Subgroups — #34034877

Order 18688.

558 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627158	C₂	1	2	yes	maximal, complemented
2	#22627145	C₂	1	2	yes	maximal, complemented
3	#22627144	C₂	1	2	yes	maximal, complemented
4	#22627142	C₂	1	2	yes	maximal, complemented
5	#22627131	C₂	1	1	yes	maximal, characteristic, complemented
6	#22627130	C₂	1	1	yes	maximal, characteristic, complemented
7	#22627129	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#14556688	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#14556687	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14556686	C₂	1	1	yes	maximal, characteristic, complemented
11	#22626735	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556688	C₂²	1	2	yes	—
13	C₂×#14556687	C₂²	1	2	yes	—
14	C₂×#14556686	C₂²	1	2	yes	—
15	#17989690	C₂²	1	2	yes	—
16	#17989690	C₂²	1	2	yes	—
17	C₄⋊#11924040	C₂²	1	2	yes	—
18	#17989684	C₂²	1	2	yes	—
19	#17989684	C₂²	1	2	yes	—
20	C₂²⋊#11924040	C₂²	1	2	yes	—
21	#17989681	C₂²	1	2	yes	—
22	#17989681	C₂²	1	2	yes	—
23	C₄×#11924040	C₂²	1	1	yes	characteristic
24	C₄×#11924040	C₂²	1	1	yes	characteristic
25	C₄×#11924040	C₂²	1	2	yes	—
26	C₄×#11924040	C₂²	1	1	yes	characteristic
27	C₄×#11924040	C₂²	1	1	yes	characteristic
28	#17989636	C₄	1	1	yes	characteristic
29	#17989636	C₂²	1	1	yes	characteristic
30	#17989615	C₄	1	1	yes	characteristic
31	#17989615	C₂²	1	1	yes	characteristic
32	#17989614	C₄	1	1	yes	characteristic
33	#17989614	C₄	1	1	yes	characteristic
34	#17989614	C₂²	1	1	yes	characteristic
35	#17989614	C₂²	1	1	yes	characteristic
36	#17989605	C₄	1	1	yes	characteristic
37	#17989605	C₄	1	1	yes	characteristic
38	#17989603	C₄	1	1	yes	characteristic
39	C₄×#11924036	C₂²	1	1	yes	characteristic
40	C₄×#11924036	C₂²	1	1	yes	characteristic
41	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
42	#17989055	C₄	1	1	yes	characteristic
43	#14556688	—	2	4	no	—
44	#14556687	—	2	4	no	—
45	#14556686	—	2	4	no	—
46	C₂×#11924040	C₂³	1	2	yes	—
47	C₂×#11924040	C₂³	1	2	yes	—
48	C₂×#11924040	C₂³	1	2	yes	—
49	C₂×#11924040	C₂³	1	2	yes	—
50	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
51	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
52	C₂×#11924036	C₂³	1	1	yes	characteristic
53	C₂×#11924036	C₂³	1	1	yes	characteristic
54	C₂²×#10596833	C₂×C₄	1	1	yes	characteristic
55	C₂²×#10596833	C₂³	1	1	yes	characteristic
56	#14556658	C₂×C₄	1	1	yes	characteristic
57	#14556658	C₂×C₄	1	1	yes	characteristic
58	#14556658	C₂×C₄	1	1	yes	characteristic
59	#14556658	C₂×C₄	1	1	yes	characteristic
60	C₄⋊#10596833	C₂×C₄	1	1	yes	characteristic
61	C₄⋊#10596833	C₂×C₄	1	1	yes	characteristic
62	#14556648	C₂×C₄	1	1	yes	characteristic
63	#14556648	C₂×C₄	1	1	yes	characteristic
64	#14556648	C₂×C₄	1	1	yes	characteristic
65	#14556648	C₂×C₄	1	1	yes	characteristic
66	C₂²⋊#10596833	C₂×C₄	1	1	yes	characteristic
67	C₂²⋊#10596833	C₂×C₄	1	1	yes	characteristic
68	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
69	C₄×#10596833	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	C₂³	1	1	yes	characteristic
75	C₄×#10596833	C₂³	1	1	yes	characteristic
76	C₄×#10596833	C₂³	1	1	yes	characteristic
77	C₄×#10596833	C₂³	1	1	yes	characteristic
78	C₂×#11924028	C₈	1	1	yes	characteristic
79	#14556556	C₈	1	1	yes	characteristic
80	#14556556	C₂×C₄	1	1	yes	characteristic
81	#14556553	C₈	1	1	yes	characteristic
82	#14556553	C₂×C₄	1	1	yes	characteristic
83	#14556551	C₈	1	1	yes	characteristic
84	#14556551	C₈	1	1	yes	characteristic
85	#14556551	C₂×C₄	1	1	yes	characteristic
86	#14556551	C₂×C₄	1	1	yes	characteristic
87	#14556548	C₈	1	1	yes	characteristic
88	#14556548	C₈	1	1	yes	characteristic
89	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
90	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
91	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
92	#117×C₇₃	C₈	1	1	yes	characteristic
93	#11924040	—	2	2	no	—
94	#11924040	—	2	2	no	—
95	#11924040	—	2	2	no	—
96	#11924040	#41	1	4	yes	complemented
97	#11924036	—	2	2	no	—
98	#11924036	—	2	2	no	—
99	#11924036	—	2	2	no	—
100	#11924036	—	2	2	no	—
101	C₂×#10596833	—	2	2	no	—
102	C₂×#10596833	—	2	2	no	—
103	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
104	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
105	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
106	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
107	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
108	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
109	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
110	C₂×#10596833	C₂⁴	1	1	yes	characteristic
111	#11924028	—	2	4	no	—
112	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
113	C₂×D₂₉₂	C₂×C₈	1	1	yes	characteristic
114	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
115	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
116	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
117	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
120	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
124	#11924007	C₂×C₈	1	1	yes	characteristic
125	#11924007	C₂×C₈	1	1	yes	characteristic
126	#11924007	C₂×C₈	1	1	yes	characteristic
127	#11924007	C₂×C₈	1	1	yes	characteristic
128	#11924005	C₂×C₈	1	1	yes	characteristic
129	#11924005	C₂×C₈	1	1	yes	characteristic
130	#11924005	C₂×C₈	1	1	yes	characteristic
131	#11924005	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
141	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
142	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
143	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
144	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
145	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
146	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
147	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
148	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₇₃	—	2	2	no	—
151	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
153	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
154	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
157	C₂²⋊D₇₃	—	2	2	no	—
158	C₂²⋊D₇₃	—	2	2	no	—
159	C₂×Dic₇₃	—	2	1	no	—
160	C₂×Dic₇₃	—	2	1	no	—
161	C₂×Dic₇₃	—	2	2	no	—
162	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
163	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
164	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
165	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
168	D₂₉₂	—	2	2	no	—
169	C₄×D₇₃	—	2	2	no	—
170	C₄×D₇₃	—	2	1	no	—
171	C₄×D₇₃	—	2	1	no	—
172	C₄×D₇₃	—	2	1	no	—
173	C₄×D₇₃	—	2	1	no	—
174	C₄×D₇₃	—	2	2	no	—
175	C₄×D₇₃	—	2	2	no	—
176	C₄×D₇₃	M₃₂	1	4	yes	complemented
177	Dic₁₄₆	—	2	2	no	—
178	#10596833	—	2	1	no	—
179	#10596833	—	2	1	no	—
180	#10596833	—	2	1	no	—
181	#10596833	—	2	1	no	—
182	#10596833	—	2	1	no	—
183	#10596833	—	2	1	no	—
184	#10596833	#131	1	2	yes	—
185	#10596833	C₂×#41	1	2	yes	—
186	C₂²×C₇₃	—	2	1	no	—
187	C₂²×C₇₃	—	2	1	no	—
188	C₂²×C₇₃	—	2	1	no	—
189	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
190	C₂×D₇₃	—	2	1	no	—
191	C₂×D₇₃	—	2	1	no	—
192	C₂×D₇₃	—	2	1	no	—
193	C₂×D₇₃	—	2	1	no	—
194	C₂×D₇₃	—	2	1	no	—
195	C₂×D₇₃	C₂×M₃₂	1	2	yes	—
196	C₄×C₇₃	—	2	1	no	—
197	C₄×C₇₃	—	2	1	no	—
198	C₄×C₇₃	—	2	1	no	—
199	C₄×C₇₃	—	2	1	no	—
200	C₄×C₇₃	—	2	1	no	—
201	C₄×C₇₃	C₂×M₃₂	1	2	yes	—
202	Dic₇₃	—	2	1	no	—
203	Dic₇₃	—	2	1	no	—
204	Dic₇₃	—	2	1	no	—
205	Dic₇₃	C₂×M₃₂	1	2	yes	—
206	Dic₇₃	#504	1	2	yes	—
207	Dic₇₃	C₄×#41	1	1	yes	characteristic
208	Dic₇₃	C₂×#131	1	1	yes	characteristic
209	#33479	—	73	1	no	maximal, Sylow
210	C₂×C₇₃	—	4	1	no	—
211	C₂×C₇₃	C₈×#41	1	1	yes	characteristic
212	C₂×C₇₃	C₂²×M₃₂	1	1	yes	characteristic
213	C₂×C₇₃	C₂×#504	1	1	yes	characteristic
214	D₇₃	—	2	2	no	—
215	D₇₃	—	4	1	no	—
216	C₈×#41	—	73	1	no	—
217	#2183	—	73	2	no	—
218	#2169	—	73	2	no	—
219	#2168	—	73	2	no	—
220	#2168	—	73	2	no	—
221	#2162	—	73	1	no	—
222	#2162	—	73	1	no	—
223	#2162	—	73	1	no	—
224	C₄×M₃₂	—	73	1	no	—
225	C₄×M₃₂	—	73	1	no	—
226	C₂×C₄×C₁₆	—	73	1	no	—
227	C₇₃	#33479	1	1	yes	characteristic, complemented, Sylow
228	C₄×#41	—	73	1	no	—
229	C₂×M₃₂	—	73	2	no	—
230	C₂×M₃₂	—	73	2	no	—
231	C₂²×C₁₆	—	73	2	no	—
232	C₈×Q₈	—	73	1	no	—
233	C₈×Q₈	—	73	1	no	—
234	C₈×D₄	—	73	1	no	—
235	C₈×D₄	—	73	1	no	—
236	C₈×D₄	—	73	1	no	—
237	C₈×D₄	—	73	1	no	—
238	C₈×D₄	—	73	1	no	—
239	C₈×D₄	—	73	1	no	—
240	#431	—	73	1	no	—
241	#431	—	73	1	no	—
242	#431	—	73	1	no	—
243	C₂×C₄×C₈	—	73	1	no	—
244	C₂×C₄×C₈	—	73	1	no	—
245	C₂×C₄×C₈	—	73	1	no	—
246	C₄⋊C₁₆	—	73	2	no	—
247	C₄⋊C₁₆	—	73	2	no	—
248	C₄⋊C₁₆	—	73	2	no	—
249	C₂²⋊C₁₆	—	73	2	no	—
250	C₂²⋊C₁₆	—	73	2	no	—
251	C₂²⋊C₁₆	—	73	2	no	—
252	#346	—	73	2	no	—
253	#346	—	73	2	no	—
254	C₄×C₁₆	—	73	1	no	—
255	C₄×C₁₆	—	73	1	no	—
256	C₄×C₁₆	—	73	2	no	—
257	C₄×C₁₆	—	73	1	no	—
258	C₄×C₁₆	—	73	1	no	—
259	C₂×#41	—	73	1	no	—
260	C₂²×C₈	—	73	1	no	—
261	C₂²×C₈	—	73	1	no	—
262	C₂²×C₈	—	73	1	no	—
263	C₂²×C₈	—	73	1	no	—
264	C₂²×C₈	—	73	1	no	—
265	C₂²×C₈	—	73	1	no	—
266	C₄×Q₈	—	73	1	no	—
267	C₄×Q₈	—	73	1	no	—
268	C₄×D₄	—	73	1	no	—
269	C₄×D₄	—	73	1	no	—
270	C₄×D₄	—	73	1	no	—
271	C₄×D₄	—	73	1	no	—
272	C₄×D₄	—	73	1	no	—
273	C₄×D₄	—	73	1	no	—
274	#117	—	73	1	no	—
275	#117	—	73	1	no	—
276	#117	#10596842	1	1	yes	characteristic
277	C₂×C₄²	—	73	1	no	—
278	C₂×C₄²	—	73	1	no	—
279	C₂×C₄²	—	73	1	no	—
280	M₃₂	—	146	4	no	—
281	M₃₂	—	146	4	no	—
282	C₂×C₁₆	—	73	2	no	—
283	C₂×C₁₆	—	73	2	no	—
284	C₂×C₁₆	—	73	2	no	—
285	C₂×C₁₆	—	73	2	no	—
286	C₂×C₁₆	—	146	4	no	—
287	C₄⋊C₈	—	73	1	no	—
288	C₄⋊C₈	—	73	1	no	—
289	C₄⋊C₈	—	73	1	no	—
290	C₄⋊C₈	—	73	1	no	—
291	C₄⋊C₈	—	73	1	no	—
292	C₄⋊C₈	—	73	1	no	—
293	C₂²⋊C₈	—	73	1	no	—
294	C₂²⋊C₈	—	73	1	no	—
295	C₂²⋊C₈	—	73	1	no	—
296	C₂²⋊C₈	—	73	1	no	—
297	C₂²⋊C₈	—	73	1	no	—
298	C₂²⋊C₈	—	73	1	no	—
299	C₄×C₈	—	73	1	no	—
300	C₄×C₈	—	73	1	no	—
301	C₄×C₈	—	73	1	no	—
302	C₄×C₈	—	73	1	no	—
303	C₄×C₈	—	73	1	no	—
304	C₄×C₈	—	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	#41	—	146	4	no	—
310	C₂×Q₈	—	73	1	no	—
311	C₂×D₄	—	73	1	no	—
312	C₂×D₄	—	73	1	no	—
313	C₂×D₄	—	73	1	no	—
314	C₂²×C₄	—	73	1	no	—
315	C₂²×C₄	—	73	1	no	—
316	C₂²×C₄	—	73	1	no	—
317	C₂²×C₄	—	73	1	no	—
318	C₂²×C₄	—	73	1	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	—	73	1	no	—
321	C₂²×C₄	—	73	1	no	—
322	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
323	C₂×C₈	—	73	1	no	—
324	C₂×C₈	—	73	1	no	—
325	C₂×C₈	—	73	1	no	—
326	C₂×C₈	—	73	1	no	—
327	C₂×C₈	—	73	1	no	—
328	C₂×C₈	—	73	1	no	—
329	C₂×C₈	—	73	1	no	—
330	C₂×C₈	—	73	1	no	—
331	C₂×C₈	—	146	2	no	—
332	C₂×C₈	—	146	2	no	—
333	C₂×C₈	—	146	2	no	—
334	C₂×C₈	—	146	2	no	—
335	C₂×C₈	—	146	2	no	—
336	C₂×C₈	—	146	2	no	—
337	C₄⋊C₄	—	73	1	no	—
338	C₄⋊C₄	—	73	1	no	—
339	C₄⋊C₄	—	73	1	no	—
340	C₄⋊C₄	—	73	1	no	—
341	C₄⋊C₄	C₂×#10596842	1	1	yes	characteristic
342	C₄⋊C₄	C₂×#10596842	1	1	yes	characteristic
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	C₂×#10596842	1	1	yes	characteristic
348	C₂²⋊C₄	C₂×#10596842	1	1	yes	characteristic
349	C₄²	—	73	1	no	—
350	C₄²	—	73	1	no	—
351	C₄²	—	73	1	no	—
352	C₄²	—	73	1	no	—
353	C₄²	—	73	1	no	—
354	C₄²	—	73	1	no	—
355	C₄²	—	73	1	no	—
356	C₄²	—	73	1	no	—
357	C₄²	C₂×#10596842	1	1	yes	characteristic
358	C₄²	C₂×#10596842	1	1	yes	characteristic
359	C₁₆	—	73	4	no	—
360	C₁₆	—	146	2	no	—
361	C₁₆	—	146	2	no	—
362	C₁₆	—	146	2	no	—
363	C₂³	—	73	1	no	—
364	C₂³	—	73	1	no	—
365	C₂³	C₂²×#10596842	1	1	yes	characteristic
366	Q₈	—	146	2	no	—
367	D₄	—	146	2	no	—
368	D₄	—	146	2	no	—
369	D₄	—	146	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	73	1	no	—
372	C₂×C₄	—	73	1	no	—
373	C₂×C₄	—	73	1	no	—
374	C₂×C₄	—	73	4	no	—
375	C₂×C₄	—	73	1	no	—
376	C₂×C₄	—	73	1	no	—
377	C₂×C₄	—	73	1	no	—
378	C₂×C₄	—	146	1	no	—
379	C₂×C₄	—	146	1	no	—
380	C₂×C₄	—	146	1	no	—
381	C₂×C₄	—	146	1	no	—
382	C₂×C₄	—	146	2	no	—
383	C₂×C₄	—	146	2	no	—
384	C₂×C₄	—	146	1	no	—
385	C₂×C₄	—	146	1	no	—
386	C₂×C₄	—	146	2	no	—
387	C₂×C₄	—	146	2	no	—
388	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
389	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
390	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
391	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
392	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
393	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
394	C₈	—	73	2	no	—
395	C₈	—	73	2	no	—
396	C₈	—	146	1	no	—
397	C₈	—	146	1	no	—
398	C₈	—	146	1	no	—
399	C₈	—	146	1	no	—
400	C₈	—	146	1	no	—
401	C₈	—	146	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	73	2	no	—
406	C₂²	—	146	1	no	—
407	C₂²	—	146	1	no	—
408	C₂²	—	146	1	no	—
409	C₂²	—	146	1	no	—
410	C₂²	—	146	1	no	—
411	C₂²	C₂³×#10596842	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	73	1	no	—
418	C₄	—	73	1	no	—
419	C₄	—	73	2	no	—
420	C₄	—	73	2	no	—
421	C₄	—	146	1	no	—
422	C₄	—	146	1	no	—
423	C₄	—	146	1	no	—
424	C₄	#17989706	1	2	yes	—
425	C₂	—	4	1	no	—
426	C₂	—	292	1	no	—
427	C₂	—	146	2	no	—
428	C₂	#41×#10596842	1	1	yes	characteristic
429	C₂	C₂×#17989706	1	1	yes	characteristic
430	C₂	#22627182	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#10596842
commutator, socle	C₂²×C₇₃	C₂³×C₈
Frattini	C₂²	C₂³×#10596842
Fitting	#117×C₇₃	C₈
prime radical	C₂×#11924028	C₈
cosocle	C₂×#10596833	C₂⁴
hypercenter	#117	#10596842
hypocenter	C₇₃	#33479
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
1. #22627158	C₂	semidirect
2. #22627145	C₂	semidirect
3. #22627144	C₂	semidirect
4. #22627142	C₂	semidirect
5. #22627131	C₂	semidirect
6. #22627130	C₂	semidirect
7. #22627129	C₂	semidirect
8. C₄×#14556688	C₂	semidirect
9. C₄×#14556687	C₂	semidirect
10. C₄×#14556686	C₂	semidirect
96. #11924040	#41	semidirect
176. C₄×D₇₃	M₃₂	semidirect
227. C₇₃	#33479	semidirect

Maximal subgroups

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

subgroup	index
#22627158	2
#22627145	2
#22627144	2
#22627142	2
#22627131	2
#22627130	2
#22627129	2
C₄×#14556688	2
C₄×#14556687	2
C₄×#14556686	2
#22626735	2
#33479	73