Subgroups — D₇₃⋊#2957 #34031457

Order 18688.

2642 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃⋊#568	C₂	1	2	yes	maximal, complemented
2	#22626711	C₂	1	2	yes	maximal, complemented
3	#22626710	C₂	1	4	yes	maximal, complemented
4	#22626709	C₂	1	4	yes	maximal, complemented
5	#22626708	C₂	1	4	yes	maximal, complemented
6	#22626707	C₂	1	2	yes	maximal, complemented
7	D₇₃⋊#444	C₂	1	4	yes	maximal, complemented
8	D₇₃⋊#443	C₂	1	4	yes	maximal, complemented
9	C₂×D₇₃⋊#108	C₂	1	1	yes	maximal, characteristic, complemented
10	D₇₃⋊#421	C₂	1	2	yes	maximal, complemented
11	C₂×#17989550	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×D₇₃	C₂	1	1	yes	maximal, characteristic
13	#17989667	C₂²	1	4	yes	complemented
14	#17989666	—	2	4	no	—
15	#17989666	C₂²	1	8	yes	complemented
16	#17989665	—	2	4	no	—
17	#17989665	C₂²	1	4	yes	complemented
18	D₇₃⋊#131	—	2	4	no	—
19	D₇₃⋊#131	C₂²	1	8	yes	complemented
20	C₂×D₇₃⋊M₁₆	—	2	4	no	—
21	C₂×D₇₃⋊M₁₆	C₂²	1	2	yes	—
22	C₂×D₇₃⋊M₁₆	C₂²	1	1	yes	characteristic
23	C₂×#14556670	C₂²	1	1	yes	characteristic
24	#17989634	C₂²	1	8	yes	complemented
25	#17989633	C₂²	1	8	yes	complemented
26	#17989632	C₂²	1	16	yes	complemented
27	#17989631	C₂²	1	8	yes	complemented
28	#17989630	C₂²	1	16	yes	complemented
29	#17989629	C₂²	1	8	yes	complemented
30	C₂×#14556662	C₂²	1	2	yes	complemented
31	D₇₃⋊#108	C₂²	1	2	yes	complemented
32	D₇₃⋊#108	C₂²	1	2	yes	complemented
33	D₇₃⋊#108	C₂²	1	2	yes	complemented
34	D₇₃⋊#108	C₂²	1	2	yes	complemented
35	C₂×#14556661	C₂²	1	2	yes	complemented
36	#17989586	C₂²	1	4	yes	complemented
37	#17989585	C₂²	1	4	yes	complemented
38	#17989584	C₂²	1	8	yes	complemented
39	D₇₃⋊#104	C₂²	1	8	yes	complemented
40	#17989550	C₂²	1	2	yes	complemented
41	#17989550	C₂²	1	2	yes	complemented
42	#17989550	C₂²	1	2	yes	complemented
43	#17989550	C₂²	1	2	yes	complemented
44	C₂×#14556645	C₂²	1	2	yes	complemented
45	C₂×C₈×#64408	C₂²	1	2	yes	complemented
46	C₂×#41×D₇₃	C₂²	1	2	yes	—
47	C₂×#14556614	C₂²	1	1	yes	characteristic
48	C₂×#14556613	C₄	1	1	yes	characteristic, complemented
49	C₂×#14556612	C₂²	1	2	yes	—
50	C₂×#14556611	C₄	1	2	yes	complemented
51	C₂×#14556610	C₂²	1	1	yes	characteristic
52	#135×D₇₃	C₄	1	2	yes	complemented
53	#135×D₇₃	C₄	1	2	yes	complemented
54	#135×D₇₃	C₄	1	2	yes	complemented
55	#135×D₇₃	C₄	1	2	yes	complemented
56	#135×D₇₃	C₂²	1	2	yes	—
57	#135×D₇₃	C₂²	1	2	yes	—
58	#135×D₇₃	C₂²	1	2	yes	—
59	#135×D₇₃	C₂²	1	2	yes	—
60	C₂×Q₁₆×D₇₃	C₄	1	1	yes	characteristic, complemented
61	C₂×SD₁₆×D₇₃	C₄	1	2	yes	complemented
62	C₂×D₈×D₇₃	C₄	1	1	yes	characteristic, complemented
63	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
64	C₂×#135×C₇₃	C₄	1	1	yes	characteristic, complemented
65	#14556679	—	2	8	no	—
66	#14556679	C₂³	1	16	yes	complemented
67	#14556678	—	2	8	no	—
68	#14556678	—	2	16	no	—
69	#14556678	—	2	16	no	—
70	#14556678	C₂³	1	16	yes	complemented
71	C₂×#11924038	—	2	8	no	—
72	C₂×#11924038	D₄	1	2	yes	—
73	C₂×#11924038	C₂³	1	4	yes	—
74	D₇₃⋊M₁₆	—	2	8	no	—
75	D₇₃⋊M₁₆	—	2	8	no	—
76	D₇₃⋊M₁₆	—	2	8	no	—
77	D₇₃⋊M₁₆	—	2	2	no	—
78	D₇₃⋊M₁₆	—	2	2	no	—
79	D₇₃⋊M₁₆	D₄	1	2	yes	—
80	D₇₃⋊M₁₆	D₄	1	2	yes	—
81	D₇₃⋊M₁₆	C₂³	1	4	yes	—
82	D₇₃⋊M₁₆	C₂³	1	4	yes	—
83	D₇₃⋊M₁₆	C₂³	1	2	yes	—
84	D₇₃⋊M₁₆	C₂³	1	2	yes	—
85	C₂×#11924037	—	2	8	no	—
86	C₂×#11924037	—	2	2	no	—
87	C₂×#11924037	D₄	1	2	yes	—
88	C₂×#11924036	—	2	8	no	—
89	C₂×#11924036	—	2	2	no	—
90	C₂×#11924036	C₂³	1	2	yes	—
91	#14556670	—	2	1	no	—
92	#14556670	—	2	1	no	—
93	#14556670	C₂³	1	2	yes	—
94	#14556670	C₂³	1	2	yes	—
95	C₂×C₄⋊#64408	—	2	1	no	—
96	C₂×C₂²⋊#64408	—	2	1	no	—
97	C₂×C₄×#64408	C₂³	1	2	yes	—
98	#14556662	C₂³	1	4	yes	complemented
99	#14556662	C₂³	1	4	yes	complemented
100	#14556661	C₂³	1	4	yes	complemented
101	#14556661	C₂³	1	4	yes	complemented
102	#14556656	C₂³	1	16	yes	complemented
103	#14556655	C₂³	1	16	yes	complemented
104	#14556645	C₂³	1	4	yes	complemented
105	#14556645	C₂³	1	4	yes	complemented
106	C₈×#64408	C₂³	1	4	yes	complemented
107	C₈×#64408	C₂³	1	4	yes	complemented
108	C₂×#11924029	C₂³	1	2	yes	—
109	C₂×#11924028	—	2	2	no	—
110	C₂×#11924028	C₂×C₄	1	2	yes	—
111	C₂×#11924027	—	2	2	no	—
112	C₂×#11924027	C₂³	1	2	yes	—
113	#41×D₇₃	—	2	2	no	—
114	#41×D₇₃	—	2	2	no	—
115	#41×D₇₃	—	2	2	no	—
116	#41×D₇₃	—	2	2	no	—
117	#41×D₇₃	C₂×C₄	1	4	yes	—
118	#41×D₇₃	C₂×C₄	1	4	yes	—
119	#41×D₇₃	C₂³	1	4	yes	—
120	#41×D₇₃	C₂³	1	4	yes	—
121	C₂×Q₈×D₇₃	C₂×C₄	1	2	yes	—
122	C₂×D₄×D₇₃	—	2	2	no	—
123	C₂×D₄×D₇₃	C₂×C₄	1	2	yes	—
124	C₂²×C₄×D₇₃	—	2	2	no	—
125	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
126	#14556614	C₂×C₄	1	2	yes	complemented
127	#14556614	C₂×C₄	1	2	yes	complemented
128	#14556614	C₂³	1	2	yes	—
129	#14556614	C₂³	1	2	yes	—
130	#14556613	C₂×C₄	1	2	yes	—
131	#14556613	C₂×C₄	1	2	yes	—
132	#14556613	C₂×C₄	1	2	yes	complemented
133	#14556613	C₂×C₄	1	2	yes	complemented
134	#14556612	C₂×C₄	1	4	yes	complemented
135	#14556612	C₂×C₄	1	4	yes	complemented
136	#14556612	C₂³	1	4	yes	—
137	#14556612	C₂³	1	4	yes	—
138	#14556611	C₂×C₄	1	4	yes	—
139	#14556611	C₂×C₄	1	4	yes	—
140	#14556611	C₂×C₄	1	4	yes	complemented
141	#14556611	C₂×C₄	1	4	yes	complemented
142	#14556610	C₂×C₄	1	2	yes	complemented
143	#14556610	C₂×C₄	1	2	yes	complemented
144	#14556610	C₂³	1	2	yes	—
145	#14556610	C₂³	1	2	yes	—
146	C₂×Dic₂₉₂	C₂×C₄	1	1	yes	characteristic, complemented
147	C₂×#11924018	C₂×C₄	1	2	yes	complemented
148	Q₁₆×D₇₃	C₂×C₄	1	2	yes	—
149	Q₁₆×D₇₃	C₂×C₄	1	2	yes	—
150	Q₁₆×D₇₃	C₂×C₄	1	2	yes	complemented
151	Q₁₆×D₇₃	C₂×C₄	1	2	yes	complemented
152	C₂×#11924017	C₂×C₄	1	2	yes	complemented
153	C₂×#11924016	C₂×C₄	1	2	yes	complemented
154	C₂×#11924015	C₂×C₄	1	2	yes	complemented
155	SD₁₆×D₇₃	C₂×C₄	1	4	yes	—
156	SD₁₆×D₇₃	C₂×C₄	1	4	yes	—
157	SD₁₆×D₇₃	C₂×C₄	1	4	yes	complemented
158	SD₁₆×D₇₃	C₂×C₄	1	4	yes	complemented
159	C₂×D₅₈₄	C₂×C₄	1	1	yes	characteristic, complemented
160	C₂×#11924013	C₂×C₄	1	2	yes	complemented
161	D₈×D₇₃	C₂×C₄	1	2	yes	—
162	D₈×D₇₃	C₂×C₄	1	2	yes	—
163	D₈×D₇₃	C₂×C₄	1	2	yes	complemented
164	D₈×D₇₃	C₂×C₄	1	2	yes	complemented
165	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
166	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
167	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
168	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
169	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
170	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
171	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
172	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
173	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
174	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
175	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
177	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
178	C₂×#41×C₇₃	C₂×C₄	1	2	yes	—
179	#135×C₇₃	C₂×C₄	1	2	yes	—
180	#135×C₇₃	C₂×C₄	1	2	yes	—
181	#135×C₇₃	C₂×C₄	1	2	yes	complemented
182	#135×C₇₃	C₂×C₄	1	2	yes	complemented
183	C₂×Q₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
184	C₂×SD₁₆×C₇₃	C₂×C₄	1	2	yes	complemented
185	C₂×D₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
186	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
187	C₂²×#64408	—	2	2	no	—
188	#11924038	—	2	4	no	—
189	#11924038	—	2	16	no	—
190	#11924038	C₂×D₄	1	4	yes	—
191	#11924038	C₂×D₄	1	4	yes	—
192	#11924038	C₂⁴	1	8	yes	—
193	#11924037	—	2	4	no	—
194	#11924037	—	2	4	no	—
195	#11924037	—	2	16	no	—
196	#11924037	C₂×D₄	1	4	yes	—
197	#11924037	C₂×D₄	1	4	yes	—
198	#11924036	—	2	4	no	—
199	#11924036	—	2	4	no	—
200	#11924036	—	2	16	no	—
201	#11924036	C₂×D₄	1	4	yes	—
202	#11924036	C₂⁴	1	4	yes	—
203	C₂×#10596833	—	2	4	no	—
204	C₂×#10596833	—	2	16	no	—
205	C₂×#10596833	C₂×D₄	1	4	yes	—
206	C₄⋊#64408	—	2	2	no	—
207	C₄⋊#64408	—	2	2	no	—
208	C₂²⋊#64408	—	2	2	no	—
209	C₂²⋊#64408	—	2	2	no	—
210	C₄×#64408	—	2	2	no	—
211	C₄×#64408	C₂⁴	1	4	yes	—
212	C₂³×D₇₃	—	2	2	no	—
213	C₂³×D₇₃	#41	1	1	yes	characteristic
214	#11924029	—	2	2	no	—
215	#11924029	—	2	2	no	—
216	#11924029	C₂²×C₄	1	4	yes	—
217	#11924029	C₂⁴	1	4	yes	—
218	#11924028	—	2	2	no	—
219	#11924028	—	2	2	no	—
220	#11924028	—	2	4	no	—
221	#11924028	—	2	4	no	—
222	#11924028	—	2	4	no	—
223	#11924028	—	2	4	no	—
224	#11924028	C₂²×C₄	1	4	yes	—
225	#11924028	C₂²×C₄	1	4	yes	—
226	#11924027	—	2	4	no	—
227	#11924027	—	2	4	no	—
228	#11924027	—	2	4	no	—
229	#11924027	—	2	4	no	—
230	#11924027	—	2	2	no	—
231	#11924027	—	2	2	no	—
232	#11924027	C₂²×C₄	1	4	yes	—
233	#11924027	C₂⁴	1	4	yes	—
234	C₂×Dic₁₄₆	—	2	2	no	—
235	C₂×Dic₁₄₆	C₂²×C₄	1	2	yes	—
236	Q₈×D₇₃	—	2	2	no	—
237	Q₈×D₇₃	—	2	2	no	—
238	Q₈×D₇₃	C₂²×C₄	1	4	yes	—
239	Q₈×D₇₃	C₂²×C₄	1	4	yes	—
240	C₂×D₂₉₂	—	2	2	no	—
241	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
242	C₂×C₂²⋊D₇₃	—	2	2	no	—
243	C₂×C₂²⋊D₇₃	—	2	2	no	—
244	C₂×C₂²⋊D₇₃	—	2	2	no	—
245	D₄×D₇₃	—	2	4	no	—
246	D₄×D₇₃	—	2	4	no	—
247	D₄×D₇₃	—	2	4	no	—
248	D₄×D₇₃	—	2	4	no	—
249	D₄×D₇₃	—	2	2	no	—
250	D₄×D₇₃	—	2	2	no	—
251	D₄×D₇₃	C₂²×C₄	1	4	yes	—
252	D₄×D₇₃	C₂²×C₄	1	4	yes	—
253	C₂²×Dic₇₃	—	2	2	no	—
254	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
255	C₂×C₄×D₇₃	—	2	2	no	—
256	C₂×C₄×D₇₃	—	2	2	no	—
257	C₂×C₄×D₇₃	—	2	2	no	—
258	C₂×C₄×D₇₃	—	2	4	no	—
259	C₂×C₄×D₇₃	—	2	4	no	—
260	C₂×C₄×D₇₃	—	2	4	no	—
261	C₂×C₄×D₇₃	—	2	4	no	—
262	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
263	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
264	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
265	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
266	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
267	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
268	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
269	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
270	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
271	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
274	Dic₂₉₂	C₂²×C₄	1	2	yes	—
275	Dic₂₉₂	C₂²×C₄	1	2	yes	—
276	#11924018	C₂²×C₄	1	4	yes	—
277	#11924018	C₂²×C₄	1	4	yes	—
278	#11924017	C₂²×C₄	1	4	yes	—
279	#11924017	C₂²×C₄	1	4	yes	—
280	#11924016	C₂²×C₄	1	4	yes	—
281	#11924016	C₂²×C₄	1	4	yes	—
282	#11924015	C₂²×C₄	1	4	yes	—
283	#11924015	C₂²×C₄	1	4	yes	—
284	D₅₈₄	C₂²×C₄	1	2	yes	—
285	D₅₈₄	C₂²×C₄	1	2	yes	—
286	#11924013	C₂²×C₄	1	4	yes	—
287	#11924013	C₂²×C₄	1	4	yes	—
288	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
289	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
290	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
291	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
292	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
293	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
294	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
295	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
296	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
297	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
298	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
299	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
300	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
301	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
302	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
303	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
304	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
305	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
306	C₈×D₇₃	C₂⁴	1	1	yes	characteristic
307	C₈×D₇₃	C₂⁴	1	1	yes	characteristic
308	C₈×D₇₃	C₂⁴	1	1	yes	characteristic
309	C₈×D₇₃	C₂⁴	1	1	yes	characteristic
310	#41×C₇₃	—	2	2	no	—
311	#41×C₇₃	—	2	2	no	—
312	#41×C₇₃	C₂²×C₄	1	4	yes	—
313	#41×C₇₃	C₂²×C₄	1	4	yes	—
314	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
315	C₂×D₄×C₇₃	—	2	2	no	—
316	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
317	C₂²×C₄×C₇₃	—	2	2	no	—
318	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
319	Q₁₆×C₇₃	C₂²×C₄	1	2	yes	—
320	Q₁₆×C₇₃	C₂²×C₄	1	2	yes	—
321	SD₁₆×C₇₃	C₂²×C₄	1	4	yes	—
322	SD₁₆×C₇₃	C₂²×C₄	1	4	yes	—
323	D₈×C₇₃	C₂²×C₄	1	2	yes	—
324	D₈×C₇₃	C₂²×C₄	1	2	yes	—
325	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
326	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
327	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
328	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
329	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
330	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
331	C₂³×C₇₃	—	2	2	no	—
332	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
333	C₂²×D₇₃	—	2	2	no	—
334	C₂²×D₇₃	—	2	4	no	—
335	C₂²×D₇₃	—	2	4	no	—
336	C₂²×D₇₃	—	4	2	no	—
337	C₂²×D₇₃	—	8	4	no	—
338	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
339	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
340	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
341	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
342	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
343	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
344	C₂×#64408	—	2	4	no	—
345	C₂×#64408	—	4	4	no	—
346	Q₈×C₇₃	—	2	2	no	—
347	Q₈×C₇₃	C₂³×C₄	1	4	yes	—
348	D₄×C₇₃	—	2	4	no	—
349	D₄×C₇₃	—	2	4	no	—
350	D₄×C₇₃	—	2	2	no	—
351	D₄×C₇₃	C₂³×C₄	1	4	yes	—
352	C₂×C₄×C₇₃	—	2	2	no	—
353	C₂×C₄×C₇₃	—	2	4	no	—
354	C₂×C₄×C₇₃	—	2	4	no	—
355	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
356	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
357	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
358	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
359	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
360	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
361	C₂²⋊D₇₃	—	2	4	no	—
362	C₂²⋊D₇₃	—	2	4	no	—
363	C₂²⋊D₇₃	—	2	4	no	—
364	C₂²⋊D₇₃	—	2	4	no	—
365	C₂²⋊D₇₃	—	2	4	no	—
366	C₂²⋊D₇₃	—	2	4	no	—
367	C₂×Dic₇₃	—	2	2	no	—
368	C₂×Dic₇₃	—	2	4	no	—
369	C₂×Dic₇₃	—	2	4	no	—
370	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
371	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
372	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
373	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
376	D₂₉₂	—	2	4	no	—
377	D₂₉₂	—	2	4	no	—
378	D₂₉₂	—	2	2	no	—
379	D₂₉₂	C₂³×C₄	1	4	yes	—
380	C₄×D₇₃	—	2	4	no	—
381	C₄×D₇₃	—	2	4	no	—
382	C₄×D₇₃	—	2	4	no	—
383	C₄×D₇₃	—	2	4	no	—
384	C₄×D₇₃	—	2	4	no	—
385	C₄×D₇₃	—	2	4	no	—
386	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
387	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
388	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
389	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
390	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
391	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
392	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
393	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
394	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
395	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
396	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
397	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
398	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
399	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
400	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
401	C₄×D₇₃	C₂⁵	1	1	yes	characteristic
402	Dic₁₄₆	—	2	2	no	—
403	Dic₁₄₆	—	2	4	no	—
404	Dic₁₄₆	—	2	4	no	—
405	Dic₁₄₆	C₂³×C₄	1	4	yes	—
406	#10596833	—	2	8	no	—
407	#10596833	C₂²×D₄	1	8	yes	—
408	C₈×C₇₃	C₂³×C₄	1	1	yes	characteristic
409	C₈×C₇₃	C₂³×C₄	1	1	yes	characteristic
410	C₈×C₇₃	C₂³×C₄	1	1	yes	characteristic
411	C₈×C₇₃	C₂³×C₄	1	1	yes	characteristic
412	#10596831	C₂³×C₄	1	1	yes	characteristic
413	#10596831	C₂³×C₄	1	1	yes	characteristic
414	#10596831	C₂³×C₄	1	1	yes	characteristic
415	#10596831	C₂³×C₄	1	1	yes	characteristic
416	C₂²×C₇₃	—	2	4	no	—
417	C₂²×C₇₃	—	4	1	no	—
418	C₂²×C₇₃	—	8	2	no	—
419	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
420	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
421	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
422	C₂×D₇₃	—	2	2	no	—
423	C₂×D₇₃	—	2	2	no	—
424	C₂×D₇₃	—	2	2	no	—
425	C₂×D₇₃	—	2	4	no	—
426	C₂×D₇₃	—	4	1	no	—
427	C₂×D₇₃	—	4	1	no	—
428	C₂×D₇₃	—	4	1	no	—
429	C₂×D₇₃	—	4	8	no	—
430	C₂×D₇₃	—	8	4	no	—
431	C₂×D₇₃	—	8	2	no	—
432	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
433	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
434	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
435	C₂×D₇₃	C₂²×#41	1	1	yes	characteristic
436	#64408	—	4	4	no	—
437	C₄×C₇₃	—	2	4	no	—
438	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
439	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
440	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
441	C₄×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
442	Dic₇₃	—	2	4	no	—
443	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
444	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
445	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
446	Dic₇₃	C₂³×D₄	1	1	yes	characteristic
447	C₂×#2957	—	73	1	no	maximal, Sylow
448	C₂×C₇₃	—	2	1	no	—
449	C₂×C₇₃	—	2	1	no	—
450	C₂×C₇₃	—	2	1	no	—
451	C₂×C₇₃	—	4	4	no	—
452	C₂×C₇₃	C₂²×C₄×D₄	1	1	yes	characteristic
453	D₇₃	—	2	1	no	—
454	D₇₃	—	2	1	no	—
455	D₇₃	—	2	1	no	—
456	D₇₃	—	4	4	no	—
457	D₇₃	#2957	1	2	yes	complemented
458	C₂²×#135	—	73	1	no	—
459	C₂×#568	—	73	2	no	—
460	#2957	—	73	2	no	—
461	#2957	—	73	4	no	—
462	#2957	—	73	4	no	—
463	#2957	—	73	4	no	—
464	#2957	—	73	2	no	—
465	C₂×#444	—	73	4	no	—
466	C₂×#443	—	73	4	no	—
467	C₂²×#108	—	73	1	no	—
468	C₂×#421	—	73	2	no	—
469	C₂×#405	—	73	1	no	—
470	C₇₃	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
471	C₂²×#41	—	73	2	no	—
472	C₂×#135	—	73	2	no	—
473	C₂×#135	—	73	2	no	—
474	C₂×#135	—	73	2	no	—
475	C₂×#135	—	73	2	no	—
476	C₂×#135	—	73	2	no	—
477	C₂×#135	—	73	2	no	—
478	C₂×#135	—	73	2	no	—
479	C₂×#135	—	73	2	no	—
480	C₂×#135	—	73	2	no	—
481	C₂×#135	—	73	1	no	—
482	C₂×#135	—	73	2	no	—
483	C₂×#135	—	73	1	no	—
484	C₂×#135	—	73	1	no	—
485	C₂×#135	#64408	1	1	yes	characteristic, complemented
486	C₂²×Q₁₆	—	73	1	no	—
487	C₂²×SD₁₆	—	73	2	no	—
488	C₂²×D₈	—	73	1	no	—
489	#568	—	73	4	no	—
490	#568	—	73	8	no	—
491	#568	—	73	4	no	—
492	#568	—	146	4	no	—
493	#568	—	146	4	no	—
494	C₂×#131	—	73	8	no	—
495	C₂×#131	—	146	4	no	—
496	C₂²×M₁₆	—	73	1	no	—
497	C₂²×M₁₆	—	73	2	no	—
498	C₂²×M₁₆	—	146	4	no	—
499	C₂³×C₈	—	73	1	no	—
500	C₂×#117	—	73	1	no	—
501	#444	—	73	16	no	—
502	#444	—	73	8	no	—
503	#444	—	73	8	no	—
504	#443	—	73	8	no	—
505	#443	—	73	16	no	—
506	#443	—	73	8	no	—
507	C₂×#108	—	73	2	no	—
508	C₂×#108	—	73	2	no	—
509	C₂×#108	—	73	2	no	—
510	C₂×#108	—	73	2	no	—
511	C₂×#108	—	73	2	no	—
512	C₂×#108	—	73	2	no	—
513	#421	—	73	8	no	—
514	#421	—	73	4	no	—
515	#421	—	73	4	no	—
516	C₂×#104	—	73	8	no	—
517	#405	—	73	2	no	—
518	#405	—	73	2	no	—
519	#405	—	73	2	no	—
520	#405	—	73	2	no	—
521	C₂×#97	—	73	2	no	—
522	C₂×C₄×C₈	—	73	2	no	—
523	C₂×#41	—	73	4	no	—
524	C₂×#41	—	73	4	no	—
525	C₂×#41	—	73	4	no	—
526	C₂×#41	—	73	4	no	—
527	C₂×#41	—	73	2	no	—
528	C₂×#41	—	73	2	no	—
529	C₂×#41	—	73	2	no	—
530	C₂×#41	—	146	2	no	—
531	C₂×#41	—	146	2	no	—
532	C₂×#41	—	146	2	no	—
533	C₂×#41	—	146	2	no	—
534	C₂×#41	—	146	2	no	—
535	C₂×#41	—	146	2	no	—
536	C₂×#41	C₂×#64408	1	2	yes	—
537	C₂²×Q₈	—	73	2	no	—
538	C₂²×D₄	—	73	2	no	—
539	C₂²×D₄	—	146	2	no	—
540	C₂³×C₄	—	73	1	no	—
541	C₂³×C₄	—	146	2	no	—
542	#135	—	73	4	no	—
543	#135	—	73	4	no	—
544	#135	—	73	4	no	—
545	#135	—	73	4	no	—
546	#135	—	73	2	no	—
547	#135	—	73	2	no	—
548	#135	—	73	2	no	—
549	#135	—	73	2	no	—
550	#135	—	73	4	no	—
551	#135	—	73	4	no	—
552	#135	—	73	4	no	—
553	#135	—	73	4	no	—
554	#135	—	73	2	no	—
555	#135	—	73	2	no	—
556	#135	—	73	2	no	—
557	#135	—	73	2	no	—
558	#135	—	73	2	no	—
559	#135	—	73	2	no	—
560	#135	—	73	2	no	—
561	#135	—	73	2	no	—
562	#135	C₂×#64408	1	2	yes	—
563	#135	C₂×#64408	1	2	yes	—
564	#135	C₂×#64408	1	2	yes	complemented
565	#135	C₂×#64408	1	2	yes	complemented
566	C₂×Q₁₆	—	73	2	no	—
567	C₂×Q₁₆	—	73	2	no	—
568	C₂×Q₁₆	—	73	2	no	—
569	C₂×Q₁₆	—	73	2	no	—
570	C₂×Q₁₆	—	73	2	no	—
571	C₂×Q₁₆	—	73	1	no	—
572	C₂×Q₁₆	C₂×#64408	1	1	yes	characteristic, complemented
573	C₂×SD₁₆	—	73	2	no	—
574	C₂×SD₁₆	—	73	2	no	—
575	C₂×SD₁₆	—	73	4	no	—
576	C₂×SD₁₆	—	73	4	no	—
577	C₂×SD₁₆	—	73	4	no	—
578	C₂×SD₁₆	—	73	4	no	—
579	C₂×SD₁₆	—	73	2	no	—
580	C₂×SD₁₆	C₂×#64408	1	2	yes	complemented
581	C₂×D₈	—	73	2	no	—
582	C₂×D₈	—	73	2	no	—
583	C₂×D₈	—	73	2	no	—
584	C₂×D₈	—	73	2	no	—
585	C₂×D₈	—	73	2	no	—
586	C₂×D₈	—	73	1	no	—
587	C₂×D₈	C₂×#64408	1	1	yes	characteristic, complemented
588	#131	—	73	16	no	—
589	#131	—	73	16	no	—
590	#131	—	146	16	no	—
591	#131	—	146	8	no	—
592	#131	—	146	16	no	—
593	#131	—	146	8	no	—
594	C₂×M₁₆	—	73	2	no	—
595	C₂×M₁₆	—	73	2	no	—
596	C₂×M₁₆	—	73	2	no	—
597	C₂×M₁₆	—	73	2	no	—
598	C₂×M₁₆	—	73	2	no	—
599	C₂×M₁₆	—	73	2	no	—
600	C₂×M₁₆	—	73	4	no	—
601	C₂×M₁₆	—	73	4	no	—
602	C₂×M₁₆	—	73	4	no	—
603	C₂×M₁₆	—	146	8	no	—
604	C₂×M₁₆	—	146	8	no	—
605	C₂×M₁₆	—	146	8	no	—
606	C₂×M₁₆	—	146	8	no	—
607	C₂×M₁₆	—	146	8	no	—
608	C₂×M₁₆	—	146	2	no	—
609	C₂×M₁₆	—	146	2	no	—
610	C₂×M₁₆	—	146	2	no	—
611	C₂²×C₈	—	73	2	no	—
612	C₂²×C₈	—	73	1	no	—
613	C₂²×C₈	—	73	1	no	—
614	C₂²×C₈	—	73	1	no	—
615	C₂²×C₈	—	73	1	no	—
616	C₂²×C₈	—	73	1	no	—
617	C₂²×C₈	—	73	1	no	—
618	C₂²×C₈	—	73	1	no	—
619	C₂²×C₈	—	73	1	no	—
620	C₂²×C₈	—	73	1	no	—
621	C₂²×C₈	—	73	1	no	—
622	C₂²×C₈	—	73	1	no	—
623	C₂²×C₈	—	73	1	no	—
624	C₂²×C₈	—	73	1	no	—
625	C₂²×C₈	—	146	8	no	—
626	C₂²×C₈	—	146	2	no	—
627	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
628	#117	—	73	2	no	—
629	#117	—	73	2	no	—
630	#117	—	146	1	no	—
631	#117	—	146	1	no	—
632	C₂×C₄⋊C₄	—	146	1	no	—
633	C₂×C₂²⋊C₄	—	146	1	no	—
634	C₂×C₄²	—	73	2	no	—
635	#108	—	73	4	no	—
636	#108	—	73	4	no	—
637	#108	—	73	4	no	—
638	#108	—	73	4	no	—
639	#104	—	73	16	no	—
640	#104	—	73	16	no	—
641	#97	—	73	4	no	—
642	#97	—	73	4	no	—
643	C₄×C₈	—	73	4	no	—
644	C₄×C₈	—	73	4	no	—
645	C₂⁴	—	73	1	no	—
646	C₂⁴	—	146	2	no	—
647	#41	—	2	2	no	—
648	#41	—	2	2	no	—
649	#41	—	73	4	no	—
650	#41	—	73	4	no	—
651	#41	—	73	4	no	—
652	#41	—	73	4	no	—
653	#41	—	73	4	no	—
654	#41	—	73	4	no	—
655	#41	—	146	4	no	—
656	#41	—	146	4	no	—
657	#41	—	146	4	no	—
658	#41	—	146	4	no	—
659	#41	—	146	4	no	—
660	#41	—	146	4	no	—
661	#41	—	146	2	no	—
662	#41	—	146	4	no	—
663	#41	—	146	4	no	—
664	#41	—	146	2	no	—
665	#41	—	146	2	no	—
666	#41	—	146	2	no	—
667	#41	—	146	2	no	—
668	#41	—	146	2	no	—
669	#41	C₂²×#64408	1	4	yes	—
670	#41	C₂²×#64408	1	4	yes	—
671	C₂×Q₈	—	73	4	no	—
672	C₂×Q₈	—	73	4	no	—
673	C₂×Q₈	—	73	2	no	—
674	C₂×Q₈	—	146	2	no	—
675	C₂×Q₈	—	146	2	no	—
676	C₂×Q₈	—	146	2	no	—
677	C₂×Q₈	C₂²×#64408	1	2	yes	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	73	4	no	—
680	C₂×D₄	—	73	4	no	—
681	C₂×D₄	—	73	2	no	—
682	C₂×D₄	—	146	2	no	—
683	C₂×D₄	—	146	2	no	—
684	C₂×D₄	—	146	2	no	—
685	C₂×D₄	—	146	2	no	—
686	C₂×D₄	—	146	4	no	—
687	C₂×D₄	—	146	4	no	—
688	C₂×D₄	—	146	4	no	—
689	C₂×D₄	—	146	4	no	—
690	C₂×D₄	—	146	2	no	—
691	C₂×D₄	—	146	2	no	—
692	C₂×D₄	C₂²×#64408	1	2	yes	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	73	1	no	—
695	C₂²×C₄	—	73	1	no	—
696	C₂²×C₄	—	73	1	no	—
697	C₂²×C₄	—	73	1	no	—
698	C₂²×C₄	—	73	1	no	—
699	C₂²×C₄	—	73	1	no	—
700	C₂²×C₄	—	73	1	no	—
701	C₂²×C₄	—	73	1	no	—
702	C₂²×C₄	—	73	1	no	—
703	C₂²×C₄	—	73	1	no	—
704	C₂²×C₄	—	73	1	no	—
705	C₂²×C₄	—	73	1	no	—
706	C₂²×C₄	—	73	1	no	—
707	C₂²×C₄	—	146	4	no	—
708	C₂²×C₄	—	146	2	no	—
709	C₂²×C₄	—	146	4	no	—
710	C₂²×C₄	—	146	4	no	—
711	C₂²×C₄	—	146	4	no	—
712	C₂²×C₄	—	146	2	no	—
713	C₂²×C₄	—	146	2	no	—
714	C₂²×C₄	—	146	2	no	—
715	C₂²×C₄	—	146	2	no	—
716	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
717	Q₁₆	—	73	4	no	—
718	Q₁₆	—	73	4	no	—
719	Q₁₆	—	73	2	no	—
720	Q₁₆	—	73	2	no	—
721	Q₁₆	C₂²×#64408	1	2	yes	—
722	Q₁₆	C₂²×#64408	1	2	yes	—
723	SD₁₆	—	73	4	no	—
724	SD₁₆	—	73	4	no	—
725	SD₁₆	—	73	4	no	—
726	SD₁₆	—	73	4	no	—
727	SD₁₆	—	73	4	no	—
728	SD₁₆	—	73	4	no	—
729	SD₁₆	C₂²×#64408	1	4	yes	—
730	SD₁₆	C₂²×#64408	1	4	yes	—
731	D₈	—	73	4	no	—
732	D₈	—	73	4	no	—
733	D₈	—	73	2	no	—
734	D₈	—	73	2	no	—
735	D₈	C₂²×#64408	1	2	yes	—
736	D₈	C₂²×#64408	1	2	yes	—
737	M₁₆	—	73	4	no	—
738	M₁₆	—	73	4	no	—
739	M₁₆	—	73	4	no	—
740	M₁₆	—	73	4	no	—
741	M₁₆	—	73	8	no	—
742	M₁₆	—	146	16	no	—
743	M₁₆	—	146	16	no	—
744	M₁₆	—	146	4	no	—
745	M₁₆	—	146	4	no	—
746	M₁₆	—	146	4	no	—
747	C₂×C₈	—	73	4	no	—
748	C₂×C₈	—	73	4	no	—
749	C₂×C₈	—	73	4	no	—
750	C₂×C₈	—	73	1	no	—
751	C₂×C₈	—	73	1	no	—
752	C₂×C₈	—	73	1	no	—
753	C₂×C₈	—	73	1	no	—
754	C₂×C₈	—	73	1	no	—
755	C₂×C₈	—	73	1	no	—
756	C₂×C₈	—	73	1	no	—
757	C₂×C₈	—	73	1	no	—
758	C₂×C₈	—	73	1	no	—
759	C₂×C₈	—	73	1	no	—
760	C₂×C₈	—	73	1	no	—
761	C₂×C₈	—	73	1	no	—
762	C₂×C₈	—	73	1	no	—
763	C₂×C₈	—	73	1	no	—
764	C₂×C₈	—	73	1	no	—
765	C₂×C₈	—	73	1	no	—
766	C₂×C₈	—	73	1	no	—
767	C₂×C₈	—	73	1	no	—
768	C₂×C₈	—	73	1	no	—
769	C₂×C₈	—	73	1	no	—
770	C₂×C₈	—	73	1	no	—
771	C₂×C₈	—	73	1	no	—
772	C₂×C₈	—	146	16	no	—
773	C₂×C₈	—	146	16	no	—
774	C₂×C₈	—	146	4	no	—
775	C₂×C₈	—	146	4	no	—
776	C₂×C₈	—	146	4	no	—
777	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
778	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
779	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
780	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
781	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
782	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
783	C₄⋊C₄	—	146	2	no	—
784	C₄⋊C₄	—	146	2	no	—
785	C₂²⋊C₄	—	146	2	no	—
786	C₂²⋊C₄	—	146	2	no	—
787	C₄²	—	73	4	no	—
788	C₄²	—	146	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	292	2	no	—
791	C₂³	—	584	4	no	—
792	C₂³	—	73	1	no	—
793	C₂³	—	73	1	no	—
794	C₂³	—	73	1	no	—
795	C₂³	—	73	1	no	—
796	C₂³	—	73	1	no	—
797	C₂³	—	73	1	no	—
798	C₂³	—	146	4	no	—
799	C₂³	—	146	4	no	—
800	C₂³	—	146	2	no	—
801	C₂³	D₄×#64408	1	1	yes	characteristic
802	Q₈	—	2	2	no	—
803	Q₈	—	73	4	no	—
804	Q₈	—	146	4	no	—
805	Q₈	—	146	4	no	—
806	Q₈	—	146	2	no	—
807	Q₈	C₂³×#64408	1	4	yes	—
808	D₄	—	2	4	no	—
809	D₄	—	2	4	no	—
810	D₄	—	2	2	no	—
811	D₄	—	73	4	no	—
812	D₄	—	146	4	no	—
813	D₄	—	146	4	no	—
814	D₄	—	146	4	no	—
815	D₄	—	146	4	no	—
816	D₄	—	146	4	no	—
817	D₄	—	146	4	no	—
818	D₄	—	146	4	no	—
819	D₄	—	146	4	no	—
820	D₄	—	146	2	no	—
821	D₄	C₂³×#64408	1	4	yes	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	292	4	no	—
826	C₂×C₄	—	73	1	no	—
827	C₂×C₄	—	73	1	no	—
828	C₂×C₄	—	73	1	no	—
829	C₂×C₄	—	73	1	no	—
830	C₂×C₄	—	73	1	no	—
831	C₂×C₄	—	73	1	no	—
832	C₂×C₄	—	73	1	no	—
833	C₂×C₄	—	73	1	no	—
834	C₂×C₄	—	73	1	no	—
835	C₂×C₄	—	73	1	no	—
836	C₂×C₄	—	73	1	no	—
837	C₂×C₄	—	73	1	no	—
838	C₂×C₄	—	73	1	no	—
839	C₂×C₄	—	73	1	no	—
840	C₂×C₄	—	73	1	no	—
841	C₂×C₄	—	73	1	no	—
842	C₂×C₄	—	73	1	no	—
843	C₂×C₄	—	73	1	no	—
844	C₂×C₄	—	73	1	no	—
845	C₂×C₄	—	73	1	no	—
846	C₂×C₄	—	73	1	no	—
847	C₂×C₄	—	73	1	no	—
848	C₂×C₄	—	146	4	no	—
849	C₂×C₄	—	146	4	no	—
850	C₂×C₄	—	146	4	no	—
851	C₂×C₄	—	146	4	no	—
852	C₂×C₄	—	146	4	no	—
853	C₂×C₄	—	146	4	no	—
854	C₂×C₄	—	146	4	no	—
855	C₂×C₄	—	146	2	no	—
856	C₂×C₄	—	146	4	no	—
857	C₂×C₄	—	146	4	no	—
858	C₂×C₄	D₄×#64408	1	1	yes	characteristic
859	C₂×C₄	D₄×#64408	1	1	yes	characteristic
860	C₂×C₄	D₄×#64408	1	1	yes	characteristic
861	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
862	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
863	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
864	C₈	—	73	8	no	—
865	C₈	—	73	1	no	—
866	C₈	—	73	1	no	—
867	C₈	—	73	1	no	—
868	C₈	—	73	1	no	—
869	C₈	—	146	8	no	—
870	C₈	C₂³×#64408	1	1	yes	characteristic
871	C₈	C₂³×#64408	1	1	yes	characteristic
872	C₈	C₂³×#64408	1	1	yes	characteristic
873	C₈	C₂³×#64408	1	1	yes	characteristic
874	C₂²	—	2	4	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	8	2	no	—
877	C₂²	—	292	1	no	—
878	C₂²	—	292	1	no	—
879	C₂²	—	292	1	no	—
880	C₂²	—	292	8	no	—
881	C₂²	—	584	2	no	—
882	C₂²	—	584	4	no	—
883	C₂²	—	73	1	no	—
884	C₂²	—	73	1	no	—
885	C₂²	—	73	1	no	—
886	C₂²	—	73	1	no	—
887	C₂²	—	146	2	no	—
888	C₂²	—	146	2	no	—
889	C₂²	—	146	2	no	—
890	C₂²	—	146	4	no	—
891	C₂²	C₂×D₄×#64408	1	1	yes	characteristic
892	C₂²	C₂×D₄×#64408	1	1	yes	characteristic
893	C₂²	C₂×D₄×#64408	1	1	yes	characteristic
894	C₄	—	2	4	no	—
895	C₄	—	292	4	no	—
896	C₄	—	73	1	no	—
897	C₄	—	73	1	no	—
898	C₄	—	73	1	no	—
899	C₄	—	73	1	no	—
900	C₄	—	146	4	no	—
901	C₄	C₂×D₄×#64408	1	1	yes	characteristic
902	C₄	C₂×D₄×#64408	1	1	yes	characteristic
903	C₄	C₂×D₄×#64408	1	1	yes	characteristic
904	C₄	C₂⁴×#64408	1	1	yes	characteristic
905	C₂	—	2	1	no	—
906	C₂	—	2	1	no	—
907	C₂	—	2	1	no	—
908	C₂	—	4	4	no	—
909	C₂	—	292	4	no	—
910	C₂	—	73	2	no	—
911	C₂	—	146	1	no	—
912	C₂	—	146	1	no	—
913	C₂	—	146	1	no	—
914	C₂	C₂²×D₄×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#64408
commutator	C₄×C₇₃	C₂⁴×C₄
Frattini	C₄	C₂⁴×#64408
Fitting	C₂×#135×C₇₃	C₄
socle	C₂×C₇₃	C₂²×C₄×D₄
prime radical	C₂×#135×D₇₃	C₂
cosocle	C₄×D₇₃	C₂⁵
hypercenter	C₂×#135	#64408
hypocenter	C₇₃	C₂×#2957
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. D₇₃⋊#568	C₂	semidirect
2. #22626711	C₂	semidirect
3. #22626710	C₂	semidirect
4. #22626709	C₂	semidirect
5. #22626708	C₂	semidirect
6. #22626707	C₂	semidirect
7. D₇₃⋊#444	C₂	semidirect
8. D₇₃⋊#443	C₂	semidirect
9. C₂×D₇₃⋊#108	C₂	semidirect
10. D₇₃⋊#421	C₂	semidirect
11. C₂×#17989550	C₂	semidirect
13. #17989667	C₂²	semidirect
15. #17989666	C₂²	semidirect
17. #17989665	C₂²	semidirect
19. D₇₃⋊#131	C₂²	semidirect
24. #17989634	C₂²	semidirect
25. #17989633	C₂²	semidirect
26. #17989632	C₂²	semidirect
27. #17989631	C₂²	semidirect
28. #17989630	C₂²	semidirect
29. #17989629	C₂²	semidirect
30. C₂×#14556662	C₂²	semidirect
31. D₇₃⋊#108	C₂²	semidirect
32. D₇₃⋊#108	C₂²	semidirect
33. D₇₃⋊#108	C₂²	semidirect
34. D₇₃⋊#108	C₂²	semidirect
35. C₂×#14556661	C₂²	semidirect
36. #17989586	C₂²	semidirect
37. #17989585	C₂²	semidirect
38. #17989584	C₂²	semidirect
39. D₇₃⋊#104	C₂²	semidirect
40. #17989550	C₂²	semidirect
41. #17989550	C₂²	semidirect
42. #17989550	C₂²	semidirect
43. #17989550	C₂²	semidirect
44. C₂×#14556645	C₂²	semidirect
45. C₂×C₈×#64408	C₂²	semidirect
48. C₂×#14556613	C₄	semidirect
50. C₂×#14556611	C₄	semidirect
52. #135×D₇₃	C₄	semidirect
53. #135×D₇₃	C₄	semidirect
54. #135×D₇₃	C₄	semidirect
55. #135×D₇₃	C₄	semidirect
60. C₂×Q₁₆×D₇₃	C₄	semidirect
61. C₂×SD₁₆×D₇₃	C₄	semidirect
62. C₂×D₈×D₇₃	C₄	semidirect
64. C₂×#135×C₇₃	C₄	semidirect
66. #14556679	C₂³	semidirect
70. #14556678	C₂³	semidirect
98. #14556662	C₂³	semidirect
99. #14556662	C₂³	semidirect
100. #14556661	C₂³	semidirect
101. #14556661	C₂³	semidirect
102. #14556656	C₂³	semidirect
103. #14556655	C₂³	semidirect
104. #14556645	C₂³	semidirect
105. #14556645	C₂³	semidirect
106. C₈×#64408	C₂³	semidirect
107. C₈×#64408	C₂³	semidirect
126. #14556614	C₂×C₄	semidirect
127. #14556614	C₂×C₄	semidirect
132. #14556613	C₂×C₄	semidirect
133. #14556613	C₂×C₄	semidirect
134. #14556612	C₂×C₄	semidirect
135. #14556612	C₂×C₄	semidirect
140. #14556611	C₂×C₄	semidirect
141. #14556611	C₂×C₄	semidirect
142. #14556610	C₂×C₄	semidirect
143. #14556610	C₂×C₄	semidirect
146. C₂×Dic₂₉₂	C₂×C₄	semidirect
147. C₂×#11924018	C₂×C₄	semidirect
150. Q₁₆×D₇₃	C₂×C₄	semidirect
151. Q₁₆×D₇₃	C₂×C₄	semidirect
152. C₂×#11924017	C₂×C₄	semidirect
153. C₂×#11924016	C₂×C₄	semidirect
154. C₂×#11924015	C₂×C₄	semidirect
157. SD₁₆×D₇₃	C₂×C₄	semidirect
158. SD₁₆×D₇₃	C₂×C₄	semidirect
159. C₂×D₅₈₄	C₂×C₄	semidirect
160. C₂×#11924013	C₂×C₄	semidirect
163. D₈×D₇₃	C₂×C₄	semidirect
164. D₈×D₇₃	C₂×C₄	semidirect
181. #135×C₇₃	C₂×C₄	semidirect
182. #135×C₇₃	C₂×C₄	semidirect
183. C₂×Q₁₆×C₇₃	C₂×C₄	semidirect
184. C₂×SD₁₆×C₇₃	C₂×C₄	semidirect
185. C₂×D₈×C₇₃	C₂×C₄	semidirect
457. D₇₃	#2957	semidirect
470. C₇₃	C₂×#2957	semidirect
485. C₂×#135	#64408	semidirect
564. #135	C₂×#64408	semidirect
565. #135	C₂×#64408	semidirect
572. C₂×Q₁₆	C₂×#64408	semidirect
580. C₂×SD₁₆	C₂×#64408	semidirect
587. C₂×D₈	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
D₇₃⋊#568	2
#22626711	2
#22626710	2
#22626709	2
#22626708	2
#22626707	2
D₇₃⋊#444	2
D₇₃⋊#443	2
C₂×D₇₃⋊#108	2
D₇₃⋊#421	2
C₂×#17989550	2
C₂×#135×D₇₃	2
C₂×#2957	73

Subgroups — D73⋊#2957 #34031457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₃⋊#2957 #34031457