Subgroups — #34022035

Order 18688.

858 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626390	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×#64408	C₂	1	1	yes	maximal, characteristic
3	#22626011	C₂	1	2	yes	maximal
4	#22625995	C₂	1	2	yes	maximal
5	#22625925	C₂	1	2	yes	maximal
6	#22625895	C₂	1	2	yes	maximal
7	C₄×#14556660	C₂	1	1	yes	maximal, characteristic
8	C₄×#14556654	C₂	1	1	yes	maximal, characteristic
9	C₄×#14556654	C₂	1	1	yes	maximal, characteristic
10	#22625644	C₂	1	1	yes	maximal, characteristic
11	C₄×Q₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×#64408	C₂²	1	2	yes	—
13	C₂×#14556660	C₂²	1	2	yes	—
14	C₂×#14556654	C₂²	1	2	yes	—
15	C₂×#14556654	C₂²	1	2	yes	—
16	C₄×#11924036	C₂²	1	1	yes	characteristic
17	(C₂×#64408)⋊Q₈	C₂²	1	2	yes	—
18	#17989538	C₂²	1	2	yes	—
19	#17989536	—	2	2	no	—
20	C₄⋊C₄×#64408	—	2	2	no	—
21	C₄⋊C₄×#64408	C₂²	1	2	yes	—
22	C₄×C₄⋊#64408	—	2	1	no	—
23	C₄×C₄⋊#64408	—	2	1	no	—
24	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
26	#17989523	—	2	1	no	—
27	C₄²×#64408	—	2	1	no	—
28	C₄²×#64408	C₂²	1	1	yes	characteristic
29	#17989461	C₂²	1	2	yes	—
30	#17989460	C₂²	1	2	yes	—
31	#17989460	C₂²	1	2	yes	—
32	#17989452	C₂²	1	2	yes	—
33	#17989452	C₂²	1	2	yes	—
34	C₂×Q₁₆×D₇₃	C₂²	1	1	yes	characteristic
35	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
36	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
37	C₄×Dic₂₉₂	C₄	1	1	yes	characteristic, complemented
38	Q₁₆×Dic₇₃	C₄	1	1	yes	characteristic, complemented
39	#17988681	C₄	1	1	yes	characteristic, complemented
40	C₄×#11924018	C₄	1	1	yes	characteristic, complemented
41	C₄×#11924018	C₄	1	1	yes	characteristic, complemented
42	#17988679	C₄	1	1	yes	characteristic, complemented
43	#17988679	C₄	1	1	yes	characteristic, complemented
44	#107×D₇₃	C₂²	1	1	yes	characteristic
45	#103×D₇₃	C₂²	1	1	yes	characteristic
46	#103×D₇₃	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
48	C₄×Q₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
49	C₂×#11924036	C₂³	1	2	yes	—
50	Q₈×#64408	—	2	4	no	—
51	Q₈×#64408	—	2	4	no	—
52	C₂×C₄⋊#64408	—	2	2	no	—
53	C₂×C₄⋊#64408	—	2	2	no	—
54	C₂×C₄⋊#64408	C₂³	1	2	yes	—
55	C₂×C₄⋊#64408	C₂³	1	2	yes	—
56	C₂×C₄×#64408	—	2	2	no	—
57	C₂×C₄×#64408	—	2	2	no	—
58	C₂×C₄×#64408	—	2	1	no	—
59	C₂×C₄×#64408	—	2	1	no	—
60	C₂×C₄×#64408	D₄	1	1	yes	characteristic
61	C₂×C₄×#64408	D₄	1	2	yes	—
62	C₂×C₄×#64408	D₄	1	1	yes	characteristic
63	C₂×C₄×#64408	C₂³	1	2	yes	—
64	#14556660	—	2	4	no	—
65	#14556654	—	2	4	no	—
66	#14556654	—	2	4	no	—
67	C₄×#10596833	—	2	1	no	—
68	C₄×#10596833	—	2	1	no	—
69	(C₂×#64408)⋊C₄	—	2	2	no	—
70	(C₂×#64408)⋊C₄	—	2	2	no	—
71	(C₂×#64408)⋊C₄	—	2	2	no	—
72	(C₂×#64408)⋊C₄	—	2	2	no	—
73	(C₂×#64408)⋊C₄	—	2	1	no	—
74	(C₂×#64408)⋊C₄	—	2	1	no	—
75	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
76	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
77	C₂×Dic₂₉₂	C₂×C₄	1	1	yes	characteristic
78	C₂×#11924018	C₂×C₄	1	1	yes	characteristic
79	C₂×#11924018	C₂×C₄	1	1	yes	characteristic
80	Q₁₆×D₇₃	—	2	4	no	—
81	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
82	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
83	Q₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
84	Q₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₁₄₆	—	2	1	no	—
86	C₄×Dic₁₄₆	—	2	1	no	—
87	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
88	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
89	#14556556	—	2	1	no	—
90	#14556556	—	2	1	no	—
91	#14556556	C₂×C₄	1	1	yes	characteristic
92	#14556556	C₂×C₄	1	1	yes	characteristic
93	C₄⋊C₄×D₇₃	—	2	1	no	—
94	C₄⋊C₄×D₇₃	—	2	1	no	—
95	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
97	C₄²×D₇₃	—	2	1	no	—
98	C₄²×D₇₃	—	2	1	no	—
99	C₄²×D₇₃	C₂³	1	1	yes	characteristic
100	#14556525	C₂×C₄	1	1	yes	characteristic
101	#14556524	C₂×C₄	1	1	yes	characteristic
102	#14556524	C₂×C₄	1	1	yes	characteristic
103	#14556516	C₂×C₄	1	1	yes	characteristic
104	#14556516	C₂×C₄	1	1	yes	characteristic
105	#14556515	C₂×C₄	1	1	yes	characteristic
106	#14556515	C₂×C₄	1	1	yes	characteristic
107	#14556514	C₂×C₄	1	1	yes	characteristic
108	#14556514	C₂×C₄	1	1	yes	characteristic
109	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
110	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
111	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
112	C₂×Q₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
114	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
115	#107×C₇₃	C₂×C₄	1	1	yes	characteristic
116	#103×C₇₃	C₂×C₄	1	1	yes	characteristic
117	#103×C₇₃	C₂×C₄	1	1	yes	characteristic
118	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
119	C₂²×#64408	—	2	2	no	—
120	C₂²×#64408	—	2	2	no	—
121	C₂²×#64408	C₂×D₄	1	2	yes	—
122	C₂²×#64408	C₂×D₄	1	2	yes	—
123	#11924036	—	2	2	no	—
124	#11924036	—	2	2	no	—
125	C₂×#10596833	—	2	2	no	—
126	C₄⋊#64408	—	2	8	no	—
127	C₄⋊#64408	—	2	2	no	—
128	C₄⋊#64408	—	2	2	no	—
129	C₄⋊#64408	—	2	2	no	—
130	C₄⋊#64408	—	4	4	no	—
131	C₄⋊#64408	#41	1	4	yes	—
132	C₄×#64408	—	2	8	no	—
133	C₄×#64408	—	2	2	no	—
134	C₄×#64408	—	2	2	no	—
135	C₄×#64408	—	2	2	no	—
136	C₄×#64408	—	4	2	no	—
137	C₄×#64408	—	4	4	no	—
138	C₄×#64408	—	4	2	no	—
139	C₄×#64408	—	4	2	no	—
140	C₄×#64408	Q₁₆	1	4	yes	complemented
141	C₂×Dic₁₄₆	—	2	1	no	—
142	C₂×Dic₁₄₆	—	2	1	no	—
143	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
145	Q₈×D₇₃	—	2	2	no	—
146	Q₈×D₇₃	—	2	2	no	—
147	Q₈×D₇₃	—	2	2	no	—
148	Q₈×D₇₃	#41	1	4	yes	—
149	C₂×C₄×D₇₃	—	2	1	no	—
150	C₂×C₄×D₇₃	—	2	1	no	—
151	C₂×C₄×D₇₃	—	2	1	no	—
152	C₂×C₄×D₇₃	—	2	1	no	—
153	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
156	Dic₂₉₂	—	2	2	no	—
157	#11924018	—	2	2	no	—
158	#11924018	—	2	2	no	—
159	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
160	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
161	C₈×D₇₃	—	2	2	no	—
162	C₈×D₇₃	—	2	2	no	—
163	C₄⋊Dic₇₃	—	2	1	no	—
164	C₄⋊Dic₇₃	—	2	1	no	—
165	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
167	#11924007	—	2	1	no	—
168	#11924007	—	2	1	no	—
169	#11924007	—	2	1	no	—
170	#11924007	—	2	1	no	—
171	#11924007	—	2	1	no	—
172	#11924007	—	2	1	no	—
173	C₄×Dic₇₃	—	2	1	no	—
174	C₄×Dic₇₃	—	2	1	no	—
175	C₄×Dic₇₃	—	2	1	no	—
176	C₄×Dic₇₃	—	2	1	no	—
177	C₄×Dic₇₃	—	2	1	no	—
178	C₄×Dic₇₃	—	2	1	no	—
179	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
180	C₄×Dic₇₃	#41	1	1	yes	characteristic
181	C₄×Dic₇₃	#41	1	1	yes	characteristic
182	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
183	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
184	Q₁₆×C₇₃	—	2	2	no	—
185	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
187	C₄⋊C₄×C₇₃	—	2	1	no	—
188	C₄⋊C₄×C₇₃	—	2	1	no	—
189	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
190	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
191	C₄²×C₇₃	—	2	1	no	—
192	C₄²×C₇₃	—	2	1	no	—
193	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
194	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×#64408	—	2	2	no	—
196	C₂×#64408	—	2	2	no	—
197	C₂×#64408	—	2	2	no	—
198	C₂×#64408	—	2	4	no	—
199	C₂×#64408	—	2	2	no	—
200	C₂×#64408	—	2	2	no	—
201	C₂×#64408	—	4	2	no	—
202	C₂×#64408	—	4	2	no	—
203	C₂×#64408	—	4	2	no	—
204	C₂×#64408	—	4	2	no	—
205	C₂×#64408	—	4	2	no	—
206	C₂×#64408	C₂×Q₁₆	1	4	yes	—
207	Q₈×C₇₃	—	2	1	no	—
208	Q₈×C₇₃	—	2	1	no	—
209	Q₈×C₇₃	—	2	1	no	—
210	Q₈×C₇₃	#117	1	2	yes	—
211	C₂×C₄×C₇₃	—	2	1	no	—
212	C₂×C₄×C₇₃	—	2	1	no	—
213	C₂×C₄×C₇₃	—	2	1	no	—
214	C₂×C₄×C₇₃	—	2	1	no	—
215	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
218	C₂×Dic₇₃	—	2	1	no	—
219	C₂×Dic₇₃	—	2	1	no	—
220	C₂×Dic₇₃	—	2	1	no	—
221	C₂×Dic₇₃	—	2	1	no	—
222	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
223	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
224	C₂×Dic₇₃	C₂×#41	1	1	yes	characteristic
225	C₄×D₇₃	—	2	4	no	—
226	C₄×D₇₃	—	2	2	no	—
227	C₄×D₇₃	—	4	2	no	—
228	C₄×D₇₃	—	4	2	no	—
229	C₄×D₇₃	—	4	2	no	—
230	C₄×D₇₃	C₂×Q₁₆	1	2	yes	—
231	C₄×D₇₃	#135	1	2	yes	—
232	C₄×D₇₃	C₂×#41	1	2	yes	—
233	C₄×D₇₃	C₂×#41	1	2	yes	—
234	Dic₁₄₆	—	2	1	no	—
235	Dic₁₄₆	—	2	4	no	—
236	Dic₁₄₆	—	2	1	no	—
237	Dic₁₄₆	—	2	1	no	—
238	Dic₁₄₆	—	4	2	no	—
239	Dic₁₄₆	#117	1	2	yes	—
240	#10596833	—	4	2	no	—
241	C₈×C₇₃	—	2	1	no	—
242	C₈×C₇₃	—	2	1	no	—
243	#10596831	—	2	1	no	—
244	#10596831	—	2	1	no	—
245	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂×D₇₃	#525	1	2	yes	—
247	C₂×D₇₃	C₂²×Q₁₆	1	1	yes	characteristic
248	C₂×D₇₃	C₂×#135	1	1	yes	characteristic
249	C₂×D₇₃	#575	1	2	yes	—
250	#64408	—	2	4	no	—
251	#64408	—	4	2	no	—
252	#64408	—	4	4	no	—
253	#64408	—	8	2	no	—
254	C₄×C₇₃	—	2	1	no	—
255	C₄×C₇₃	—	2	2	no	—
256	C₄×C₇₃	—	4	1	no	—
257	C₄×C₇₃	—	4	1	no	—
258	C₄×C₇₃	—	4	1	no	—
259	C₄×C₇₃	C₄×Q₁₆	1	2	yes	—
260	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
261	C₄×C₇₃	C₄×#41	1	1	yes	characteristic
262	Dic₇₃	—	2	1	no	—
263	Dic₇₃	—	2	2	no	—
264	Dic₇₃	—	4	1	no	—
265	Dic₇₃	—	4	1	no	—
266	Dic₇₃	—	4	1	no	—
267	Dic₇₃	C₄×Q₁₆	1	2	yes	—
268	Dic₇₃	#529	1	2	yes	—
269	#21119	—	73	1	no	maximal, Sylow
270	C₂×C₇₃	#2290	1	1	yes	characteristic
271	C₂×C₇₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
272	C₂×C₇₃	#2943	1	1	yes	characteristic
273	D₇₃	#3102	1	2	yes	—
274	D₇₃	#3104	1	2	yes	—
275	C₂×C₄×Q₁₆	—	73	1	no	—
276	#2295	—	73	1	no	—
277	C₄²×Q₈	—	73	1	no	—
278	#1928	—	73	2	no	—
279	#1921	—	73	2	no	—
280	#1878	—	73	2	no	—
281	#1863	—	73	2	no	—
282	C₄×#107	—	73	1	no	—
283	C₄×#103	—	73	1	no	—
284	C₄×#103	—	73	1	no	—
285	#1744	—	73	1	no	—
286	C₇₃	#21119	1	1	yes	characteristic, complemented, Sylow
287	C₂²×Q₁₆	—	73	1	no	—
288	C₂×C₄×Q₈	—	73	1	no	—
289	C₂×C₄×Q₈	—	73	1	no	—
290	C₂×C₄×Q₈	—	73	2	no	—
291	C₄×Q₁₆	—	73	1	no	—
292	C₄×Q₁₆	—	73	1	no	—
293	C₄×Q₁₆	—	73	1	no	—
294	C₄×Q₁₆	—	73	1	no	—
295	C₄×Q₁₆	—	73	1	no	—
296	C₄×Q₁₆	—	73	1	no	—
297	C₄×Q₁₆	—	73	1	no	—
298	C₄×Q₁₆	#64408	1	1	yes	characteristic, complemented
299	C₂×#107	—	73	1	no	—
300	C₂×#107	—	73	2	no	—
301	C₂×#103	—	73	1	no	—
302	C₂×#103	—	73	1	no	—
303	C₂×#103	—	73	2	no	—
304	C₂×#103	—	73	2	no	—
305	C₂×C₄×C₈	—	73	1	no	—
306	C₂×C₄×C₈	—	73	1	no	—
307	#391	—	73	2	no	—
308	#389	—	73	2	no	—
309	#387	—	146	2	no	—
310	C₄×C₄⋊C₄	—	73	2	no	—
311	C₄×C₄⋊C₄	—	73	1	no	—
312	C₄×C₄⋊C₄	—	73	1	no	—
313	C₄×C₄⋊C₄	—	146	1	no	—
314	C₄×C₄⋊C₄	—	146	1	no	—
315	C₄×C₄⋊C₄	—	146	2	no	—
316	#376	—	146	1	no	—
317	C₄³	—	73	1	no	—
318	C₄³	—	146	1	no	—
319	#340	—	73	2	no	—
320	#340	—	73	2	no	—
321	#340	—	73	2	no	—
322	#336	—	73	2	no	—
323	#336	—	73	2	no	—
324	C₂²×Q₈	—	73	1	no	—
325	C₂²×Q₈	—	73	1	no	—
326	C₂×Q₁₆	—	73	1	no	—
327	C₂×Q₁₆	—	73	1	no	—
328	C₂×Q₁₆	—	73	1	no	—
329	C₂×Q₁₆	—	146	4	no	—
330	C₂×Q₁₆	C₂×#64408	1	1	yes	characteristic
331	C₂²×C₈	—	73	1	no	—
332	C₂²×C₈	—	73	1	no	—
333	C₂²×C₈	—	73	2	no	—
334	C₄×Q₈	—	73	1	no	—
335	C₄×Q₈	—	73	1	no	—
336	C₄×Q₈	—	73	1	no	—
337	C₄×Q₈	—	73	1	no	—
338	C₄×Q₈	—	73	1	no	—
339	C₄×Q₈	—	73	1	no	—
340	C₄×Q₈	—	146	1	no	—
341	C₄×Q₈	—	146	1	no	—
342	C₄×Q₈	—	146	1	no	—
343	C₄×Q₈	—	146	1	no	—
344	C₄×Q₈	—	146	4	no	—
345	C₄×Q₈	—	146	4	no	—
346	C₄×Q₈	C₂×#64408	1	1	yes	characteristic
347	C₄×Q₈	C₂×#64408	1	1	yes	characteristic
348	C₂×C₄⋊C₄	—	73	2	no	—
349	C₂×C₄⋊C₄	—	73	1	no	—
350	C₂×C₄⋊C₄	—	73	1	no	—
351	C₂×C₄⋊C₄	—	73	2	no	—
352	C₂×C₄⋊C₄	—	146	1	no	—
353	C₂×C₄⋊C₄	—	146	1	no	—
354	C₂×C₄⋊C₄	—	146	2	no	—
355	C₂×C₄⋊C₄	—	146	2	no	—
356	C₂×C₄²	—	73	2	no	—
357	C₂×C₄²	—	73	1	no	—
358	C₂×C₄²	—	73	1	no	—
359	C₂×C₄²	—	73	2	no	—
360	C₂×C₄²	—	73	1	no	—
361	C₂×C₄²	—	146	1	no	—
362	C₂×C₄²	—	146	1	no	—
363	C₂×C₄²	—	146	1	no	—
364	C₂×C₄²	—	146	2	no	—
365	C₂×C₄²	—	146	1	no	—
366	C₂×C₄²	—	146	2	no	—
367	#107	—	73	1	no	—
368	#107	—	73	1	no	—
369	#107	—	73	1	no	—
370	#107	—	146	4	no	—
371	#107	C₂×#64408	1	1	yes	characteristic
372	#103	—	73	1	no	—
373	#103	—	73	1	no	—
374	#103	—	73	1	no	—
375	#103	—	73	1	no	—
376	#103	—	73	1	no	—
377	#103	—	73	1	no	—
378	#103	—	146	4	no	—
379	#103	—	146	4	no	—
380	#103	C₂×#64408	1	1	yes	characteristic
381	#103	C₂×#64408	1	1	yes	characteristic
382	C₄×C₈	—	73	1	no	—
383	C₄×C₈	—	73	1	no	—
384	C₄×C₈	—	73	1	no	—
385	C₄×C₈	—	146	1	no	—
386	C₄×C₈	—	146	1	no	—
387	C₄×C₈	C₂×#64408	1	1	yes	characteristic
388	#95	—	146	2	no	—
389	#95	—	146	2	no	—
390	#95	—	146	1	no	—
391	#95	—	146	2	no	—
392	#95	—	146	1	no	—
393	#95	—	146	2	no	—
394	C₂×Q₈	—	73	4	no	—
395	C₂×Q₈	—	73	1	no	—
396	C₂×Q₈	—	73	1	no	—
397	C₂×Q₈	—	146	1	no	—
398	C₂×Q₈	—	146	1	no	—
399	C₂×Q₈	—	146	2	no	—
400	C₂×Q₈	—	146	2	no	—
401	C₂×Q₈	—	146	2	no	—
402	C₂×Q₈	C₂²×#64408	1	1	yes	characteristic
403	C₂×Q₈	C₂²×#64408	1	1	yes	characteristic
404	C₂²×C₄	—	73	1	no	—
405	C₂²×C₄	—	73	1	no	—
406	C₂²×C₄	—	73	2	no	—
407	C₂²×C₄	—	73	1	no	—
408	C₂²×C₄	—	73	2	no	—
409	C₂²×C₄	—	146	1	no	—
410	C₂²×C₄	—	146	1	no	—
411	C₂²×C₄	—	146	1	no	—
412	C₂²×C₄	—	146	1	no	—
413	C₂²×C₄	—	146	2	no	—
414	C₂²×C₄	—	146	2	no	—
415	Q₁₆	—	2	2	no	—
416	Q₁₆	—	146	2	no	—
417	Q₁₆	—	146	2	no	—
418	Q₁₆	—	146	2	no	—
419	C₂×C₈	—	73	1	no	—
420	C₂×C₈	—	73	1	no	—
421	C₂×C₈	—	146	2	no	—
422	C₂×C₈	—	146	2	no	—
423	C₂×C₈	—	146	2	no	—
424	C₂×C₈	—	146	2	no	—
425	C₂×C₈	—	146	2	no	—
426	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
427	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	292	4	no	—
431	C₄⋊C₄	—	73	4	no	—
432	C₄⋊C₄	—	73	1	no	—
433	C₄⋊C₄	—	73	1	no	—
434	C₄⋊C₄	—	146	1	no	—
435	C₄⋊C₄	—	146	1	no	—
436	C₄⋊C₄	—	146	1	no	—
437	C₄⋊C₄	—	146	1	no	—
438	C₄⋊C₄	—	146	1	no	—
439	C₄⋊C₄	—	146	1	no	—
440	C₄⋊C₄	—	146	2	no	—
441	C₄⋊C₄	—	146	2	no	—
442	C₄⋊C₄	—	146	2	no	—
443	C₄⋊C₄	—	146	8	no	—
444	C₄⋊C₄	—	146	1	no	—
445	C₄⋊C₄	—	146	1	no	—
446	C₄⋊C₄	C₂²×#64408	1	1	yes	characteristic
447	C₄⋊C₄	C₂²×#64408	1	1	yes	characteristic
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	292	2	no	—
451	C₄²	—	292	2	no	—
452	C₄²	—	292	4	no	—
453	C₄²	—	292	2	no	—
454	C₄²	—	73	4	no	—
455	C₄²	—	73	1	no	—
456	C₄²	—	73	1	no	—
457	C₄²	—	73	1	no	—
458	C₄²	—	146	1	no	—
459	C₄²	—	146	1	no	—
460	C₄²	—	146	1	no	—
461	C₄²	—	146	1	no	—
462	C₄²	—	146	2	no	—
463	C₄²	—	146	2	no	—
464	C₄²	—	146	2	no	—
465	C₄²	—	146	8	no	—
466	C₄²	—	146	1	no	—
467	C₄²	—	146	1	no	—
468	C₄²	C₂²×#64408	1	1	yes	characteristic
469	C₂³	—	73	1	no	—
470	Q₈	—	2	1	no	—
471	Q₈	—	2	1	no	—
472	Q₈	—	2	1	no	—
473	Q₈	—	292	2	no	—
474	Q₈	—	73	2	no	—
475	Q₈	—	146	4	no	—
476	Q₈	—	146	1	no	—
477	Q₈	—	146	1	no	—
478	Q₈	—	146	1	no	—
479	Q₈	#14556670	1	2	yes	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	292	2	no	—
485	C₂×C₄	—	292	2	no	—
486	C₂×C₄	—	292	2	no	—
487	C₂×C₄	—	292	2	no	—
488	C₂×C₄	—	292	2	no	—
489	C₂×C₄	—	292	2	no	—
490	C₂×C₄	—	292	2	no	—
491	C₂×C₄	—	292	2	no	—
492	C₂×C₄	—	73	1	no	—
493	C₂×C₄	—	73	1	no	—
494	C₂×C₄	—	73	2	no	—
495	C₂×C₄	—	73	2	no	—
496	C₂×C₄	—	73	2	no	—
497	C₂×C₄	—	73	2	no	—
498	C₂×C₄	—	73	4	no	—
499	C₂×C₄	—	73	1	no	—
500	C₂×C₄	—	146	2	no	—
501	C₂×C₄	—	146	4	no	—
502	C₂×C₄	—	146	2	no	—
503	C₂×C₄	—	146	4	no	—
504	C₂×C₄	—	146	2	no	—
505	C₂×C₄	—	146	2	no	—
506	C₂×C₄	—	146	1	no	—
507	C₂×C₄	—	146	1	no	—
508	C₂×C₄	—	146	1	no	—
509	C₂×C₄	—	146	2	no	—
510	C₂×C₄	—	146	2	no	—
511	C₂×C₄	—	146	1	no	—
512	C₂×C₄	D₄×#64408	1	1	yes	characteristic
513	C₂×C₄	D₄×#64408	1	1	yes	characteristic
514	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
515	C₈	—	2	1	no	—
516	C₈	—	2	1	no	—
517	C₈	—	292	2	no	—
518	C₈	—	146	1	no	—
519	C₈	—	146	1	no	—
520	C₂²	—	73	2	no	—
521	C₂²	—	73	1	no	—
522	C₂²	—	73	1	no	—
523	C₂²	—	73	2	no	—
524	C₂²	C₂×D₄×#64408	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	2	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	292	4	no	—
531	C₄	—	292	2	no	—
532	C₄	—	292	1	no	—
533	C₄	—	292	1	no	—
534	C₄	—	292	1	no	—
535	C₄	—	584	2	no	—
536	C₄	—	73	2	no	—
537	C₄	—	73	2	no	—
538	C₄	—	146	4	no	—
539	C₄	—	146	2	no	—
540	C₄	—	146	1	no	—
541	C₄	Q₁₆×#64408	1	2	yes	—
542	C₄	C₂×#14556670	1	1	yes	characteristic
543	C₄	#41×#64408	1	1	yes	characteristic
544	C₂	—	73	2	no	—
545	C₂	—	73	2	no	—
546	C₂	#22626385	1	1	yes	characteristic
547	C₂	C₂×Q₁₆×#64408	1	1	yes	characteristic
548	C₂	#22626685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₄×Q₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂²×D₇₃	C₂²×D₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₄×Q₁₆	#64408
hypocenter	C₇₃	#21119
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
37. C₄×Dic₂₉₂	C₄	semidirect
38. Q₁₆×Dic₇₃	C₄	semidirect
39. #17988681	C₄	semidirect
40. C₄×#11924018	C₄	semidirect
41. C₄×#11924018	C₄	semidirect
42. #17988679	C₄	semidirect
43. #17988679	C₄	semidirect
48. C₄×Q₁₆×C₇₃	C₄	semidirect
140. C₄×#64408	Q₁₆	semidirect
286. C₇₃	#21119	semidirect
298. C₄×Q₁₆	#64408	semidirect

Maximal subgroups

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

subgroup	index
#22626390	2
C₄×Q₈×#64408	2
#22626011	2
#22625995	2
#22625925	2
#22625895	2
C₄×#14556660	2
C₄×#14556654	2
#22625644	2
C₄×Q₁₆×D₇₃	2
#21119	73