Subgroups — #34020247

Order 18688.

1010 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989597	C₂	1	1	yes	maximal, characteristic
3	#22626494	C₂	1	2	yes	maximal
4	#22625737	C₂	1	4	yes	maximal, complemented
5	#22625733	C₂	1	4	yes	maximal, complemented
6	#22625612	C₂	1	2	yes	maximal
7	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×D₇₃⋊M₁₆	C₂²	1	2	yes	—
9	C₂×#14556670	C₂²	1	2	yes	—
10	C₂×#14556662	C₄	1	2	yes	complemented
11	D₇₃⋊#108	C₄	1	2	yes	complemented
12	D₇₃⋊#108	C₄	1	2	yes	complemented
13	D₇₃⋊#108	C₂²	1	2	yes	—
14	D₇₃⋊#108	C₂²	1	2	yes	—
15	C₂×#14556661	C₄	1	2	yes	complemented
16	#17989597	C₄	1	2	yes	complemented
17	#17989597	C₄	1	2	yes	complemented
18	#17989597	C₂²	1	2	yes	—
19	#17989597	C₂²	1	2	yes	—
20	C₂×#14556660	C₄	1	2	yes	complemented
21	C₂×#14556659	C₄	1	2	yes	complemented
22	#17989553	—	2	4	no	—
23	#17989550	C₂²	1	8	yes	—
24	M₁₆×#64408	—	2	4	no	—
25	#17989458	C₂²	1	8	yes	—
26	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
28	#117×D₇₃	C₂²	1	1	yes	characteristic
29	#17988545	C₄	1	1	yes	characteristic, complemented
30	#17988544	C₄	1	2	yes	complemented
31	#17988543	C₄	1	1	yes	characteristic, complemented
32	#17988542	C₄	1	1	yes	characteristic, complemented
33	#17988541	C₄	1	2	yes	complemented
34	#97×D₇₃	C₂²	1	2	yes	—
35	C₄×C₈×D₇₃	C₂²	1	2	yes	—
36	#405×C₇₃	C₄	1	1	yes	characteristic, complemented
37	C₂×#11924038	C₂×C₄	1	4	yes	—
38	D₇₃⋊M₁₆	—	2	2	no	—
39	D₇₃⋊M₁₆	—	2	2	no	—
40	D₇₃⋊M₁₆	C₂×C₄	1	4	yes	—
41	D₇₃⋊M₁₆	C₂³	1	4	yes	—
42	C₂×#11924037	—	2	2	no	—
43	C₂×#11924036	—	2	2	no	—
44	#14556670	—	2	2	no	—
45	#14556670	—	2	2	no	—
46	#14556670	C₂×C₄	1	4	yes	—
47	#14556670	C₂³	1	4	yes	—
48	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
49	C₂×C₂²⋊#64408	—	2	2	no	—
50	C₂×C₄×#64408	—	2	2	no	—
51	#14556662	C₂×C₄	1	4	yes	complemented
52	#14556662	C₂×C₄	1	4	yes	complemented
53	#14556661	C₂×C₄	1	4	yes	complemented
54	#14556661	C₂×C₄	1	4	yes	complemented
55	#14556660	C₂×C₄	1	4	yes	—
56	#14556660	C₂×C₄	1	4	yes	—
57	#14556659	C₂×C₄	1	4	yes	—
58	#14556659	C₂×C₄	1	4	yes	—
59	#14556645	—	2	8	no	—
60	C₈×#64408	—	2	8	no	—
61	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
62	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
63	C₂×#11924011	C₂×C₄	1	2	yes	—
64	M₁₆×D₇₃	D₄	1	2	yes	—
65	M₁₆×D₇₃	D₄	1	2	yes	—
66	M₁₆×D₇₃	Q₈	1	2	yes	—
67	M₁₆×D₇₃	Q₈	1	2	yes	—
68	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
80	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
81	C₂×C₈×D₇₃	C₂³	1	2	yes	—
82	#14556550	C₂×C₄	1	1	yes	characteristic
83	#14556549	—	2	1	no	—
84	#14556548	C₂×C₄	1	2	yes	—
85	#14556547	—	2	1	no	—
86	C₄⋊C₄×D₇₃	—	2	1	no	—
87	C₂²⋊C₄×D₇₃	—	2	1	no	—
88	C₄²×D₇₃	C₂³	1	2	yes	—
89	#14556502	C₂×C₄	1	2	yes	complemented
90	#14556501	C₂×C₄	1	2	yes	complemented
91	#14556501	C₂×C₄	1	2	yes	complemented
92	C₄×#10596831	C₂×C₄	1	2	yes	complemented
93	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
94	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
95	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
97	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
98	#97×C₇₃	C₂×C₄	1	2	yes	complemented
99	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
100	C₂²×#64408	—	2	4	no	—
101	#11924038	—	2	4	no	—
102	#11924038	C₂²×C₄	1	8	yes	—
103	#11924037	—	2	4	no	—
104	#11924037	—	2	4	no	—
105	#11924036	—	2	4	no	—
106	#11924036	—	2	4	no	—
107	C₂×#10596833	—	2	4	no	—
108	C₄⋊#64408	—	2	4	no	—
109	C₄⋊#64408	C₂²×C₄	1	8	yes	—
110	C₂²⋊#64408	—	2	4	no	—
111	C₂²⋊#64408	—	2	4	no	—
112	C₄×#64408	—	2	4	no	—
113	C₄×#64408	—	2	4	no	—
114	C₂³×D₇₃	#41	1	1	yes	characteristic
115	C₂²×Dic₇₃	#41	1	1	yes	characteristic
116	C₂×C₄×D₇₃	—	2	2	no	—
117	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
125	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
126	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
127	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
128	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
129	#11924012	C₄⋊C₄	1	2	yes	—
130	#11924012	C₄⋊C₄	1	2	yes	—
131	#11924011	C₄⋊C₄	1	4	yes	—
132	#11924011	C₄⋊C₄	1	4	yes	—
133	C₂×#10596831	C₄²	1	1	yes	characteristic
134	C₂×#10596831	C₄²	1	1	yes	characteristic
135	C₂×#10596831	C₄²	1	1	yes	characteristic
136	C₂×#10596831	C₄²	1	1	yes	characteristic
137	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
138	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
139	C₂×#10596831	C₂²×C₄	1	2	yes	—
140	C₈×D₇₃	C₄²	1	1	yes	characteristic
141	C₈×D₇₃	C₄²	1	1	yes	characteristic
142	C₈×D₇₃	C₄²	1	1	yes	characteristic
143	C₈×D₇₃	C₄²	1	1	yes	characteristic
144	C₈×D₇₃	C₄²	1	1	yes	characteristic
145	C₈×D₇₃	C₄²	1	1	yes	characteristic
146	C₈×D₇₃	C₄²	1	1	yes	characteristic
147	C₈×D₇₃	C₄²	1	1	yes	characteristic
148	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
149	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
150	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
151	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
153	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
154	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₈×D₇₃	C₂×D₄	1	4	yes	—
157	C₈×D₇₃	C₂×Q₈	1	4	yes	—
158	C₄⋊Dic₇₃	—	2	1	no	—
159	#11924007	—	2	2	no	—
160	C₂²⋊Dic₇₃	—	2	1	no	—
161	#11924005	—	2	2	no	—
162	C₄×Dic₇₃	—	2	2	no	—
163	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
165	M₁₆×C₇₃	C₄⋊C₄	1	2	yes	—
166	M₁₆×C₇₃	C₄⋊C₄	1	2	yes	—
167	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
168	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
169	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
170	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
171	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
174	C₄⋊C₄×C₇₃	—	2	1	no	—
175	C₂²⋊C₄×C₇₃	—	2	1	no	—
176	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
177	C₂³×C₇₃	#117	1	1	yes	characteristic
178	C₂²×D₇₃	—	4	2	no	—
179	C₂²×D₇₃	#117	1	1	yes	characteristic
180	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
181	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
182	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
183	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
184	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
185	C₂×#64408	—	2	8	no	—
186	C₂×#64408	—	8	4	no	—
187	C₂×C₄×C₇₃	—	2	2	no	—
188	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×Dic₇₃	—	2	2	no	—
195	C₂×Dic₇₃	#117	1	1	yes	characteristic
196	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
197	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
198	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
199	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
200	C₂×Dic₇₃	C₂×#41	1	1	yes	characteristic
201	C₄×D₇₃	—	4	4	no	—
202	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
203	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
204	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
207	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
208	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
209	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
210	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
211	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
212	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
213	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
214	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
215	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
216	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
217	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
218	#10596833	—	2	8	no	—
219	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
220	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
221	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
222	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
223	C₈×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
224	#10596831	C₂×C₄²	1	1	yes	characteristic
225	#10596831	C₂×C₄²	1	1	yes	characteristic
226	#10596831	C₂×C₄²	1	1	yes	characteristic
227	#10596831	C₂×C₄²	1	1	yes	characteristic
228	#10596831	C₂×C₄⋊C₄	1	4	yes	—
229	C₂²×C₇₃	—	4	1	no	—
230	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
231	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
233	C₂×D₇₃	—	2	2	no	—
234	C₂×D₇₃	—	2	2	no	—
235	C₂×D₇₃	—	2	2	no	—
236	C₂×D₇₃	—	4	1	no	—
237	C₂×D₇₃	—	4	1	no	—
238	C₂×D₇₃	—	4	1	no	—
239	C₂×D₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
240	C₂×D₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
241	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
242	C₂×D₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
243	#64408	—	4	8	no	—
244	C₄×C₇₃	—	4	2	no	—
245	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
246	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
247	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
248	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
249	Dic₇₃	—	4	2	no	—
250	Dic₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
251	Dic₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
252	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
253	Dic₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
254	#20446	—	73	1	no	maximal, Sylow
255	C₂×C₇₃	—	2	1	no	—
256	C₂×C₇₃	—	2	1	no	—
257	C₂×C₇₃	—	2	1	no	—
258	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
259	D₇₃	—	2	1	no	—
260	D₇₃	—	2	1	no	—
261	D₇₃	—	2	1	no	—
262	D₇₃	#2957	1	2	yes	—
263	C₂²×#108	—	73	1	no	—
264	C₂×#427	—	73	1	no	—
265	#2873	—	73	2	no	—
266	C₂×#405	—	73	1	no	—
267	#1773	—	73	4	no	—
268	#1772	—	73	4	no	—
269	#1733	—	73	2	no	—
270	C₇₃	#20446	1	1	yes	characteristic, complemented, Sylow
271	C₂²×M₁₆	—	73	1	no	—
272	C₂²×M₁₆	—	73	2	no	—
273	C₂³×C₈	—	73	1	no	—
274	C₂×#117	—	73	1	no	—
275	C₂×#117	—	73	2	no	—
276	C₂×#108	—	73	2	no	—
277	C₂×#108	—	73	2	no	—
278	C₂×#108	—	73	2	no	—
279	C₂×#108	—	73	2	no	—
280	C₂×#108	—	73	2	no	—
281	C₂×#108	—	73	2	no	—
282	#427	—	73	2	no	—
283	#427	—	73	2	no	—
284	#427	—	73	2	no	—
285	#427	—	73	2	no	—
286	C₂×#107	—	73	2	no	—
287	C₂×#106	—	73	2	no	—
288	#405	—	73	1	no	—
289	#405	—	73	1	no	—
290	#405	—	73	1	no	—
291	#405	—	73	2	no	—
292	#405	—	73	2	no	—
293	#405	—	73	8	no	—
294	#405	—	146	4	no	—
295	#405	#64408	1	1	yes	characteristic, complemented
296	C₄×M₁₆	—	146	4	no	—
297	C₂×#97	—	73	2	no	—
298	C₂×C₄×C₈	—	73	2	no	—
299	#339	—	73	8	no	—
300	C₂³×C₄	—	73	1	no	—
301	C₂×M₁₆	—	73	1	no	—
302	C₂×M₁₆	—	73	2	no	—
303	C₂×M₁₆	—	73	2	no	—
304	C₂×M₁₆	—	73	2	no	—
305	C₂×M₁₆	—	73	2	no	—
306	C₂×M₁₆	—	73	2	no	—
307	C₂×M₁₆	—	73	4	no	—
308	C₂×M₁₆	—	73	4	no	—
309	C₂×M₁₆	—	73	4	no	—
310	C₂×M₁₆	—	146	2	no	—
311	C₂×M₁₆	—	146	2	no	—
312	C₂×M₁₆	—	146	2	no	—
313	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
314	C₂²×C₈	—	73	1	no	—
315	C₂²×C₈	—	73	1	no	—
316	C₂²×C₈	—	73	1	no	—
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	—	73	1	no	—
322	C₂²×C₈	—	73	1	no	—
323	C₂²×C₈	—	73	1	no	—
324	C₂²×C₈	—	73	1	no	—
325	C₂²×C₈	—	73	1	no	—
326	C₂²×C₈	—	73	1	no	—
327	C₂²×C₈	—	73	2	no	—
328	C₂²×C₈	—	146	2	no	—
329	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
330	#117	—	73	1	no	—
331	#117	—	73	2	no	—
332	#117	—	73	4	no	—
333	#117	—	73	4	no	—
334	#117	—	146	1	no	—
335	#117	—	146	1	no	—
336	#117	—	146	2	no	—
337	#117	—	146	2	no	—
338	#117	C₂×#64408	1	1	yes	characteristic
339	C₂×C₄⋊C₄	—	73	4	no	—
340	C₂×C₄⋊C₄	—	146	1	no	—
341	C₂×C₂²⋊C₄	—	146	1	no	—
342	C₂×C₂²⋊C₄	—	146	2	no	—
343	C₂×C₄²	—	73	2	no	—
344	C₂×C₄²	—	146	2	no	—
345	#108	—	73	4	no	—
346	#108	—	73	4	no	—
347	#108	—	73	4	no	—
348	#108	—	73	4	no	—
349	#107	—	73	4	no	—
350	#107	—	73	4	no	—
351	#106	—	73	4	no	—
352	#106	—	73	4	no	—
353	#97	—	73	2	no	—
354	#97	—	73	2	no	—
355	#97	—	73	2	no	—
356	#97	—	146	8	no	—
357	#97	C₂×#64408	1	2	yes	complemented
358	C₄×C₈	—	73	2	no	—
359	C₄×C₈	—	73	2	no	—
360	C₄×C₈	—	73	2	no	—
361	C₄×C₈	—	146	8	no	—
362	C₄×C₈	C₂×#64408	1	2	yes	complemented
363	C₂⁴	—	73	1	no	—
364	C₂²×C₄	—	73	1	no	—
365	C₂²×C₄	—	73	1	no	—
366	C₂²×C₄	—	73	1	no	—
367	C₂²×C₄	—	73	1	no	—
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	—	73	1	no	—
373	C₂²×C₄	—	73	1	no	—
374	C₂²×C₄	—	73	1	no	—
375	C₂²×C₄	—	73	1	no	—
376	C₂²×C₄	—	73	1	no	—
377	C₂²×C₄	—	146	2	no	—
378	C₂²×C₄	—	146	4	no	—
379	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
380	M₁₆	—	73	2	no	—
381	M₁₆	—	73	2	no	—
382	M₁₆	—	73	4	no	—
383	M₁₆	—	73	4	no	—
384	M₁₆	—	73	8	no	—
385	M₁₆	—	146	4	no	—
386	M₁₆	—	146	4	no	—
387	M₁₆	—	146	4	no	—
388	M₁₆	C₄⋊#64408	1	2	yes	—
389	M₁₆	C₄⋊#64408	1	2	yes	—
390	C₂×C₈	—	73	1	no	—
391	C₂×C₈	—	73	2	no	—
392	C₂×C₈	—	73	1	no	—
393	C₂×C₈	—	73	1	no	—
394	C₂×C₈	—	73	1	no	—
395	C₂×C₈	—	73	1	no	—
396	C₂×C₈	—	73	1	no	—
397	C₂×C₈	—	73	1	no	—
398	C₂×C₈	—	73	1	no	—
399	C₂×C₈	—	73	1	no	—
400	C₂×C₈	—	73	1	no	—
401	C₂×C₈	—	73	1	no	—
402	C₂×C₈	—	73	1	no	—
403	C₂×C₈	—	73	1	no	—
404	C₂×C₈	—	73	1	no	—
405	C₂×C₈	—	73	1	no	—
406	C₂×C₈	—	73	1	no	—
407	C₂×C₈	—	73	1	no	—
408	C₂×C₈	—	73	1	no	—
409	C₂×C₈	—	73	1	no	—
410	C₂×C₈	—	73	1	no	—
411	C₂×C₈	—	73	1	no	—
412	C₂×C₈	—	73	1	no	—
413	C₂×C₈	—	73	4	no	—
414	C₂×C₈	—	73	4	no	—
415	C₂×C₈	—	146	4	no	—
416	C₂×C₈	—	146	4	no	—
417	C₂×C₈	—	146	4	no	—
418	C₂×C₈	C₄×#64408	1	1	yes	characteristic
419	C₂×C₈	C₄×#64408	1	1	yes	characteristic
420	C₂×C₈	C₄×#64408	1	1	yes	characteristic
421	C₂×C₈	C₄×#64408	1	1	yes	characteristic
422	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
423	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
424	C₂×C₈	C₂²×#64408	1	2	yes	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	73	8	no	—
427	C₄⋊C₄	—	146	2	no	—
428	C₄⋊C₄	—	146	4	no	—
429	C₄⋊C₄	—	146	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	146	2	no	—
432	C₂²⋊C₄	—	146	4	no	—
433	C₂²⋊C₄	—	146	4	no	—
434	C₂²⋊C₄	—	146	1	no	—
435	C₄²	—	73	2	no	—
436	C₄²	—	146	2	no	—
437	C₄²	—	146	4	no	—
438	C₄²	—	146	4	no	—
439	C₄²	C₂²×#64408	1	2	yes	—
440	C₂³	—	292	2	no	—
441	C₂³	—	73	1	no	—
442	C₂³	—	73	1	no	—
443	C₂³	—	73	1	no	—
444	C₂³	—	73	1	no	—
445	C₂³	—	73	1	no	—
446	C₂³	—	73	1	no	—
447	C₂³	#14556670	1	1	yes	characteristic
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	292	4	no	—
450	C₂×C₄	—	584	4	no	—
451	C₂×C₄	—	73	1	no	—
452	C₂×C₄	—	73	1	no	—
453	C₂×C₄	—	73	1	no	—
454	C₂×C₄	—	73	1	no	—
455	C₂×C₄	—	73	1	no	—
456	C₂×C₄	—	73	1	no	—
457	C₂×C₄	—	73	1	no	—
458	C₂×C₄	—	73	1	no	—
459	C₂×C₄	—	73	1	no	—
460	C₂×C₄	—	73	1	no	—
461	C₂×C₄	—	73	1	no	—
462	C₂×C₄	—	73	1	no	—
463	C₂×C₄	—	73	1	no	—
464	C₂×C₄	—	73	1	no	—
465	C₂×C₄	—	73	1	no	—
466	C₂×C₄	—	73	1	no	—
467	C₂×C₄	—	73	1	no	—
468	C₂×C₄	—	73	1	no	—
469	C₂×C₄	—	73	1	no	—
470	C₂×C₄	—	73	1	no	—
471	C₂×C₄	—	73	1	no	—
472	C₂×C₄	—	73	1	no	—
473	C₂×C₄	—	146	8	no	—
474	C₂×C₄	—	146	2	no	—
475	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
476	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
477	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
478	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
479	C₂×C₄	#14556670	1	1	yes	characteristic
480	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
481	C₈	—	73	1	no	—
482	C₈	—	73	1	no	—
483	C₈	—	73	1	no	—
484	C₈	—	73	1	no	—
485	C₈	—	73	4	no	—
486	C₈	—	146	8	no	—
487	C₈	C₂×C₄×#64408	1	1	yes	characteristic
488	C₈	C₂×C₄×#64408	1	1	yes	characteristic
489	C₈	C₂×C₄×#64408	1	1	yes	characteristic
490	C₈	C₂×C₄×#64408	1	1	yes	characteristic
491	C₈	C₂×C₄⋊#64408	1	4	yes	—
492	C₂²	—	4	1	no	—
493	C₂²	—	292	1	no	—
494	C₂²	—	292	1	no	—
495	C₂²	—	292	1	no	—
496	C₂²	—	73	1	no	—
497	C₂²	—	73	1	no	—
498	C₂²	—	73	1	no	—
499	C₂²	—	73	1	no	—
500	C₂²	—	146	2	no	—
501	C₂²	—	146	2	no	—
502	C₂²	—	146	2	no	—
503	C₂²	C₄×C₄⋊#64408	1	1	yes	characteristic
504	C₂²	C₄×C₄⋊#64408	1	1	yes	characteristic
505	C₂²	C₂×#14556670	1	1	yes	characteristic
506	C₄	—	4	2	no	—
507	C₄	—	292	2	no	—
508	C₄	—	292	8	no	—
509	C₄	—	73	1	no	—
510	C₄	—	73	1	no	—
511	C₄	—	73	1	no	—
512	C₄	—	73	1	no	—
513	C₄	C₄×C₄⋊#64408	1	1	yes	characteristic
514	C₄	C₄×C₄⋊#64408	1	1	yes	characteristic
515	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
516	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
517	C₂	—	2	1	no	—
518	C₂	—	2	1	no	—
519	C₂	—	2	1	no	—
520	C₂	—	73	2	no	—
521	C₂	—	146	1	no	—
522	C₂	—	146	1	no	—
523	C₂	—	146	1	no	—
524	C₂	C₂×C₄×C₄⋊#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×C₄⋊#64408
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	#405×C₇₃	C₄
socle	C₂×C₇₃	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₇₃	#41
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#20446
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #405

Complements

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

N	H ≅ G/N	type
4. #22625737	C₂	semidirect
5. #22625733	C₂	semidirect
10. C₂×#14556662	C₄	semidirect
11. D₇₃⋊#108	C₄	semidirect
12. D₇₃⋊#108	C₄	semidirect
15. C₂×#14556661	C₄	semidirect
16. #17989597	C₄	semidirect
17. #17989597	C₄	semidirect
20. C₂×#14556660	C₄	semidirect
21. C₂×#14556659	C₄	semidirect
29. #17988545	C₄	semidirect
30. #17988544	C₄	semidirect
31. #17988543	C₄	semidirect
32. #17988542	C₄	semidirect
33. #17988541	C₄	semidirect
36. #405×C₇₃	C₄	semidirect
51. #14556662	C₂×C₄	semidirect
52. #14556662	C₂×C₄	semidirect
53. #14556661	C₂×C₄	semidirect
54. #14556661	C₂×C₄	semidirect
89. #14556502	C₂×C₄	semidirect
90. #14556501	C₂×C₄	semidirect
91. #14556501	C₂×C₄	semidirect
92. C₄×#10596831	C₂×C₄	semidirect
93. C₈×Dic₇₃	C₂×C₄	semidirect
94. C₈×Dic₇₃	C₂×C₄	semidirect
98. #97×C₇₃	C₂×C₄	semidirect
99. C₄×C₈×C₇₃	C₂×C₄	semidirect
270. C₇₃	#20446	semidirect
295. #405	#64408	semidirect
357. #97	C₂×#64408	semidirect
362. C₄×C₈	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₇₃⋊#108	2
C₂×#17989597	2
#22626494	2
#22625737	2
#22625733	2
#22625612	2
#405×D₇₃	2
#20446	73