	—	2	2	no	—
161	C₂×Dic₇₃	#117	1	1	yes	characteristic
162	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
163	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
164	C₂×Dic₇₃	C₂×#41	1	1	yes	characteristic
165	C₄×D₇₃	—	4	4	no	—
166	C₄×D₇₃	C₂×C₄²	1	2	yes	—
167	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
168	C₄×D₇₃	C₄×D₄	1	2	yes	—
169	C₄×D₇₃	C₄×D₄	1	2	yes	—
170	C₄×D₇₃	C₄×Q₈	1	2	yes	—
171	C₄×D₇₃	C₄×Q₈	1	2	yes	—
172	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
173	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
174	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
175	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
176	#10596833	—	2	8	no	—
177	C₈×C₇₃	C₂×C₄²	1	4	yes	—
178	C₈×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
180	C₈×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	#10596831	C₂×C₄²	1	4	yes	—
182	#10596831	C₂×C₄⋊C₄	1	1	yes	characteristic
183	#10596831	C₂×C₄⋊C₄	1	2	yes	—
184	#10596831	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂²×C₇₃	—	4	1	no	—
186	C₂²×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
187	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
188	C₂×D₇₃	—	2	2	no	—
189	C₂×D₇₃	—	2	4	no	—
190	C₂×D₇₃	—	4	1	no	—
191	C₂×D₇₃	—	4	2	no	—
192	C₂×D₇₃	C₄×C₄⋊C₄	1	2	yes	—
193	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂×D₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
195	#64408	—	4	8	no	—
196	C₄×C₇₃	—	4	2	no	—
197	C₄×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
198	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
199	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
200	Dic₇₃	—	4	2	no	—
201	Dic₇₃	C₄×C₄⋊C₄	1	2	yes	—
202	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
203	Dic₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
204	#20444	—	73	1	no	maximal, Sylow
205	C₂×C₇₃	—	2	1	no	—
206	C₂×C₇₃	—	2	2	no	—
207	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
208	D₇₃	—	2	1	no	—
209	D₇₃	—	2	2	no	—
210	D₇₃	#2955	1	2	yes	—
211	C₂×#430	—	73	1	no	—
212	#2911	—	73	1	no	—
213	C₂×#405	—	73	1	no	—
214	C₂×#405	—	73	2	no	—
215	#1773	—	73	4	no	—
216	#1772	—	73	4	no	—
217	#1733	—	73	2	no	—
218	C₇₃	#20444	1	1	yes	characteristic, complemented, Sylow
219	C₂²×M₁₆	—	73	1	no	—
220	C₂²×M₁₆	—	73	2	no	—
221	C₂³×C₈	—	73	1	no	—
222	C₂×#117	—	73	1	no	—
223	C₂×#117	—	73	2	no	—
224	#430	—	73	8	no	—
225	C₂×#108	—	73	4	no	—
226	#428	—	73	8	no	—
227	#427	—	73	4	no	—
228	#405	—	73	1	no	—
229	#405	—	73	1	no	—
230	#405	—	73	1	no	—
231	#405	—	73	2	no	—
232	#405	—	73	2	no	—
233	#405	—	73	4	no	—
234	#405	—	73	4	no	—
235	#405	—	146	2	no	—
236	#405	—	146	2	no	—
237	#405	#64408	1	1	yes	characteristic, complemented
238	C₂×#97	—	73	2	no	—
239	C₂×#97	—	146	2	no	—
240	C₂×C₄×C₈	—	73	2	no	—
241	C₂×C₄×C₈	—	146	2	no	—
242	#339	—	73	8	no	—
243	C₂³×C₄	—	73	1	no	—
244	C₂×M₁₆	—	73	1	no	—
245	C₂×M₁₆	—	73	4	no	—
246	C₂×M₁₆	—	73	4	no	—
247	C₂×M₁₆	—	73	2	no	—
248	C₂×M₁₆	—	73	4	no	—
249	C₂×M₁₆	—	73	4	no	—
250	C₂×M₁₆	—	73	4	no	—
251	C₂×M₁₆	—	146	2	no	—
252	C₂×M₁₆	—	146	2	no	—
253	C₂×M₁₆	—	146	2	no	—
254	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
255	C₂²×C₈	—	73	1	no	—
256	C₂²×C₈	—	73	2	no	—
257	C₂²×C₈	—	73	2	no	—
258	C₂²×C₈	—	73	2	no	—
259	C₂²×C₈	—	73	2	no	—
260	C₂²×C₈	—	73	1	no	—
261	C₂²×C₈	—	73	1	no	—
262	C₂²×C₈	—	73	1	no	—
263	C₂²×C₈	—	73	1	no	—
264	C₂²×C₈	—	73	2	no	—
265	C₂²×C₈	—	146	2	no	—
266	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
267	#117	—	73	1	no	—
268	#117	—	73	2	no	—
269	#117	—	73	4	no	—
270	#117	—	73	4	no	—
271	#117	—	146	1	no	—
272	#117	—	146	1	no	—
273	#117	—	146	2	no	—
274	#117	—	146	2	no	—
275	#117	C₂×#64408	1	1	yes	characteristic
276	C₂×C₄⋊C₄	—	73	4	no	—
277	C₂×C₄⋊C₄	—	146	1	no	—
278	C₂×C₂²⋊C₄	—	146	1	no	—
279	C₂×C₂²⋊C₄	—	146	2	no	—
280	C₂×C₄²	—	73	2	no	—
281	C₂×C₄²	—	146	2	no	—
282	#108	—	73	8	no	—
283	#108	—	73	8	no	—
284	#107	—	73	8	no	—
285	#106	—	73	8	no	—
286	#97	—	73	2	no	—
287	#97	—	73	2	no	—
288	#97	—	73	2	no	—
289	#97	—	146	4	no	—
290	#97	—	146	4	no	—
291	#97	C₂×#64408	1	2	yes	complemented
292	C₄×C₈	—	73	2	no	—
293	C₄×C₈	—	73	2	no	—
294	C₄×C₈	—	73	2	no	—
295	C₄×C₈	—	146	4	no	—
296	C₄×C₈	—	146	4	no	—
297	C₄×C₈	C₂×#64408	1	2	yes	complemented
298	C₂⁴	—	73	1	no	—
299	C₂²×C₄	—	73	1	no	—
300	C₂²×C₄	—	73	1	no	—
301	C₂²×C₄	—	73	1	no	—
302	C₂²×C₄	—	73	2	no	—
303	C₂²×C₄	—	73	2	no	—
304	C₂²×C₄	—	73	2	no	—
305	C₂²×C₄	—	73	2	no	—
306	C₂²×C₄	—	73	1	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	146	2	no	—
309	C₂²×C₄	—	146	4	no	—
310	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
311	M₁₆	—	73	4	no	—
312	M₁₆	—	73	8	no	—
313	M₁₆	—	73	8	no	—
314	M₁₆	—	146	4	no	—
315	M₁₆	—	146	4	no	—
316	M₁₆	—	146	4	no	—
317	M₁₆	C₄×#64408	1	4	yes	—
318	C₂×C₈	—	73	1	no	—
319	C₂×C₈	—	73	2	no	—
320	C₂×C₈	—	73	1	no	—
321	C₂×C₈	—	73	2	no	—
322	C₂×C₈	—	73	2	no	—
323	C₂×C₈	—	73	4	no	—
324	C₂×C₈	—	73	4	no	—
325	C₂×C₈	—	73	2	no	—
326	C₂×C₈	—	73	2	no	—
327	C₂×C₈	—	73	2	no	—
328	C₂×C₈	—	73	2	no	—
329	C₂×C₈	—	73	1	no	—
330	C₂×C₈	—	73	1	no	—
331	C₂×C₈	—	73	2	no	—
332	C₂×C₈	—	73	2	no	—
333	C₂×C₈	—	73	1	no	—
334	C₂×C₈	—	73	1	no	—
335	C₂×C₈	—	146	4	no	—
336	C₂×C₈	—	146	4	no	—
337	C₂×C₈	—	146	4	no	—
338	C₂×C₈	C₄⋊#64408	1	2	yes	—
339	C₂×C₈	C₄⋊#64408	1	2	yes	—
340	C₂×C₈	C₂²×#64408	1	2	yes	—
341	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
342	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	73	8	no	—
345	C₄⋊C₄	—	146	2	no	—
346	C₄⋊C₄	—	146	4	no	—
347	C₄⋊C₄	—	146	1	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	146	2	no	—
350	C₂²⋊C₄	—	146	4	no	—
351	C₂²⋊C₄	—	146	4	no	—
352	C₂²⋊C₄	—	146	1	no	—
353	C₄²	—	73	2	no	—
354	C₄²	—	146	2	no	—
355	C₄²	—	146	4	no	—
356	C₄²	—	146	4	no	—
357	C₄²	C₂²×#64408	1	2	yes	—
358	C₂³	—	292	2	no	—
359	C₂³	—	73	1	no	—
360	C₂³	—	73	2	no	—
361	C₂³	—	73	1	no	—
362	C₂³	—	73	2	no	—
363	C₂³	#14556670	1	1	yes	characteristic
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	292	4	no	—
366	C₂×C₄	—	292	8	no	—
367	C₂×C₄	—	73	1	no	—
368	C₂×C₄	—	73	1	no	—
369	C₂×C₄	—	73	2	no	—
370	C₂×C₄	—	73	2	no	—
371	C₂×C₄	—	73	1	no	—
372	C₂×C₄	—	73	1	no	—
373	C₂×C₄	—	73	2	no	—
374	C₂×C₄	—	73	1	no	—
375	C₂×C₄	—	73	2	no	—
376	C₂×C₄	—	73	1	no	—
377	C₂×C₄	—	73	2	no	—
378	C₂×C₄	—	73	2	no	—
379	C₂×C₄	—	73	2	no	—
380	C₂×C₄	—	73	2	no	—
381	C₂×C₄	—	146	8	no	—
382	C₂×C₄	—	146	2	no	—
383	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
384	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
385	C₂×C₄	#14556670	1	1	yes	characteristic
386	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
387	C₈	—	73	4	no	—
388	C₈	—	73	1	no	—
389	C₈	—	73	1	no	—
390	C₈	—	73	2	no	—
391	C₈	—	146	8	no	—
392	C₈	C₂×C₄×#64408	1	4	yes	—
393	C₈	C₂×C₄⋊#64408	1	2	yes	—
394	C₈	C₂×C₄⋊#64408	1	1	yes	characteristic
395	C₈	C₂×C₄⋊#64408	1	1	yes	characteristic
396	C₂²	—	4	1	no	—
397	C₂²	—	292	1	no	—
398	C₂²	—	292	2	no	—
399	C₂²	—	73	1	no	—
400	C₂²	—	73	1	no	—
401	C₂²	—	73	2	no	—
402	C₂²	—	146	2	no	—
403	C₂²	—	146	4	no	—
404	C₂²	C₄×C₄⋊#64408	1	2	yes	—
405	C₂²	C₂×#14556670	1	1	yes	characteristic
406	C₄	—	4	2	no	—
407	C₄	—	292	2	no	—
408	C₄	—	292	8	no	—
409	C₄	—	73	1	no	—
410	C₄	—	73	1	no	—
411	C₄	—	73	2	no	—
412	C₄	C₄×C₄⋊#64408	1	2	yes	—
413	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
414	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	2	2	no	—
417	C₂	—	73	2	no	—
418	C₂	—	146	1	no	—
419	C₂	—	146	2	no	—
420	C₂	C₂×C₄×C₄⋊#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×C₄⋊#64408
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	#405×C₇₃	C₄
socle	C₂×C₇₃	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₇₃	#41
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#20444
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
4. #22625737	C₂	semidirect
5. #22625733	C₂	semidirect
10. #17989602	C₄	semidirect
12. #17989598	C₄	semidirect
24. #17988545	C₄	semidirect
25. #17988544	C₄	semidirect
26. #17988543	C₄	semidirect
27. #17988542	C₄	semidirect
28. #17988541	C₄	semidirect
31. #405×C₇₃	C₄	semidirect
46. #14556662	C₂×C₄	semidirect
47. #14556661	C₂×C₄	semidirect
76. #14556502	C₂×C₄	semidirect
77. #14556501	C₂×C₄	semidirect
78. #14556501	C₂×C₄	semidirect
79. C₄×#10596831	C₂×C₄	semidirect
80. C₈×Dic₇₃	C₂×C₄	semidirect
81. C₈×Dic₇₃	C₂×C₄	semidirect
85. #97×C₇₃	C₂×C₄	semidirect
86. C₄×C₈×C₇₃	C₂×C₄	semidirect
218. C₇₃	#20444	semidirect
237. #405	#64408	semidirect
291. #97	C₂×#64408	semidirect
297. C₄×C₈	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
D₇₃⋊#430	2
#22626584	2
C₂×#17989550	2
#22625737	2
#22625733	2
#22625612	2
#405×D₇₃	2
#20444	73