Subgroups — C₂×#22623597 #33994291

Order 18688.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556637	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×#11924029	C₂	1	1	yes	maximal, characteristic, complemented
3	#22623597	C₂	1	32	yes	maximal, direct product factor
4	C₂×#17989259	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#17989256	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#17989248	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#17989230	C₂	1	3	yes	maximal, complemented
8	C₂×#17989228	C₂	1	3	yes	maximal, complemented
9	C₂×D₄×D₂₉₂	C₂	1	3	yes	maximal, complemented
10	C₂×#17989221	C₂	1	3	yes	maximal, complemented
11	C₂×#17989167	C₂	1	3	yes	maximal, complemented
12	C₂×#17989155	C₂	1	3	yes	maximal, complemented
13	C₂×#17989096	C₂	1	3	yes	maximal, complemented
14	C₂×#121×D₇₃	C₂	1	3	yes	maximal, complemented
15	C₂×#17989069	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#548×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#14556637	—	2	16	no	—
18	C₂×#14556637	C₂²	1	16	yes	complemented
19	C₂²×#11924029	—	2	16	no	—
20	C₂²×#11924029	C₂²	1	1	yes	characteristic
21	C₂²×#11924029	C₂²	1	3	yes	complemented
22	C₂²×#11924029	C₂²	1	3	yes	complemented
23	C₂²×#11924029	C₂²	1	1	yes	characteristic, complemented
24	C₂²×#11924029	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#11924029	C₂²	1	16	yes	complemented
26	C₂²×#11924028	C₂²	1	3	yes	complemented
27	C₂³×D₂₉₂	C₂²	1	3	yes	complemented
28	C₂³×D₂₉₂	C₂²	1	3	yes	complemented
29	C₂²×D₄×D₇₃	C₂²	1	3	yes	complemented
30	C₂²×D₄×D₇₃	C₂²	1	3	yes	complemented
31	C₂²×D₄×D₇₃	C₂²	1	6	yes	complemented
32	C₂³×C₄×D₇₃	C₂²	1	3	yes	complemented
33	#17989259	C₂²	1	16	yes	complemented
34	#17989256	C₂²	1	16	yes	complemented
35	#17989248	C₂²	1	16	yes	complemented
36	#17989230	C₂²	1	48	yes	complemented
37	#17989228	C₂²	1	48	yes	complemented
38	D₄×D₂₉₂	C₂²	1	48	yes	complemented
39	#17989221	C₂²	1	48	yes	complemented
40	#17989167	C₂²	1	48	yes	complemented
41	#17989155	C₂²	1	48	yes	complemented
42	C₂×#14556588	C₂²	1	3	yes	complemented
43	C₂×#14556587	C₂²	1	3	yes	complemented
44	C₂×#14556580	C₂²	1	3	yes	complemented
45	#17989096	C₂²	1	48	yes	complemented
46	C₂×#14556576	C₂²	1	3	yes	complemented
47	C₂×#14556573	C₂²	1	3	yes	complemented
48	C₂×#14556569	C₂²	1	3	yes	complemented
49	C₂×#14556568	C₂²	1	1	yes	characteristic, complemented
50	C₂×#14556567	C₂²	1	3	yes	complemented
51	C₂×#14556566	C₂²	1	3	yes	complemented
52	C₂×#14556566	C₂²	1	6	yes	complemented
53	C₂×#14556566	C₂²	1	3	yes	complemented
54	C₂×#14556565	C₂²	1	3	yes	complemented
55	C₂×#14556565	C₂²	1	3	yes	complemented
56	C₂×#14556564	C₂²	1	3	yes	complemented
57	C₂×#14556564	C₂²	1	6	yes	complemented
58	C₂×#14556564	C₂²	1	6	yes	complemented
59	C₂×#14556563	C₂²	1	3	yes	complemented
60	C₂×#14556562	C₂²	1	3	yes	complemented
61	#121×D₇₃	C₂²	1	48	yes	complemented
62	C₂×#14556561	C₂²	1	6	yes	complemented
63	C₂×#14556561	C₂²	1	6	yes	complemented
64	C₂×#14556561	C₂²	1	3	yes	complemented
65	C₂×#14556559	C₂²	1	3	yes	complemented
66	#17989069	C₂²	1	16	yes	complemented
67	C₂×Q₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₄×D₂₉₂	C₂²	1	3	yes	complemented
69	C₂×C₄×D₂₉₂	C₂²	1	3	yes	complemented
70	C₂×#14556553	C₂²	1	3	yes	complemented
71	C₂×C₄×C₂²⋊D₇₃	C₂²	1	3	yes	complemented
72	C₂×C₄×C₂²⋊D₇₃	C₂²	1	3	yes	complemented
73	C₂×#14556548	C₂²	1	3	yes	complemented
74	C₂×C₄⋊C₄×D₇₃	C₂²	1	3	yes	complemented
75	C₂×C₂²⋊C₄×D₇₃	C₂²	1	6	yes	complemented
76	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
77	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
78	#548×C₇₃	C₂²	1	16	yes	complemented
79	C₂×#124×C₇₃	C₂²	1	3	yes	complemented
80	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	3	yes	complemented
81	C₂×#121×C₇₃	C₂²	1	3	yes	complemented
82	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×D₄×C₇₃	C₂²	1	3	yes	complemented
84	C₂⁴×D₇₃	C₂³	1	3	yes	—
85	C₂⁴×D₇₃	C₂³	1	6	yes	—
86	#14556637	—	2	128	no	—
87	C₂×#11924029	—	2	128	no	—
88	C₂×#11924029	—	2	24	no	—
89	C₂×#11924029	—	2	24	no	—
90	C₂×#11924029	—	2	8	no	—
91	C₂×#11924029	—	2	8	no	—
92	C₂×#11924029	D₄	1	16	yes	complemented
93	C₂×#11924029	C₂³	1	8	yes	—
94	C₂×#11924029	C₂³	1	24	yes	complemented
95	C₂×#11924029	C₂³	1	24	yes	complemented
96	C₂×#11924029	C₂³	1	8	yes	complemented
97	C₂×#11924029	C₂³	1	8	yes	complemented
98	C₂×#11924028	—	2	24	no	—
99	C₂×#11924028	C₂³	1	24	yes	complemented
100	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
101	C₂²×D₂₉₂	—	2	24	no	—
102	C₂²×D₂₉₂	—	2	24	no	—
103	C₂²×D₂₉₂	C₂³	1	3	yes	—
104	C₂²×D₂₉₂	C₂³	1	3	yes	—
105	C₂²×D₂₉₂	C₂³	1	3	yes	—
106	C₂²×D₂₉₂	C₂³	1	6	yes	—
107	C₂²×D₂₉₂	C₂³	1	3	yes	—
108	C₂²×D₂₉₂	C₂³	1	6	yes	—
109	C₂²×D₂₉₂	C₂³	1	3	yes	—
110	C₂²×D₂₉₂	C₂³	1	24	yes	complemented
111	C₂²×D₂₉₂	C₂³	1	24	yes	complemented
112	C₂²×C₂²⋊D₇₃	C₂³	1	3	yes	—
113	C₂²×C₂²⋊D₇₃	C₂³	1	3	yes	—
114	C₂²×C₂²⋊D₇₃	C₂³	1	3	yes	—
115	C₂²×C₂²⋊D₇₃	C₂³	1	3	yes	—
116	C₂²×C₂²⋊D₇₃	C₂³	1	6	yes	—
117	C₂×D₄×D₇₃	—	2	24	no	—
118	C₂×D₄×D₇₃	—	2	24	no	—
119	C₂×D₄×D₇₃	—	4	24	no	—
120	C₂×D₄×D₇₃	C₂³	1	24	yes	complemented
121	C₂×D₄×D₇₃	C₂³	1	24	yes	complemented
122	C₂×D₄×D₇₃	C₂³	1	48	yes	complemented
123	C₂³×Dic₇₃	C₂³	1	1	yes	characteristic
124	C₂²×C₄×D₇₃	—	2	24	no	—
125	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
126	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
127	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
128	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
129	C₂²×C₄×D₇₃	C₂³	1	6	yes	—
130	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
131	C₂²×C₄×D₇₃	C₂³	1	24	yes	complemented
132	#14556588	C₂³	1	24	yes	complemented
133	#14556587	C₂³	1	24	yes	complemented
134	#14556580	C₂³	1	24	yes	complemented
135	#14556576	C₂³	1	24	yes	complemented
136	#14556573	C₂³	1	24	yes	complemented
137	#14556569	C₂³	1	24	yes	complemented
138	#14556568	C₂³	1	8	yes	complemented
139	#14556567	C₂³	1	24	yes	complemented
140	#14556566	C₂³	1	24	yes	complemented
141	#14556566	C₂³	1	48	yes	complemented
142	#14556566	C₂³	1	24	yes	complemented
143	#14556565	C₂³	1	24	yes	complemented
144	#14556565	C₂³	1	24	yes	complemented
145	#14556564	C₂³	1	24	yes	complemented
146	#14556564	C₂³	1	48	yes	complemented
147	#14556564	C₂³	1	48	yes	complemented
148	#14556563	C₂³	1	24	yes	complemented
149	#14556562	C₂³	1	24	yes	complemented
150	#14556561	C₂³	1	48	yes	complemented
151	#14556561	C₂³	1	48	yes	complemented
152	#14556561	C₂³	1	24	yes	complemented
153	#14556559	C₂³	1	24	yes	complemented
154	Q₈×Dic₇₃	C₂³	1	8	yes	complemented
155	C₄×D₂₉₂	C₂³	1	24	yes	complemented
156	C₄×D₂₉₂	C₂³	1	24	yes	complemented
157	#14556553	C₂³	1	24	yes	complemented
158	C₄×C₂²⋊D₇₃	C₂³	1	24	yes	complemented
159	C₄×C₂²⋊D₇₃	C₂³	1	24	yes	complemented
160	#14556548	C₂³	1	24	yes	complemented
161	C₂×C₄⋊Dic₇₃	C₂³	1	3	yes	—
162	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
163	C₂×#11924007	C₂³	1	3	yes	—
164	C₂×#11924007	C₂³	1	1	yes	characteristic
165	C₂×#11924007	C₂³	1	1	yes	characteristic
166	C₂×#11924007	C₂³	1	3	yes	—
167	C₄⋊C₄×D₇₃	C₂³	1	24	yes	complemented
168	C₂×C₂²⋊Dic₇₃	C₂³	1	3	yes	—
169	C₂×C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
170	C₂×#11924005	C₂³	1	3	yes	—
171	C₂×#11924005	C₂³	1	6	yes	—
172	C₂×#11924005	C₂³	1	3	yes	—
173	C₂×#11924005	C₂³	1	3	yes	—
174	C₂×#11924005	C₂³	1	3	yes	—
175	C₂×#11924005	C₂³	1	3	yes	—
176	C₂×#11924005	C₂³	1	3	yes	—
177	C₂²⋊C₄×D₇₃	C₂³	1	48	yes	complemented
178	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
179	C₂×#41×C₇₃	—	2	8	no	—
180	C₂×#41×C₇₃	C₂³	1	8	yes	complemented
181	C₂²×Q₈×C₇₃	—	2	8	no	—
182	C₂²×Q₈×C₇₃	C₂³	1	3	yes	—
183	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
184	C₂²×Q₈×C₇₃	C₂³	1	8	yes	complemented
185	C₂²×D₄×C₇₃	C₂³	1	3	yes	—
186	C₂²×D₄×C₇₃	C₂³	1	3	yes	—
187	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
188	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
189	#124×C₇₃	C₂³	1	24	yes	complemented
190	C₂²⋊Q₈×C₇₃	C₂³	1	24	yes	complemented
191	#121×C₇₃	C₂³	1	24	yes	complemented
192	C₄×Q₈×C₇₃	C₂³	1	8	yes	complemented
193	C₄×D₄×C₇₃	C₂³	1	24	yes	complemented
194	C₂×C₄⋊C₄×C₇₃	C₂³	1	3	yes	—
195	C₂×C₄⋊C₄×C₇₃	C₂³	1	3	yes	—
196	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₇₃	C₂³	1	3	yes	—
198	C₂×C₂²⋊C₄×C₇₃	C₂³	1	6	yes	—
199	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
200	C₂³×D₇₃	—	2	12	no	—
201	C₂³×D₇₃	—	2	12	no	—
202	C₂³×D₇₃	—	2	24	no	—
203	C₂³×D₇₃	—	4	6	no	—
204	C₂³×D₇₃	—	4	12	no	—
205	C₂³×D₇₃	—	4	12	no	—
206	C₂³×D₇₃	C₂⁴	1	3	yes	—
207	C₂³×D₇₃	C₂⁴	1	3	yes	—
208	C₂³×D₇₃	C₂⁴	1	12	yes	—
209	C₂³×D₇₃	C₂⁴	1	3	yes	—
210	C₂³×D₇₃	C₂⁴	1	24	yes	—
211	#11924029	—	2	32	no	—
212	#11924029	—	2	32	no	—
213	#11924029	—	2	96	no	—
214	#11924029	—	2	96	no	—
215	#11924029	C₂×D₄	1	64	yes	complemented
216	#11924028	—	2	96	no	—
217	C₂×Dic₁₄₆	—	2	4	no	—
218	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
219	C₂×D₂₉₂	—	2	12	no	—
220	C₂×D₂₉₂	—	2	24	no	—
221	C₂×D₂₉₂	—	2	12	no	—
222	C₂×D₂₉₂	—	2	12	no	—
223	C₂×D₂₉₂	—	2	96	no	—
224	C₂×D₂₉₂	—	2	96	no	—
225	C₂×D₂₉₂	—	4	12	no	—
226	C₂×D₂₉₂	—	4	6	no	—
227	C₂×D₂₉₂	C₂×D₄	1	24	yes	complemented
228	C₂×D₂₉₂	C₂⁴	1	24	yes	—
229	C₂×D₂₉₂	C₂⁴	1	12	yes	—
230	C₂×D₂₉₂	C₂⁴	1	12	yes	—
231	C₂×D₂₉₂	C₂⁴	1	12	yes	—
232	C₂×D₂₉₂	C₂⁴	1	12	yes	—
233	C₂×D₂₉₂	C₂⁴	1	24	yes	—
234	C₂×D₂₉₂	C₂⁴	1	12	yes	—
235	C₂×C₂²⋊D₇₃	—	2	12	no	—
236	C₂×C₂²⋊D₇₃	—	2	12	no	—
237	C₂×C₂²⋊D₇₃	—	2	12	no	—
238	C₂×C₂²⋊D₇₃	—	4	12	no	—
239	C₂×C₂²⋊D₇₃	—	4	6	no	—
240	C₂×C₂²⋊D₇₃	C₂⁴	1	12	yes	—
241	C₂×C₂²⋊D₇₃	C₂⁴	1	12	yes	—
242	C₂×C₂²⋊D₇₃	C₂⁴	1	12	yes	—
243	C₂×C₂²⋊D₇₃	C₂⁴	1	12	yes	—
244	C₂×C₂²⋊D₇₃	C₂⁴	1	24	yes	—
245	D₄×D₇₃	—	2	96	no	—
246	D₄×D₇₃	—	2	96	no	—
247	D₄×D₇₃	—	4	96	no	—
248	C₂²×Dic₇₃	—	2	4	no	—
249	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
250	C₂²×Dic₇₃	C₂⁴	1	3	yes	—
251	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
252	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
253	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
254	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×D₇₃	—	2	12	no	—
256	C₂×C₄×D₇₃	—	2	12	no	—
257	C₂×C₄×D₇₃	—	2	12	no	—
258	C₂×C₄×D₇₃	—	2	12	no	—
259	C₂×C₄×D₇₃	—	2	96	no	—
260	C₂×C₄×D₇₃	—	4	12	no	—
261	C₂×C₄×D₇₃	C₂×D₄	1	24	yes	complemented
262	C₂×C₄×D₇₃	C₂⁴	1	12	yes	—
263	C₂×C₄×D₇₃	C₂⁴	1	12	yes	—
264	C₂×C₄×D₇₃	C₂⁴	1	12	yes	—
265	C₂×C₄×D₇₃	C₂⁴	1	12	yes	—
266	C₂×C₄×D₇₃	C₂⁴	1	24	yes	—
267	C₂×C₄×D₇₃	C₂⁴	1	12	yes	—
268	C₄⋊Dic₇₃	C₂⁴	1	12	yes	—
269	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
270	#11924007	C₂⁴	1	12	yes	—
271	#11924007	C₂⁴	1	4	yes	—
272	#11924007	C₂⁴	1	4	yes	—
273	#11924007	C₂⁴	1	12	yes	—
274	C₂²⋊Dic₇₃	C₂⁴	1	12	yes	—
275	C₂²⋊Dic₇₃	C₂⁴	1	4	yes	—
276	#11924005	C₂⁴	1	12	yes	—
277	#11924005	C₂⁴	1	24	yes	—
278	#11924005	C₂⁴	1	12	yes	—
279	#11924005	C₂⁴	1	12	yes	—
280	#11924005	C₂⁴	1	12	yes	—
281	#11924005	C₂⁴	1	12	yes	—
282	#11924005	C₂⁴	1	12	yes	—
283	C₄×Dic₇₃	C₂⁴	1	12	yes	—
284	C₂⁴×C₇₃	C₂⁴	1	3	yes	—
285	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
286	#41×C₇₃	—	2	32	no	—
287	C₂×Q₈×C₇₃	—	2	32	no	—
288	C₂×Q₈×C₇₃	—	2	12	no	—
289	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	complemented
290	C₂×Q₈×C₇₃	C₂⁴	1	12	yes	—
291	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
292	C₂×D₄×C₇₃	—	2	12	no	—
293	C₂×D₄×C₇₃	—	2	12	no	—
294	C₂×D₄×C₇₃	C₂⁴	1	12	yes	—
295	C₂×D₄×C₇₃	C₂⁴	1	12	yes	—
296	C₂²×C₄×C₇₃	—	2	12	no	—
297	C₂²×C₄×C₇₃	—	2	12	no	—
298	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
300	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
301	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₇₃	C₂⁴	1	12	yes	—
303	C₂²×C₄×C₇₃	C₂⁴	1	12	yes	—
304	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
305	C₄⋊C₄×C₇₃	C₂⁴	1	12	yes	—
306	C₄⋊C₄×C₇₃	C₂⁴	1	12	yes	—
307	C₂²⋊C₄×C₇₃	C₂⁴	1	4	yes	—
308	C₂²⋊C₄×C₇₃	C₂⁴	1	12	yes	—
309	C₂²⋊C₄×C₇₃	C₂⁴	1	24	yes	—
310	C₄²×C₇₃	C₂⁴	1	12	yes	—
311	C₂³×C₇₃	—	2	2	no	—
312	C₂³×C₇₃	—	2	2	no	—
313	C₂³×C₇₃	—	2	6	no	—
314	C₂³×C₇₃	—	2	6	no	—
315	C₂³×C₇₃	—	2	6	no	—
316	C₂³×C₇₃	H(5,𝔽₂)	1	4	yes	complemented
317	C₂³×C₇₃	C₂⁵	1	6	yes	—
318	C₂³×C₇₃	C₂⁵	1	2	yes	—
319	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
320	C₂²×D₇₃	—	2	6	no	—
321	C₂²×D₇₃	—	2	6	no	—
322	C₂²×D₇₃	—	2	6	no	—
323	C₂²×D₇₃	—	2	6	no	—
324	C₂²×D₇₃	—	2	6	no	—
325	C₂²×D₇₃	—	2	6	no	—
326	C₂²×D₇₃	—	2	24	no	—
327	C₂²×D₇₃	—	2	6	no	—
328	C₂²×D₇₃	—	2	6	no	—
329	C₂²×D₇₃	—	2	24	no	—
330	C₂²×D₇₃	—	2	48	no	—
331	C₂²×D₇₃	—	4	12	no	—
332	C₂²×D₇₃	—	4	24	no	—
333	C₂²×D₇₃	—	4	24	no	—
334	C₂²×D₇₃	—	4	48	no	—
335	C₂²×D₇₃	—	8	48	no	—
336	C₂²×D₇₃	C₂²×D₄	1	12	yes	—
337	C₂²×D₇₃	C₂⁵	1	6	yes	—
338	C₂²×D₇₃	C₂⁵	1	6	yes	—
339	C₂²×D₇₃	C₂⁵	1	6	yes	—
340	Q₈×C₇₃	—	2	24	no	—
341	Q₈×C₇₃	C₂²×D₄	1	16	yes	complemented
342	D₄×C₇₃	—	2	24	no	—
343	D₄×C₇₃	—	2	24	no	—
344	C₂×C₄×C₇₃	—	2	2	no	—
345	C₂×C₄×C₇₃	—	2	6	no	—
346	C₂×C₄×C₇₃	—	2	6	no	—
347	C₂×C₄×C₇₃	—	2	2	no	—
348	C₂×C₄×C₇₃	—	2	24	no	—
349	C₂×C₄×C₇₃	—	2	24	no	—
350	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
351	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
352	C₂×C₄×C₇₃	C₂⁵	1	6	yes	—
353	C₂×C₄×C₇₃	C₂⁵	1	6	yes	—
354	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
355	C₂×C₄×C₇₃	C₂⁵	1	6	yes	—
356	C₂²⋊D₇₃	—	2	24	no	—
357	C₂²⋊D₇₃	—	2	24	no	—
358	C₂²⋊D₇₃	—	2	24	no	—
359	C₂²⋊D₇₃	—	4	24	no	—
360	C₂²⋊D₇₃	—	4	12	no	—
361	C₂×Dic₇₃	—	2	2	no	—
362	C₂×Dic₇₃	—	2	2	no	—
363	C₂×Dic₇₃	—	2	6	no	—
364	C₂×Dic₇₃	—	2	2	no	—
365	C₂×Dic₇₃	—	2	8	no	—
366	C₂×Dic₇₃	C₂²×D₄	1	4	yes	—
367	C₂×Dic₇₃	C₂⁵	1	2	yes	—
368	C₂×Dic₇₃	C₂⁵	1	6	yes	—
369	C₂×Dic₇₃	C₂⁵	1	2	yes	—
370	C₂×Dic₇₃	C₂⁵	1	2	yes	—
371	C₂×Dic₇₃	C₂⁵	1	2	yes	—
372	D₂₉₂	—	2	24	no	—
373	D₂₉₂	—	2	48	no	—
374	D₂₉₂	—	2	24	no	—
375	D₂₉₂	—	2	24	no	—
376	D₂₉₂	—	4	24	no	—
377	D₂₉₂	—	4	12	no	—
378	D₂₉₂	C₂²×D₄	1	48	yes	complemented
379	C₄×D₇₃	—	2	24	no	—
380	C₄×D₇₃	—	2	24	no	—
381	C₄×D₇₃	—	2	24	no	—
382	C₄×D₇₃	—	2	24	no	—
383	C₄×D₇₃	—	4	24	no	—
384	C₄×D₇₃	C₂²×D₄	1	48	yes	complemented
385	Dic₁₄₆	—	2	8	no	—
386	C₂²×C₇₃	—	2	2	no	—
387	C₂²×C₇₃	—	2	2	no	—
388	C₂²×C₇₃	—	2	8	no	—
389	C₂²×C₇₃	—	2	6	no	—
390	C₂²×C₇₃	—	2	6	no	—
391	C₂²×C₇₃	—	2	6	no	—
392	C₂²×C₇₃	—	4	12	no	—
393	C₂²×C₇₃	C₂³×D₄	1	2	yes	—
394	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
395	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
396	C₂²×C₇₃	#585	1	2	yes	—
397	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
398	C₂×D₇₃	—	2	6	no	—
399	C₂×D₇₃	—	2	6	no	—
400	C₂×D₇₃	—	2	24	no	—
401	C₂×D₇₃	—	2	6	no	—
402	C₂×D₇₃	—	2	6	no	—
403	C₂×D₇₃	—	2	6	no	—
404	C₂×D₇₃	—	2	6	no	—
405	C₂×D₇₃	—	2	6	no	—
406	C₂×D₇₃	—	2	6	no	—
407	C₂×D₇₃	—	4	48	no	—
408	C₂×D₇₃	—	4	12	no	—
409	C₂×D₇₃	—	4	12	no	—
410	C₂×D₇₃	—	8	48	no	—
411	C₂×D₇₃	C₂³×D₄	1	12	yes	—
412	C₄×C₇₃	—	2	2	no	—
413	C₄×C₇₃	—	2	6	no	—
414	C₄×C₇₃	—	2	6	no	—
415	C₄×C₇₃	—	2	2	no	—
416	C₄×C₇₃	C₂³×D₄	1	12	yes	—
417	Dic₇₃	—	2	2	no	—
418	Dic₇₃	—	2	2	no	—
419	Dic₇₃	—	2	6	no	—
420	Dic₇₃	—	2	2	no	—
421	Dic₇₃	C₂³×D₄	1	4	yes	—
422	C₂×#3488	—	73	1	no	maximal, Sylow
423	C₂×C₇₃	—	2	4	no	—
424	C₂×C₇₃	—	4	6	no	—
425	C₂×C₇₃	#3488	1	4	yes	complemented
426	C₂×C₇₃	C₂⁴×D₄	1	1	yes	characteristic
427	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂×C₇₃	C₂×#585	1	1	yes	characteristic
429	D₇₃	—	2	12	no	—
430	D₇₃	—	4	6	no	—
431	D₇₃	—	4	6	no	—
432	C₂²×H(5,𝔽₂)	—	73	1	no	—
433	C₂³×#41	—	73	1	no	—
434	#3488	—	73	32	no	—
435	C₂×#550	—	73	1	no	—
436	C₂×#550	—	73	1	no	—
437	C₂×#548	—	73	1	no	—
438	C₂×#548	D₇₃	1	1	yes	characteristic, complemented
439	C₂×#546	—	73	3	no	—
440	C₂×#546	—	73	3	no	—
441	C₂×D₄²	—	73	3	no	—
442	C₂×D₄²	—	73	3	no	—
443	C₂×#537	—	73	3	no	—
444	C₂×#535	—	73	3	no	—
445	C₂×#525	—	73	3	no	—
446	C₂²×#121	—	73	3	no	—
447	C₂×#520	—	73	1	no	—
448	C₇₃	C₂×#3488	1	1	yes	characteristic, complemented, Sylow
449	C₂×H(5,𝔽₂)	—	73	16	no	—
450	C₂×H(5,𝔽₂)	—	146	16	no	—
451	C₂²×#41	—	73	1	no	—
452	C₂²×#41	—	73	3	no	—
453	C₂²×#41	—	73	3	no	—
454	C₂²×#41	—	73	1	no	—
455	C₂²×#41	—	73	1	no	—
456	C₂²×#41	—	73	16	no	—
457	C₂²×#41	—	73	3	no	—
458	C₂²×#41	—	146	16	no	—
459	C₂²×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
460	C₂³×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
461	C₂³×D₄	—	73	6	no	—
462	C₂³×D₄	—	73	3	no	—
463	C₂³×D₄	—	73	3	no	—
464	C₂³×D₄	—	73	3	no	—
465	C₂³×D₄	—	73	3	no	—
466	C₂⁴×C₄	—	73	3	no	—
467	#550	—	73	16	no	—
468	#550	—	73	16	no	—
469	#548	—	73	16	no	—
470	#548	C₂×D₇₃	1	16	yes	complemented
471	#546	—	73	48	no	—
472	#546	—	73	48	no	—
473	D₄²	—	73	48	no	—
474	D₄²	—	73	48	no	—
475	#537	—	73	48	no	—
476	#535	—	73	48	no	—
477	C₂×#127	—	73	3	no	—
478	C₂×#127	—	73	3	no	—
479	C₂×#124	—	73	3	no	—
480	C₂×#124	C₂×D₇₃	1	3	yes	complemented
481	#525	—	73	48	no	—
482	C₂×#123	—	73	3	no	—
483	C₂×#123	—	73	3	no	—
484	C₂×C₂²⋊Q₈	—	73	3	no	—
485	C₂×C₂²⋊Q₈	—	73	3	no	—
486	C₂×C₂²⋊Q₈	—	73	1	no	—
487	C₂×C₂²⋊Q₈	C₂×D₇₃	1	3	yes	complemented
488	C₂×#121	—	73	3	no	—
489	C₂×#121	—	73	3	no	—
490	C₂×#121	—	73	3	no	—
491	C₂×#121	—	73	3	no	—
492	C₂×#121	—	73	48	no	—
493	C₂×#121	—	73	3	no	—
494	C₂×#121	—	73	6	no	—
495	C₂×#121	—	73	3	no	—
496	C₂×#121	—	73	6	no	—
497	C₂×#121	—	73	3	no	—
498	C₂×#121	—	73	6	no	—
499	C₂×#121	C₂×D₇₃	1	3	yes	complemented
500	C₂×#120	—	73	3	no	—
501	C₂×#120	—	73	3	no	—
502	C₂×#120	—	73	6	no	—
503	C₂×#120	—	73	6	no	—
504	#520	—	73	16	no	—
505	C₂×C₄×Q₈	—	73	1	no	—
506	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
507	C₂×C₄×D₄	—	73	3	no	—
508	C₂×C₄×D₄	—	73	3	no	—
509	C₂×C₄×D₄	—	73	3	no	—
510	C₂×C₄×D₄	—	73	3	no	—
511	C₂×C₄×D₄	—	73	3	no	—
512	C₂×C₄×D₄	C₂×D₇₃	1	3	yes	complemented
513	C₂×#117	—	73	3	no	—
514	C₂²×C₄⋊C₄	—	73	3	no	—
515	C₂²×C₂²⋊C₄	—	73	6	no	—
516	C₂⁵	—	73	6	no	—
517	C₂⁵	—	73	3	no	—
518	H(5,𝔽₂)	—	146	128	no	—
519	C₂×#41	—	2	8	no	—
520	C₂×#41	—	73	16	no	—
521	C₂×#41	—	73	8	no	—
522	C₂×#41	—	73	24	no	—
523	C₂×#41	—	73	24	no	—
524	C₂×#41	—	73	8	no	—
525	C₂×#41	—	73	8	no	—
526	C₂×#41	—	73	24	no	—
527	C₂×#41	—	146	24	no	—
528	C₂×#41	—	146	24	no	—
529	C₂×#41	—	146	24	no	—
530	C₂×#41	—	146	128	no	—
531	C₂×#41	—	146	8	no	—
532	C₂×#41	—	146	8	no	—
533	C₂×#41	C₂²×D₇₃	1	8	yes	complemented
534	C₂²×Q₈	—	2	8	no	—
535	C₂²×Q₈	—	73	1	no	—
536	C₂²×Q₈	C₂²×D₇₃	1	3	yes	—
537	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
538	C₂²×Q₈	C₂²×D₇₃	1	8	yes	complemented
539	C₂²×D₄	—	292	24	no	—
540	C₂²×D₄	—	73	3	no	—
541	C₂²×D₄	—	73	6	no	—
542	C₂²×D₄	—	73	48	no	—
543	C₂²×D₄	—	73	3	no	—
544	C₂²×D₄	—	73	3	no	—
545	C₂²×D₄	—	73	3	no	—
546	C₂²×D₄	—	73	24	no	—
547	C₂²×D₄	—	73	24	no	—
548	C₂²×D₄	—	73	3	no	—
549	C₂²×D₄	—	73	6	no	—
550	C₂²×D₄	—	73	3	no	—
551	C₂²×D₄	—	73	6	no	—
552	C₂²×D₄	—	73	3	no	—
553	C₂²×D₄	—	73	3	no	—
554	C₂²×D₄	—	73	3	no	—
555	C₂²×D₄	—	73	24	no	—
556	C₂²×D₄	—	73	24	no	—
557	C₂²×D₄	—	146	24	no	—
558	C₂²×D₄	—	146	24	no	—
559	C₂²×D₄	—	146	24	no	—
560	C₂²×D₄	—	146	24	no	—
561	C₂²×D₄	C₂²×D₇₃	1	3	yes	—
562	C₂²×D₄	C₂²×D₇₃	1	3	yes	—
563	C₂³×C₄	—	73	6	no	—
564	C₂³×C₄	—	73	3	no	—
565	C₂³×C₄	—	73	1	no	—
566	C₂³×C₄	—	73	3	no	—
567	C₂³×C₄	—	73	3	no	—
568	C₂³×C₄	—	73	3	no	—
569	C₂³×C₄	—	73	3	no	—
570	C₂³×C₄	—	73	24	no	—
571	C₂³×C₄	—	146	24	no	—
572	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
573	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
574	#127	—	73	24	no	—
575	#127	—	73	24	no	—
576	#124	—	73	24	no	—
577	#124	C₂²×D₇₃	1	24	yes	complemented
578	#123	—	73	24	no	—
579	#123	—	73	24	no	—
580	C₂²⋊Q₈	—	73	24	no	—
581	C₂²⋊Q₈	—	73	24	no	—
582	C₂²⋊Q₈	—	73	8	no	—
583	C₂²⋊Q₈	C₂²×D₇₃	1	24	yes	complemented
584	#121	—	73	24	no	—
585	#121	—	73	24	no	—
586	#121	—	73	24	no	—
587	#121	—	73	24	no	—
588	#121	—	73	24	no	—
589	#121	—	73	48	no	—
590	#121	—	73	24	no	—
591	#121	—	73	48	no	—
592	#121	—	73	24	no	—
593	#121	—	73	48	no	—
594	#121	C₂²×D₇₃	1	24	yes	complemented
595	#120	—	73	24	no	—
596	#120	—	73	24	no	—
597	#120	—	73	48	no	—
598	#120	—	73	48	no	—
599	C₄×Q₈	—	73	8	no	—
600	C₄×Q₈	C₂²×D₇₃	1	8	yes	complemented
601	C₄×D₄	—	73	24	no	—
602	C₄×D₄	—	73	24	no	—
603	C₄×D₄	—	73	24	no	—
604	C₄×D₄	—	73	24	no	—
605	C₄×D₄	—	73	24	no	—
606	C₄×D₄	C₂²×D₇₃	1	24	yes	complemented
607	#117	—	73	24	no	—
608	C₂×C₄⋊C₄	—	73	3	no	—
609	C₂×C₄⋊C₄	—	73	3	no	—
610	C₂×C₄⋊C₄	—	73	1	no	—
611	C₂×C₄⋊C₄	—	73	1	no	—
612	C₂×C₄⋊C₄	—	73	1	no	—
613	C₂×C₄⋊C₄	—	73	3	no	—
614	C₂×C₄⋊C₄	—	73	24	no	—
615	C₂×C₄⋊C₄	C₂²×D₇₃	1	3	yes	—
616	C₂×C₄⋊C₄	C₂²×D₇₃	1	3	yes	—
617	C₂×C₂²⋊C₄	—	73	3	no	—
618	C₂×C₂²⋊C₄	—	73	1	no	—
619	C₂×C₂²⋊C₄	—	73	3	no	—
620	C₂×C₂²⋊C₄	—	73	6	no	—
621	C₂×C₂²⋊C₄	—	73	3	no	—
622	C₂×C₂²⋊C₄	—	73	3	no	—
623	C₂×C₂²⋊C₄	—	73	3	no	—
624	C₂×C₂²⋊C₄	—	73	3	no	—
625	C₂×C₂²⋊C₄	—	73	3	no	—
626	C₂×C₂²⋊C₄	—	73	48	no	—
627	C₂×C₂²⋊C₄	C₂²×D₇₃	1	6	yes	—
628	C₂×C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂²×D₇₃	1	3	yes	—
630	C₂×C₄²	—	73	3	no	—
631	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
632	C₂⁴	—	292	6	no	—
633	C₂⁴	—	292	12	no	—
634	C₂⁴	—	292	12	no	—
635	C₂⁴	—	73	24	no	—
636	C₂⁴	—	73	12	no	—
637	C₂⁴	—	73	3	no	—
638	C₂⁴	—	73	3	no	—
639	C₂⁴	—	73	3	no	—
640	C₂⁴	—	146	12	no	—
641	C₂⁴	—	146	24	no	—
642	C₂⁴	—	146	12	no	—
643	C₂⁴	C₂³×D₇₃	1	3	yes	—
644	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
645	#41	—	2	32	no	—
646	#41	—	73	64	no	—
647	#41	—	146	96	no	—
648	#41	—	146	96	no	—
649	#41	—	146	96	no	—
650	#41	—	146	32	no	—
651	#41	—	146	32	no	—
652	C₂×Q₈	—	2	32	no	—
653	C₂×Q₈	—	2	12	no	—
654	C₂×Q₈	—	73	4	no	—
655	C₂×Q₈	—	146	4	no	—
656	C₂×Q₈	D₄×D₇₃	1	8	yes	complemented
657	C₂×Q₈	C₂³×D₇₃	1	12	yes	—
658	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
659	C₂×D₄	—	2	12	no	—
660	C₂×D₄	—	2	12	no	—
661	C₂×D₄	—	292	12	no	—
662	C₂×D₄	—	292	6	no	—
663	C₂×D₄	—	292	96	no	—
664	C₂×D₄	—	292	12	no	—
665	C₂×D₄	—	292	6	no	—
666	C₂×D₄	—	73	12	no	—
667	C₂×D₄	—	73	24	no	—
668	C₂×D₄	—	73	12	no	—
669	C₂×D₄	—	73	12	no	—
670	C₂×D₄	—	73	12	no	—
671	C₂×D₄	—	73	24	no	—
672	C₂×D₄	—	73	12	no	—
673	C₂×D₄	—	73	24	no	—
674	C₂×D₄	—	73	12	no	—
675	C₂×D₄	—	73	24	no	—
676	C₂×D₄	—	73	12	no	—
677	C₂×D₄	—	73	12	no	—
678	C₂×D₄	—	73	12	no	—
679	C₂×D₄	—	146	96	no	—
680	C₂×D₄	—	146	96	no	—
681	C₂×D₄	—	146	12	no	—
682	C₂×D₄	—	146	24	no	—
683	C₂×D₄	—	146	96	no	—
684	C₂×D₄	—	146	12	no	—
685	C₂×D₄	—	146	96	no	—
686	C₂×D₄	—	146	12	no	—
687	C₂×D₄	—	146	12	no	—
688	C₂×D₄	—	146	12	no	—
689	C₂×D₄	—	146	12	no	—
690	C₂×D₄	C₂³×D₇₃	1	12	yes	—
691	C₂×D₄	C₂³×D₇₃	1	12	yes	—
692	C₂²×C₄	—	2	12	no	—
693	C₂²×C₄	—	2	12	no	—
694	C₂²×C₄	—	292	12	no	—
695	C₂²×C₄	—	73	24	no	—
696	C₂²×C₄	—	73	1	no	—
697	C₂²×C₄	—	73	24	no	—
698	C₂²×C₄	—	73	12	no	—
699	C₂²×C₄	—	73	4	no	—
700	C₂²×C₄	—	73	1	no	—
701	C₂²×C₄	—	73	3	no	—
702	C₂²×C₄	—	73	1	no	—
703	C₂²×C₄	—	73	1	no	—
704	C₂²×C₄	—	73	12	no	—
705	C₂²×C₄	—	73	12	no	—
706	C₂²×C₄	—	73	12	no	—
707	C₂²×C₄	—	73	12	no	—
708	C₂²×C₄	—	146	12	no	—
709	C₂²×C₄	—	146	96	no	—
710	C₂²×C₄	—	146	12	no	—
711	C₂²×C₄	—	146	4	no	—
712	C₂²×C₄	—	146	12	no	—
713	C₂²×C₄	—	146	12	no	—
714	C₂²×C₄	C₂³×D₇₃	1	12	yes	—
715	C₂²×C₄	C₂³×D₇₃	1	12	yes	—
716	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
717	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
718	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
719	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
720	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
721	C₄⋊C₄	—	73	12	no	—
722	C₄⋊C₄	—	73	4	no	—
723	C₄⋊C₄	—	73	4	no	—
724	C₄⋊C₄	—	73	12	no	—
725	C₄⋊C₄	—	73	12	no	—
726	C₄⋊C₄	—	73	4	no	—
727	C₄⋊C₄	C₂³×D₇₃	1	12	yes	—
728	C₄⋊C₄	C₂³×D₇₃	1	12	yes	—
729	C₂²⋊C₄	—	73	12	no	—
730	C₂²⋊C₄	—	73	4	no	—
731	C₂²⋊C₄	—	73	12	no	—
732	C₂²⋊C₄	—	73	24	no	—
733	C₂²⋊C₄	—	73	12	no	—
734	C₂²⋊C₄	—	73	12	no	—
735	C₂²⋊C₄	—	73	12	no	—
736	C₂²⋊C₄	—	73	12	no	—
737	C₂²⋊C₄	—	73	12	no	—
738	C₂²⋊C₄	C₂³×D₇₃	1	24	yes	—
739	C₂²⋊C₄	C₂³×D₇₃	1	4	yes	—
740	C₂²⋊C₄	C₂³×D₇₃	1	12	yes	—
741	C₄²	—	73	12	no	—
742	C₄²	C₂³×D₇₃	1	12	yes	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	6	no	—
746	C₂³	—	2	6	no	—
747	C₂³	—	2	6	no	—
748	C₂³	—	292	48	no	—
749	C₂³	—	292	12	no	—
750	C₂³	—	292	24	no	—
751	C₂³	—	292	24	no	—
752	C₂³	—	584	48	no	—
753	C₂³	—	73	12	no	—
754	C₂³	—	73	6	no	—
755	C₂³	—	73	6	no	—
756	C₂³	—	73	6	no	—
757	C₂³	—	146	24	no	—
758	C₂³	—	146	48	no	—
759	C₂³	—	146	6	no	—
760	C₂³	—	146	6	no	—
761	C₂³	—	146	6	no	—
762	C₂³	—	146	6	no	—
763	C₂³	—	146	24	no	—
764	C₂³	—	146	6	no	—
765	C₂³	—	146	6	no	—
766	C₂³	—	146	6	no	—
767	C₂³	—	146	6	no	—
768	C₂³	#14556637	1	4	yes	complemented
769	C₂³	C₂⁴×D₇₃	1	6	yes	—
770	C₂³	C₂⁴×D₇₃	1	2	yes	—
771	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
772	Q₈	—	2	24	no	—
773	Q₈	—	146	8	no	—
774	Q₈	C₂×D₄×D₇₃	1	16	yes	complemented
775	D₄	—	2	24	no	—
776	D₄	—	2	24	no	—
777	D₄	—	292	24	no	—
778	D₄	—	292	12	no	—
779	D₄	—	292	24	no	—
780	D₄	—	292	12	no	—
781	D₄	—	73	48	no	—
782	D₄	—	146	24	no	—
783	D₄	—	146	48	no	—
784	D₄	—	146	24	no	—
785	D₄	—	146	24	no	—
786	D₄	—	146	24	no	—
787	D₄	—	146	24	no	—
788	D₄	—	146	24	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	6	no	—
791	C₂×C₄	—	2	6	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	24	no	—
794	C₂×C₄	—	2	24	no	—
795	C₂×C₄	—	292	24	no	—
796	C₂×C₄	—	73	4	no	—
797	C₂×C₄	—	73	2	no	—
798	C₂×C₄	—	73	48	no	—
799	C₂×C₄	—	73	2	no	—
800	C₂×C₄	—	73	6	no	—
801	C₂×C₄	—	73	2	no	—
802	C₂×C₄	—	73	2	no	—
803	C₂×C₄	—	146	24	no	—
804	C₂×C₄	—	146	24	no	—
805	C₂×C₄	—	146	8	no	—
806	C₂×C₄	—	146	2	no	—
807	C₂×C₄	—	146	2	no	—
808	C₂×C₄	—	146	6	no	—
809	C₂×C₄	—	146	2	no	—
810	C₂×C₄	—	146	24	no	—
811	C₂×C₄	—	146	24	no	—
812	C₂×C₄	C₂×D₄×D₇₃	1	12	yes	—
813	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
814	C₂×C₄	C₂⁴×D₇₃	1	6	yes	—
815	C₂×C₄	C₂⁴×D₇₃	1	6	yes	—
816	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
817	C₂×C₄	C₂⁴×D₇₃	1	6	yes	—
818	C₂²	—	2	8	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	6	no	—
822	C₂²	—	2	6	no	—
823	C₂²	—	2	6	no	—
824	C₂²	—	4	12	no	—
825	C₂²	—	292	48	no	—
826	C₂²	—	292	12	no	—
827	C₂²	—	292	12	no	—
828	C₂²	—	584	48	no	—
829	C₂²	—	73	12	no	—
830	C₂²	—	146	6	no	—
831	C₂²	—	146	6	no	—
832	C₂²	—	146	6	no	—
833	C₂²	—	146	6	no	—
834	C₂²	—	146	6	no	—
835	C₂²	—	146	6	no	—
836	C₂²	—	146	24	no	—
837	C₂²	—	146	6	no	—
838	C₂²	—	146	6	no	—
839	C₂²	C₂²×D₄×D₇₃	1	2	yes	—
840	C₂²	C₂×#14556637	1	2	yes	—
841	C₂²	C₂×#14556637	1	4	yes	complemented
842	C₂²	#17989424	1	2	yes	—
843	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
844	C₄	—	2	2	no	—
845	C₄	—	2	6	no	—
846	C₄	—	2	6	no	—
847	C₄	—	2	2	no	—
848	C₄	—	73	4	no	—
849	C₄	—	146	2	no	—
850	C₄	—	146	2	no	—
851	C₄	—	146	6	no	—
852	C₄	—	146	2	no	—
853	C₄	C₂²×D₄×D₇₃	1	12	yes	—
854	C₂	—	2	4	no	—
855	C₂	—	4	6	no	—
856	C₂	—	292	6	no	—
857	C₂	—	292	6	no	—
858	C₂	—	146	12	no	—
859	C₂	#22623597	1	4	yes	direct product factor
860	C₂	C₂³×D₄×D₇₃	1	1	yes	characteristic
861	C₂	C₂²×#14556637	1	1	yes	characteristic
862	C₂	C₂×#17989424	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₃
commutator, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×#548×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
hypercenter	C₂×#548	D₇₃
hypocenter	C₇₃	C₂×#3488
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×#548

Complements

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

N	H ≅ G/N	type
1. C₂²×#14556637	C₂	semidirect
2. C₂³×#11924029	C₂	semidirect
3. #22623597	C₂	direct (N × H)
4. C₂×#17989259	C₂	semidirect
5. C₂×#17989256	C₂	semidirect
6. C₂×#17989248	C₂	semidirect
7. C₂×#17989230	C₂	semidirect
8. C₂×#17989228	C₂	semidirect
9. C₂×D₄×D₂₉₂	C₂	semidirect
10. C₂×#17989221	C₂	semidirect
11. C₂×#17989167	C₂	semidirect
12. C₂×#17989155	C₂	semidirect
13. C₂×#17989096	C₂	semidirect
14. C₂×#121×D₇₃	C₂	semidirect
15. C₂×#17989069	C₂	semidirect
16. C₂×#548×C₇₃	C₂	semidirect
18. C₂×#14556637	C₂²	semidirect
21. C₂²×#11924029	C₂²	semidirect
22. C₂²×#11924029	C₂²	semidirect
23. C₂²×#11924029	C₂²	semidirect
24. C₂²×#11924029	C₂²	semidirect
25. C₂²×#11924029	C₂²	semidirect
26. C₂²×#11924028	C₂²	semidirect
27. C₂³×D₂₉₂	C₂²	semidirect
28. C₂³×D₂₉₂	C₂²	semidirect
29. C₂²×D₄×D₇₃	C₂²	semidirect
30. C₂²×D₄×D₇₃	C₂²	semidirect
31. C₂²×D₄×D₇₃	C₂²	semidirect
32. C₂³×C₄×D₇₃	C₂²	semidirect
33. #17989259	C₂²	semidirect
34. #17989256	C₂²	semidirect
35. #17989248	C₂²	semidirect
36. #17989230	C₂²	semidirect
37. #17989228	C₂²	semidirect
38. D₄×D₂₉₂	C₂²	semidirect
39. #17989221	C₂²	semidirect
40. #17989167	C₂²	semidirect
41. #17989155	C₂²	semidirect
42. C₂×#14556588	C₂²	semidirect
43. C₂×#14556587	C₂²	semidirect
44. C₂×#14556580	C₂²	semidirect
45. #17989096	C₂²	semidirect
46. C₂×#14556576	C₂²	semidirect
47. C₂×#14556573	C₂²	semidirect
48. C₂×#14556569	C₂²	semidirect
49. C₂×#14556568	C₂²	semidirect
50. C₂×#14556567	C₂²	semidirect
51. C₂×#14556566	C₂²	semidirect
52. C₂×#14556566	C₂²	semidirect
53. C₂×#14556566	C₂²	semidirect
54. C₂×#14556565	C₂²	semidirect
55. C₂×#14556565	C₂²	semidirect
56. C₂×#14556564	C₂²	semidirect
57. C₂×#14556564	C₂²	semidirect
58. C₂×#14556564	C₂²	semidirect
59. C₂×#14556563	C₂²	semidirect
60. C₂×#14556562	C₂²	semidirect
61. #121×D₇₃	C₂²	semidirect
62. C₂×#14556561	C₂²	semidirect
63. C₂×#14556561	C₂²	semidirect
64. C₂×#14556561	C₂²	semidirect
65. C₂×#14556559	C₂²	semidirect
66. #17989069	C₂²	semidirect
67. C₂×Q₈×Dic₇₃	C₂²	semidirect
68. C₂×C₄×D₂₉₂	C₂²	semidirect
69. C₂×C₄×D₂₉₂	C₂²	semidirect
70. C₂×#14556553	C₂²	semidirect
71. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
72. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
73. C₂×#14556548	C₂²	semidirect
74. C₂×C₄⋊C₄×D₇₃	C₂²	semidirect
75. C₂×C₂²⋊C₄×D₇₃	C₂²	semidirect
76. C₂²×#41×C₇₃	C₂²	semidirect
77. C₂³×Q₈×C₇₃	C₂²	semidirect
78. #548×C₇₃	C₂²	semidirect
79. C₂×#124×C₇₃	C₂²	semidirect
80. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
81. C₂×#121×C₇₃	C₂²	semidirect
82. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
83. C₂×C₄×D₄×C₇₃	C₂²	semidirect
92. C₂×#11924029	D₄	semidirect
94. C₂×#11924029	C₂³	semidirect
95. C₂×#11924029	C₂³	semidirect
96. C₂×#11924029	C₂³	semidirect
97. C₂×#11924029	C₂³	semidirect
99. C₂×#11924028	C₂³	semidirect
110. C₂²×D₂₉₂	C₂³	semidirect
111. C₂²×D₂₉₂	C₂³	semidirect
120. C₂×D₄×D₇₃	C₂³	semidirect
121. C₂×D₄×D₇₃	C₂³	semidirect
122. C₂×D₄×D₇₃	C₂³	semidirect
131. C₂²×C₄×D₇₃	C₂³	semidirect
132. #14556588	C₂³	semidirect
133. #14556587	C₂³	semidirect
134. #14556580	C₂³	semidirect
135. #14556576	C₂³	semidirect
136. #14556573	C₂³	semidirect
137. #14556569	C₂³	semidirect
138. #14556568	C₂³	semidirect
139. #14556567	C₂³	semidirect
140. #14556566	C₂³	semidirect
141. #14556566	C₂³	semidirect
142. #14556566	C₂³	semidirect
143. #14556565	C₂³	semidirect
144. #14556565	C₂³	semidirect
145. #14556564	C₂³	semidirect
146. #14556564	C₂³	semidirect
147. #14556564	C₂³	semidirect
148. #14556563	C₂³	semidirect
149. #14556562	C₂³	semidirect
150. #14556561	C₂³	semidirect
151. #14556561	C₂³	semidirect
152. #14556561	C₂³	semidirect
153. #14556559	C₂³	semidirect
154. Q₈×Dic₇₃	C₂³	semidirect
155. C₄×D₂₉₂	C₂³	semidirect
156. C₄×D₂₉₂	C₂³	semidirect
157. #14556553	C₂³	semidirect
158. C₄×C₂²⋊D₇₃	C₂³	semidirect
159. C₄×C₂²⋊D₇₃	C₂³	semidirect
160. #14556548	C₂³	semidirect
167. C₄⋊C₄×D₇₃	C₂³	semidirect
177. C₂²⋊C₄×D₇₃	C₂³	semidirect
180. C₂×#41×C₇₃	C₂³	semidirect
184. C₂²×Q₈×C₇₃	C₂³	semidirect
189. #124×C₇₃	C₂³	semidirect
190. C₂²⋊Q₈×C₇₃	C₂³	semidirect
191. #121×C₇₃	C₂³	semidirect
192. C₄×Q₈×C₇₃	C₂³	semidirect
193. C₄×D₄×C₇₃	C₂³	semidirect
215. #11924029	C₂×D₄	semidirect
227. C₂×D₂₉₂	C₂×D₄	semidirect
261. C₂×C₄×D₇₃	C₂×D₄	semidirect
289. C₂×Q₈×C₇₃	C₂×D₄	semidirect
316. C₂³×C₇₃	H(5,𝔽₂)	semidirect
341. Q₈×C₇₃	C₂²×D₄	semidirect
378. D₂₉₂	C₂²×D₄	semidirect
384. C₄×D₇₃	C₂²×D₄	semidirect
395. C₂²×C₇₃	C₂×H(5,𝔽₂)	semidirect
425. C₂×C₇₃	#3488	semidirect
438. C₂×#548	D₇₃	semidirect
448. C₇₃	C₂×#3488	semidirect
459. C₂²×#41	C₂×D₇₃	semidirect
460. C₂³×Q₈	C₂×D₇₃	semidirect
470. #548	C₂×D₇₃	semidirect
480. C₂×#124	C₂×D₇₃	semidirect
487. C₂×C₂²⋊Q₈	C₂×D₇₃	semidirect
499. C₂×#121	C₂×D₇₃	semidirect
506. C₂×C₄×Q₈	C₂×D₇₃	semidirect
512. C₂×C₄×D₄	C₂×D₇₃	semidirect
533. C₂×#41	C₂²×D₇₃	semidirect
538. C₂²×Q₈	C₂²×D₇₃	semidirect
577. #124	C₂²×D₇₃	semidirect
583. C₂²⋊Q₈	C₂²×D₇₃	semidirect
594. #121	C₂²×D₇₃	semidirect
600. C₄×Q₈	C₂²×D₇₃	semidirect
606. C₄×D₄	C₂²×D₇₃	semidirect
656. C₂×Q₈	D₄×D₇₃	semidirect
768. C₂³	#14556637	semidirect
774. Q₈	C₂×D₄×D₇₃	semidirect
841. C₂²	C₂×#14556637	semidirect
859. C₂	#22623597	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14556637	2
C₂³×#11924029	2
#22623597	2
C₂×#17989259	2
C₂×#17989256	2
C₂×#17989248	2
C₂×#17989230	2
C₂×#17989228	2
C₂×D₄×D₂₉₂	2
C₂×#17989221	2
C₂×#17989167	2
C₂×#17989155	2
C₂×#17989096	2
C₂×#121×D₇₃	2
C₂×#17989069	2
C₂×#548×C₇₃	2
C₂×#3488	73

Subgroups — C2×#22623597 #33994291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22623597 #33994291