Subgroups — #33104431

Order 18688.

858 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988710	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988708	C₂	1	1	yes	maximal, characteristic
3	#22618702	C₂	1	1	yes	maximal, characteristic
4	#22618498	C₂	1	2	yes	maximal, complemented
5	#22610685	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610207	C₂	1	2	yes	maximal, complemented
7	#22610205	C₂	1	2	yes	maximal, complemented
8	#22610101	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609950	C₂	1	2	yes	maximal, complemented
10	#22609799	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1946	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556613	C₂²	1	1	yes	characteristic
13	C₂×#14556599	C₂²	1	2	yes	—
14	C₂×#14556597	C₂²	1	2	yes	—
15	#17989055	C₂²	1	2	yes	—
16	#17988710	—	2	4	no	—
17	#17988708	—	2	4	no	—
18	#17988681	C₄	1	1	yes	characteristic, complemented
19	#17988681	C₄	1	1	yes	characteristic, complemented
20	#17988674	C₄	1	2	yes	complemented
21	#17988674	C₄	1	2	yes	complemented
22	#17988669	C₄	1	1	yes	characteristic, complemented
23	#17988669	C₄	1	1	yes	characteristic, complemented
24	C₂×#14556527	C₂²	1	1	yes	characteristic
25	C₂×#14556526	C₂²	1	2	yes	—
26	#17988614	C₂²	1	2	yes	—
27	#17988612	—	2	2	no	—
28	#17988612	—	2	2	no	—
29	#17988610	C₂²	1	2	yes	—
30	#17988609	—	2	2	no	—
31	C₂×#14556520	C₂²	1	1	yes	characteristic
32	C₄⋊C₈×D₇₃	—	2	2	no	—
33	C₂×#14556519	C₂²	1	2	yes	—
34	C₂×#14556517	C₂²	1	2	yes	—
35	#17988581	C₂²	1	2	yes	—
36	C₂×#14556501	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
38	C₄×#11924007	C₂²	1	1	yes	characteristic
39	#17988346	C₂²	1	2	yes	—
40	#17988342	C₂²	1	1	yes	characteristic
41	#17988341	C₂²	1	1	yes	characteristic
42	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
43	#427×C₇₃	C₂²	1	1	yes	characteristic
44	#424×C₇₃	C₂²	1	2	yes	—
45	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
46	#339×C₇₃	C₂²	1	2	yes	—
47	C₂×#11924028	C₂³	1	2	yes	—
48	#14556613	D₄	1	4	yes	—
49	#14556613	Q₈	1	4	yes	—
50	C₂×Dic₂₉₂	C₂×C₄	1	1	yes	characteristic
51	C₂×#11924017	C₂×C₄	1	2	yes	—
52	C₂×D₅₈₄	C₂×C₄	1	1	yes	characteristic
53	#14556599	—	2	4	no	—
54	#14556599	—	4	2	no	—
55	#14556597	—	2	4	no	—
56	#14556597	—	4	2	no	—
57	C₂×#11924012	C₂³	1	2	yes	—
58	C₂×#11924011	—	2	2	no	—
59	C₂×#11924011	—	2	2	no	—
60	C₂²×#10596831	C₂³	1	1	yes	characteristic
61	C₂²×#10596831	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₇₃	—	2	2	no	—
63	C₂×C₈×D₇₃	—	2	2	no	—
64	#14556556	C₂×C₄	1	2	yes	—
65	#14556556	C₂×C₄	1	2	yes	—
66	#14556553	C₂×C₄	1	2	yes	—
67	#14556553	C₂×C₄	1	2	yes	—
68	#14556551	—	2	2	no	—
69	#14556551	—	2	2	no	—
70	#14556548	—	2	2	no	—
71	C₂×#11924007	—	2	1	no	—
72	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
74	C₄²×D₇₃	—	2	2	no	—
75	#14556527	—	2	2	no	—
76	#14556526	—	4	2	no	—
77	C₄⋊#10596831	—	2	2	no	—
78	C₄⋊#10596831	—	2	2	no	—
79	#14556520	—	2	2	no	—
80	#14556520	—	2	2	no	—
81	#14556520	D₄	1	2	yes	—
82	#14556520	D₄	1	2	yes	—
83	#14556519	—	2	4	no	—
84	#14556517	—	2	4	no	—
85	#14556514	C₂×C₄	1	2	yes	—
86	#14556514	C₂×C₄	1	2	yes	—
87	#14556511	C₂×C₄	1	2	yes	—
88	#14556511	C₂×C₄	1	2	yes	—
89	#14556501	—	2	2	no	—
90	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
94	#14556498	—	2	1	no	—
95	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
96	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
98	#117×C₇₃	C₂³	1	2	yes	—
99	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
100	#108×C₇₃	—	2	2	no	—
101	#107×C₇₃	C₂×C₄	1	1	yes	characteristic
102	#107×C₇₃	C₂×C₄	1	1	yes	characteristic
103	#106×C₇₃	C₂×C₄	1	2	yes	—
104	C₄⋊C₈×C₇₃	—	2	2	no	—
105	C₄⋊C₈×C₇₃	—	2	2	no	—
106	#97×C₇₃	—	2	2	no	—
107	#11924028	—	2	2	no	—
108	#11924028	—	2	2	no	—
109	#11924028	C₂×D₄	1	4	yes	—
110	#11924028	C₂×Q₈	1	4	yes	—
111	C₂×Dic₁₄₆	C₂²×C₄	1	2	yes	—
112	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
113	C₂×C₂²⋊D₇₃	—	2	2	no	—
114	C₂²×Dic₇₃	—	2	1	no	—
115	C₂²×Dic₇₃	#41	1	1	yes	characteristic
116	C₂²×Dic₇₃	#41	1	1	yes	characteristic
117	C₂×C₄×D₇₃	—	2	2	no	—
118	C₂×C₄×D₇₃	—	2	2	no	—
119	C₂×C₄×D₇₃	—	2	2	no	—
120	Dic₂₉₂	C₄⋊C₄	1	4	yes	complemented
121	#11924017	C₄⋊C₄	1	8	yes	complemented
122	D₅₈₄	C₄⋊C₄	1	4	yes	complemented
123	#11924012	—	2	2	no	—
124	#11924012	—	2	2	no	—
125	#11924011	—	4	4	no	—
126	#11924011	—	4	4	no	—
127	C₂×#10596831	—	2	1	no	—
128	C₂×#10596831	—	2	1	no	—
129	C₂×#10596831	—	2	1	no	—
130	C₂×#10596831	—	2	1	no	—
131	C₂×#10596831	—	2	2	no	—
132	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
133	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
134	C₂×#10596831	C₂×D₄	1	2	yes	—
135	C₈×D₇₃	—	4	4	no	—
136	C₈×D₇₃	—	4	4	no	—
137	#11924007	—	2	2	no	—
138	#11924007	—	2	2	no	—
139	#11924007	—	4	2	no	—
140	#11924005	—	2	2	no	—
141	#11924005	—	2	2	no	—
142	C₄×Dic₇₃	—	2	2	no	—
143	C₄×Dic₇₃	—	2	2	no	—
144	C₄×Dic₇₃	—	2	1	no	—
145	C₄×Dic₇₃	—	2	1	no	—
146	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	—	2	1	no	—
151	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
152	M₁₆×C₇₃	—	2	2	no	—
153	M₁₆×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	2	1	no	—
155	C₂×C₈×C₇₃	—	2	1	no	—
156	C₂×C₈×C₇₃	—	2	2	no	—
157	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
162	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
163	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
164	C₂²⋊C₄×C₇₃	—	2	2	no	—
165	C₄²×C₇₃	—	2	2	no	—
166	C₄²×C₇₃	—	2	1	no	—
167	C₄²×C₇₃	—	2	1	no	—
168	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
169	C₂²×D₇₃	—	2	2	no	—
170	C₂×C₄×C₇₃	—	2	2	no	—
171	C₂×C₄×C₇₃	—	2	2	no	—
172	C₂×C₄×C₇₃	—	4	1	no	—
173	C₂×C₄×C₇₃	—	4	1	no	—
174	C₂×C₄×C₇₃	—	4	1	no	—
175	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
181	C₂²⋊D₇₃	—	2	4	no	—
182	C₂²⋊D₇₃	—	2	4	no	—
183	C₂×Dic₇₃	—	2	2	no	—
184	C₂×Dic₇₃	—	2	2	no	—
185	C₂×Dic₇₃	—	4	1	no	—
186	C₂×Dic₇₃	—	4	1	no	—
187	C₂×Dic₇₃	—	4	1	no	—
188	C₂×Dic₇₃	—	4	1	no	—
189	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
190	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
191	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
192	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
193	D₂₉₂	—	2	2	no	—
194	D₂₉₂	C₂×C₄⋊C₄	1	4	yes	—
195	C₄×D₇₃	—	2	4	no	—
196	C₄×D₇₃	—	2	4	no	—
197	C₄×D₇₃	—	4	4	no	—
198	C₄×D₇₃	—	8	2	no	—
199	Dic₁₄₆	—	2	2	no	—
200	Dic₁₄₆	C₂×C₄⋊C₄	1	4	yes	—
201	C₈×C₇₃	—	2	2	no	—
202	C₈×C₇₃	—	4	2	no	—
203	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
204	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
205	#10596831	—	2	1	no	—
206	#10596831	—	2	1	no	—
207	#10596831	—	2	2	no	—
208	#10596831	—	4	2	no	—
209	C₂²×C₇₃	—	2	1	no	—
210	C₂²×C₇₃	—	2	1	no	—
211	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂²×C₇₃	#547	1	1	yes	characteristic
213	C₂²×C₇₃	#554	1	1	yes	characteristic
214	C₂×D₇₃	—	2	4	no	—
215	C₂×D₇₃	—	4	2	no	—
216	C₂×D₇₃	—	4	2	no	—
217	C₄×C₇₃	—	4	2	no	—
218	C₄×C₇₃	—	4	2	no	—
219	C₄×C₇₃	—	8	1	no	—
220	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
221	C₄×C₇₃	#520	1	1	yes	characteristic
222	C₄×C₇₃	D₄²	1	1	yes	characteristic
223	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
224	Dic₇₃	—	2	4	no	—
225	Dic₇₃	—	2	1	no	—
226	Dic₇₃	—	2	1	no	—
227	Dic₇₃	—	2	1	no	—
228	Dic₇₃	—	8	1	no	—
229	Dic₇₃	#444	1	2	yes	complemented
230	#22686	—	73	1	no	maximal, Sylow
231	C₂×C₇₃	—	2	1	no	—
232	C₂×C₇₃	—	2	1	no	—
233	C₂×C₇₃	D₄×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₇₃	C₂×#444	1	1	yes	characteristic
235	C₂×C₇₃	#2957	1	1	yes	characteristic
236	D₇₃	—	4	4	no	—
237	C₂×#444	—	73	1	no	—
238	C₂×#444	—	73	1	no	—
239	C₄×#135	—	73	1	no	—
240	#2906	—	73	2	no	—
241	#1946	—	73	1	no	—
242	#1946	D₇₃	1	1	yes	characteristic, complemented
243	#1866	—	73	2	no	—
244	#1866	—	73	2	no	—
245	#1848	—	73	1	no	—
246	#1806	—	73	2	no	—
247	#1770	—	73	1	no	—
248	C₇₃	#22686	1	1	yes	characteristic, complemented, Sylow
249	C₂×#135	—	73	1	no	—
250	C₂×#131	—	73	2	no	—
251	C₂×#131	—	73	2	no	—
252	C₄×#41	—	73	2	no	—
253	#444	—	146	4	no	—
254	#444	—	146	4	no	—
255	C₄×Q₁₆	—	73	1	no	—
256	C₄×Q₁₆	—	73	1	no	—
257	C₄×SD₁₆	—	73	2	no	—
258	C₄×SD₁₆	—	73	2	no	—
259	C₄×D₈	—	73	1	no	—
260	C₄×D₈	—	73	1	no	—
261	C₂×#108	—	73	2	no	—
262	C₂×#108	—	73	1	no	—
263	C₂×#108	C₂×D₇₃	1	1	yes	characteristic
264	#427	C₂×D₇₃	1	1	yes	characteristic
265	#424	—	73	2	no	—
266	#424	—	146	2	no	—
267	#424	—	146	2	no	—
268	#424	C₂×D₇₃	1	2	yes	—
269	#423	—	73	2	no	—
270	#423	—	146	2	no	—
271	C₂×C₄⋊C₈	—	73	1	no	—
272	C₂×C₄⋊C₈	—	146	2	no	—
273	C₂×#104	—	73	2	no	—
274	C₂×#104	—	73	2	no	—
275	#416	—	73	2	no	—
276	C₂×#97	—	73	1	no	—
277	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
278	C₂×C₄×C₈	—	73	1	no	—
279	C₄×C₄⋊C₄	—	73	1	no	—
280	#339	—	73	2	no	—
281	#339	C₂×D₇₃	1	2	yes	—
282	#336	—	73	1	no	—
283	#336	—	73	1	no	—
284	C₂×#41	—	73	2	no	—
285	#135	—	73	4	no	—
286	#135	—	73	4	no	—
287	C₂×Q₁₆	—	73	1	no	—
288	C₂×SD₁₆	—	73	2	no	—
289	C₂×D₈	—	73	1	no	—
290	#131	—	292	2	no	—
291	#131	—	292	2	no	—
292	#131	—	146	4	no	—
293	#131	—	146	4	no	—
294	C₂×M₁₆	—	73	2	no	—
295	C₂×M₁₆	—	146	2	no	—
296	C₂×M₁₆	—	146	2	no	—
297	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
298	C₂²×C₈	—	73	1	no	—
299	C₂²×C₈	—	73	1	no	—
300	C₂²×C₈	—	146	2	no	—
301	C₂²×C₈	—	146	2	no	—
302	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
303	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
304	C₄×Q₈	—	73	2	no	—
305	C₄×Q₈	—	73	2	no	—
306	C₄×D₄	—	73	2	no	—
307	C₄×D₄	—	73	2	no	—
308	C₄×D₄	—	146	2	no	—
309	C₄×D₄	—	146	2	no	—
310	#117	—	146	2	no	—
311	#117	C₂²×D₇₃	1	2	yes	—
312	C₂×C₄⋊C₄	—	146	1	no	—
313	C₂×C₄²	—	73	1	no	—
314	C₂×C₄²	—	73	1	no	—
315	C₂×C₄²	—	146	2	no	—
316	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
317	#108	—	2	2	no	—
318	#108	—	292	2	no	—
319	#108	—	146	2	no	—
320	#107	C₄×D₇₃	1	1	yes	characteristic
321	#107	C₄×D₇₃	1	1	yes	characteristic
322	#106	C₄×D₇₃	1	2	yes	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	73	2	no	—
326	C₄⋊C₈	—	73	2	no	—
327	C₄⋊C₈	—	146	2	no	—
328	C₄⋊C₈	—	146	2	no	—
329	C₄⋊C₈	—	146	2	no	—
330	C₄⋊C₈	—	146	2	no	—
331	#104	—	146	4	no	—
332	#104	—	146	4	no	—
333	#103	—	73	2	no	—
334	#103	—	73	2	no	—
335	#102	—	73	2	no	—
336	#102	—	73	2	no	—
337	#97	—	2	2	no	—
338	#97	—	146	2	no	—
339	C₄×C₈	—	73	1	no	—
340	C₄×C₈	—	73	1	no	—
341	C₄×C₈	—	73	1	no	—
342	C₄×C₈	—	73	1	no	—
343	#95	—	146	1	no	—
344	#41	—	73	4	no	—
345	#41	—	73	4	no	—
346	#41	—	146	2	no	—
347	#41	—	146	2	no	—
348	C₂×Q₈	—	73	2	no	—
349	C₂×D₄	—	73	2	no	—
350	C₂×D₄	—	146	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	73	1	no	—
353	C₂²×C₄	—	73	1	no	—
354	C₂²×C₄	—	146	2	no	—
355	C₂²×C₄	—	146	2	no	—
356	C₂²×C₄	—	146	1	no	—
357	C₂²×C₄	—	146	2	no	—
358	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
359	Q₁₆	—	73	4	no	—
360	SD₁₆	—	73	8	no	—
361	D₈	—	73	4	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	292	4	no	—
365	M₁₆	—	292	4	no	—
366	M₁₆	—	146	2	no	—
367	M₁₆	—	146	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	292	4	no	—
372	C₂×C₈	—	292	4	no	—
373	C₂×C₈	—	73	1	no	—
374	C₂×C₈	—	73	1	no	—
375	C₂×C₈	—	73	2	no	—
376	C₂×C₈	—	146	2	no	—
377	C₂×C₈	—	146	1	no	—
378	C₂×C₈	—	146	1	no	—
379	C₂×C₈	—	146	1	no	—
380	C₂×C₈	—	146	1	no	—
381	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
382	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
383	C₂×C₈	D₄×D₇₃	1	2	yes	—
384	C₂×C₈	D₄×D₇₃	1	2	yes	—
385	C₂×C₈	Q₈×D₇₃	1	2	yes	—
386	C₄⋊C₄	—	292	2	no	—
387	C₄⋊C₄	—	146	2	no	—
388	C₄⋊C₄	—	146	2	no	—
389	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
390	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	146	2	no	—
393	C₂²⋊C₄	—	146	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	73	1	no	—
398	C₄²	—	73	1	no	—
399	C₄²	—	73	1	no	—
400	C₄²	—	73	1	no	—
401	C₄²	—	146	2	no	—
402	C₄²	—	146	2	no	—
403	C₄²	—	146	1	no	—
404	C₄²	—	146	1	no	—
405	C₂³	—	146	2	no	—
406	C₂³	#41×D₇₃	1	1	yes	characteristic
407	Q₈	—	73	4	no	—
408	Q₈	—	146	2	no	—
409	D₄	—	73	4	no	—
410	D₄	—	146	4	no	—
411	D₄	—	146	4	no	—
412	D₄	—	146	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	292	4	no	—
419	C₂×C₄	—	292	1	no	—
420	C₂×C₄	—	292	1	no	—
421	C₂×C₄	—	292	1	no	—
422	C₂×C₄	—	292	1	no	—
423	C₂×C₄	—	584	2	no	—
424	C₂×C₄	—	73	1	no	—
425	C₂×C₄	—	73	1	no	—
426	C₂×C₄	—	73	1	no	—
427	C₂×C₄	—	73	1	no	—
428	C₂×C₄	—	146	2	no	—
429	C₂×C₄	—	146	2	no	—
430	C₂×C₄	—	146	4	no	—
431	C₂×C₄	—	146	4	no	—
432	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
433	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
434	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
435	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
436	C₂×C₄	#14556637	1	1	yes	characteristic
437	C₂×C₄	#14556639	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	4	2	no	—
440	C₈	—	292	2	no	—
441	C₈	—	146	2	no	—
442	C₈	—	146	1	no	—
443	C₈	—	146	1	no	—
444	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
445	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	292	2	no	—
449	C₂²	—	292	2	no	—
450	C₂²	—	146	4	no	—
451	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
452	C₂²	#17989239	1	1	yes	characteristic
453	C₂²	#17989293	1	1	yes	characteristic
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	584	1	no	—
458	C₄	—	73	2	no	—
459	C₄	—	146	4	no	—
460	C₄	—	146	1	no	—
461	C₄	—	146	1	no	—
462	C₄	—	146	1	no	—
463	C₄	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
464	C₄	#17989069	1	1	yes	characteristic
465	C₄	#17989221	1	1	yes	characteristic
466	C₄	#17989252	1	1	yes	characteristic
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	292	4	no	—
470	C₂	#22612832	1	1	yes	characteristic
471	C₂	#444×D₇₃	1	1	yes	characteristic
472	C₂	#22618845	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1946	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#14556613	C₂²
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1946	D₇₃
hypocenter	C₇₃	#22686
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1946

Complements

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

N	H ≅ G/N	type
4. #22618498	C₂	semidirect
5. #22610685	C₂	semidirect
6. #22610207	C₂	semidirect
7. #22610205	C₂	semidirect
8. #22610101	C₂	semidirect
9. #22609950	C₂	semidirect
10. #22609799	C₂	semidirect
11. C₇₃×#1946	C₂	semidirect
18. #17988681	C₄	semidirect
19. #17988681	C₄	semidirect
20. #17988674	C₄	semidirect
21. #17988674	C₄	semidirect
22. #17988669	C₄	semidirect
23. #17988669	C₄	semidirect
120. Dic₂₉₂	C₄⋊C₄	semidirect
121. #11924017	C₄⋊C₄	semidirect
122. D₅₈₄	C₄⋊C₄	semidirect
229. Dic₇₃	#444	semidirect
242. #1946	D₇₃	semidirect
248. C₇₃	#22686	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988710	2
C₂×#17988708	2
#22618702	2
#22618498	2
#22610685	2
#22610207	2
#22610205	2
#22610101	2
#22609950	2
#22609799	2
C₇₃×#1946	2
#22686	73