Subgroups — #34015782

Order 18688.

734 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626736	C₂	1	1	yes	maximal, characteristic
2	#22626614	C₂	1	1	yes	maximal, characteristic
3	#22625153	C₂	1	1	yes	maximal, characteristic, complemented
4	#22625152	C₂	1	1	yes	maximal, characteristic, complemented
5	#22625151	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625150	C₂	1	1	yes	maximal, characteristic, complemented
7	#22625147	C₂	1	1	yes	maximal, characteristic, complemented
8	#22625146	C₂	1	1	yes	maximal, characteristic, complemented
9	#22625142	C₂	1	1	yes	maximal, characteristic, complemented
10	#22625136	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#11924037	C₂	1	1	yes	maximal, characteristic, complemented
12	#22625129	C₂	1	1	yes	maximal, characteristic, complemented
13	M₁₆×#10596833	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#17989428	C₂	1	1	yes	maximal, characteristic, complemented
15	#22618891	C₂	1	1	yes	maximal, characteristic
16	#17989636	C₄	1	2	yes	—
17	#17989614	C₄	1	2	yes	—
18	#17989614	C₄	1	2	yes	—
19	D₄×#10596833	C₄	1	2	yes	—
20	#17989612	C₄	1	2	yes	—
21	#17989611	C₄	1	2	yes	—
22	#17989606	C₂²	1	1	yes	characteristic
23	#17989606	C₂²	1	1	yes	characteristic
24	#17989605	C₂²	1	1	yes	characteristic
25	#17989604	C₂²	1	1	yes	characteristic
26	#17989604	C₂²	1	1	yes	characteristic
27	#17989604	C₂²	1	1	yes	characteristic
28	#17989603	C₂²	1	1	yes	characteristic
29	#17989593	C₄	1	2	yes	—
30	#17989560	C₄	1	2	yes	—
31	C₄×#11924037	C₂²	1	1	yes	characteristic
32	C₄×#11924036	C₂²	1	1	yes	characteristic
33	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
34	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
35	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
36	#17989429	C₂²	1	1	yes	characteristic
37	#17989429	C₂²	1	1	yes	characteristic
38	#17989429	C₂²	1	1	yes	characteristic
39	#17989429	C₂²	1	1	yes	characteristic
40	#17989429	C₂²	1	1	yes	characteristic
41	#17989429	C₂²	1	1	yes	characteristic
42	#17989428	C₂²	1	1	yes	characteristic
43	#17989428	C₂²	1	1	yes	characteristic
44	#17989428	C₂²	1	1	yes	characteristic
45	#17989428	C₂²	1	1	yes	characteristic
46	#17989428	C₂²	1	1	yes	characteristic
47	#17989428	C₂²	1	1	yes	characteristic
48	C₈×#10596833	C₂²	1	1	yes	characteristic
49	C₈×#10596833	C₂²	1	1	yes	characteristic
50	C₈×#10596833	C₂²	1	1	yes	characteristic
51	C₈×#10596833	C₂²	1	1	yes	characteristic
52	C₄×#11924027	C₂²	1	1	yes	characteristic
53	#17988716	C₄	1	1	yes	characteristic
54	#17988715	C₄	1	1	yes	characteristic
55	#17988663	C₄	1	1	yes	characteristic
56	#17988662	C₄	1	1	yes	characteristic
57	#17988659	C₄	1	1	yes	characteristic
58	#17988658	C₄	1	1	yes	characteristic
59	#17988655	C₄	1	1	yes	characteristic
60	#17988639	C₂²	1	1	yes	characteristic
61	#17988637	C₂²	1	1	yes	characteristic
62	#17988637	C₂²	1	1	yes	characteristic
63	#17988539	C₂²	1	1	yes	characteristic
64	M₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
65	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
66	#435×C₇₃	C₄	1	1	yes	characteristic
67	C₂×#11924037	C₂×C₄	1	2	yes	—
68	C₂×#11924036	C₂×C₄	1	2	yes	—
69	C₂²×#10596833	C₂×C₄	1	2	yes	—
70	C₂²×#10596833	C₂×C₄	1	2	yes	—
71	C₂²×#10596833	C₂×C₄	1	2	yes	—
72	#14556658	C₂×C₄	1	2	yes	—
73	#14556658	C₂×C₄	1	2	yes	—
74	#14556658	C₂×C₄	1	2	yes	—
75	#14556658	C₂×C₄	1	2	yes	—
76	C₄⋊#10596833	C₂×C₄	1	2	yes	—
77	C₄⋊#10596833	C₂×C₄	1	2	yes	—
78	C₄⋊#10596833	C₂×C₄	1	2	yes	—
79	#14556648	C₂×C₄	1	2	yes	—
80	#14556648	C₂×C₄	1	2	yes	—
81	#14556648	C₂×C₄	1	2	yes	—
82	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
83	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
84	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
85	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
86	#14556646	C₂×C₄	1	2	yes	—
87	C₄×#10596833	C₂×C₄	1	2	yes	—
88	C₄×#10596833	C₂×C₄	1	2	yes	—
89	C₄×#10596833	C₂×C₄	1	2	yes	—
90	C₄×#10596833	C₂×C₄	1	2	yes	—
91	C₄×#10596833	C₂³	1	1	yes	characteristic
92	C₄×#10596833	C₂³	1	1	yes	characteristic
93	C₄×#10596833	C₂³	1	1	yes	characteristic
94	C₄×#10596833	C₂³	1	1	yes	characteristic
95	C₄×#10596833	C₂³	1	1	yes	characteristic
96	C₄×#10596833	C₂³	1	1	yes	characteristic
97	C₄×#10596833	C₂³	1	1	yes	characteristic
98	C₄×#10596833	C₂³	1	1	yes	characteristic
99	C₂×#11924027	C₂×C₄	1	1	yes	characteristic
100	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
101	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
102	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
103	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
105	#14556556	C₂×C₄	1	1	yes	characteristic
106	D₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
107	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
108	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
109	#14556551	C₂×C₄	1	1	yes	characteristic
110	#14556551	C₂×C₄	1	1	yes	characteristic
111	#14556549	C₂×C₄	1	1	yes	characteristic
112	#14556547	C₂×C₄	1	1	yes	characteristic
113	#14556547	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
115	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
116	C₄²×D₇₃	C₂³	1	1	yes	characteristic
117	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
118	#14556520	C₂×C₄	1	1	yes	characteristic
119	#14556520	C₂×C₄	1	1	yes	characteristic
120	#14556520	C₂×C₄	1	1	yes	characteristic
121	#14556520	C₂×C₄	1	1	yes	characteristic
122	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
123	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
124	#14556503	C₂×C₄	1	1	yes	characteristic
125	#14556503	C₂×C₄	1	1	yes	characteristic
126	#14556502	C₂×C₄	1	1	yes	characteristic
127	#14556501	C₂×C₄	1	1	yes	characteristic
128	#14556501	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
132	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
133	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
134	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
135	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
136	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
137	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
138	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
141	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
142	#11924037	—	2	4	no	—
143	#11924036	—	4	2	no	—
144	C₂×#10596833	—	2	4	no	—
145	C₂×#10596833	—	4	2	no	—
146	C₂×#10596833	—	4	2	no	—
147	C₂×#10596833	C₂²×C₄	1	2	yes	—
148	C₂×#10596833	C₂²×C₄	1	2	yes	—
149	C₂×#10596833	C₂²×C₄	1	2	yes	—
150	C₂×#10596833	C₂²×C₄	1	2	yes	—
151	C₂×#10596833	C₂²×C₄	1	2	yes	—
152	C₂×#10596833	C₂²×C₄	1	2	yes	—
153	C₂×#10596833	C₂²×C₄	1	2	yes	—
154	C₂×#10596833	C₂²×C₄	1	2	yes	—
155	#11924027	—	2	4	no	—
156	C₂×Dic₁₄₆	C₄²	1	1	yes	characteristic
157	C₂×C₂²⋊D₇₃	C₄²	1	1	yes	characteristic
158	C₂×C₂²⋊D₇₃	C₄²	1	1	yes	characteristic
159	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
166	#11924012	—	2	2	no	—
167	#11924011	—	2	2	no	—
168	#11924011	—	2	2	no	—
169	C₂×#10596831	—	2	2	no	—
170	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
171	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
172	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
173	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊Dic₇₃	C₄²	1	1	yes	characteristic
175	#11924007	C₄²	1	1	yes	characteristic
176	#11924007	C₄²	1	1	yes	characteristic
177	#11924007	C₄²	1	1	yes	characteristic
178	#11924007	C₄²	1	1	yes	characteristic
179	C₂²⋊Dic₇₃	C₄²	1	1	yes	characteristic
180	C₂²⋊Dic₇₃	C₄²	1	1	yes	characteristic
181	#11924005	C₄²	1	1	yes	characteristic
182	#11924005	C₄²	1	1	yes	characteristic
183	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
184	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
185	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
186	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
187	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
188	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
189	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
190	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
191	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
192	C₂×D₄×C₇₃	C₄²	1	1	yes	characteristic
193	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
195	M₁₆×C₇₃	—	2	2	no	—
196	C₂×C₈×C₇₃	—	2	2	no	—
197	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
201	C₄⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
202	C₂²⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
203	C₂²⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
204	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
205	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
206	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
207	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
208	D₄×C₇₃	—	2	2	no	—
209	C₂×C₄×C₇₃	—	2	1	no	—
210	C₂×C₄×C₇₃	—	2	1	no	—
211	C₂×C₄×C₇₃	—	2	1	no	—
212	C₂×C₄×C₇₃	—	2	1	no	—
213	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
214	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
215	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
217	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
218	C₂²⋊D₇₃	—	2	2	no	—
219	C₂²⋊D₇₃	—	2	2	no	—
220	C₂×Dic₇₃	—	2	2	no	—
221	C₂×Dic₇₃	—	2	2	no	—
222	C₂×Dic₇₃	—	2	2	no	—
223	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
224	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
225	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
226	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
227	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
228	C₂×Dic₇₃	#131	1	4	yes	—
229	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
230	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
231	C₄×D₇₃	—	2	1	no	—
232	C₄×D₇₃	—	2	1	no	—
233	C₄×D₇₃	—	2	2	no	—
234	C₄×D₇₃	—	2	2	no	—
235	Dic₁₄₆	—	2	2	no	—
236	#10596833	—	2	2	no	—
237	#10596833	—	2	2	no	—
238	#10596833	—	2	2	no	—
239	#10596833	—	2	2	no	—
240	#10596833	—	2	2	no	—
241	#10596833	—	2	2	no	—
242	#10596833	—	2	2	no	—
243	#10596833	—	2	2	no	—
244	C₈×C₇₃	—	2	1	no	—
245	C₈×C₇₃	—	2	1	no	—
246	C₈×C₇₃	—	2	1	no	—
247	C₈×C₇₃	#131	1	2	yes	—
248	#10596831	—	2	1	no	—
249	#10596831	—	2	1	no	—
250	#10596831	—	2	1	no	—
251	#10596831	#131	1	2	yes	—
252	C₂²×C₇₃	—	2	1	no	—
253	C₂²×C₇₃	—	2	1	no	—
254	C₂²×C₇₃	—	2	1	no	—
255	C₂²×C₇₃	—	2	1	no	—
256	C₂²×C₇₃	—	2	1	no	—
257	C₂²×C₇₃	#405	1	2	yes	—
258	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
259	C₂×D₇₃	—	2	1	no	—
260	C₂×D₇₃	—	2	1	no	—
261	C₂×D₇₃	—	2	1	no	—
262	C₄×C₇₃	—	2	1	no	—
263	C₄×C₇₃	—	2	1	no	—
264	C₄×C₇₃	—	2	1	no	—
265	C₄×C₇₃	—	2	1	no	—
266	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
267	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
268	Dic₇₃	—	2	1	no	—
269	Dic₇₃	—	2	1	no	—
270	Dic₇₃	—	2	1	no	—
271	Dic₇₃	—	2	1	no	—
272	Dic₇₃	#405	1	2	yes	—
273	Dic₇₃	C₂×#131	1	2	yes	—
274	Dic₇₃	#568	1	2	yes	—
275	#17331	—	73	1	no	maximal, Sylow
276	C₂×C₇₃	—	2	2	no	—
277	C₂×C₇₃	—	4	1	no	—
278	C₂×C₇₃	C₂×#405	1	1	yes	characteristic
279	C₂×C₇₃	C₄×#131	1	1	yes	characteristic
280	C₂×C₇₃	#2875	1	1	yes	characteristic
281	D₇₃	—	4	1	no	—
282	#2965	—	73	1	no	—
283	C₈×#41	—	73	1	no	—
284	#2922	—	73	1	no	—
285	#1454	—	73	1	no	—
286	#1454	—	73	1	no	—
287	#1453	—	73	1	no	—
288	#1453	—	73	1	no	—
289	#1452	—	73	1	no	—
290	#1452	—	73	1	no	—
291	#1451	—	73	1	no	—
292	#1450	—	73	1	no	—
293	C₈×M₁₆	—	73	1	no	—
294	C₈×M₁₆	—	73	1	no	—
295	C₈×M₁₆	—	73	1	no	—
296	C₂×#322	—	73	1	no	—
297	C₇₃	#17331	1	1	yes	characteristic, complemented, Sylow
298	C₄×#41	—	73	1	no	—
299	#446	—	73	1	no	—
300	#446	—	73	1	no	—
301	C₈×Q₈	—	73	2	no	—
302	#436	—	73	1	no	—
303	#436	—	73	1	no	—
304	#435	—	73	1	no	—
305	#435	—	73	1	no	—
306	#435	—	73	1	no	—
307	#435	#64408	1	1	yes	characteristic
308	C₈×D₄	—	73	2	no	—
309	C₈×D₄	—	73	2	no	—
310	C₈×D₄	—	73	2	no	—
311	#433	—	73	2	no	—
312	#433	—	73	2	no	—
313	#431	—	73	1	no	—
314	#431	—	73	1	no	—
315	#431	—	73	1	no	—
316	#431	—	73	1	no	—
317	#431	—	73	1	no	—
318	#431	—	73	1	no	—
319	#431	—	73	1	no	—
320	#431	—	73	1	no	—
321	#431	—	73	1	no	—
322	#431	—	73	1	no	—
323	#424	—	73	2	no	—
324	#408	—	73	2	no	—
325	C₄×M₁₆	—	73	1	no	—
326	C₄×M₁₆	—	73	1	no	—
327	C₄×M₁₆	—	73	1	no	—
328	C₂×C₄×C₈	—	73	1	no	—
329	C₂×C₄×C₈	—	73	1	no	—
330	C₂×C₄×C₈	—	73	1	no	—
331	C₂×C₄×C₈	—	73	1	no	—
332	C₂×C₄×C₈	—	73	1	no	—
333	#322	—	73	1	no	—
334	#322	—	73	1	no	—
335	#322	—	73	1	no	—
336	#322	—	73	1	no	—
337	#322	—	73	1	no	—
338	#322	—	73	1	no	—
339	#322	—	73	1	no	—
340	#322	—	73	1	no	—
341	#322	—	73	1	no	—
342	#322	—	73	1	no	—
343	#322	—	73	1	no	—
344	#322	—	73	1	no	—
345	C₈²	—	73	1	no	—
346	C₈²	—	73	1	no	—
347	C₈²	—	73	1	no	—
348	C₈²	—	73	1	no	—
349	C₂×#41	—	73	1	no	—
350	C₂×M₁₆	—	73	2	no	—
351	C₂×M₁₆	—	73	1	no	—
352	C₂×M₁₆	—	73	1	no	—
353	C₂×M₁₆	—	73	1	no	—
354	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
355	C₂²×C₈	—	73	2	no	—
356	C₂²×C₈	—	73	2	no	—
357	C₂²×C₈	—	73	2	no	—
358	C₂²×C₈	—	73	2	no	—
359	C₂²×C₈	—	73	1	no	—
360	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
361	C₄×Q₈	—	73	1	no	—
362	C₄×Q₈	—	73	1	no	—
363	C₄×D₄	—	73	1	no	—
364	C₄×D₄	—	73	1	no	—
365	C₄×D₄	—	73	1	no	—
366	C₄×D₄	—	73	1	no	—
367	C₄×D₄	—	73	1	no	—
368	C₄×D₄	C₂×#64408	1	1	yes	characteristic
369	#117	—	73	1	no	—
370	#117	—	73	1	no	—
371	#117	—	73	1	no	—
372	C₂×C₄²	—	73	1	no	—
373	C₂×C₄²	—	73	1	no	—
374	C₂×C₄²	—	73	1	no	—
375	C₄⋊C₈	—	73	2	no	—
376	C₄⋊C₈	—	73	2	no	—
377	C₄⋊C₈	—	73	2	no	—
378	C₄⋊C₈	—	73	2	no	—
379	C₄⋊C₈	—	73	2	no	—
380	C₄⋊C₈	—	73	2	no	—
381	C₄⋊C₈	—	73	2	no	—
382	C₄⋊C₈	—	73	1	no	—
383	C₄⋊C₈	—	73	1	no	—
384	C₄⋊C₈	—	73	1	no	—
385	C₄⋊C₈	—	73	1	no	—
386	C₄⋊C₈	—	73	1	no	—
387	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
388	C₂²⋊C₈	—	73	2	no	—
389	C₂²⋊C₈	—	73	2	no	—
390	C₂²⋊C₈	—	73	2	no	—
391	C₂²⋊C₈	—	73	2	no	—
392	C₂²⋊C₈	—	73	2	no	—
393	C₂²⋊C₈	—	73	2	no	—
394	C₂²⋊C₈	—	73	2	no	—
395	C₂²⋊C₈	—	73	1	no	—
396	C₂²⋊C₈	—	73	1	no	—
397	C₂²⋊C₈	—	73	1	no	—
398	C₂²⋊C₈	—	73	1	no	—
399	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
400	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
401	#97	—	73	2	no	—
402	#97	—	73	1	no	—
403	#97	—	73	1	no	—
404	#97	—	73	1	no	—
405	#97	C₂×#64408	1	1	yes	characteristic
406	C₄×C₈	—	73	1	no	—
407	C₄×C₈	—	73	1	no	—
408	C₄×C₈	—	73	1	no	—
409	C₄×C₈	—	73	1	no	—
410	C₄×C₈	—	73	1	no	—
411	C₄×C₈	—	73	1	no	—
412	C₄×C₈	—	73	1	no	—
413	C₄×C₈	—	73	1	no	—
414	C₄×C₈	—	73	2	no	—
415	C₄×C₈	—	73	2	no	—
416	C₄×C₈	—	73	2	no	—
417	C₄×C₈	—	73	2	no	—
418	C₄×C₈	—	73	1	no	—
419	C₄×C₈	—	73	1	no	—
420	C₄×C₈	—	73	1	no	—
421	C₄×C₈	—	73	1	no	—
422	C₄×C₈	—	73	1	no	—
423	C₄×C₈	—	73	1	no	—
424	#41	—	146	4	no	—
425	C₂×Q₈	—	73	1	no	—
426	C₂×D₄	—	73	1	no	—
427	C₂×D₄	—	73	1	no	—
428	C₂×D₄	C₄×#64408	1	1	yes	characteristic
429	C₂²×C₄	—	73	1	no	—
430	C₂²×C₄	—	73	1	no	—
431	C₂²×C₄	—	73	1	no	—
432	C₂²×C₄	—	73	1	no	—
433	C₂²×C₄	—	73	1	no	—
434	C₂²×C₄	—	73	1	no	—
435	C₂²×C₄	—	73	1	no	—
436	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
437	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
438	M₁₆	—	2	2	no	—
439	M₁₆	—	146	2	no	—
440	M₁₆	—	146	2	no	—
441	M₁₆	—	146	4	no	—
442	M₁₆	—	146	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	292	2	no	—
445	C₂×C₈	—	292	2	no	—
446	C₂×C₈	—	292	2	no	—
447	C₂×C₈	—	73	1	no	—
448	C₂×C₈	—	73	2	no	—
449	C₂×C₈	—	73	2	no	—
450	C₂×C₈	—	73	2	no	—
451	C₂×C₈	—	73	2	no	—
452	C₂×C₈	—	73	2	no	—
453	C₂×C₈	—	73	2	no	—
454	C₂×C₈	—	73	2	no	—
455	C₂×C₈	—	73	2	no	—
456	C₂×C₈	—	73	1	no	—
457	C₂×C₈	—	73	1	no	—
458	C₂×C₈	—	73	1	no	—
459	C₂×C₈	—	146	2	no	—
460	C₂×C₈	—	146	4	no	—
461	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
462	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
463	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
464	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
465	C₄⋊C₄	—	73	1	no	—
466	C₄⋊C₄	—	73	1	no	—
467	C₄⋊C₄	—	73	1	no	—
468	C₄⋊C₄	—	73	1	no	—
469	C₄⋊C₄	—	73	1	no	—
470	C₄⋊C₄	C₄×#64408	1	1	yes	characteristic
471	C₂²⋊C₄	—	73	1	no	—
472	C₂²⋊C₄	—	73	1	no	—
473	C₂²⋊C₄	—	73	1	no	—
474	C₂²⋊C₄	—	73	1	no	—
475	C₂²⋊C₄	C₄×#64408	1	1	yes	characteristic
476	C₂²⋊C₄	C₄×#64408	1	1	yes	characteristic
477	C₄²	—	73	1	no	—
478	C₄²	—	73	1	no	—
479	C₄²	—	73	1	no	—
480	C₄²	—	73	1	no	—
481	C₄²	—	73	1	no	—
482	C₄²	—	73	1	no	—
483	C₄²	—	73	1	no	—
484	C₄²	—	73	1	no	—
485	C₄²	—	73	1	no	—
486	C₄²	C₂²×#64408	1	1	yes	characteristic
487	C₂³	—	73	1	no	—
488	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
489	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
490	Q₈	—	146	2	no	—
491	D₄	—	2	2	no	—
492	D₄	—	146	2	no	—
493	D₄	—	146	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	73	1	no	—
499	C₂×C₄	—	73	1	no	—
500	C₂×C₄	—	73	1	no	—
501	C₂×C₄	—	73	4	no	—
502	C₂×C₄	—	73	1	no	—
503	C₂×C₄	—	73	1	no	—
504	C₂×C₄	—	73	1	no	—
505	C₂×C₄	—	73	1	no	—
506	C₂×C₄	—	146	2	no	—
507	C₂×C₄	—	146	2	no	—
508	C₂×C₄	—	146	2	no	—
509	C₂×C₄	—	146	2	no	—
510	C₂×C₄	—	146	2	no	—
511	C₂×C₄	—	146	1	no	—
512	C₂×C₄	—	146	1	no	—
513	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
514	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
515	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
516	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
517	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	1	no	—
521	C₈	—	73	2	no	—
522	C₈	—	146	2	no	—
523	C₈	—	146	2	no	—
524	C₈	—	146	2	no	—
525	C₈	—	146	2	no	—
526	C₈	—	146	2	no	—
527	C₈	—	146	2	no	—
528	C₈	—	146	2	no	—
529	C₈	—	146	2	no	—
530	C₈	—	146	1	no	—
531	C₈	—	146	1	no	—
532	C₈	—	146	1	no	—
533	C₈	#14556678	1	2	yes	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	146	1	no	—
540	C₂²	—	146	1	no	—
541	C₂²	—	146	1	no	—
542	C₂²	#17989553	1	2	yes	—
543	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	73	2	no	—
549	C₄	—	73	2	no	—
550	C₄	—	73	2	no	—
551	C₄	—	146	1	no	—
552	C₄	—	146	1	no	—
553	C₄	—	146	1	no	—
554	C₄	—	146	1	no	—
555	C₄	C₂×#14556678	1	1	yes	characteristic
556	C₄	D₇₃⋊#131	1	1	yes	characteristic
557	C₂	—	2	2	no	—
558	C₂	—	4	1	no	—
559	C₂	—	292	1	no	—
560	C₂	C₂×#17989553	1	1	yes	characteristic
561	C₂	C₄×#14556678	1	1	yes	characteristic
562	C₂	#22626501	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Fitting	#435×C₇₃	C₄
prime radical	C₂×#11924027	C₂×C₄
cosocle	C₄×Dic₇₃	C₂⁴
hypercenter	#435	#64408
hypocenter	C₇₃	#17331
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
3. #22625153	C₂	semidirect
4. #22625152	C₂	semidirect
5. #22625151	C₂	semidirect
6. #22625150	C₂	semidirect
7. #22625147	C₂	semidirect
8. #22625146	C₂	semidirect
9. #22625142	C₂	semidirect
10. #22625136	C₂	semidirect
11. C₈×#11924037	C₂	semidirect
12. #22625129	C₂	semidirect
13. M₁₆×#10596833	C₂	semidirect
14. C₂×#17989428	C₂	semidirect
297. C₇₃	#17331	semidirect

Maximal subgroups

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

subgroup	index
#22626736	2
#22626614	2
#22625153	2
#22625152	2
#22625151	2
#22625150	2
#22625147	2
#22625146	2
#22625142	2
#22625136	2
C₈×#11924037	2
#22625129	2
M₁₆×#10596833	2
C₂×#17989428	2
#22618891	2
#17331	73