Subgroups — #34015806

Order 18688.

814 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626741	C₂	1	1	yes	maximal, characteristic
2	C₄×#14556678	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	#22625149	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625148	C₂	1	1	yes	maximal, characteristic, complemented
7	#22625142	C₂	1	1	yes	maximal, characteristic, complemented
8	#22625140	C₂	1	1	yes	maximal, characteristic, complemented
9	#22625136	C₂	1	1	yes	maximal, characteristic, complemented
10	#22625133	C₂	1	1	yes	maximal, characteristic, complemented
11	#22625132	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×C₈×#10596833	C₂	1	1	yes	maximal, characteristic, complemented
15	#22618891	C₂	1	1	yes	maximal, characteristic
16	C₂×#14556678	C₄	1	2	yes	—
17	#17989639	C₄	1	2	yes	—
18	#17989620	C₄	1	2	yes	—
19	#17989618	C₄	1	2	yes	—
20	#17989616	C₄	1	2	yes	—
21	#17989605	C₂²	1	1	yes	characteristic
22	#17989604	C₂²	1	1	yes	characteristic
23	#17989603	C₂²	1	1	yes	characteristic
24	#17989552	C₄	1	2	yes	—
25	#17989551	C₄	1	2	yes	—
26	#17989551	C₄	1	2	yes	—
27	C₄×#11924038	C₂²	1	1	yes	characteristic
28	C₄×#11924038	C₂²	1	1	yes	characteristic
29	C₄×#11924037	C₂²	1	1	yes	characteristic
30	C₄×#11924037	C₂²	1	1	yes	characteristic
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	C₈×#10596833	C₂²	1	1	yes	characteristic
47	C₈×#10596833	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	#14556678	—	2	8	no	—
68	C₂×#11924038	C₂×C₄	1	2	yes	—
69	C₂×#11924038	C₂×C₄	1	2	yes	—
70	C₂×#11924037	C₂×C₄	1	2	yes	—
71	C₂×#11924037	C₂×C₄	1	2	yes	—
72	C₂×#11924037	C₂×C₄	1	2	yes	—
73	C₂×#11924036	C₂×C₄	1	2	yes	—
74	C₂²×#10596833	C₂×C₄	1	2	yes	—
75	C₂²×#10596833	C₂×C₄	1	2	yes	—
76	C₂²×#10596833	C₂×C₄	1	2	yes	—
77	#14556658	C₂×C₄	1	2	yes	—
78	#14556658	C₂×C₄	1	2	yes	—
79	C₄⋊#10596833	C₂×C₄	1	2	yes	—
80	#14556648	C₂×C₄	1	2	yes	—
81	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
82	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
83	#14556646	C₂×C₄	1	2	yes	—
84	#14556646	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	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	C₂×C₄	1	2	yes	—
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	C₄×#10596833	C₂³	1	1	yes	characteristic
100	C₂×#11924027	C₂×C₄	1	1	yes	characteristic
101	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
102	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
103	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
104	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
106	#14556556	C₂×C₄	1	1	yes	characteristic
107	D₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
108	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
109	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
110	#14556551	C₂×C₄	1	1	yes	characteristic
111	#14556551	C₂×C₄	1	1	yes	characteristic
112	#14556549	C₂×C₄	1	1	yes	characteristic
113	#14556547	C₂×C₄	1	1	yes	characteristic
114	#14556547	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
116	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
117	C₄²×D₇₃	C₂³	1	1	yes	characteristic
118	C₄⋊#10596831	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	#14556520	C₂×C₄	1	1	yes	characteristic
123	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
124	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
125	#14556503	C₂×C₄	1	1	yes	characteristic
126	#14556503	C₂×C₄	1	1	yes	characteristic
127	#14556502	C₂×C₄	1	1	yes	characteristic
128	#14556501	C₂×C₄	1	1	yes	characteristic
129	#14556501	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₇₃	C₂×C₄	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	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
137	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
138	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
139	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
142	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
143	#11924038	—	2	4	no	—
144	#11924038	—	2	4	no	—
145	#11924037	—	2	4	no	—
146	#11924037	—	2	4	no	—
147	#11924037	—	2	4	no	—
148	#11924036	—	2	4	no	—
149	C₂×#10596833	—	2	4	no	—
150	C₂×#10596833	—	2	4	no	—
151	C₂×#10596833	M₁₆	1	8	yes	complemented
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	C₂×#10596833	C₂²×C₄	1	2	yes	—
159	C₂×#10596833	C₂²×C₄	1	2	yes	—
160	#11924027	—	2	4	no	—
161	C₂×Dic₁₄₆	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	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
167	C₂²×Dic₇₃	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	#11924012	—	2	2	no	—
172	#11924011	—	2	2	no	—
173	#11924011	—	2	2	no	—
174	C₂×#10596831	—	2	2	no	—
175	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
176	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
177	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
178	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊Dic₇₃	C₄²	1	1	yes	characteristic
180	#11924007	C₄²	1	1	yes	characteristic
181	#11924007	C₄²	1	1	yes	characteristic
182	#11924007	C₄²	1	1	yes	characteristic
183	#11924007	C₄²	1	1	yes	characteristic
184	C₂²⋊Dic₇₃	C₄²	1	1	yes	characteristic
185	C₂²⋊Dic₇₃	C₄²	1	1	yes	characteristic
186	#11924005	C₄²	1	1	yes	characteristic
187	#11924005	C₄²	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	C₂²×C₄	1	1	yes	characteristic
192	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₇₃	C₂²×C₄	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	C₂⁴	1	1	yes	characteristic
197	C₂×D₄×C₇₃	C₄²	1	1	yes	characteristic
198	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
200	M₁₆×C₇₃	—	2	2	no	—
201	C₂×C₈×C₇₃	—	2	2	no	—
202	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
207	C₂²⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
208	C₂²⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
209	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
210	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
211	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
212	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
213	D₄×C₇₃	—	2	2	no	—
214	C₂×C₄×C₇₃	—	2	1	no	—
215	C₂×C₄×C₇₃	—	2	1	no	—
216	C₂×C₄×C₇₃	—	2	1	no	—
217	C₂×C₄×C₇₃	—	2	1	no	—
218	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
219	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
221	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
223	C₂²⋊D₇₃	—	2	2	no	—
224	C₂²⋊D₇₃	—	2	2	no	—
225	C₂×Dic₇₃	—	2	2	no	—
226	C₂×Dic₇₃	—	2	2	no	—
227	C₂×Dic₇₃	—	2	2	no	—
228	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
229	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
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×M₁₆	1	4	yes	—
234	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
235	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
236	C₄×D₇₃	—	2	1	no	—
237	C₄×D₇₃	—	2	1	no	—
238	C₄×D₇₃	—	2	2	no	—
239	C₄×D₇₃	—	2	2	no	—
240	Dic₁₄₆	—	2	2	no	—
241	#10596833	—	2	2	no	—
242	#10596833	—	2	2	no	—
243	#10596833	—	2	2	no	—
244	#10596833	—	2	2	no	—
245	#10596833	—	2	2	no	—
246	#10596833	C₂×M₁₆	1	4	yes	—
247	#10596833	C₂×M₁₆	1	4	yes	—
248	#10596833	#131	1	4	yes	complemented
249	C₈×C₇₃	—	2	1	no	—
250	C₈×C₇₃	—	2	1	no	—
251	C₈×C₇₃	—	2	1	no	—
252	C₈×C₇₃	#131	1	2	yes	complemented
253	#10596831	—	2	1	no	—
254	#10596831	—	2	1	no	—
255	#10596831	—	2	1	no	—
256	#10596831	#131	1	2	yes	complemented
257	C₂²×C₇₃	—	2	1	no	—
258	C₂²×C₇₃	—	2	1	no	—
259	C₂²×C₇₃	—	2	1	no	—
260	C₂²×C₇₃	—	2	1	no	—
261	C₂²×C₇₃	—	2	1	no	—
262	C₂²×C₇₃	C₄×M₁₆	1	2	yes	—
263	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
264	C₂×D₇₃	—	2	1	no	—
265	C₂×D₇₃	—	2	1	no	—
266	C₂×D₇₃	—	2	1	no	—
267	C₄×C₇₃	—	2	1	no	—
268	C₄×C₇₃	—	2	1	no	—
269	C₄×C₇₃	—	2	1	no	—
270	C₄×C₇₃	—	2	1	no	—
271	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
272	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
273	Dic₇₃	—	2	1	no	—
274	Dic₇₃	—	2	1	no	—
275	Dic₇₃	—	2	1	no	—
276	Dic₇₃	—	2	1	no	—
277	Dic₇₃	C₄×M₁₆	1	2	yes	—
278	Dic₇₃	C₂²×M₁₆	1	2	yes	—
279	Dic₇₃	C₂×#131	1	2	yes	—
280	#17335	—	73	1	no	maximal, Sylow
281	C₂×C₇₃	—	2	2	no	—
282	C₂×C₇₃	—	4	1	no	—
283	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
284	C₂×C₇₃	C₄×#131	1	1	yes	characteristic
285	C₂×C₇₃	C₄×#131	1	1	yes	characteristic
286	D₇₃	—	4	1	no	—
287	#2965	—	73	1	no	—
288	#2965	—	73	1	no	—
289	C₄×#131	—	73	1	no	—
290	#1455	—	73	1	no	—
291	#1455	—	73	1	no	—
292	#1453	—	73	1	no	—
293	#1453	—	73	1	no	—
294	#1451	—	73	1	no	—
295	#1451	—	73	1	no	—
296	#1450	—	73	1	no	—
297	C₈×M₁₆	—	73	1	no	—
298	C₈×M₁₆	—	73	1	no	—
299	C₈×M₁₆	—	73	1	no	—
300	C₈×M₁₆	—	73	1	no	—
301	C₂×C₈²	—	73	1	no	—
302	C₇₃	#17335	1	1	yes	characteristic, complemented, Sylow
303	C₂×#131	—	73	2	no	—
304	C₄×#41	—	73	1	no	—
305	#446	—	73	2	no	—
306	#446	—	73	1	no	—
307	#446	—	73	1	no	—
308	#436	—	73	2	no	—
309	#436	—	73	1	no	—
310	#436	—	73	1	no	—
311	#435	—	73	2	no	—
312	#435	—	73	2	no	—
313	#435	—	73	1	no	—
314	#435	—	73	1	no	—
315	#435	—	73	1	no	—
316	#435	#64408	1	1	yes	characteristic
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	#405	—	73	2	no	—
324	#405	—	73	2	no	—
325	#405	—	73	2	no	—
326	C₄×M₁₆	—	73	1	no	—
327	C₄×M₁₆	—	73	1	no	—
328	C₄×M₁₆	—	73	1	no	—
329	C₄×M₁₆	—	73	1	no	—
330	C₄×M₁₆	—	73	1	no	—
331	C₄×M₁₆	—	73	1	no	—
332	C₄×M₁₆	—	73	1	no	—
333	C₂×C₄×C₈	—	73	1	no	—
334	C₂×C₄×C₈	—	73	1	no	—
335	C₂×C₄×C₈	—	73	1	no	—
336	C₂×C₄×C₈	—	73	1	no	—
337	C₂×C₄×C₈	—	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	#322	—	73	1	no	—
346	#322	—	73	1	no	—
347	#322	—	73	1	no	—
348	C₈²	—	73	1	no	—
349	C₈²	—	73	1	no	—
350	C₈²	—	73	1	no	—
351	C₈²	—	73	1	no	—
352	C₈²	—	73	1	no	—
353	C₈²	—	73	1	no	—
354	C₂×#41	—	73	1	no	—
355	#131	—	146	8	no	—
356	C₂×M₁₆	—	73	2	no	—
357	C₂×M₁₆	—	73	2	no	—
358	C₂×M₁₆	—	73	2	no	—
359	C₂×M₁₆	—	73	2	no	—
360	C₂×M₁₆	—	73	2	no	—
361	C₂×M₁₆	—	73	1	no	—
362	C₂×M₁₆	—	73	1	no	—
363	C₂×M₁₆	—	73	1	no	—
364	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
365	C₂²×C₈	—	73	2	no	—
366	C₂²×C₈	—	73	2	no	—
367	C₂²×C₈	—	73	2	no	—
368	C₂²×C₈	—	73	2	no	—
369	C₂²×C₈	—	73	1	no	—
370	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
371	C₄×Q₈	—	73	1	no	—
372	C₄×Q₈	—	73	1	no	—
373	C₄×D₄	—	73	1	no	—
374	C₄×D₄	—	73	1	no	—
375	C₄×D₄	—	73	1	no	—
376	C₄×D₄	—	73	1	no	—
377	C₄×D₄	—	73	1	no	—
378	C₄×D₄	C₂×#64408	1	1	yes	characteristic
379	#117	—	73	1	no	—
380	#117	—	73	1	no	—
381	#117	—	73	1	no	—
382	C₂×C₄²	—	73	1	no	—
383	C₂×C₄²	—	73	1	no	—
384	C₂×C₄²	—	73	1	no	—
385	C₄⋊C₈	—	73	2	no	—
386	C₄⋊C₈	—	73	2	no	—
387	C₄⋊C₈	—	73	2	no	—
388	C₄⋊C₈	—	73	1	no	—
389	C₄⋊C₈	—	73	1	no	—
390	C₄⋊C₈	—	73	1	no	—
391	C₄⋊C₈	—	73	1	no	—
392	C₄⋊C₈	—	73	1	no	—
393	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
394	C₂²⋊C₈	—	73	2	no	—
395	C₂²⋊C₈	—	73	2	no	—
396	C₂²⋊C₈	—	73	2	no	—
397	C₂²⋊C₈	—	73	1	no	—
398	C₂²⋊C₈	—	73	1	no	—
399	C₂²⋊C₈	—	73	1	no	—
400	C₂²⋊C₈	—	73	1	no	—
401	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
402	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
403	#97	—	73	2	no	—
404	#97	—	73	2	no	—
405	#97	—	73	2	no	—
406	#97	—	73	2	no	—
407	#97	—	73	2	no	—
408	#97	—	73	1	no	—
409	#97	—	73	1	no	—
410	#97	—	73	1	no	—
411	#97	C₂×#64408	1	1	yes	characteristic
412	C₄×C₈	—	73	1	no	—
413	C₄×C₈	—	73	1	no	—
414	C₄×C₈	—	73	1	no	—
415	C₄×C₈	—	73	1	no	—
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	2	no	—
421	C₄×C₈	—	73	2	no	—
422	C₄×C₈	—	73	2	no	—
423	C₄×C₈	—	73	2	no	—
424	C₄×C₈	—	73	1	no	—
425	C₄×C₈	—	73	1	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	#41	—	146	4	no	—
431	C₂×Q₈	—	73	1	no	—
432	C₂×D₄	—	73	1	no	—
433	C₂×D₄	—	73	1	no	—
434	C₂×D₄	C₄×#64408	1	1	yes	characteristic
435	C₂²×C₄	—	73	1	no	—
436	C₂²×C₄	—	73	1	no	—
437	C₂²×C₄	—	73	1	no	—
438	C₂²×C₄	—	73	1	no	—
439	C₂²×C₄	—	73	1	no	—
440	C₂²×C₄	—	73	1	no	—
441	C₂²×C₄	—	73	1	no	—
442	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
443	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
444	M₁₆	—	2	2	no	—
445	M₁₆	—	146	2	no	—
446	M₁₆	—	146	2	no	—
447	M₁₆	—	146	4	no	—
448	M₁₆	—	146	4	no	—
449	M₁₆	—	146	4	no	—
450	M₁₆	—	146	4	no	—
451	M₁₆	—	146	4	no	—
452	M₁₆	—	146	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	73	8	no	—
455	C₂×C₈	—	73	2	no	—
456	C₂×C₈	—	73	2	no	—
457	C₂×C₈	—	73	2	no	—
458	C₂×C₈	—	73	1	no	—
459	C₂×C₈	—	73	2	no	—
460	C₂×C₈	—	73	2	no	—
461	C₂×C₈	—	73	2	no	—
462	C₂×C₈	—	73	2	no	—
463	C₂×C₈	—	73	2	no	—
464	C₂×C₈	—	73	1	no	—
465	C₂×C₈	—	73	1	no	—
466	C₂×C₈	—	73	1	no	—
467	C₂×C₈	—	146	2	no	—
468	C₂×C₈	—	146	4	no	—
469	C₂×C₈	—	146	4	no	—
470	C₂×C₈	—	146	4	no	—
471	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
472	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
473	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
474	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
475	C₄⋊C₄	—	73	1	no	—
476	C₄⋊C₄	—	73	1	no	—
477	C₄⋊C₄	—	73	1	no	—
478	C₄⋊C₄	—	73	1	no	—
479	C₄⋊C₄	—	73	1	no	—
480	C₄⋊C₄	C₄×#64408	1	1	yes	characteristic
481	C₂²⋊C₄	—	73	1	no	—
482	C₂²⋊C₄	—	73	1	no	—
483	C₂²⋊C₄	—	73	1	no	—
484	C₂²⋊C₄	—	73	1	no	—
485	C₂²⋊C₄	C₄×#64408	1	1	yes	characteristic
486	C₂²⋊C₄	C₄×#64408	1	1	yes	characteristic
487	C₄²	—	73	1	no	—
488	C₄²	—	73	1	no	—
489	C₄²	—	73	1	no	—
490	C₄²	—	73	1	no	—
491	C₄²	—	73	1	no	—
492	C₄²	—	73	1	no	—
493	C₄²	—	73	1	no	—
494	C₄²	—	73	1	no	—
495	C₄²	—	73	1	no	—
496	C₄²	C₂²×#64408	1	1	yes	characteristic
497	C₂³	—	73	1	no	—
498	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
499	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
500	Q₈	—	146	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	146	2	no	—
503	D₄	—	146	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	73	1	no	—
509	C₂×C₄	—	73	1	no	—
510	C₂×C₄	—	73	1	no	—
511	C₂×C₄	—	73	4	no	—
512	C₂×C₄	—	73	1	no	—
513	C₂×C₄	—	73	1	no	—
514	C₂×C₄	—	73	1	no	—
515	C₂×C₄	—	73	1	no	—
516	C₂×C₄	—	146	2	no	—
517	C₂×C₄	—	146	2	no	—
518	C₂×C₄	—	146	2	no	—
519	C₂×C₄	—	146	2	no	—
520	C₂×C₄	—	146	2	no	—
521	C₂×C₄	—	146	1	no	—
522	C₂×C₄	—	146	1	no	—
523	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
524	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
525	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
526	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
527	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	73	4	no	—
532	C₈	—	73	4	no	—
533	C₈	—	73	4	no	—
534	C₈	—	73	2	no	—
535	C₈	—	146	2	no	—
536	C₈	—	146	2	no	—
537	C₈	—	146	2	no	—
538	C₈	—	146	2	no	—
539	C₈	—	146	2	no	—
540	C₈	—	146	1	no	—
541	C₈	—	146	1	no	—
542	C₈	—	146	1	no	—
543	C₈	#14556678	1	2	yes	complemented
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	146	1	no	—
550	C₂²	—	146	1	no	—
551	C₂²	—	146	1	no	—
552	C₂²	M₁₆×#64408	1	2	yes	—
553	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	73	2	no	—
559	C₄	—	73	2	no	—
560	C₄	—	73	2	no	—
561	C₄	—	146	1	no	—
562	C₄	—	146	1	no	—
563	C₄	—	146	1	no	—
564	C₄	—	146	1	no	—
565	C₄	C₂×#14556678	1	1	yes	characteristic
566	C₄	D₇₃⋊#131	1	1	yes	characteristic
567	C₂	—	2	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	292	1	no	—
570	C₂	C₂×M₁₆×#64408	1	1	yes	characteristic
571	C₂	#131×#64408	1	1	yes	characteristic
572	C₂	C₄×#14556678	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	#17335
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. #22625155	C₂	semidirect
4. #22625154	C₂	semidirect
5. #22625149	C₂	semidirect
6. #22625148	C₂	semidirect
7. #22625142	C₂	semidirect
8. #22625140	C₂	semidirect
9. #22625136	C₂	semidirect
10. #22625133	C₂	semidirect
11. #22625132	C₂	semidirect
12. #22625129	C₂	semidirect
13. M₁₆×#10596833	C₂	semidirect
14. C₂×C₈×#10596833	C₂	semidirect
151. C₂×#10596833	M₁₆	semidirect
248. #10596833	#131	semidirect
252. C₈×C₇₃	#131	semidirect
256. #10596831	#131	semidirect
302. C₇₃	#17335	semidirect
543. C₈	#14556678	semidirect

Maximal subgroups

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

subgroup	index
#22626741	2
C₄×#14556678	2
#22625155	2
#22625154	2
#22625149	2
#22625148	2
#22625142	2
#22625140	2
#22625136	2
#22625133	2
#22625132	2
#22625129	2
M₁₆×#10596833	2
C₂×C₈×#10596833	2
#22618891	2
#17335	73