Subgroups — #34033246

Order 18688.

714 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989700	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989700	C₂	1	1	yes	maximal, characteristic
3	#22626942	C₂	1	4	yes	maximal
4	#117×#64408	C₂	1	1	yes	maximal, characteristic
5	#17989700	—	2	1	no	—
6	#17989700	—	2	1	no	—
7	#17989700	—	2	1	no	—
8	#17989700	—	2	1	no	—
9	#17989700	—	2	1	no	—
10	#17989700	—	2	1	no	—
11	#17989700	C₄	1	2	yes	complemented
12	#17989700	C₄	1	2	yes	complemented
13	C₂×C₄⋊#10596842	—	2	1	no	—
14	C₂×C₄⋊#10596842	C₄	1	2	yes	complemented
15	C₂×C₂²⋊#10596842	C₂²	1	2	yes	—
16	C₂×C₂²⋊#10596842	C₂²	1	2	yes	—
17	C₂×C₄×#10596842	—	2	1	no	—
18	C₂×C₄×#10596842	C₄	1	2	yes	complemented
19	C₂×#14556670	C₄	1	1	yes	characteristic
20	C₂²×C₄×#64408	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×#64408	—	2	1	no	—
22	C₄⋊C₄×#64408	—	2	1	no	—
23	C₂²⋊C₄×#64408	C₄	1	2	yes	—
24	C₂²⋊C₄×#64408	C₂²	1	2	yes	—
25	#17989523	—	2	1	no	—
26	C₄²×#64408	—	2	1	no	—
27	#117×D₇₃	C₄	1	1	yes	characteristic
28	C₂²×#10596842	—	2	2	no	—
29	C₂²×#10596842	C₂×C₄	1	4	yes	—
30	C₄⋊#10596842	—	2	2	no	—
31	C₄⋊#10596842	—	2	2	no	—
32	C₄⋊#10596842	—	2	2	no	—
33	C₄⋊#10596842	—	2	2	no	—
34	C₂²⋊#10596842	—	2	2	no	—
35	C₂²⋊#10596842	—	2	2	no	—
36	C₂²⋊#10596842	—	2	2	no	—
37	C₂²⋊#10596842	C₂×C₄	1	4	yes	—
38	C₄×#10596842	—	2	2	no	—
39	C₄×#10596842	—	2	2	no	—
40	C₄×#10596842	—	2	2	no	—
41	C₄×#10596842	—	2	2	no	—
42	C₂³×#64408	C₂×C₄	1	1	yes	characteristic
43	C₂³×#64408	C₂³	1	1	yes	characteristic
44	#14556670	—	2	1	no	—
45	#14556670	—	2	1	no	—
46	#14556670	C₈	1	2	yes	complemented
47	#14556670	C₈	1	2	yes	complemented
48	C₂×C₄⋊#64408	—	2	1	no	—
49	C₂×C₂²⋊#64408	C₂×C₄	1	2	yes	—
50	C₂×C₄×#64408	—	2	2	no	—
51	C₂×C₄×#64408	—	2	2	no	—
52	C₂×C₄×#64408	—	2	1	no	—
53	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×#64408	D₄	1	1	yes	characteristic
58	C₂×C₄×#64408	D₄	1	1	yes	characteristic
59	C₂×C₄×#64408	D₄	1	1	yes	characteristic
60	C₂×C₄×#64408	D₄	1	1	yes	characteristic
61	C₂×C₄×#64408	D₄	1	1	yes	characteristic
62	C₂×C₄×#64408	D₄	1	1	yes	characteristic
63	C₂×C₄×#64408	Q₈	1	1	yes	characteristic
64	C₂×C₄×#64408	Q₈	1	1	yes	characteristic
65	(C₂×#64408)⋊C₄	—	2	2	no	—
66	(C₂×#64408)⋊C₄	—	2	2	no	—
67	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
68	#14556550	C₈	1	1	yes	characteristic, complemented
69	#14556549	—	2	1	no	—
70	#14556548	—	2	1	no	—
71	#14556547	C₈	1	2	yes	complemented
72	C₄⋊C₄×D₇₃	—	2	1	no	—
73	C₂²⋊C₄×D₇₃	C₂×C₄	1	2	yes	—
74	C₄²×D₇₃	—	2	1	no	—
75	#117×C₇₃	C₈	1	1	yes	characteristic, complemented
76	C₂×#10596842	—	2	4	no	—
77	C₂×#10596842	—	2	4	no	—
78	C₂×#10596842	—	4	4	no	—
79	C₂×#10596842	—	4	4	no	—
80	C₂²×#64408	—	2	2	no	—
81	C₂²×#64408	—	4	2	no	—
82	C₂²×#64408	—	4	2	no	—
83	C₂²×#64408	C₄²	1	1	yes	characteristic
84	C₂²×#64408	C₄²	1	1	yes	characteristic
85	C₂²×#64408	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×#64408	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×#64408	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×#64408	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
90	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
91	C₂²×#64408	C₂×D₄	1	1	yes	characteristic
92	C₂²×#64408	C₂×D₄	1	1	yes	characteristic
93	C₂²×#64408	C₂×D₄	1	1	yes	characteristic
94	C₂²×#64408	C₂×Q₈	1	1	yes	characteristic
95	C₄⋊#64408	—	2	2	no	—
96	C₄⋊#64408	—	2	2	no	—
97	C₂²⋊#64408	—	2	2	no	—
98	C₂²⋊#64408	C₂×C₈	1	4	yes	—
99	C₄×#64408	—	2	2	no	—
100	C₄×#64408	—	2	2	no	—
101	C₄×#64408	—	4	4	no	—
102	C₄×#64408	—	4	4	no	—
103	C₄×#64408	C₂²⋊C₄	1	1	yes	characteristic
104	C₄×#64408	C₂²⋊C₄	1	1	yes	characteristic
105	C₄×#64408	C₂²⋊C₄	1	1	yes	characteristic
106	C₄×#64408	C₂²⋊C₄	1	1	yes	characteristic
107	C₄×#64408	C₂²⋊C₄	1	1	yes	characteristic
108	C₄×#64408	C₂²⋊C₄	1	1	yes	characteristic
109	C₄×#64408	C₂²⋊C₄	1	1	yes	characteristic
110	C₄×#64408	C₂²⋊C₄	1	1	yes	characteristic
111	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
112	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
113	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
114	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
115	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
116	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
117	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
118	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
119	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₇₃	—	2	2	no	—
122	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
124	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
129	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
130	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
131	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
132	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
133	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
134	C₄⋊Dic₇₃	—	2	1	no	—
135	#11924007	—	2	2	no	—
136	C₂²⋊Dic₇₃	C₂×C₈	1	2	yes	—
137	#11924005	—	2	2	no	—
138	C₄×Dic₇₃	—	2	1	no	—
139	C₄×Dic₇₃	—	2	2	no	—
140	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
141	C₄⋊C₄×C₇₃	—	2	1	no	—
142	C₂²⋊C₄×C₇₃	C₂×C₈	1	2	yes	—
143	C₄²×C₇₃	—	2	1	no	—
144	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
145	C₂²×D₇₃	—	4	1	no	—
146	C₂²×D₇₃	—	4	1	no	—
147	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
148	C₂²×D₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
151	C₂²×D₇₃	C₂×M₁₆	1	1	yes	characteristic
152	C₂²×D₇₃	C₂×M₁₆	1	1	yes	characteristic
153	C₂×#64408	—	2	2	no	—
154	C₂×#64408	—	2	2	no	—
155	C₂×#64408	—	2	2	no	—
156	C₂×#64408	—	2	2	no	—
157	C₂×#64408	—	2	2	no	—
158	C₂×#64408	—	2	2	no	—
159	C₂×#64408	—	2	4	no	—
160	C₂×#64408	—	4	1	no	—
161	C₂×#64408	—	4	1	no	—
162	C₂×#64408	—	4	1	no	—
163	C₂×#64408	—	4	1	no	—
164	C₂×#64408	—	4	1	no	—
165	C₂×#64408	—	4	1	no	—
166	C₂×#64408	—	4	2	no	—
167	C₂×#64408	—	4	2	no	—
168	C₂×#64408	#95	1	1	yes	characteristic
169	C₂×#64408	#95	1	1	yes	characteristic
170	C₂×#64408	#95	1	1	yes	characteristic
171	C₂×#64408	#95	1	1	yes	characteristic
172	C₂×#64408	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×#64408	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×#64408	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×#64408	C₂×C₄⋊C₄	1	1	yes	characteristic
176	#10596842	—	4	4	no	—
177	#10596842	—	4	4	no	—
178	C₂×C₄×C₇₃	—	2	2	no	—
179	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
182	C₂×C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
183	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
184	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
185	C₂×Dic₇₃	—	2	2	no	—
186	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
187	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
188	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
189	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
190	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
191	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
192	C₄×D₇₃	—	4	2	no	—
193	C₄×D₇₃	—	4	2	no	—
194	C₄×D₇₃	#95	1	1	yes	characteristic
195	C₄×D₇₃	#95	1	1	yes	characteristic
196	C₄×D₇₃	#95	1	1	yes	characteristic
197	C₄×D₇₃	#95	1	1	yes	characteristic
198	C₄×D₇₃	#97	1	1	yes	characteristic
199	C₄×D₇₃	#97	1	1	yes	characteristic
200	C₄×D₇₃	#97	1	1	yes	characteristic
201	C₄×D₇₃	#97	1	1	yes	characteristic
202	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
203	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
204	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
205	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
206	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
207	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
208	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
209	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
210	C₂²×C₇₃	—	4	1	no	—
211	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
212	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
213	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
214	C₂×D₇₃	—	2	1	no	—
215	C₂×D₇₃	—	2	1	no	—
216	C₂×D₇₃	—	2	1	no	—
217	C₂×D₇₃	—	2	1	no	—
218	C₂×D₇₃	—	2	1	no	—
219	C₂×D₇₃	—	2	1	no	—
220	C₂×D₇₃	—	4	1	no	—
221	C₂×D₇₃	—	4	1	no	—
222	C₂×D₇₃	—	4	1	no	—
223	C₂×D₇₃	C₂×#95	1	1	yes	characteristic
224	C₂×D₇₃	C₂×#97	1	1	yes	characteristic
225	C₂×D₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
226	C₂×D₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
227	#64408	—	2	1	no	—
228	#64408	—	2	1	no	—
229	#64408	—	2	1	no	—
230	#64408	—	2	1	no	—
231	#64408	—	2	1	no	—
232	#64408	—	2	1	no	—
233	#64408	—	4	4	no	—
234	#64408	#344	1	2	yes	—
235	#64408	#410	1	2	yes	—
236	C₄×C₇₃	—	4	2	no	—
237	C₄×C₇₃	#336	1	1	yes	characteristic
238	C₄×C₇₃	#336	1	1	yes	characteristic
239	C₄×C₇₃	#336	1	1	yes	characteristic
240	C₄×C₇₃	#336	1	1	yes	characteristic
241	Dic₇₃	—	4	2	no	—
242	Dic₇₃	#336	1	1	yes	characteristic
243	Dic₇₃	#336	1	1	yes	characteristic
244	Dic₇₃	#336	1	1	yes	characteristic
245	Dic₇₃	#336	1	1	yes	characteristic
246	#7924	—	73	1	no	maximal, Sylow
247	C₂×C₇₃	—	2	1	no	—
248	C₂×C₇₃	—	2	1	no	—
249	C₂×C₇₃	—	2	1	no	—
250	C₂×C₇₃	C₂×#336	1	1	yes	characteristic
251	D₇₃	—	2	1	no	—
252	D₇₃	—	2	1	no	—
253	D₇₃	—	2	1	no	—
254	D₇₃	#1740	1	1	yes	characteristic
255	D₇₃	C₂×#344	1	1	yes	characteristic
256	C₂×#431	—	73	1	no	—
257	C₂×#431	—	73	1	no	—
258	C₄×#117	—	73	1	no	—
259	#1282	—	73	4	no	—
260	C₇₃	#7924	1	1	yes	characteristic, complemented, Sylow
261	C₂×#117	—	73	1	no	—
262	C₂×#117	—	73	1	no	—
263	C₂²×C₄²	—	73	1	no	—
264	#431	—	73	2	no	—
265	#431	—	73	2	no	—
266	#431	—	146	1	no	—
267	#431	—	146	1	no	—
268	#431	—	146	1	no	—
269	#431	—	146	1	no	—
270	#431	—	146	1	no	—
271	#431	—	146	1	no	—
272	C₂×C₄⋊C₈	—	73	2	no	—
273	C₂×C₄⋊C₈	—	146	1	no	—
274	C₂×C₂²⋊C₈	—	73	2	no	—
275	C₂×C₂²⋊C₈	—	73	2	no	—
276	C₂×C₄×C₈	—	73	2	no	—
277	C₂×C₄×C₈	—	146	1	no	—
278	C₄×C₄⋊C₄	—	146	1	no	—
279	C₄×C₄⋊C₄	—	146	1	no	—
280	C₄×C₂²⋊C₄	—	73	2	no	—
281	C₄×C₂²⋊C₄	—	73	2	no	—
282	#376	—	146	1	no	—
283	C₄³	—	146	1	no	—
284	C₂³×C₄	—	73	1	no	—
285	C₂³×C₄	—	73	1	no	—
286	C₂³×C₄	—	73	1	no	—
287	C₂²×C₈	—	73	4	no	—
288	C₂²×C₈	—	146	2	no	—
289	#117	—	73	2	no	—
290	#117	—	73	2	no	—
291	#117	—	73	1	no	—
292	#117	—	73	2	no	—
293	#117	—	146	1	no	—
294	#117	—	146	1	no	—
295	#117	—	146	1	no	—
296	#117	—	146	1	no	—
297	#117	#10596842	1	1	yes	characteristic, complemented
298	C₂×C₄⋊C₄	—	146	1	no	—
299	C₂×C₄⋊C₄	—	146	1	no	—
300	C₂×C₂²⋊C₄	—	73	2	no	—
301	C₂×C₂²⋊C₄	—	73	2	no	—
302	C₂×C₄²	—	73	1	no	—
303	C₂×C₄²	—	73	1	no	—
304	C₂×C₄²	—	73	1	no	—
305	C₂×C₄²	—	73	1	no	—
306	C₂×C₄²	—	73	1	no	—
307	C₂×C₄²	—	73	1	no	—
308	C₂×C₄²	—	73	1	no	—
309	C₂×C₄²	—	73	1	no	—
310	C₂×C₄²	—	73	1	no	—
311	C₂×C₄²	—	73	1	no	—
312	C₂×C₄²	—	73	1	no	—
313	C₂×C₄²	—	73	1	no	—
314	C₂×C₄²	—	146	1	no	—
315	C₂×C₄²	—	146	2	no	—
316	C₂×C₄²	—	146	2	no	—
317	C₂×C₄²	—	146	1	no	—
318	C₄⋊C₈	—	146	2	no	—
319	C₄⋊C₈	—	146	2	no	—
320	C₄⋊C₈	—	146	2	no	—
321	C₄⋊C₈	—	146	2	no	—
322	C₂²⋊C₈	—	73	4	no	—
323	C₂²⋊C₈	—	146	2	no	—
324	C₂²⋊C₈	—	146	2	no	—
325	C₂²⋊C₈	—	146	2	no	—
326	C₄×C₈	—	146	2	no	—
327	C₄×C₈	—	146	2	no	—
328	C₄×C₈	—	146	2	no	—
329	C₄×C₈	—	146	2	no	—
330	#95	—	146	2	no	—
331	#95	—	146	2	no	—
332	C₂⁴	—	73	1	no	—
333	C₂²×C₄	—	292	2	no	—
334	C₂²×C₄	—	292	2	no	—
335	C₂²×C₄	—	73	1	no	—
336	C₂²×C₄	—	73	1	no	—
337	C₂²×C₄	—	73	1	no	—
338	C₂²×C₄	—	73	1	no	—
339	C₂²×C₄	—	73	1	no	—
340	C₂²×C₄	—	73	1	no	—
341	C₂²×C₄	—	73	1	no	—
342	C₂²×C₄	—	73	1	no	—
343	C₂²×C₄	—	73	1	no	—
344	C₂²×C₄	—	73	1	no	—
345	C₂²×C₄	—	73	1	no	—
346	C₂²×C₄	—	73	1	no	—
347	C₂²×C₄	—	73	1	no	—
348	C₂²×C₄	—	73	1	no	—
349	C₂²×C₄	—	73	1	no	—
350	C₂²×C₄	—	73	1	no	—
351	C₂²×C₄	—	73	1	no	—
352	C₂²×C₄	—	73	1	no	—
353	C₂²×C₄	—	73	1	no	—
354	C₂²×C₄	—	73	1	no	—
355	C₂²×C₄	—	73	1	no	—
356	C₂²×C₄	—	73	1	no	—
357	C₂²×C₄	—	73	1	no	—
358	C₂²×C₄	—	73	1	no	—
359	C₂²×C₄	—	73	1	no	—
360	C₂²×C₄	—	146	2	no	—
361	C₂²×C₄	—	146	2	no	—
362	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
363	C₂×C₈	—	292	4	no	—
364	C₂×C₈	—	292	4	no	—
365	C₂×C₈	—	146	4	no	—
366	C₂×C₈	—	146	4	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	146	2	no	—
369	C₄⋊C₄	—	146	2	no	—
370	C₄⋊C₄	—	146	2	no	—
371	C₄⋊C₄	—	146	1	no	—
372	C₂²⋊C₄	—	73	4	no	—
373	C₂²⋊C₄	—	73	2	no	—
374	C₂²⋊C₄	—	146	2	no	—
375	C₂²⋊C₄	—	146	2	no	—
376	C₂²⋊C₄	C₂×#10596842	1	2	yes	—
377	C₄²	—	2	1	no	—
378	C₄²	—	292	4	no	—
379	C₄²	—	292	4	no	—
380	C₄²	—	73	1	no	—
381	C₄²	—	73	1	no	—
382	C₄²	—	73	1	no	—
383	C₄²	—	73	1	no	—
384	C₄²	—	73	1	no	—
385	C₄²	—	73	1	no	—
386	C₄²	—	73	1	no	—
387	C₄²	—	73	1	no	—
388	C₄²	—	73	1	no	—
389	C₄²	—	73	1	no	—
390	C₄²	—	73	1	no	—
391	C₄²	—	73	1	no	—
392	C₄²	—	73	1	no	—
393	C₄²	—	73	1	no	—
394	C₄²	—	73	1	no	—
395	C₄²	—	73	1	no	—
396	C₄²	—	146	2	no	—
397	C₄²	—	146	2	no	—
398	C₄²	—	146	2	no	—
399	C₄²	—	146	1	no	—
400	C₂³	—	292	1	no	—
401	C₂³	—	292	1	no	—
402	C₂³	—	73	1	no	—
403	C₂³	—	73	1	no	—
404	C₂³	—	73	1	no	—
405	C₂³	—	73	1	no	—
406	C₂³	—	73	1	no	—
407	C₂³	—	73	1	no	—
408	C₂³	C₂²×#10596842	1	1	yes	characteristic
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	292	2	no	—
411	C₂×C₄	—	292	2	no	—
412	C₂×C₄	—	292	2	no	—
413	C₂×C₄	—	292	2	no	—
414	C₂×C₄	—	292	1	no	—
415	C₂×C₄	—	292	1	no	—
416	C₂×C₄	—	292	1	no	—
417	C₂×C₄	—	292	1	no	—
418	C₂×C₄	—	292	1	no	—
419	C₂×C₄	—	292	1	no	—
420	C₂×C₄	—	73	1	no	—
421	C₂×C₄	—	73	1	no	—
422	C₂×C₄	—	73	1	no	—
423	C₂×C₄	—	73	1	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	—	73	1	no	—
429	C₂×C₄	—	73	1	no	—
430	C₂×C₄	—	73	1	no	—
431	C₂×C₄	—	73	1	no	—
432	C₂×C₄	—	73	1	no	—
433	C₂×C₄	—	73	1	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	—	73	1	no	—
439	C₂×C₄	—	73	1	no	—
440	C₂×C₄	—	73	1	no	—
441	C₂×C₄	—	73	1	no	—
442	C₂×C₄	—	73	1	no	—
443	C₂×C₄	—	73	1	no	—
444	C₂×C₄	—	73	1	no	—
445	C₂×C₄	—	73	1	no	—
446	C₂×C₄	—	73	1	no	—
447	C₂×C₄	—	73	1	no	—
448	C₂×C₄	—	73	1	no	—
449	C₂×C₄	—	73	1	no	—
450	C₂×C₄	—	146	4	no	—
451	C₂×C₄	—	146	2	no	—
452	C₂×C₄	—	146	2	no	—
453	C₂×C₄	—	146	2	no	—
454	C₂×C₄	—	146	2	no	—
455	C₂×C₄	—	146	2	no	—
456	C₂×C₄	—	146	2	no	—
457	C₂×C₄	—	146	2	no	—
458	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
459	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
460	C₂×C₄	C₂²⋊#10596842	1	1	yes	characteristic
461	C₂×C₄	C₂²⋊#10596842	1	1	yes	characteristic
462	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
463	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
464	C₈	—	292	4	no	—
465	C₈	—	292	4	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	292	1	no	—
468	C₂²	—	292	1	no	—
469	C₂²	—	292	1	no	—
470	C₂²	—	73	1	no	—
471	C₂²	—	73	1	no	—
472	C₂²	—	73	1	no	—
473	C₂²	—	73	1	no	—
474	C₂²	—	146	1	no	—
475	C₂²	—	146	1	no	—
476	C₂²	—	146	1	no	—
477	C₂²	—	146	1	no	—
478	C₂²	—	146	1	no	—
479	C₂²	—	146	1	no	—
480	C₂²	C₂×C₄×#10596842	1	1	yes	characteristic
481	C₂²	C₂×C₂²⋊#10596842	1	1	yes	characteristic
482	C₂²	C₂×C₄⋊#10596842	1	1	yes	characteristic
483	C₄	—	4	2	no	—
484	C₄	—	292	2	no	—
485	C₄	—	292	4	no	—
486	C₄	—	73	2	no	—
487	C₄	—	73	2	no	—
488	C₄	—	73	1	no	—
489	C₄	—	73	1	no	—
490	C₄	—	73	1	no	—
491	C₄	—	73	1	no	—
492	C₄	—	146	1	no	—
493	C₄	—	146	1	no	—
494	C₄	—	146	1	no	—
495	C₄	—	146	1	no	—
496	C₄	—	146	1	no	—
497	C₄	—	146	1	no	—
498	C₄	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
499	C₄	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
500	C₄	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
501	C₄	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	73	1	no	—
506	C₂	—	73	1	no	—
507	C₂	—	146	1	no	—
508	C₂	—	146	1	no	—
509	C₂	—	146	1	no	—
510	C₂	C₂×(C₂×#10596842)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	(C₂×#10596842)⋊C₄
commutator	C₂²×C₇₃	C₂×C₄×C₈
Frattini	C₂³	C₂²×#10596842
Fitting	#117×C₇₃	C₈
socle	C₂×C₇₃	C₂×#336
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂³×#64408	C₂³
hypercenter	#117	#10596842
hypocenter	C₇₃	#7924
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
11. #17989700	C₄	semidirect
12. #17989700	C₄	semidirect
14. C₂×C₄⋊#10596842	C₄	semidirect
18. C₂×C₄×#10596842	C₄	semidirect
46. #14556670	C₈	semidirect
47. #14556670	C₈	semidirect
68. #14556550	C₈	semidirect
71. #14556547	C₈	semidirect
75. #117×C₇₃	C₈	semidirect
260. C₇₃	#7924	semidirect
297. #117	#10596842	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989700	2
#22626942	2
#117×#64408	2
#7924	73