Subgroups — C₂×#22623728 #33993882

Order 18688.

7738 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623728	C₂	1	32	yes	maximal, direct product factor
2	C₂×#17989298	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17989295	C₂	1	4	yes	maximal, complemented
4	C₂×#17989294	C₂	1	2	yes	maximal, complemented
5	C₂×#17989293	C₂	1	2	yes	maximal, complemented
6	C₂×#17989292	C₂	1	2	yes	maximal, complemented
7	C₂×Q₈×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#17989250	C₂	1	2	yes	maximal, complemented
10	C₂×#17989217	C₂	1	2	yes	maximal, complemented
11	C₂×#17989212	C₂	1	4	yes	maximal, complemented
12	C₂×#17989142	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#17989141	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#14556571	C₂	1	2	yes	maximal, complemented
15	C₂×C₂²⋊Q₈×D₇₃	C₂	1	2	yes	maximal, complemented
16	C₂×#17989059	C₂	1	2	yes	maximal
17	C₂×C₄×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic
18	C₂×#554×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂³×Dic₁₄₆	C₂²	1	2	yes	complemented
20	C₂²×Q₈×D₇₃	C₂²	1	2	yes	complemented
21	C₂²×D₄×D₇₃	C₂²	1	1	yes	characteristic
22	C₂³×C₄×D₇₃	C₂²	1	2	yes	—
23	#17989298	C₂²	1	16	yes	complemented
24	#17989295	C₂²	1	64	yes	complemented
25	#17989294	C₂²	1	32	yes	complemented
26	#17989293	C₂²	1	32	yes	complemented
27	#17989292	C₂²	1	32	yes	complemented
28	Q₈×D₂₉₂	C₂²	1	16	yes	complemented
29	D₄×Dic₁₄₆	C₂²	1	16	yes	complemented
30	#17989250	C₂²	1	32	yes	complemented
31	#17989217	C₂²	1	32	yes	complemented
32	#17989212	C₂²	1	64	yes	complemented
33	#17989142	C₂²	1	16	yes	complemented
34	#17989141	C₂²	1	16	yes	complemented
35	C₂×#14556591	C₂²	1	2	yes	complemented
36	C₂×#14556591	C₂²	1	1	yes	characteristic, complemented
37	C₂×#14556590	C₂²	1	4	yes	complemented
38	C₂×#14556590	C₂²	1	2	yes	complemented
39	C₂×#14556590	C₂²	1	1	yes	characteristic, complemented
40	C₂×#14556589	C₂²	1	1	yes	characteristic, complemented
41	C₂×#14556582	C₂²	1	2	yes	complemented
42	C₂×#14556582	C₂²	1	2	yes	complemented
43	C₂×#14556581	C₂²	1	4	yes	complemented
44	C₂×#14556581	C₂²	1	2	yes	complemented
45	C₂×#14556571	C₂²	1	4	yes	—
46	C₂×#14556571	C₂²	1	2	yes	—
47	C₂×#14556571	C₂²	1	1	yes	characteristic
48	C₂×#14556571	C₂²	1	4	yes	complemented
49	C₂×#14556571	C₂²	1	2	yes	complemented
50	C₂×#14556571	C₂²	1	2	yes	complemented
51	C₂×#14556571	C₂²	1	4	yes	complemented
52	C₂×#14556571	C₂²	1	32	yes	complemented
53	C₂×#14556570	C₂²	1	4	yes	complemented
54	C₂×#14556570	C₂²	1	2	yes	complemented
55	C₂×#14556569	C₂²	1	2	yes	—
56	C₂×#14556569	C₂²	1	4	yes	—
57	C₂×#14556569	C₂²	1	4	yes	complemented
58	C₂×#14556569	C₂²	1	4	yes	complemented
59	C₂×#14556568	C₂²	1	4	yes	complemented
60	C₂×#14556568	C₂²	1	4	yes	complemented
61	C₂×#14556568	C₂²	1	4	yes	complemented
62	C₂×#14556567	C₂²	1	2	yes	—
63	C₂×#14556567	C₂²	1	1	yes	characteristic
64	C₂×#14556567	C₂²	1	4	yes	complemented
65	C₂²⋊Q₈×D₇₃	C₂²	1	32	yes	complemented
66	#17989059	C₂²	1	32	yes	—
67	C₂×Q₈×Dic₇₃	C₂²	1	2	yes	complemented
68	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₄×Dic₁₄₆	C₂²	1	2	yes	complemented
70	C₂×#14556556	C₂²	1	2	yes	complemented
71	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
72	C₂×C₄×D₂₉₂	C₂²	1	2	yes	—
73	C₂×D₄×Dic₇₃	C₂²	1	1	yes	characteristic
74	C₂×D₄×Dic₇₃	C₂²	1	2	yes	—
75	C₂×#14556553	C₂²	1	1	yes	characteristic
76	C₂×#14556553	C₂²	1	2	yes	—
77	C₂×C₄×C₂²⋊D₇₃	C₂²	1	2	yes	—
78	C₂×C₄×C₂²⋊D₇₃	C₂²	1	4	yes	—
79	C₂×#14556551	C₂²	1	2	yes	—
80	C₂×#14556551	C₂²	1	4	yes	—
81	C₄×D₄×D₇₃	C₂²	1	16	yes	—
82	C₂×#14556549	C₂²	1	2	yes	—
83	C₂×#14556548	C₂²	1	2	yes	—
84	C₂²×C₄⋊Dic₇₃	C₂²	1	4	yes	complemented
85	C₂×C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic
86	C₂×C₄⋊C₄×D₇₃	C₂²	1	2	yes	complemented
87	C₂×C₄⋊C₄×D₇₃	C₂²	1	4	yes	complemented
88	C₂²×#11924005	C₂²	1	4	yes	—
89	C₂×C₂²⋊C₄×D₇₃	C₂²	1	2	yes	—
90	C₂×C₂²⋊C₄×D₇₃	C₂²	1	4	yes	—
91	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
92	#554×C₇₃	C₂²	1	16	yes	complemented
93	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
94	C₂×#125×C₇₃	C₂²	1	2	yes	complemented
95	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	complemented
96	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
97	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
99	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
100	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
101	C₂⁴×D₇₃	C₂³	1	2	yes	—
102	C₂²×Dic₁₄₆	—	4	8	no	—
103	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
104	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
105	C₂²×Dic₁₄₆	C₂³	1	4	yes	—
106	C₂²×Dic₁₄₆	C₂³	1	4	yes	—
107	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
108	C₂²×Dic₁₄₆	C₂³	1	16	yes	complemented
109	C₂×Q₈×D₇₃	—	4	8	no	—
110	C₂×Q₈×D₇₃	C₂³	1	16	yes	complemented
111	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
112	C₂²×C₂²⋊D₇₃	C₂³	1	2	yes	—
113	C₂×D₄×D₇₃	Q₈	1	16	yes	complemented
114	C₂×D₄×D₇₃	C₂³	1	8	yes	—
115	C₂³×Dic₇₃	C₂³	1	2	yes	—
116	C₂³×Dic₇₃	C₂³	1	4	yes	—
117	C₂²×C₄×D₇₃	—	4	8	no	—
118	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
119	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
120	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
121	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
122	C₂²×C₄×D₇₃	C₂³	1	16	yes	—
123	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
124	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
125	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
126	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
127	#14556591	C₂³	1	8	yes	complemented
128	#14556591	C₂³	1	16	yes	complemented
129	#14556590	C₂³	1	8	yes	complemented
130	#14556590	C₂³	1	32	yes	complemented
131	#14556590	C₂³	1	16	yes	complemented
132	#14556589	C₂³	1	8	yes	complemented
133	#14556582	C₂³	1	16	yes	complemented
134	#14556582	C₂³	1	16	yes	complemented
135	#14556581	C₂³	1	16	yes	complemented
136	#14556581	C₂³	1	32	yes	complemented
137	#14556571	C₂³	1	8	yes	—
138	#14556571	C₂³	1	16	yes	—
139	#14556571	C₂³	1	32	yes	—
140	#14556571	C₂³	1	32	yes	complemented
141	#14556571	C₂³	1	16	yes	complemented
142	#14556571	C₂³	1	16	yes	complemented
143	#14556571	C₂³	1	32	yes	complemented
144	#14556570	C₂³	1	32	yes	complemented
145	#14556570	C₂³	1	16	yes	complemented
146	#14556569	C₂³	1	16	yes	—
147	#14556569	C₂³	1	32	yes	—
148	#14556569	C₂³	1	32	yes	complemented
149	#14556569	C₂³	1	32	yes	complemented
150	#14556568	C₂³	1	32	yes	complemented
151	#14556568	C₂³	1	32	yes	complemented
152	#14556568	C₂³	1	32	yes	complemented
153	#14556567	C₂³	1	8	yes	—
154	#14556567	C₂³	1	16	yes	—
155	#14556567	C₂³	1	32	yes	complemented
156	Q₈×Dic₇₃	C₂³	1	16	yes	complemented
157	C₄×Dic₁₄₆	C₂³	1	8	yes	complemented
158	C₄×Dic₁₄₆	C₂³	1	16	yes	complemented
159	#14556556	C₂³	1	16	yes	complemented
160	C₄×D₂₉₂	C₂³	1	16	yes	—
161	C₄×D₂₉₂	C₂³	1	8	yes	—
162	D₄×Dic₇₃	C₂³	1	16	yes	—
163	D₄×Dic₇₃	C₂³	1	8	yes	—
164	#14556553	C₂³	1	8	yes	—
165	#14556553	C₂³	1	16	yes	—
166	C₄×C₂²⋊D₇₃	C₂³	1	16	yes	—
167	C₄×C₂²⋊D₇₃	C₂³	1	32	yes	—
168	#14556551	C₂³	1	32	yes	—
169	#14556551	C₂³	1	16	yes	—
170	#14556549	C₂³	1	16	yes	—
171	#14556548	C₂³	1	16	yes	—
172	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
173	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
175	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
177	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
178	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
179	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
180	C₂×C₄⋊Dic₇₃	C₂³	1	32	yes	complemented
181	C₂×#11924007	C₂³	1	2	yes	—
182	C₂×#11924007	C₂³	1	2	yes	—
183	C₂×#11924007	C₂³	1	2	yes	—
184	C₂×#11924007	C₂³	1	4	yes	—
185	C₂×#11924007	C₂³	1	2	yes	—
186	C₂×#11924007	C₂³	1	2	yes	—
187	C₂×#11924007	C₂³	1	4	yes	—
188	C₂×#11924007	C₂³	1	4	yes	—
189	C₂×#11924007	C₂³	1	2	yes	—
190	C₄⋊C₄×D₇₃	C₂³	1	8	yes	—
191	C₄⋊C₄×D₇₃	C₂³	1	16	yes	complemented
192	C₄⋊C₄×D₇₃	C₂³	1	32	yes	complemented
193	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊Dic₇₃	C₂³	1	4	yes	—
195	C₂×#11924005	C₂³	1	32	yes	—
196	C₂×#11924005	C₂³	1	2	yes	—
197	C₂×#11924005	C₂³	1	4	yes	—
198	C₂×#11924005	C₂³	1	2	yes	—
199	C₂×#11924005	C₂³	1	2	yes	—
200	C₂×#11924005	C₂³	1	2	yes	—
201	C₂×#11924005	C₂³	1	4	yes	—
202	C₂×#11924005	C₂³	1	4	yes	—
203	C₂²⋊C₄×D₇₃	C₂³	1	16	yes	—
204	C₂²⋊C₄×D₇₃	C₂³	1	32	yes	—
205	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
206	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
207	C₂×C₄×Dic₇₃	C₂³	1	4	yes	—
208	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
209	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
210	C₄²×D₇₃	C₂³	1	8	yes	—
211	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
212	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
213	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
214	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
215	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
216	C₄⋊Q₈×C₇₃	C₂³	1	8	yes	complemented
217	#125×C₇₃	C₂³	1	16	yes	complemented
218	C₂²⋊Q₈×C₇₃	C₂³	1	32	yes	complemented
219	C₂²⋊Q₈×C₇₃	C₂³	1	16	yes	complemented
220	C₄×Q₈×C₇₃	C₂³	1	8	yes	complemented
221	C₄×D₄×C₇₃	C₂³	1	8	yes	—
222	C₄×D₄×C₇₃	C₂³	1	16	yes	—
223	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
226	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
227	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₇₃	C₂³	1	16	yes	complemented
231	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
232	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
233	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
234	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
235	C₂³×D₇₃	—	4	4	no	—
236	C₂³×D₇₃	—	4	4	no	—
237	C₂³×D₇₃	C₂×Q₈	1	16	yes	complemented
238	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
239	C₂³×D₇₃	C₂⁴	1	2	yes	—
240	C₂³×D₇₃	C₂⁴	1	8	yes	—
241	C₂×Dic₁₄₆	—	2	8	no	—
242	C₂×Dic₁₄₆	—	2	4	no	—
243	C₂×Dic₁₄₆	—	4	32	no	—
244	C₂×Dic₁₄₆	—	4	8	no	—
245	C₂×Dic₁₄₆	—	4	8	no	—
246	C₂×Dic₁₄₆	—	4	4	no	—
247	C₂×Dic₁₄₆	C₂⁴	1	8	yes	—
248	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
249	C₂×Dic₁₄₆	C₂⁴	1	8	yes	—
250	C₂×Dic₁₄₆	C₂⁴	1	16	yes	—
251	C₂×Dic₁₄₆	C₂⁴	1	16	yes	—
252	Q₈×D₇₃	—	4	32	no	—
253	C₂×D₂₉₂	C₂×Q₈	1	8	yes	complemented
254	C₂×D₂₉₂	C₂⁴	1	4	yes	—
255	C₂×C₂²⋊D₇₃	C₂×Q₈	1	16	yes	complemented
256	C₂×C₂²⋊D₇₃	C₂⁴	1	8	yes	—
257	D₄×D₇₃	C₂×Q₈	1	64	yes	complemented
258	C₂²×Dic₇₃	—	4	4	no	—
259	C₂²×Dic₇₃	—	4	8	no	—
260	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
261	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
262	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
263	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
264	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
265	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
266	C₂²×Dic₇₃	C₂⁴	1	16	yes	—
267	C₂²×Dic₇₃	C₂⁴	1	8	yes	—
268	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×D₇₃	—	2	4	no	—
270	C₂×C₄×D₇₃	—	2	8	no	—
271	C₂×C₄×D₇₃	—	4	32	no	—
272	C₂×C₄×D₇₃	—	4	4	no	—
273	C₂×C₄×D₇₃	—	4	4	no	—
274	C₂×C₄×D₇₃	—	4	8	no	—
275	C₂×C₄×D₇₃	—	4	2	no	—
276	C₂×C₄×D₇₃	—	4	8	no	—
277	C₂×C₄×D₇₃	C₂×Q₈	1	8	yes	complemented
278	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
279	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
280	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
281	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
282	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
283	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
284	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
285	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
286	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
287	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
288	C₄⋊Dic₇₃	C₂⁴	1	16	yes	—
289	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
290	C₄⋊Dic₇₃	C₂⁴	1	16	yes	—
291	C₄⋊Dic₇₃	C₂⁴	1	16	yes	—
292	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
293	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
294	#11924007	C₂⁴	1	8	yes	—
295	#11924007	C₂⁴	1	8	yes	—
296	#11924007	C₂⁴	1	16	yes	—
297	#11924007	C₂⁴	1	16	yes	—
298	#11924007	C₂⁴	1	8	yes	—
299	#11924007	C₂⁴	1	8	yes	—
300	#11924007	C₂⁴	1	16	yes	—
301	#11924007	C₂⁴	1	8	yes	—
302	#11924007	C₂⁴	1	8	yes	—
303	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
304	C₂²⋊Dic₇₃	C₂⁴	1	16	yes	—
305	#11924005	C₂⁴	1	8	yes	—
306	#11924005	C₂⁴	1	16	yes	—
307	#11924005	C₂⁴	1	8	yes	—
308	#11924005	C₂⁴	1	8	yes	—
309	#11924005	C₂⁴	1	8	yes	—
310	#11924005	C₂⁴	1	16	yes	—
311	#11924005	C₂⁴	1	16	yes	—
312	C₄×Dic₇₃	C₂⁴	1	4	yes	—
313	C₄×Dic₇₃	C₂⁴	1	4	yes	—
314	C₄×Dic₇₃	C₂⁴	1	4	yes	—
315	C₄×Dic₇₃	C₂⁴	1	8	yes	—
316	C₄×Dic₇₃	C₂⁴	1	16	yes	—
317	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
318	C₂×Q₈×C₇₃	—	2	4	no	—
319	C₂×Q₈×C₇₃	—	4	4	no	—
320	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
321	C₂×Q₈×C₇₃	C₂⁴	1	8	yes	—
322	C₂×D₄×C₇₃	C₂×Q₈	1	8	yes	complemented
323	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
324	C₂²×C₄×C₇₃	—	2	8	no	—
325	C₂²×C₄×C₇₃	—	4	8	no	—
326	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
331	C₂²×C₄×C₇₃	C₂⁴	1	8	yes	—
332	C₂²×C₄×C₇₃	C₂⁴	1	16	yes	—
333	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
336	C₄⋊C₄×C₇₃	C₂⁴	1	16	yes	—
337	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
338	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
339	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
340	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
341	C₄⋊C₄×C₇₃	C₂⁴	1	16	yes	—
342	C₂²⋊C₄×C₇₃	C₂⁴	1	16	yes	—
343	C₂²⋊C₄×C₇₃	C₂⁴	1	8	yes	—
344	C₄²×C₇₃	C₂⁴	1	8	yes	—
345	C₄²×C₇₃	C₂⁴	1	4	yes	—
346	C₂³×C₇₃	—	2	4	no	—
347	C₂³×C₇₃	—	2	4	no	—
348	C₂³×C₇₃	C₂²×Q₈	1	8	yes	—
349	C₂³×C₇₃	C₂⁵	1	4	yes	—
350	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
351	C₂²×D₇₃	—	2	4	no	—
352	C₂²×D₇₃	—	2	2	no	—
353	C₂²×D₇₃	—	2	4	no	—
354	C₂²×D₇₃	—	2	2	no	—
355	C₂²×D₇₃	—	4	8	no	—
356	C₂²×D₇₃	—	4	32	no	—
357	C₂²×D₇₃	—	4	8	no	—
358	C₂²×D₇₃	C₂²×Q₈	1	4	yes	—
359	C₂²×D₇₃	C₂²×Q₈	1	8	yes	—
360	C₂²×D₇₃	C₂²×Q₈	1	32	yes	complemented
361	C₂²×D₇₃	C₂⁵	1	2	yes	—
362	C₂²×D₇₃	C₂⁵	1	4	yes	—
363	Q₈×C₇₃	—	2	8	no	—
364	Q₈×C₇₃	—	4	8	no	—
365	D₄×C₇₃	C₂²×Q₈	1	16	yes	complemented
366	C₂×C₄×C₇₃	—	2	4	no	—
367	C₂×C₄×C₇₃	—	2	4	no	—
368	C₂×C₄×C₇₃	—	2	4	no	—
369	C₂×C₄×C₇₃	—	2	8	no	—
370	C₂×C₄×C₇₃	—	2	2	no	—
371	C₂×C₄×C₇₃	—	2	16	no	—
372	C₂×C₄×C₇₃	—	4	16	no	—
373	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
374	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
375	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
376	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
377	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
378	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
379	C₂×C₄×C₇₃	C₂⁵	1	8	yes	—
380	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
381	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
382	C₂²⋊D₇₃	C₂²×Q₈	1	32	yes	complemented
383	C₂×Dic₇₃	—	2	2	no	—
384	C₂×Dic₇₃	—	2	4	no	—
385	C₂×Dic₇₃	—	2	8	no	—
386	C₂×Dic₇₃	—	2	4	no	—
387	C₂×Dic₇₃	—	2	4	no	—
388	C₂×Dic₇₃	—	2	2	no	—
389	C₂×Dic₇₃	—	4	8	no	—
390	C₂×Dic₇₃	—	4	16	no	—
391	C₂×Dic₇₃	C₂²×Q₈	1	4	yes	—
392	C₂×Dic₇₃	C₂⁵	1	2	yes	—
393	C₂×Dic₇₃	C₂⁵	1	2	yes	—
394	C₂×Dic₇₃	C₂⁵	1	4	yes	—
395	C₂×Dic₇₃	C₂⁵	1	8	yes	—
396	C₂×Dic₇₃	C₂⁵	1	4	yes	—
397	C₂×Dic₇₃	C₂⁵	1	4	yes	—
398	C₂×Dic₇₃	C₂⁵	1	2	yes	—
399	D₂₉₂	C₂²×Q₈	1	16	yes	complemented
400	C₄×D₇₃	—	2	8	no	—
401	C₄×D₇₃	—	2	16	no	—
402	C₄×D₇₃	—	4	8	no	—
403	C₄×D₇₃	—	4	8	no	—
404	C₄×D₇₃	—	4	4	no	—
405	C₄×D₇₃	—	4	16	no	—
406	C₄×D₇₃	—	4	16	no	—
407	C₄×D₇₃	C₂²×Q₈	1	16	yes	complemented
408	Dic₁₄₆	—	2	16	no	—
409	Dic₁₄₆	—	2	8	no	—
410	Dic₁₄₆	—	4	16	no	—
411	Dic₁₄₆	—	4	16	no	—
412	Dic₁₄₆	—	4	8	no	—
413	C₂²×C₇₃	—	2	4	no	—
414	C₂²×C₇₃	—	2	4	no	—
415	C₂²×C₇₃	—	2	16	no	—
416	C₂²×C₇₃	C₂³×Q₈	1	8	yes	—
417	C₂²×C₇₃	C₂³×Q₈	1	2	yes	—
418	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
419	C₂²×C₇₃	#585	1	2	yes	—
420	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
421	C₂×D₇₃	—	2	4	no	—
422	C₂×D₇₃	—	2	2	no	—
423	C₂×D₇₃	—	2	4	no	—
424	C₂×D₇₃	—	2	2	no	—
425	C₂×D₇₃	—	2	8	no	—
426	C₂×D₇₃	—	2	16	no	—
427	C₂×D₇₃	—	4	32	no	—
428	C₂×D₇₃	C₂³×Q₈	1	4	yes	—
429	C₂×D₇₃	C₂³×Q₈	1	8	yes	—
430	C₄×C₇₃	—	2	4	no	—
431	C₄×C₇₃	—	2	4	no	—
432	C₄×C₇₃	—	2	4	no	—
433	C₄×C₇₃	—	2	8	no	—
434	C₄×C₇₃	—	2	2	no	—
435	C₄×C₇₃	C₂³×Q₈	1	4	yes	—
436	C₄×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
437	Dic₇₃	—	2	8	no	—
438	Dic₇₃	—	2	4	no	—
439	Dic₇₃	—	2	4	no	—
440	Dic₇₃	—	2	2	no	—
441	Dic₇₃	—	2	2	no	—
442	Dic₇₃	—	2	4	no	—
443	Dic₇₃	C₂³×Q₈	1	4	yes	—
444	C₂×#3501	—	73	1	no	maximal, Sylow
445	C₂×C₇₃	—	2	8	no	—
446	C₂×C₇₃	#3501	1	4	yes	complemented
447	C₂×C₇₃	C₂⁴×Q₈	1	1	yes	characteristic
448	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂×C₇₃	C₂×#585	1	1	yes	characteristic
450	D₇₃	—	2	4	no	—
451	D₇₃	—	2	8	no	—
452	#3501	—	73	32	no	—
453	C₂×#554	—	73	1	no	—
454	C₂×#554	—	73	2	no	—
455	C₂×#554	—	73	4	no	—
456	C₂×#554	—	73	2	no	—
457	C₂×#554	—	73	2	no	—
458	C₂×#554	D₇₃	1	1	yes	characteristic, complemented
459	C₂×D₄×Q₈	—	73	2	no	—
460	C₂×D₄×Q₈	—	73	1	no	—
461	C₂×D₄×Q₈	—	73	1	no	—
462	C₂×#544	—	73	2	no	—
463	C₂×#543	—	73	4	no	—
464	C₂×#533	—	73	1	no	—
465	C₂×#533	—	73	1	no	—
466	C₂²×C₂²⋊Q₈	—	73	2	no	—
467	C₂²×C₂²⋊Q₈	—	73	2	no	—
468	C₂×#518	—	73	2	no	—
469	C₂²×C₄×D₄	—	73	1	no	—
470	C₇₃	C₂×#3501	1	1	yes	characteristic, complemented, Sylow
471	C₂³×Q₈	—	73	2	no	—
472	C₂³×Q₈	—	73	2	no	—
473	C₂³×D₄	—	73	1	no	—
474	C₂⁴×C₄	—	73	2	no	—
475	#554	—	73	16	no	—
476	#554	—	73	32	no	—
477	#554	—	73	64	no	—
478	#554	—	73	32	no	—
479	#554	—	73	32	no	—
480	#554	C₂×D₇₃	1	16	yes	complemented
481	D₄×Q₈	—	73	32	no	—
482	D₄×Q₈	—	73	16	no	—
483	D₄×Q₈	—	73	16	no	—
484	#544	—	73	32	no	—
485	#543	—	73	64	no	—
486	#533	—	73	16	no	—
487	#533	—	73	16	no	—
488	C₂×C₄⋊Q₈	—	73	1	no	—
489	C₂×C₄⋊Q₈	—	73	1	no	—
490	C₂×C₄⋊Q₈	—	73	4	no	—
491	C₂×C₄⋊Q₈	—	73	2	no	—
492	C₂×C₄⋊Q₈	—	73	1	no	—
493	C₂×C₄⋊Q₈	—	73	2	no	—
494	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
495	C₂×#125	—	73	2	no	—
496	C₂×#125	—	73	2	no	—
497	C₂×#125	—	73	4	no	—
498	C₂×#125	—	73	2	no	—
499	C₂×#125	C₂×D₇₃	1	2	yes	complemented
500	C₂×C₂²⋊Q₈	—	73	1	no	—
501	C₂×C₂²⋊Q₈	—	73	2	no	—
502	C₂×C₂²⋊Q₈	—	73	4	no	—
503	C₂×C₂²⋊Q₈	—	73	2	no	—
504	C₂×C₂²⋊Q₈	—	73	4	no	—
505	C₂×C₂²⋊Q₈	—	73	32	no	—
506	C₂×C₂²⋊Q₈	—	73	2	no	—
507	C₂×C₂²⋊Q₈	—	73	1	no	—
508	C₂×C₂²⋊Q₈	—	73	4	no	—
509	C₂×C₂²⋊Q₈	—	73	4	no	—
510	C₂×C₂²⋊Q₈	—	73	2	no	—
511	C₂×C₂²⋊Q₈	—	73	2	no	—
512	C₂×C₂²⋊Q₈	—	73	4	no	—
513	C₂×C₂²⋊Q₈	—	73	2	no	—
514	C₂×C₂²⋊Q₈	—	73	4	no	—
515	C₂×C₂²⋊Q₈	—	73	4	no	—
516	C₂×C₂²⋊Q₈	—	73	4	no	—
517	C₂×C₂²⋊Q₈	—	73	32	no	—
518	C₂×C₂²⋊Q₈	—	73	4	no	—
519	C₂×C₂²⋊Q₈	—	73	4	no	—
520	C₂×C₂²⋊Q₈	—	73	4	no	—
521	C₂×C₂²⋊Q₈	C₂×D₇₃	1	2	yes	complemented
522	C₂×C₂²⋊Q₈	C₂×D₇₃	1	4	yes	complemented
523	#518	—	73	32	no	—
524	C₂×C₄×Q₈	—	73	2	no	—
525	C₂×C₄×Q₈	—	73	2	no	—
526	C₂×C₄×Q₈	—	73	1	no	—
527	C₂×C₄×Q₈	—	73	2	no	—
528	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
529	C₂×C₄×D₄	—	73	1	no	—
530	C₂×C₄×D₄	—	73	2	no	—
531	C₂×C₄×D₄	—	73	2	no	—
532	C₂×C₄×D₄	—	73	4	no	—
533	C₂×C₄×D₄	—	73	16	no	—
534	C₂×C₄×D₄	—	73	1	no	—
535	C₂×C₄×D₄	—	73	2	no	—
536	C₂×C₄×D₄	—	73	2	no	—
537	C₂×C₄×D₄	—	73	4	no	—
538	C₂×C₄×D₄	—	73	1	no	—
539	C₂×C₄×D₄	—	73	2	no	—
540	C₂×C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
541	C₂×C₄×D₄	C₂×D₇₃	1	2	yes	—
542	C₂×#117	—	73	2	no	—
543	C₂×#117	—	73	2	no	—
544	C₂²×C₄⋊C₄	—	73	4	no	—
545	C₂²×C₄⋊C₄	—	73	1	no	—
546	C₂²×C₄⋊C₄	—	73	4	no	—
547	C₂²×C₄⋊C₄	—	73	2	no	—
548	C₂²×C₄⋊C₄	C₂×D₇₃	1	2	yes	complemented
549	C₂²×C₂²⋊C₄	—	73	4	no	—
550	C₂²×C₂²⋊C₄	—	73	2	no	—
551	C₂²×C₂²⋊C₄	—	73	4	no	—
552	C₂²×C₄²	—	73	1	no	—
553	C₂⁵	—	73	2	no	—
554	C₂²×Q₈	—	292	8	no	—
555	C₂²×Q₈	—	292	8	no	—
556	C₂²×Q₈	—	73	16	no	—
557	C₂²×Q₈	—	73	2	no	—
558	C₂²×Q₈	—	73	4	no	—
559	C₂²×Q₈	—	73	4	no	—
560	C₂²×Q₈	—	73	16	no	—
561	C₂²×Q₈	—	73	2	no	—
562	C₂²×Q₈	—	73	1	no	—
563	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
564	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
565	C₂²×D₄	—	73	2	no	—
566	C₂²×D₄	—	73	16	no	—
567	C₂²×D₄	—	73	8	no	—
568	C₂²×D₄	—	73	1	no	—
569	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
570	C₂³×C₄	—	292	8	no	—
571	C₂³×C₄	—	73	4	no	—
572	C₂³×C₄	—	73	2	no	—
573	C₂³×C₄	—	73	1	no	—
574	C₂³×C₄	—	73	4	no	—
575	C₂³×C₄	—	73	4	no	—
576	C₂³×C₄	—	73	2	no	—
577	C₂³×C₄	—	73	2	no	—
578	C₂³×C₄	—	73	16	no	—
579	C₂³×C₄	—	73	1	no	—
580	C₂³×C₄	—	73	2	no	—
581	C₂³×C₄	—	73	1	no	—
582	C₂³×C₄	C₂²×D₇₃	1	2	yes	—
583	C₂³×C₄	C₂²×D₇₃	1	4	yes	—
584	C₄⋊Q₈	—	73	8	no	—
585	C₄⋊Q₈	—	73	8	no	—
586	C₄⋊Q₈	—	73	32	no	—
587	C₄⋊Q₈	—	73	16	no	—
588	C₄⋊Q₈	—	73	8	no	—
589	C₄⋊Q₈	—	73	16	no	—
590	C₄⋊Q₈	C₂²×D₇₃	1	8	yes	complemented
591	#125	—	73	16	no	—
592	#125	—	73	16	no	—
593	#125	—	73	32	no	—
594	#125	—	73	16	no	—
595	#125	C₂²×D₇₃	1	16	yes	complemented
596	C₂²⋊Q₈	—	73	8	no	—
597	C₂²⋊Q₈	—	73	16	no	—
598	C₂²⋊Q₈	—	73	32	no	—
599	C₂²⋊Q₈	—	73	16	no	—
600	C₂²⋊Q₈	—	73	32	no	—
601	C₂²⋊Q₈	—	73	16	no	—
602	C₂²⋊Q₈	—	73	8	no	—
603	C₂²⋊Q₈	—	73	32	no	—
604	C₂²⋊Q₈	—	73	32	no	—
605	C₂²⋊Q₈	—	73	16	no	—
606	C₂²⋊Q₈	—	73	16	no	—
607	C₂²⋊Q₈	—	73	32	no	—
608	C₂²⋊Q₈	—	73	16	no	—
609	C₂²⋊Q₈	—	73	32	no	—
610	C₂²⋊Q₈	—	73	32	no	—
611	C₂²⋊Q₈	—	73	32	no	—
612	C₂²⋊Q₈	—	73	32	no	—
613	C₂²⋊Q₈	—	73	32	no	—
614	C₂²⋊Q₈	—	73	32	no	—
615	C₂²⋊Q₈	C₂²×D₇₃	1	16	yes	complemented
616	C₂²⋊Q₈	C₂²×D₇₃	1	32	yes	complemented
617	C₄×Q₈	—	73	16	no	—
618	C₄×Q₈	—	73	16	no	—
619	C₄×Q₈	—	73	8	no	—
620	C₄×Q₈	—	73	16	no	—
621	C₄×Q₈	C₂²×D₇₃	1	8	yes	complemented
622	C₄×D₄	—	73	8	no	—
623	C₄×D₄	—	73	16	no	—
624	C₄×D₄	—	73	16	no	—
625	C₄×D₄	—	73	32	no	—
626	C₄×D₄	—	73	8	no	—
627	C₄×D₄	—	73	16	no	—
628	C₄×D₄	—	73	16	no	—
629	C₄×D₄	—	73	32	no	—
630	C₄×D₄	—	73	8	no	—
631	C₄×D₄	—	73	16	no	—
632	C₄×D₄	C₂²×D₇₃	1	8	yes	—
633	C₄×D₄	C₂²×D₇₃	1	16	yes	—
634	#117	—	73	16	no	—
635	#117	—	73	16	no	—
636	C₂×C₄⋊C₄	—	73	2	no	—
637	C₂×C₄⋊C₄	—	73	4	no	—
638	C₂×C₄⋊C₄	—	73	2	no	—
639	C₂×C₄⋊C₄	—	73	1	no	—
640	C₂×C₄⋊C₄	—	73	2	no	—
641	C₂×C₄⋊C₄	—	73	1	no	—
642	C₂×C₄⋊C₄	—	73	4	no	—
643	C₂×C₄⋊C₄	—	73	4	no	—
644	C₂×C₄⋊C₄	—	73	4	no	—
645	C₂×C₄⋊C₄	—	73	4	no	—
646	C₂×C₄⋊C₄	—	73	32	no	—
647	C₂×C₄⋊C₄	—	73	2	no	—
648	C₂×C₄⋊C₄	—	73	2	no	—
649	C₂×C₄⋊C₄	—	73	2	no	—
650	C₂×C₄⋊C₄	—	73	4	no	—
651	C₂×C₄⋊C₄	—	73	2	no	—
652	C₂×C₄⋊C₄	—	73	2	no	—
653	C₂×C₄⋊C₄	—	73	2	no	—
654	C₂×C₄⋊C₄	—	73	8	no	—
655	C₂×C₄⋊C₄	—	73	32	no	—
656	C₂×C₄⋊C₄	—	73	16	no	—
657	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
660	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
662	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂²×D₇₃	1	16	yes	complemented
665	C₂×C₂²⋊C₄	—	73	2	no	—
666	C₂×C₂²⋊C₄	—	73	4	no	—
667	C₂×C₂²⋊C₄	—	73	2	no	—
668	C₂×C₂²⋊C₄	—	73	4	no	—
669	C₂×C₂²⋊C₄	—	73	2	no	—
670	C₂×C₂²⋊C₄	—	73	2	no	—
671	C₂×C₂²⋊C₄	—	73	4	no	—
672	C₂×C₂²⋊C₄	—	73	4	no	—
673	C₂×C₂²⋊C₄	—	73	2	no	—
674	C₂×C₂²⋊C₄	—	73	32	no	—
675	C₂×C₂²⋊C₄	—	73	16	no	—
676	C₂×C₂²⋊C₄	—	73	32	no	—
677	C₂×C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
679	C₂×C₄²	—	73	4	no	—
680	C₂×C₄²	—	73	2	no	—
681	C₂×C₄²	—	73	1	no	—
682	C₂×C₄²	—	73	1	no	—
683	C₂×C₄²	—	73	1	no	—
684	C₂×C₄²	—	73	8	no	—
685	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
686	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
687	C₂⁴	—	292	4	no	—
688	C₂⁴	—	292	4	no	—
689	C₂⁴	—	73	16	no	—
690	C₂⁴	—	73	8	no	—
691	C₂⁴	—	73	1	no	—
692	C₂⁴	—	73	2	no	—
693	C₂⁴	C₂³×D₇₃	1	2	yes	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	4	4	no	—
696	C₂×Q₈	—	292	32	no	—
697	C₂×Q₈	—	292	8	no	—
698	C₂×Q₈	—	292	8	no	—
699	C₂×Q₈	—	292	4	no	—
700	C₂×Q₈	—	292	32	no	—
701	C₂×Q₈	—	73	8	no	—
702	C₂×Q₈	—	73	16	no	—
703	C₂×Q₈	—	73	16	no	—
704	C₂×Q₈	—	73	8	no	—
705	C₂×Q₈	—	73	4	no	—
706	C₂×Q₈	—	146	8	no	—
707	C₂×Q₈	—	146	4	no	—
708	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
709	C₂×Q₈	C₂³×D₇₃	1	8	yes	—
710	C₂×D₄	—	73	16	no	—
711	C₂×D₄	—	73	8	no	—
712	C₂×D₄	—	73	64	no	—
713	C₂×D₄	—	73	8	no	—
714	C₂×D₄	—	73	4	no	—
715	C₂×D₄	Q₈×D₇₃	1	8	yes	complemented
716	C₂×D₄	C₂³×D₇₃	1	4	yes	—
717	C₂²×C₄	—	2	8	no	—
718	C₂²×C₄	—	4	8	no	—
719	C₂²×C₄	—	292	4	no	—
720	C₂²×C₄	—	292	4	no	—
721	C₂²×C₄	—	292	8	no	—
722	C₂²×C₄	—	292	2	no	—
723	C₂²×C₄	—	292	8	no	—
724	C₂²×C₄	—	292	32	no	—
725	C₂²×C₄	—	292	4	no	—
726	C₂²×C₄	—	292	8	no	—
727	C₂²×C₄	—	73	16	no	—
728	C₂²×C₄	—	73	8	no	—
729	C₂²×C₄	—	73	4	no	—
730	C₂²×C₄	—	73	16	no	—
731	C₂²×C₄	—	73	16	no	—
732	C₂²×C₄	—	73	8	no	—
733	C₂²×C₄	—	73	8	no	—
734	C₂²×C₄	—	73	1	no	—
735	C₂²×C₄	—	73	8	no	—
736	C₂²×C₄	—	73	4	no	—
737	C₂²×C₄	—	73	1	no	—
738	C₂²×C₄	—	73	1	no	—
739	C₂²×C₄	—	73	2	no	—
740	C₂²×C₄	—	73	2	no	—
741	C₂²×C₄	—	73	4	no	—
742	C₂²×C₄	—	73	2	no	—
743	C₂²×C₄	—	73	4	no	—
744	C₂²×C₄	—	73	8	no	—
745	C₂²×C₄	—	146	4	no	—
746	C₂²×C₄	—	146	8	no	—
747	C₂²×C₄	C₂³×D₇₃	1	8	yes	—
748	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
749	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
750	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
751	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
752	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
753	C₂²×C₄	C₂³×D₇₃	1	16	yes	—
754	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
755	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
756	C₄⋊C₄	—	73	8	no	—
757	C₄⋊C₄	—	73	8	no	—
758	C₄⋊C₄	—	73	16	no	—
759	C₄⋊C₄	—	73	16	no	—
760	C₄⋊C₄	—	73	8	no	—
761	C₄⋊C₄	—	73	8	no	—
762	C₄⋊C₄	—	73	16	no	—
763	C₄⋊C₄	—	73	8	no	—
764	C₄⋊C₄	—	73	8	no	—
765	C₄⋊C₄	—	73	16	no	—
766	C₄⋊C₄	—	73	8	no	—
767	C₄⋊C₄	—	73	4	no	—
768	C₄⋊C₄	—	73	4	no	—
769	C₄⋊C₄	—	73	16	no	—
770	C₄⋊C₄	—	73	16	no	—
771	C₄⋊C₄	—	73	8	no	—
772	C₄⋊C₄	—	73	8	no	—
773	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
774	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
775	C₄⋊C₄	C₂³×D₇₃	1	16	yes	—
776	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
777	C₄⋊C₄	C₂³×D₇₃	1	16	yes	—
778	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
779	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
780	C₂²⋊C₄	—	73	8	no	—
781	C₂²⋊C₄	—	73	16	no	—
782	C₂²⋊C₄	—	73	8	no	—
783	C₂²⋊C₄	—	73	16	no	—
784	C₂²⋊C₄	—	73	8	no	—
785	C₂²⋊C₄	—	73	8	no	—
786	C₂²⋊C₄	—	73	16	no	—
787	C₂²⋊C₄	—	73	16	no	—
788	C₂²⋊C₄	—	73	8	no	—
789	C₂²⋊C₄	C₂³×D₇₃	1	8	yes	—
790	C₂²⋊C₄	C₂³×D₇₃	1	16	yes	—
791	C₄²	—	73	4	no	—
792	C₄²	—	73	4	no	—
793	C₄²	—	73	4	no	—
794	C₄²	—	73	16	no	—
795	C₄²	—	73	8	no	—
796	C₄²	C₂³×D₇₃	1	4	yes	—
797	C₄²	C₂³×D₇₃	1	8	yes	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	292	8	no	—
801	C₂³	—	292	8	no	—
802	C₂³	—	292	32	no	—
803	C₂³	—	73	32	no	—
804	C₂³	—	73	4	no	—
805	C₂³	—	73	8	no	—
806	C₂³	—	73	2	no	—
807	C₂³	—	73	4	no	—
808	C₂³	—	146	4	no	—
809	C₂³	—	146	2	no	—
810	C₂³	—	146	4	no	—
811	C₂³	—	146	2	no	—
812	C₂³	C₂×Q₈×D₇₃	1	8	yes	—
813	C₂³	C₂⁴×D₇₃	1	4	yes	—
814	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
815	Q₈	—	2	8	no	—
816	Q₈	—	4	8	no	—
817	Q₈	—	292	16	no	—
818	Q₈	—	292	16	no	—
819	Q₈	—	292	8	no	—
820	Q₈	—	146	8	no	—
821	Q₈	—	146	16	no	—
822	D₄	—	73	32	no	—
823	D₄	—	73	16	no	—
824	D₄	C₂×Q₈×D₇₃	1	16	yes	complemented
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	8	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	16	no	—
831	C₂×C₄	—	4	16	no	—
832	C₂×C₄	—	292	8	no	—
833	C₂×C₄	—	292	8	no	—
834	C₂×C₄	—	292	16	no	—
835	C₂×C₄	—	292	16	no	—
836	C₂×C₄	—	292	4	no	—
837	C₂×C₄	—	292	8	no	—
838	C₂×C₄	—	292	16	no	—
839	C₂×C₄	—	73	4	no	—
840	C₂×C₄	—	73	2	no	—
841	C₂×C₄	—	73	16	no	—
842	C₂×C₄	—	73	2	no	—
843	C₂×C₄	—	73	2	no	—
844	C₂×C₄	—	73	4	no	—
845	C₂×C₄	—	73	8	no	—
846	C₂×C₄	—	73	4	no	—
847	C₂×C₄	—	73	4	no	—
848	C₂×C₄	—	146	2	no	—
849	C₂×C₄	—	146	4	no	—
850	C₂×C₄	—	146	8	no	—
851	C₂×C₄	—	146	4	no	—
852	C₂×C₄	—	146	4	no	—
853	C₂×C₄	—	146	2	no	—
854	C₂×C₄	—	146	8	no	—
855	C₂×C₄	—	146	16	no	—
856	C₂×C₄	C₂×Q₈×D₇₃	1	4	yes	—
857	C₂×C₄	#14556637	1	4	yes	—
858	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
859	C₂×C₄	C₂⁴×D₇₃	1	8	yes	—
860	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
861	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
862	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
863	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
864	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	16	no	—
868	C₂²	—	292	32	no	—
869	C₂²	—	73	4	no	—
870	C₂²	—	73	8	no	—
871	C₂²	—	146	4	no	—
872	C₂²	—	146	2	no	—
873	C₂²	—	146	4	no	—
874	C₂²	—	146	2	no	—
875	C₂²	—	146	8	no	—
876	C₂²	—	146	16	no	—
877	C₂²	C₂²×Q₈×D₇₃	1	8	yes	—
878	C₂²	C₂²×Q₈×D₇₃	1	2	yes	—
879	C₂²	C₂×#14556637	1	2	yes	—
880	C₂²	#17989422	1	2	yes	—
881	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
882	C₄	—	2	4	no	—
883	C₄	—	2	4	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	8	no	—
886	C₄	—	2	2	no	—
887	C₄	—	73	4	no	—
888	C₄	—	146	2	no	—
889	C₄	—	146	4	no	—
890	C₄	—	146	8	no	—
891	C₄	—	146	4	no	—
892	C₄	—	146	4	no	—
893	C₄	—	146	2	no	—
894	C₄	C₂²×Q₈×D₇₃	1	4	yes	—
895	C₄	C₂×#14556637	1	4	yes	—
896	C₂	—	2	8	no	—
897	C₂	—	146	4	no	—
898	C₂	—	146	8	no	—
899	C₂	#22623728	1	4	yes	direct product factor
900	C₂	C₂³×Q₈×D₇₃	1	1	yes	characteristic
901	C₂	C₂²×#14556637	1	1	yes	characteristic
902	C₂	C₂×#17989422	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₃
commutator, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×#554×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
prime radical	C₂²×D₄×D₇₃	C₂²
hypercenter	C₂×#554	D₇₃
hypocenter	C₇₃	C₂×#3501
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×#554

Complements

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

N	H ≅ G/N	type
1. #22623728	C₂	direct (N × H)
2. C₂×#17989298	C₂	semidirect
3. C₂×#17989295	C₂	semidirect
4. C₂×#17989294	C₂	semidirect
5. C₂×#17989293	C₂	semidirect
6. C₂×#17989292	C₂	semidirect
7. C₂×Q₈×D₂₉₂	C₂	semidirect
8. C₂×D₄×Dic₁₄₆	C₂	semidirect
9. C₂×#17989250	C₂	semidirect
10. C₂×#17989217	C₂	semidirect
11. C₂×#17989212	C₂	semidirect
12. C₂×#17989142	C₂	semidirect
13. C₂×#17989141	C₂	semidirect
14. C₂²×#14556571	C₂	semidirect
15. C₂×C₂²⋊Q₈×D₇₃	C₂	semidirect
18. C₂×#554×C₇₃	C₂	semidirect
19. C₂³×Dic₁₄₆	C₂²	semidirect
20. C₂²×Q₈×D₇₃	C₂²	semidirect
23. #17989298	C₂²	semidirect
24. #17989295	C₂²	semidirect
25. #17989294	C₂²	semidirect
26. #17989293	C₂²	semidirect
27. #17989292	C₂²	semidirect
28. Q₈×D₂₉₂	C₂²	semidirect
29. D₄×Dic₁₄₆	C₂²	semidirect
30. #17989250	C₂²	semidirect
31. #17989217	C₂²	semidirect
32. #17989212	C₂²	semidirect
33. #17989142	C₂²	semidirect
34. #17989141	C₂²	semidirect
35. C₂×#14556591	C₂²	semidirect
36. C₂×#14556591	C₂²	semidirect
37. C₂×#14556590	C₂²	semidirect
38. C₂×#14556590	C₂²	semidirect
39. C₂×#14556590	C₂²	semidirect
40. C₂×#14556589	C₂²	semidirect
41. C₂×#14556582	C₂²	semidirect
42. C₂×#14556582	C₂²	semidirect
43. C₂×#14556581	C₂²	semidirect
44. C₂×#14556581	C₂²	semidirect
48. C₂×#14556571	C₂²	semidirect
49. C₂×#14556571	C₂²	semidirect
50. C₂×#14556571	C₂²	semidirect
51. C₂×#14556571	C₂²	semidirect
52. C₂×#14556571	C₂²	semidirect
53. C₂×#14556570	C₂²	semidirect
54. C₂×#14556570	C₂²	semidirect
57. C₂×#14556569	C₂²	semidirect
58. C₂×#14556569	C₂²	semidirect
59. C₂×#14556568	C₂²	semidirect
60. C₂×#14556568	C₂²	semidirect
61. C₂×#14556568	C₂²	semidirect
64. C₂×#14556567	C₂²	semidirect
65. C₂²⋊Q₈×D₇₃	C₂²	semidirect
67. C₂×Q₈×Dic₇₃	C₂²	semidirect
68. C₂×C₄×Dic₁₄₆	C₂²	semidirect
69. C₂×C₄×Dic₁₄₆	C₂²	semidirect
70. C₂×#14556556	C₂²	semidirect
84. C₂²×C₄⋊Dic₇₃	C₂²	semidirect
86. C₂×C₄⋊C₄×D₇₃	C₂²	semidirect
87. C₂×C₄⋊C₄×D₇₃	C₂²	semidirect
92. #554×C₇₃	C₂²	semidirect
93. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
94. C₂×#125×C₇₃	C₂²	semidirect
95. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
96. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
97. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
100. C₂²×C₄⋊C₄×C₇₃	C₂²	semidirect
108. C₂²×Dic₁₄₆	C₂³	semidirect
110. C₂×Q₈×D₇₃	C₂³	semidirect
113. C₂×D₄×D₇₃	Q₈	semidirect
127. #14556591	C₂³	semidirect
128. #14556591	C₂³	semidirect
129. #14556590	C₂³	semidirect
130. #14556590	C₂³	semidirect
131. #14556590	C₂³	semidirect
132. #14556589	C₂³	semidirect
133. #14556582	C₂³	semidirect
134. #14556582	C₂³	semidirect
135. #14556581	C₂³	semidirect
136. #14556581	C₂³	semidirect
140. #14556571	C₂³	semidirect
141. #14556571	C₂³	semidirect
142. #14556571	C₂³	semidirect
143. #14556571	C₂³	semidirect
144. #14556570	C₂³	semidirect
145. #14556570	C₂³	semidirect
148. #14556569	C₂³	semidirect
149. #14556569	C₂³	semidirect
150. #14556568	C₂³	semidirect
151. #14556568	C₂³	semidirect
152. #14556568	C₂³	semidirect
155. #14556567	C₂³	semidirect
156. Q₈×Dic₇₃	C₂³	semidirect
157. C₄×Dic₁₄₆	C₂³	semidirect
158. C₄×Dic₁₄₆	C₂³	semidirect
159. #14556556	C₂³	semidirect
180. C₂×C₄⋊Dic₇₃	C₂³	semidirect
191. C₄⋊C₄×D₇₃	C₂³	semidirect
192. C₄⋊C₄×D₇₃	C₂³	semidirect
216. C₄⋊Q₈×C₇₃	C₂³	semidirect
217. #125×C₇₃	C₂³	semidirect
218. C₂²⋊Q₈×C₇₃	C₂³	semidirect
219. C₂²⋊Q₈×C₇₃	C₂³	semidirect
220. C₄×Q₈×C₇₃	C₂³	semidirect
230. C₂×C₄⋊C₄×C₇₃	C₂³	semidirect
237. C₂³×D₇₃	C₂×Q₈	semidirect
253. C₂×D₂₉₂	C₂×Q₈	semidirect
255. C₂×C₂²⋊D₇₃	C₂×Q₈	semidirect
257. D₄×D₇₃	C₂×Q₈	semidirect
277. C₂×C₄×D₇₃	C₂×Q₈	semidirect
322. C₂×D₄×C₇₃	C₂×Q₈	semidirect
360. C₂²×D₇₃	C₂²×Q₈	semidirect
365. D₄×C₇₃	C₂²×Q₈	semidirect
382. C₂²⋊D₇₃	C₂²×Q₈	semidirect
399. D₂₉₂	C₂²×Q₈	semidirect
407. C₄×D₇₃	C₂²×Q₈	semidirect
446. C₂×C₇₃	#3501	semidirect
458. C₂×#554	D₇₃	semidirect
470. C₇₃	C₂×#3501	semidirect
480. #554	C₂×D₇₃	semidirect
494. C₂×C₄⋊Q₈	C₂×D₇₃	semidirect
499. C₂×#125	C₂×D₇₃	semidirect
521. C₂×C₂²⋊Q₈	C₂×D₇₃	semidirect
522. C₂×C₂²⋊Q₈	C₂×D₇₃	semidirect
528. C₂×C₄×Q₈	C₂×D₇₃	semidirect
548. C₂²×C₄⋊C₄	C₂×D₇₃	semidirect
590. C₄⋊Q₈	C₂²×D₇₃	semidirect
595. #125	C₂²×D₇₃	semidirect
615. C₂²⋊Q₈	C₂²×D₇₃	semidirect
616. C₂²⋊Q₈	C₂²×D₇₃	semidirect
621. C₄×Q₈	C₂²×D₇₃	semidirect
664. C₂×C₄⋊C₄	C₂²×D₇₃	semidirect
715. C₂×D₄	Q₈×D₇₃	semidirect
824. D₄	C₂×Q₈×D₇₃	semidirect
899. C₂	#22623728	direct (N × H)

Maximal subgroups

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

subgroup	index
#22623728	2
C₂×#17989298	2
C₂×#17989295	2
C₂×#17989294	2
C₂×#17989293	2
C₂×#17989292	2
C₂×Q₈×D₂₉₂	2
C₂×D₄×Dic₁₄₆	2
C₂×#17989250	2
C₂×#17989217	2
C₂×#17989212	2
C₂×#17989142	2
C₂×#17989141	2
C₂²×#14556571	2
C₂×C₂²⋊Q₈×D₇₃	2
C₂×#17989059	2
C₂×C₄×D₄×D₇₃	2
C₂×#554×C₇₃	2
C₂×#3501	73

Subgroups — C2×#22623728 #33993882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22623728 #33993882