Subgroups — #22623859

Order 9344.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989320	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989294	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989283	C₂	1	2	yes	maximal, complemented
4	#17989281	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989276	C₂	1	1	yes	maximal, characteristic, complemented
6	#17989266	C₂	1	2	yes	maximal, complemented
7	#17989263	C₂	1	2	yes	maximal, complemented
8	#17989242	C₂	1	1	yes	maximal, characteristic, complemented
9	#17989232	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989231	C₂	1	1	yes	maximal, characteristic, complemented
11	#17989227	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#17989208	C₂	1	1	yes	maximal, characteristic, complemented
14	#17989188	C₂	1	1	yes	maximal, characteristic, complemented
15	#17989179	C₂	1	2	yes	maximal, complemented
16	#17989175	C₂	1	2	yes	maximal, complemented
17	#17989119	C₂	1	1	yes	maximal, characteristic, complemented
18	#17989115	C₂	1	1	yes	maximal, characteristic, complemented
19	#17989096	C₂	1	2	yes	maximal, complemented
20	C₂×#14556573	C₂	1	2	yes	maximal, complemented
21	#17989066	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#518×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11924028	C₂²	1	2	yes	complemented
25	C₂×#11924027	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₇₃	C₂²	1	2	yes	—
27	C₂×D₄×D₇₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₇₃	C₂²	1	2	yes	complemented
29	#14556591	C₂²	1	1	yes	characteristic, complemented
30	#14556587	C₂²	1	1	yes	characteristic
31	#14556586	C₂²	1	2	yes	complemented
32	#14556586	C₂²	1	1	yes	characteristic, complemented
33	#14556585	C₂²	1	2	yes	complemented
34	#14556584	C₂²	1	2	yes	complemented
35	#14556584	C₂²	1	2	yes	complemented
36	#14556584	C₂²	1	1	yes	characteristic, complemented
37	#14556583	C₂²	1	2	yes	complemented
38	#14556582	C₂²	1	1	yes	characteristic, complemented
39	#14556582	C₂²	1	1	yes	characteristic, complemented
40	#14556581	C₂²	1	1	yes	characteristic, complemented
41	#14556579	C₂²	1	1	yes	characteristic, complemented
42	#14556578	C₂²	1	1	yes	characteristic, complemented
43	#14556577	C₂²	1	1	yes	characteristic, complemented
44	#14556577	C₂²	1	2	yes	complemented
45	#14556577	C₂²	1	2	yes	complemented
46	#14556576	C₂²	1	1	yes	characteristic, complemented
47	#14556575	C₂²	1	2	yes	complemented
48	#14556574	C₂²	1	2	yes	complemented
49	#14556574	C₂²	1	2	yes	complemented
50	#14556573	C₂²	1	2	yes	—
51	#14556573	C₂²	1	1	yes	characteristic
52	#14556573	C₂²	1	2	yes	complemented
53	#14556573	C₂²	1	2	yes	complemented
54	#14556573	C₂²	1	2	yes	complemented
55	#14556573	C₂²	1	2	yes	complemented
56	#14556573	C₂²	1	2	yes	complemented
57	#14556573	C₂²	1	2	yes	complemented
58	#14556573	C₂²	1	2	yes	complemented
59	#14556572	C₂²	1	2	yes	complemented
60	#14556571	C₂²	1	1	yes	characteristic, complemented
61	#14556570	C₂²	1	2	yes	complemented
62	#14556570	C₂²	1	2	yes	complemented
63	#14556570	C₂²	1	1	yes	characteristic, complemented
64	#14556569	C₂²	1	2	yes	complemented
65	#14556569	C₂²	1	1	yes	characteristic, complemented
66	#14556568	C₂²	1	2	yes	complemented
67	#14556568	C₂²	1	2	yes	complemented
68	#14556566	C₂²	1	1	yes	characteristic, complemented
69	#14556565	C₂²	1	1	yes	characteristic
70	#14556565	C₂²	1	2	yes	complemented
71	#14556565	C₂²	1	2	yes	complemented
72	#14556564	C₂²	1	1	yes	characteristic
73	#14556564	C₂²	1	2	yes	complemented
74	#14556564	C₂²	1	2	yes	complemented
75	#14556563	C₂²	1	2	yes	—
76	#14556563	C₂²	1	2	yes	complemented
77	#14556562	C₂²	1	1	yes	characteristic
78	#14556562	C₂²	1	1	yes	characteristic, complemented
79	#14556561	C₂²	1	2	yes	complemented
80	#14556560	C₂²	1	2	yes	—
81	#14556560	C₂²	1	2	yes	complemented
82	#14556559	C₂²	1	2	yes	—
83	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
84	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
85	#14556556	C₂²	1	1	yes	characteristic, complemented
86	C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
88	C₄×D₂₉₂	C₂²	1	2	yes	complemented
89	D₄×Dic₇₃	C₂²	1	1	yes	characteristic
90	D₄×Dic₇₃	C₂²	1	1	yes	characteristic
91	#14556553	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
97	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
98	#14556551	C₂²	1	2	yes	complemented
99	#14556551	C₂²	1	2	yes	complemented
100	#14556550	C₂²	1	2	yes	complemented
101	#14556548	C₂²	1	1	yes	characteristic, complemented
102	#14556548	C₂²	1	2	yes	complemented
103	#14556547	C₂²	1	2	yes	complemented
104	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	complemented
105	C₂×#11924007	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₂²⋊Dic₇₃	C₂²	1	2	yes	complemented
109	C₂×#11924005	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₇₃	C₂²	1	2	yes	complemented
111	C₄²×D₇₃	C₂²	1	1	yes	characteristic, complemented
112	C₂²×D₄×C₇₃	C₂²	1	1	yes	characteristic
113	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
114	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
115	C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
116	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
119	#117×C₇₃	C₂²	1	1	yes	characteristic, complemented
120	#117×C₇₃	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
123	C₂³×D₇₃	C₂³	1	2	yes	—
124	#11924028	—	4	4	no	—
125	#11924027	—	2	4	no	—
126	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₄₆	C₂³	1	2	yes	—
129	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
130	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
131	C₂×D₂₉₂	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₇₃	—	4	4	no	—
133	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
142	D₄×D₇₃	—	2	4	no	—
143	C₂²×Dic₇₃	C₂³	1	2	yes	—
144	C₂²×Dic₇₃	C₂³	1	2	yes	—
145	C₂²×Dic₇₃	C₂³	1	2	yes	—
146	C₂×C₄×D₇₃	—	4	4	no	—
147	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₇₃	C₂³	1	2	yes	—
150	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₇₃	C₂³	1	2	yes	—
153	C₂×C₄×D₇₃	C₂³	1	2	yes	—
154	C₂×C₄×D₇₃	C₂³	1	2	yes	—
155	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₇₃	C₂³	1	2	yes	—
159	C₄⋊Dic₇₃	C₂³	1	2	yes	—
160	C₄⋊Dic₇₃	C₂³	1	2	yes	—
161	C₄⋊Dic₇₃	C₂³	1	2	yes	—
162	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
163	#11924007	C₂³	1	2	yes	—
164	#11924007	C₂³	1	2	yes	—
165	#11924007	C₂³	1	1	yes	characteristic
166	#11924007	C₂³	1	2	yes	—
167	#11924007	C₂³	1	2	yes	—
168	#11924007	C₂³	1	1	yes	characteristic
169	#11924007	C₂³	1	2	yes	—
170	#11924007	C₂³	1	2	yes	—
171	#11924007	C₂³	1	1	yes	characteristic
172	#11924007	C₂³	1	1	yes	characteristic
173	#11924007	C₂³	1	2	yes	—
174	#11924007	C₂³	1	1	yes	characteristic
175	#11924007	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
185	#11924005	C₂³	1	2	yes	—
186	#11924005	C₂³	1	2	yes	—
187	#11924005	C₂³	1	1	yes	characteristic
188	#11924005	C₂³	1	2	yes	—
189	#11924005	C₂³	1	2	yes	—
190	#11924005	C₂³	1	2	yes	—
191	#11924005	C₂³	1	1	yes	characteristic
192	#11924005	C₂³	1	1	yes	characteristic
193	#11924005	C₂³	1	1	yes	characteristic
194	#11924005	C₂³	1	1	yes	characteristic
195	#11924005	C₂³	1	2	yes	—
196	#11924005	C₂³	1	2	yes	—
197	#11924005	C₂³	1	1	yes	characteristic
198	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₇₃	C₂³	1	2	yes	—
202	C₄×Dic₇₃	C₂³	1	2	yes	—
203	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
204	C₂⁴×C₇₃	C₂³	1	2	yes	—
205	C₂×D₄×C₇₃	—	2	4	no	—
206	C₂×D₄×C₇₃	C₂³	1	2	yes	—
207	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
211	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
212	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
213	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
214	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
225	C₄²×C₇₃	C₂³	1	1	yes	characteristic
226	C₄²×C₇₃	C₂³	1	1	yes	characteristic
227	C₄²×C₇₃	C₂³	1	2	yes	—
228	C₂³×C₇₃	—	2	4	no	—
229	C₂³×C₇₃	—	4	2	no	—
230	C₂³×C₇₃	—	4	2	no	—
231	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₇₃	C₂⁴	1	2	yes	—
233	C₂³×C₇₃	C₂⁴	1	2	yes	—
234	C₂²×D₇₃	—	2	4	no	—
235	C₂²×D₇₃	—	2	4	no	—
236	C₂²×D₇₃	—	4	2	no	—
237	C₂²×D₇₃	C₂⁴	1	2	yes	—
238	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
239	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
240	D₄×C₇₃	—	2	4	no	—
241	D₄×C₇₃	—	2	2	no	—
242	D₄×C₇₃	#41	1	4	yes	complemented
243	C₂×C₄×C₇₃	—	2	2	no	—
244	C₂×C₄×C₇₃	—	4	2	no	—
245	C₂×C₄×C₇₃	—	4	2	no	—
246	C₂×C₄×C₇₃	—	4	2	no	—
247	C₂×C₄×C₇₃	—	4	2	no	—
248	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₇₃	—	2	4	no	—
257	C₂²⋊D₇₃	—	2	4	no	—
258	C₂²⋊D₇₃	—	2	2	no	—
259	C₂²⋊D₇₃	—	2	4	no	—
260	C₂²⋊D₇₃	—	4	2	no	—
261	C₂²⋊D₇₃	—	4	2	no	—
262	C₂²⋊D₇₃	—	4	1	no	—
263	C₂²⋊D₇₃	—	4	2	no	—
264	C₂²⋊D₇₃	—	4	2	no	—
265	C₂×Dic₇₃	—	2	4	no	—
266	C₂×Dic₇₃	—	4	2	no	—
267	C₂×Dic₇₃	—	4	2	no	—
268	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₇₃	C₂⁴	1	2	yes	—
270	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₇₃	C₂⁴	1	2	yes	—
274	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₇₃	C₂⁴	1	2	yes	—
277	D₂₉₂	—	2	2	no	—
278	D₂₉₂	—	2	2	no	—
279	D₂₉₂	—	4	2	no	—
280	C₄×D₇₃	—	2	2	no	—
281	C₄×D₇₃	—	2	4	no	—
282	C₄×D₇₃	—	2	2	no	—
283	C₄×D₇₃	—	2	2	no	—
284	C₄×D₇₃	—	4	2	no	—
285	C₄×D₇₃	—	4	2	no	—
286	C₄×D₇₃	—	4	1	no	—
287	C₄×D₇₃	—	4	2	no	—
288	Dic₁₄₆	—	2	2	no	—
289	Dic₁₄₆	—	4	1	no	—
290	Dic₁₄₆	—	4	2	no	—
291	C₂²×C₇₃	—	2	2	no	—
292	C₂²×C₇₃	—	2	2	no	—
293	C₂²×C₇₃	—	2	1	no	—
294	C₂²×C₇₃	—	2	2	no	—
295	C₂²×C₇₃	—	2	2	no	—
296	C₂²×C₇₃	—	2	1	no	—
297	C₂²×C₇₃	—	2	2	no	—
298	C₂²×C₇₃	—	2	1	no	—
299	C₂²×C₇₃	—	8	4	no	—
300	C₂²×C₇₃	C₂×#41	1	4	yes	—
301	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
302	C₂×D₇₃	—	2	1	no	—
303	C₂×D₇₃	—	2	1	no	—
304	C₂×D₇₃	—	2	1	no	—
305	C₂×D₇₃	—	2	2	no	—
306	C₂×D₇₃	—	2	1	no	—
307	C₂×D₇₃	—	2	2	no	—
308	C₂×D₇₃	—	2	1	no	—
309	C₂×D₇₃	—	2	2	no	—
310	C₂×D₇₃	—	4	8	no	—
311	C₂×D₇₃	H(5,𝔽₂)	1	2	yes	—
312	C₄×C₇₃	—	2	1	no	—
313	C₄×C₇₃	—	2	1	no	—
314	C₄×C₇₃	—	2	1	no	—
315	C₄×C₇₃	—	2	2	no	—
316	C₄×C₇₃	—	2	1	no	—
317	C₄×C₇₃	—	2	1	no	—
318	C₄×C₇₃	—	2	2	no	—
319	C₄×C₇₃	C₂×#41	1	2	yes	—
320	Dic₇₃	—	2	2	no	—
321	Dic₇₃	—	2	1	no	—
322	Dic₇₃	—	2	1	no	—
323	Dic₇₃	—	2	2	no	—
324	Dic₇₃	—	2	2	no	—
325	Dic₇₃	—	2	1	no	—
326	Dic₇₃	—	2	1	no	—
327	Dic₇₃	—	2	1	no	—
328	Dic₇₃	—	2	1	no	—
329	C₂×C₇₃	—	2	4	no	—
330	C₂×C₇₃	—	4	2	no	—
331	C₂×C₇₃	—	4	1	no	—
332	C₂×C₇₃	C₂²×#41	1	1	yes	characteristic
333	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₇₃	#585	1	1	yes	characteristic
335	D₇₃	—	2	2	no	—
336	D₇₃	—	4	1	no	—
337	D₇₃	—	4	2	no	—
338	#3513	—	73	1	no	maximal, Sylow
339	C₇₃	#3513	1	1	yes	characteristic, complemented, Sylow
340	#559	—	73	1	no	—
341	#554	—	73	1	no	—
342	#553	—	73	2	no	—
343	#553	—	73	1	no	—
344	#552	—	73	1	no	—
345	#551	—	73	2	no	—
346	#551	—	73	2	no	—
347	#547	—	73	1	no	—
348	#546	—	73	1	no	—
349	#546	—	73	1	no	—
350	#546	—	73	2	no	—
351	D₄²	—	73	1	no	—
352	#542	—	73	1	no	—
353	#540	—	73	1	no	—
354	#539	—	73	2	no	—
355	#538	—	73	2	no	—
356	#529	—	73	1	no	—
357	#529	—	73	1	no	—
358	#525	—	73	2	no	—
359	C₂×#123	—	73	2	no	—
360	#520	—	73	1	no	—
361	#518	D₇₃	1	1	yes	characteristic, complemented
362	C₂×C₄×D₄	—	73	1	no	—
363	C₂×#41	—	73	1	no	—
364	C₂×#41	—	73	2	no	—
365	C₂²×D₄	—	73	2	no	—
366	C₂²×D₄	—	73	1	no	—
367	C₂²×D₄	C₂×D₇₃	1	1	yes	characteristic
368	C₂³×C₄	—	73	2	no	—
369	C₄⋊Q₈	—	73	1	no	—
370	#127	—	73	1	no	—
371	#126	—	73	1	no	—
372	#126	—	73	2	no	—
373	#126	—	73	2	no	—
374	#126	—	73	1	no	—
375	#126	—	73	2	no	—
376	#126	—	73	2	no	—
377	#125	—	73	1	no	—
378	#125	—	73	1	no	—
379	#125	—	73	1	no	—
380	#125	—	73	2	no	—
381	#124	—	73	1	no	—
382	#124	—	73	1	no	—
383	#124	—	73	2	no	—
384	#124	—	73	2	no	—
385	#124	—	73	1	no	—
386	#123	—	73	2	no	—
387	#123	—	73	2	no	—
388	#123	—	73	2	no	—
389	#123	—	73	1	no	—
390	#123	—	73	1	no	—
391	#123	—	73	2	no	—
392	#123	—	73	2	no	—
393	#123	—	73	2	no	—
394	#123	—	73	2	no	—
395	#123	—	73	2	no	—
396	#123	—	73	2	no	—
397	#123	—	73	2	no	—
398	#123	—	73	2	no	—
399	#123	—	73	2	no	—
400	C₂²⋊Q₈	—	73	2	no	—
401	C₂²⋊Q₈	—	73	2	no	—
402	C₂²⋊Q₈	—	73	1	no	—
403	C₂²⋊Q₈	—	73	2	no	—
404	C₂²⋊Q₈	—	73	1	no	—
405	C₂²⋊Q₈	—	73	1	no	—
406	C₂²⋊Q₈	—	73	2	no	—
407	C₂²⋊Q₈	—	73	2	no	—
408	#121	—	73	2	no	—
409	#121	—	73	1	no	—
410	#121	—	73	2	no	—
411	#121	—	73	1	no	—
412	#121	—	73	2	no	—
413	#121	—	73	2	no	—
414	#121	—	73	1	no	—
415	#121	—	73	1	no	—
416	#121	—	73	2	no	—
417	#121	—	73	1	no	—
418	#121	—	73	2	no	—
419	#120	—	73	2	no	—
420	#120	—	73	2	no	—
421	#120	—	73	2	no	—
422	#120	—	73	2	no	—
423	C₄×Q₈	—	73	1	no	—
424	C₄×Q₈	—	73	1	no	—
425	C₄×Q₈	—	73	1	no	—
426	C₄×D₄	—	73	1	no	—
427	C₄×D₄	—	73	1	no	—
428	C₄×D₄	—	73	2	no	—
429	C₄×D₄	—	73	2	no	—
430	C₄×D₄	—	73	2	no	—
431	C₄×D₄	—	73	1	no	—
432	C₄×D₄	—	73	2	no	—
433	C₄×D₄	—	73	1	no	—
434	C₄×D₄	—	73	1	no	—
435	C₄×D₄	—	73	2	no	—
436	C₄×D₄	—	73	2	no	—
437	C₄×D₄	—	73	1	no	—
438	C₄×D₄	—	73	2	no	—
439	C₄×D₄	—	73	1	no	—
440	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
441	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
442	C₄×D₄	C₂×D₇₃	1	2	yes	complemented
443	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
444	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
445	C₄×D₄	C₂×D₇₃	1	2	yes	complemented
446	#117	—	73	2	no	—
447	#117	—	73	2	no	—
448	#117	—	73	1	no	—
449	#117	—	73	2	no	—
450	#117	C₂×D₇₃	1	1	yes	characteristic, complemented
451	#117	C₂×D₇₃	1	1	yes	characteristic, complemented
452	C₂×C₄⋊C₄	—	73	2	no	—
453	C₂×C₄⋊C₄	—	73	2	no	—
454	C₂×C₄⋊C₄	—	73	1	no	—
455	C₂×C₄⋊C₄	—	73	1	no	—
456	C₂×C₂²⋊C₄	—	73	2	no	—
457	C₂×C₂²⋊C₄	—	73	2	no	—
458	C₂×C₂²⋊C₄	—	73	2	no	—
459	C₂×C₂²⋊C₄	C₂×D₇₃	1	2	yes	complemented
460	C₂×C₂²⋊C₄	C₂×D₇₃	1	2	yes	complemented
461	C₂×C₄²	—	73	1	no	—
462	C₂⁴	—	73	2	no	—
463	C₂⁴	C₂²×D₇₃	1	2	yes	—
464	#41	—	292	4	no	—
465	#41	—	146	4	no	—
466	C₂×Q₈	—	73	1	no	—
467	C₂×Q₈	—	73	2	no	—
468	C₂×Q₈	—	73	1	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	292	4	no	—
471	C₂×D₄	—	73	1	no	—
472	C₂×D₄	—	73	2	no	—
473	C₂×D₄	—	73	2	no	—
474	C₂×D₄	—	73	2	no	—
475	C₂×D₄	—	73	2	no	—
476	C₂×D₄	—	73	2	no	—
477	C₂×D₄	—	73	2	no	—
478	C₂×D₄	—	73	2	no	—
479	C₂×D₄	—	73	1	no	—
480	C₂×D₄	—	73	2	no	—
481	C₂×D₄	—	73	1	no	—
482	C₂×D₄	—	73	1	no	—
483	C₂×D₄	—	146	4	no	—
484	C₂×D₄	C₂²×D₇₃	1	2	yes	—
485	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
487	C₂²×C₄	—	292	4	no	—
488	C₂²×C₄	—	73	2	no	—
489	C₂²×C₄	—	73	2	no	—
490	C₂²×C₄	—	73	1	no	—
491	C₂²×C₄	—	73	2	no	—
492	C₂²×C₄	—	73	2	no	—
493	C₂²×C₄	—	73	2	no	—
494	C₂²×C₄	—	73	2	no	—
495	C₂²×C₄	—	73	1	no	—
496	C₂²×C₄	—	73	1	no	—
497	C₂²×C₄	—	73	2	no	—
498	C₂²×C₄	—	73	1	no	—
499	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
501	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
502	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
503	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
504	C₄⋊C₄	—	73	2	no	—
505	C₄⋊C₄	—	73	1	no	—
506	C₄⋊C₄	—	73	2	no	—
507	C₄⋊C₄	—	73	2	no	—
508	C₄⋊C₄	—	73	2	no	—
509	C₄⋊C₄	—	73	1	no	—
510	C₄⋊C₄	—	73	2	no	—
511	C₄⋊C₄	—	73	2	no	—
512	C₄⋊C₄	—	73	1	no	—
513	C₄⋊C₄	—	73	1	no	—
514	C₄⋊C₄	—	73	2	no	—
515	C₄⋊C₄	—	73	1	no	—
516	C₄⋊C₄	—	73	1	no	—
517	C₄⋊C₄	—	73	1	no	—
518	C₄⋊C₄	—	73	2	no	—
519	C₄⋊C₄	—	73	1	no	—
520	C₄⋊C₄	—	73	1	no	—
521	C₄⋊C₄	—	73	2	no	—
522	C₄⋊C₄	—	73	2	no	—
523	C₄⋊C₄	—	73	2	no	—
524	C₄⋊C₄	—	73	1	no	—
525	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
529	C₂²⋊C₄	—	73	1	no	—
530	C₂²⋊C₄	—	73	2	no	—
531	C₂²⋊C₄	—	73	2	no	—
532	C₂²⋊C₄	—	73	2	no	—
533	C₂²⋊C₄	—	73	2	no	—
534	C₂²⋊C₄	—	73	2	no	—
535	C₂²⋊C₄	—	73	2	no	—
536	C₂²⋊C₄	—	73	1	no	—
537	C₂²⋊C₄	—	73	2	no	—
538	C₂²⋊C₄	—	73	1	no	—
539	C₂²⋊C₄	—	73	2	no	—
540	C₂²⋊C₄	—	73	2	no	—
541	C₂²⋊C₄	—	73	2	no	—
542	C₂²⋊C₄	—	73	2	no	—
543	C₂²⋊C₄	—	73	2	no	—
544	C₂²⋊C₄	—	73	1	no	—
545	C₂²⋊C₄	—	73	1	no	—
546	C₂²⋊C₄	—	73	1	no	—
547	C₂²⋊C₄	—	73	1	no	—
548	C₂²⋊C₄	—	73	2	no	—
549	C₂²⋊C₄	—	73	2	no	—
550	C₂²⋊C₄	—	73	1	no	—
551	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
558	C₄²	—	73	1	no	—
559	C₄²	—	73	1	no	—
560	C₄²	—	73	1	no	—
561	C₄²	—	73	2	no	—
562	C₄²	—	73	2	no	—
563	C₄²	—	73	1	no	—
564	C₄²	C₂²×D₇₃	1	1	yes	characteristic
565	C₄²	C₂²×D₇₃	1	2	yes	—
566	C₄²	C₂²×D₇₃	1	1	yes	characteristic
567	C₂³	—	2	4	no	—
568	C₂³	—	4	2	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	292	2	no	—
571	C₂³	—	73	1	no	—
572	C₂³	—	73	2	no	—
573	C₂³	—	73	1	no	—
574	C₂³	—	146	4	no	—
575	C₂³	—	146	4	no	—
576	C₂³	C₂³×D₇₃	1	1	yes	characteristic
577	C₂³	C₂³×D₇₃	1	2	yes	—
578	C₂³	C₂³×D₇₃	1	2	yes	—
579	Q₈	—	292	2	no	—
580	Q₈	—	292	1	no	—
581	Q₈	—	146	2	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	292	2	no	—
585	D₄	—	292	2	no	—
586	D₄	—	292	2	no	—
587	D₄	—	292	2	no	—
588	D₄	—	292	1	no	—
589	D₄	—	292	2	no	—
590	D₄	—	146	2	no	—
591	D₄	—	146	2	no	—
592	D₄	—	146	4	no	—
593	D₄	—	146	4	no	—
594	D₄	—	146	4	no	—
595	D₄	—	146	2	no	—
596	D₄	#11924028	1	4	yes	complemented
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	292	2	no	—
603	C₂×C₄	—	292	2	no	—
604	C₂×C₄	—	292	2	no	—
605	C₂×C₄	—	292	1	no	—
606	C₂×C₄	—	292	2	no	—
607	C₂×C₄	—	292	2	no	—
608	C₂×C₄	—	73	1	no	—
609	C₂×C₄	—	73	2	no	—
610	C₂×C₄	—	73	1	no	—
611	C₂×C₄	—	73	1	no	—
612	C₂×C₄	—	73	1	no	—
613	C₂×C₄	—	73	2	no	—
614	C₂×C₄	—	73	1	no	—
615	C₂×C₄	—	73	1	no	—
616	C₂×C₄	—	73	2	no	—
617	C₂×C₄	—	146	2	no	—
618	C₂×C₄	—	146	4	no	—
619	C₂×C₄	—	146	4	no	—
620	C₂×C₄	—	146	2	no	—
621	C₂×C₄	—	146	2	no	—
622	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₇₃	1	2	yes	—
625	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₇₃	1	2	yes	—
628	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	8	4	no	—
639	C₂²	—	292	8	no	—
640	C₂²	—	73	2	no	—
641	C₂²	—	146	1	no	—
642	C₂²	—	146	2	no	—
643	C₂²	—	146	1	no	—
644	C₂²	—	146	2	no	—
645	C₂²	—	146	1	no	—
646	C₂²	—	146	2	no	—
647	C₂²	—	146	1	no	—
648	C₂²	—	146	1	no	—
649	C₂²	C₂×#11924028	1	4	yes	—
650	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	146	1	no	—
659	C₄	—	146	1	no	—
660	C₄	—	146	2	no	—
661	C₄	—	146	1	no	—
662	C₄	—	146	2	no	—
663	C₄	—	146	1	no	—
664	C₄	—	146	2	no	—
665	C₄	—	146	1	no	—
666	C₄	—	146	1	no	—
667	C₄	C₂×#11924028	1	2	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	4	1	no	—
670	C₂	—	4	2	no	—
671	C₂	—	292	2	no	—
672	C₂	—	292	1	no	—
673	C₂	—	146	2	no	—
674	C₂	C₂²×#11924028	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₇₃	1	1	yes	characteristic
676	C₂	#17989422	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#518×C₇₃	C₂
hypercenter	#518	D₇₃
hypocenter	C₇₃	#3513
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. #17989320	C₂	semidirect
2. #17989294	C₂	semidirect
3. #17989283	C₂	semidirect
4. #17989281	C₂	semidirect
5. #17989276	C₂	semidirect
6. #17989266	C₂	semidirect
7. #17989263	C₂	semidirect
8. #17989242	C₂	semidirect
9. #17989232	C₂	semidirect
10. #17989231	C₂	semidirect
11. #17989227	C₂	semidirect
12. D₄×C₂²⋊D₇₃	C₂	semidirect
13. #17989208	C₂	semidirect
14. #17989188	C₂	semidirect
15. #17989179	C₂	semidirect
16. #17989175	C₂	semidirect
17. #17989119	C₂	semidirect
18. #17989115	C₂	semidirect
19. #17989096	C₂	semidirect
20. C₂×#14556573	C₂	semidirect
21. #17989066	C₂	semidirect
22. C₄×D₄×D₇₃	C₂	semidirect
23. #518×C₇₃	C₂	semidirect
24. C₂×#11924028	C₂²	semidirect
28. C₂²×C₄×D₇₃	C₂²	semidirect
29. #14556591	C₂²	semidirect
31. #14556586	C₂²	semidirect
32. #14556586	C₂²	semidirect
33. #14556585	C₂²	semidirect
34. #14556584	C₂²	semidirect
35. #14556584	C₂²	semidirect
36. #14556584	C₂²	semidirect
37. #14556583	C₂²	semidirect
38. #14556582	C₂²	semidirect
39. #14556582	C₂²	semidirect
40. #14556581	C₂²	semidirect
41. #14556579	C₂²	semidirect
42. #14556578	C₂²	semidirect
43. #14556577	C₂²	semidirect
44. #14556577	C₂²	semidirect
45. #14556577	C₂²	semidirect
46. #14556576	C₂²	semidirect
47. #14556575	C₂²	semidirect
48. #14556574	C₂²	semidirect
49. #14556574	C₂²	semidirect
52. #14556573	C₂²	semidirect
53. #14556573	C₂²	semidirect
54. #14556573	C₂²	semidirect
55. #14556573	C₂²	semidirect
56. #14556573	C₂²	semidirect
57. #14556573	C₂²	semidirect
58. #14556573	C₂²	semidirect
59. #14556572	C₂²	semidirect
60. #14556571	C₂²	semidirect
61. #14556570	C₂²	semidirect
62. #14556570	C₂²	semidirect
63. #14556570	C₂²	semidirect
64. #14556569	C₂²	semidirect
65. #14556569	C₂²	semidirect
66. #14556568	C₂²	semidirect
67. #14556568	C₂²	semidirect
68. #14556566	C₂²	semidirect
70. #14556565	C₂²	semidirect
71. #14556565	C₂²	semidirect
73. #14556564	C₂²	semidirect
74. #14556564	C₂²	semidirect
76. #14556563	C₂²	semidirect
78. #14556562	C₂²	semidirect
79. #14556561	C₂²	semidirect
81. #14556560	C₂²	semidirect
83. C₄×Dic₁₄₆	C₂²	semidirect
84. C₄×Dic₁₄₆	C₂²	semidirect
85. #14556556	C₂²	semidirect
86. C₄×D₂₉₂	C₂²	semidirect
87. C₄×D₂₉₂	C₂²	semidirect
88. C₄×D₂₉₂	C₂²	semidirect
91. #14556553	C₂²	semidirect
93. C₄×C₂²⋊D₇₃	C₂²	semidirect
94. C₄×C₂²⋊D₇₃	C₂²	semidirect
95. C₄×C₂²⋊D₇₃	C₂²	semidirect
96. C₄×C₂²⋊D₇₃	C₂²	semidirect
97. C₄×C₂²⋊D₇₃	C₂²	semidirect
98. #14556551	C₂²	semidirect
99. #14556551	C₂²	semidirect
100. #14556550	C₂²	semidirect
101. #14556548	C₂²	semidirect
102. #14556548	C₂²	semidirect
103. #14556547	C₂²	semidirect
104. C₂×C₄⋊Dic₇₃	C₂²	semidirect
105. C₂×#11924007	C₂²	semidirect
106. C₄⋊C₄×D₇₃	C₂²	semidirect
107. C₄⋊C₄×D₇₃	C₂²	semidirect
108. C₂×C₂²⋊Dic₇₃	C₂²	semidirect
109. C₂×#11924005	C₂²	semidirect
110. C₂²⋊C₄×D₇₃	C₂²	semidirect
111. C₄²×D₇₃	C₂²	semidirect
115. C₄×D₄×C₇₃	C₂²	semidirect
116. C₄×D₄×C₇₃	C₂²	semidirect
117. C₄×D₄×C₇₃	C₂²	semidirect
118. C₄×D₄×C₇₃	C₂²	semidirect
119. #117×C₇₃	C₂²	semidirect
120. #117×C₇₃	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₇₃	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₇₃	C₂²	semidirect
242. D₄×C₇₃	#41	semidirect
339. C₇₃	#3513	semidirect
361. #518	D₇₃	semidirect
442. C₄×D₄	C₂×D₇₃	semidirect
443. C₄×D₄	C₂×D₇₃	semidirect
444. C₄×D₄	C₂×D₇₃	semidirect
445. C₄×D₄	C₂×D₇₃	semidirect
450. #117	C₂×D₇₃	semidirect
451. #117	C₂×D₇₃	semidirect
459. C₂×C₂²⋊C₄	C₂×D₇₃	semidirect
460. C₂×C₂²⋊C₄	C₂×D₇₃	semidirect
596. D₄	#11924028	semidirect