Subgroups — #33952673

Order 18688.

4770 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624741	C₂	1	1	yes	maximal, characteristic, complemented
2	#22624718	C₂	1	2	yes	maximal, complemented
3	#22619309	C₂	1	6	yes	maximal, complemented
4	#22619287	C₂	1	6	yes	maximal, complemented
5	#22619279	C₂	1	6	yes	maximal, complemented
6	C₂×#17988764	C₂	1	6	yes	maximal, complemented
7	#22618479	C₂	1	2	yes	maximal, complemented
8	#22618410	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989423	—	2	2	no	—
11	#17989423	C₂²	1	6	yes	—
12	#17989423	C₂²	1	2	yes	—
13	#17989422	—	2	8	no	—
14	C₂×#14556636	—	2	6	no	—
15	C₂×#14556636	C₂²	1	6	yes	—
16	H(5,𝔽₂)×D₇₃	—	2	8	no	—
17	#17989402	—	2	8	no	—
18	#17989395	—	2	8	no	—
19	#17989385	C₂²	1	12	yes	complemented
20	C₂×#14556622	C₂²	1	12	yes	complemented
21	#17989354	C₂²	1	2	yes	complemented
22	#17988769	C₂²	1	12	yes	complemented
23	#17988764	C₂²	1	12	yes	complemented
24	#17988764	C₂²	1	24	yes	complemented
25	#17988759	C₂²	1	4	yes	complemented
26	#17988754	C₂²	1	12	yes	complemented
27	#17988605	C₂²	1	12	yes	complemented
28	C₂×#14556519	C₂²	1	12	yes	complemented
29	#17988571	C₂²	1	6	yes	complemented
30	C₂×#14556508	C₂²	1	6	yes	complemented
31	C₂×2₋¹⁺⁴×C₇₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	1	yes	characteristic
33	#548×C₇₃	—	2	2	no	—
34	#546×C₇₃	—	2	6	no	—
35	#536×C₇₃	C₂²	1	3	yes	complemented
36	#535×C₇₃	C₂²	1	3	yes	complemented
37	#532×C₇₃	C₂²	1	3	yes	complemented
38	C₂×#124×C₇₃	C₂²	1	3	yes	complemented
39	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
40	#14556639	—	2	2	no	—
41	#14556639	C₂³	1	4	yes	—
42	#14556638	—	2	8	no	—
43	#14556638	—	2	12	no	—
44	#14556638	D₄	1	8	yes	complemented
45	#14556637	—	2	8	no	—
46	#14556637	—	2	12	no	—
47	#14556637	D₄	1	8	yes	complemented
48	#14556636	—	2	48	no	—
49	#14556636	—	2	24	no	—
50	#14556636	—	2	12	no	—
51	#14556636	—	2	6	no	—
52	#14556636	—	2	12	no	—
53	#14556636	C₂³	1	12	yes	—
54	C₂×#11924028	—	2	12	no	—
55	C₂×#11924028	C₂³	1	12	yes	—
56	C₂×#11924027	—	2	24	no	—
57	C₂×#11924027	—	2	12	no	—
58	#41×D₇₃	—	2	16	no	—
59	#41×D₇₃	—	2	24	no	—
60	#41×D₇₃	—	2	8	no	—
61	C₂²×C₂²⋊D₇₃	—	2	12	no	—
62	C₂×D₄×D₇₃	—	2	24	no	—
63	C₂×D₄×D₇₃	—	2	12	no	—
64	#14556622	—	2	24	no	—
65	#14556622	C₂³	1	24	yes	complemented
66	#14556621	—	2	12	no	—
67	#14556617	C₂³	1	8	yes	complemented
68	#14556616	—	2	12	no	—
69	#14556611	—	2	24	no	—
70	C₂×#11924018	—	2	12	no	—
71	C₂×#11924015	—	2	12	no	—
72	#14556598	—	2	8	no	—
73	C₂×#11924012	C₂³	1	12	yes	complemented
74	#14556519	C₂³	1	24	yes	complemented
75	#14556519	C₂³	1	8	yes	complemented
76	#14556510	C₂³	1	4	yes	complemented
77	#14556508	C₂³	1	12	yes	complemented
78	2₋¹⁺⁴×C₇₃	—	2	8	no	—
79	H(5,𝔽₂)×C₇₃	—	2	8	no	—
80	C₂×#41×C₇₃	—	2	3	no	—
81	C₂×#41×C₇₃	D₄	1	2	yes	—
82	C₂×#41×C₇₃	C₂³	1	3	yes	—
83	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×#41×C₇₃	C₂³	1	3	yes	complemented
85	C₂²×Q₈×C₇₃	—	2	1	no	—
86	C₂²×Q₈×C₇₃	C₂³	1	3	yes	complemented
87	C₂²×D₄×C₇₃	D₄	1	6	yes	—
88	C₂²×D₄×C₇₃	C₂³	1	3	yes	—
89	C₄⋊Q₈×C₇₃	C₂³	1	3	yes	complemented
90	#127×C₇₃	C₂³	1	3	yes	complemented
91	#124×C₇₃	—	2	6	no	—
92	#124×C₇₃	C₂³	1	3	yes	complemented
93	#124×C₇₃	C₂³	1	6	yes	complemented
94	#124×C₇₃	C₂³	1	1	yes	characteristic, complemented
95	#123×C₇₃	—	2	6	no	—
96	C₂²⋊Q₈×C₇₃	—	2	6	no	—
97	#121×C₇₃	—	2	6	no	—
98	#121×C₇₃	—	2	6	no	—
99	#120×C₇₃	—	2	6	no	—
100	C₄×Q₈×C₇₃	—	2	1	no	—
101	C₄×D₄×C₇₃	—	2	3	no	—
102	C₄×D₄×C₇₃	—	2	6	no	—
103	#117×C₇₃	C₂³	1	3	yes	complemented
104	C₂×C₂²⋊C₄×C₇₃	—	2	6	no	—
105	C₂×C₄²×C₇₃	C₂³	1	3	yes	complemented
106	C₂³×D₇₃	—	2	12	no	—
107	#11924029	—	2	8	no	—
108	#11924029	—	2	8	no	—
109	#11924028	—	2	24	no	—
110	#11924028	—	2	24	no	—
111	#11924028	—	2	12	no	—
112	#11924028	—	2	8	no	—
113	#11924028	—	2	12	no	—
114	#11924028	C₂×D₄	1	24	yes	—
115	#11924028	C₂⁴	1	8	yes	—
116	#11924027	—	2	48	no	—
117	#11924027	—	2	48	no	—
118	#11924027	—	2	24	no	—
119	#11924027	—	2	24	no	—
120	C₂×Dic₁₄₆	—	2	12	no	—
121	C₂×Dic₁₄₆	C₂×D₄	1	12	yes	—
122	Q₈×D₇₃	—	2	8	no	—
123	Q₈×D₇₃	—	2	8	no	—
124	C₂×D₂₉₂	—	2	12	no	—
125	C₂×D₂₉₂	C₂×D₄	1	12	yes	—
126	C₂×C₂²⋊D₇₃	—	2	48	no	—
127	C₂×C₂²⋊D₇₃	—	2	24	no	—
128	C₂×C₂²⋊D₇₃	—	2	24	no	—
129	C₂×C₂²⋊D₇₃	—	2	12	no	—
130	D₄×D₇₃	—	2	48	no	—
131	D₄×D₇₃	—	2	48	no	—
132	D₄×D₇₃	—	2	24	no	—
133	D₄×D₇₃	—	2	24	no	—
134	C₂²×Dic₇₃	—	2	12	no	—
135	C₂×C₄×D₇₃	—	2	24	no	—
136	C₂×C₄×D₇₃	—	2	12	no	—
137	#11924018	—	2	24	no	—
138	#11924016	—	2	8	no	—
139	#11924015	—	2	24	no	—
140	#11924013	—	2	8	no	—
141	#11924012	—	2	12	no	—
142	#11924012	C₂⁴	1	8	yes	—
143	C₂×#10596831	—	2	12	no	—
144	C₂⁴×C₇₃	C₂×D₄	1	6	yes	—
145	#41×C₇₃	—	2	8	no	—
146	#41×C₇₃	—	2	12	no	—
147	#41×C₇₃	—	2	12	no	—
148	#41×C₇₃	—	4	12	no	—
149	#41×C₇₃	C₂×D₄	1	8	yes	—
150	C₂×Q₈×C₇₃	—	2	3	no	—
151	C₂×Q₈×C₇₃	—	2	12	no	—
152	C₂×Q₈×C₇₃	—	4	4	no	—
153	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₇₃	C₂⁴	1	3	yes	—
155	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
156	C₂×D₄×C₇₃	—	2	24	no	—
157	C₂×D₄×C₇₃	—	2	3	no	—
158	C₂×D₄×C₇₃	—	2	6	no	—
159	C₂×D₄×C₇₃	—	2	12	no	—
160	C₂×D₄×C₇₃	C₂×D₄	1	6	yes	—
161	C₂×D₄×C₇₃	C₂×D₄	1	6	yes	—
162	C₂×D₄×C₇₃	C₂×D₄	1	3	yes	—
163	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
164	C₂×D₄×C₇₃	C₂⁴	1	3	yes	—
165	C₂²×C₄×C₇₃	—	2	3	no	—
166	C₂²×C₄×C₇₃	—	2	3	no	—
167	C₂²×C₄×C₇₃	—	2	3	no	—
168	C₂²×C₄×C₇₃	C₂×D₄	1	6	yes	—
169	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
170	C₄⋊C₄×C₇₃	—	2	3	no	—
171	C₄⋊C₄×C₇₃	—	2	6	no	—
172	C₂²⋊C₄×C₇₃	—	2	6	no	—
173	C₂²⋊C₄×C₇₃	—	2	12	no	—
174	C₂²⋊C₄×C₇₃	—	2	3	no	—
175	C₂²⋊C₄×C₇₃	—	2	2	no	—
176	C₄²×C₇₃	—	2	3	no	—
177	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
178	C₄²×C₇₃	C₂⁴	1	3	yes	—
179	C₂³×C₇₃	—	2	12	no	—
180	C₂³×C₇₃	—	2	1	no	—
181	C₂³×C₇₃	—	8	6	no	—
182	C₂³×C₇₃	C₂²×D₄	1	6	yes	—
183	C₂³×C₇₃	C₂²×D₄	1	3	yes	—
184	C₂²×D₇₃	—	2	24	no	—
185	C₂²×D₇₃	—	2	12	no	—
186	C₂²×D₇₃	—	16	12	no	—
187	Q₈×C₇₃	—	2	2	no	—
188	Q₈×C₇₃	—	2	6	no	—
189	Q₈×C₇₃	—	4	6	no	—
190	Q₈×C₇₃	#120	1	4	yes	—
191	D₄×C₇₃	—	2	12	no	—
192	D₄×C₇₃	—	2	12	no	—
193	D₄×C₇₃	—	2	6	no	—
194	D₄×C₇₃	—	2	2	no	—
195	D₄×C₇₃	—	4	6	no	—
196	D₄×C₇₃	—	8	6	no	—
197	D₄×C₇₃	#120	1	12	yes	—
198	C₂×C₄×C₇₃	—	2	12	no	—
199	C₂×C₄×C₇₃	—	2	1	no	—
200	C₂×C₄×C₇₃	—	2	3	no	—
201	C₂×C₄×C₇₃	—	2	3	no	—
202	C₂×C₄×C₇₃	—	4	6	no	—
203	C₂×C₄×C₇₃	—	4	6	no	—
204	C₂×C₄×C₇₃	—	8	3	no	—
205	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
206	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
208	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
209	C₂²⋊D₇₃	—	2	48	no	—
210	C₂²⋊D₇₃	—	2	24	no	—
211	C₂²⋊D₇₃	—	2	8	no	—
212	C₂×Dic₇₃	—	2	24	no	—
213	C₂×Dic₇₃	—	2	12	no	—
214	D₂₉₂	—	2	8	no	—
215	D₂₉₂	—	2	12	no	—
216	D₂₉₂	C₂²×D₄	1	8	yes	—
217	C₄×D₇₃	—	2	16	no	—
218	C₄×D₇₃	—	2	24	no	—
219	C₄×D₇₃	—	2	8	no	—
220	Dic₁₄₆	—	2	8	no	—
221	Dic₁₄₆	—	2	12	no	—
222	Dic₁₄₆	C₂²×D₄	1	8	yes	—
223	#10596831	—	2	8	no	—
224	C₂²×C₇₃	—	2	6	no	—
225	C₂²×C₇₃	—	4	3	no	—
226	C₂²×C₇₃	—	4	6	no	—
227	C₂²×C₇₃	—	4	2	no	—
228	C₂²×C₇₃	—	4	1	no	—
229	C₂²×C₇₃	—	8	12	no	—
230	C₂²×C₇₃	C₂×#120	1	6	yes	—
231	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
232	C₂×D₇₃	—	2	8	no	—
233	C₂×D₇₃	—	8	12	no	—
234	C₂×D₇₃	—	8	24	no	—
235	C₄×C₇₃	—	2	2	no	—
236	C₄×C₇₃	—	4	1	no	—
237	C₄×C₇₃	—	4	3	no	—
238	C₄×C₇₃	—	4	3	no	—
239	C₄×C₇₃	C₂×#120	1	6	yes	—
240	C₄×C₇₃	C₂³×D₄	1	2	yes	—
241	Dic₇₃	—	2	8	no	—
242	#60389	—	73	1	no	maximal, Sylow
243	C₂×C₇₃	—	2	1	no	—
244	C₂×C₇₃	—	2	6	no	—
245	C₂×C₇₃	—	4	6	no	—
246	C₂×C₇₃	—	8	1	no	—
247	C₂×C₇₃	C₂²×#120	1	1	yes	characteristic
248	D₇₃	—	4	8	no	—
249	H(7,𝔽₂)	—	73	1	no	—
250	#3586	—	73	2	no	—
251	#3500	D₇₃	1	1	yes	characteristic, complemented
252	#3022	—	73	6	no	—
253	#3019	—	73	6	no	—
254	#3018	—	73	6	no	—
255	C₂×#455	—	73	6	no	—
256	#2901	—	73	2	no	—
257	#2888	—	73	1	no	—
258	C₇₃	#60389	1	1	yes	characteristic, complemented, Sylow
259	#585	—	73	2	no	—
260	#585	—	73	6	no	—
261	#585	—	146	8	no	—
262	#585	—	146	2	no	—
263	C₂×2₋¹⁺⁴	C₂×D₇₃	1	1	yes	characteristic, complemented
264	C₂×H(5,𝔽₂)	—	73	6	no	—
265	C₂×H(5,𝔽₂)	—	146	8	no	—
266	C₂×H(5,𝔽₂)	—	146	6	no	—
267	C₂×H(5,𝔽₂)	C₂×D₇₃	1	1	yes	characteristic
268	#578	—	146	8	no	—
269	#577	—	146	8	no	—
270	#575	—	73	12	no	—
271	C₂×#137	—	73	12	no	—
272	#568	—	73	2	no	—
273	#548	—	2	2	no	—
274	#546	—	2	6	no	—
275	#536	C₂×D₇₃	1	3	yes	complemented
276	#535	C₂×D₇₃	1	3	yes	complemented
277	#532	C₂×D₇₃	1	3	yes	complemented
278	C₂×#124	C₂×D₇₃	1	3	yes	complemented
279	C₄×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
280	#456	—	73	12	no	—
281	#455	—	73	12	no	—
282	#455	—	73	24	no	—
283	#454	—	73	4	no	—
284	#453	—	73	12	no	—
285	#421	—	73	12	no	—
286	C₂×#104	—	73	12	no	—
287	#413	—	73	6	no	—
288	C₂×#100	—	73	6	no	—
289	2₋¹⁺⁴	—	2	8	no	—
290	2₋¹⁺⁴	—	73	8	no	—
291	2₋¹⁺⁴	—	73	4	no	—
292	2₋¹⁺⁴	—	146	12	no	—
293	2₋¹⁺⁴	—	146	8	no	—
294	2₋¹⁺⁴	—	146	2	no	—
295	H(5,𝔽₂)	—	2	8	no	—
296	H(5,𝔽₂)	—	73	8	no	—
297	H(5,𝔽₂)	—	73	12	no	—
298	H(5,𝔽₂)	—	146	24	no	—
299	H(5,𝔽₂)	—	146	48	no	—
300	H(5,𝔽₂)	—	146	12	no	—
301	H(5,𝔽₂)	—	146	8	no	—
302	H(5,𝔽₂)	—	146	12	no	—
303	H(5,𝔽₂)	—	146	12	no	—
304	H(5,𝔽₂)	—	146	6	no	—
305	C₂×#41	—	2	3	no	—
306	C₂×#41	—	73	12	no	—
307	C₂×#41	—	146	12	no	—
308	C₂×#41	—	146	24	no	—
309	C₂×#41	—	146	24	no	—
310	C₂×#41	—	146	16	no	—
311	C₂×#41	—	146	8	no	—
312	C₂×#41	—	146	12	no	—
313	C₂×#41	C₂²⋊D₇₃	1	2	yes	—
314	C₂×#41	C₂²×D₇₃	1	3	yes	—
315	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
316	C₂×#41	C₂²×D₇₃	1	3	yes	complemented
317	C₂²×Q₈	—	2	1	no	—
318	C₂²×Q₈	C₂²×D₇₃	1	3	yes	complemented
319	C₂²×D₄	—	146	12	no	—
320	C₂²×D₄	—	146	24	no	—
321	C₂²×D₄	—	146	12	no	—
322	C₂²×D₄	C₂²⋊D₇₃	1	6	yes	—
323	C₂²×D₄	C₂²×D₇₃	1	3	yes	—
324	#137	—	73	24	no	—
325	#137	—	146	24	no	—
326	#137	—	146	12	no	—
327	AGL(1,ℤ/8)	—	73	8	no	—
328	AGL(1,ℤ/8)	—	146	12	no	—
329	#135	—	146	24	no	—
330	C₂×Q₁₆	—	146	12	no	—
331	C₂×SD₁₆	—	146	12	no	—
332	#131	—	146	8	no	—
333	C₂×M₁₆	—	73	12	no	—
334	C₄⋊Q₈	C₂²×D₇₃	1	3	yes	complemented
335	#127	C₂²×D₇₃	1	3	yes	complemented
336	#124	—	2	6	no	—
337	#124	C₂²×D₇₃	1	3	yes	complemented
338	#124	C₂²×D₇₃	1	6	yes	complemented
339	#124	C₂²×D₇₃	1	1	yes	characteristic, complemented
340	#123	—	2	6	no	—
341	C₂²⋊Q₈	—	2	6	no	—
342	#121	—	2	6	no	—
343	#121	—	2	6	no	—
344	#120	—	2	6	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×D₄	—	2	3	no	—
347	C₄×D₄	—	2	6	no	—
348	#117	C₂²×D₇₃	1	3	yes	complemented
349	C₂×C₂²⋊C₄	—	2	6	no	—
350	C₂×C₄²	C₂²×D₇₃	1	3	yes	complemented
351	#104	—	73	8	no	—
352	#104	—	73	24	no	—
353	#101	—	73	4	no	—
354	#100	—	73	12	no	—
355	C₂⁴	—	146	12	no	—
356	C₂⁴	C₂×C₂²⋊D₇₃	1	6	yes	—
357	#41	—	2	8	no	—
358	#41	—	2	12	no	—
359	#41	—	2	12	no	—
360	#41	—	4	12	no	—
361	#41	—	73	24	no	—
362	#41	—	73	8	no	—
363	#41	—	146	24	no	—
364	#41	—	146	24	no	—
365	#41	—	146	24	no	—
366	#41	—	146	48	no	—
367	#41	—	146	48	no	—
368	#41	—	146	8	no	—
369	#41	—	146	8	no	—
370	#41	—	146	24	no	—
371	#41	—	146	12	no	—
372	#41	—	146	12	no	—
373	#41	—	146	8	no	—
374	#41	D₄×D₇₃	1	8	yes	—
375	C₂×Q₈	—	2	3	no	—
376	C₂×Q₈	—	2	12	no	—
377	C₂×Q₈	—	4	4	no	—
378	C₂×Q₈	—	73	12	no	—
379	C₂×Q₈	—	146	12	no	—
380	C₂×Q₈	—	146	8	no	—
381	C₂×Q₈	—	146	8	no	—
382	C₂×Q₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
383	C₂×Q₈	C₂³×D₇₃	1	3	yes	—
384	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
385	C₂×D₄	—	2	24	no	—
386	C₂×D₄	—	2	3	no	—
387	C₂×D₄	—	2	6	no	—
388	C₂×D₄	—	2	12	no	—
389	C₂×D₄	—	73	12	no	—
390	C₂×D₄	—	146	12	no	—
391	C₂×D₄	—	146	24	no	—
392	C₂×D₄	—	146	48	no	—
393	C₂×D₄	—	146	48	no	—
394	C₂×D₄	—	146	48	no	—
395	C₂×D₄	—	146	24	no	—
396	C₂×D₄	—	146	12	no	—
397	C₂×D₄	—	146	24	no	—
398	C₂×D₄	—	146	24	no	—
399	C₂×D₄	C₂×C₂²⋊D₇₃	1	6	yes	—
400	C₂×D₄	C₂×C₂²⋊D₇₃	1	6	yes	—
401	C₂×D₄	C₂×C₂²⋊D₇₃	1	3	yes	—
402	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
403	C₂×D₄	C₂³×D₇₃	1	3	yes	—
404	C₂²×C₄	—	2	3	no	—
405	C₂²×C₄	—	2	3	no	—
406	C₂²×C₄	—	2	3	no	—
407	C₂²×C₄	—	146	24	no	—
408	C₂²×C₄	—	146	12	no	—
409	C₂²×C₄	—	146	12	no	—
410	C₂²×C₄	C₂×C₂²⋊D₇₃	1	6	yes	—
411	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
412	Q₁₆	—	146	24	no	—
413	SD₁₆	—	146	8	no	—
414	SD₁₆	—	146	24	no	—
415	D₈	—	146	8	no	—
416	M₁₆	—	73	8	no	—
417	M₁₆	—	146	12	no	—
418	C₂×C₈	—	146	12	no	—
419	C₄⋊C₄	—	2	3	no	—
420	C₄⋊C₄	—	2	6	no	—
421	C₂²⋊C₄	—	2	6	no	—
422	C₂²⋊C₄	—	2	12	no	—
423	C₂²⋊C₄	—	2	3	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₄²	—	2	3	no	—
426	C₄²	C₂³×D₇₃	1	1	yes	characteristic
427	C₄²	C₂³×D₇₃	1	3	yes	—
428	C₂³	—	2	12	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	8	6	no	—
431	C₂³	—	1168	12	no	—
432	C₂³	—	146	24	no	—
433	C₂³	—	146	12	no	—
434	C₂³	C₂²×C₂²⋊D₇₃	1	6	yes	—
435	C₂³	C₂²×C₂²⋊D₇₃	1	3	yes	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	6	no	—
438	Q₈	—	4	6	no	—
439	Q₈	—	73	8	no	—
440	Q₈	—	146	8	no	—
441	Q₈	—	146	12	no	—
442	Q₈	#14556559	1	4	yes	—
443	D₄	—	2	12	no	—
444	D₄	—	2	6	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	12	no	—
447	D₄	—	4	6	no	—
448	D₄	—	8	6	no	—
449	D₄	—	73	8	no	—
450	D₄	—	146	8	no	—
451	D₄	—	146	48	no	—
452	D₄	—	146	8	no	—
453	D₄	—	146	24	no	—
454	D₄	—	146	12	no	—
455	D₄	#14556559	1	12	yes	—
456	C₂×C₄	—	2	12	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	3	no	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	4	6	no	—
461	C₂×C₄	—	4	6	no	—
462	C₂×C₄	—	8	3	no	—
463	C₂×C₄	—	146	16	no	—
464	C₂×C₄	—	146	24	no	—
465	C₂×C₄	—	146	12	no	—
466	C₂×C₄	—	146	8	no	—
467	C₂×C₄	—	146	24	no	—
468	C₂×C₄	C₂×D₄×D₇₃	1	12	yes	—
469	C₂×C₄	C₂²×C₂²⋊D₇₃	1	2	yes	—
470	C₂×C₄	C₂²×C₂²⋊D₇₃	1	3	yes	—
471	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
472	C₈	—	146	8	no	—
473	C₂²	—	2	6	no	—
474	C₂²	—	4	3	no	—
475	C₂²	—	4	6	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	8	12	no	—
479	C₂²	—	584	12	no	—
480	C₂²	—	584	24	no	—
481	C₂²	—	146	8	no	—
482	C₂²	C₂×#14556559	1	6	yes	—
483	C₂²	C₂³×C₂²⋊D₇₃	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	3	no	—
487	C₄	—	4	3	no	—
488	C₄	—	146	8	no	—
489	C₄	C₂×#14556559	1	6	yes	—
490	C₄	C₂²×D₄×D₇₃	1	2	yes	—
491	C₂	—	2	1	no	—
492	C₂	—	2	6	no	—
493	C₂	—	4	6	no	—
494	C₂	—	8	1	no	—
495	C₂	—	292	8	no	—
496	C₂	C₂²×#14556559	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×#14556559
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3500	C₂
socle	C₂×C₇₃	C₂²×#120
hypercenter	#3500	D₇₃
hypocenter	C₇₃	#60389
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ #3500

Complements

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

N	H ≅ G/N	type
1. #22624741	C₂	semidirect
2. #22624718	C₂	semidirect
3. #22619309	C₂	semidirect
4. #22619287	C₂	semidirect
5. #22619279	C₂	semidirect
6. C₂×#17988764	C₂	semidirect
7. #22618479	C₂	semidirect
8. #22618410	C₂	semidirect
9. C₇₃×#3500	C₂	semidirect
19. #17989385	C₂²	semidirect
20. C₂×#14556622	C₂²	semidirect
21. #17989354	C₂²	semidirect
22. #17988769	C₂²	semidirect
23. #17988764	C₂²	semidirect
24. #17988764	C₂²	semidirect
25. #17988759	C₂²	semidirect
26. #17988754	C₂²	semidirect
27. #17988605	C₂²	semidirect
28. C₂×#14556519	C₂²	semidirect
29. #17988571	C₂²	semidirect
30. C₂×#14556508	C₂²	semidirect
31. C₂×2₋¹⁺⁴×C₇₃	C₂²	semidirect
35. #536×C₇₃	C₂²	semidirect
36. #535×C₇₃	C₂²	semidirect
37. #532×C₇₃	C₂²	semidirect
38. C₂×#124×C₇₃	C₂²	semidirect
39. C₄×#41×C₇₃	C₂²	semidirect
44. #14556638	D₄	semidirect
47. #14556637	D₄	semidirect
65. #14556622	C₂³	semidirect
67. #14556617	C₂³	semidirect
73. C₂×#11924012	C₂³	semidirect
74. #14556519	C₂³	semidirect
75. #14556519	C₂³	semidirect
76. #14556510	C₂³	semidirect
77. #14556508	C₂³	semidirect
84. C₂×#41×C₇₃	C₂³	semidirect
86. C₂²×Q₈×C₇₃	C₂³	semidirect
89. C₄⋊Q₈×C₇₃	C₂³	semidirect
90. #127×C₇₃	C₂³	semidirect
92. #124×C₇₃	C₂³	semidirect
93. #124×C₇₃	C₂³	semidirect
94. #124×C₇₃	C₂³	semidirect
103. #117×C₇₃	C₂³	semidirect
105. C₂×C₄²×C₇₃	C₂³	semidirect
251. #3500	D₇₃	semidirect
258. C₇₃	#60389	semidirect
263. C₂×2₋¹⁺⁴	C₂×D₇₃	semidirect
275. #536	C₂×D₇₃	semidirect
276. #535	C₂×D₇₃	semidirect
277. #532	C₂×D₇₃	semidirect
278. C₂×#124	C₂×D₇₃	semidirect
279. C₄×#41	C₂×D₇₃	semidirect
316. C₂×#41	C₂²×D₇₃	semidirect
318. C₂²×Q₈	C₂²×D₇₃	semidirect
334. C₄⋊Q₈	C₂²×D₇₃	semidirect
335. #127	C₂²×D₇₃	semidirect
337. #124	C₂²×D₇₃	semidirect
338. #124	C₂²×D₇₃	semidirect
339. #124	C₂²×D₇₃	semidirect
348. #117	C₂²×D₇₃	semidirect
350. C₂×C₄²	C₂²×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22624741	2
#22624718	2
#22619309	2
#22619287	2
#22619279	2
C₂×#17988764	2
#22618479	2
#22618410	2
C₇₃×#3500	2
#60389	73