Subgroups — #34020266

Order 18688.

1126 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989598	C₂	1	2	yes	maximal
2	#22626368	C₂	1	2	yes	maximal
3	#22625745	C₂	1	4	yes	maximal, complemented
4	C₄×#14556660	C₂	1	2	yes	maximal, complemented
5	C₄×#14556659	C₂	1	2	yes	maximal, complemented
6	#22625617	C₂	1	1	yes	maximal, characteristic
7	C₂×#17989461	C₂	1	1	yes	maximal, characteristic
8	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂×#14556670	C₂²	1	2	yes	—
10	C₂²×C₄⋊#64408	C₂²	1	2	yes	—
11	#17989598	C₄	1	16	yes	complemented
12	C₂×#14556660	C₂²	1	4	yes	—
13	C₂×#14556659	C₂²	1	4	yes	—
14	C₄⋊C₄×#64408	—	2	2	no	—
15	C₄⋊C₄×#64408	—	2	2	no	—
16	C₄×C₄⋊#64408	C₂²	1	4	yes	—
17	C₄×C₄⋊#64408	C₂²	1	4	yes	—
18	C₂²⋊C₄×#64408	—	2	4	no	—
19	#17989461	C₂²	1	2	yes	—
20	#17989461	C₂²	1	2	yes	—
21	#17989461	C₂²	1	1	yes	characteristic
22	#17989461	C₂²	1	1	yes	characteristic
23	#17989461	C₂²	1	2	yes	—
24	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
25	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
26	#117×D₇₃	C₂²	1	1	yes	characteristic
27	#17988545	C₄	1	1	yes	characteristic, complemented
28	#17988544	C₄	1	2	yes	complemented
29	#17988543	C₄	1	1	yes	characteristic, complemented
30	#17988542	C₄	1	1	yes	characteristic, complemented
31	#17988541	C₄	1	2	yes	complemented
32	#97×D₇₃	C₂²	1	2	yes	—
33	C₄×C₈×D₇₃	C₂²	1	2	yes	—
34	#405×C₇₃	C₄	1	1	yes	characteristic, complemented
35	C₂³×#64408	—	2	2	no	—
36	#14556670	—	2	4	no	—
37	#14556670	C₂×C₄	1	8	yes	—
38	C₂×C₄⋊#64408	—	2	2	no	—
39	C₂×C₄⋊#64408	—	2	4	no	—
40	C₂×C₄⋊#64408	C₂×C₄	1	8	yes	—
41	C₂×C₄⋊#64408	C₂³	1	4	yes	—
42	C₂×C₄⋊#64408	C₂³	1	2	yes	—
43	C₂×C₄⋊#64408	C₂³	1	2	yes	—
44	C₂×C₂²⋊#64408	—	2	2	no	—
45	C₂×C₄×#64408	—	2	2	no	—
46	C₂×C₄×#64408	—	2	4	no	—
47	C₂×C₄×#64408	—	2	4	no	—
48	#14556660	C₂×C₄	1	16	yes	complemented
49	#14556659	C₂×C₄	1	16	yes	complemented
50	(C₂×#64408)⋊C₄	—	2	4	no	—
51	(C₂×#64408)⋊C₄	—	2	4	no	—
52	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
53	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
54	C₂×#11924011	C₂×C₄	1	2	yes	—
55	M₁₆×D₇₃	C₂×C₄	1	8	yes	—
56	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₇₃	—	2	4	no	—
58	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₇₃	C₂³	1	2	yes	—
63	#14556550	C₂×C₄	1	1	yes	characteristic
64	#14556549	Q₈	1	1	yes	characteristic
65	#14556549	Q₈	1	1	yes	characteristic
66	#14556548	C₂×C₄	1	2	yes	—
67	#14556547	Q₈	1	2	yes	—
68	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
69	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
70	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
71	C₄²×D₇₃	C₂³	1	2	yes	—
72	#14556502	C₂×C₄	1	2	yes	complemented
73	#14556501	C₂×C₄	1	2	yes	complemented
74	#14556501	C₂×C₄	1	2	yes	complemented
75	C₄×#10596831	C₂×C₄	1	2	yes	complemented
76	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
77	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
78	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
80	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
81	#97×C₇₃	C₂×C₄	1	2	yes	complemented
82	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
83	C₂²×#64408	—	2	4	no	—
84	C₂²×#64408	—	2	2	no	—
85	C₂²×#64408	—	2	2	no	—
86	C₂²×#64408	—	2	8	no	—
87	C₂²×#64408	—	8	2	no	—
88	C₂²×#64408	—	8	2	no	—
89	C₄⋊#64408	—	2	8	no	—
90	C₄⋊#64408	—	2	4	no	—
91	C₄⋊#64408	—	2	2	no	—
92	C₄⋊#64408	—	2	2	no	—
93	C₄⋊#64408	C₂²×C₄	1	4	yes	—
94	C₄⋊#64408	C₂²×C₄	1	8	yes	—
95	C₄⋊#64408	C₂²×C₄	1	4	yes	—
96	C₂²⋊#64408	—	2	8	no	—
97	C₄×#64408	—	2	8	no	—
98	C₄×#64408	—	8	4	no	—
99	C₄×#64408	—	8	4	no	—
100	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
102	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂²×C₄	1	4	yes	—
104	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
105	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
106	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄×D₇₃	#41	1	4	yes	—
109	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
110	#11924012	C₄²	1	4	yes	complemented
111	#11924011	C₄²	1	8	yes	complemented
112	C₂×#10596831	—	2	2	no	—
113	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
114	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
115	C₂×#10596831	C₂²×C₄	1	2	yes	—
116	C₈×D₇₃	—	2	2	no	—
117	C₈×D₇₃	—	2	2	no	—
118	C₈×D₇₃	—	2	2	no	—
119	C₈×D₇₃	—	2	2	no	—
120	C₈×D₇₃	C₂²×C₄	1	8	yes	—
121	C₄⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
122	C₄⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
123	#11924007	C₄⋊C₄	1	2	yes	—
124	#11924007	C₄⋊C₄	1	2	yes	—
125	C₂²⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
126	#11924005	C₄⋊C₄	1	2	yes	—
127	#11924005	C₄⋊C₄	1	2	yes	—
128	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
129	C₄×Dic₇₃	C₂×Q₈	1	2	yes	—
130	C₄×Dic₇₃	C₂×Q₈	1	2	yes	—
131	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
132	M₁₆×C₇₃	C₄²	1	4	yes	complemented
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
137	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
138	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
140	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
141	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂²×D₇₃	—	2	1	no	—
143	C₂²×D₇₃	—	2	2	no	—
144	C₂²×D₇₃	—	2	1	no	—
145	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂²×D₇₃	C₄×D₄	1	4	yes	—
147	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
148	C₂×#64408	—	2	4	no	—
149	C₂×#64408	—	2	4	no	—
150	C₂×#64408	—	2	8	no	—
151	C₂×#64408	—	4	2	no	—
152	C₂×#64408	—	4	4	no	—
153	C₂×#64408	—	4	2	no	—
154	C₂×#64408	—	4	4	no	—
155	C₂×#64408	—	4	2	no	—
156	C₂×#64408	—	4	2	no	—
157	C₂×#64408	—	8	8	no	—
158	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
159	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₇₃	#117	1	2	yes	—
163	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×Dic₇₃	C₄×Q₈	1	4	yes	—
168	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
169	C₄×D₇₃	—	2	2	no	—
170	C₄×D₇₃	—	2	4	no	—
171	C₄×D₇₃	—	2	2	no	—
172	C₄×D₇₃	C₂×C₄²	1	2	yes	—
173	C₄×D₇₃	#117	1	2	yes	—
174	C₄×D₇₃	C₄×D₄	1	4	yes	—
175	C₄×D₇₃	C₄×Q₈	1	4	yes	—
176	C₄×D₇₃	C₂³×C₄	1	2	yes	—
177	C₄×D₇₃	C₂×#41	1	2	yes	—
178	C₈×C₇₃	—	2	1	no	—
179	C₈×C₇₃	—	2	1	no	—
180	C₈×C₇₃	C₂×C₄²	1	4	yes	—
181	#10596831	—	2	1	no	—
182	#10596831	—	2	1	no	—
183	#10596831	C₂×C₄²	1	4	yes	—
184	C₂²×C₇₃	—	2	1	no	—
185	C₂²×C₇₃	—	2	1	no	—
186	C₂²×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
187	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
188	C₂×D₇₃	—	2	1	no	—
189	C₂×D₇₃	—	2	1	no	—
190	C₂×D₇₃	—	2	4	no	—
191	C₂×D₇₃	—	2	4	no	—
192	C₂×D₇₃	C₄×C₄⋊C₄	1	2	yes	—
193	C₂×D₇₃	C₂×C₄×D₄	1	2	yes	—
194	C₂×D₇₃	#576	1	1	yes	characteristic
195	C₂×D₇₃	#577	1	2	yes	—
196	C₂×D₇₃	#578	1	1	yes	characteristic
197	#64408	—	4	4	no	—
198	#64408	—	4	8	no	—
199	#64408	—	4	4	no	—
200	C₄×C₇₃	—	2	2	no	—
201	C₄×C₇₃	—	2	2	no	—
202	C₄×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
203	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
204	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
205	Dic₇₃	—	2	2	no	—
206	Dic₇₃	—	2	2	no	—
207	Dic₇₃	C₄×C₄⋊C₄	1	2	yes	—
208	Dic₇₃	C₂×C₄×Q₈	1	2	yes	—
209	#20453	—	73	1	no	maximal, Sylow
210	C₂×C₇₃	—	2	2	no	—
211	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₇₃	#2912	1	1	yes	characteristic
213	C₂×C₇₃	#2913	1	1	yes	characteristic
214	D₇₃	—	2	2	no	—
215	D₇₃	#2946	1	2	yes	—
216	D₇₃	#2947	1	2	yes	—
217	C₂×#428	—	73	2	no	—
218	C₂×#405	—	73	1	no	—
219	#2274	—	73	2	no	—
220	#1776	—	73	4	no	—
221	C₄×#107	—	73	2	no	—
222	C₄×#106	—	73	2	no	—
223	#1735	—	73	1	no	—
224	C₂×#340	—	73	1	no	—
225	C₇₃	#20453	1	1	yes	characteristic, complemented, Sylow
226	C₂²×M₁₆	—	73	1	no	—
227	C₂³×C₈	—	73	1	no	—
228	C₂×#117	—	73	1	no	—
229	C₂×#117	—	73	2	no	—
230	C₂²×C₄⋊C₄	—	73	2	no	—
231	#428	—	73	16	no	—
232	C₂×#107	—	73	4	no	—
233	C₂×#106	—	73	4	no	—
234	#405	—	73	1	no	—
235	#405	—	73	1	no	—
236	#405	—	73	1	no	—
237	#405	—	73	2	no	—
238	#405	—	73	2	no	—
239	#405	#64408	1	1	yes	characteristic, complemented
240	C₂×#97	—	73	2	no	—
241	C₂×C₄×C₈	—	73	2	no	—
242	C₄×C₄⋊C₄	—	73	4	no	—
243	C₄×C₄⋊C₄	—	73	4	no	—
244	C₄×C₄⋊C₄	—	146	2	no	—
245	C₄×C₄⋊C₄	—	146	2	no	—
246	C₄×C₂²⋊C₄	—	146	4	no	—
247	#340	—	73	2	no	—
248	#340	—	73	2	no	—
249	#340	—	73	1	no	—
250	#340	—	73	1	no	—
251	#340	—	73	2	no	—
252	C₂³×C₄	—	73	1	no	—
253	C₂³×C₄	—	146	2	no	—
254	C₂×M₁₆	—	73	1	no	—
255	C₂×M₁₆	—	73	8	no	—
256	C₂×M₁₆	—	73	2	no	—
257	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
258	C₂²×C₈	—	73	2	no	—
259	C₂²×C₈	—	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	—	146	4	no	—
265	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
266	#117	—	73	1	no	—
267	#117	—	73	1	no	—
268	#117	—	73	1	no	—
269	#117	—	73	2	no	—
270	#117	—	73	2	no	—
271	#117	—	73	8	no	—
272	#117	—	146	4	no	—
273	#117	C₂×#64408	1	1	yes	characteristic
274	C₂×C₄⋊C₄	—	73	1	no	—
275	C₂×C₄⋊C₄	—	73	1	no	—
276	C₂×C₄⋊C₄	—	73	4	no	—
277	C₂×C₄⋊C₄	—	73	8	no	—
278	C₂×C₄⋊C₄	—	73	2	no	—
279	C₂×C₄⋊C₄	—	73	2	no	—
280	C₂×C₄⋊C₄	—	146	2	no	—
281	C₂×C₄⋊C₄	—	146	4	no	—
282	C₂×C₂²⋊C₄	—	73	2	no	—
283	C₂×C₂²⋊C₄	—	146	2	no	—
284	C₂×C₄²	—	73	2	no	—
285	C₂×C₄²	—	146	4	no	—
286	C₂×C₄²	—	146	4	no	—
287	C₂×C₄²	—	146	2	no	—
288	#107	—	73	16	no	—
289	#106	—	73	16	no	—
290	#97	—	73	2	no	—
291	#97	—	73	2	no	—
292	#97	—	73	2	no	—
293	#97	C₂×#64408	1	2	yes	complemented
294	C₄×C₈	—	73	2	no	—
295	C₄×C₈	—	73	2	no	—
296	C₄×C₈	—	73	2	no	—
297	C₄×C₈	C₂×#64408	1	2	yes	complemented
298	#95	—	146	4	no	—
299	#95	—	146	4	no	—
300	C₂⁴	—	73	1	no	—
301	C₂²×C₄	—	584	2	no	—
302	C₂²×C₄	—	584	2	no	—
303	C₂²×C₄	—	73	1	no	—
304	C₂²×C₄	—	73	1	no	—
305	C₂²×C₄	—	73	1	no	—
306	C₂²×C₄	—	73	4	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	4	no	—
310	C₂²×C₄	—	73	2	no	—
311	C₂²×C₄	—	73	2	no	—
312	C₂²×C₄	—	146	2	no	—
313	C₂²×C₄	—	146	2	no	—
314	C₂²×C₄	—	146	4	no	—
315	C₂²×C₄	—	146	8	no	—
316	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
317	M₁₆	—	73	4	no	—
318	M₁₆	—	73	8	no	—
319	M₁₆	C₄×#64408	1	4	yes	complemented
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	73	2	no	—
322	C₂×C₈	—	73	8	no	—
323	C₂×C₈	—	73	1	no	—
324	C₂×C₈	—	73	1	no	—
325	C₂×C₈	—	146	2	no	—
326	C₂×C₈	—	146	2	no	—
327	C₂×C₈	—	146	2	no	—
328	C₂×C₈	—	146	2	no	—
329	C₂×C₈	—	146	2	no	—
330	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
331	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
332	C₂×C₈	C₂²×#64408	1	2	yes	—
333	C₄⋊C₄	—	73	2	no	—
334	C₄⋊C₄	—	73	2	no	—
335	C₄⋊C₄	—	73	1	no	—
336	C₄⋊C₄	—	73	1	no	—
337	C₄⋊C₄	—	73	4	no	—
338	C₄⋊C₄	—	73	8	no	—
339	C₄⋊C₄	—	73	4	no	—
340	C₄⋊C₄	—	146	4	no	—
341	C₄⋊C₄	—	146	8	no	—
342	C₄⋊C₄	—	146	2	no	—
343	C₄⋊C₄	—	146	2	no	—
344	C₄⋊C₄	C₄⋊#64408	1	1	yes	characteristic
345	C₄⋊C₄	C₄⋊#64408	1	1	yes	characteristic
346	C₂²⋊C₄	—	73	2	no	—
347	C₂²⋊C₄	—	73	2	no	—
348	C₂²⋊C₄	—	73	2	no	—
349	C₂²⋊C₄	—	146	8	no	—
350	C₂²⋊C₄	C₄⋊#64408	1	2	yes	—
351	C₄²	—	584	4	no	—
352	C₄²	—	584	4	no	—
353	C₄²	—	73	2	no	—
354	C₄²	—	73	2	no	—
355	C₄²	—	73	2	no	—
356	C₄²	—	146	8	no	—
357	C₄²	C₂²×#64408	1	2	yes	—
358	C₂³	—	73	1	no	—
359	C₂³	—	73	1	no	—
360	C₂³	—	73	4	no	—
361	C₂³	—	146	1	no	—
362	C₂³	—	146	2	no	—
363	C₂³	—	146	1	no	—
364	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
365	C₂×C₄	—	292	2	no	—
366	C₂×C₄	—	292	2	no	—
367	C₂×C₄	—	292	4	no	—
368	C₂×C₄	—	292	4	no	—
369	C₂×C₄	—	292	2	no	—
370	C₂×C₄	—	292	2	no	—
371	C₂×C₄	—	584	8	no	—
372	C₂×C₄	—	73	1	no	—
373	C₂×C₄	—	73	1	no	—
374	C₂×C₄	—	73	4	no	—
375	C₂×C₄	—	73	2	no	—
376	C₂×C₄	—	73	2	no	—
377	C₂×C₄	—	73	2	no	—
378	C₂×C₄	—	73	2	no	—
379	C₂×C₄	—	73	4	no	—
380	C₂×C₄	—	73	4	no	—
381	C₂×C₄	—	73	2	no	—
382	C₂×C₄	—	73	2	no	—
383	C₂×C₄	—	146	2	no	—
384	C₂×C₄	—	146	4	no	—
385	C₂×C₄	—	146	2	no	—
386	C₂×C₄	—	146	4	no	—
387	C₂×C₄	—	146	4	no	—
388	C₂×C₄	—	146	8	no	—
389	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
390	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
391	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
392	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
393	C₂×C₄	#14556670	1	2	yes	—
394	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	73	4	no	—
398	C₈	—	146	1	no	—
399	C₈	—	146	1	no	—
400	C₈	C₂×C₄×#64408	1	4	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	73	2	no	—
404	C₂²	—	73	1	no	—
405	C₂²	—	73	1	no	—
406	C₂²	—	73	2	no	—
407	C₂²	—	73	2	no	—
408	C₂²	—	146	4	no	—
409	C₂²	—	146	4	no	—
410	C₂²	—	146	1	no	—
411	C₂²	—	146	1	no	—
412	C₂²	C₄×C₄⋊#64408	1	2	yes	—
413	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	292	8	no	—
417	C₄	—	292	4	no	—
418	C₄	—	292	4	no	—
419	C₄	—	73	2	no	—
420	C₄	—	73	2	no	—
421	C₄	—	146	2	no	—
422	C₄	—	146	2	no	—
423	C₄	C₄×C₄⋊#64408	1	2	yes	—
424	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
425	C₄	C₂×#14556670	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	73	2	no	—
428	C₂	—	73	2	no	—
429	C₂	—	146	2	no	—
430	C₂	C₂×C₄×C₄⋊#64408	1	1	yes	characteristic
431	C₂	#22626585	1	1	yes	characteristic
432	C₂	#22626586	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#64408
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	#405×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₂×D₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#20453
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
3. #22625745	C₂	semidirect
4. C₄×#14556660	C₂	semidirect
5. C₄×#14556659	C₂	semidirect
11. #17989598	C₄	semidirect
27. #17988545	C₄	semidirect
28. #17988544	C₄	semidirect
29. #17988543	C₄	semidirect
30. #17988542	C₄	semidirect
31. #17988541	C₄	semidirect
34. #405×C₇₃	C₄	semidirect
48. #14556660	C₂×C₄	semidirect
49. #14556659	C₂×C₄	semidirect
72. #14556502	C₂×C₄	semidirect
73. #14556501	C₂×C₄	semidirect
74. #14556501	C₂×C₄	semidirect
75. C₄×#10596831	C₂×C₄	semidirect
76. C₈×Dic₇₃	C₂×C₄	semidirect
77. C₈×Dic₇₃	C₂×C₄	semidirect
81. #97×C₇₃	C₂×C₄	semidirect
82. C₄×C₈×C₇₃	C₂×C₄	semidirect
110. #11924012	C₄²	semidirect
111. #11924011	C₄²	semidirect
132. M₁₆×C₇₃	C₄²	semidirect
225. C₇₃	#20453	semidirect
239. #405	#64408	semidirect
293. #97	C₂×#64408	semidirect
297. C₄×C₈	C₂×#64408	semidirect
319. M₁₆	C₄×#64408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989598	2
#22626368	2
#22625745	2
C₄×#14556660	2
C₄×#14556659	2
#22625617	2
C₂×#17989461	2
#405×D₇₃	2
#20453	73