Subgroups — #33057406

Order 18688.

794 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₇₃	C₂	1	1	yes	maximal, characteristic
2	#22618667	C₂	1	2	yes	maximal, complemented
3	#22608816	C₂	1	1	yes	maximal, characteristic, complemented
4	#22608763	C₂	1	2	yes	maximal, complemented
5	#22608758	C₂	1	2	yes	maximal, complemented
6	C₈×D₅₈₄	C₂	1	1	yes	maximal, characteristic, complemented
7	#22608725	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608688	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608354	C₂	1	2	yes	maximal, complemented
10	C₈×#11924011	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₇₃	C₄	1	1	yes	characteristic
13	C₂×M₁₆×D₇₃	—	2	2	no	—
14	C₄×D₄×D₇₃	C₂²	1	2	yes	—
15	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
16	D₈×Dic₇₃	C₄	1	1	yes	characteristic
17	#17988669	C₄	1	1	yes	characteristic
18	C₄×#11924013	C₂²	1	2	yes	—
19	#17988667	C₄	1	2	yes	—
20	#17988665	C₂²	1	2	yes	complemented
21	#17988661	—	2	2	no	—
22	#17988656	—	2	2	no	—
23	C₈×D₂₉₂	C₂²	1	2	yes	complemented
24	#17988652	C₂²	1	2	yes	complemented
25	#17988638	C₂²	1	1	yes	characteristic
26	#107×D₇₃	C₄	1	1	yes	characteristic
27	#17988609	C₂²	1	2	yes	—
28	#102×D₇₃	C₄	1	2	yes	—
29	#17988549	—	2	2	no	—
30	C₄×#11924011	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
32	#17988340	C₂²	1	1	yes	characteristic, complemented
33	#17988339	C₂²	1	2	yes	complemented
34	#17988316	C₂²	1	2	yes	complemented
35	D₄⋊#10596831	C₂²	1	2	yes	complemented
36	#17988314	C₂²	1	2	yes	complemented
37	#17988309	C₂²	1	1	yes	characteristic, complemented
38	#17988308	C₂²	1	1	yes	characteristic, complemented
39	C₈×#10596831	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic
41	#436×C₇₃	C₂²	1	2	yes	complemented
42	#335×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
44	C₈²×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₇₃	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₇₃	—	2	2	no	—
47	C₂×D₅₈₄	C₂×C₄	1	1	yes	characteristic
48	C₂×#11924013	C₂×C₄	1	2	yes	—
49	D₈×D₇₃	—	2	4	no	—
50	C₂×#11924012	—	2	2	no	—
51	C₂×#11924011	—	2	2	no	—
52	C₂×#11924011	D₄	1	1	yes	characteristic
53	C₂×#11924011	D₄	1	1	yes	characteristic
54	M₁₆×D₇₃	—	4	8	no	—
55	C₂×C₈×D₇₃	—	2	2	no	—
56	C₂×C₈×D₇₃	—	2	2	no	—
57	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₄×D₂₉₂	C₂³	1	2	yes	—
60	D₄×Dic₇₃	C₂×C₄	1	2	yes	—
61	#14556553	C₂×C₄	1	2	yes	—
62	C₄×C₂²⋊D₇₃	—	2	2	no	—
63	#14556551	—	2	2	no	—
64	C₄⋊C₄×D₇₃	C₂×C₄	1	2	yes	—
65	C₂²⋊C₄×D₇₃	—	2	2	no	—
66	C₄²×D₇₃	C₂³	1	1	yes	characteristic
67	#14556525	C₂×C₄	1	1	yes	characteristic
68	#14556524	C₂×C₄	1	2	yes	—
69	C₄⋊#10596831	C₂³	1	2	yes	—
70	#14556520	—	2	2	no	—
71	#14556520	—	2	1	no	—
72	#14556513	C₂×C₄	1	2	yes	—
73	#14556512	C₂×C₄	1	2	yes	—
74	#14556511	C₂×C₄	1	2	yes	—
75	C₂²⋊#10596831	—	2	2	no	—
76	#14556503	—	2	1	no	—
77	#14556503	—	2	2	no	—
78	#14556503	—	2	2	no	—
79	#14556501	D₄	1	1	yes	characteristic
80	#14556501	D₄	1	1	yes	characteristic
81	C₄×#10596831	C₂³	1	1	yes	characteristic
82	C₄×#10596831	C₂³	1	1	yes	characteristic
83	C₄×#10596831	C₂³	1	1	yes	characteristic
84	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
86	C₂×D₈×C₇₃	C₂×C₄	1	1	yes	characteristic
87	C₂×M₁₆×C₇₃	—	2	2	no	—
88	C₄×D₄×C₇₃	C₂³	1	2	yes	—
89	#107×C₇₃	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
91	#102×C₇₃	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₇₃	—	2	2	no	—
93	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
96	C₂³×D₇₃	—	2	2	no	—
97	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
98	C₂×C₂²⋊D₇₃	—	2	2	no	—
99	D₄×D₇₃	—	2	4	no	—
100	D₄×D₇₃	—	4	2	no	—
101	C₂²×Dic₇₃	—	2	2	no	—
102	C₂×C₄×D₇₃	—	2	2	no	—
103	C₂×C₄×D₇₃	—	2	2	no	—
104	C₂×C₄×D₇₃	—	2	2	no	—
105	C₂×C₄×D₇₃	—	4	4	no	—
106	C₂×C₄×D₇₃	—	4	4	no	—
107	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
110	D₅₈₄	M₁₆	1	4	yes	complemented
111	#11924013	—	2	4	no	—
112	#11924012	—	4	4	no	—
113	#11924011	—	2	2	no	—
114	#11924011	—	4	4	no	—
115	#11924011	D₈	1	4	yes	complemented
116	C₂×#10596831	—	2	2	no	—
117	C₂×#10596831	—	2	1	no	—
118	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
119	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
120	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
121	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
122	C₈×D₇₃	—	2	2	no	—
123	C₈×D₇₃	—	4	1	no	—
124	C₈×D₇₃	—	4	4	no	—
125	C₈×D₇₃	—	4	4	no	—
126	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
127	#11924007	—	2	2	no	—
128	C₂²⋊Dic₇₃	—	2	2	no	—
129	#11924005	—	2	2	no	—
130	#11924005	—	2	2	no	—
131	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
133	C₄×Dic₇₃	#41	1	1	yes	characteristic
134	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₇₃	—	2	2	no	—
136	D₈×C₇₃	—	2	2	no	—
137	M₁₆×C₇₃	—	4	4	no	—
138	C₂×C₈×C₇₃	—	2	2	no	—
139	C₂×C₈×C₇₃	—	2	1	no	—
140	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
145	C₂²⋊C₄×C₇₃	—	2	2	no	—
146	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
147	C₂³×C₇₃	—	2	2	no	—
148	C₂²×D₇₃	—	2	2	no	—
149	C₂²×D₇₃	—	4	4	no	—
150	C₂²×D₇₃	—	4	4	no	—
151	C₂²×D₇₃	—	8	2	no	—
152	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
153	D₄×C₇₃	—	2	2	no	—
154	D₄×C₇₃	—	2	2	no	—
155	C₂×C₄×C₇₃	—	2	2	no	—
156	C₂×C₄×C₇₃	—	4	2	no	—
157	C₂×C₄×C₇₃	—	4	2	no	—
158	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
161	C₂²⋊D₇₃	—	4	4	no	—
162	C₂×Dic₇₃	—	2	2	no	—
163	C₂×Dic₇₃	—	4	4	no	—
164	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
165	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
166	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
167	D₂₉₂	—	2	2	no	—
168	D₂₉₂	C₂×M₁₆	1	4	yes	complemented
169	C₄×D₇₃	—	2	1	no	—
170	C₄×D₇₃	—	2	1	no	—
171	C₄×D₇₃	—	4	1	no	—
172	C₄×D₇₃	—	4	4	no	—
173	C₄×D₇₃	—	4	2	no	—
174	C₄×D₇₃	—	4	2	no	—
175	C₄×D₇₃	—	4	4	no	—
176	C₄×D₇₃	C₂×D₈	1	2	yes	—
177	C₄×D₇₃	#135	1	2	yes	—
178	C₈×C₇₃	—	2	1	no	—
179	C₈×C₇₃	—	2	1	no	—
180	C₈×C₇₃	—	4	1	no	—
181	C₈×C₇₃	—	4	2	no	—
182	C₈×C₇₃	C₂×M₁₆	1	2	yes	complemented
183	C₈×C₇₃	C₂×D₈	1	2	yes	complemented
184	#10596831	—	2	1	no	—
185	#10596831	—	2	1	no	—
186	#10596831	—	2	1	no	—
187	#10596831	—	4	1	no	—
188	#10596831	—	4	2	no	—
189	#10596831	C₂×D₈	1	2	yes	complemented
190	C₂²×C₇₃	—	4	2	no	—
191	C₂²×C₇₃	—	4	2	no	—
192	C₂²×C₇₃	—	4	2	no	—
193	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂×D₇₃	—	2	1	no	—
195	C₂×D₇₃	—	2	1	no	—
196	C₂×D₇₃	—	2	4	no	—
197	C₂×D₇₃	—	4	2	no	—
198	C₂×D₇₃	—	4	2	no	—
199	C₂×D₇₃	—	8	8	no	—
200	C₂×D₇₃	C₄×D₈	1	2	yes	—
201	C₄×C₇₃	—	2	1	no	—
202	C₄×C₇₃	—	4	2	no	—
203	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
204	C₄×C₇₃	#568	1	1	yes	characteristic
205	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
206	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
207	Dic₇₃	—	2	1	no	—
208	Dic₇₃	—	2	1	no	—
209	Dic₇₃	—	4	2	no	—
210	Dic₇₃	C₄×D₈	1	2	yes	—
211	M₁₆×D₈	—	73	1	no	maximal, Sylow
212	C₂×C₇₃	—	8	2	no	—
213	C₂×C₇₃	D₄×M₁₆	1	1	yes	characteristic
214	C₂×C₇₃	C₂×C₄×D₈	1	1	yes	characteristic
215	C₂×C₇₃	#2957	1	1	yes	characteristic
216	D₇₃	—	2	2	no	—
217	D₇₃	—	4	4	no	—
218	C₂×C₄×D₈	—	73	1	no	—
219	D₄×M₁₆	—	73	2	no	—
220	#1589	—	73	1	no	—
221	#1589	D₇₃	1	1	yes	characteristic, complemented
222	#1581	—	73	2	no	—
223	#1581	—	73	2	no	—
224	C₈×D₈	—	73	1	no	—
225	C₈×D₈	—	73	1	no	—
226	#1567	—	73	1	no	—
227	#1486	—	73	2	no	—
228	C₈×M₁₆	—	73	1	no	—
229	C₇₃	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
230	C₂²×D₈	—	73	1	no	—
231	C₂²×M₁₆	—	146	2	no	—
232	C₂×C₄×D₄	—	73	2	no	—
233	C₄×D₈	—	73	1	no	—
234	C₄×D₈	—	73	2	no	—
235	C₄×D₈	—	73	1	no	—
236	C₄×D₈	—	73	2	no	—
237	C₄×D₈	—	73	1	no	—
238	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic
239	#436	—	73	2	no	—
240	#436	C₂×D₇₃	1	2	yes	complemented
241	#435	—	146	2	no	—
242	#435	—	146	2	no	—
243	C₈×D₄	—	73	2	no	—
244	C₈×D₄	—	73	2	no	—
245	#431	—	73	1	no	—
246	C₂×#107	—	73	1	no	—
247	#423	—	73	2	no	—
248	C₂×#102	—	73	2	no	—
249	#407	—	146	2	no	—
250	C₄×M₁₆	—	73	1	no	—
251	C₂×C₄×C₈	—	73	1	no	—
252	#335	—	73	2	no	—
253	#335	—	73	1	no	—
254	#335	C₂×D₇₃	1	1	yes	characteristic, complemented
255	D₄⋊C₈	—	73	2	no	—
256	D₄⋊C₈	—	73	2	no	—
257	D₄⋊C₈	—	73	2	no	—
258	D₄⋊C₈	C₂×D₇₃	1	2	yes	complemented
259	#322	—	73	1	no	—
260	#322	—	73	1	no	—
261	C₈²	—	73	1	no	—
262	C₈²	C₂×D₇₃	1	1	yes	characteristic, complemented
263	C₂²×D₄	—	73	2	no	—
264	C₂³×C₄	—	146	2	no	—
265	C₂×D₈	—	73	2	no	—
266	C₂×D₈	—	73	1	no	—
267	C₂×D₈	—	146	4	no	—
268	C₂×D₈	C₄×D₇₃	1	1	yes	characteristic
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	292	8	no	—
271	C₂×M₁₆	—	73	1	no	—
272	C₂×M₁₆	—	73	1	no	—
273	C₂×M₁₆	—	146	2	no	—
274	C₂×M₁₆	—	146	2	no	—
275	C₂²×C₈	—	73	1	no	—
276	C₂²×C₈	—	73	1	no	—
277	C₂²×C₈	—	146	2	no	—
278	C₂²×C₈	—	146	2	no	—
279	C₄×D₄	—	73	2	no	—
280	C₄×D₄	—	73	2	no	—
281	C₄×D₄	—	73	2	no	—
282	C₄×D₄	—	146	2	no	—
283	C₄×D₄	—	146	2	no	—
284	C₄×D₄	C₂²×D₇₃	1	2	yes	—
285	C₂×C₄⋊C₄	—	73	2	no	—
286	C₂×C₂²⋊C₄	—	146	2	no	—
287	C₂×C₄²	—	73	1	no	—
288	#107	—	73	1	no	—
289	#107	—	73	2	no	—
290	#107	C₄×D₇₃	1	1	yes	characteristic
291	C₄⋊C₈	—	73	2	no	—
292	C₄⋊C₈	—	146	2	no	—
293	C₄⋊C₈	—	146	1	no	—
294	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
295	#102	—	73	2	no	—
296	#102	—	73	2	no	—
297	#102	—	73	2	no	—
298	#102	C₄×D₇₃	1	2	yes	—
299	C₂²⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	146	2	no	—
301	C₂²⋊C₈	—	146	1	no	—
302	C₂²⋊C₈	—	146	2	no	—
303	C₂²⋊C₈	—	146	2	no	—
304	#97	—	73	1	no	—
305	#97	—	73	1	no	—
306	C₄×C₈	—	73	1	no	—
307	C₄×C₈	—	73	1	no	—
308	C₄×C₈	—	73	1	no	—
309	C₄×C₈	—	73	1	no	—
310	C₄×C₈	—	73	1	no	—
311	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
314	C₂⁴	—	146	2	no	—
315	C₂×D₄	—	292	2	no	—
316	C₂×D₄	—	73	2	no	—
317	C₂×D₄	—	146	2	no	—
318	C₂×D₄	—	146	4	no	—
319	C₂×D₄	C₂×C₄×D₇₃	1	2	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	292	4	no	—
322	C₂²×C₄	—	292	4	no	—
323	C₂²×C₄	—	73	1	no	—
324	C₂²×C₄	—	73	1	no	—
325	C₂²×C₄	—	73	1	no	—
326	C₂²×C₄	—	146	2	no	—
327	C₂²×C₄	—	146	2	no	—
328	C₂²×C₄	—	146	2	no	—
329	C₂²×C₄	—	146	2	no	—
330	D₈	—	2	2	no	—
331	D₈	—	73	4	no	—
332	D₈	—	146	4	no	—
333	M₁₆	—	4	4	no	—
334	M₁₆	—	292	4	no	—
335	M₁₆	—	292	4	no	—
336	M₁₆	—	73	4	no	—
337	M₁₆	—	146	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	292	1	no	—
341	C₂×C₈	—	292	4	no	—
342	C₂×C₈	—	292	4	no	—
343	C₂×C₈	—	73	1	no	—
344	C₂×C₈	—	73	1	no	—
345	C₂×C₈	—	73	1	no	—
346	C₂×C₈	—	73	1	no	—
347	C₂×C₈	—	146	2	no	—
348	C₂×C₈	—	146	1	no	—
349	C₂×C₈	—	146	2	no	—
350	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
351	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
352	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
353	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
354	C₄⋊C₄	—	73	2	no	—
355	C₄⋊C₄	—	146	2	no	—
356	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	146	2	no	—
359	C₂²⋊C₄	—	146	2	no	—
360	C₂²⋊C₄	—	146	2	no	—
361	C₄²	—	73	1	no	—
362	C₄²	—	73	1	no	—
363	C₄²	—	73	1	no	—
364	C₄²	C₂³×D₇₃	1	1	yes	characteristic
365	C₂³	—	2	2	no	—
366	C₂³	—	292	4	no	—
367	C₂³	—	292	4	no	—
368	C₂³	—	584	2	no	—
369	C₂³	—	73	1	no	—
370	C₂³	—	146	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	292	4	no	—
374	D₄	—	73	4	no	—
375	D₄	—	146	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	292	1	no	—
380	C₂×C₄	—	292	4	no	—
381	C₂×C₄	—	292	4	no	—
382	C₂×C₄	—	292	4	no	—
383	C₂×C₄	—	292	2	no	—
384	C₂×C₄	—	292	2	no	—
385	C₂×C₄	—	73	1	no	—
386	C₂×C₄	—	73	2	no	—
387	C₂×C₄	—	73	2	no	—
388	C₂×C₄	—	73	1	no	—
389	C₂×C₄	—	73	1	no	—
390	C₂×C₄	—	146	2	no	—
391	C₂×C₄	—	146	1	no	—
392	C₂×C₄	—	146	1	no	—
393	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
394	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
395	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	292	1	no	—
401	C₈	—	292	2	no	—
402	C₈	—	73	2	no	—
403	C₈	—	146	1	no	—
404	C₈	—	146	1	no	—
405	C₈	—	146	1	no	—
406	C₈	M₁₆×D₇₃	1	2	yes	complemented
407	C₈	D₈×D₇₃	1	2	yes	complemented
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	292	2	no	—
412	C₂²	—	292	2	no	—
413	C₂²	—	584	8	no	—
414	C₂²	—	73	2	no	—
415	C₂²	—	146	4	no	—
416	C₂²	—	146	1	no	—
417	C₂²	—	146	1	no	—
418	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	4	2	no	—
421	C₄	—	292	2	no	—
422	C₄	—	73	2	no	—
423	C₄	—	146	1	no	—
424	C₄	—	146	1	no	—
425	C₄	C₂×M₁₆×D₇₃	1	1	yes	characteristic
426	C₄	#17989352	1	1	yes	characteristic
427	C₄	C₂×D₈×D₇₃	1	1	yes	characteristic
428	C₄	#135×D₇₃	1	1	yes	characteristic
429	C₂	—	8	2	no	—
430	C₂	—	292	4	no	—
431	C₂	—	146	2	no	—
432	C₂	#22618667	1	1	yes	characteristic
433	C₂	C₄×D₈×D₇₃	1	1	yes	characteristic
434	C₂	#22618843	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1589	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₇₃	C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#1589	D₇₃
hypocenter	C₇₃	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1589

Complements

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

N	H ≅ G/N	type
2. #22618667	C₂	semidirect
3. #22608816	C₂	semidirect
4. #22608763	C₂	semidirect
5. #22608758	C₂	semidirect
6. C₈×D₅₈₄	C₂	semidirect
7. #22608725	C₂	semidirect
8. #22608688	C₂	semidirect
9. #22608354	C₂	semidirect
10. C₈×#11924011	C₂	semidirect
11. C₇₃×#1589	C₂	semidirect
20. #17988665	C₂²	semidirect
23. C₈×D₂₉₂	C₂²	semidirect
24. #17988652	C₂²	semidirect
32. #17988340	C₂²	semidirect
33. #17988339	C₂²	semidirect
34. #17988316	C₂²	semidirect
35. D₄⋊#10596831	C₂²	semidirect
36. #17988314	C₂²	semidirect
37. #17988309	C₂²	semidirect
38. #17988308	C₂²	semidirect
39. C₈×#10596831	C₂²	semidirect
41. #436×C₇₃	C₂²	semidirect
42. #335×C₇₃	C₂²	semidirect
43. D₄⋊C₈×C₇₃	C₂²	semidirect
44. C₈²×C₇₃	C₂²	semidirect
110. D₅₈₄	M₁₆	semidirect
115. #11924011	D₈	semidirect
168. D₂₉₂	C₂×M₁₆	semidirect
182. C₈×C₇₃	C₂×M₁₆	semidirect
183. C₈×C₇₃	C₂×D₈	semidirect
189. #10596831	C₂×D₈	semidirect
221. #1589	D₇₃	semidirect
229. C₇₃	M₁₆×D₈	semidirect
240. #436	C₂×D₇₃	semidirect
254. #335	C₂×D₇₃	semidirect
258. D₄⋊C₈	C₂×D₇₃	semidirect
262. C₈²	C₂×D₇₃	semidirect
406. C₈	M₁₆×D₇₃	semidirect
407. C₈	D₈×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₇₃	2
#22618667	2
#22608816	2
#22608763	2
#22608758	2
C₈×D₅₈₄	2
#22608725	2
#22608688	2
#22608354	2
C₈×#11924011	2
C₇₃×#1589	2
M₁₆×D₈	73