Subgroups — #33104200

Order 18688.

1022 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988666	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988628	C₂	1	2	yes	maximal, complemented
3	#22612878	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₄×D₂₉₂	C₂	1	1	yes	maximal, characteristic
5	#22610694	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610689	C₂	1	1	yes	maximal, characteristic, complemented
7	#22610131	C₂	1	2	yes	maximal, complemented
8	#22610125	C₂	1	2	yes	maximal, complemented
9	#22610088	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609965	C₂	1	2	yes	maximal, complemented
11	C₄×#107×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11924011	C₂²	1	2	yes	—
13	C₂×C₄×D₂₉₂	—	2	1	no	—
14	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
15	C₂×#14556549	C₂²	1	2	yes	—
16	C₂×C₄⋊C₄×D₇₃	C₂²	1	2	yes	—
17	#17988666	C₄	1	8	yes	complemented
18	#17988628	—	2	8	no	—
19	C₂×#14556524	C₂²	1	2	yes	—
20	C₂×#14556523	C₂²	1	2	yes	—
21	C₂×#14556523	C₂²	1	2	yes	—
22	C₂×#14556522	C₂²	1	2	yes	—
23	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
24	C₂×#14556503	C₂²	1	2	yes	—
25	#17988489	—	2	1	no	—
26	#17988485	—	2	1	no	—
27	#17988479	—	2	2	no	—
28	#17988461	—	2	2	no	—
29	#17988457	C₂²	1	1	yes	characteristic
30	#17988457	C₂²	1	1	yes	characteristic
31	#17988444	C₂²	1	2	yes	—
32	#17988444	C₂²	1	2	yes	—
33	C₄×C₄⋊Dic₇₃	—	2	1	no	—
34	#17988349	C₂²	1	2	yes	—
35	#17988349	C₂²	1	2	yes	—
36	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
41	#340×C₇₃	C₂²	1	1	yes	characteristic
42	#340×C₇₃	C₂²	1	1	yes	characteristic
43	C₂²×D₂₉₂	D₄	1	1	yes	characteristic
44	C₂²×C₄×D₇₃	—	2	2	no	—
45	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
46	C₂×#11924011	—	2	4	no	—
47	C₂×#11924011	—	2	4	no	—
48	C₂×#11924011	C₂×C₄	1	8	yes	complemented
49	C₂²×#10596831	C₂³	1	2	yes	—
50	C₄×D₂₉₂	—	4	4	no	—
51	C₄×D₂₉₂	C₂×C₄	1	4	yes	—
52	C₄×D₂₉₂	Q₈	1	4	yes	—
53	#14556549	—	2	4	no	—
54	#14556549	—	4	2	no	—
55	C₂×C₄⋊Dic₇₃	—	2	1	no	—
56	C₂×C₄⋊Dic₇₃	—	2	1	no	—
57	C₂×C₄⋊Dic₇₃	—	2	1	no	—
58	C₂×C₄⋊Dic₇₃	—	2	1	no	—
59	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
60	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
62	C₂×#11924007	—	2	2	no	—
63	C₄⋊C₄×D₇₃	—	2	4	no	—
64	C₄⋊C₄×D₇₃	—	4	2	no	—
65	C₂×#11924005	—	2	2	no	—
66	C₂×#11924005	—	2	2	no	—
67	C₂×#11924005	—	2	2	no	—
68	C₂×#11924005	D₄	1	2	yes	—
69	C₂×C₄×Dic₇₃	—	2	2	no	—
70	#14556524	—	2	4	no	—
71	#14556523	—	2	4	no	—
72	#14556523	—	4	2	no	—
73	#14556522	—	2	4	no	—
74	C₄⋊#10596831	C₂×C₄	1	4	yes	complemented
75	#14556503	C₂×C₄	1	8	yes	complemented
76	#14556498	—	2	2	no	—
77	#14556498	—	2	2	no	—
78	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₇₃	—	2	1	no	—
85	C₂×C₄²×C₇₃	—	2	1	no	—
86	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
87	#107×C₇₃	—	2	2	no	—
88	#107×C₇₃	D₄	1	4	yes	complemented
89	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
90	#95×C₇₃	—	2	1	no	—
91	#95×C₇₃	—	2	1	no	—
92	C₂³×D₇₃	C₂×D₄	1	2	yes	—
93	C₂×D₂₉₂	—	2	2	no	—
94	C₂×D₂₉₂	—	2	2	no	—
95	C₂×D₂₉₂	C₄⋊C₄	1	4	yes	—
96	C₂²×Dic₇₃	—	2	2	no	—
97	C₂²×Dic₇₃	—	2	2	no	—
98	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
99	C₂×C₄×D₇₃	—	2	2	no	—
100	C₂×C₄×D₇₃	—	2	2	no	—
101	C₂×C₄×D₇₃	—	2	2	no	—
102	C₂×C₄×D₇₃	—	2	2	no	—
103	C₂×C₄×D₇₃	—	4	4	no	—
104	C₂×C₄×D₇₃	—	4	4	no	—
105	C₂×C₄×D₇₃	—	8	2	no	—
106	C₂×C₄×D₇₃	C₂²×C₄	1	4	yes	—
107	C₂×C₄×D₇₃	C₂×Q₈	1	4	yes	—
108	#11924011	—	2	16	no	—
109	C₂×#10596831	—	2	2	no	—
110	C₂×#10596831	—	2	2	no	—
111	C₂×#10596831	C₂²×C₄	1	4	yes	—
112	C₄⋊Dic₇₃	—	2	2	no	—
113	C₄⋊Dic₇₃	—	2	2	no	—
114	C₄⋊Dic₇₃	—	2	2	no	—
115	C₄⋊Dic₇₃	—	2	2	no	—
116	C₄⋊Dic₇₃	—	4	2	no	—
117	C₄⋊Dic₇₃	—	4	2	no	—
118	C₄⋊Dic₇₃	—	8	1	no	—
119	C₄⋊Dic₇₃	—	8	1	no	—
120	C₄⋊Dic₇₃	C₄⋊C₄	1	4	yes	—
121	#11924007	—	4	4	no	—
122	#11924005	—	4	4	no	—
123	#11924005	—	4	4	no	—
124	#11924005	—	8	2	no	—
125	#11924005	C₄⋊C₄	1	8	yes	—
126	C₄×Dic₇₃	—	4	4	no	—
127	C₂²×C₄×C₇₃	—	2	1	no	—
128	C₂²×C₄×C₇₃	—	2	1	no	—
129	C₂²×C₄×C₇₃	—	2	1	no	—
130	C₂²×C₄×C₇₃	—	2	1	no	—
131	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₇₃	—	2	1	no	—
135	C₂×C₈×C₇₃	—	2	1	no	—
136	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₇₃	#41	1	2	yes	—
140	C₄⋊C₄×C₇₃	—	2	1	no	—
141	C₄⋊C₄×C₇₃	—	2	1	no	—
142	C₄⋊C₄×C₇₃	—	2	1	no	—
143	C₄⋊C₄×C₇₃	—	2	1	no	—
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₄⋊C₄×C₇₃	—	2	1	no	—
146	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
148	C₄²×C₇₃	—	4	2	no	—
149	C₄²×C₇₃	—	4	2	no	—
150	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
151	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
152	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
153	C₂²×D₇₃	—	2	2	no	—
154	C₂²×D₇₃	—	2	2	no	—
155	C₂²×D₇₃	—	2	2	no	—
156	C₂²×D₇₃	—	2	2	no	—
157	C₂²×D₇₃	—	2	2	no	—
158	C₂²×D₇₃	—	2	2	no	—
159	C₂²×D₇₃	C₂×C₄⋊C₄	1	4	yes	—
160	C₂×C₄×C₇₃	—	2	1	no	—
161	C₂×C₄×C₇₃	—	2	1	no	—
162	C₂×C₄×C₇₃	—	2	2	no	—
163	C₂×C₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	—	4	1	no	—
165	C₂×C₄×C₇₃	—	4	1	no	—
166	C₂×C₄×C₇₃	—	4	1	no	—
167	C₂×C₄×C₇₃	—	4	1	no	—
168	C₂×C₄×C₇₃	—	4	1	no	—
169	C₂×C₄×C₇₃	—	4	1	no	—
170	C₂×C₄×C₇₃	—	4	1	no	—
171	C₂×C₄×C₇₃	—	4	1	no	—
172	C₂×C₄×C₇₃	—	4	1	no	—
173	C₂×C₄×C₇₃	—	4	1	no	—
174	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₇₃	#137	1	2	yes	—
178	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×Dic₇₃	—	2	2	no	—
185	C₂×Dic₇₃	—	2	2	no	—
186	C₂×Dic₇₃	—	4	2	no	—
187	C₂×Dic₇₃	—	4	2	no	—
188	C₂×Dic₇₃	—	4	2	no	—
189	C₂×Dic₇₃	—	4	2	no	—
190	C₂×Dic₇₃	—	4	2	no	—
191	C₂×Dic₇₃	—	4	2	no	—
192	C₂×Dic₇₃	C₂×C₄⋊C₄	1	4	yes	—
193	D₂₉₂	—	2	8	no	—
194	C₄×D₇₃	—	2	4	no	—
195	C₄×D₇₃	—	2	4	no	—
196	C₄×D₇₃	—	2	4	no	—
197	C₄×D₇₃	—	2	4	no	—
198	C₄×D₇₃	—	8	8	no	—
199	C₈×C₇₃	—	2	2	no	—
200	C₈×C₇₃	C₄×D₄	1	4	yes	complemented
201	#10596831	—	2	4	no	—
202	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	C₂²×C₇₃	D₄²	1	1	yes	characteristic
204	C₂²×C₇₃	#547	1	1	yes	characteristic
205	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
207	C₂²×C₇₃	#577	1	1	yes	characteristic
208	C₂²×C₇₃	#577	1	1	yes	characteristic
209	C₂×D₇₃	—	2	4	no	—
210	C₂×D₇₃	—	2	4	no	—
211	C₂×D₇₃	—	2	4	no	—
212	C₂×D₇₃	—	4	2	no	—
213	C₂×D₇₃	—	4	2	no	—
214	C₂×D₇₃	—	4	2	no	—
215	C₂×D₇₃	—	4	2	no	—
216	C₄×C₇₃	—	2	2	no	—
217	C₄×C₇₃	—	4	2	no	—
218	C₄×C₇₃	—	4	2	no	—
219	C₄×C₇₃	—	8	1	no	—
220	C₄×C₇₃	—	8	1	no	—
221	C₄×C₇₃	#428	1	4	yes	complemented
222	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
223	C₄×C₇₃	#520	1	1	yes	characteristic
224	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
225	C₄×C₇₃	#554	1	1	yes	characteristic
226	Dic₇₃	—	2	4	no	—
227	Dic₇₃	—	8	2	no	—
228	Dic₇₃	—	8	2	no	—
229	#22663	—	73	1	no	maximal, Sylow
230	C₂×C₇₃	D₄×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₇₃	C₂×#428	1	1	yes	characteristic
232	C₂×C₇₃	#2912	1	1	yes	characteristic
233	C₂×C₇₃	#3272	1	1	yes	characteristic
234	C₂×C₇₃	#3278	1	1	yes	characteristic
235	C₂×C₇₃	#3354	1	1	yes	characteristic
236	C₂×C₇₃	#3356	1	1	yes	characteristic
237	D₇₃	—	4	4	no	—
238	C₂×#436	—	73	1	no	—
239	C₂×#428	—	73	2	no	—
240	#2354	—	73	1	no	—
241	D₄×C₄⋊C₄	—	73	1	no	—
242	#1948	—	73	1	no	—
243	#1947	—	73	1	no	—
244	#1854	—	73	2	no	—
245	#1853	—	73	2	no	—
246	#1844	—	73	1	no	—
247	#1809	—	73	2	no	—
248	C₄×#107	D₇₃	1	1	yes	characteristic, complemented
249	C₇₃	#22663	1	1	yes	characteristic, complemented, Sylow
250	C₂²×M₁₆	—	73	2	no	—
251	C₂×C₄×D₄	—	73	1	no	—
252	C₂×C₄×D₄	—	146	1	no	—
253	C₂×#117	—	73	2	no	—
254	C₂²×C₄⋊C₄	—	73	2	no	—
255	#436	—	73	8	no	—
256	#428	—	146	8	no	—
257	C₂×#107	—	73	2	no	—
258	C₂×#107	C₂×D₇₃	1	1	yes	characteristic
259	C₂×#107	C₂×D₇₃	1	1	yes	characteristic
260	C₂×#106	—	73	2	no	—
261	C₂×#106	—	73	2	no	—
262	C₂×#106	—	73	2	no	—
263	C₂×C₄⋊C₈	—	73	1	no	—
264	C₂×C₂²⋊C₈	—	73	2	no	—
265	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
266	#390	—	146	1	no	—
267	#389	—	146	1	no	—
268	#388	—	146	2	no	—
269	#385	—	146	2	no	—
270	#384	—	73	1	no	—
271	#384	—	73	1	no	—
272	#380	—	73	2	no	—
273	#380	—	73	2	no	—
274	C₄×C₄⋊C₄	—	146	1	no	—
275	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
277	#340	—	73	2	no	—
278	#340	—	73	2	no	—
279	#340	C₂×D₇₃	1	1	yes	characteristic
280	#340	C₂×D₇₃	1	1	yes	characteristic
281	C₂²×D₄	—	73	1	no	—
282	C₂³×C₄	—	73	2	no	—
283	C₂³×C₄	—	146	2	no	—
284	C₂×M₁₆	—	73	8	no	—
285	C₂×M₁₆	—	146	4	no	—
286	C₂×M₁₆	—	146	4	no	—
287	C₂²×C₈	—	73	2	no	—
288	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
290	C₄×D₄	—	292	4	no	—
291	C₄×D₄	—	73	4	no	—
292	C₄×D₄	—	73	4	no	—
293	#117	—	292	2	no	—
294	#117	—	146	4	no	—
295	C₂×C₄⋊C₄	—	292	2	no	—
296	C₂×C₄⋊C₄	—	73	1	no	—
297	C₂×C₄⋊C₄	—	73	2	no	—
298	C₂×C₄⋊C₄	—	73	2	no	—
299	C₂×C₄⋊C₄	—	146	2	no	—
300	C₂×C₄⋊C₄	—	146	1	no	—
301	C₂×C₄⋊C₄	—	146	1	no	—
302	C₂×C₄⋊C₄	—	146	4	no	—
303	C₂×C₄⋊C₄	—	146	1	no	—
304	C₂×C₄⋊C₄	—	146	1	no	—
305	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	73	2	no	—
310	C₂×C₂²⋊C₄	—	146	2	no	—
311	C₂×C₂²⋊C₄	—	146	2	no	—
312	C₂×C₂²⋊C₄	—	146	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	—	146	2	no	—
316	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
317	#107	—	2	2	no	—
318	#107	—	146	4	no	—
319	#107	D₂₉₂	1	4	yes	complemented
320	#106	—	292	2	no	—
321	#106	—	146	4	no	—
322	#106	—	146	4	no	—
323	C₄⋊C₈	—	73	4	no	—
324	C₂²⋊C₈	—	73	8	no	—
325	C₄×C₈	C₄×D₇₃	1	4	yes	complemented
326	#95	—	2	1	no	—
327	#95	—	2	1	no	—
328	#95	—	146	2	no	—
329	#95	—	146	2	no	—
330	C₂⁴	—	73	2	no	—
331	C₂×D₄	—	73	4	no	—
332	C₂×D₄	—	146	2	no	—
333	C₂×D₄	—	146	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	292	4	no	—
339	C₂²×C₄	—	292	4	no	—
340	C₂²×C₄	—	584	2	no	—
341	C₂²×C₄	—	73	2	no	—
342	C₂²×C₄	—	73	4	no	—
343	C₂²×C₄	—	73	4	no	—
344	C₂²×C₄	—	146	2	no	—
345	C₂²×C₄	—	146	2	no	—
346	C₂²×C₄	—	146	2	no	—
347	C₂²×C₄	—	146	2	no	—
348	C₂²×C₄	—	146	2	no	—
349	C₂²×C₄	—	146	2	no	—
350	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
352	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
353	M₁₆	—	146	16	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	73	4	no	—
357	C₂×C₈	—	146	2	no	—
358	C₂×C₈	—	146	2	no	—
359	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
360	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
361	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
362	C₂×C₈	#11924028	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	292	4	no	—
370	C₄⋊C₄	—	292	2	no	—
371	C₄⋊C₄	—	292	2	no	—
372	C₄⋊C₄	—	584	1	no	—
373	C₄⋊C₄	—	584	1	no	—
374	C₄⋊C₄	—	73	4	no	—
375	C₄⋊C₄	—	146	2	no	—
376	C₄⋊C₄	—	146	2	no	—
377	C₄⋊C₄	—	146	2	no	—
378	C₄⋊C₄	—	146	2	no	—
379	C₄⋊C₄	C₂×D₂₉₂	1	2	yes	—
380	C₄⋊C₄	C₂×D₂₉₂	1	2	yes	—
381	C₂²⋊C₄	—	292	4	no	—
382	C₂²⋊C₄	—	292	4	no	—
383	C₂²⋊C₄	—	584	2	no	—
384	C₂²⋊C₄	—	73	8	no	—
385	C₄²	—	4	2	no	—
386	C₄²	—	4	2	no	—
387	C₄²	—	292	4	no	—
388	C₄²	C₂×C₄×D₇₃	1	2	yes	—
389	C₄²	Q₈×D₇₃	1	2	yes	—
390	C₂³	—	73	4	no	—
391	C₂³	—	146	2	no	—
392	C₂³	—	146	2	no	—
393	C₂³	—	146	2	no	—
394	C₂³	—	146	2	no	—
395	C₂³	—	146	2	no	—
396	C₂³	—	146	2	no	—
397	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
398	D₄	—	146	8	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	292	2	no	—
414	C₂×C₄	—	292	2	no	—
415	C₂×C₄	—	292	2	no	—
416	C₂×C₄	—	292	2	no	—
417	C₂×C₄	—	292	2	no	—
418	C₂×C₄	—	292	2	no	—
419	C₂×C₄	—	584	8	no	—
420	C₂×C₄	—	73	4	no	—
421	C₂×C₄	—	146	2	no	—
422	C₂×C₄	—	146	2	no	—
423	C₂×C₄	—	146	4	no	—
424	C₂×C₄	—	146	4	no	—
425	C₂×C₄	—	146	4	no	—
426	C₂×C₄	—	146	4	no	—
427	C₂×C₄	C₄⋊C₄×D₇₃	1	2	yes	—
428	C₂×C₄	C₄⋊C₄×D₇₃	1	2	yes	—
429	C₂×C₄	#14556615	1	2	yes	—
430	C₂×C₄	#14556623	1	2	yes	—
431	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
433	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
434	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
435	C₂×C₄	#14556637	1	1	yes	characteristic
436	C₂×C₄	#14556638	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	146	4	no	—
439	C₈	C₄×D₂₉₂	1	4	yes	complemented
440	C₂²	—	292	2	no	—
441	C₂²	—	292	2	no	—
442	C₂²	—	292	2	no	—
443	C₂²	—	292	2	no	—
444	C₂²	—	146	4	no	—
445	C₂²	—	146	4	no	—
446	C₂²	—	146	4	no	—
447	C₂²	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
448	C₂²	D₄×D₂₉₂	1	1	yes	characteristic
449	C₂²	#17989242	1	1	yes	characteristic
450	C₂²	C₂×#14556615	1	1	yes	characteristic
451	C₂²	C₂×#14556623	1	1	yes	characteristic
452	C₂²	#17989394	1	1	yes	characteristic
453	C₂²	#17989394	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	584	2	no	—
460	C₄	—	584	2	no	—
461	C₄	—	146	4	no	—
462	C₄	#17988628	1	4	yes	complemented
463	C₄	C₂×C₄×D₂₉₂	1	1	yes	characteristic
464	C₄	#17989067	1	1	yes	characteristic
465	C₄	Q₈×D₂₉₂	1	1	yes	characteristic
466	C₄	#17989297	1	1	yes	characteristic
467	C₂	—	292	4	no	—
468	C₂	C₄⋊C₄×D₂₉₂	1	1	yes	characteristic
469	C₂	C₂×#17988628	1	1	yes	characteristic
470	C₂	#22618523	1	1	yes	characteristic
471	C₂	#22621532	1	1	yes	characteristic
472	C₂	#22621598	1	1	yes	characteristic
473	C₂	#22622528	1	1	yes	characteristic
474	C₂	#22622548	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₄×#107×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×D₄
prime radical	C₂²×D₂₉₂	D₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₄×#107	D₇₃
hypocenter	C₇₃	#22663
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
2. C₂×#17988628	C₂	semidirect
5. #22610694	C₂	semidirect
6. #22610689	C₂	semidirect
7. #22610131	C₂	semidirect
8. #22610125	C₂	semidirect
9. #22610088	C₂	semidirect
10. #22609965	C₂	semidirect
11. C₄×#107×C₇₃	C₂	semidirect
17. #17988666	C₄	semidirect
48. C₂×#11924011	C₂×C₄	semidirect
74. C₄⋊#10596831	C₂×C₄	semidirect
75. #14556503	C₂×C₄	semidirect
88. #107×C₇₃	D₄	semidirect
89. C₄×C₈×C₇₃	C₂×C₄	semidirect
200. C₈×C₇₃	C₄×D₄	semidirect
221. C₄×C₇₃	#428	semidirect
248. C₄×#107	D₇₃	semidirect
249. C₇₃	#22663	semidirect
319. #107	D₂₉₂	semidirect
325. C₄×C₈	C₄×D₇₃	semidirect
439. C₈	C₄×D₂₉₂	semidirect
462. C₄	#17988628	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988666	2
C₂×#17988628	2
#22612878	2
C₄⋊C₄×D₂₉₂	2
#22610694	2
#22610689	2
#22610131	2
#22610125	2
#22610088	2
#22609965	2
C₄×#107×C₇₃	2
#22663	73