Subgroups — #22623602

Order 9344.

1522 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556638	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#11924027	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989250	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989245	C₂	1	1	yes	maximal, characteristic, complemented
6	#17989243	C₂	1	1	yes	maximal, characteristic, complemented
7	#17989241	C₂	1	1	yes	maximal, characteristic, complemented
8	#17989237	C₂	1	2	yes	maximal, complemented
9	#17989236	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989235	C₂	1	2	yes	maximal, complemented
11	#17989231	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989227	C₂	1	2	yes	maximal, complemented
13	#17989224	C₂	1	2	yes	maximal, complemented
14	#17989166	C₂	1	1	yes	maximal, characteristic, complemented
15	#17989164	C₂	1	2	yes	maximal, complemented
16	#17989159	C₂	1	2	yes	maximal, complemented
17	#17989157	C₂	1	1	yes	maximal, characteristic, complemented
18	#17989096	C₂	1	1	yes	maximal, characteristic, complemented
19	#17989093	C₂	1	2	yes	maximal, complemented
20	C₂×#14556568	C₂	1	2	yes	maximal, complemented
21	C₂²⋊Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#17989066	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	#14556638	—	2	8	no	—
25	C₂×#11924028	C₂²	1	1	yes	characteristic, complemented
26	C₂×#11924028	C₂²	1	2	yes	complemented
27	C₂×#11924027	—	2	8	no	—
28	C₂×#11924027	C₂²	1	1	yes	characteristic
29	C₂×#11924027	C₂²	1	2	yes	—
30	C₂×#11924027	C₂²	1	2	yes	—
31	C₂×#11924027	C₂²	1	1	yes	characteristic
32	C₂×#11924027	C₂²	1	1	yes	characteristic
33	C₂×#11924027	C₂²	1	1	yes	characteristic
34	C₂×#11924027	C₂²	1	2	yes	complemented
35	C₂×#11924027	C₂²	1	2	yes	complemented
36	C₂×#11924027	C₂²	1	1	yes	characteristic, complemented
37	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
38	C₂²×Dic₁₄₆	C₂²	1	2	yes	complemented
39	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
40	C₂×Q₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×Q₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₂²⋊D₇₃	C₂²	1	2	yes	—
43	C₂³×Dic₇₃	C₂²	1	2	yes	—
44	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
45	#14556591	C₂²	1	1	yes	characteristic, complemented
46	#14556590	C₂²	1	2	yes	complemented
47	#14556590	C₂²	1	2	yes	complemented
48	#14556589	C₂²	1	1	yes	characteristic, complemented
49	#14556578	C₂²	1	1	yes	characteristic, complemented
50	#14556577	C₂²	1	2	yes	complemented
51	#14556577	C₂²	1	2	yes	complemented
52	#14556576	C₂²	1	1	yes	characteristic, complemented
53	#14556575	C₂²	1	2	yes	complemented
54	#14556575	C₂²	1	2	yes	complemented
55	#14556574	C₂²	1	2	yes	complemented
56	#14556573	C₂²	1	2	yes	complemented
57	#14556573	C₂²	1	2	yes	complemented
58	#14556573	C₂²	1	1	yes	characteristic, complemented
59	#14556572	C₂²	1	2	yes	complemented
60	#14556572	C₂²	1	2	yes	complemented
61	#14556571	C₂²	1	1	yes	characteristic, complemented
62	#14556571	C₂²	1	1	yes	characteristic, complemented
63	#14556570	C₂²	1	1	yes	characteristic
64	#14556570	C₂²	1	1	yes	characteristic, complemented
65	#14556569	C₂²	1	1	yes	characteristic, complemented
66	#14556569	C₂²	1	2	yes	complemented
67	#14556569	C₂²	1	2	yes	complemented
68	#14556568	C₂²	1	2	yes	—
69	#14556568	C₂²	1	2	yes	—
70	#14556568	C₂²	1	2	yes	—
71	#14556568	C₂²	1	1	yes	characteristic
72	#14556568	C₂²	1	2	yes	complemented
73	#14556568	C₂²	1	2	yes	complemented
74	#14556568	C₂²	1	2	yes	complemented
75	#14556568	C₂²	1	2	yes	complemented
76	#14556568	C₂²	1	2	yes	complemented
77	#14556568	C₂²	1	2	yes	complemented
78	#14556567	C₂²	1	1	yes	characteristic, complemented
79	#14556565	C₂²	1	2	yes	complemented
80	#14556564	C₂²	1	1	yes	characteristic, complemented
81	#14556564	C₂²	1	2	yes	complemented
82	#14556564	C₂²	1	2	yes	complemented
83	#14556563	C₂²	1	1	yes	characteristic
84	#14556563	C₂²	1	2	yes	complemented
85	#14556563	C₂²	1	2	yes	complemented
86	#14556563	C₂²	1	2	yes	complemented
87	#14556563	C₂²	1	2	yes	complemented
88	#14556562	C₂²	1	2	yes	complemented
89	#14556562	C₂²	1	1	yes	characteristic, complemented
90	#14556561	C₂²	1	1	yes	characteristic
91	#14556560	C₂²	1	2	yes	—
92	#14556559	C₂²	1	1	yes	characteristic
93	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
94	#14556556	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₇₃	C₂²	1	2	yes	—
97	D₄×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
98	D₄×Dic₇₃	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
102	#14556551	C₂²	1	2	yes	—
103	#14556551	C₂²	1	2	yes	complemented
104	#14556551	C₂²	1	2	yes	complemented
105	#14556548	C₂²	1	1	yes	characteristic, complemented
106	#14556547	C₂²	1	2	yes	complemented
107	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	complemented
108	C₂×#11924007	C₂²	1	2	yes	complemented
109	C₂×#11924007	C₂²	1	2	yes	complemented
110	C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic, complemented
111	C₄⋊C₄×D₇₃	C₂²	1	2	yes	complemented
112	C₂×C₂²⋊Dic₇₃	C₂²	1	2	yes	—
113	C₂²⋊C₄×D₇₃	C₂²	1	2	yes	—
114	C₂×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
115	C₂²×D₄×C₇₃	C₂²	1	1	yes	characteristic
116	#124×C₇₃	C₂²	1	1	yes	characteristic, complemented
117	#123×C₇₃	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
119	#121×C₇₃	C₂²	1	2	yes	complemented
120	#121×C₇₃	C₂²	1	1	yes	characteristic, complemented
121	#120×C₇₃	C₂²	1	2	yes	—
122	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
123	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
125	C₂³×D₇₃	C₂³	1	1	yes	characteristic
126	#11924028	—	2	8	no	—
127	#11924028	—	2	4	no	—
128	#11924027	—	2	4	no	—
129	#11924027	—	2	4	no	—
130	#11924027	—	2	8	no	—
131	#11924027	—	2	8	no	—
132	#11924027	—	2	8	no	—
133	#11924027	—	2	8	no	—
134	#11924027	—	2	4	no	—
135	#11924027	—	2	4	no	—
136	#11924027	D₄	1	8	yes	complemented
137	C₂×Dic₁₄₆	—	2	8	no	—
138	C₂×Dic₁₄₆	—	2	4	no	—
139	C₂×Dic₁₄₆	—	2	4	no	—
140	C₂×Dic₁₄₆	C₂³	1	2	yes	—
141	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
142	C₂×Dic₁₄₆	C₂³	1	2	yes	—
143	C₂×Dic₁₄₆	C₂³	1	2	yes	—
144	C₂×Dic₁₄₆	C₂³	1	2	yes	—
145	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
146	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
147	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
148	Q₈×D₇₃	—	2	4	no	—
149	Q₈×D₇₃	—	2	4	no	—
150	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
151	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₇₃	—	2	8	no	—
153	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
163	C₂²×Dic₇₃	—	2	8	no	—
164	C₂²×Dic₇₃	C₂³	1	2	yes	—
165	C₂²×Dic₇₃	C₂³	1	2	yes	—
166	C₂²×Dic₇₃	C₂³	1	2	yes	—
167	C₂²×Dic₇₃	C₂³	1	2	yes	—
168	C₂²×Dic₇₃	C₂³	1	2	yes	—
169	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
170	C₂²×Dic₇₃	C₂³	1	2	yes	—
171	C₂²×Dic₇₃	C₂³	1	2	yes	—
172	C₂²×Dic₇₃	C₂³	1	2	yes	—
173	C₂×C₄×D₇₃	—	2	4	no	—
174	C₂×C₄×D₇₃	C₂³	1	2	yes	—
175	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₄×D₇₃	C₂³	1	2	yes	—
177	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
179	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₇₃	C₂³	1	2	yes	—
181	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₇₃	C₂³	1	2	yes	—
183	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
184	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₇₃	C₂³	1	2	yes	—
186	C₄⋊Dic₇₃	C₂³	1	2	yes	—
187	C₄⋊Dic₇₃	C₂³	1	2	yes	—
188	#11924007	C₂³	1	2	yes	—
189	#11924007	C₂³	1	2	yes	—
190	#11924007	C₂³	1	2	yes	—
191	#11924007	C₂³	1	1	yes	characteristic
192	#11924007	C₂³	1	1	yes	characteristic
193	#11924007	C₂³	1	2	yes	—
194	#11924007	C₂³	1	2	yes	—
195	#11924007	C₂³	1	2	yes	—
196	#11924007	C₂³	1	2	yes	—
197	#11924007	C₂³	1	1	yes	characteristic
198	#11924007	C₂³	1	2	yes	—
199	#11924007	C₂³	1	1	yes	characteristic
200	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
201	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
202	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
203	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
204	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
205	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
206	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
207	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
208	#11924005	C₂³	1	2	yes	—
209	#11924005	C₂³	1	2	yes	—
210	#11924005	C₂³	1	1	yes	characteristic
211	#11924005	C₂³	1	1	yes	characteristic
212	#11924005	C₂³	1	2	yes	—
213	#11924005	C₂³	1	1	yes	characteristic
214	#11924005	C₂³	1	1	yes	characteristic
215	#11924005	C₂³	1	1	yes	characteristic
216	#11924005	C₂³	1	1	yes	characteristic
217	C₄×Dic₇₃	C₂³	1	2	yes	—
218	C₄×Dic₇₃	C₂³	1	2	yes	—
219	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
220	C₂⁴×C₇₃	C₂³	1	2	yes	—
221	#41×C₇₃	—	2	4	no	—
222	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
223	C₂×D₄×C₇₃	—	2	4	no	—
224	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
225	C₂×D₄×C₇₃	C₂³	1	2	yes	—
226	C₂×D₄×C₇₃	C₂³	1	2	yes	—
227	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
228	C₂×D₄×C₇₃	C₂³	1	2	yes	—
229	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
230	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
231	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
232	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
233	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
234	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
235	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
237	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
238	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
239	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
240	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
241	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
242	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
243	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
244	C₄²×C₇₃	C₂³	1	1	yes	characteristic
245	C₂³×C₇₃	—	2	4	no	—
246	C₂³×C₇₃	—	2	4	no	—
247	C₂³×C₇₃	—	4	2	no	—
248	C₂³×C₇₃	C₂⁴	1	2	yes	—
249	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
250	C₂³×C₇₃	C₂⁴	1	2	yes	—
251	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
252	C₂²×D₇₃	—	2	2	no	—
253	C₂²×D₇₃	—	2	2	no	—
254	C₂²×D₇₃	—	4	1	no	—
255	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
256	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
257	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
258	Q₈×C₇₃	—	2	2	no	—
259	D₄×C₇₃	—	2	4	no	—
260	D₄×C₇₃	—	2	4	no	—
261	D₄×C₇₃	—	2	2	no	—
262	D₄×C₇₃	—	2	2	no	—
263	D₄×C₇₃	—	4	2	no	—
264	D₄×C₇₃	C₂×D₄	1	4	yes	—
265	C₂×C₄×C₇₃	—	2	4	no	—
266	C₂×C₄×C₇₃	—	2	2	no	—
267	C₂×C₄×C₇₃	—	2	2	no	—
268	C₂×C₄×C₇₃	—	4	2	no	—
269	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
272	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
274	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
276	C₂²⋊D₇₃	—	2	4	no	—
277	C₂²⋊D₇₃	—	2	4	no	—
278	C₂²⋊D₇₃	—	2	2	no	—
279	C₂²⋊D₇₃	—	2	4	no	—
280	C₂²⋊D₇₃	—	2	2	no	—
281	C₂²⋊D₇₃	—	2	4	no	—
282	C₂²⋊D₇₃	—	2	2	no	—
283	C₂²⋊D₇₃	—	4	2	no	—
284	C₂²⋊D₇₃	—	4	1	no	—
285	C₂²⋊D₇₃	C₂×D₄	1	8	yes	—
286	C₂×Dic₇₃	—	2	4	no	—
287	C₂×Dic₇₃	—	2	4	no	—
288	C₂×Dic₇₃	—	2	2	no	—
289	C₂×Dic₇₃	—	2	4	no	—
290	C₂×Dic₇₃	—	2	4	no	—
291	C₂×Dic₇₃	—	2	4	no	—
292	C₂×Dic₇₃	—	2	4	no	—
293	C₂×Dic₇₃	—	4	2	no	—
294	C₂×Dic₇₃	C₂×D₄	1	8	yes	—
295	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
297	C₂×Dic₇₃	C₂⁴	1	2	yes	—
298	C₂×Dic₇₃	C₂⁴	1	2	yes	—
299	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
301	C₂×Dic₇₃	C₂⁴	1	2	yes	—
302	C₂×Dic₇₃	C₂⁴	1	2	yes	—
303	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
304	D₂₉₂	—	2	2	no	—
305	D₂₉₂	—	4	1	no	—
306	C₄×D₇₃	—	2	2	no	—
307	C₄×D₇₃	—	2	4	no	—
308	C₄×D₇₃	—	2	2	no	—
309	C₄×D₇₃	—	2	2	no	—
310	C₄×D₇₃	—	2	2	no	—
311	C₄×D₇₃	—	2	4	no	—
312	C₄×D₇₃	—	4	2	no	—
313	C₄×D₇₃	C₂×D₄	1	4	yes	—
314	Dic₁₄₆	—	2	2	no	—
315	Dic₁₄₆	—	2	2	no	—
316	Dic₁₄₆	—	2	4	no	—
317	Dic₁₄₆	—	2	4	no	—
318	Dic₁₄₆	—	2	4	no	—
319	Dic₁₄₆	—	2	2	no	—
320	Dic₁₄₆	—	2	4	no	—
321	Dic₁₄₆	C₂×D₄	1	4	yes	—
322	C₂²×C₇₃	—	2	1	no	—
323	C₂²×C₇₃	—	2	2	no	—
324	C₂²×C₇₃	—	2	2	no	—
325	C₂²×C₇₃	—	2	1	no	—
326	C₂²×C₇₃	—	2	1	no	—
327	C₂²×C₇₃	—	2	2	no	—
328	C₂²×C₇₃	—	2	1	no	—
329	C₂²×C₇₃	—	2	2	no	—
330	C₂²×C₇₃	—	2	1	no	—
331	C₂²×C₇₃	—	2	2	no	—
332	C₂²×C₇₃	—	4	8	no	—
333	C₂²×C₇₃	C₂²×D₄	1	4	yes	—
334	C₂²×C₇₃	2₋¹⁺⁴	1	2	yes	complemented
335	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
336	C₂×D₇₃	—	2	1	no	—
337	C₂×D₇₃	—	2	1	no	—
338	C₂×D₇₃	—	2	1	no	—
339	C₂×D₇₃	—	2	1	no	—
340	C₂×D₇₃	—	2	1	no	—
341	C₂×D₇₃	—	2	1	no	—
342	C₂×D₇₃	—	2	1	no	—
343	C₂×D₇₃	—	2	1	no	—
344	C₂×D₇₃	—	4	4	no	—
345	C₂×D₇₃	C₂²×D₄	1	2	yes	—
346	C₄×C₇₃	—	2	1	no	—
347	C₄×C₇₃	—	2	1	no	—
348	C₄×C₇₃	—	2	2	no	—
349	C₄×C₇₃	—	2	1	no	—
350	C₄×C₇₃	—	2	2	no	—
351	C₄×C₇₃	—	2	1	no	—
352	C₄×C₇₃	C₂²×D₄	1	2	yes	—
353	Dic₇₃	—	2	2	no	—
354	Dic₇₃	—	2	1	no	—
355	Dic₇₃	—	2	2	no	—
356	Dic₇₃	—	2	1	no	—
357	Dic₇₃	—	2	1	no	—
358	Dic₇₃	—	2	2	no	—
359	Dic₇₃	—	2	1	no	—
360	Dic₇₃	C₂²×D₄	1	4	yes	—
361	Dic₇₃	C₂²×D₄	1	2	yes	—
362	C₂×C₇₃	—	2	2	no	—
363	C₂×C₇₃	—	2	4	no	—
364	C₂×C₇₃	—	4	1	no	—
365	C₂×C₇₃	—	4	2	no	—
366	C₂×C₇₃	C₂³×D₄	1	1	yes	characteristic
367	C₂×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
368	C₂×C₇₃	#585	1	1	yes	characteristic
369	D₇₃	—	2	2	no	—
370	D₇₃	—	4	1	no	—
371	D₇₃	—	4	1	no	—
372	#3489	—	73	1	no	maximal, Sylow
373	C₇₃	#3489	1	1	yes	characteristic, complemented, Sylow
374	C₂×2₋¹⁺⁴	—	73	1	no	—
375	C₂²×#41	—	73	1	no	—
376	D₄×Q₈	—	73	1	no	—
377	D₄×Q₈	—	73	1	no	—
378	#548	—	73	1	no	—
379	#548	—	73	1	no	—
380	#547	—	73	1	no	—
381	#547	—	73	2	no	—
382	#547	—	73	2	no	—
383	#547	—	73	1	no	—
384	#546	—	73	1	no	—
385	#546	—	73	2	no	—
386	#546	—	73	2	no	—
387	#546	D₇₃	1	1	yes	characteristic, complemented
388	#537	—	73	2	no	—
389	#537	—	73	1	no	—
390	#536	—	73	1	no	—
391	#536	—	73	2	no	—
392	#525	—	73	2	no	—
393	#525	—	73	1	no	—
394	C₂×C₂²⋊Q₈	—	73	1	no	—
395	C₂×C₂²⋊Q₈	—	73	2	no	—
396	#520	—	73	1	no	—
397	2₋¹⁺⁴	—	146	8	no	—
398	C₂×#41	—	73	1	no	—
399	C₂×#41	—	73	2	no	—
400	C₂×#41	—	73	2	no	—
401	C₂×#41	—	73	1	no	—
402	C₂×#41	—	73	1	no	—
403	C₂×#41	—	73	2	no	—
404	C₂×#41	—	73	1	no	—
405	C₂×#41	—	73	2	no	—
406	C₂×#41	—	73	1	no	—
407	C₂×#41	—	73	1	no	—
408	C₂×#41	—	73	2	no	—
409	C₂×#41	—	146	8	no	—
410	C₂×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
411	C₂²×Q₈	—	73	1	no	—
412	C₂²×Q₈	—	73	1	no	—
413	C₂²×Q₈	—	73	2	no	—
414	C₂²×Q₈	—	73	1	no	—
415	C₂²×Q₈	—	73	1	no	—
416	C₂²×D₄	—	73	2	no	—
417	C₂²×D₄	C₂×D₇₃	1	1	yes	characteristic
418	C₂³×C₄	—	73	2	no	—
419	C₂³×C₄	—	73	1	no	—
420	C₄⋊Q₈	—	73	1	no	—
421	C₄⋊Q₈	—	73	2	no	—
422	C₄⋊Q₈	—	73	2	no	—
423	C₄⋊Q₈	—	73	1	no	—
424	#124	—	73	1	no	—
425	#124	—	73	2	no	—
426	#124	—	73	2	no	—
427	#124	C₂×D₇₃	1	1	yes	characteristic, complemented
428	#123	—	73	2	no	—
429	#123	—	73	2	no	—
430	#123	—	73	2	no	—
431	#123	—	73	1	no	—
432	#123	—	73	1	no	—
433	#123	—	73	2	no	—
434	#123	—	73	2	no	—
435	#123	—	73	2	no	—
436	#123	—	73	2	no	—
437	#123	C₂×D₇₃	1	2	yes	complemented
438	C₂²⋊Q₈	—	73	1	no	—
439	C₂²⋊Q₈	—	73	1	no	—
440	C₂²⋊Q₈	—	73	1	no	—
441	C₂²⋊Q₈	—	73	2	no	—
442	C₂²⋊Q₈	—	73	1	no	—
443	C₂²⋊Q₈	—	73	1	no	—
444	C₂²⋊Q₈	—	73	2	no	—
445	C₂²⋊Q₈	—	73	1	no	—
446	C₂²⋊Q₈	—	73	2	no	—
447	C₂²⋊Q₈	—	73	1	no	—
448	C₂²⋊Q₈	—	73	2	no	—
449	C₂²⋊Q₈	—	73	2	no	—
450	C₂²⋊Q₈	—	73	2	no	—
451	C₂²⋊Q₈	—	73	2	no	—
452	C₂²⋊Q₈	—	73	2	no	—
453	C₂²⋊Q₈	—	73	2	no	—
454	C₂²⋊Q₈	—	73	2	no	—
455	C₂²⋊Q₈	—	73	2	no	—
456	C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
457	#121	—	73	1	no	—
458	#121	—	73	2	no	—
459	#121	—	73	2	no	—
460	#121	—	73	2	no	—
461	#121	—	73	2	no	—
462	#121	—	73	1	no	—
463	#121	—	73	2	no	—
464	#121	—	73	2	no	—
465	#121	—	73	1	no	—
466	#121	—	73	2	no	—
467	#121	—	73	2	no	—
468	#121	C₂×D₇₃	1	2	yes	complemented
469	#121	C₂×D₇₃	1	1	yes	characteristic, complemented
470	#120	—	73	2	no	—
471	#120	—	73	1	no	—
472	#120	—	73	1	no	—
473	#120	C₂×D₇₃	1	2	yes	—
474	C₄×Q₈	—	73	1	no	—
475	C₄×Q₈	—	73	1	no	—
476	C₄×D₄	—	73	1	no	—
477	C₄×D₄	—	73	2	no	—
478	C₄×D₄	—	73	2	no	—
479	C₄×D₄	—	73	2	no	—
480	C₄×D₄	—	73	1	no	—
481	C₄×D₄	—	73	1	no	—
482	C₄×D₄	—	73	2	no	—
483	C₄×D₄	—	73	2	no	—
484	C₄×D₄	—	73	2	no	—
485	C₄×D₄	—	73	1	no	—
486	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
487	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
488	#117	—	73	2	no	—
489	#117	—	73	1	no	—
490	C₂×C₄⋊C₄	—	73	2	no	—
491	C₂×C₄⋊C₄	—	73	2	no	—
492	C₂×C₄⋊C₄	—	73	2	no	—
493	C₂×C₄⋊C₄	—	73	1	no	—
494	C₂×C₄⋊C₄	—	73	2	no	—
495	C₂×C₂²⋊C₄	—	73	2	no	—
496	C₂×C₂²⋊C₄	—	73	2	no	—
497	C₂×C₂²⋊C₄	C₂×D₇₃	1	2	yes	—
498	C₂⁴	—	73	1	no	—
499	C₂⁴	C₂²×D₇₃	1	2	yes	—
500	#41	—	2	4	no	—
501	#41	—	73	8	no	—
502	#41	—	146	4	no	—
503	#41	—	146	8	no	—
504	#41	—	146	8	no	—
505	#41	—	146	4	no	—
506	#41	—	146	8	no	—
507	#41	—	146	8	no	—
508	#41	—	146	8	no	—
509	#41	—	146	4	no	—
510	#41	—	146	4	no	—
511	#41	—	146	4	no	—
512	C₂×Q₈	—	73	1	no	—
513	C₂×Q₈	—	73	2	no	—
514	C₂×Q₈	—	73	1	no	—
515	C₂×Q₈	—	73	2	no	—
516	C₂×Q₈	—	73	2	no	—
517	C₂×Q₈	—	73	1	no	—
518	C₂×Q₈	—	73	2	no	—
519	C₂×Q₈	—	73	1	no	—
520	C₂×Q₈	—	146	8	no	—
521	C₂×Q₈	—	146	4	no	—
522	C₂×Q₈	—	146	4	no	—
523	C₂×Q₈	—	146	4	no	—
524	C₂×Q₈	—	146	4	no	—
525	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	73	1	no	—
528	C₂×D₄	—	73	2	no	—
529	C₂×D₄	—	73	2	no	—
530	C₂×D₄	—	73	1	no	—
531	C₂×D₄	—	73	1	no	—
532	C₂×D₄	—	73	2	no	—
533	C₂×D₄	—	73	1	no	—
534	C₂×D₄	—	73	2	no	—
535	C₂×D₄	—	73	2	no	—
536	C₂×D₄	—	73	2	no	—
537	C₂×D₄	—	73	1	no	—
538	C₂×D₄	—	73	1	no	—
539	C₂×D₄	—	146	8	no	—
540	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
541	C₂×D₄	C₂²×D₇₃	1	2	yes	—
542	C₂×D₄	C₂²×D₇₃	1	2	yes	—
543	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
544	C₂×D₄	C₂²×D₇₃	1	2	yes	—
545	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
546	C₂²×C₄	—	73	2	no	—
547	C₂²×C₄	—	73	2	no	—
548	C₂²×C₄	—	73	2	no	—
549	C₂²×C₄	—	73	1	no	—
550	C₂²×C₄	—	73	2	no	—
551	C₂²×C₄	—	73	2	no	—
552	C₂²×C₄	—	73	2	no	—
553	C₂²×C₄	—	73	2	no	—
554	C₂²×C₄	—	73	2	no	—
555	C₂²×C₄	—	73	1	no	—
556	C₂²×C₄	—	73	2	no	—
557	C₂²×C₄	—	73	2	no	—
558	C₂²×C₄	—	73	1	no	—
559	C₂²×C₄	—	73	2	no	—
560	C₂²×C₄	—	73	1	no	—
561	C₂²×C₄	—	73	1	no	—
562	C₂²×C₄	—	73	1	no	—
563	C₂²×C₄	—	146	4	no	—
564	C₂²×C₄	—	146	8	no	—
565	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
566	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
567	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
568	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
569	C₄⋊C₄	—	73	2	no	—
570	C₄⋊C₄	—	73	1	no	—
571	C₄⋊C₄	—	73	2	no	—
572	C₄⋊C₄	—	73	1	no	—
573	C₄⋊C₄	—	73	2	no	—
574	C₄⋊C₄	—	73	2	no	—
575	C₄⋊C₄	—	73	2	no	—
576	C₄⋊C₄	—	73	2	no	—
577	C₄⋊C₄	—	73	2	no	—
578	C₄⋊C₄	—	73	1	no	—
579	C₄⋊C₄	—	73	1	no	—
580	C₄⋊C₄	—	73	2	no	—
581	C₄⋊C₄	—	73	2	no	—
582	C₄⋊C₄	—	73	1	no	—
583	C₄⋊C₄	—	73	1	no	—
584	C₄⋊C₄	—	73	2	no	—
585	C₄⋊C₄	—	73	2	no	—
586	C₄⋊C₄	—	73	2	no	—
587	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
588	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
589	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
590	C₂²⋊C₄	—	73	2	no	—
591	C₂²⋊C₄	—	73	1	no	—
592	C₂²⋊C₄	—	73	2	no	—
593	C₂²⋊C₄	—	73	2	no	—
594	C₂²⋊C₄	—	73	2	no	—
595	C₂²⋊C₄	—	73	1	no	—
596	C₂²⋊C₄	—	73	2	no	—
597	C₂²⋊C₄	—	73	2	no	—
598	C₂²⋊C₄	—	73	2	no	—
599	C₂²⋊C₄	—	73	2	no	—
600	C₂²⋊C₄	—	73	1	no	—
601	C₂²⋊C₄	—	73	1	no	—
602	C₂²⋊C₄	—	73	1	no	—
603	C₂²⋊C₄	—	73	1	no	—
604	C₂²⋊C₄	—	73	1	no	—
605	C₂²⋊C₄	—	73	1	no	—
606	C₂²⋊C₄	—	73	2	no	—
607	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
608	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
609	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
610	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
611	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
612	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
613	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
614	C₄²	—	73	2	no	—
615	C₄²	—	73	2	no	—
616	C₄²	—	73	1	no	—
617	C₄²	C₂²×D₇₃	1	1	yes	characteristic
618	C₂³	—	2	4	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	4	2	no	—
621	C₂³	—	292	1	no	—
622	C₂³	—	73	1	no	—
623	C₂³	—	73	1	no	—
624	C₂³	—	73	1	no	—
625	C₂³	—	146	2	no	—
626	C₂³	—	146	2	no	—
627	C₂³	C₂³×D₇₃	1	2	yes	—
628	C₂³	C₂³×D₇₃	1	1	yes	characteristic
629	C₂³	C₂³×D₇₃	1	2	yes	—
630	C₂³	C₂³×D₇₃	1	1	yes	characteristic
631	Q₈	—	2	2	no	—
632	Q₈	—	73	4	no	—
633	Q₈	—	146	2	no	—
634	Q₈	—	146	4	no	—
635	Q₈	—	146	4	no	—
636	Q₈	—	146	4	no	—
637	Q₈	—	146	4	no	—
638	Q₈	—	146	2	no	—
639	Q₈	—	146	2	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	4	no	—
642	D₄	—	2	2	no	—
643	D₄	—	2	2	no	—
644	D₄	—	4	2	no	—
645	D₄	—	292	1	no	—
646	D₄	—	292	1	no	—
647	D₄	—	292	2	no	—
648	D₄	—	73	8	no	—
649	D₄	—	146	2	no	—
650	D₄	—	146	4	no	—
651	D₄	—	146	2	no	—
652	D₄	—	146	4	no	—
653	D₄	—	146	2	no	—
654	D₄	—	146	4	no	—
655	D₄	—	146	4	no	—
656	D₄	—	146	2	no	—
657	D₄	D₄×D₇₃	1	4	yes	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	292	2	no	—
663	C₂×C₄	—	292	2	no	—
664	C₂×C₄	—	73	8	no	—
665	C₂×C₄	—	73	2	no	—
666	C₂×C₄	—	73	1	no	—
667	C₂×C₄	—	73	4	no	—
668	C₂×C₄	—	73	1	no	—
669	C₂×C₄	—	73	1	no	—
670	C₂×C₄	—	73	2	no	—
671	C₂×C₄	—	73	1	no	—
672	C₂×C₄	—	73	2	no	—
673	C₂×C₄	—	73	1	no	—
674	C₂×C₄	—	73	2	no	—
675	C₂×C₄	—	146	2	no	—
676	C₂×C₄	—	146	4	no	—
677	C₂×C₄	—	146	2	no	—
678	C₂×C₄	—	146	4	no	—
679	C₂×C₄	—	146	2	no	—
680	C₂×C₄	—	146	4	no	—
681	C₂×C₄	—	146	4	no	—
682	C₂×C₄	—	146	4	no	—
683	C₂×C₄	—	146	4	no	—
684	C₂×C₄	—	146	4	no	—
685	C₂×C₄	—	146	4	no	—
686	C₂×C₄	—	146	2	no	—
687	C₂×C₄	—	146	2	no	—
688	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
689	C₂×C₄	C₂³×D₇₃	1	2	yes	—
690	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
691	C₂×C₄	C₂³×D₇₃	1	2	yes	—
692	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
693	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
694	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
695	C₂²	—	2	1	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	4	8	no	—
706	C₂²	—	292	4	no	—
707	C₂²	—	73	2	no	—
708	C₂²	—	146	1	no	—
709	C₂²	—	146	1	no	—
710	C₂²	—	146	1	no	—
711	C₂²	—	146	1	no	—
712	C₂²	—	146	1	no	—
713	C₂²	—	146	1	no	—
714	C₂²	—	146	1	no	—
715	C₂²	—	146	1	no	—
716	C₂²	C₂×D₄×D₇₃	1	4	yes	—
717	C₂²	#14556638	1	2	yes	complemented
718	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	2	no	—
725	C₄	—	73	2	no	—
726	C₄	—	73	4	no	—
727	C₄	—	146	1	no	—
728	C₄	—	146	2	no	—
729	C₄	—	146	2	no	—
730	C₄	—	146	1	no	—
731	C₄	—	146	1	no	—
732	C₄	—	146	2	no	—
733	C₄	—	146	1	no	—
734	C₄	C₂×D₄×D₇₃	1	2	yes	—
735	C₂	—	2	2	no	—
736	C₂	—	2	4	no	—
737	C₂	—	4	2	no	—
738	C₂	—	4	1	no	—
739	C₂	—	292	1	no	—
740	C₂	—	292	1	no	—
741	C₂	—	146	2	no	—
742	C₂	C₂²×D₄×D₇₃	1	1	yes	characteristic
743	C₂	C₂×#14556638	1	1	yes	characteristic
744	C₂	#17989422	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#546×C₇₃	C₂
hypercenter	#546	D₇₃
hypocenter	C₇₃	#3489
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂×#14556638	C₂	semidirect
2. C₂²×#11924027	C₂	semidirect
3. D₄×Dic₁₄₆	C₂	semidirect
4. #17989250	C₂	semidirect
5. #17989245	C₂	semidirect
6. #17989243	C₂	semidirect
7. #17989241	C₂	semidirect
8. #17989237	C₂	semidirect
9. #17989236	C₂	semidirect
10. #17989235	C₂	semidirect
11. #17989231	C₂	semidirect
12. #17989227	C₂	semidirect
13. #17989224	C₂	semidirect
14. #17989166	C₂	semidirect
15. #17989164	C₂	semidirect
16. #17989159	C₂	semidirect
17. #17989157	C₂	semidirect
18. #17989096	C₂	semidirect
19. #17989093	C₂	semidirect
20. C₂×#14556568	C₂	semidirect
21. C₂²⋊Q₈×D₇₃	C₂	semidirect
22. #17989066	C₂	semidirect
23. #546×C₇₃	C₂	semidirect
25. C₂×#11924028	C₂²	semidirect
26. C₂×#11924028	C₂²	semidirect
34. C₂×#11924027	C₂²	semidirect
35. C₂×#11924027	C₂²	semidirect
36. C₂×#11924027	C₂²	semidirect
38. C₂²×Dic₁₄₆	C₂²	semidirect
39. C₂²×Dic₁₄₆	C₂²	semidirect
40. C₂×Q₈×D₇₃	C₂²	semidirect
41. C₂×Q₈×D₇₃	C₂²	semidirect
45. #14556591	C₂²	semidirect
46. #14556590	C₂²	semidirect
47. #14556590	C₂²	semidirect
48. #14556589	C₂²	semidirect
49. #14556578	C₂²	semidirect
50. #14556577	C₂²	semidirect
51. #14556577	C₂²	semidirect
52. #14556576	C₂²	semidirect
53. #14556575	C₂²	semidirect
54. #14556575	C₂²	semidirect
55. #14556574	C₂²	semidirect
56. #14556573	C₂²	semidirect
57. #14556573	C₂²	semidirect
58. #14556573	C₂²	semidirect
59. #14556572	C₂²	semidirect
60. #14556572	C₂²	semidirect
61. #14556571	C₂²	semidirect
62. #14556571	C₂²	semidirect
64. #14556570	C₂²	semidirect
65. #14556569	C₂²	semidirect
66. #14556569	C₂²	semidirect
67. #14556569	C₂²	semidirect
72. #14556568	C₂²	semidirect
73. #14556568	C₂²	semidirect
74. #14556568	C₂²	semidirect
75. #14556568	C₂²	semidirect
76. #14556568	C₂²	semidirect
77. #14556568	C₂²	semidirect
78. #14556567	C₂²	semidirect
79. #14556565	C₂²	semidirect
80. #14556564	C₂²	semidirect
81. #14556564	C₂²	semidirect
82. #14556564	C₂²	semidirect
84. #14556563	C₂²	semidirect
85. #14556563	C₂²	semidirect
86. #14556563	C₂²	semidirect
87. #14556563	C₂²	semidirect
88. #14556562	C₂²	semidirect
89. #14556562	C₂²	semidirect
93. C₄×Dic₁₄₆	C₂²	semidirect
94. #14556556	C₂²	semidirect
95. C₄×D₂₉₂	C₂²	semidirect
97. D₄×Dic₇₃	C₂²	semidirect
98. D₄×Dic₇₃	C₂²	semidirect
100. C₄×C₂²⋊D₇₃	C₂²	semidirect
101. C₄×C₂²⋊D₇₃	C₂²	semidirect
103. #14556551	C₂²	semidirect
104. #14556551	C₂²	semidirect
105. #14556548	C₂²	semidirect
106. #14556547	C₂²	semidirect
107. C₂×C₄⋊Dic₇₃	C₂²	semidirect
108. C₂×#11924007	C₂²	semidirect
109. C₂×#11924007	C₂²	semidirect
110. C₄⋊C₄×D₇₃	C₂²	semidirect
111. C₄⋊C₄×D₇₃	C₂²	semidirect
114. C₂×#41×C₇₃	C₂²	semidirect
116. #124×C₇₃	C₂²	semidirect
117. #123×C₇₃	C₂²	semidirect
119. #121×C₇₃	C₂²	semidirect
120. #121×C₇₃	C₂²	semidirect
123. C₄×D₄×C₇₃	C₂²	semidirect
136. #11924027	D₄	semidirect
334. C₂²×C₇₃	2₋¹⁺⁴	semidirect
373. C₇₃	#3489	semidirect
387. #546	D₇₃	semidirect
410. C₂×#41	C₂×D₇₃	semidirect
427. #124	C₂×D₇₃	semidirect
437. #123	C₂×D₇₃	semidirect
468. #121	C₂×D₇₃	semidirect
469. #121	C₂×D₇₃	semidirect
487. C₄×D₄	C₂×D₇₃	semidirect
717. C₂²	#14556638	semidirect