Subgroups — D₇₃⋊#435 #22626639

Order 9344.

564 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#11924036	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989619	C₂	1	2	yes	maximal, complemented
4	#17989618	C₂	1	2	yes	maximal, complemented
5	#17989617	C₂	1	2	yes	maximal, complemented
6	#17989616	C₂	1	2	yes	maximal, complemented
7	#17989588	C₂	1	1	yes	maximal, characteristic, complemented
8	#17989555	C₂	1	1	yes	maximal, characteristic, complemented
9	#17989555	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#11924038	C₂²	1	2	yes	complemented
13	D₇₃⋊M₁₆	—	2	4	no	—
14	C₂×#11924037	C₂²	1	2	yes	complemented
15	C₂×#11924036	—	2	4	no	—
16	C₂×#11924036	C₂²	1	1	yes	characteristic
17	C₂×#11924036	C₂²	1	1	yes	characteristic
18	C₂×#11924036	C₂²	1	1	yes	characteristic
19	C₂×#11924036	C₂²	1	1	yes	characteristic
20	C₂×#11924036	C₂²	1	2	yes	complemented
21	C₂²×#10596833	C₂²	1	2	yes	complemented
22	#14556658	C₂²	1	2	yes	complemented
23	C₄⋊#10596833	C₂²	1	2	yes	complemented
24	#14556648	C₂²	1	2	yes	complemented
25	#14556648	C₂²	1	2	yes	complemented
26	C₂²⋊#10596833	C₂²	1	2	yes	complemented
27	C₂²⋊#10596833	C₂²	1	2	yes	complemented
28	#14556646	C₂²	1	2	yes	complemented
29	#14556646	C₂²	1	2	yes	complemented
30	C₂×D₄×D₇₃	C₄	1	1	yes	characteristic
31	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
33	C₄×D₂₉₂	C₄	1	1	yes	characteristic
34	D₄×Dic₇₃	C₂²	1	1	yes	characteristic
35	#14556553	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
37	C₄×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
38	#14556551	C₂²	1	1	yes	characteristic
39	#14556551	C₂²	1	1	yes	characteristic
40	C₄⋊C₄×D₇₃	C₄	1	1	yes	characteristic
41	C₂²⋊C₄×D₇₃	C₄	1	1	yes	characteristic
42	C₂²⋊C₄×D₇₃	C₄	1	1	yes	characteristic
43	C₄²×D₇₃	C₂²	1	1	yes	characteristic
44	C₄×D₄×C₇₃	C₄	1	1	yes	characteristic
45	#11924038	—	2	4	no	—
46	#11924037	—	2	4	no	—
47	#11924036	—	2	2	no	—
48	#11924036	—	2	2	no	—
49	#11924036	—	2	2	no	—
50	#11924036	—	2	4	no	—
51	#11924036	D₄	1	4	yes	complemented
52	C₂×#10596833	—	2	4	no	—
53	C₂×#10596833	C₂³	1	2	yes	—
54	C₂×#10596833	C₂³	1	2	yes	—
55	C₂×#10596833	C₂³	1	2	yes	—
56	C₂×#10596833	C₂³	1	2	yes	—
57	C₂³×D₇₃	C₂×C₄	1	1	yes	characteristic
58	C₂³×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂×D₂₉₂	C₂×C₄	1	1	yes	characteristic
60	C₂×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
62	D₄×D₇₃	—	2	4	no	—
63	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
64	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
65	C₂×C₄×D₇₃	—	2	2	no	—
66	C₂×C₄×D₇₃	—	2	2	no	—
67	C₂×C₄×D₇₃	—	2	2	no	—
68	C₂×C₄×D₇₃	—	2	2	no	—
69	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
76	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
78	C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
79	#11924007	C₂×C₄	1	1	yes	characteristic
80	#11924007	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
83	#11924005	C₂×C₄	1	1	yes	characteristic
84	#11924005	C₂×C₄	1	1	yes	characteristic
85	#11924005	C₂×C₄	1	1	yes	characteristic
86	#11924005	C₂×C₄	1	1	yes	characteristic
87	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
88	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
89	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
90	C₂×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
93	C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
96	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
97	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
98	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×D₇₃	—	2	2	no	—
100	C₂²×D₇₃	—	2	2	no	—
101	C₂²×D₇₃	—	2	2	no	—
102	C₂²×D₇₃	—	2	2	no	—
103	C₂²×D₇₃	—	2	2	no	—
104	C₂²×D₇₃	M₁₆	1	4	yes	complemented
105	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	D₄×C₇₃	—	2	2	no	—
109	C₂×C₄×C₇₃	—	2	2	no	—
110	C₂×C₄×C₇₃	—	2	2	no	—
111	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²⋊D₇₃	—	2	2	no	—
117	C₂²⋊D₇₃	—	2	2	no	—
118	C₂×Dic₇₃	—	2	1	no	—
119	C₂×Dic₇₃	—	2	1	no	—
120	C₂×Dic₇₃	—	2	1	no	—
121	C₂×Dic₇₃	—	2	1	no	—
122	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
127	D₂₉₂	—	2	2	no	—
128	C₄×D₇₃	—	2	2	no	—
129	C₄×D₇₃	—	2	2	no	—
130	C₄×D₇₃	—	2	2	no	—
131	C₄×D₇₃	—	2	2	no	—
132	C₄×D₇₃	—	2	2	no	—
133	C₄×D₇₃	—	2	2	no	—
134	C₄×D₇₃	—	2	1	no	—
135	C₄×D₇₃	—	2	1	no	—
136	C₄×D₇₃	—	2	1	no	—
137	C₄×D₇₃	—	2	1	no	—
138	C₄×D₇₃	C₂×D₄	1	2	yes	—
139	C₄×D₇₃	#41	1	2	yes	—
140	#10596833	—	2	2	no	—
141	#10596833	—	2	2	no	—
142	#10596833	—	2	2	no	—
143	#10596833	C₂×D₄	1	4	yes	complemented
144	C₂²×C₇₃	—	2	1	no	—
145	C₂²×C₇₃	—	2	1	no	—
146	C₂²×C₇₃	—	2	1	no	—
147	C₂²×C₇₃	—	2	1	no	—
148	C₂²×C₇₃	—	2	1	no	—
149	C₂²×C₇₃	C₂×M₁₆	1	2	yes	complemented
150	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
151	C₂×D₇₃	—	2	1	no	—
152	C₂×D₇₃	—	2	1	no	—
153	C₂×D₇₃	—	2	8	no	—
154	C₂×D₇₃	—	2	1	no	—
155	C₂×D₇₃	—	2	1	no	—
156	C₂×D₇₃	—	2	1	no	—
157	C₂×D₇₃	—	4	4	no	—
158	C₂×D₇₃	C₄×D₄	1	2	yes	—
159	C₂×D₇₃	C₂×M₁₆	1	2	yes	—
160	C₂×D₇₃	C₂×M₁₆	1	2	yes	complemented
161	C₂×D₇₃	#131	1	2	yes	—
162	C₄×C₇₃	—	2	1	no	—
163	C₄×C₇₃	—	2	1	no	—
164	C₄×C₇₃	—	2	1	no	—
165	C₄×C₇₃	—	2	1	no	—
166	C₄×C₇₃	C₄×D₄	1	2	yes	—
167	Dic₇₃	—	2	1	no	—
168	Dic₇₃	—	2	1	no	—
169	Dic₇₃	—	2	1	no	—
170	Dic₇₃	—	2	1	no	—
171	Dic₇₃	C₂²×D₄	1	1	yes	characteristic
172	Dic₇₃	C₂×#41	1	1	yes	characteristic
173	C₂×C₇₃	—	2	2	no	—
174	C₂×C₇₃	—	4	1	no	—
175	C₂×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
176	C₂×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
177	C₂×C₇₃	C₂×#131	1	1	yes	characteristic
178	D₇₃	—	2	2	no	—
179	D₇₃	—	4	1	no	—
180	D₇₃	#435	1	4	yes	complemented
181	C₂×#435	—	73	1	no	maximal, Sylow
182	C₇₃	C₂×#435	1	1	yes	characteristic, complemented, Sylow
183	C₂²×M₁₆	—	73	1	no	—
184	C₂³×C₈	—	73	1	no	—
185	C₂×C₄×D₄	—	73	1	no	—
186	#435	—	73	2	no	—
187	#435	—	73	2	no	—
188	#435	—	73	2	no	—
189	#435	—	73	2	no	—
190	C₂×C₄⋊C₈	—	73	1	no	—
191	C₂×C₂²⋊C₈	—	73	1	no	—
192	C₂×C₂²⋊C₈	—	73	1	no	—
193	C₂×#97	—	73	1	no	—
194	C₂²×D₄	—	73	1	no	—
195	C₂³×C₄	—	73	1	no	—
196	C₂³×C₄	—	73	1	no	—
197	C₂×M₁₆	—	73	2	no	—
198	C₂×M₁₆	—	73	2	no	—
199	C₂×M₁₆	—	146	4	no	—
200	C₂²×C₈	—	73	1	no	—
201	C₂²×C₈	—	73	2	no	—
202	C₂²×C₈	—	73	1	no	—
203	C₂²×C₈	—	73	1	no	—
204	C₂²×C₈	—	73	1	no	—
205	C₂²×C₈	—	73	2	no	—
206	C₂²×C₈	—	146	4	no	—
207	C₄×D₄	—	73	1	no	—
208	C₄×D₄	—	73	1	no	—
209	C₄×D₄	—	73	1	no	—
210	C₄×D₄	—	73	1	no	—
211	C₄×D₄	—	73	1	no	—
212	C₄×D₄	—	73	1	no	—
213	C₄×D₄	—	73	1	no	—
214	C₄×D₄	#64408	1	1	yes	characteristic
215	C₂×C₄⋊C₄	—	73	1	no	—
216	C₂×C₂²⋊C₄	—	73	1	no	—
217	C₂×C₂²⋊C₄	—	73	1	no	—
218	C₂×C₄²	—	73	1	no	—
219	C₄⋊C₈	—	73	2	no	—
220	C₄⋊C₈	—	73	2	no	—
221	C₂²⋊C₈	—	73	2	no	—
222	C₂²⋊C₈	—	73	2	no	—
223	C₂²⋊C₈	—	73	2	no	—
224	C₂²⋊C₈	—	73	2	no	—
225	#97	—	73	2	no	—
226	#97	—	73	2	no	—
227	C₂⁴	—	73	1	no	—
228	C₂⁴	—	73	1	no	—
229	C₂×D₄	—	73	1	no	—
230	C₂×D₄	—	73	1	no	—
231	C₂×D₄	—	73	1	no	—
232	C₂×D₄	—	146	4	no	—
233	C₂×D₄	C₂×#64408	1	1	yes	characteristic
234	C₂²×C₄	—	73	1	no	—
235	C₂²×C₄	—	73	1	no	—
236	C₂²×C₄	—	73	1	no	—
237	C₂²×C₄	—	73	1	no	—
238	C₂²×C₄	—	73	1	no	—
239	C₂²×C₄	—	73	1	no	—
240	C₂²×C₄	—	73	1	no	—
241	C₂²×C₄	—	73	1	no	—
242	C₂²×C₄	—	73	1	no	—
243	C₂²×C₄	—	73	1	no	—
244	C₂²×C₄	—	73	1	no	—
245	C₂²×C₄	—	146	2	no	—
246	C₂²×C₄	—	146	2	no	—
247	C₂²×C₄	—	146	2	no	—
248	C₂²×C₄	—	146	2	no	—
249	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
250	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
251	M₁₆	—	146	4	no	—
252	M₁₆	—	146	4	no	—
253	C₂×C₈	—	73	2	no	—
254	C₂×C₈	—	73	4	no	—
255	C₂×C₈	—	73	2	no	—
256	C₂×C₈	—	73	2	no	—
257	C₂×C₈	—	73	2	no	—
258	C₂×C₈	—	146	4	no	—
259	C₂×C₈	—	146	4	no	—
260	C₂×C₈	—	146	2	no	—
261	C₂×C₈	—	146	2	no	—
262	C₂×C₈	—	146	2	no	—
263	C₄⋊C₄	—	73	1	no	—
264	C₄⋊C₄	—	73	1	no	—
265	C₄⋊C₄	—	73	1	no	—
266	C₄⋊C₄	C₂×#64408	1	1	yes	characteristic
267	C₂²⋊C₄	—	73	1	no	—
268	C₂²⋊C₄	—	73	1	no	—
269	C₂²⋊C₄	—	73	1	no	—
270	C₂²⋊C₄	—	73	1	no	—
271	C₂²⋊C₄	—	73	1	no	—
272	C₂²⋊C₄	—	73	1	no	—
273	C₂²⋊C₄	C₂×#64408	1	1	yes	characteristic
274	C₂²⋊C₄	C₂×#64408	1	1	yes	characteristic
275	C₄²	—	73	1	no	—
276	C₄²	—	73	1	no	—
277	C₄²	—	73	1	no	—
278	C₄²	C₂×#64408	1	1	yes	characteristic
279	C₂³	—	73	1	no	—
280	C₂³	—	73	4	no	—
281	C₂³	—	73	1	no	—
282	C₂³	—	73	1	no	—
283	C₂³	—	146	2	no	—
284	C₂³	—	146	2	no	—
285	C₂³	—	146	2	no	—
286	C₂³	—	146	2	no	—
287	C₂³	—	146	2	no	—
288	C₂³	C₂²×#64408	1	1	yes	characteristic
289	C₂³	C₂²×#64408	1	1	yes	characteristic
290	D₄	—	2	2	no	—
291	D₄	—	146	2	no	—
292	D₄	—	146	2	no	—
293	D₄	—	146	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	73	1	no	—
297	C₂×C₄	—	73	2	no	—
298	C₂×C₄	—	73	2	no	—
299	C₂×C₄	—	73	1	no	—
300	C₂×C₄	—	73	1	no	—
301	C₂×C₄	—	73	1	no	—
302	C₂×C₄	—	73	1	no	—
303	C₂×C₄	—	146	1	no	—
304	C₂×C₄	—	146	1	no	—
305	C₂×C₄	—	146	1	no	—
306	C₂×C₄	—	146	1	no	—
307	C₂×C₄	—	146	2	no	—
308	C₂×C₄	—	146	2	no	—
309	C₂×C₄	—	146	2	no	—
310	C₂×C₄	—	146	2	no	—
311	C₂×C₄	—	146	1	no	—
312	C₂×C₄	—	146	1	no	—
313	C₂×C₄	—	146	1	no	—
314	C₂×C₄	—	146	1	no	—
315	C₂×C₄	—	146	2	no	—
316	C₂×C₄	—	146	2	no	—
317	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
318	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
319	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
320	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
321	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
322	C₈	—	73	4	no	—
323	C₈	—	146	2	no	—
324	C₈	—	146	2	no	—
325	C₈	—	146	2	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	292	4	no	—
332	C₂²	—	73	2	no	—
333	C₂²	—	73	2	no	—
334	C₂²	—	73	2	no	—
335	C₂²	—	73	2	no	—
336	C₂²	—	146	8	no	—
337	C₂²	—	146	1	no	—
338	C₂²	—	146	1	no	—
339	C₂²	—	146	1	no	—
340	C₂²	—	146	1	no	—
341	C₂²	—	146	1	no	—
342	C₂²	D₇₃⋊M₁₆	1	2	yes	complemented
343	C₂²	C₂³×#64408	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	73	1	no	—
349	C₄	—	73	1	no	—
350	C₄	—	146	1	no	—
351	C₄	—	146	1	no	—
352	C₄	—	146	1	no	—
353	C₄	—	146	1	no	—
354	C₄	D₄×#64408	1	2	yes	—
355	C₂	—	2	2	no	—
356	C₂	—	4	1	no	—
357	C₂	—	292	1	no	—
358	C₂	—	73	4	no	—
359	C₂	—	146	2	no	—
360	C₂	C₂×D₄×#64408	1	1	yes	characteristic
361	C₂	C₂×D₇₃⋊M₁₆	1	1	yes	characteristic
362	C₂	D₇₃⋊#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₄
Frattini	C₂²	C₂³×#64408
Fitting	C₄×D₄×C₇₃	C₄
hypercenter	C₄×D₄	#64408
hypocenter	C₇₃	C₂×#435
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₇₃⋊M₁₆	C₂	semidirect
2. C₂²×#11924036	C₂	semidirect
3. #17989619	C₂	semidirect
4. #17989618	C₂	semidirect
5. #17989617	C₂	semidirect
6. #17989616	C₂	semidirect
7. #17989588	C₂	semidirect
8. #17989555	C₂	semidirect
9. #17989555	C₂	semidirect
10. #17989546	C₂	semidirect
12. C₂×#11924038	C₂²	semidirect
14. C₂×#11924037	C₂²	semidirect
20. C₂×#11924036	C₂²	semidirect
21. C₂²×#10596833	C₂²	semidirect
22. #14556658	C₂²	semidirect
23. C₄⋊#10596833	C₂²	semidirect
24. #14556648	C₂²	semidirect
25. #14556648	C₂²	semidirect
26. C₂²⋊#10596833	C₂²	semidirect
27. C₂²⋊#10596833	C₂²	semidirect
28. #14556646	C₂²	semidirect
29. #14556646	C₂²	semidirect
51. #11924036	D₄	semidirect
104. C₂²×D₇₃	M₁₆	semidirect
143. #10596833	C₂×D₄	semidirect
149. C₂²×C₇₃	C₂×M₁₆	semidirect
160. C₂×D₇₃	C₂×M₁₆	semidirect
180. D₇₃	#435	semidirect
182. C₇₃	C₂×#435	semidirect
342. C₂²	D₇₃⋊M₁₆	semidirect

Subgroups — D73⋊#435 #22626639

Conjugacy classes of subgroups

Complements

Subgroups — D₇₃⋊#435 #22626639