Subgroups — #34015816

Order 18688.

798 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626742	C₂	1	1	yes	maximal, characteristic
2	#22626742	C₂	1	1	yes	maximal, characteristic
3	#22625155	C₂	1	1	yes	maximal, characteristic, complemented
4	#22625154	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	#22625145	C₂	1	1	yes	maximal, characteristic, complemented
8	#22625141	C₂	1	1	yes	maximal, characteristic, complemented
9	#22625140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11924038	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	#22625129	C₂	1	1	yes	maximal, characteristic, complemented
14	#22625127	C₂	1	1	yes	maximal, characteristic, complemented
15	#22618353	C₂	1	1	yes	maximal, characteristic
16	#17989639	C₄	1	2	yes	—
17	#17989639	C₄	1	2	yes	—
18	#17989620	C₄	1	2	yes	—
19	#17989620	C₄	1	2	yes	—
20	#17989619	C₄	1	2	yes	—
21	#17989619	C₄	1	2	yes	—
22	#17989617	C₄	1	2	yes	—
23	#17989617	C₄	1	2	yes	—
24	#17989606	C₂²	1	1	yes	characteristic
25	#17989606	C₂²	1	1	yes	characteristic
26	#17989605	C₂²	1	1	yes	characteristic
27	#17989605	C₂²	1	1	yes	characteristic
28	#17989604	C₂²	1	1	yes	characteristic
29	#17989604	C₂²	1	1	yes	characteristic
30	C₄×#11924038	C₂²	1	1	yes	characteristic
31	C₄×#11924038	C₂²	1	1	yes	characteristic
32	C₄×#11924037	C₂²	1	1	yes	characteristic
33	C₄×#11924037	C₂²	1	1	yes	characteristic
34	C₄×#11924036	C₂²	1	1	yes	characteristic
35	C₄×#11924036	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	#17989429	C₂²	1	1	yes	characteristic
43	#17989429	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	C₂×#14556599	C₄	1	1	yes	characteristic
53	C₂×#14556597	C₄	1	1	yes	characteristic
54	#17989055	C₂²	1	1	yes	characteristic
55	#17988544	C₄	1	1	yes	characteristic
56	#17988544	C₄	1	1	yes	characteristic
57	#17988543	C₄	1	1	yes	characteristic
58	#17988541	C₄	1	1	yes	characteristic
59	#17988541	C₄	1	1	yes	characteristic
60	#17988539	C₂²	1	1	yes	characteristic
61	#17988539	C₂²	1	1	yes	characteristic
62	M₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
63	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
64	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
65	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
66	#405×C₇₃	C₄	1	1	yes	characteristic
67	C₂×#11924038	C₂×C₄	1	2	yes	—
68	C₂×#11924038	C₂×C₄	1	2	yes	—
69	C₂×#11924037	C₂×C₄	1	2	yes	—
70	C₂×#11924037	C₂×C₄	1	2	yes	—
71	C₂×#11924036	C₂×C₄	1	2	yes	—
72	C₂×#11924036	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	#14556658	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	#14556648	C₂×C₄	1	2	yes	—
83	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
84	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
85	#14556646	C₂×C₄	1	2	yes	—
86	#14556646	C₂×C₄	1	2	yes	—
87	#14556646	C₂×C₄	1	2	yes	—
88	#14556646	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×#11924028	C₂×C₄	1	1	yes	characteristic
100	#14556599	—	2	4	no	—
101	#14556597	—	2	4	no	—
102	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
103	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
104	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
105	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
106	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
107	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
108	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
112	#14556556	C₂×C₄	1	1	yes	characteristic
113	#14556556	C₂×C₄	1	1	yes	characteristic
114	#14556553	C₂×C₄	1	1	yes	characteristic
115	#14556553	C₂×C₄	1	1	yes	characteristic
116	#14556551	C₂×C₄	1	1	yes	characteristic
117	#14556551	C₂×C₄	1	1	yes	characteristic
118	#14556551	C₂×C₄	1	1	yes	characteristic
119	#14556551	C₂×C₄	1	1	yes	characteristic
120	#14556548	C₂×C₄	1	1	yes	characteristic
121	#14556548	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
123	C₄²×D₇₃	C₂³	1	1	yes	characteristic
124	C₄²×D₇₃	C₂³	1	1	yes	characteristic
125	#14556502	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	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
130	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
134	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
135	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
136	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
139	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
140	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
141	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
142	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
143	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
144	#11924038	—	2	4	no	—
145	#11924038	—	4	2	no	—
146	#11924037	—	2	4	no	—
147	#11924037	—	4	2	no	—
148	#11924036	—	2	4	no	—
149	#11924036	—	4	2	no	—
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	C₂×#10596833	C₂²×C₄	1	2	yes	—
156	C₂×#10596833	C₂²×C₄	1	2	yes	—
157	C₂×#10596833	C₂²×C₄	1	2	yes	—
158	#11924028	—	2	2	no	—
159	#11924028	—	2	2	no	—
160	C₂×Dic₁₄₆	C₄²	1	1	yes	characteristic
161	C₂×D₂₉₂	C₄²	1	1	yes	characteristic
162	C₂×C₂²⋊D₇₃	C₄²	1	1	yes	characteristic
163	C₂×C₂²⋊D₇₃	C₄²	1	1	yes	characteristic
164	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
165	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
172	#11924012	—	2	2	no	—
173	#11924011	—	2	2	no	—
174	#11924011	—	2	2	no	—
175	#11924011	M₁₆	1	4	yes	complemented
176	#11924011	M₁₆	1	4	yes	complemented
177	C₂×#10596831	—	2	2	no	—
178	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
179	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
180	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
181	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
182	C₈×D₇₃	—	2	2	no	—
183	C₈×D₇₃	—	2	2	no	—
184	C₈×D₇₃	—	2	2	no	—
185	C₈×D₇₃	—	2	2	no	—
186	#11924007	C₄²	1	1	yes	characteristic
187	#11924007	C₄²	1	1	yes	characteristic
188	#11924007	C₄²	1	1	yes	characteristic
189	#11924007	C₄²	1	1	yes	characteristic
190	#11924005	C₄²	1	1	yes	characteristic
191	#11924005	C₄²	1	1	yes	characteristic
192	#11924005	C₄²	1	1	yes	characteristic
193	#11924005	C₄²	1	1	yes	characteristic
194	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
196	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
201	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
203	M₁₆×C₇₃	—	2	2	no	—
204	C₂×C₈×C₇₃	—	2	2	no	—
205	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
209	C₄⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
210	C₄⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
211	C₂²⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
212	C₂²⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
213	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
215	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
216	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
217	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
218	C₂×C₄×C₇₃	—	2	1	no	—
219	C₂×C₄×C₇₃	—	2	1	no	—
220	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
221	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
223	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
224	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
225	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
226	C₂²⋊D₇₃	—	2	2	no	—
227	C₂²⋊D₇₃	—	2	2	no	—
228	C₂×Dic₇₃	—	2	2	no	—
229	C₂×Dic₇₃	—	2	2	no	—
230	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
231	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
232	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
233	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
234	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
235	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
236	D₂₉₂	—	2	2	no	—
237	C₄×D₇₃	—	2	1	no	—
238	C₄×D₇₃	—	2	1	no	—
239	C₄×D₇₃	—	2	2	no	—
240	C₄×D₇₃	—	2	2	no	—
241	C₄×D₇₃	—	2	2	no	—
242	C₄×D₇₃	—	2	2	no	—
243	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
244	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
245	Dic₁₄₆	—	2	2	no	—
246	#10596833	—	2	2	no	—
247	#10596833	—	2	2	no	—
248	#10596833	—	2	2	no	—
249	#10596833	—	2	2	no	—
250	#10596833	—	2	2	no	—
251	#10596833	—	2	2	no	—
252	#10596833	—	2	2	no	—
253	#10596833	#131	1	4	yes	complemented
254	C₈×C₇₃	—	2	1	no	—
255	C₈×C₇₃	—	2	1	no	—
256	C₈×C₇₃	C₂×M₁₆	1	2	yes	—
257	C₈×C₇₃	C₂×M₁₆	1	2	yes	—
258	#10596831	—	2	1	no	—
259	#10596831	—	2	1	no	—
260	#10596831	C₂×M₁₆	1	2	yes	—
261	#10596831	C₂×M₁₆	1	2	yes	—
262	C₂²×C₇₃	—	2	1	no	—
263	C₂²×C₇₃	—	2	1	no	—
264	C₂²×C₇₃	—	2	1	no	—
265	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
266	C₂×D₇₃	—	2	1	no	—
267	C₂×D₇₃	—	2	1	no	—
268	C₂×D₇₃	—	2	1	no	—
269	C₂×D₇₃	—	2	1	no	—
270	C₂×D₇₃	—	2	1	no	—
271	C₂×D₇₃	C₄×M₁₆	1	2	yes	—
272	C₄×C₇₃	—	2	1	no	—
273	C₄×C₇₃	—	2	1	no	—
274	C₄×C₇₃	—	2	1	no	—
275	C₄×C₇₃	—	2	1	no	—
276	C₄×C₇₃	—	2	1	no	—
277	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
278	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
279	Dic₇₃	—	2	1	no	—
280	Dic₇₃	—	2	1	no	—
281	Dic₇₃	—	2	1	no	—
282	Dic₇₃	C₄×M₁₆	1	2	yes	—
283	Dic₇₃	C₂×#131	1	2	yes	—
284	Dic₇₃	#568	1	2	yes	—
285	#17337	—	73	1	no	maximal, Sylow
286	C₂×C₇₃	—	4	1	no	—
287	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
288	C₂×C₇₃	C₄×#131	1	1	yes	characteristic
289	C₂×C₇₃	#2875	1	1	yes	characteristic
290	D₇₃	—	2	2	no	—
291	D₇₃	—	4	1	no	—
292	#2965	—	73	1	no	—
293	#2965	—	73	1	no	—
294	C₄×#131	—	73	1	no	—
295	#1455	—	73	1	no	—
296	#1455	—	73	1	no	—
297	#1453	—	73	1	no	—
298	#1453	—	73	1	no	—
299	#1452	—	73	1	no	—
300	#1451	—	73	1	no	—
301	#1451	—	73	1	no	—
302	C₈×M₁₆	—	73	1	no	—
303	C₈×M₁₆	—	73	1	no	—
304	C₈×M₁₆	—	73	1	no	—
305	C₈×M₁₆	—	73	1	no	—
306	C₂×#322	—	73	1	no	—
307	C₇₃	#17337	1	1	yes	characteristic, complemented, Sylow
308	C₂×#131	—	73	1	no	—
309	C₂×#131	—	73	1	no	—
310	C₄×#41	—	73	1	no	—
311	#446	—	73	2	no	—
312	#446	—	73	2	no	—
313	#436	—	73	2	no	—
314	#436	—	73	2	no	—
315	#435	—	73	2	no	—
316	#435	—	73	2	no	—
317	#435	—	73	2	no	—
318	#435	—	73	2	no	—
319	#431	—	73	1	no	—
320	#431	—	73	1	no	—
321	#431	—	73	1	no	—
322	#431	—	73	1	no	—
323	#431	—	73	1	no	—
324	#431	—	73	1	no	—
325	#405	—	73	1	no	—
326	#405	—	73	1	no	—
327	#405	—	73	1	no	—
328	#405	—	73	1	no	—
329	#405	—	73	1	no	—
330	#405	#64408	1	1	yes	characteristic
331	C₄×M₁₆	—	73	1	no	—
332	C₄×M₁₆	—	73	1	no	—
333	C₄×M₁₆	—	73	1	no	—
334	C₄×M₁₆	—	73	1	no	—
335	C₄×M₁₆	—	73	1	no	—
336	C₄×M₁₆	—	73	1	no	—
337	C₄×M₁₆	—	73	1	no	—
338	C₂×C₄×C₈	—	73	1	no	—
339	C₂×C₄×C₈	—	73	1	no	—
340	C₂×C₄×C₈	—	73	1	no	—
341	C₂×C₄×C₈	—	73	1	no	—
342	C₂×C₄×C₈	—	73	1	no	—
343	#322	—	73	1	no	—
344	#322	—	73	1	no	—
345	#322	—	73	1	no	—
346	#322	—	73	1	no	—
347	#322	—	73	1	no	—
348	#322	—	73	1	no	—
349	#322	—	73	1	no	—
350	#322	—	73	1	no	—
351	#322	—	73	1	no	—
352	#322	—	73	1	no	—
353	#322	—	73	1	no	—
354	#322	—	73	1	no	—
355	C₈²	—	73	1	no	—
356	C₈²	—	73	1	no	—
357	C₈²	—	73	1	no	—
358	C₈²	—	73	1	no	—
359	C₂×#41	—	73	1	no	—
360	#131	—	146	4	no	—
361	#131	—	146	4	no	—
362	C₂×M₁₆	—	73	2	no	—
363	C₂×M₁₆	—	73	2	no	—
364	C₂×M₁₆	—	73	2	no	—
365	C₂×M₁₆	—	73	2	no	—
366	C₂×M₁₆	—	73	1	no	—
367	C₂×M₁₆	—	73	1	no	—
368	C₂×M₁₆	—	73	1	no	—
369	C₂×M₁₆	—	73	1	no	—
370	C₂×M₁₆	—	73	1	no	—
371	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
372	C₂²×C₈	—	73	2	no	—
373	C₂²×C₈	—	73	2	no	—
374	C₂²×C₈	—	73	1	no	—
375	C₂²×C₈	—	73	1	no	—
376	C₂²×C₈	—	73	1	no	—
377	C₂²×C₈	—	73	1	no	—
378	C₂²×C₈	—	73	1	no	—
379	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
380	C₄×Q₈	—	73	1	no	—
381	C₄×Q₈	—	73	1	no	—
382	C₄×D₄	—	73	1	no	—
383	C₄×D₄	—	73	1	no	—
384	C₄×D₄	—	73	1	no	—
385	C₄×D₄	—	73	1	no	—
386	C₄×D₄	—	73	1	no	—
387	C₄×D₄	—	73	1	no	—
388	#117	—	73	1	no	—
389	#117	—	73	1	no	—
390	#117	C₂×#64408	1	1	yes	characteristic
391	C₂×C₄²	—	73	1	no	—
392	C₂×C₄²	—	73	1	no	—
393	C₂×C₄²	—	73	1	no	—
394	C₄⋊C₈	—	73	2	no	—
395	C₄⋊C₈	—	73	2	no	—
396	C₄⋊C₈	—	73	2	no	—
397	C₄⋊C₈	—	73	2	no	—
398	C₄⋊C₈	—	73	2	no	—
399	C₄⋊C₈	—	73	2	no	—
400	C₂²⋊C₈	—	73	2	no	—
401	C₂²⋊C₈	—	73	2	no	—
402	C₂²⋊C₈	—	73	2	no	—
403	C₂²⋊C₈	—	73	2	no	—
404	C₂²⋊C₈	—	73	2	no	—
405	C₂²⋊C₈	—	73	2	no	—
406	#97	—	73	2	no	—
407	#97	—	73	2	no	—
408	#97	—	73	2	no	—
409	#97	—	73	2	no	—
410	#97	—	73	1	no	—
411	#97	—	73	1	no	—
412	#97	—	73	1	no	—
413	#97	—	73	1	no	—
414	#97	C₂×#64408	1	1	yes	characteristic
415	#97	C₂×#64408	1	1	yes	characteristic
416	C₄×C₈	—	73	1	no	—
417	C₄×C₈	—	73	1	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	C₄×C₈	—	73	2	no	—
425	C₄×C₈	—	73	2	no	—
426	C₄×C₈	—	73	1	no	—
427	C₄×C₈	—	73	1	no	—
428	C₄×C₈	—	73	1	no	—
429	C₄×C₈	—	73	1	no	—
430	C₄×C₈	—	73	1	no	—
431	C₄×C₈	—	73	1	no	—
432	C₄×C₈	—	73	1	no	—
433	C₄×C₈	—	73	1	no	—
434	C₄×C₈	C₂×#64408	1	1	yes	characteristic
435	C₄×C₈	C₂×#64408	1	1	yes	characteristic
436	#41	—	146	2	no	—
437	#41	—	146	2	no	—
438	C₂×Q₈	—	73	1	no	—
439	C₂×D₄	—	73	1	no	—
440	C₂×D₄	—	73	1	no	—
441	C₂×D₄	—	73	1	no	—
442	C₂²×C₄	—	73	1	no	—
443	C₂²×C₄	—	73	1	no	—
444	C₂²×C₄	—	73	1	no	—
445	C₂²×C₄	—	73	1	no	—
446	C₂²×C₄	—	73	1	no	—
447	C₂²×C₄	—	73	1	no	—
448	C₂²×C₄	—	73	1	no	—
449	C₂²×C₄	—	73	1	no	—
450	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
451	M₁₆	—	2	2	no	—
452	M₁₆	—	292	2	no	—
453	M₁₆	—	292	2	no	—
454	M₁₆	—	73	4	no	—
455	M₁₆	—	73	4	no	—
456	M₁₆	—	146	2	no	—
457	M₁₆	—	146	2	no	—
458	M₁₆	—	146	4	no	—
459	M₁₆	—	146	4	no	—
460	M₁₆	—	146	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	292	2	no	—
463	C₂×C₈	—	73	2	no	—
464	C₂×C₈	—	73	1	no	—
465	C₂×C₈	—	73	1	no	—
466	C₂×C₈	—	73	2	no	—
467	C₂×C₈	—	73	2	no	—
468	C₂×C₈	—	73	2	no	—
469	C₂×C₈	—	73	2	no	—
470	C₂×C₈	—	73	2	no	—
471	C₂×C₈	—	73	2	no	—
472	C₂×C₈	—	73	2	no	—
473	C₂×C₈	—	73	1	no	—
474	C₂×C₈	—	73	1	no	—
475	C₂×C₈	—	146	2	no	—
476	C₂×C₈	—	146	2	no	—
477	C₂×C₈	—	146	2	no	—
478	C₂×C₈	—	146	2	no	—
479	C₂×C₈	—	146	4	no	—
480	C₂×C₈	—	146	2	no	—
481	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
482	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
483	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
484	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
485	C₄⋊C₄	—	73	1	no	—
486	C₄⋊C₄	—	73	1	no	—
487	C₄⋊C₄	—	73	1	no	—
488	C₄⋊C₄	—	73	1	no	—
489	C₄⋊C₄	C₄×#64408	1	1	yes	characteristic
490	C₄⋊C₄	C₄×#64408	1	1	yes	characteristic
491	C₂²⋊C₄	—	73	1	no	—
492	C₂²⋊C₄	—	73	1	no	—
493	C₂²⋊C₄	—	73	1	no	—
494	C₂²⋊C₄	—	73	1	no	—
495	C₂²⋊C₄	C₄×#64408	1	1	yes	characteristic
496	C₂²⋊C₄	C₄×#64408	1	1	yes	characteristic
497	C₄²	—	73	1	no	—
498	C₄²	—	73	1	no	—
499	C₄²	—	73	1	no	—
500	C₄²	—	73	1	no	—
501	C₄²	—	73	1	no	—
502	C₄²	—	73	1	no	—
503	C₄²	—	73	1	no	—
504	C₄²	—	73	1	no	—
505	C₄²	C₂²×#64408	1	1	yes	characteristic
506	C₄²	C₂²×#64408	1	1	yes	characteristic
507	C₂³	—	73	1	no	—
508	C₂³	—	73	1	no	—
509	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
510	Q₈	—	146	2	no	—
511	D₄	—	146	2	no	—
512	D₄	—	146	2	no	—
513	D₄	—	146	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	73	1	no	—
517	C₂×C₄	—	73	1	no	—
518	C₂×C₄	—	73	1	no	—
519	C₂×C₄	—	73	2	no	—
520	C₂×C₄	—	73	2	no	—
521	C₂×C₄	—	73	1	no	—
522	C₂×C₄	—	73	1	no	—
523	C₂×C₄	—	73	1	no	—
524	C₂×C₄	—	146	2	no	—
525	C₂×C₄	—	146	2	no	—
526	C₂×C₄	—	146	2	no	—
527	C₂×C₄	—	146	2	no	—
528	C₂×C₄	—	146	2	no	—
529	C₂×C₄	—	146	2	no	—
530	C₂×C₄	—	146	1	no	—
531	C₂×C₄	—	146	1	no	—
532	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
533	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
534	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
535	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
536	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
537	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	73	4	no	—
541	C₈	—	73	2	no	—
542	C₈	—	73	2	no	—
543	C₈	—	146	2	no	—
544	C₈	—	146	2	no	—
545	C₈	—	146	2	no	—
546	C₈	—	146	2	no	—
547	C₈	—	146	2	no	—
548	C₈	—	146	2	no	—
549	C₈	—	146	2	no	—
550	C₈	—	146	1	no	—
551	C₈	—	146	1	no	—
552	C₈	D₇₃⋊M₁₆	1	2	yes	—
553	C₈	D₇₃⋊M₁₆	1	2	yes	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	73	2	no	—
558	C₂²	—	146	1	no	—
559	C₂²	—	146	1	no	—
560	C₂²	—	146	1	no	—
561	C₂²	—	146	1	no	—
562	C₂²	—	146	1	no	—
563	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	73	2	no	—
570	C₄	—	73	2	no	—
571	C₄	—	73	2	no	—
572	C₄	—	146	1	no	—
573	C₄	—	146	1	no	—
574	C₄	—	146	1	no	—
575	C₄	C₂×D₇₃⋊M₁₆	1	1	yes	characteristic
576	C₄	C₂×D₇₃⋊M₁₆	1	1	yes	characteristic
577	C₂	—	4	1	no	—
578	C₂	—	292	1	no	—
579	C₂	—	146	2	no	—
580	C₂	C₄×D₇₃⋊M₁₆	1	1	yes	characteristic
581	C₂	#131×#64408	1	1	yes	characteristic
582	C₂	#22626501	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Fitting	#405×C₇₃	C₄
prime radical	C₂×#11924028	C₂×C₄
cosocle	C₄×Dic₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#17337
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #22625155	C₂	semidirect
4. #22625154	C₂	semidirect
5. #22625151	C₂	semidirect
6. #22625150	C₂	semidirect
7. #22625145	C₂	semidirect
8. #22625141	C₂	semidirect
9. #22625140	C₂	semidirect
10. C₈×#11924038	C₂	semidirect
11. C₈×#11924037	C₂	semidirect
12. #22625129	C₂	semidirect
13. #22625129	C₂	semidirect
14. #22625127	C₂	semidirect
175. #11924011	M₁₆	semidirect
176. #11924011	M₁₆	semidirect
253. #10596833	#131	semidirect
307. C₇₃	#17337	semidirect

Maximal subgroups

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

subgroup	index
#22626742	2
#22625155	2
#22625154	2
#22625151	2
#22625150	2
#22625145	2
#22625141	2
#22625140	2
C₈×#11924038	2
C₈×#11924037	2
#22625129	2
#22625127	2
#22618353	2
#17337	73