Subgroups — #33104446

Order 18688.

870 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988704	C₂	1	1	yes	maximal, characteristic
2	#135×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	#22618497	C₂	1	2	yes	maximal, complemented
4	#22610679	C₂	1	1	yes	maximal, characteristic, complemented
5	#22610677	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610206	C₂	1	2	yes	maximal, complemented
7	#22610204	C₂	1	2	yes	maximal, complemented
8	#22610101	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609949	C₂	1	2	yes	maximal, complemented
10	C₈×#11924007	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#443×C₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556598	C₂²	1	2	yes	—
13	#41×Dic₇₃	C₂²	1	2	yes	—
14	#17988704	—	2	4	no	—
15	Q₁₆×Dic₇₃	C₄	1	1	yes	characteristic, complemented
16	Q₁₆×Dic₇₃	C₄	1	1	yes	characteristic, complemented
17	SD₁₆×Dic₇₃	C₄	1	2	yes	complemented
18	SD₁₆×Dic₇₃	C₄	1	2	yes	complemented
19	D₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
20	D₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
21	C₂×#14556527	C₂²	1	1	yes	characteristic
22	C₂×#14556526	C₂²	1	2	yes	—
23	#17988625	C₂²	1	1	yes	characteristic
24	#17988615	—	2	2	no	—
25	#17988615	C₂²	1	2	yes	—
26	#17988613	—	2	2	no	—
27	#17988613	C₂²	1	2	yes	—
28	#17988610	—	2	2	no	—
29	#17988610	C₂²	1	2	yes	—
30	C₂×#14556520	—	2	2	no	—
31	C₂×#14556520	C₂²	1	1	yes	characteristic
32	C₂×#14556518	C₂²	1	2	yes	—
33	#17988583	C₂²	1	2	yes	—
34	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
36	C₄×#11924007	C₂²	1	1	yes	characteristic
37	#17988348	C₂²	1	2	yes	—
38	#17988347	C₂²	1	2	yes	—
39	#17988342	C₂²	1	1	yes	characteristic
40	#17988341	C₂²	1	1	yes	characteristic
41	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×#131×C₇₃	C₂²	1	2	yes	—
43	#443×C₇₃	—	2	4	no	—
44	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×#104×C₇₃	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
47	#14556598	—	2	4	no	—
48	#14556598	—	4	2	no	—
49	C₂×#11924012	—	2	2	no	—
50	C₂×#11924012	C₂³	1	2	yes	—
51	C₂²×#10596831	—	2	2	no	—
52	C₂²×#10596831	C₂³	1	1	yes	characteristic
53	C₂²×#10596831	C₂³	1	1	yes	characteristic
54	Q₈×Dic₇₃	C₂×C₄	1	2	yes	—
55	Q₈×Dic₇₃	C₂×C₄	1	2	yes	—
56	D₄×Dic₇₃	—	2	2	no	—
57	D₄×Dic₇₃	—	2	2	no	—
58	D₄×Dic₇₃	C₂×C₄	1	2	yes	—
59	D₄×Dic₇₃	C₂×C₄	1	2	yes	—
60	#14556550	—	2	2	no	—
61	#14556550	C₂³	1	2	yes	—
62	C₂×#11924007	—	2	1	no	—
63	C₂×C₄×Dic₇₃	—	2	2	no	—
64	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
66	#14556527	—	2	2	no	—
67	#14556526	—	4	2	no	—
68	#14556525	C₂×C₄	1	1	yes	characteristic
69	#14556525	C₂×C₄	1	1	yes	characteristic
70	#14556523	C₂×C₄	1	2	yes	—
71	#14556520	—	2	2	no	—
72	#14556520	—	2	2	no	—
73	#14556520	—	2	2	no	—
74	#14556520	—	2	2	no	—
75	#14556520	—	2	2	no	—
76	#14556520	—	2	2	no	—
77	#14556520	D₄	1	1	yes	characteristic
78	#14556520	D₄	1	1	yes	characteristic
79	#14556520	D₄	1	1	yes	characteristic
80	#14556520	D₄	1	1	yes	characteristic
81	#14556518	—	2	4	no	—
82	#14556515	C₂×C₄	1	2	yes	—
83	#14556515	C₂×C₄	1	2	yes	—
84	#14556512	C₂×C₄	1	2	yes	—
85	#14556512	C₂×C₄	1	2	yes	—
86	C₈×Dic₇₃	—	2	2	no	—
87	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
90	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
91	#14556498	—	2	1	no	—
92	C₂×#41×C₇₃	C₂³	1	2	yes	—
93	#135×C₇₃	D₄	1	4	yes	—
94	#135×C₇₃	Q₈	1	4	yes	—
95	C₂×Q₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
96	C₂×SD₁₆×C₇₃	C₂×C₄	1	2	yes	—
97	C₂×D₈×C₇₃	C₂×C₄	1	1	yes	characteristic
98	#131×C₇₃	—	2	4	no	—
99	#131×C₇₃	—	4	2	no	—
100	C₂×M₁₆×C₇₃	—	2	2	no	—
101	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
102	C₂²×C₈×C₇₃	—	2	2	no	—
103	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
106	#108×C₇₃	—	2	2	no	—
107	#104×C₇₃	—	2	4	no	—
108	C₄×C₈×C₇₃	—	2	2	no	—
109	C₂²×Dic₇₃	—	2	1	no	—
110	C₂²×Dic₇₃	—	2	2	no	—
111	C₂²×Dic₇₃	—	2	2	no	—
112	C₂²×Dic₇₃	#41	1	1	yes	characteristic
113	C₂²×Dic₇₃	#41	1	1	yes	characteristic
114	#11924012	—	2	2	no	—
115	#11924012	—	2	2	no	—
116	#11924012	—	4	4	no	—
117	C₂×#10596831	—	2	1	no	—
118	C₂×#10596831	—	2	1	no	—
119	C₂×#10596831	—	2	1	no	—
120	C₂×#10596831	—	2	1	no	—
121	C₂×#10596831	—	2	2	no	—
122	C₂×#10596831	—	4	4	no	—
123	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
124	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
125	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
126	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
127	C₄⋊Dic₇₃	—	2	2	no	—
128	C₄⋊Dic₇₃	—	2	2	no	—
129	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
130	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
131	#11924007	—	2	4	no	—
132	C₂²⋊Dic₇₃	—	2	2	no	—
133	C₂²⋊Dic₇₃	—	2	2	no	—
134	C₂²⋊Dic₇₃	—	2	2	no	—
135	C₄×Dic₇₃	—	2	2	no	—
136	C₄×Dic₇₃	—	2	2	no	—
137	C₄×Dic₇₃	—	2	2	no	—
138	C₄×Dic₇₃	—	2	1	no	—
139	C₄×Dic₇₃	—	2	1	no	—
140	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
144	#41×C₇₃	—	2	2	no	—
145	#41×C₇₃	—	2	2	no	—
146	#41×C₇₃	C₂×D₄	1	4	yes	—
147	#41×C₇₃	C₂×Q₈	1	4	yes	—
148	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₇₃	—	2	2	no	—
150	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₇₃	—	2	2	no	—
152	C₂²×C₄×C₇₃	—	2	1	no	—
153	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₇₃	C₄⋊C₄	1	4	yes	complemented
155	SD₁₆×C₇₃	C₄⋊C₄	1	8	yes	complemented
156	D₈×C₇₃	C₄⋊C₄	1	4	yes	complemented
157	M₁₆×C₇₃	—	2	2	no	—
158	M₁₆×C₇₃	—	2	2	no	—
159	M₁₆×C₇₃	—	4	4	no	—
160	C₂×C₈×C₇₃	—	2	1	no	—
161	C₂×C₈×C₇₃	—	2	1	no	—
162	C₂×C₈×C₇₃	—	2	2	no	—
163	C₂×C₈×C₇₃	—	4	4	no	—
164	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
169	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
170	C₄²×C₇₃	—	2	1	no	—
171	C₄²×C₇₃	—	2	1	no	—
172	C₂³×C₇₃	—	2	2	no	—
173	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
174	Q₈×C₇₃	—	2	2	no	—
175	Q₈×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
176	D₄×C₇₃	—	2	4	no	—
177	D₄×C₇₃	—	2	4	no	—
178	D₄×C₇₃	—	2	2	no	—
179	D₄×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
180	C₂×C₄×C₇₃	—	2	2	no	—
181	C₂×C₄×C₇₃	—	2	4	no	—
182	C₂×C₄×C₇₃	—	2	4	no	—
183	C₂×C₄×C₇₃	—	2	2	no	—
184	C₂×C₄×C₇₃	—	4	1	no	—
185	C₂×C₄×C₇₃	—	4	1	no	—
186	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
192	C₂×Dic₇₃	—	2	2	no	—
193	C₂×Dic₇₃	—	2	2	no	—
194	C₂×Dic₇₃	—	2	2	no	—
195	C₂×Dic₇₃	—	2	2	no	—
196	C₂×Dic₇₃	—	4	1	no	—
197	C₂×Dic₇₃	—	4	1	no	—
198	C₂×Dic₇₃	—	4	1	no	—
199	C₂×Dic₇₃	—	4	4	no	—
200	C₂×Dic₇₃	—	8	2	no	—
201	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
202	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
203	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
204	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
205	C₈×C₇₃	—	2	1	no	—
206	C₈×C₇₃	—	2	1	no	—
207	C₈×C₇₃	—	4	2	no	—
208	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
209	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
210	#10596831	—	2	1	no	—
211	#10596831	—	2	1	no	—
212	#10596831	—	2	1	no	—
213	#10596831	—	2	1	no	—
214	#10596831	—	4	2	no	—
215	C₂²×C₇₃	—	2	1	no	—
216	C₂²×C₇₃	—	2	1	no	—
217	C₂²×C₇₃	—	2	4	no	—
218	C₂²×C₇₃	—	4	2	no	—
219	C₂²×C₇₃	—	4	2	no	—
220	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂²×C₇₃	#547	1	1	yes	characteristic
222	C₂²×C₇₃	#554	1	1	yes	characteristic
223	C₄×C₇₃	—	2	4	no	—
224	C₄×C₇₃	—	4	2	no	—
225	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
226	C₄×C₇₃	#520	1	1	yes	characteristic
227	C₄×C₇₃	D₄²	1	1	yes	characteristic
228	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
229	Dic₇₃	—	2	1	no	—
230	Dic₇₃	—	2	1	no	—
231	Dic₇₃	—	2	1	no	—
232	Dic₇₃	—	4	2	no	—
233	Dic₇₃	—	4	2	no	—
234	Dic₇₃	—	4	2	no	—
235	Dic₇₃	#443	1	2	yes	complemented
236	#22688	—	73	1	no	maximal, Sylow
237	C₂×C₇₃	—	2	1	no	—
238	C₂×C₇₃	—	2	1	no	—
239	C₂×C₇₃	—	4	4	no	—
240	C₂×C₇₃	D₄×C₄⋊C₄	1	1	yes	characteristic
241	C₂×C₇₃	C₂×#443	1	1	yes	characteristic
242	C₂×C₇₃	#2957	1	1	yes	characteristic
243	C₂×#443	—	73	1	no	—
244	C₂×#443	D₇₃	1	1	yes	characteristic
245	C₄×#135	—	73	1	no	—
246	#2906	—	73	2	no	—
247	#1945	—	73	1	no	—
248	#1945	—	73	1	no	—
249	#1866	—	73	2	no	—
250	#1866	—	73	2	no	—
251	#1848	—	73	1	no	—
252	#1806	—	73	2	no	—
253	C₈×C₄⋊C₄	—	73	1	no	—
254	C₇₃	#22688	1	1	yes	characteristic, complemented, Sylow
255	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
256	C₂×#131	—	73	2	no	—
257	C₂×#131	C₂×D₇₃	1	2	yes	—
258	C₄×#41	—	73	2	no	—
259	#443	—	2	4	no	—
260	#443	—	146	4	no	—
261	C₄×Q₁₆	—	73	1	no	—
262	C₄×Q₁₆	—	73	1	no	—
263	C₄×SD₁₆	—	73	2	no	—
264	C₄×SD₁₆	—	73	2	no	—
265	C₄×D₈	—	73	1	no	—
266	C₄×D₈	—	73	1	no	—
267	C₂×#108	—	73	2	no	—
268	C₂×#108	—	73	1	no	—
269	C₂×#108	C₂×D₇₃	1	1	yes	characteristic
270	#427	—	73	1	no	—
271	#424	—	73	2	no	—
272	#424	—	73	2	no	—
273	#424	—	146	2	no	—
274	#424	—	146	2	no	—
275	#423	—	73	2	no	—
276	#423	—	146	2	no	—
277	C₂×C₄⋊C₈	—	73	1	no	—
278	C₂×C₄⋊C₈	—	146	2	no	—
279	C₂×#104	—	73	2	no	—
280	C₂×#104	C₂×D₇₃	1	2	yes	—
281	#416	—	73	2	no	—
282	C₂×C₄×C₈	—	73	1	no	—
283	C₂×C₄×C₈	—	73	1	no	—
284	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
285	C₄×C₄⋊C₄	—	73	1	no	—
286	#339	—	73	2	no	—
287	#339	—	73	2	no	—
288	#336	—	73	1	no	—
289	#336	—	73	1	no	—
290	C₂×#41	C₂²×D₇₃	1	2	yes	—
291	#135	Dic₁₄₆	1	4	yes	—
292	#135	C₂²⋊D₇₃	1	4	yes	—
293	C₂×Q₁₆	C₄×D₇₃	1	1	yes	characteristic
294	C₂×SD₁₆	C₄×D₇₃	1	2	yes	—
295	C₂×D₈	C₄×D₇₃	1	1	yes	characteristic
296	#131	—	2	4	no	—
297	#131	—	4	2	no	—
298	#131	—	292	2	no	—
299	#131	—	146	4	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	73	2	no	—
302	C₂×M₁₆	—	146	2	no	—
303	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	—	73	1	no	—
306	C₂²×C₈	—	73	1	no	—
307	C₂²×C₈	—	146	2	no	—
308	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
309	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
310	C₄×Q₈	—	73	2	no	—
311	C₄×Q₈	—	73	2	no	—
312	C₄×D₄	—	73	2	no	—
313	C₄×D₄	—	73	2	no	—
314	C₄×D₄	—	146	2	no	—
315	C₄×D₄	—	146	2	no	—
316	#117	—	73	2	no	—
317	#117	—	146	2	no	—
318	C₂×C₄⋊C₄	—	146	1	no	—
319	C₂×C₄²	—	73	1	no	—
320	C₂×C₄²	—	73	1	no	—
321	C₂×C₄²	—	146	2	no	—
322	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
323	#108	—	2	2	no	—
324	#108	—	292	2	no	—
325	#108	—	146	2	no	—
326	#107	—	73	1	no	—
327	#107	—	73	1	no	—
328	#106	—	73	2	no	—
329	C₄⋊C₈	—	73	1	no	—
330	C₄⋊C₈	—	73	1	no	—
331	C₄⋊C₈	—	73	1	no	—
332	C₄⋊C₈	—	73	1	no	—
333	C₄⋊C₈	—	146	2	no	—
334	C₄⋊C₈	—	146	2	no	—
335	C₄⋊C₈	—	146	2	no	—
336	C₄⋊C₈	—	146	2	no	—
337	C₄⋊C₈	—	146	2	no	—
338	C₄⋊C₈	—	146	2	no	—
339	#104	—	2	4	no	—
340	#104	—	146	4	no	—
341	#103	—	73	2	no	—
342	#103	—	73	2	no	—
343	#102	—	73	2	no	—
344	#102	—	73	2	no	—
345	C₄×C₈	—	2	2	no	—
346	C₄×C₈	—	73	1	no	—
347	C₄×C₈	—	73	1	no	—
348	C₄×C₈	—	73	1	no	—
349	C₄×C₈	—	73	1	no	—
350	C₄×C₈	—	146	2	no	—
351	#95	—	146	1	no	—
352	#41	—	2	2	no	—
353	#41	—	2	2	no	—
354	#41	C₂×C₂²⋊D₇₃	1	4	yes	—
355	#41	C₂×Dic₁₄₆	1	4	yes	—
356	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	C₂×C₄×D₇₃	1	2	yes	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	73	1	no	—
362	C₂²×C₄	—	73	1	no	—
363	C₂²×C₄	—	146	2	no	—
364	C₂²×C₄	—	146	1	no	—
365	C₂²×C₄	—	146	2	no	—
366	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
367	Q₁₆	#11924007	1	4	yes	complemented
368	SD₁₆	#11924007	1	8	yes	complemented
369	D₈	#11924007	1	4	yes	complemented
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	4	4	no	—
373	M₁₆	—	292	4	no	—
374	M₁₆	—	146	2	no	—
375	M₁₆	—	146	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	4	4	no	—
380	C₂×C₈	—	292	4	no	—
381	C₂×C₈	—	73	1	no	—
382	C₂×C₈	—	73	1	no	—
383	C₂×C₈	—	73	1	no	—
384	C₂×C₈	—	73	1	no	—
385	C₂×C₈	—	146	2	no	—
386	C₂×C₈	—	146	1	no	—
387	C₂×C₈	—	146	1	no	—
388	C₂×C₈	—	146	1	no	—
389	C₂×C₈	—	146	1	no	—
390	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
391	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
392	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
393	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
394	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
395	C₂×C₈	C₂×Dic₁₄₆	1	2	yes	—
396	C₄⋊C₄	—	73	2	no	—
397	C₄⋊C₄	—	73	2	no	—
398	C₄⋊C₄	—	146	2	no	—
399	C₄⋊C₄	—	146	2	no	—
400	C₄⋊C₄	—	146	4	no	—
401	C₂²⋊C₄	—	146	2	no	—
402	C₂²⋊C₄	—	146	2	no	—
403	C₂²⋊C₄	—	146	2	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	73	1	no	—
407	C₄²	—	73	1	no	—
408	C₄²	—	73	1	no	—
409	C₄²	—	73	1	no	—
410	C₄²	—	146	2	no	—
411	C₄²	—	146	2	no	—
412	C₄²	—	146	1	no	—
413	C₄²	—	146	1	no	—
414	C₄²	—	146	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	#41×D₇₃	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	C₂×#11924007	1	4	yes	—
419	D₄	—	2	4	no	—
420	D₄	—	2	4	no	—
421	D₄	—	2	2	no	—
422	D₄	C₂×#11924007	1	4	yes	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	292	1	no	—
430	C₂×C₄	—	292	1	no	—
431	C₂×C₄	—	292	4	no	—
432	C₂×C₄	—	292	1	no	—
433	C₂×C₄	—	584	2	no	—
434	C₂×C₄	—	73	1	no	—
435	C₂×C₄	—	73	1	no	—
436	C₂×C₄	—	73	1	no	—
437	C₂×C₄	—	73	1	no	—
438	C₂×C₄	—	146	2	no	—
439	C₂×C₄	—	146	2	no	—
440	C₂×C₄	—	146	2	no	—
441	C₂×C₄	—	146	2	no	—
442	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
443	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
445	C₂×C₄	C₂²×Dic₁₄₆	1	1	yes	characteristic
446	C₂×C₄	#14556636	1	1	yes	characteristic
447	C₂×C₄	#14556638	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	292	2	no	—
452	C₈	—	146	1	no	—
453	C₈	—	146	1	no	—
454	C₈	—	146	1	no	—
455	C₈	—	146	1	no	—
456	C₈	C₂×#11924007	1	2	yes	—
457	C₈	C₂×#11924007	1	2	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
464	C₂²	#17989236	1	1	yes	characteristic
465	C₂²	#17989296	1	1	yes	characteristic
466	C₄	—	2	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	292	2	no	—
469	C₄	—	292	2	no	—
470	C₄	—	292	2	no	—
471	C₄	—	73	2	no	—
472	C₄	—	146	1	no	—
473	C₄	—	146	1	no	—
474	C₄	—	146	1	no	—
475	C₄	C₂²×#11924007	1	1	yes	characteristic
476	C₄	#17989066	1	1	yes	characteristic
477	C₄	D₄×C₂²⋊D₇₃	1	1	yes	characteristic
478	C₄	D₄×Dic₁₄₆	1	1	yes	characteristic
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	4	4	no	—
482	C₂	D₄×#11924007	1	1	yes	characteristic
483	C₂	#443×D₇₃	1	1	yes	characteristic
484	C₂	#22618843	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	C₂×#443×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#135×C₇₃	C₂²
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₂×#443	D₇₃
hypocenter	C₇₃	#22688
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
3. #22618497	C₂	semidirect
4. #22610679	C₂	semidirect
5. #22610677	C₂	semidirect
6. #22610206	C₂	semidirect
7. #22610204	C₂	semidirect
8. #22610101	C₂	semidirect
9. #22609949	C₂	semidirect
10. C₈×#11924007	C₂	semidirect
15. Q₁₆×Dic₇₃	C₄	semidirect
16. Q₁₆×Dic₇₃	C₄	semidirect
17. SD₁₆×Dic₇₃	C₄	semidirect
18. SD₁₆×Dic₇₃	C₄	semidirect
19. D₈×Dic₇₃	C₄	semidirect
20. D₈×Dic₇₃	C₄	semidirect
154. Q₁₆×C₇₃	C₄⋊C₄	semidirect
155. SD₁₆×C₇₃	C₄⋊C₄	semidirect
156. D₈×C₇₃	C₄⋊C₄	semidirect
235. Dic₇₃	#443	semidirect
254. C₇₃	#22688	semidirect
367. Q₁₆	#11924007	semidirect
368. SD₁₆	#11924007	semidirect
369. D₈	#11924007	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988704	2
#135×Dic₇₃	2
#22618497	2
#22610679	2
#22610677	2
#22610206	2
#22610204	2
#22610101	2
#22609949	2
C₈×#11924007	2
C₂×#443×C₇₃	2
#22688	73