Subgroups — #33978165

Order 18688.

2168 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623709	C₂	1	1	yes	maximal, characteristic
2	#22622908	C₂	1	2	yes	maximal, complemented
3	#22622602	C₂	1	2	yes	maximal, complemented
4	#22621749	C₂	1	6	yes	maximal, complemented
5	D₄×#11924015	C₂	1	6	yes	maximal, complemented
6	#22621243	C₂	1	3	yes	maximal, complemented
7	#22620869	C₂	1	3	yes	maximal, complemented
8	#22619962	C₂	1	3	yes	maximal, complemented
9	C₂×#17988787	C₂	1	3	yes	maximal, complemented
10	#22619042	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×#41×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556637	—	2	1	no	—
13	C₂²×#11924015	C₂²	1	6	yes	complemented
14	#17989259	—	2	1	no	—
15	#17989259	C₂²	1	2	yes	—
16	D₄×D₂₉₂	—	2	3	no	—
17	D₄×D₂₉₂	C₂²	1	6	yes	—
18	#17989156	—	2	3	no	—
19	#17989137	C₂²	1	3	yes	—
20	C₂×#14556588	C₂²	1	3	yes	—
21	#17988961	C₂²	1	6	yes	complemented
22	#17988935	C₂²	1	6	yes	complemented
23	#17988905	C₂²	1	6	yes	complemented
24	#17988874	C₂²	1	6	yes	complemented
25	#17988872	C₂²	1	1	yes	characteristic, complemented
26	#17988872	C₂²	1	3	yes	complemented
27	#17988818	C₂²	1	12	yes	complemented
28	#17988789	C₂²	1	6	yes	complemented
29	#17988787	C₂²	1	6	yes	complemented
30	#17988787	C₂²	1	3	yes	complemented
31	#17988787	C₂²	1	3	yes	complemented
32	#17988787	C₂²	1	6	yes	complemented
33	#17988787	C₂²	1	6	yes	complemented
34	#17988737	C₂²	1	12	yes	complemented
35	#17988726	C₂²	1	6	yes	complemented
36	Q₈×#10596831	C₂²	1	2	yes	complemented
37	C₄×#11924015	C₂²	1	6	yes	complemented
38	C₄×#11924015	C₂²	1	6	yes	complemented
39	D₄×#10596831	C₂²	1	6	yes	complemented
40	#17988640	C₂²	1	3	yes	complemented
41	C₂×C₄⋊#10596831	C₂²	1	3	yes	complemented
42	C₂×#14556511	C₂²	1	6	yes	complemented
43	Q₈²×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	#557×C₇₃	—	2	1	no	—
45	#557×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	#554×C₇₃	—	2	3	no	—
47	#554×C₇₃	C₂²	1	3	yes	complemented
48	D₄×Q₈×C₇₃	C₂²	1	3	yes	complemented
49	#533×C₇₃	—	2	3	no	—
50	#533×C₇₃	C₂²	1	3	yes	complemented
51	C₄×#41×C₇₃	—	2	1	no	—
52	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×Q₈×C₇₃	C₂²	1	3	yes	complemented
54	#14556637	—	4	8	no	—
55	C₂×#11924029	—	2	2	no	—
56	C₂×#11924028	—	2	3	no	—
57	C₂²×D₂₉₂	—	2	3	no	—
58	C₂²×D₂₉₂	—	2	3	no	—
59	C₂²×D₂₉₂	C₂³	1	6	yes	—
60	C₂×D₄×D₇₃	—	2	6	no	—
61	C₂×#11924015	—	4	12	no	—
62	C₂×#11924015	C₂³	1	6	yes	—
63	C₂×#11924015	C₂³	1	6	yes	—
64	C₂×#11924015	C₂³	1	12	yes	—
65	C₂²×#10596831	C₂³	1	6	yes	—
66	#14556591	C₂³	1	1	yes	characteristic
67	#14556588	—	2	3	no	—
68	#14556588	—	2	3	no	—
69	#14556588	C₂³	1	3	yes	—
70	#14556588	C₂³	1	6	yes	—
71	#14556579	—	2	3	no	—
72	#14556566	—	2	6	no	—
73	#14556566	—	2	6	no	—
74	#14556565	—	2	3	no	—
75	#14556565	C₂³	1	6	yes	—
76	#14556561	—	2	12	no	—
77	C₄×D₂₉₂	—	2	3	no	—
78	C₄×D₂₉₂	C₂³	1	6	yes	—
79	#14556522	C₂³	1	6	yes	—
80	#14556522	C₂³	1	2	yes	—
81	C₄⋊#10596831	C₂³	1	3	yes	—
82	C₄⋊#10596831	C₂³	1	6	yes	—
83	C₄⋊#10596831	C₂³	1	1	yes	characteristic
84	#14556515	C₂³	1	2	yes	—
85	#14556515	C₂³	1	6	yes	—
86	#14556511	C₂³	1	12	yes	—
87	#14556511	C₂³	1	6	yes	—
88	#14556511	C₂³	1	6	yes	—
89	C₂²⋊#10596831	C₂³	1	6	yes	—
90	C₄×#10596831	C₂³	1	6	yes	—
91	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
92	C₂²×Q₈×C₇₃	C₂³	1	3	yes	—
93	C₄⋊Q₈×C₇₃	—	2	3	no	—
94	C₄⋊Q₈×C₇₃	—	2	3	no	—
95	C₄⋊Q₈×C₇₃	C₂³	1	3	yes	—
96	C₄⋊Q₈×C₇₃	C₂³	1	3	yes	—
97	#125×C₇₃	—	2	3	no	—
98	#125×C₇₃	—	2	3	no	—
99	#125×C₇₃	—	2	3	no	—
100	C₂²⋊Q₈×C₇₃	—	2	3	no	—
101	C₂²⋊Q₈×C₇₃	—	2	6	no	—
102	C₂²⋊Q₈×C₇₃	—	2	6	no	—
103	C₂²⋊Q₈×C₇₃	C₂³	1	6	yes	—
104	C₄×Q₈×C₇₃	—	2	1	no	—
105	C₄×Q₈×C₇₃	—	2	1	no	—
106	C₄×Q₈×C₇₃	—	2	3	no	—
107	C₄×Q₈×C₇₃	—	2	3	no	—
108	C₄×Q₈×C₇₃	—	2	3	no	—
109	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
110	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₄×Q₈×C₇₃	C₂³	1	3	yes	—
112	C₄×Q₈×C₇₃	C₂³	1	3	yes	—
113	C₄×Q₈×C₇₃	C₂³	1	3	yes	—
114	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₇₃	—	2	3	no	—
116	C₄×D₄×C₇₃	—	2	3	no	—
117	C₄×D₄×C₇₃	D₄	1	3	yes	—
118	C₄×D₄×C₇₃	C₂³	1	3	yes	—
119	#117×C₇₃	—	2	3	no	—
120	#117×C₇₃	D₄	1	3	yes	—
121	C₂×C₄⋊C₄×C₇₃	—	2	3	no	—
122	C₂×C₄⋊C₄×C₇₃	C₂³	1	3	yes	—
123	C₂×C₄²×C₇₃	—	2	3	no	—
124	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
125	C₂³×D₇₃	—	2	6	no	—
126	#11924029	—	4	8	no	—
127	#11924028	—	4	12	no	—
128	C₂×Dic₁₄₆	—	2	1	no	—
129	C₂×D₂₉₂	—	2	3	no	—
130	C₂×D₂₉₂	—	2	6	no	—
131	C₂×D₂₉₂	—	2	3	no	—
132	C₂×D₂₉₂	—	2	6	no	—
133	C₂×D₂₉₂	—	2	6	no	—
134	C₂×D₂₉₂	—	4	6	no	—
135	C₂×D₂₉₂	—	4	6	no	—
136	C₂×D₂₉₂	—	4	12	no	—
137	C₂×D₂₉₂	—	8	6	no	—
138	C₂×D₂₉₂	C₂⁴	1	6	yes	—
139	C₂×C₂²⋊D₇₃	—	2	6	no	—
140	D₄×D₇₃	—	4	24	no	—
141	C₂×C₄×D₇₃	—	2	6	no	—
142	#11924015	—	2	12	no	—
143	#11924015	—	4	12	no	—
144	#11924015	—	4	6	no	—
145	C₂×#10596831	—	4	6	no	—
146	C₂×#10596831	C₂⁴	1	2	yes	—
147	C₂×#10596831	C₂⁴	1	6	yes	—
148	C₄⋊Dic₇₃	—	2	1	no	—
149	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
150	#11924005	—	2	6	no	—
151	#11924005	—	2	6	no	—
152	#41×C₇₃	SD₁₆	1	8	yes	complemented
153	C₂×Q₈×C₇₃	—	2	3	no	—
154	C₂×Q₈×C₇₃	—	2	3	no	—
155	C₂×Q₈×C₇₃	—	2	6	no	—
156	C₂×Q₈×C₇₃	—	4	3	no	—
157	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₇₃	C₂⁴	1	3	yes	—
159	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
160	C₂×D₄×C₇₃	C₂×D₄	1	3	yes	—
161	C₂²×C₄×C₇₃	—	2	3	no	—
162	C₂²×C₄×C₇₃	—	2	3	no	—
163	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
164	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
165	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
166	C₄⋊C₄×C₇₃	—	2	1	no	—
167	C₄⋊C₄×C₇₃	—	2	3	no	—
168	C₄⋊C₄×C₇₃	—	2	3	no	—
169	C₄⋊C₄×C₇₃	—	2	3	no	—
170	C₄⋊C₄×C₇₃	—	2	3	no	—
171	C₄⋊C₄×C₇₃	—	2	3	no	—
172	C₄⋊C₄×C₇₃	—	2	3	no	—
173	C₄⋊C₄×C₇₃	—	2	3	no	—
174	C₄⋊C₄×C₇₃	—	2	6	no	—
175	C₄⋊C₄×C₇₃	C₂×D₄	1	3	yes	—
176	C₄⋊C₄×C₇₃	C₂×D₄	1	3	yes	—
177	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
178	C₄⋊C₄×C₇₃	C₂⁴	1	3	yes	—
179	C₂²⋊C₄×C₇₃	—	2	6	no	—
180	C₂²⋊C₄×C₇₃	C₂×D₄	1	6	yes	—
181	C₄²×C₇₃	—	2	1	no	—
182	C₄²×C₇₃	—	2	3	no	—
183	C₄²×C₇₃	—	2	3	no	—
184	C₄²×C₇₃	—	2	3	no	—
185	C₄²×C₇₃	C₂×D₄	1	3	yes	—
186	C₄²×C₇₃	C₂×D₄	1	3	yes	—
187	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
188	C₄²×C₇₃	C₂⁴	1	3	yes	—
189	C₂³×C₇₃	C₂²×D₄	1	3	yes	—
190	C₂²×D₇₃	—	2	6	no	—
191	C₂²×D₇₃	—	4	12	no	—
192	C₂²×D₇₃	—	8	6	no	—
193	C₂²×D₇₃	—	8	6	no	—
194	Q₈×C₇₃	—	2	1	no	—
195	Q₈×C₇₃	—	2	3	no	—
196	Q₈×C₇₃	—	2	3	no	—
197	Q₈×C₇₃	—	4	6	no	—
198	Q₈×C₇₃	—	8	3	no	—
199	Q₈×C₇₃	C₂×SD₁₆	1	4	yes	complemented
200	Q₈×C₇₃	H(5,𝔽₂)	1	2	yes	complemented
201	D₄×C₇₃	C₂×SD₁₆	1	12	yes	complemented
202	C₂×C₄×C₇₃	—	2	1	no	—
203	C₂×C₄×C₇₃	—	2	3	no	—
204	C₂×C₄×C₇₃	—	2	3	no	—
205	C₂×C₄×C₇₃	—	2	1	no	—
206	C₂×C₄×C₇₃	—	2	3	no	—
207	C₂×C₄×C₇₃	—	2	3	no	—
208	C₂×C₄×C₇₃	—	4	3	no	—
209	C₂×C₄×C₇₃	—	4	6	no	—
210	C₂×C₄×C₇₃	—	8	3	no	—
211	C₂×C₄×C₇₃	C₂×SD₁₆	1	12	yes	complemented
212	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
214	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
215	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
217	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
218	C₂²⋊D₇₃	—	4	12	no	—
219	C₂×Dic₇₃	—	2	2	no	—
220	D₂₉₂	—	2	6	no	—
221	D₂₉₂	—	2	6	no	—
222	D₂₉₂	—	4	6	no	—
223	D₂₉₂	—	4	12	no	—
224	D₂₉₂	—	4	6	no	—
225	D₂₉₂	—	8	6	no	—
226	D₂₉₂	—	8	6	no	—
227	C₄×D₇₃	—	4	12	no	—
228	Dic₁₄₆	—	4	2	no	—
229	#10596831	—	2	6	no	—
230	#10596831	—	2	2	no	—
231	C₂²×C₇₃	—	2	3	no	—
232	C₂²×C₇₃	—	2	3	no	—
233	C₂²×C₇₃	C₂²×SD₁₆	1	6	yes	—
234	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
235	C₂×D₇₃	—	4	6	no	—
236	C₂×D₇₃	—	4	6	no	—
237	C₂×D₇₃	—	4	6	no	—
238	C₂×D₇₃	—	16	12	no	—
239	C₄×C₇₃	—	2	1	no	—
240	C₄×C₇₃	—	2	3	no	—
241	C₄×C₇₃	—	2	3	no	—
242	C₄×C₇₃	—	2	2	no	—
243	C₄×C₇₃	—	4	1	no	—
244	C₄×C₇₃	—	4	3	no	—
245	C₄×C₇₃	—	4	3	no	—
246	C₄×C₇₃	C₂²×SD₁₆	1	2	yes	—
247	C₄×C₇₃	C₂²×SD₁₆	1	6	yes	—
248	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
249	C₄×C₇₃	#585	1	1	yes	characteristic
250	Dic₇₃	—	4	2	no	—
251	#61951	—	73	1	no	maximal, Sylow
252	C₂×C₇₃	—	2	6	no	—
253	C₂×C₇₃	#3488	1	1	yes	characteristic
254	C₂×C₇₃	C₂³×SD₁₆	1	1	yes	characteristic
255	C₂×C₇₃	#3585	1	1	yes	characteristic
256	D₇₃	—	8	6	no	—
257	#3498	—	73	1	no	—
258	Q₈×#41	D₇₃	1	1	yes	characteristic, complemented
259	#3392	—	73	2	no	—
260	#3362	—	73	2	no	—
261	#3295	—	73	6	no	—
262	D₄×SD₁₆	—	73	6	no	—
263	#3246	—	73	3	no	—
264	#3208	—	73	3	no	—
265	#3103	—	73	3	no	—
266	C₂×#460	—	73	3	no	—
267	#2988	—	73	1	no	—
268	C₇₃	#61951	1	1	yes	characteristic, complemented, Sylow
269	C₂×H(5,𝔽₂)	—	146	1	no	—
270	C₂²×SD₁₆	—	73	6	no	—
271	Q₈²	C₂×D₇₃	1	1	yes	characteristic, complemented
272	#557	—	2	1	no	—
273	#557	C₂×D₇₃	1	1	yes	characteristic, complemented
274	#554	—	2	3	no	—
275	#554	C₂×D₇₃	1	3	yes	complemented
276	#550	—	73	2	no	—
277	#550	—	146	1	no	—
278	D₄×Q₈	C₂×D₇₃	1	3	yes	complemented
279	D₄²	—	73	6	no	—
280	D₄²	—	146	3	no	—
281	#535	—	146	3	no	—
282	#533	—	2	3	no	—
283	#533	C₂×D₇₃	1	3	yes	complemented
284	#532	—	73	3	no	—
285	C₂×#127	—	73	3	no	—
286	C₄×#41	—	2	1	no	—
287	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₂×D₇₃	1	3	yes	complemented
289	#492	—	73	6	no	—
290	#486	—	73	6	no	—
291	#481	—	73	6	no	—
292	#476	—	73	6	no	—
293	#475	—	73	1	no	—
294	#475	—	73	3	no	—
295	#465	—	73	12	no	—
296	#461	—	73	6	no	—
297	#460	—	73	3	no	—
298	#460	—	73	3	no	—
299	#460	—	73	6	no	—
300	#460	—	73	6	no	—
301	#460	—	73	6	no	—
302	#450	—	73	12	no	—
303	#448	—	73	6	no	—
304	C₈×Q₈	—	73	2	no	—
305	C₄×SD₁₆	—	73	6	no	—
306	C₄×SD₁₆	—	73	6	no	—
307	C₈×D₄	—	73	6	no	—
308	#431	—	73	3	no	—
309	C₂×C₄⋊C₈	—	73	3	no	—
310	C₂×#102	—	73	6	no	—
311	H(5,𝔽₂)	—	292	8	no	—
312	C₂×#41	—	146	2	no	—
313	C₂×#41	—	146	3	no	—
314	C₂×#41	C₂²⋊D₇₃	1	1	yes	characteristic
315	C₂²×Q₈	C₂²×D₇₃	1	3	yes	—
316	C₂²×D₄	—	73	6	no	—
317	C₂²×D₄	—	146	6	no	—
318	C₂²×D₄	—	146	3	no	—
319	C₂²×D₄	—	146	3	no	—
320	C₂×SD₁₆	—	292	12	no	—
321	C₂×SD₁₆	—	73	12	no	—
322	C₂×SD₁₆	—	73	6	no	—
323	C₂×SD₁₆	—	73	6	no	—
324	C₂²×C₈	—	73	6	no	—
325	C₄⋊Q₈	—	2	3	no	—
326	C₄⋊Q₈	—	2	3	no	—
327	C₄⋊Q₈	—	73	1	no	—
328	C₄⋊Q₈	C₂²×D₇₃	1	3	yes	—
329	C₄⋊Q₈	C₂²×D₇₃	1	3	yes	—
330	#127	—	73	3	no	—
331	#127	—	73	6	no	—
332	#127	—	146	3	no	—
333	#127	—	146	3	no	—
334	#125	—	2	3	no	—
335	#125	—	2	3	no	—
336	#125	—	2	3	no	—
337	#124	—	146	3	no	—
338	C₂²⋊Q₈	—	2	3	no	—
339	C₂²⋊Q₈	—	2	6	no	—
340	C₂²⋊Q₈	—	2	6	no	—
341	C₂²⋊Q₈	C₂²×D₇₃	1	6	yes	—
342	#121	—	73	6	no	—
343	#121	—	146	3	no	—
344	#121	—	146	6	no	—
345	#121	—	146	6	no	—
346	#120	—	146	12	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	3	no	—
350	C₄×Q₈	—	2	3	no	—
351	C₄×Q₈	—	2	3	no	—
352	C₄×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
353	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
354	C₄×Q₈	C₂²×D₇₃	1	3	yes	—
355	C₄×Q₈	C₂²×D₇₃	1	3	yes	—
356	C₄×Q₈	C₂²×D₇₃	1	3	yes	—
357	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
358	C₄×D₄	—	2	3	no	—
359	C₄×D₄	—	2	3	no	—
360	C₄×D₄	—	73	6	no	—
361	C₄×D₄	—	146	3	no	—
362	C₄×D₄	C₂²⋊D₇₃	1	3	yes	—
363	C₄×D₄	C₂²×D₇₃	1	3	yes	—
364	#117	—	2	3	no	—
365	#117	C₂²⋊D₇₃	1	3	yes	—
366	C₂×C₄⋊C₄	—	2	3	no	—
367	C₂×C₄⋊C₄	C₂²×D₇₃	1	3	yes	—
368	C₂×C₄²	—	2	3	no	—
369	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
370	#106	—	73	2	no	—
371	#106	—	73	6	no	—
372	C₄⋊C₈	—	73	3	no	—
373	C₄⋊C₈	—	73	6	no	—
374	C₄⋊C₈	—	73	1	no	—
375	#103	—	73	2	no	—
376	#103	—	73	6	no	—
377	#102	—	73	6	no	—
378	#102	—	73	12	no	—
379	#102	—	73	6	no	—
380	C₂²⋊C₈	—	73	6	no	—
381	C₄×C₈	—	73	6	no	—
382	C₂⁴	—	146	6	no	—
383	#41	—	292	8	no	—
384	#41	—	292	12	no	—
385	#41	#11924015	1	8	yes	complemented
386	C₂×Q₈	—	2	3	no	—
387	C₂×Q₈	—	2	3	no	—
388	C₂×Q₈	—	2	6	no	—
389	C₂×Q₈	—	4	3	no	—
390	C₂×Q₈	—	146	1	no	—
391	C₂×Q₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
392	C₂×Q₈	C₂³×D₇₃	1	3	yes	—
393	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
394	C₂×D₄	—	292	6	no	—
395	C₂×D₄	—	292	6	no	—
396	C₂×D₄	—	292	24	no	—
397	C₂×D₄	—	292	12	no	—
398	C₂×D₄	—	584	6	no	—
399	C₂×D₄	—	73	6	no	—
400	C₂×D₄	—	146	6	no	—
401	C₂×D₄	—	146	3	no	—
402	C₂×D₄	—	146	6	no	—
403	C₂×D₄	—	146	3	no	—
404	C₂×D₄	—	146	6	no	—
405	C₂×D₄	—	146	6	no	—
406	C₂×D₄	C₂×C₂²⋊D₇₃	1	3	yes	—
407	C₂²×C₄	—	2	3	no	—
408	C₂²×C₄	—	2	3	no	—
409	C₂²×C₄	—	146	6	no	—
410	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
411	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
412	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
413	SD₁₆	—	292	12	no	—
414	SD₁₆	—	292	6	no	—
415	SD₁₆	—	146	12	no	—
416	C₂×C₈	—	292	6	no	—
417	C₂×C₈	—	73	2	no	—
418	C₂×C₈	—	73	6	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	3	no	—
421	C₄⋊C₄	—	2	3	no	—
422	C₄⋊C₄	—	2	3	no	—
423	C₄⋊C₄	—	2	3	no	—
424	C₄⋊C₄	—	2	3	no	—
425	C₄⋊C₄	—	2	3	no	—
426	C₄⋊C₄	—	2	3	no	—
427	C₄⋊C₄	—	2	6	no	—
428	C₄⋊C₄	—	73	2	no	—
429	C₄⋊C₄	—	146	1	no	—
430	C₄⋊C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
431	C₄⋊C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
432	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
433	C₄⋊C₄	C₂³×D₇₃	1	3	yes	—
434	C₂²⋊C₄	—	2	6	no	—
435	C₂²⋊C₄	—	146	6	no	—
436	C₂²⋊C₄	—	146	6	no	—
437	C₂²⋊C₄	C₂×C₂²⋊D₇₃	1	6	yes	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	3	no	—
440	C₄²	—	2	3	no	—
441	C₄²	—	2	3	no	—
442	C₄²	C₂×C₂²⋊D₇₃	1	3	yes	—
443	C₄²	C₂×C₂²⋊D₇₃	1	3	yes	—
444	C₄²	C₂³×D₇₃	1	3	yes	—
445	C₄²	C₂³×D₇₃	1	1	yes	characteristic
446	C₂³	—	292	12	no	—
447	C₂³	—	584	6	no	—
448	C₂³	—	584	6	no	—
449	C₂³	—	146	6	no	—
450	C₂³	C₂²×C₂²⋊D₇₃	1	3	yes	—
451	Q₈	—	2	1	no	—
452	Q₈	—	2	3	no	—
453	Q₈	—	2	3	no	—
454	Q₈	—	4	6	no	—
455	Q₈	—	8	3	no	—
456	Q₈	—	292	2	no	—
457	Q₈	C₂×#11924015	1	4	yes	complemented
458	Q₈	#14556637	1	2	yes	complemented
459	D₄	—	292	6	no	—
460	D₄	—	292	12	no	—
461	D₄	—	292	12	no	—
462	D₄	—	292	6	no	—
463	D₄	—	584	6	no	—
464	D₄	—	584	6	no	—
465	D₄	—	146	6	no	—
466	D₄	—	146	6	no	—
467	D₄	C₂×#11924015	1	12	yes	complemented
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	3	no	—
470	C₂×C₄	—	2	3	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	3	no	—
473	C₂×C₄	—	2	3	no	—
474	C₂×C₄	—	4	3	no	—
475	C₂×C₄	—	4	6	no	—
476	C₂×C₄	—	8	3	no	—
477	C₂×C₄	—	292	12	no	—
478	C₂×C₄	—	146	2	no	—
479	C₂×C₄	C₂×#11924015	1	12	yes	complemented
480	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
481	C₂×C₄	C₂²×C₂²⋊D₇₃	1	3	yes	—
482	C₂×C₄	C₂²×C₂²⋊D₇₃	1	3	yes	—
483	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
484	C₂×C₄	C₂²×C₂²⋊D₇₃	1	3	yes	—
485	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
486	C₈	—	146	6	no	—
487	C₈	—	146	2	no	—
488	C₂²	—	2	3	no	—
489	C₂²	—	2	3	no	—
490	C₂²	—	292	6	no	—
491	C₂²	—	292	6	no	—
492	C₂²	—	292	6	no	—
493	C₂²	—	1168	12	no	—
494	C₂²	C₂²×#11924015	1	6	yes	—
495	C₂²	C₂³×C₂²⋊D₇₃	1	1	yes	characteristic
496	C₄	—	2	3	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	3	no	—
500	C₄	—	4	3	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	3	no	—
503	C₄	—	292	2	no	—
504	C₄	C₂²×#11924015	1	6	yes	—
505	C₄	C₂²×#11924015	1	2	yes	—
506	C₄	C₂×#14556637	1	1	yes	characteristic
507	C₄	#17989423	1	1	yes	characteristic
508	C₂	—	2	6	no	—
509	C₂	—	584	6	no	—
510	C₂	#22623600	1	1	yes	characteristic
511	C₂	C₂³×#11924015	1	1	yes	characteristic
512	C₂	#22624710	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	Q₈×#41×C₇₃	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#22623709	C₂
hypercenter	Q₈×#41	D₇₃
hypocenter	C₇₃	#61951
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ Q₈×#41

Complements

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

N	H ≅ G/N	type
2. #22622908	C₂	semidirect
3. #22622602	C₂	semidirect
4. #22621749	C₂	semidirect
5. D₄×#11924015	C₂	semidirect
6. #22621243	C₂	semidirect
7. #22620869	C₂	semidirect
8. #22619962	C₂	semidirect
9. C₂×#17988787	C₂	semidirect
10. #22619042	C₂	semidirect
11. Q₈×#41×C₇₃	C₂	semidirect
13. C₂²×#11924015	C₂²	semidirect
21. #17988961	C₂²	semidirect
22. #17988935	C₂²	semidirect
23. #17988905	C₂²	semidirect
24. #17988874	C₂²	semidirect
25. #17988872	C₂²	semidirect
26. #17988872	C₂²	semidirect
27. #17988818	C₂²	semidirect
28. #17988789	C₂²	semidirect
29. #17988787	C₂²	semidirect
30. #17988787	C₂²	semidirect
31. #17988787	C₂²	semidirect
32. #17988787	C₂²	semidirect
33. #17988787	C₂²	semidirect
34. #17988737	C₂²	semidirect
35. #17988726	C₂²	semidirect
36. Q₈×#10596831	C₂²	semidirect
37. C₄×#11924015	C₂²	semidirect
38. C₄×#11924015	C₂²	semidirect
39. D₄×#10596831	C₂²	semidirect
40. #17988640	C₂²	semidirect
41. C₂×C₄⋊#10596831	C₂²	semidirect
42. C₂×#14556511	C₂²	semidirect
43. Q₈²×C₇₃	C₂²	semidirect
45. #557×C₇₃	C₂²	semidirect
47. #554×C₇₃	C₂²	semidirect
48. D₄×Q₈×C₇₃	C₂²	semidirect
50. #533×C₇₃	C₂²	semidirect
53. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
152. #41×C₇₃	SD₁₆	semidirect
199. Q₈×C₇₃	C₂×SD₁₆	semidirect
200. Q₈×C₇₃	H(5,𝔽₂)	semidirect
201. D₄×C₇₃	C₂×SD₁₆	semidirect
211. C₂×C₄×C₇₃	C₂×SD₁₆	semidirect
258. Q₈×#41	D₇₃	semidirect
268. C₇₃	#61951	semidirect
271. Q₈²	C₂×D₇₃	semidirect
273. #557	C₂×D₇₃	semidirect
275. #554	C₂×D₇₃	semidirect
278. D₄×Q₈	C₂×D₇₃	semidirect
283. #533	C₂×D₇₃	semidirect
288. C₂×C₄×Q₈	C₂×D₇₃	semidirect
385. #41	#11924015	semidirect
457. Q₈	C₂×#11924015	semidirect
458. Q₈	#14556637	semidirect
467. D₄	C₂×#11924015	semidirect
479. C₂×C₄	C₂×#11924015	semidirect

Maximal subgroups

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

subgroup	index
#22623709	2
#22622908	2
#22622602	2
#22621749	2
D₄×#11924015	2
#22621243	2
#22620869	2
#22619962	2
C₂×#17988787	2
#22619042	2
Q₈×#41×C₇₃	2
#61951	73