Subgroups — #34034781

Order 18688.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627137	C₂	1	2	yes	maximal, complemented
2	#22627136	C₂	1	2	yes	maximal, complemented
3	#22627135	C₂	1	1	yes	maximal, characteristic, complemented
4	#22627132	C₂	1	1	yes	maximal, characteristic, complemented
5	#22627130	C₂	1	1	yes	maximal, characteristic, complemented
6	#22627129	C₂	1	1	yes	maximal, characteristic, complemented
7	#22627119	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#17989690	C₂	1	1	yes	maximal, characteristic, complemented
9	#22627101	C₂	1	2	yes	maximal
10	#22627092	C₂	1	2	yes	maximal, complemented
11	C₄×#14556678	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556687	C₂²	1	2	yes	—
13	C₂²×#11924040	C₂²	1	2	yes	—
14	#17989690	C₂²	1	1	yes	characteristic
15	#17989690	C₂²	1	1	yes	characteristic
16	#17989690	C₂²	1	2	yes	—
17	#17989690	C₂²	1	1	yes	characteristic
18	#17989690	C₂²	1	1	yes	characteristic
19	C₄⋊#11924040	C₂²	1	2	yes	—
20	#17989684	C₂²	1	2	yes	—
21	#17989684	C₂²	1	2	yes	—
22	C₂²⋊#11924040	C₂²	1	2	yes	—
23	C₂²⋊#11924040	C₂²	1	2	yes	—
24	#17989681	C₂²	1	2	yes	—
25	#17989681	C₂²	1	2	yes	—
26	C₄×#11924040	C₂²	1	2	yes	—
27	C₄×#11924040	C₂²	1	2	yes	—
28	C₂×#14556678	C₄	1	1	yes	characteristic
29	C₂×#14556678	C₂²	1	1	yes	characteristic
30	#17989552	C₄	1	1	yes	characteristic
31	#17989552	C₂²	1	1	yes	characteristic
32	#17989551	C₄	1	1	yes	characteristic
33	#17989551	C₄	1	1	yes	characteristic
34	#17989551	C₂²	1	1	yes	characteristic
35	#17989551	C₂²	1	1	yes	characteristic
36	C₄×#11924038	C₄	1	1	yes	characteristic
37	C₄×#11924037	C₄	1	1	yes	characteristic
38	C₄×#11924037	C₄	1	1	yes	characteristic
39	C₄×#11924036	C₂²	1	1	yes	characteristic
40	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
41	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
42	C₄×#11924027	C₄	1	1	yes	characteristic
43	#14556687	—	2	4	no	—
44	C₂×#11924040	—	2	4	no	—
45	C₂×#11924040	C₂³	1	2	yes	—
46	C₂×#11924040	C₂³	1	2	yes	—
47	C₂×#11924040	C₂³	1	2	yes	—
48	C₂×#11924040	C₂³	1	2	yes	—
49	#14556678	—	2	4	no	—
50	#14556678	—	2	2	no	—
51	#14556678	—	2	2	no	—
52	C₂×#11924038	C₂×C₄	1	1	yes	characteristic
53	C₂×#11924038	C₂×C₄	1	1	yes	characteristic
54	C₂×#11924037	C₂×C₄	1	1	yes	characteristic
55	C₂×#11924037	C₂×C₄	1	1	yes	characteristic
56	C₂×#11924037	C₂×C₄	1	1	yes	characteristic
57	C₂×#11924037	C₂×C₄	1	1	yes	characteristic
58	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
59	C₂×#11924036	C₂³	1	1	yes	characteristic
60	C₂²×#10596833	C₂×C₄	1	1	yes	characteristic
61	C₂²×#10596833	C₂×C₄	1	1	yes	characteristic
62	C₂²×#10596833	C₂³	1	1	yes	characteristic
63	C₂²×#10596833	C₂³	1	1	yes	characteristic
64	#14556646	C₂×C₄	1	1	yes	characteristic
65	#14556646	C₂×C₄	1	1	yes	characteristic
66	#14556646	C₂×C₄	1	1	yes	characteristic
67	#14556646	C₂×C₄	1	1	yes	characteristic
68	#14556646	C₂×C₄	1	1	yes	characteristic
69	#14556646	C₂×C₄	1	1	yes	characteristic
70	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
71	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
72	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
73	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
74	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
75	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
76	C₄×#10596833	C₂³	1	1	yes	characteristic
77	C₄×#10596833	C₂³	1	1	yes	characteristic
78	C₄×#10596833	C₂³	1	1	yes	characteristic
79	C₄×#10596833	C₂³	1	1	yes	characteristic
80	C₂×#11924027	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₄₆	C₈	1	1	yes	characteristic
82	#14556556	C₈	1	1	yes	characteristic
83	D₄×Dic₇₃	C₈	1	1	yes	characteristic
84	C₄×C₂²⋊D₇₃	C₈	1	1	yes	characteristic
85	C₄×C₂²⋊D₇₃	C₈	1	1	yes	characteristic
86	#14556551	C₈	1	1	yes	characteristic
87	#14556551	C₈	1	1	yes	characteristic
88	#14556549	C₂×C₄	1	1	yes	characteristic
89	#14556547	C₂×C₄	1	1	yes	characteristic
90	#14556547	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
93	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₇₃	C₈	1	1	yes	characteristic
95	#11924040	—	2	2	no	—
96	#11924040	—	2	2	no	—
97	#11924040	—	2	2	no	—
98	#11924040	—	2	2	no	—
99	#11924038	—	2	2	no	—
100	#11924038	—	2	2	no	—
101	#11924037	—	2	2	no	—
102	#11924037	—	2	2	no	—
103	#11924037	—	2	2	no	—
104	#11924037	M₁₆	1	4	yes	—
105	#11924036	—	2	2	no	—
106	#11924036	—	2	1	no	—
107	#11924036	—	2	1	no	—
108	C₂×#10596833	—	2	2	no	—
109	C₂×#10596833	—	2	2	no	—
110	C₂×#10596833	—	2	1	no	—
111	C₂×#10596833	—	2	1	no	—
112	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
113	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
114	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
115	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
116	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
117	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
118	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
119	C₂×#10596833	#41	1	2	yes	—
120	C₂×#10596833	#41	1	2	yes	—
121	C₂×#10596833	C₂⁴	1	1	yes	characteristic
122	#11924027	—	2	2	no	—
123	#11924027	—	2	2	no	—
124	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
125	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
126	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
127	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
128	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
129	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
132	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
133	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
135	#11924007	C₂×C₈	1	1	yes	characteristic
136	#11924007	C₂×C₈	1	1	yes	characteristic
137	#11924007	C₂×C₈	1	1	yes	characteristic
138	#11924007	C₂×C₈	1	1	yes	characteristic
139	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
140	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
141	#11924005	C₂×C₈	1	1	yes	characteristic
142	#11924005	C₂×C₈	1	1	yes	characteristic
143	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
144	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
145	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
146	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
147	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
148	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₇₃	C₂×C₈	1	1	yes	characteristic
153	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
154	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
155	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
156	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
157	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
158	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
159	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
160	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
162	D₄×C₇₃	—	2	2	no	—
163	C₂×C₄×C₇₃	—	4	1	no	—
164	C₂×C₄×C₇₃	—	4	1	no	—
165	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
170	C₂²⋊D₇₃	—	2	2	no	—
171	C₂²⋊D₇₃	—	2	2	no	—
172	C₂×Dic₇₃	—	2	1	no	—
173	C₂×Dic₇₃	—	2	1	no	—
174	C₂×Dic₇₃	—	2	2	no	—
175	C₂×Dic₇₃	—	2	2	no	—
176	C₂×Dic₇₃	#117	1	2	yes	—
177	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
182	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×Dic₇₃	C₂×M₁₆	1	2	yes	—
184	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
185	C₄×D₇₃	—	2	1	no	—
186	C₄×D₇₃	—	2	1	no	—
187	C₄×D₇₃	—	2	2	no	—
188	C₄×D₇₃	—	4	1	no	—
189	Dic₁₄₆	—	2	2	no	—
190	#10596833	—	2	1	no	—
191	#10596833	—	2	1	no	—
192	#10596833	—	2	1	no	—
193	#10596833	—	2	1	no	—
194	#10596833	#117	1	2	yes	—
195	#10596833	C₂×M₁₆	1	2	yes	—
196	#10596833	C₂×M₁₆	1	2	yes	—
197	#10596833	C₂×#41	1	1	yes	characteristic
198	#10596833	C₂×#41	1	1	yes	characteristic
199	C₂²×C₇₃	—	2	1	no	—
200	C₂²×C₇₃	—	2	1	no	—
201	C₂²×C₇₃	—	2	1	no	—
202	C₂²×C₇₃	—	2	1	no	—
203	C₂²×C₇₃	—	2	1	no	—
204	C₂²×C₇₃	#431	1	2	yes	—
205	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
206	C₂×D₇₃	—	2	1	no	—
207	C₂×D₇₃	—	2	1	no	—
208	C₂×D₇₃	—	2	1	no	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	2	1	no	—
211	C₄×C₇₃	—	2	1	no	—
212	C₄×C₇₃	—	2	1	no	—
213	C₄×C₇₃	—	2	1	no	—
214	Dic₇₃	—	2	1	no	—
215	Dic₇₃	—	2	1	no	—
216	Dic₇₃	—	2	1	no	—
217	Dic₇₃	—	2	1	no	—
218	Dic₇₃	#431	1	2	yes	—
219	Dic₇₃	#504	1	2	yes	—
220	Dic₇₃	C₂×#117	1	1	yes	characteristic
221	Dic₇₃	C₂²×M₁₆	1	1	yes	characteristic
222	#33423	—	73	1	no	maximal, Sylow
223	C₂×C₇₃	—	2	2	no	—
224	C₂×C₇₃	—	4	1	no	—
225	C₂×C₇₃	C₂×#431	1	1	yes	characteristic
226	C₂×C₇₃	C₂×#504	1	1	yes	characteristic
227	C₂×C₇₃	#3407	1	1	yes	characteristic
228	D₇₃	—	4	1	no	—
229	C₄×#131	—	73	1	no	—
230	#2164	—	73	2	no	—
231	#2164	—	73	2	no	—
232	#2163	—	73	1	no	—
233	#2163	—	73	1	no	—
234	#2162	—	73	1	no	—
235	#2162	—	73	1	no	—
236	#2150	—	73	1	no	—
237	C₂×C₄⋊C₁₆	—	73	1	no	—
238	#2113	—	73	2	no	—
239	#2108	—	73	2	no	—
240	C₇₃	#33423	1	1	yes	characteristic, complemented, Sylow
241	C₂×#131	—	73	1	no	—
242	C₂×#131	—	73	1	no	—
243	C₄×#41	—	73	1	no	—
244	C₂×M₃₂	—	73	2	no	—
245	C₂²×C₁₆	—	73	2	no	—
246	#405	—	73	1	no	—
247	#405	—	73	1	no	—
248	#405	—	73	1	no	—
249	#405	—	73	1	no	—
250	#405	—	73	1	no	—
251	#405	—	73	1	no	—
252	C₄×M₁₆	—	73	1	no	—
253	C₄×M₁₆	—	73	1	no	—
254	C₄×M₁₆	—	73	1	no	—
255	C₂×C₄×C₈	—	73	1	no	—
256	C₂×C₄×C₈	—	73	1	no	—
257	C₂×C₄×C₈	—	73	1	no	—
258	C₄⋊C₁₆	—	73	2	no	—
259	C₄⋊C₁₆	—	73	1	no	—
260	C₄⋊C₁₆	—	73	1	no	—
261	C₄⋊C₁₆	—	73	2	no	—
262	C₄⋊C₁₆	—	73	1	no	—
263	C₄⋊C₁₆	—	73	1	no	—
264	C₂²⋊C₁₆	—	73	2	no	—
265	C₂²⋊C₁₆	—	73	2	no	—
266	C₂²⋊C₁₆	—	73	2	no	—
267	C₂²⋊C₁₆	—	73	2	no	—
268	#346	—	73	2	no	—
269	#346	—	73	2	no	—
270	C₄×C₁₆	—	73	2	no	—
271	C₄×C₁₆	—	73	2	no	—
272	C₂×#41	—	73	1	no	—
273	#131	—	146	2	no	—
274	#131	—	146	2	no	—
275	#131	—	146	4	no	—
276	C₂×M₁₆	—	73	1	no	—
277	C₂×M₁₆	—	73	1	no	—
278	C₂×M₁₆	—	73	1	no	—
279	C₂×M₁₆	—	73	1	no	—
280	C₂×M₁₆	—	73	1	no	—
281	C₂×M₁₆	—	73	1	no	—
282	C₂²×C₈	—	73	1	no	—
283	C₂²×C₈	—	73	1	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	C₄×Q₈	—	73	1	no	—
289	C₄×Q₈	—	73	1	no	—
290	C₄×D₄	—	73	1	no	—
291	C₄×D₄	—	73	1	no	—
292	C₄×D₄	—	73	1	no	—
293	C₄×D₄	—	73	1	no	—
294	C₄×D₄	—	73	1	no	—
295	C₄×D₄	#10596842	1	1	yes	characteristic
296	#117	—	73	1	no	—
297	#117	—	73	1	no	—
298	#117	—	73	1	no	—
299	C₂×C₄²	—	73	1	no	—
300	C₂×C₄²	—	73	1	no	—
301	C₂×C₄²	—	73	1	no	—
302	M₃₂	—	146	4	no	—
303	C₂×C₁₆	—	73	2	no	—
304	C₂×C₁₆	—	73	2	no	—
305	C₂×C₁₆	—	73	2	no	—
306	C₂×C₁₆	—	73	2	no	—
307	C₂×C₁₆	—	146	4	no	—
308	#97	—	73	1	no	—
309	#97	—	73	1	no	—
310	#97	—	73	1	no	—
311	#97	—	73	1	no	—
312	#97	—	73	1	no	—
313	#97	—	73	1	no	—
314	C₄×C₈	—	73	1	no	—
315	C₄×C₈	—	73	1	no	—
316	C₄×C₈	—	73	1	no	—
317	C₄×C₈	—	73	1	no	—
318	C₄×C₈	—	73	1	no	—
319	C₄×C₈	—	73	1	no	—
320	C₄×C₈	—	73	1	no	—
321	C₄×C₈	—	73	1	no	—
322	C₄×C₈	—	73	1	no	—
323	C₄×C₈	—	73	1	no	—
324	#41	—	146	2	no	—
325	#41	—	146	2	no	—
326	C₂×Q₈	—	73	1	no	—
327	C₂×D₄	—	73	1	no	—
328	C₂×D₄	—	73	1	no	—
329	C₂×D₄	C₂×#10596842	1	1	yes	characteristic
330	C₂²×C₄	—	73	1	no	—
331	C₂²×C₄	—	73	1	no	—
332	C₂²×C₄	—	73	1	no	—
333	C₂²×C₄	—	73	1	no	—
334	C₂²×C₄	—	73	1	no	—
335	C₂²×C₄	—	73	1	no	—
336	C₂²×C₄	—	73	1	no	—
337	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
338	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
339	M₁₆	—	73	4	no	—
340	M₁₆	—	146	2	no	—
341	M₁₆	—	146	2	no	—
342	M₁₆	—	146	2	no	—
343	M₁₆	—	146	2	no	—
344	M₁₆	—	146	2	no	—
345	C₂×C₈	—	73	1	no	—
346	C₂×C₈	—	73	1	no	—
347	C₂×C₈	—	73	1	no	—
348	C₂×C₈	—	73	2	no	—
349	C₂×C₈	—	73	2	no	—
350	C₂×C₈	—	73	1	no	—
351	C₂×C₈	—	73	1	no	—
352	C₂×C₈	—	73	1	no	—
353	C₂×C₈	—	73	1	no	—
354	C₂×C₈	—	73	1	no	—
355	C₂×C₈	—	146	1	no	—
356	C₂×C₈	—	146	1	no	—
357	C₂×C₈	—	146	2	no	—
358	C₂×C₈	—	146	1	no	—
359	C₂×C₈	—	146	1	no	—
360	C₂×C₈	—	146	2	no	—
361	C₂×C₈	—	146	2	no	—
362	C₄⋊C₄	—	73	1	no	—
363	C₄⋊C₄	—	73	1	no	—
364	C₄⋊C₄	—	73	1	no	—
365	C₄⋊C₄	—	73	1	no	—
366	C₄⋊C₄	—	73	1	no	—
367	C₄⋊C₄	C₂×#10596842	1	1	yes	characteristic
368	C₂²⋊C₄	—	73	1	no	—
369	C₂²⋊C₄	—	73	1	no	—
370	C₂²⋊C₄	—	73	1	no	—
371	C₂²⋊C₄	—	73	1	no	—
372	C₂²⋊C₄	C₂×#10596842	1	1	yes	characteristic
373	C₂²⋊C₄	C₂×#10596842	1	1	yes	characteristic
374	C₄²	—	73	1	no	—
375	C₄²	—	73	1	no	—
376	C₄²	—	73	1	no	—
377	C₄²	—	73	1	no	—
378	C₄²	—	73	1	no	—
379	C₄²	—	73	1	no	—
380	C₄²	—	73	1	no	—
381	C₄²	—	73	1	no	—
382	C₄²	—	73	1	no	—
383	C₄²	C₂×#10596842	1	1	yes	characteristic
384	C₁₆	—	146	2	no	—
385	C₁₆	—	146	2	no	—
386	C₁₆	—	146	2	no	—
387	C₁₆	—	146	2	no	—
388	C₂³	—	73	1	no	—
389	C₂³	C₂²×#10596842	1	1	yes	characteristic
390	C₂³	C₂²×#10596842	1	1	yes	characteristic
391	Q₈	—	146	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	146	2	no	—
394	D₄	—	146	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	292	1	no	—
398	C₂×C₄	—	73	2	no	—
399	C₂×C₄	—	73	2	no	—
400	C₂×C₄	—	73	1	no	—
401	C₂×C₄	—	73	1	no	—
402	C₂×C₄	—	73	1	no	—
403	C₂×C₄	—	73	1	no	—
404	C₂×C₄	—	73	1	no	—
405	C₂×C₄	—	73	1	no	—
406	C₂×C₄	—	73	1	no	—
407	C₂×C₄	—	146	1	no	—
408	C₂×C₄	—	146	1	no	—
409	C₂×C₄	—	146	2	no	—
410	C₂×C₄	—	146	1	no	—
411	C₂×C₄	—	146	1	no	—
412	C₂×C₄	—	146	2	no	—
413	C₂×C₄	—	146	2	no	—
414	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
415	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
416	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
417	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
418	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
419	C₈	—	73	1	no	—
420	C₈	—	73	1	no	—
421	C₈	—	73	2	no	—
422	C₈	—	73	2	no	—
423	C₈	—	73	2	no	—
424	C₈	—	146	1	no	—
425	C₈	—	146	1	no	—
426	C₈	—	146	1	no	—
427	C₈	—	146	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	146	1	no	—
434	C₂²	—	146	1	no	—
435	C₂²	—	146	1	no	—
436	C₂²	#17989700	1	2	yes	—
437	C₂²	C₂³×#10596842	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	73	1	no	—
444	C₄	—	73	1	no	—
445	C₄	—	73	2	no	—
446	C₄	—	73	2	no	—
447	C₄	—	146	1	no	—
448	C₄	—	146	1	no	—
449	C₄	—	146	1	no	—
450	C₄	—	146	1	no	—
451	C₂	—	2	2	no	—
452	C₂	—	4	1	no	—
453	C₂	—	292	1	no	—
454	C₂	C₂×#17989700	1	1	yes	characteristic
455	C₂	#22627182	1	1	yes	characteristic
456	C₂	#22627184	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#10596842
commutator, socle	C₂²×C₇₃	C₂³×C₈
Fitting	C₄×D₄×C₇₃	C₈
prime radical	C₂×#11924027	C₂×C₄
cosocle	C₂×#10596833	C₂⁴
hypercenter	C₄×D₄	#10596842
hypocenter	C₇₃	#33423
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #22627137	C₂	semidirect
2. #22627136	C₂	semidirect
3. #22627135	C₂	semidirect
4. #22627132	C₂	semidirect
5. #22627130	C₂	semidirect
6. #22627129	C₂	semidirect
7. #22627119	C₂	semidirect
8. C₂×#17989690	C₂	semidirect
10. #22627092	C₂	semidirect
240. C₇₃	#33423	semidirect

Maximal subgroups

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

subgroup	index
#22627137	2
#22627136	2
#22627135	2
#22627132	2
#22627130	2
#22627129	2
#22627119	2
C₂×#17989690	2
#22627101	2
#22627092	2
C₄×#14556678	2
#33423	73