Subgroups — #34018152

Order 18688.

610 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626626	C₂	1	2	yes	maximal
2	#22625503	C₂	1	2	yes	maximal, complemented
3	#22625502	C₂	1	2	yes	maximal, complemented
4	#22625500	C₂	1	2	yes	maximal, complemented
5	#22625492	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625491	C₂	1	1	yes	maximal, characteristic, complemented
7	#22625485	C₂	1	1	yes	maximal, characteristic, complemented
8	#22625479	C₂	1	1	yes	maximal, characteristic, complemented
9	#22625478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#17989448	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#11924027	C₂	1	1	yes	maximal, characteristic
12	#17989612	—	2	2	no	—
13	#17989611	—	2	2	no	—
14	#17989609	C₂²	1	2	yes	—
15	#17989608	C₂²	1	2	yes	—
16	#17989606	C₂²	1	2	yes	—
17	#17989603	C₂²	1	2	yes	—
18	#17989590	C₂²	1	2	yes	—
19	C₂×C₄⋊#10596833	C₂²	1	2	yes	—
20	#17989560	—	2	2	no	—
21	#17989551	—	2	2	no	—
22	#17989451	C₂²	1	2	yes	—
23	#17989451	C₂²	1	2	yes	—
24	#17989450	C₂²	1	2	yes	—
25	#17989450	C₂²	1	2	yes	—
26	#17989449	C₂²	1	2	yes	—
27	#17989448	C₂²	1	1	yes	characteristic
28	#17989448	C₂²	1	1	yes	characteristic
29	#17989448	C₂²	1	2	yes	—
30	#17989448	C₂²	1	1	yes	characteristic
31	#17989448	C₂²	1	1	yes	characteristic
32	C₄×#11924027	C₂²	1	1	yes	characteristic
33	C₈×Dic₁₄₆	C₄	1	1	yes	characteristic
34	#17988711	C₄	1	1	yes	characteristic
35	D₄×#10596831	C₄	1	1	yes	characteristic
36	C₈×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
37	C₈×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
38	#17988650	C₄	1	1	yes	characteristic
39	#17988650	C₄	1	1	yes	characteristic
40	#17988639	C₂²	1	1	yes	characteristic
41	#17988637	C₂²	1	1	yes	characteristic
42	#17988637	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
46	C₈×D₄×C₇₃	C₄	1	1	yes	characteristic
47	C₂×#11924037	—	2	2	no	—
48	C₂²×#10596833	—	2	2	no	—
49	#14556658	—	2	2	no	—
50	C₄⋊#10596833	—	2	2	no	—
51	C₄⋊#10596833	C₂³	1	2	yes	—
52	C₄⋊#10596833	C₂³	1	2	yes	—
53	C₄⋊#10596833	C₂³	1	2	yes	—
54	C₄⋊#10596833	C₂³	1	2	yes	—
55	#14556648	—	2	2	no	—
56	#14556648	—	2	2	no	—
57	C₂²⋊#10596833	—	2	2	no	—
58	C₂²⋊#10596833	—	2	2	no	—
59	#14556646	—	2	2	no	—
60	#14556646	—	2	2	no	—
61	C₄×#10596833	—	2	2	no	—
62	C₄×#10596833	—	2	2	no	—
63	C₂×#11924027	D₄	1	1	yes	characteristic
64	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
65	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
68	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
69	#14556556	Q₈	1	1	yes	characteristic
70	D₄×Dic₇₃	Q₈	1	1	yes	characteristic
71	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
73	#14556551	Q₈	1	1	yes	characteristic
74	#14556551	Q₈	1	1	yes	characteristic
75	#14556549	D₄	1	1	yes	characteristic
76	#14556547	D₄	1	1	yes	characteristic
77	#14556547	D₄	1	1	yes	characteristic
78	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
80	C₄²×D₇₃	C₂³	1	1	yes	characteristic
81	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
82	#14556520	C₂×C₄	1	1	yes	characteristic
83	#14556520	C₂×C₄	1	1	yes	characteristic
84	#14556520	C₂×C₄	1	1	yes	characteristic
85	#14556520	C₂×C₄	1	1	yes	characteristic
86	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
88	#14556503	C₂×C₄	1	1	yes	characteristic
89	#14556503	C₂×C₄	1	1	yes	characteristic
90	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
96	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
97	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
101	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
102	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
105	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
106	#11924037	—	4	4	no	—
107	C₂×#10596833	—	2	2	no	—
108	C₂×#10596833	—	2	2	no	—
109	C₂×#10596833	—	2	2	no	—
110	C₂×#10596833	—	2	2	no	—
111	C₂×#10596833	—	4	4	no	—
112	#11924027	—	2	4	no	—
113	C₂×Dic₁₄₆	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₇₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₂²⋊D₇₃	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
119	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
120	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
123	C₂×#10596831	—	4	1	no	—
124	C₂×#10596831	—	4	1	no	—
125	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
126	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
127	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
128	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
129	C₈×D₇₃	—	2	2	no	—
130	C₈×D₇₃	—	4	1	no	—
131	C₄⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
132	#11924007	C₄⋊C₄	1	1	yes	characteristic
133	#11924007	C₄⋊C₄	1	1	yes	characteristic
134	#11924007	C₄⋊C₄	1	1	yes	characteristic
135	#11924007	C₄⋊C₄	1	1	yes	characteristic
136	C₂²⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
137	C₂²⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
138	#11924005	C₄⋊C₄	1	1	yes	characteristic
139	#11924005	C₄⋊C₄	1	1	yes	characteristic
140	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
144	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
145	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
146	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
147	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
148	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
149	C₂×D₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
158	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
159	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
160	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
161	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
162	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	D₄×C₇₃	—	2	2	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	2	1	no	—
168	C₂×C₄×C₇₃	—	2	1	no	—
169	C₂×C₄×C₇₃	—	2	1	no	—
170	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
175	C₂²⋊D₇₃	—	2	2	no	—
176	C₂²⋊D₇₃	—	2	2	no	—
177	C₂×Dic₇₃	—	2	2	no	—
178	C₂×Dic₇₃	—	4	1	no	—
179	C₂×Dic₇₃	—	4	1	no	—
180	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×Dic₇₃	#135	1	4	yes	—
186	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
188	C₄×D₇₃	—	2	1	no	—
189	C₄×D₇₃	—	2	1	no	—
190	C₄×D₇₃	—	2	2	no	—
191	C₄×D₇₃	—	4	1	no	—
192	Dic₁₄₆	—	2	2	no	—
193	#10596833	—	4	2	no	—
194	#10596833	—	4	2	no	—
195	#10596833	—	4	2	no	—
196	#10596833	—	4	2	no	—
197	C₈×C₇₃	—	2	1	no	—
198	C₈×C₇₃	—	2	1	no	—
199	C₈×C₇₃	—	2	1	no	—
200	C₈×C₇₃	#131	1	2	yes	—
201	#10596831	—	2	1	no	—
202	#10596831	—	2	1	no	—
203	#10596831	—	2	1	no	—
204	#10596831	—	2	1	no	—
205	C₂²×C₇₃	—	2	1	no	—
206	C₂²×C₇₃	—	2	1	no	—
207	C₂²×C₇₃	—	2	1	no	—
208	C₂²×C₇₃	—	2	1	no	—
209	C₂²×C₇₃	—	2	1	no	—
210	C₂²×C₇₃	#427	1	2	yes	—
211	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
212	C₂×D₇₃	—	2	1	no	—
213	C₂×D₇₃	—	2	1	no	—
214	C₂×D₇₃	—	2	1	no	—
215	C₄×C₇₃	—	2	1	no	—
216	C₄×C₇₃	—	2	1	no	—
217	C₄×C₇₃	—	2	1	no	—
218	C₄×C₇₃	—	2	1	no	—
219	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
220	C₄×C₇₃	#568	1	1	yes	characteristic
221	Dic₇₃	—	2	1	no	—
222	Dic₇₃	—	2	1	no	—
223	Dic₇₃	—	2	1	no	—
224	Dic₇₃	—	2	1	no	—
225	Dic₇₃	—	2	1	no	—
226	Dic₇₃	#427	1	2	yes	—
227	Dic₇₃	C₂×#135	1	2	yes	—
228	#17827	—	73	1	no	maximal, Sylow
229	C₂×C₇₃	—	2	2	no	—
230	C₂×C₇₃	—	4	1	no	—
231	C₂×C₇₃	#2906	1	1	yes	characteristic
232	C₂×C₇₃	C₂×#427	1	1	yes	characteristic
233	C₂×C₇₃	#2916	1	1	yes	characteristic
234	D₇₃	—	4	1	no	—
235	C₈×#41	—	73	1	no	—
236	#2925	—	73	2	no	—
237	#1572	—	73	2	no	—
238	#1572	—	73	2	no	—
239	#1571	—	73	2	no	—
240	#1568	—	73	1	no	—
241	#1568	—	73	1	no	—
242	#1566	—	73	1	no	—
243	#1564	—	73	1	no	—
244	#1564	—	73	1	no	—
245	C₂×#334	—	73	1	no	—
246	C₇₃	#17827	1	1	yes	characteristic, complemented, Sylow
247	C₄×#41	—	73	1	no	—
248	C₈×Q₈	—	73	1	no	—
249	C₈×Q₈	—	73	1	no	—
250	C₈×D₄	—	73	1	no	—
251	C₈×D₄	—	73	1	no	—
252	C₈×D₄	—	73	1	no	—
253	C₈×D₄	—	73	1	no	—
254	C₈×D₄	—	73	1	no	—
255	C₈×D₄	#64408	1	1	yes	characteristic
256	#433	—	146	2	no	—
257	#433	—	146	2	no	—
258	#432	—	73	2	no	—
259	#432	—	73	2	no	—
260	#431	—	73	1	no	—
261	#431	—	73	1	no	—
262	#431	—	73	1	no	—
263	#431	—	73	2	no	—
264	#431	—	73	2	no	—
265	#423	—	73	2	no	—
266	C₂×C₄⋊C₈	—	73	2	no	—
267	#408	—	146	2	no	—
268	#405	—	146	2	no	—
269	C₂×C₄×C₈	—	73	1	no	—
270	C₂×C₄×C₈	—	73	1	no	—
271	C₂×C₄×C₈	—	73	1	no	—
272	#335	—	73	2	no	—
273	#335	—	73	2	no	—
274	#335	—	73	2	no	—
275	#335	—	73	2	no	—
276	#334	—	73	1	no	—
277	#334	—	73	1	no	—
278	#334	—	73	2	no	—
279	#334	—	73	1	no	—
280	#334	—	73	1	no	—
281	#334	—	73	2	no	—
282	C₂×#41	—	73	1	no	—
283	C₂×M₁₆	—	146	2	no	—
284	C₂²×C₈	—	73	1	no	—
285	C₂²×C₈	—	73	1	no	—
286	C₂²×C₈	—	73	1	no	—
287	C₂²×C₈	—	73	1	no	—
288	C₂²×C₈	—	146	2	no	—
289	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
290	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
291	C₄×Q₈	—	73	1	no	—
292	C₄×Q₈	—	73	1	no	—
293	C₄×D₄	—	73	1	no	—
294	C₄×D₄	—	73	1	no	—
295	C₄×D₄	—	73	1	no	—
296	C₄×D₄	—	73	1	no	—
297	C₄×D₄	—	73	1	no	—
298	C₄×D₄	C₂×#64408	1	1	yes	characteristic
299	#117	—	73	1	no	—
300	#117	—	73	1	no	—
301	#117	—	73	1	no	—
302	C₂×C₄²	—	73	1	no	—
303	C₂×C₄²	—	73	1	no	—
304	C₂×C₄²	—	73	1	no	—
305	C₄⋊C₈	—	73	1	no	—
306	C₄⋊C₈	—	73	1	no	—
307	C₄⋊C₈	—	73	1	no	—
308	C₄⋊C₈	—	73	1	no	—
309	C₄⋊C₈	—	73	2	no	—
310	C₄⋊C₈	—	73	2	no	—
311	C₄⋊C₈	—	73	2	no	—
312	C₄⋊C₈	—	73	2	no	—
313	C₄⋊C₈	—	73	1	no	—
314	C₄⋊C₈	—	146	2	no	—
315	C₄⋊C₈	—	146	2	no	—
316	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
317	C₂²⋊C₈	—	73	1	no	—
318	C₂²⋊C₈	—	73	1	no	—
319	C₂²⋊C₈	—	73	1	no	—
320	C₂²⋊C₈	—	73	1	no	—
321	C₂²⋊C₈	—	146	2	no	—
322	C₂²⋊C₈	—	146	2	no	—
323	C₂²⋊C₈	—	146	2	no	—
324	C₂²⋊C₈	—	146	2	no	—
325	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
326	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
327	#97	—	146	2	no	—
328	#97	—	146	2	no	—
329	C₄×C₈	—	73	1	no	—
330	C₄×C₈	—	73	1	no	—
331	C₄×C₈	—	73	1	no	—
332	C₄×C₈	—	73	1	no	—
333	C₄×C₈	—	73	1	no	—
334	C₄×C₈	—	73	1	no	—
335	C₄×C₈	—	73	1	no	—
336	C₄×C₈	—	73	1	no	—
337	C₄×C₈	—	73	1	no	—
338	C₄×C₈	—	146	2	no	—
339	C₄×C₈	—	146	2	no	—
340	C₄×C₈	C₂×#64408	1	1	yes	characteristic
341	#41	—	146	4	no	—
342	C₂×Q₈	—	73	1	no	—
343	C₂×D₄	—	73	1	no	—
344	C₂×D₄	—	73	1	no	—
345	C₂×D₄	C₄⋊#64408	1	1	yes	characteristic
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	C₂²×#64408	1	1	yes	characteristic
354	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
355	M₁₆	—	292	4	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	292	1	no	—
359	C₂×C₈	—	292	4	no	—
360	C₂×C₈	—	292	1	no	—
361	C₂×C₈	—	292	1	no	—
362	C₂×C₈	—	73	1	no	—
363	C₂×C₈	—	73	1	no	—
364	C₂×C₈	—	73	1	no	—
365	C₂×C₈	—	73	1	no	—
366	C₂×C₈	—	146	2	no	—
367	C₂×C₈	—	146	2	no	—
368	C₂×C₈	—	146	2	no	—
369	C₂×C₈	—	146	2	no	—
370	C₂×C₈	—	146	2	no	—
371	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
372	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
373	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
374	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
375	C₄⋊C₄	—	73	1	no	—
376	C₄⋊C₄	—	73	1	no	—
377	C₄⋊C₄	—	73	1	no	—
378	C₄⋊C₄	—	73	1	no	—
379	C₄⋊C₄	—	73	1	no	—
380	C₄⋊C₄	C₄⋊#64408	1	1	yes	characteristic
381	C₂²⋊C₄	—	73	1	no	—
382	C₂²⋊C₄	—	73	1	no	—
383	C₂²⋊C₄	—	73	1	no	—
384	C₂²⋊C₄	—	73	1	no	—
385	C₂²⋊C₄	C₄⋊#64408	1	1	yes	characteristic
386	C₂²⋊C₄	C₄⋊#64408	1	1	yes	characteristic
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	C₂²×#64408	1	1	yes	characteristic
397	C₂³	—	73	1	no	—
398	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
399	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
400	Q₈	—	146	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	146	2	no	—
403	D₄	—	146	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	292	1	no	—
409	C₂×C₄	—	292	1	no	—
410	C₂×C₄	—	292	1	no	—
411	C₂×C₄	—	73	1	no	—
412	C₂×C₄	—	73	1	no	—
413	C₂×C₄	—	73	4	no	—
414	C₂×C₄	—	73	1	no	—
415	C₂×C₄	—	73	1	no	—
416	C₂×C₄	—	73	1	no	—
417	C₂×C₄	—	73	1	no	—
418	C₂×C₄	—	73	1	no	—
419	C₂×C₄	—	146	2	no	—
420	C₂×C₄	—	146	2	no	—
421	C₂×C₄	—	146	1	no	—
422	C₂×C₄	—	146	1	no	—
423	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
424	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
427	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	292	2	no	—
432	C₈	—	292	2	no	—
433	C₈	—	292	2	no	—
434	C₈	—	292	2	no	—
435	C₈	—	146	1	no	—
436	C₈	—	146	1	no	—
437	C₈	—	146	1	no	—
438	C₈	—	146	1	no	—
439	C₈	#14556678	1	2	yes	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	146	1	no	—
446	C₂²	—	146	1	no	—
447	C₂²	—	146	1	no	—
448	C₂²	#17989597	1	2	yes	—
449	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	73	2	no	—
455	C₄	—	73	2	no	—
456	C₄	—	146	1	no	—
457	C₄	—	146	1	no	—
458	C₄	—	146	1	no	—
459	C₄	—	146	1	no	—
460	C₄	—	146	1	no	—
461	C₄	C₂×#14556678	1	1	yes	characteristic
462	C₄	#17989666	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	1	no	—
465	C₂	—	292	1	no	—
466	C₂	#22626576	1	1	yes	characteristic
467	C₂	C₂×#17989597	1	1	yes	characteristic
468	C₂	#22626592	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₈×D₄×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂×#11924027	D₄
cosocle	C₄×Dic₇₃	C₂⁴
hypercenter	C₈×D₄	#64408
hypocenter	C₇₃	#17827
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
2. #22625503	C₂	semidirect
3. #22625502	C₂	semidirect
4. #22625500	C₂	semidirect
5. #22625492	C₂	semidirect
6. #22625491	C₂	semidirect
7. #22625485	C₂	semidirect
8. #22625479	C₂	semidirect
9. #22625478	C₂	semidirect
10. C₂×#17989448	C₂	semidirect
246. C₇₃	#17827	semidirect

Maximal subgroups

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

subgroup	index
#22626626	2
#22625503	2
#22625502	2
#22625500	2
#22625492	2
#22625491	2
#22625485	2
#22625479	2
#22625478	2
C₂×#17989448	2
C₈×#11924027	2
#17827	73