Subgroups — #33994378

Order 18688.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624016	C₂	1	2	yes	maximal, complemented
2	#22623963	C₂	1	6	yes	maximal, complemented
3	#22623937	C₂	1	2	yes	maximal, complemented
4	#22623892	C₂	1	6	yes	maximal, complemented
5	#22623842	C₂	1	3	yes	maximal, complemented
6	#22623807	C₂	1	3	yes	maximal, complemented
7	#22623750	C₂	1	1	yes	maximal, characteristic, complemented
8	#22623709	C₂	1	1	yes	maximal, characteristic, complemented
9	#22623666	C₂	1	6	yes	maximal, complemented
10	#22623600	C₂	1	2	yes	maximal, complemented
11	#22623557	C₂	1	2	yes	maximal, complemented
12	#22623541	C₂	1	6	yes	maximal, complemented
13	#22623526	C₂	1	2	yes	maximal, complemented
14	D₄×#11924028	C₂	1	6	yes	maximal, complemented
15	#22623347	C₂	1	6	yes	maximal, complemented
16	#22623227	C₂	1	3	yes	maximal, complemented
17	C₂×#17989137	C₂	1	3	yes	maximal, complemented
18	C₄×#14556637	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×#41×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14556637	C₂²	1	2	yes	—
21	C₂²×#11924028	C₂²	1	6	yes	complemented
22	#17989322	C₂²	1	6	yes	complemented
23	#17989322	C₂²	1	6	yes	complemented
24	Q₈×Dic₁₄₆	C₂²	1	2	yes	complemented
25	#17989316	C₂²	1	2	yes	complemented
26	#17989310	C₂²	1	6	yes	complemented
27	#17989302	C₂²	1	6	yes	complemented
28	#17989300	C₂²	1	12	yes	complemented
29	#17989297	C₂²	1	6	yes	complemented
30	#17989294	C₂²	1	6	yes	complemented
31	#17989285	C₂²	1	12	yes	complemented
32	#17989283	C₂²	1	12	yes	complemented
33	#17989281	C₂²	1	12	yes	complemented
34	#17989261	C₂²	1	24	yes	complemented
35	#17989259	C₂²	1	2	yes	complemented
36	#17989259	C₂²	1	2	yes	complemented
37	#17989258	C₂²	1	6	yes	complemented
38	#17989258	C₂²	1	6	yes	complemented
39	#17989256	C₂²	1	4	yes	complemented
40	D₄×Dic₁₄₆	C₂²	1	6	yes	complemented
41	#17989248	C₂²	1	4	yes	complemented
42	#17989246	C₂²	1	12	yes	complemented
43	#17989242	C₂²	1	6	yes	complemented
44	#17989238	C₂²	1	12	yes	complemented
45	#17989233	C₂²	1	12	yes	complemented
46	#17989233	C₂²	1	12	yes	complemented
47	#17989227	C₂²	1	24	yes	complemented
48	#17989225	C₂²	1	12	yes	complemented
49	D₄×D₂₉₂	C₂²	1	6	yes	complemented
50	D₄×D₂₉₂	C₂²	1	6	yes	complemented
51	D₄×C₂²⋊D₇₃	C₂²	1	12	yes	complemented
52	#17989215	C₂²	1	6	yes	complemented
53	#17989209	C₂²	1	12	yes	complemented
54	#17989208	C₂²	1	12	yes	complemented
55	#17989192	C₂²	1	12	yes	complemented
56	#17989188	C₂²	1	12	yes	complemented
57	#17989170	C₂²	1	24	yes	complemented
58	#17989165	C₂²	1	6	yes	complemented
59	#17989156	C₂²	1	6	yes	complemented
60	#17989151	C₂²	1	6	yes	complemented
61	#17989144	C₂²	1	3	yes	complemented
62	#17989144	C₂²	1	3	yes	complemented
63	#17989144	C₂²	1	1	yes	characteristic, complemented
64	#17989137	C₂²	1	6	yes	complemented
65	#17989137	C₂²	1	6	yes	complemented
66	#17989137	C₂²	1	6	yes	complemented
67	#17989137	C₂²	1	3	yes	complemented
68	#17989137	C₂²	1	6	yes	complemented
69	#17989137	C₂²	1	3	yes	complemented
70	#17989137	C₂²	1	6	yes	complemented
71	#17989137	C₂²	1	6	yes	complemented
72	#17989137	C₂²	1	6	yes	complemented
73	#17989137	C₂²	1	3	yes	complemented
74	#17989134	C₂²	1	12	yes	complemented
75	C₂×#14556591	C₂²	1	3	yes	complemented
76	C₂×#14556588	C₂²	1	3	yes	complemented
77	#17989124	C₂²	1	12	yes	complemented
78	#17989121	C₂²	1	6	yes	complemented
79	#17989121	C₂²	1	6	yes	complemented
80	#17989121	C₂²	1	6	yes	complemented
81	#17989121	C₂²	1	6	yes	complemented
82	#17989121	C₂²	1	6	yes	complemented
83	#17989121	C₂²	1	6	yes	complemented
84	C₂×#14556579	C₂²	1	6	yes	complemented
85	#17989098	C₂²	1	6	yes	complemented
86	#17989098	C₂²	1	6	yes	complemented
87	#17989098	C₂²	1	6	yes	complemented
88	#17989096	C₂²	1	24	yes	complemented
89	C₂×#14556565	C₂²	1	6	yes	complemented
90	C₂×#14556565	C₂²	1	6	yes	complemented
91	#17989070	C₂²	1	2	yes	—
92	#17989069	C₂²	1	4	yes	complemented
93	#17989067	C₂²	1	6	yes	complemented
94	#17989061	C₂²	1	6	yes	complemented
95	#17989059	C₂²	1	12	yes	complemented
96	C₄×#11924029	C₂²	1	4	yes	complemented
97	C₄×#11924028	C₂²	1	6	yes	complemented
98	C₄×#11924028	C₂²	1	6	yes	complemented
99	C₄×#11924028	C₂²	1	6	yes	complemented
100	C₂×C₄×D₂₉₂	C₂²	1	6	yes	complemented
101	C₂×C₄×D₂₉₂	C₂²	1	6	yes	complemented
102	C₄×D₄×D₇₃	C₂²	1	12	yes	complemented
103	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
104	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
105	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
106	C₄×#41×C₇₃	C₂²	1	3	yes	complemented
107	C₄×#41×C₇₃	C₂²	1	3	yes	complemented
108	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
109	C₄×#41×C₇₃	C₂²	1	3	yes	complemented
110	C₄×#41×C₇₃	C₂²	1	3	yes	complemented
111	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×D₄×C₇₃	C₂²	1	3	yes	complemented
115	C₂×C₄×D₄×C₇₃	C₂²	1	3	yes	complemented
116	C₂×#117×C₇₃	C₂²	1	3	yes	complemented
117	C₂²×C₄²×C₇₃	C₂²	1	3	yes	complemented
118	#14556637	—	2	16	no	—
119	C₂×#11924029	C₂³	1	4	yes	—
120	C₂×#11924028	—	4	24	no	—
121	C₂×#11924028	C₂³	1	6	yes	—
122	C₂×#11924028	C₂³	1	6	yes	—
123	C₂×#11924028	C₂³	1	12	yes	—
124	C₂×#11924028	C₂³	1	12	yes	—
125	C₂×#11924028	C₂³	1	12	yes	—
126	C₂×#11924028	C₂³	1	6	yes	—
127	C₂²×Dic₁₄₆	C₂³	1	6	yes	—
128	C₂²×D₂₉₂	C₂³	1	6	yes	—
129	C₂²×D₂₉₂	C₂³	1	6	yes	—
130	C₂²×D₂₉₂	C₂³	1	6	yes	—
131	C₂²×C₂²⋊D₇₃	C₂³	1	12	yes	—
132	C₂×D₄×D₇₃	C₂³	1	12	yes	—
133	C₂²×C₄×D₇₃	C₂³	1	12	yes	—
134	#14556591	C₂³	1	3	yes	—
135	#14556591	C₂³	1	6	yes	—
136	#14556591	C₂³	1	6	yes	—
137	#14556591	C₂³	1	6	yes	—
138	#14556591	C₂³	1	1	yes	characteristic
139	#14556591	C₂³	1	1	yes	characteristic
140	#14556590	C₂³	1	12	yes	—
141	#14556588	C₂³	1	3	yes	—
142	#14556588	C₂³	1	6	yes	—
143	#14556588	C₂³	1	6	yes	—
144	#14556588	C₂³	1	6	yes	—
145	#14556587	C₂³	1	12	yes	—
146	#14556586	C₂³	1	24	yes	—
147	#14556585	C₂³	1	12	yes	—
148	#14556585	C₂³	1	12	yes	—
149	#14556583	C₂³	1	2	yes	—
150	#14556583	C₂³	1	6	yes	—
151	#14556583	C₂³	1	6	yes	—
152	#14556582	C₂³	1	12	yes	—
153	#14556580	C₂³	1	12	yes	—
154	#14556579	C₂³	1	6	yes	—
155	#14556579	C₂³	1	6	yes	—
156	#14556579	C₂³	1	6	yes	—
157	#14556579	C₂³	1	12	yes	—
158	#14556579	C₂³	1	12	yes	—
159	#14556579	C₂³	1	12	yes	—
160	#14556577	C₂³	1	24	yes	—
161	#14556576	C₂³	1	24	yes	—
162	#14556576	C₂³	1	24	yes	—
163	#14556574	C₂³	1	12	yes	—
164	#14556574	C₂³	1	12	yes	—
165	#14556574	C₂³	1	12	yes	—
166	#14556573	C₂³	1	24	yes	—
167	#14556570	C₂³	1	2	yes	—
168	#14556570	C₂³	1	2	yes	—
169	#14556570	C₂³	1	6	yes	—
170	#14556570	C₂³	1	6	yes	—
171	#14556570	C₂³	1	6	yes	—
172	#14556570	C₂³	1	6	yes	—
173	#14556569	C₂³	1	24	yes	—
174	#14556568	C₂³	1	24	yes	—
175	#14556567	C₂³	1	12	yes	—
176	#14556566	C₂³	1	12	yes	—
177	#14556566	C₂³	1	12	yes	—
178	#14556565	C₂³	1	6	yes	—
179	#14556565	C₂³	1	6	yes	—
180	#14556565	C₂³	1	6	yes	—
181	#14556565	C₂³	1	6	yes	—
182	#14556565	C₂³	1	6	yes	—
183	#14556565	C₂³	1	6	yes	—
184	#14556565	C₂³	1	12	yes	—
185	#14556565	C₂³	1	12	yes	—
186	#14556565	C₂³	1	12	yes	—
187	#14556565	C₂³	1	12	yes	—
188	#14556565	C₂³	1	12	yes	—
189	#14556565	C₂³	1	12	yes	—
190	#14556564	C₂³	1	24	yes	—
191	#14556564	C₂³	1	24	yes	—
192	#14556563	C₂³	1	24	yes	—
193	#14556562	C₂³	1	12	yes	—
194	#14556561	C₂³	1	24	yes	—
195	#14556560	C₂³	1	12	yes	—
196	#14556559	C₂³	1	24	yes	—
197	Q₈×Dic₇₃	C₂³	1	4	yes	—
198	C₄×Dic₁₄₆	C₂³	1	2	yes	—
199	C₄×Dic₁₄₆	C₂³	1	2	yes	—
200	C₄×Dic₁₄₆	C₂³	1	6	yes	—
201	C₄×Dic₁₄₆	C₂³	1	6	yes	—
202	C₄×Dic₁₄₆	C₂³	1	6	yes	—
203	C₄×Dic₁₄₆	C₂³	1	6	yes	—
204	C₄×D₂₉₂	C₂³	1	6	yes	—
205	C₄×D₂₉₂	C₂³	1	6	yes	—
206	C₄×D₂₉₂	C₂³	1	6	yes	—
207	C₄×D₂₉₂	C₂³	1	6	yes	—
208	C₄×D₂₉₂	C₂³	1	6	yes	—
209	C₄×D₂₉₂	C₂³	1	6	yes	—
210	C₄×D₂₉₂	C₂³	1	12	yes	—
211	C₄×D₂₉₂	C₂³	1	12	yes	—
212	C₄×D₂₉₂	C₂³	1	12	yes	—
213	C₄×D₂₉₂	C₂³	1	12	yes	—
214	C₄×D₂₉₂	C₂³	1	12	yes	—
215	C₄×D₂₉₂	C₂³	1	12	yes	—
216	D₄×Dic₇₃	C₂³	1	12	yes	—
217	#14556553	C₂³	1	12	yes	—
218	#14556553	C₂³	1	12	yes	—
219	C₄×C₂²⋊D₇₃	C₂³	1	12	yes	—
220	C₄×C₂²⋊D₇₃	C₂³	1	12	yes	—
221	C₄×C₂²⋊D₇₃	C₂³	1	12	yes	—
222	C₄×C₂²⋊D₇₃	C₂³	1	12	yes	—
223	C₄×C₂²⋊D₇₃	C₂³	1	12	yes	—
224	C₄×C₂²⋊D₇₃	C₂³	1	12	yes	—
225	#14556551	C₂³	1	24	yes	—
226	#14556550	C₂³	1	6	yes	—
227	#14556550	C₂³	1	6	yes	—
228	#14556550	C₂³	1	2	yes	—
229	#14556549	C₂³	1	12	yes	—
230	#14556548	C₂³	1	12	yes	—
231	#14556548	C₂³	1	12	yes	—
232	#14556548	C₂³	1	12	yes	—
233	C₂×C₄⋊Dic₇₃	C₂³	1	6	yes	—
234	C₂×C₄⋊Dic₇₃	C₂³	1	6	yes	—
235	C₄⋊C₄×D₇₃	C₂³	1	12	yes	—
236	C₂×#11924005	C₂³	1	12	yes	—
237	C₂×#11924005	C₂³	1	12	yes	—
238	C₂²⋊C₄×D₇₃	C₂³	1	24	yes	—
239	C₄²×D₇₃	C₂³	1	12	yes	—
240	C₂×#41×C₇₃	—	2	8	no	—
241	C₂×#41×C₇₃	C₂³	1	3	yes	—
242	C₂×#41×C₇₃	C₂³	1	3	yes	—
243	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
244	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
245	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
246	C₂²×D₄×C₇₃	C₂³	1	3	yes	—
247	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
248	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
249	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
250	C₄×Q₈×C₇₃	C₂³	1	3	yes	—
251	C₄×Q₈×C₇₃	C₂³	1	3	yes	—
252	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
254	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
255	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
256	C₄×Q₈×C₇₃	C₂³	1	3	yes	—
257	C₄×Q₈×C₇₃	C₂³	1	3	yes	—
258	C₄×D₄×C₇₃	C₂³	1	3	yes	—
259	C₄×D₄×C₇₃	C₂³	1	6	yes	—
260	C₄×D₄×C₇₃	C₂³	1	3	yes	—
261	C₄×D₄×C₇₃	C₂³	1	3	yes	—
262	C₄×D₄×C₇₃	C₂³	1	3	yes	—
263	C₄×D₄×C₇₃	C₂³	1	6	yes	—
264	C₄×D₄×C₇₃	C₂³	1	6	yes	—
265	C₄×D₄×C₇₃	C₂³	1	3	yes	—
266	C₄×D₄×C₇₃	C₂³	1	3	yes	—
267	C₄×D₄×C₇₃	C₂³	1	3	yes	—
268	C₄×D₄×C₇₃	C₂³	1	3	yes	—
269	C₄×D₄×C₇₃	C₂³	1	6	yes	—
270	#117×C₇₃	C₂³	1	3	yes	—
271	#117×C₇₃	C₂³	1	6	yes	—
272	#117×C₇₃	C₂³	1	3	yes	—
273	#117×C₇₃	C₂³	1	6	yes	—
274	#117×C₇₃	C₂³	1	3	yes	—
275	#117×C₇₃	C₂³	1	3	yes	—
276	C₂×C₄⋊C₄×C₇₃	C₂³	1	3	yes	—
277	C₂×C₄⋊C₄×C₇₃	C₂³	1	3	yes	—
278	C₂×C₂²⋊C₄×C₇₃	C₂³	1	6	yes	—
279	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
280	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
281	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
282	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
283	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
284	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
285	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
286	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
287	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
288	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
289	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
290	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
291	C₂³×D₇₃	C₂⁴	1	12	yes	—
292	#11924029	—	2	16	no	—
293	#11924028	—	2	24	no	—
294	#11924028	—	2	24	no	—
295	#11924028	—	4	24	no	—
296	#11924028	—	4	12	no	—
297	#11924028	—	4	24	no	—
298	#11924028	—	4	24	no	—
299	C₂×Dic₁₄₆	—	4	12	no	—
300	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
301	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
302	C₂×Dic₁₄₆	C₂⁴	1	6	yes	—
303	C₂×Dic₁₄₆	C₂⁴	1	12	yes	—
304	C₂×D₂₉₂	—	2	24	no	—
305	C₂×D₂₉₂	—	4	12	no	—
306	C₂×D₂₉₂	—	4	12	no	—
307	C₂×D₂₉₂	C₂⁴	1	12	yes	—
308	C₂×D₂₉₂	C₂⁴	1	6	yes	—
309	C₂×D₂₉₂	C₂⁴	1	6	yes	—
310	C₂×D₂₉₂	C₂⁴	1	6	yes	—
311	C₂×D₂₉₂	C₂⁴	1	12	yes	—
312	C₂×D₂₉₂	C₂⁴	1	12	yes	—
313	C₂×C₂²⋊D₇₃	—	4	24	no	—
314	C₂×C₂²⋊D₇₃	C₂⁴	1	12	yes	—
315	C₂×C₂²⋊D₇₃	C₂⁴	1	12	yes	—
316	C₂×C₂²⋊D₇₃	C₂⁴	1	12	yes	—
317	C₂×C₂²⋊D₇₃	C₂⁴	1	24	yes	—
318	D₄×D₇₃	—	2	48	no	—
319	C₂²×Dic₇₃	C₂⁴	1	12	yes	—
320	C₂×C₄×D₇₃	—	4	24	no	—
321	C₂×C₄×D₇₃	C₂⁴	1	12	yes	—
322	C₂×C₄×D₇₃	C₂⁴	1	12	yes	—
323	C₂×C₄×D₇₃	C₂⁴	1	12	yes	—
324	C₂×C₄×D₇₃	C₂⁴	1	24	yes	—
325	C₄⋊Dic₇₃	C₂⁴	1	12	yes	—
326	C₄⋊Dic₇₃	C₂⁴	1	6	yes	—
327	C₄⋊Dic₇₃	C₂⁴	1	6	yes	—
328	C₄⋊Dic₇₃	C₂⁴	1	12	yes	—
329	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
330	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
331	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
332	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
333	#11924007	C₂⁴	1	12	yes	—
334	#11924007	C₂⁴	1	4	yes	—
335	#11924007	C₂⁴	1	4	yes	—
336	#11924007	C₂⁴	1	12	yes	—
337	#11924007	C₂⁴	1	12	yes	—
338	#11924007	C₂⁴	1	12	yes	—
339	C₂²⋊Dic₇₃	C₂⁴	1	12	yes	—
340	C₂²⋊Dic₇₃	C₂⁴	1	4	yes	—
341	C₂²⋊Dic₇₃	C₂⁴	1	12	yes	—
342	#11924005	C₂⁴	1	12	yes	—
343	#11924005	C₂⁴	1	24	yes	—
344	#11924005	C₂⁴	1	12	yes	—
345	#11924005	C₂⁴	1	12	yes	—
346	#11924005	C₂⁴	1	24	yes	—
347	#11924005	C₂⁴	1	12	yes	—
348	#11924005	C₂⁴	1	12	yes	—
349	#11924005	C₂⁴	1	12	yes	—
350	C₄×Dic₇₃	C₂⁴	1	4	yes	—
351	C₄×Dic₇₃	C₂⁴	1	12	yes	—
352	C₄×Dic₇₃	C₂⁴	1	12	yes	—
353	C₂⁴×C₇₃	C₂⁴	1	3	yes	—
354	#41×C₇₃	—	2	4	no	—
355	#41×C₇₃	—	2	12	no	—
356	#41×C₇₃	—	2	12	no	—
357	#41×C₇₃	#41	1	8	yes	complemented
358	C₂×Q₈×C₇₃	—	2	4	no	—
359	C₂×Q₈×C₇₃	C₂⁴	1	3	yes	—
360	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
361	C₂×D₄×C₇₃	—	2	12	no	—
362	C₂×D₄×C₇₃	C₂⁴	1	6	yes	—
363	C₂×D₄×C₇₃	C₂⁴	1	3	yes	—
364	C₂×D₄×C₇₃	C₂⁴	1	3	yes	—
365	C₂²×C₄×C₇₃	—	2	12	no	—
366	C₂²×C₄×C₇₃	—	2	12	no	—
367	C₂²×C₄×C₇₃	—	4	6	no	—
368	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
371	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
372	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
373	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
374	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
375	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
376	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
377	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
378	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
379	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
380	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
381	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
382	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
383	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
384	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
385	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₇₃	C₂⁴	1	3	yes	—
387	C₄⋊C₄×C₇₃	C₂⁴	1	3	yes	—
388	C₄⋊C₄×C₇₃	C₂⁴	1	3	yes	—
389	C₄⋊C₄×C₇₃	C₂⁴	1	3	yes	—
390	C₄⋊C₄×C₇₃	C₂⁴	1	6	yes	—
391	C₄⋊C₄×C₇₃	C₂⁴	1	6	yes	—
392	C₂²⋊C₄×C₇₃	C₂⁴	1	6	yes	—
393	C₂²⋊C₄×C₇₃	C₂⁴	1	6	yes	—
394	C₂²⋊C₄×C₇₃	C₂⁴	1	6	yes	—
395	C₂²⋊C₄×C₇₃	C₂⁴	1	6	yes	—
396	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
397	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
398	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
399	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
400	C₄²×C₇₃	C₂⁴	1	3	yes	—
401	C₄²×C₇₃	C₂⁴	1	3	yes	—
402	C₄²×C₇₃	C₂⁴	1	3	yes	—
403	C₄²×C₇₃	C₂⁴	1	3	yes	—
404	C₄²×C₇₃	C₂⁴	1	3	yes	—
405	C₄²×C₇₃	C₂⁴	1	3	yes	—
406	C₄²×C₇₃	C₂⁴	1	3	yes	—
407	C₄²×C₇₃	C₂⁴	1	3	yes	—
408	C₄²×C₇₃	C₂⁴	1	3	yes	—
409	C₄²×C₇₃	C₂⁴	1	3	yes	—
410	C₄²×C₇₃	C₂⁴	1	3	yes	—
411	C₄²×C₇₃	C₂⁴	1	3	yes	—
412	C₂³×C₇₃	—	2	6	no	—
413	C₂³×C₇₃	—	2	6	no	—
414	C₂³×C₇₃	—	4	3	no	—
415	C₂³×C₇₃	C₂⁵	1	3	yes	—
416	C₂³×C₇₃	C₂⁵	1	3	yes	—
417	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
418	C₂²×D₇₃	—	2	24	no	—
419	C₂²×D₇₃	—	4	12	no	—
420	C₂²×D₇₃	—	4	12	no	—
421	C₂²×D₇₃	C₂⁵	1	12	yes	—
422	Q₈×C₇₃	—	2	6	no	—
423	Q₈×C₇₃	C₂×#41	1	4	yes	complemented
424	D₄×C₇₃	—	2	12	no	—
425	D₄×C₇₃	—	2	6	no	—
426	D₄×C₇₃	C₂×#41	1	12	yes	complemented
427	C₂×C₄×C₇₃	—	2	6	no	—
428	C₂×C₄×C₇₃	—	2	6	no	—
429	C₂×C₄×C₇₃	—	2	2	no	—
430	C₂×C₄×C₇₃	—	2	6	no	—
431	C₂×C₄×C₇₃	—	2	6	no	—
432	C₂×C₄×C₇₃	—	2	6	no	—
433	C₂×C₄×C₇₃	—	2	6	no	—
434	C₂×C₄×C₇₃	—	2	6	no	—
435	C₂×C₄×C₇₃	—	2	6	no	—
436	C₂×C₄×C₇₃	—	2	6	no	—
437	C₂×C₄×C₇₃	—	2	2	no	—
438	C₂×C₄×C₇₃	—	2	6	no	—
439	C₂×C₄×C₇₃	—	2	6	no	—
440	C₂×C₄×C₇₃	—	4	3	no	—
441	C₂×C₄×C₇₃	—	4	3	no	—
442	C₂×C₄×C₇₃	—	4	3	no	—
443	C₂×C₄×C₇₃	C₂×#41	1	12	yes	complemented
444	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	complemented
445	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
446	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
447	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
448	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
449	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
450	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
451	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
452	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
453	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
454	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
455	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
456	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
457	C₂²⋊D₇₃	—	2	24	no	—
458	C₂²⋊D₇₃	—	2	24	no	—
459	C₂²⋊D₇₃	—	4	24	no	—
460	C₂²⋊D₇₃	—	4	12	no	—
461	C₂×Dic₇₃	—	4	12	no	—
462	C₂×Dic₇₃	C₂⁵	1	4	yes	—
463	C₂×Dic₇₃	C₂⁵	1	4	yes	—
464	C₂×Dic₇₃	C₂⁵	1	12	yes	—
465	D₂₉₂	—	2	24	no	—
466	D₂₉₂	—	2	12	no	—
467	D₂₉₂	—	2	12	no	—
468	D₂₉₂	—	2	12	no	—
469	D₂₉₂	—	4	12	no	—
470	D₂₉₂	—	4	12	no	—
471	C₄×D₇₃	—	2	24	no	—
472	C₄×D₇₃	—	2	24	no	—
473	C₄×D₇₃	—	4	24	no	—
474	C₄×D₇₃	—	4	12	no	—
475	Dic₁₄₆	—	2	4	no	—
476	Dic₁₄₆	—	2	12	no	—
477	Dic₁₄₆	—	2	4	no	—
478	Dic₁₄₆	—	4	12	no	—
479	C₂²×C₇₃	—	2	1	no	—
480	C₂²×C₇₃	—	2	3	no	—
481	C₂²×C₇₃	—	2	1	no	—
482	C₂²×C₇₃	—	2	3	no	—
483	C₂²×C₇₃	—	2	3	no	—
484	C₂²×C₇₃	—	2	3	no	—
485	C₂²×C₇₃	—	2	3	no	—
486	C₂²×C₇₃	—	4	12	no	—
487	C₂²×C₇₃	C₂²×#41	1	6	yes	—
488	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
489	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
490	C₂×D₇₃	—	2	12	no	—
491	C₂×D₇₃	—	2	12	no	—
492	C₂×D₇₃	—	2	12	no	—
493	C₂×D₇₃	—	8	24	no	—
494	C₄×C₇₃	—	2	1	no	—
495	C₄×C₇₃	—	2	3	no	—
496	C₄×C₇₃	—	2	3	no	—
497	C₄×C₇₃	—	2	3	no	—
498	C₄×C₇₃	—	2	3	no	—
499	C₄×C₇₃	—	2	3	no	—
500	C₄×C₇₃	—	2	1	no	—
501	C₄×C₇₃	C₂²×#41	1	2	yes	—
502	C₄×C₇₃	C₂²×#41	1	6	yes	—
503	C₄×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
504	C₄×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
505	C₄×C₇₃	#585	1	2	yes	—
506	Dic₇₃	—	2	4	no	—
507	Dic₇₃	—	2	12	no	—
508	Dic₇₃	—	2	4	no	—
509	#62800	—	73	1	no	maximal, Sylow
510	C₂×C₇₃	—	2	6	no	—
511	C₂×C₇₃	—	2	2	no	—
512	C₂×C₇₃	—	4	3	no	—
513	C₂×C₇₃	C₂³×#41	1	1	yes	characteristic
514	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂×C₇₃	C₂×#585	1	1	yes	characteristic
516	D₇₃	—	4	12	no	—
517	#3522	—	73	2	no	—
518	#3519	—	73	6	no	—
519	#3517	—	73	2	no	—
520	#3514	—	73	6	no	—
521	#3511	—	73	3	no	—
522	#3508	—	73	3	no	—
523	#3503	—	73	1	no	—
524	#3498	—	73	1	no	—
525	#3494	—	73	6	no	—
526	#3488	—	73	2	no	—
527	#3483	—	73	2	no	—
528	#3481	—	73	6	no	—
529	#3480	—	73	2	no	—
530	D₄×#41	—	73	6	no	—
531	#3460	—	73	6	no	—
532	#3444	—	73	3	no	—
533	C₂×#532	—	73	3	no	—
534	C₄×H(5,𝔽₂)	—	73	2	no	—
535	C₂×C₄×#41	D₇₃	1	1	yes	characteristic, complemented
536	C₇₃	#62800	1	1	yes	characteristic, complemented, Sylow
537	C₂×H(5,𝔽₂)	—	73	2	no	—
538	C₂²×#41	—	73	6	no	—
539	C₂²×#41	C₂×D₇₃	1	1	yes	characteristic
540	#559	—	73	6	no	—
541	#559	—	73	6	no	—
542	Q₈²	—	73	2	no	—
543	#557	—	73	2	no	—
544	#556	—	73	6	no	—
545	#555	—	73	6	no	—
546	#555	—	73	12	no	—
547	#554	—	73	6	no	—
548	#554	—	73	6	no	—
549	#553	—	73	12	no	—
550	#553	—	73	12	no	—
551	#553	—	73	12	no	—
552	#551	—	73	24	no	—
553	#550	—	73	4	no	—
554	#550	—	73	2	no	—
555	#550	—	73	2	no	—
556	#550	—	73	6	no	—
557	#550	—	73	6	no	—
558	D₄×Q₈	—	73	6	no	—
559	#548	—	73	4	no	—
560	#548	—	73	12	no	—
561	#547	—	73	6	no	—
562	#547	—	73	12	no	—
563	#546	—	73	12	no	—
564	#546	—	73	12	no	—
565	#546	—	73	12	no	—
566	#546	—	73	24	no	—
567	D₄²	—	73	12	no	—
568	D₄²	—	73	6	no	—
569	D₄²	—	73	6	no	—
570	#544	—	73	6	no	—
571	#542	—	73	12	no	—
572	#542	—	73	12	no	—
573	#540	—	73	12	no	—
574	#540	—	73	12	no	—
575	#538	—	73	24	no	—
576	#537	—	73	6	no	—
577	#535	—	73	6	no	—
578	#535	—	73	6	no	—
579	#533	—	73	1	no	—
580	#533	—	73	3	no	—
581	#533	—	73	3	no	—
582	#532	—	73	12	no	—
583	#532	—	73	3	no	—
584	#532	—	73	6	no	—
585	#532	—	73	6	no	—
586	#532	—	73	6	no	—
587	#532	—	73	6	no	—
588	#532	—	73	6	no	—
589	#532	—	73	6	no	—
590	#532	—	73	6	no	—
591	#532	—	73	3	no	—
592	#532	—	73	3	no	—
593	C₂×C₄⋊Q₈	—	73	3	no	—
594	C₂×#127	—	73	3	no	—
595	#529	—	73	12	no	—
596	#529	—	73	6	no	—
597	#529	—	73	6	no	—
598	#529	—	73	6	no	—
599	#529	—	73	6	no	—
600	#529	—	73	6	no	—
601	#529	—	73	6	no	—
602	C₂×#124	—	73	6	no	—
603	#525	—	73	6	no	—
604	#525	—	73	6	no	—
605	#525	—	73	6	no	—
606	#525	—	73	24	no	—
607	C₂×#121	—	73	6	no	—
608	C₂×#121	—	73	6	no	—
609	#520	—	73	2	no	—
610	#520	—	73	4	no	—
611	#520	—	73	6	no	—
612	#518	—	73	12	no	—
613	#518	—	73	6	no	—
614	C₄×#41	—	73	4	no	—
615	C₄×#41	—	73	6	no	—
616	C₄×#41	—	73	6	no	—
617	C₄×#41	—	73	6	no	—
618	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
619	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
620	C₄×#41	C₂×D₇₃	1	3	yes	complemented
621	C₄×#41	C₂×D₇₃	1	3	yes	complemented
622	C₄×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
623	C₄×#41	C₂×D₇₃	1	3	yes	complemented
624	C₄×#41	C₂×D₇₃	1	3	yes	complemented
625	C₄×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
626	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
627	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
628	C₂×C₄×D₄	—	73	12	no	—
629	C₂×C₄×D₄	—	73	6	no	—
630	C₂×C₄×D₄	—	73	6	no	—
631	C₂×C₄×D₄	C₂×D₇₃	1	3	yes	complemented
632	C₂×C₄×D₄	C₂×D₇₃	1	3	yes	complemented
633	C₂×#117	C₂×D₇₃	1	3	yes	complemented
634	C₂²×C₄²	C₂×D₇₃	1	3	yes	complemented
635	H(5,𝔽₂)	—	146	16	no	—
636	C₂×#41	—	2	8	no	—
637	C₂×#41	—	292	24	no	—
638	C₂×#41	—	73	4	no	—
639	C₂×#41	—	73	6	no	—
640	C₂×#41	—	73	12	no	—
641	C₂×#41	—	73	12	no	—
642	C₂×#41	—	73	12	no	—
643	C₂×#41	—	73	6	no	—
644	C₂×#41	—	73	6	no	—
645	C₂×#41	C₂²×D₇₃	1	3	yes	—
646	C₂×#41	C₂²×D₇₃	1	3	yes	—
647	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
648	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
649	C₂²×Q₈	—	73	6	no	—
650	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
651	C₂²×D₄	—	73	12	no	—
652	C₂²×D₄	—	73	12	no	—
653	C₂²×D₄	—	73	6	no	—
654	C₂²×D₄	—	73	6	no	—
655	C₂²×D₄	—	73	6	no	—
656	C₂²×D₄	C₂²×D₇₃	1	3	yes	—
657	C₂³×C₄	—	73	12	no	—
658	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
659	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
660	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
661	C₄⋊Q₈	—	73	12	no	—
662	C₄⋊Q₈	—	73	3	no	—
663	C₄⋊Q₈	—	73	6	no	—
664	C₄⋊Q₈	—	73	6	no	—
665	C₄⋊Q₈	—	73	6	no	—
666	C₄⋊Q₈	—	73	1	no	—
667	C₄⋊Q₈	—	73	1	no	—
668	#127	—	73	12	no	—
669	#127	—	73	3	no	—
670	#127	—	73	6	no	—
671	#127	—	73	6	no	—
672	#127	—	73	6	no	—
673	#126	—	73	24	no	—
674	#126	—	73	12	no	—
675	#126	—	73	12	no	—
676	#125	—	73	12	no	—
677	#125	—	73	2	no	—
678	#125	—	73	6	no	—
679	#125	—	73	6	no	—
680	#124	—	73	12	no	—
681	#124	—	73	24	no	—
682	#124	—	73	6	no	—
683	#124	—	73	12	no	—
684	#124	—	73	12	no	—
685	#124	—	73	12	no	—
686	#124	—	73	6	no	—
687	#124	—	73	6	no	—
688	#123	—	73	12	no	—
689	#123	—	73	12	no	—
690	#123	—	73	12	no	—
691	#123	—	73	24	no	—
692	#123	—	73	24	no	—
693	#123	—	73	24	no	—
694	C₂²⋊Q₈	—	73	12	no	—
695	C₂²⋊Q₈	—	73	2	no	—
696	C₂²⋊Q₈	—	73	2	no	—
697	C₂²⋊Q₈	—	73	6	no	—
698	C₂²⋊Q₈	—	73	6	no	—
699	C₂²⋊Q₈	—	73	6	no	—
700	C₂²⋊Q₈	—	73	6	no	—
701	C₂²⋊Q₈	—	73	24	no	—
702	C₂²⋊Q₈	—	73	24	no	—
703	#121	—	73	24	no	—
704	#121	—	73	12	no	—
705	#121	—	73	6	no	—
706	#121	—	73	6	no	—
707	#121	—	73	12	no	—
708	#121	—	73	12	no	—
709	#121	—	73	12	no	—
710	#121	—	73	12	no	—
711	#121	—	73	12	no	—
712	#121	—	73	12	no	—
713	#121	—	73	6	no	—
714	#121	—	73	6	no	—
715	#121	—	73	6	no	—
716	#121	—	73	6	no	—
717	#121	—	73	12	no	—
718	#121	—	73	12	no	—
719	#121	—	73	24	no	—
720	#121	—	73	24	no	—
721	#120	—	73	12	no	—
722	#120	—	73	24	no	—
723	#120	—	73	24	no	—
724	C₄×Q₈	—	73	4	no	—
725	C₄×Q₈	—	73	2	no	—
726	C₄×Q₈	—	73	2	no	—
727	C₄×Q₈	—	73	6	no	—
728	C₄×Q₈	—	73	6	no	—
729	C₄×Q₈	—	73	6	no	—
730	C₄×Q₈	—	73	6	no	—
731	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
732	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
733	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
734	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
735	C₄×Q₈	C₂²×D₇₃	1	3	yes	—
736	C₄×Q₈	C₂²×D₇₃	1	3	yes	—
737	C₄×Q₈	C₂²×D₇₃	1	3	yes	—
738	C₄×Q₈	C₂²×D₇₃	1	3	yes	—
739	C₄×D₄	—	73	12	no	—
740	C₄×D₄	—	73	12	no	—
741	C₄×D₄	—	73	12	no	—
742	C₄×D₄	—	73	12	no	—
743	C₄×D₄	—	73	12	no	—
744	C₄×D₄	—	73	12	no	—
745	C₄×D₄	—	73	12	no	—
746	C₄×D₄	—	73	12	no	—
747	C₄×D₄	—	73	12	no	—
748	C₄×D₄	—	73	24	no	—
749	C₄×D₄	—	73	12	no	—
750	C₄×D₄	—	73	6	no	—
751	C₄×D₄	—	73	6	no	—
752	C₄×D₄	—	73	12	no	—
753	C₄×D₄	—	73	12	no	—
754	C₄×D₄	—	73	12	no	—
755	C₄×D₄	—	73	12	no	—
756	C₄×D₄	—	73	12	no	—
757	C₄×D₄	—	73	6	no	—
758	C₄×D₄	—	73	6	no	—
759	C₄×D₄	—	73	6	no	—
760	C₄×D₄	—	73	6	no	—
761	C₄×D₄	C₂²×D₇₃	1	3	yes	—
762	C₄×D₄	C₂²×D₇₃	1	3	yes	—
763	C₄×D₄	C₂²×D₇₃	1	3	yes	—
764	C₄×D₄	C₂²×D₇₃	1	3	yes	—
765	C₄×D₄	C₂²×D₇₃	1	6	yes	—
766	C₄×D₄	C₂²×D₇₃	1	3	yes	—
767	C₄×D₄	C₂²×D₇₃	1	6	yes	—
768	C₄×D₄	C₂²×D₇₃	1	3	yes	—
769	C₄×D₄	C₂²×D₇₃	1	6	yes	—
770	C₄×D₄	C₂²×D₇₃	1	6	yes	—
771	C₄×D₄	C₂²×D₇₃	1	3	yes	—
772	C₄×D₄	C₂²×D₇₃	1	3	yes	—
773	#117	—	73	2	no	—
774	#117	—	73	6	no	—
775	#117	—	73	6	no	—
776	#117	—	73	12	no	—
777	#117	—	73	12	no	—
778	#117	—	73	12	no	—
779	#117	—	73	12	no	—
780	#117	C₂²×D₇₃	1	3	yes	—
781	#117	C₂²×D₇₃	1	3	yes	—
782	#117	C₂²×D₇₃	1	6	yes	—
783	#117	C₂²×D₇₃	1	6	yes	—
784	#117	C₂²×D₇₃	1	3	yes	—
785	#117	C₂²×D₇₃	1	3	yes	—
786	C₂×C₄⋊C₄	—	73	6	no	—
787	C₂×C₄⋊C₄	—	73	6	no	—
788	C₂×C₄⋊C₄	—	73	12	no	—
789	C₂×C₄⋊C₄	C₂²×D₇₃	1	3	yes	—
790	C₂×C₄⋊C₄	C₂²×D₇₃	1	3	yes	—
791	C₂×C₂²⋊C₄	—	73	12	no	—
792	C₂×C₂²⋊C₄	—	73	12	no	—
793	C₂×C₂²⋊C₄	—	73	24	no	—
794	C₂×C₂²⋊C₄	C₂²×D₇₃	1	6	yes	—
795	C₂×C₄²	—	73	12	no	—
796	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
797	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
798	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
799	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
800	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
801	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
802	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
803	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
804	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
805	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
806	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
807	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
808	C₂⁴	—	73	12	no	—
809	C₂⁴	C₂³×D₇₃	1	3	yes	—
810	#41	—	2	4	no	—
811	#41	—	2	12	no	—
812	#41	—	2	12	no	—
813	#41	—	292	24	no	—
814	#41	—	292	12	no	—
815	#41	—	292	24	no	—
816	#41	—	292	24	no	—
817	#41	—	146	16	no	—
818	#41	—	146	24	no	—
819	#41	—	146	24	no	—
820	#41	#11924028	1	8	yes	complemented
821	C₂×Q₈	—	2	4	no	—
822	C₂×Q₈	—	292	12	no	—
823	C₂×Q₈	—	73	12	no	—
824	C₂×Q₈	—	73	2	no	—
825	C₂×Q₈	—	73	2	no	—
826	C₂×Q₈	—	73	6	no	—
827	C₂×Q₈	C₂³×D₇₃	1	3	yes	—
828	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
829	C₂×D₄	—	2	12	no	—
830	C₂×D₄	—	292	12	no	—
831	C₂×D₄	—	292	12	no	—
832	C₂×D₄	—	292	24	no	—
833	C₂×D₄	—	73	12	no	—
834	C₂×D₄	—	73	24	no	—
835	C₂×D₄	—	73	12	no	—
836	C₂×D₄	—	73	12	no	—
837	C₂×D₄	—	73	12	no	—
838	C₂×D₄	—	73	12	no	—
839	C₂×D₄	—	73	12	no	—
840	C₂×D₄	—	73	6	no	—
841	C₂×D₄	—	73	6	no	—
842	C₂×D₄	—	73	6	no	—
843	C₂×D₄	—	146	48	no	—
844	C₂×D₄	—	146	24	no	—
845	C₂×D₄	C₂³×D₇₃	1	6	yes	—
846	C₂×D₄	C₂³×D₇₃	1	3	yes	—
847	C₂×D₄	C₂³×D₇₃	1	3	yes	—
848	C₂²×C₄	—	2	12	no	—
849	C₂²×C₄	—	2	12	no	—
850	C₂²×C₄	—	4	6	no	—
851	C₂²×C₄	—	292	24	no	—
852	C₂²×C₄	—	73	12	no	—
853	C₂²×C₄	—	73	12	no	—
854	C₂²×C₄	—	73	24	no	—
855	C₂²×C₄	—	73	12	no	—
856	C₂²×C₄	—	73	12	no	—
857	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
858	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
859	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
860	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
861	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
862	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
863	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
864	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
865	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
866	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
867	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
868	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
869	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
870	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
871	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
872	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
873	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
874	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
875	C₄⋊C₄	—	73	12	no	—
876	C₄⋊C₄	—	73	4	no	—
877	C₄⋊C₄	—	73	4	no	—
878	C₄⋊C₄	—	73	12	no	—
879	C₄⋊C₄	—	73	12	no	—
880	C₄⋊C₄	—	73	12	no	—
881	C₄⋊C₄	—	73	12	no	—
882	C₄⋊C₄	—	73	6	no	—
883	C₄⋊C₄	—	73	6	no	—
884	C₄⋊C₄	—	73	12	no	—
885	C₄⋊C₄	—	73	2	no	—
886	C₄⋊C₄	—	73	2	no	—
887	C₄⋊C₄	—	73	2	no	—
888	C₄⋊C₄	—	73	2	no	—
889	C₄⋊C₄	C₂³×D₇₃	1	3	yes	—
890	C₄⋊C₄	C₂³×D₇₃	1	3	yes	—
891	C₄⋊C₄	C₂³×D₇₃	1	3	yes	—
892	C₄⋊C₄	C₂³×D₇₃	1	3	yes	—
893	C₄⋊C₄	C₂³×D₇₃	1	6	yes	—
894	C₄⋊C₄	C₂³×D₇₃	1	6	yes	—
895	C₂²⋊C₄	—	73	12	no	—
896	C₂²⋊C₄	—	73	4	no	—
897	C₂²⋊C₄	—	73	12	no	—
898	C₂²⋊C₄	—	73	12	no	—
899	C₂²⋊C₄	—	73	24	no	—
900	C₂²⋊C₄	—	73	12	no	—
901	C₂²⋊C₄	—	73	12	no	—
902	C₂²⋊C₄	—	73	24	no	—
903	C₂²⋊C₄	—	73	12	no	—
904	C₂²⋊C₄	—	73	12	no	—
905	C₂²⋊C₄	—	73	12	no	—
906	C₂²⋊C₄	C₂³×D₇₃	1	6	yes	—
907	C₂²⋊C₄	C₂³×D₇₃	1	6	yes	—
908	C₂²⋊C₄	C₂³×D₇₃	1	6	yes	—
909	C₂²⋊C₄	C₂³×D₇₃	1	6	yes	—
910	C₄²	—	73	12	no	—
911	C₄²	—	73	12	no	—
912	C₄²	—	73	4	no	—
913	C₄²	C₂³×D₇₃	1	1	yes	characteristic
914	C₄²	C₂³×D₇₃	1	1	yes	characteristic
915	C₄²	C₂³×D₇₃	1	3	yes	—
916	C₄²	C₂³×D₇₃	1	3	yes	—
917	C₄²	C₂³×D₇₃	1	3	yes	—
918	C₄²	C₂³×D₇₃	1	3	yes	—
919	C₄²	C₂³×D₇₃	1	3	yes	—
920	C₄²	C₂³×D₇₃	1	3	yes	—
921	C₄²	C₂³×D₇₃	1	3	yes	—
922	C₄²	C₂³×D₇₃	1	3	yes	—
923	C₄²	C₂³×D₇₃	1	3	yes	—
924	C₄²	C₂³×D₇₃	1	3	yes	—
925	C₄²	C₂³×D₇₃	1	3	yes	—
926	C₄²	C₂³×D₇₃	1	1	yes	characteristic
927	C₄²	C₂³×D₇₃	1	1	yes	characteristic
928	C₄²	C₂³×D₇₃	1	3	yes	—
929	C₂³	—	2	6	no	—
930	C₂³	—	2	6	no	—
931	C₂³	—	4	3	no	—
932	C₂³	—	292	12	no	—
933	C₂³	—	292	12	no	—
934	C₂³	—	73	12	no	—
935	C₂³	—	146	24	no	—
936	C₂³	C₂⁴×D₇₃	1	3	yes	—
937	C₂³	C₂⁴×D₇₃	1	3	yes	—
938	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
939	Q₈	—	2	6	no	—
940	Q₈	—	292	12	no	—
941	Q₈	—	146	4	no	—
942	Q₈	—	146	12	no	—
943	Q₈	—	146	4	no	—
944	Q₈	C₂×#11924028	1	4	yes	complemented
945	D₄	—	2	12	no	—
946	D₄	—	2	6	no	—
947	D₄	—	292	12	no	—
948	D₄	—	292	12	no	—
949	D₄	—	292	24	no	—
950	D₄	—	292	12	no	—
951	D₄	—	146	24	no	—
952	D₄	—	146	24	no	—
953	D₄	—	146	12	no	—
954	D₄	—	146	24	no	—
955	D₄	—	146	12	no	—
956	D₄	—	146	12	no	—
957	D₄	C₂×#11924028	1	12	yes	complemented
958	C₂×C₄	—	2	6	no	—
959	C₂×C₄	—	2	6	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	6	no	—
962	C₂×C₄	—	2	6	no	—
963	C₂×C₄	—	2	6	no	—
964	C₂×C₄	—	2	6	no	—
965	C₂×C₄	—	2	6	no	—
966	C₂×C₄	—	2	6	no	—
967	C₂×C₄	—	2	6	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	6	no	—
970	C₂×C₄	—	2	6	no	—
971	C₂×C₄	—	4	3	no	—
972	C₂×C₄	—	4	3	no	—
973	C₂×C₄	—	4	3	no	—
974	C₂×C₄	—	292	24	no	—
975	C₂×C₄	—	292	12	no	—
976	C₂×C₄	—	292	12	no	—
977	C₂×C₄	—	73	4	no	—
978	C₂×C₄	—	73	4	no	—
979	C₂×C₄	—	73	12	no	—
980	C₂×C₄	—	146	24	no	—
981	C₂×C₄	—	146	24	no	—
982	C₂×C₄	C₂×#11924028	1	12	yes	complemented
983	C₂×C₄	#14556637	1	4	yes	complemented
984	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
985	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
986	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
987	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
988	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
989	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
990	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
991	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
992	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
993	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
994	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
995	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
996	C₂²	—	2	1	no	—
997	C₂²	—	2	3	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	3	no	—
1000	C₂²	—	2	3	no	—
1001	C₂²	—	2	3	no	—
1002	C₂²	—	2	3	no	—
1003	C₂²	—	4	12	no	—
1004	C₂²	—	584	24	no	—
1005	C₂²	—	146	12	no	—
1006	C₂²	—	146	12	no	—
1007	C₂²	—	146	12	no	—
1008	C₂²	C₂²×#11924028	1	6	yes	—
1009	C₂²	C₂×#14556637	1	2	yes	—
1010	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
1011	C₄	—	2	1	no	—
1012	C₄	—	2	3	no	—
1013	C₄	—	2	3	no	—
1014	C₄	—	2	3	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	3	no	—
1017	C₄	—	2	3	no	—
1018	C₄	—	146	4	no	—
1019	C₄	—	146	12	no	—
1020	C₄	—	146	4	no	—
1021	C₄	C₂²×#11924028	1	2	yes	—
1022	C₄	C₂²×#11924028	1	6	yes	—
1023	C₄	C₂×#14556637	1	2	yes	—
1024	C₄	C₂×#14556637	1	2	yes	—
1025	C₄	#17989423	1	2	yes	—
1026	C₂	—	2	2	no	—
1027	C₂	—	2	6	no	—
1028	C₂	—	4	3	no	—
1029	C₂	—	292	12	no	—
1030	C₂	C₂³×#11924028	1	1	yes	characteristic
1031	C₂	C₂²×#14556637	1	1	yes	characteristic
1032	C₂	C₂×#17989423	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₇₃
commutator, socle, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×C₄×#41×C₇₃	C₂
hypercenter	C₂×C₄×#41	D₇₃
hypocenter	C₇₃	#62800
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #22624016	C₂	semidirect
2. #22623963	C₂	semidirect
3. #22623937	C₂	semidirect
4. #22623892	C₂	semidirect
5. #22623842	C₂	semidirect
6. #22623807	C₂	semidirect
7. #22623750	C₂	semidirect
8. #22623709	C₂	semidirect
9. #22623666	C₂	semidirect
10. #22623600	C₂	semidirect
11. #22623557	C₂	semidirect
12. #22623541	C₂	semidirect
13. #22623526	C₂	semidirect
14. D₄×#11924028	C₂	semidirect
15. #22623347	C₂	semidirect
16. #22623227	C₂	semidirect
17. C₂×#17989137	C₂	semidirect
18. C₄×#14556637	C₂	semidirect
19. C₂×C₄×#41×C₇₃	C₂	semidirect
21. C₂²×#11924028	C₂²	semidirect
22. #17989322	C₂²	semidirect
23. #17989322	C₂²	semidirect
24. Q₈×Dic₁₄₆	C₂²	semidirect
25. #17989316	C₂²	semidirect
26. #17989310	C₂²	semidirect
27. #17989302	C₂²	semidirect
28. #17989300	C₂²	semidirect
29. #17989297	C₂²	semidirect
30. #17989294	C₂²	semidirect
31. #17989285	C₂²	semidirect
32. #17989283	C₂²	semidirect
33. #17989281	C₂²	semidirect
34. #17989261	C₂²	semidirect
35. #17989259	C₂²	semidirect
36. #17989259	C₂²	semidirect
37. #17989258	C₂²	semidirect
38. #17989258	C₂²	semidirect
39. #17989256	C₂²	semidirect
40. D₄×Dic₁₄₆	C₂²	semidirect
41. #17989248	C₂²	semidirect
42. #17989246	C₂²	semidirect
43. #17989242	C₂²	semidirect
44. #17989238	C₂²	semidirect
45. #17989233	C₂²	semidirect
46. #17989233	C₂²	semidirect
47. #17989227	C₂²	semidirect
48. #17989225	C₂²	semidirect
49. D₄×D₂₉₂	C₂²	semidirect
50. D₄×D₂₉₂	C₂²	semidirect
51. D₄×C₂²⋊D₇₃	C₂²	semidirect
52. #17989215	C₂²	semidirect
53. #17989209	C₂²	semidirect
54. #17989208	C₂²	semidirect
55. #17989192	C₂²	semidirect
56. #17989188	C₂²	semidirect
57. #17989170	C₂²	semidirect
58. #17989165	C₂²	semidirect
59. #17989156	C₂²	semidirect
60. #17989151	C₂²	semidirect
61. #17989144	C₂²	semidirect
62. #17989144	C₂²	semidirect
63. #17989144	C₂²	semidirect
64. #17989137	C₂²	semidirect
65. #17989137	C₂²	semidirect
66. #17989137	C₂²	semidirect
67. #17989137	C₂²	semidirect
68. #17989137	C₂²	semidirect
69. #17989137	C₂²	semidirect
70. #17989137	C₂²	semidirect
71. #17989137	C₂²	semidirect
72. #17989137	C₂²	semidirect
73. #17989137	C₂²	semidirect
74. #17989134	C₂²	semidirect
75. C₂×#14556591	C₂²	semidirect
76. C₂×#14556588	C₂²	semidirect
77. #17989124	C₂²	semidirect
78. #17989121	C₂²	semidirect
79. #17989121	C₂²	semidirect
80. #17989121	C₂²	semidirect
81. #17989121	C₂²	semidirect
82. #17989121	C₂²	semidirect
83. #17989121	C₂²	semidirect
84. C₂×#14556579	C₂²	semidirect
85. #17989098	C₂²	semidirect
86. #17989098	C₂²	semidirect
87. #17989098	C₂²	semidirect
88. #17989096	C₂²	semidirect
89. C₂×#14556565	C₂²	semidirect
90. C₂×#14556565	C₂²	semidirect
92. #17989069	C₂²	semidirect
93. #17989067	C₂²	semidirect
94. #17989061	C₂²	semidirect
95. #17989059	C₂²	semidirect
96. C₄×#11924029	C₂²	semidirect
97. C₄×#11924028	C₂²	semidirect
98. C₄×#11924028	C₂²	semidirect
99. C₄×#11924028	C₂²	semidirect
100. C₂×C₄×D₂₉₂	C₂²	semidirect
101. C₂×C₄×D₂₉₂	C₂²	semidirect
102. C₄×D₄×D₇₃	C₂²	semidirect
106. C₄×#41×C₇₃	C₂²	semidirect
107. C₄×#41×C₇₃	C₂²	semidirect
108. C₄×#41×C₇₃	C₂²	semidirect
109. C₄×#41×C₇₃	C₂²	semidirect
110. C₄×#41×C₇₃	C₂²	semidirect
111. C₄×#41×C₇₃	C₂²	semidirect
112. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
113. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
114. C₂×C₄×D₄×C₇₃	C₂²	semidirect
115. C₂×C₄×D₄×C₇₃	C₂²	semidirect
116. C₂×#117×C₇₃	C₂²	semidirect
117. C₂²×C₄²×C₇₃	C₂²	semidirect
357. #41×C₇₃	#41	semidirect
423. Q₈×C₇₃	C₂×#41	semidirect
426. D₄×C₇₃	C₂×#41	semidirect
443. C₂×C₄×C₇₃	C₂×#41	semidirect
444. C₂×C₄×C₇₃	H(5,𝔽₂)	semidirect
535. C₂×C₄×#41	D₇₃	semidirect
536. C₇₃	#62800	semidirect
620. C₄×#41	C₂×D₇₃	semidirect
621. C₄×#41	C₂×D₇₃	semidirect
622. C₄×#41	C₂×D₇₃	semidirect
623. C₄×#41	C₂×D₇₃	semidirect
624. C₄×#41	C₂×D₇₃	semidirect
625. C₄×#41	C₂×D₇₃	semidirect
626. C₂×C₄×Q₈	C₂×D₇₃	semidirect
627. C₂×C₄×Q₈	C₂×D₇₃	semidirect
631. C₂×C₄×D₄	C₂×D₇₃	semidirect
632. C₂×C₄×D₄	C₂×D₇₃	semidirect
633. C₂×#117	C₂×D₇₃	semidirect
634. C₂²×C₄²	C₂×D₇₃	semidirect
820. #41	#11924028	semidirect
944. Q₈	C₂×#11924028	semidirect
957. D₄	C₂×#11924028	semidirect
982. C₂×C₄	C₂×#11924028	semidirect
983. C₂×C₄	#14556637	semidirect

Maximal subgroups

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

subgroup	index
#22624016	2
#22623963	2
#22623937	2
#22623892	2
#22623842	2
#22623807	2
#22623750	2
#22623709	2
#22623666	2
#22623600	2
#22623557	2
#22623541	2
#22623526	2
D₄×#11924028	2
#22623347	2
#22623227	2
C₂×#17989137	2
C₄×#14556637	2
C₂×C₄×#41×C₇₃	2
#62800	73