Subgroups — #22624231

Order 9344.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989339	C₂	1	2	yes	maximal, complemented
2	#17989331	C₂	1	2	yes	maximal, complemented
3	#17989298	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989297	C₂	1	2	yes	maximal, complemented
5	#17989288	C₂	1	2	yes	maximal, complemented
6	#17989281	C₂	1	1	yes	maximal, characteristic, complemented
7	#17989276	C₂	1	1	yes	maximal, characteristic, complemented
8	#17989250	C₂	1	1	yes	maximal, characteristic, complemented
9	#17989249	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989246	C₂	1	1	yes	maximal, characteristic, complemented
11	#17989239	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989211	C₂	1	1	yes	maximal, characteristic, complemented
13	#17989209	C₂	1	2	yes	maximal, complemented
14	#17989195	C₂	1	1	yes	maximal, characteristic, complemented
15	#17989178	C₂	1	2	yes	maximal, complemented
16	#17989176	C₂	1	2	yes	maximal, complemented
17	#17989171	C₂	1	2	yes	maximal, complemented
18	#17989167	C₂	1	1	yes	maximal, characteristic, complemented
19	#17989163	C₂	1	1	yes	maximal, characteristic, complemented
20	#17989099	C₂	1	1	yes	maximal, characteristic, complemented
21	#17989096	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11924029	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11924028	C₂²	1	1	yes	characteristic
26	C₂×#11924028	C₂²	1	1	yes	characteristic
27	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
28	C₂×Q₈×D₇₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
30	#14556591	C₂²	1	2	yes	complemented
31	#14556590	C₂²	1	2	yes	complemented
32	#14556589	C₂²	1	1	yes	characteristic, complemented
33	#14556586	C₂²	1	2	yes	—
34	#14556586	C₂²	1	2	yes	complemented
35	#14556585	C₂²	1	2	yes	—
36	#14556585	C₂²	1	2	yes	complemented
37	#14556584	C₂²	1	2	yes	—
38	#14556583	C₂²	1	2	yes	complemented
39	#14556583	C₂²	1	2	yes	complemented
40	#14556582	C₂²	1	2	yes	complemented
41	#14556582	C₂²	1	1	yes	characteristic, complemented
42	#14556581	C₂²	1	2	yes	complemented
43	#14556580	C₂²	1	2	yes	—
44	#14556579	C₂²	1	2	yes	—
45	#14556579	C₂²	1	2	yes	complemented
46	#14556579	C₂²	1	1	yes	characteristic, complemented
47	#14556577	C₂²	1	2	yes	—
48	#14556576	C₂²	1	2	yes	—
49	#14556576	C₂²	1	1	yes	characteristic
50	#14556576	C₂²	1	2	yes	complemented
51	#14556575	C₂²	1	2	yes	—
52	#14556575	C₂²	1	2	yes	—
53	#14556575	C₂²	1	2	yes	complemented
54	#14556573	C₂²	1	2	yes	—
55	#14556573	C₂²	1	2	yes	—
56	#14556573	C₂²	1	1	yes	characteristic
57	#14556573	C₂²	1	2	yes	complemented
58	#14556571	C₂²	1	1	yes	characteristic
59	#14556571	C₂²	1	1	yes	characteristic
60	#14556571	C₂²	1	1	yes	characteristic
61	#14556571	C₂²	1	1	yes	characteristic, complemented
62	#14556571	C₂²	1	1	yes	characteristic, complemented
63	#14556571	C₂²	1	2	yes	complemented
64	#14556570	C₂²	1	1	yes	characteristic
65	#14556569	C₂²	1	2	yes	—
66	#14556569	C₂²	1	2	yes	—
67	#14556569	C₂²	1	1	yes	characteristic
68	#14556569	C₂²	1	2	yes	complemented
69	#14556569	C₂²	1	2	yes	complemented
70	#14556568	C₂²	1	2	yes	—
71	#14556568	C₂²	1	1	yes	characteristic
72	#14556568	C₂²	1	2	yes	complemented
73	#14556567	C₂²	1	1	yes	characteristic
74	#14556567	C₂²	1	2	yes	—
75	#14556567	C₂²	1	2	yes	complemented
76	#14556567	C₂²	1	2	yes	complemented
77	#14556566	C₂²	1	2	yes	—
78	#14556566	C₂²	1	1	yes	characteristic
79	#14556566	C₂²	1	2	yes	—
80	#14556566	C₂²	1	1	yes	characteristic
81	#14556565	C₂²	1	1	yes	characteristic, complemented
82	#14556564	C₂²	1	2	yes	—
83	#14556564	C₂²	1	2	yes	—
84	#14556564	C₂²	1	2	yes	—
85	#14556564	C₂²	1	1	yes	characteristic
86	#14556564	C₂²	1	2	yes	complemented
87	#14556563	C₂²	1	2	yes	—
88	#14556563	C₂²	1	1	yes	characteristic
89	#14556561	C₂²	1	2	yes	—
90	#14556561	C₂²	1	1	yes	characteristic
91	#14556559	C₂²	1	1	yes	characteristic
92	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
93	#14556556	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₂₉₂	C₂²	1	2	yes	—
95	C₄×D₂₉₂	C₂²	1	2	yes	—
96	C₄×D₂₉₂	C₂²	1	2	yes	—
97	C₄×D₂₉₂	C₂²	1	1	yes	characteristic
98	C₄×D₂₉₂	C₂²	1	2	yes	—
99	#14556553	C₂²	1	2	yes	—
100	#14556553	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
103	#14556551	C₂²	1	2	yes	—
104	#14556551	C₂²	1	2	yes	complemented
105	#14556548	C₂²	1	1	yes	characteristic
106	#14556548	C₂²	1	2	yes	complemented
107	C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₇₃	C₂²	1	2	yes	—
109	C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic, complemented
110	C₄⋊C₄×D₇₃	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₇₃	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
113	#126×C₇₃	C₂²	1	2	yes	—
114	#126×C₇₃	C₂²	1	2	yes	complemented
115	#124×C₇₃	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
120	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
121	#117×C₇₃	C₂²	1	1	yes	characteristic
122	#117×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₇₃	C₂³	1	1	yes	characteristic
124	#11924029	—	4	2	no	—
125	#11924028	—	4	2	no	—
126	#11924028	—	4	2	no	—
127	C₂×Dic₁₄₆	—	4	2	no	—
128	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₄₆	C₂³	1	2	yes	—
131	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
132	C₂×Dic₁₄₆	C₂³	1	2	yes	—
133	Q₈×D₇₃	—	4	2	no	—
134	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
135	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
136	C₂×D₂₉₂	C₂³	1	2	yes	—
137	C₂×D₂₉₂	C₂³	1	2	yes	—
138	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
139	C₂×D₂₉₂	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
146	C₂²×Dic₇₃	C₂³	1	2	yes	—
147	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₇₃	—	4	2	no	—
149	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
155	C₂×C₄×D₇₃	C₂³	1	2	yes	—
156	C₂×C₄×D₇₃	C₂³	1	2	yes	—
157	C₂×C₄×D₇₃	C₂³	1	2	yes	—
158	C₂×C₄×D₇₃	C₂³	1	2	yes	—
159	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₇₃	C₂³	1	2	yes	—
162	C₄⋊Dic₇₃	C₂³	1	2	yes	—
163	C₄⋊Dic₇₃	C₂³	1	2	yes	—
164	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₇₃	C₂³	1	2	yes	—
166	C₄⋊Dic₇₃	C₂³	1	2	yes	—
167	C₄⋊Dic₇₃	C₂³	1	2	yes	—
168	#11924007	C₂³	1	2	yes	—
169	#11924007	C₂³	1	2	yes	—
170	#11924007	C₂³	1	2	yes	—
171	#11924007	C₂³	1	1	yes	characteristic
172	#11924007	C₂³	1	2	yes	—
173	#11924007	C₂³	1	2	yes	—
174	#11924007	C₂³	1	1	yes	characteristic
175	#11924007	C₂³	1	1	yes	characteristic
176	#11924007	C₂³	1	2	yes	—
177	#11924007	C₂³	1	2	yes	—
178	#11924007	C₂³	1	1	yes	characteristic
179	#11924007	C₂³	1	2	yes	—
180	#11924007	C₂³	1	2	yes	—
181	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
184	#11924005	C₂³	1	2	yes	—
185	#11924005	C₂³	1	2	yes	—
186	#11924005	C₂³	1	1	yes	characteristic
187	#11924005	C₂³	1	1	yes	characteristic
188	#11924005	C₂³	1	1	yes	characteristic
189	#11924005	C₂³	1	2	yes	—
190	#11924005	C₂³	1	2	yes	—
191	#11924005	C₂³	1	2	yes	—
192	#11924005	C₂³	1	1	yes	characteristic
193	#11924005	C₂³	1	2	yes	—
194	#11924005	C₂³	1	2	yes	—
195	#11924005	C₂³	1	1	yes	characteristic
196	#11924005	C₂³	1	2	yes	—
197	#11924005	C₂³	1	1	yes	characteristic
198	#11924005	C₂³	1	2	yes	—
199	#11924005	C₂³	1	2	yes	—
200	#11924005	C₂³	1	2	yes	—
201	#11924005	C₂³	1	2	yes	—
202	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
203	C₄×Dic₇₃	C₂³	1	2	yes	—
204	C₄×Dic₇₃	C₂³	1	2	yes	—
205	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₇₃	C₂³	1	2	yes	—
207	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
215	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
216	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
217	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
224	C₄²×C₇₃	C₂³	1	2	yes	—
225	C₄²×C₇₃	C₂³	1	2	yes	—
226	C₄²×C₇₃	C₂³	1	1	yes	characteristic
227	C₄²×C₇₃	C₂³	1	2	yes	—
228	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
229	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
230	C₂²×D₇₃	—	2	2	no	—
231	C₂²×D₇₃	—	4	1	no	—
232	C₂²×D₇₃	—	4	1	no	—
233	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
234	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
235	C₂²×D₇₃	C₂⁴	1	2	yes	—
236	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
237	Q₈×C₇₃	—	2	2	no	—
238	Q₈×C₇₃	—	4	2	no	—
239	D₄×C₇₃	—	4	1	no	—
240	C₂×C₄×C₇₃	—	2	2	no	—
241	C₂×C₄×C₇₃	—	2	2	no	—
242	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₇₃	—	2	2	no	—
252	C₂²⋊D₇₃	—	4	1	no	—
253	C₂²⋊D₇₃	—	4	2	no	—
254	C₂²⋊D₇₃	—	4	2	no	—
255	C₂²⋊D₇₃	—	4	1	no	—
256	C₂²⋊D₇₃	—	4	1	no	—
257	C₂×Dic₇₃	—	4	1	no	—
258	C₂×Dic₇₃	—	4	2	no	—
259	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₇₃	C₂⁴	1	2	yes	—
261	C₂×Dic₇₃	C₂⁴	1	2	yes	—
262	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₇₃	C₂⁴	1	2	yes	—
264	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
267	D₂₉₂	—	2	2	no	—
268	D₂₉₂	—	2	4	no	—
269	D₂₉₂	—	2	2	no	—
270	D₂₉₂	—	4	2	no	—
271	D₂₉₂	—	4	1	no	—
272	D₂₉₂	—	4	2	no	—
273	C₄×D₇₃	—	2	2	no	—
274	C₄×D₇₃	—	2	2	no	—
275	C₄×D₇₃	—	2	2	no	—
276	C₄×D₇₃	—	4	1	no	—
277	C₄×D₇₃	—	4	1	no	—
278	C₄×D₇₃	—	4	2	no	—
279	C₄×D₇₃	—	4	2	no	—
280	C₄×D₇₃	—	4	2	no	—
281	C₄×D₇₃	—	4	2	no	—
282	C₄×D₇₃	—	4	2	no	—
283	C₄×D₇₃	—	4	2	no	—
284	Dic₁₄₆	—	2	2	no	—
285	Dic₁₄₆	—	2	2	no	—
286	Dic₁₄₆	—	4	2	no	—
287	Dic₁₄₆	—	4	2	no	—
288	Dic₁₄₆	—	4	1	no	—
289	C₂²×C₇₃	—	2	1	no	—
290	C₂²×C₇₃	—	2	1	no	—
291	C₂²×C₇₃	—	2	1	no	—
292	C₂²×C₇₃	—	2	1	no	—
293	C₂²×C₇₃	—	2	1	no	—
294	C₂²×C₇₃	—	2	1	no	—
295	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
296	C₂×D₇₃	—	2	1	no	—
297	C₂×D₇₃	—	2	1	no	—
298	C₂×D₇₃	—	2	1	no	—
299	C₂×D₇₃	—	2	1	no	—
300	C₂×D₇₃	—	2	2	no	—
301	C₂×D₇₃	—	2	1	no	—
302	C₂×D₇₃	—	2	2	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	—	4	4	no	—
308	C₂×D₇₃	2₋¹⁺⁴	1	2	yes	—
309	C₄×C₇₃	—	2	1	no	—
310	C₄×C₇₃	—	2	2	no	—
311	C₄×C₇₃	—	2	1	no	—
312	C₄×C₇₃	—	2	2	no	—
313	C₄×C₇₃	—	2	1	no	—
314	C₄×C₇₃	—	2	2	no	—
315	C₄×C₇₃	—	2	2	no	—
316	C₄×C₇₃	—	2	1	no	—
317	C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
318	Dic₇₃	—	2	2	no	—
319	Dic₇₃	—	2	2	no	—
320	Dic₇₃	—	2	1	no	—
321	Dic₇₃	—	2	1	no	—
322	Dic₇₃	—	2	1	no	—
323	Dic₇₃	—	2	1	no	—
324	Dic₇₃	—	2	2	no	—
325	Dic₇₃	—	2	1	no	—
326	C₂×C₇₃	—	4	1	no	—
327	C₂×C₇₃	—	4	1	no	—
328	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
329	C₂×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
330	C₂×C₇₃	#585	1	1	yes	characteristic
331	D₇₃	—	2	2	no	—
332	D₇₃	—	4	1	no	—
333	D₇₃	—	4	2	no	—
334	D₇₃	—	4	1	no	—
335	#3541	—	73	1	no	maximal, Sylow
336	C₇₃	#3541	1	1	yes	characteristic, complemented, Sylow
337	#563	—	73	2	no	—
338	#562	—	73	2	no	—
339	#556	D₇₃	1	1	yes	characteristic, complemented
340	#554	—	73	1	no	—
341	#554	—	73	2	no	—
342	#553	—	73	2	no	—
343	#553	—	73	1	no	—
344	#552	—	73	1	no	—
345	D₄×Q₈	—	73	1	no	—
346	#548	—	73	1	no	—
347	#548	—	73	1	no	—
348	#547	—	73	1	no	—
349	#542	—	73	1	no	—
350	#542	—	73	2	no	—
351	#541	—	73	1	no	—
352	#539	—	73	2	no	—
353	#538	—	73	2	no	—
354	#538	—	73	2	no	—
355	#537	—	73	1	no	—
356	#536	—	73	1	no	—
357	#525	—	73	1	no	—
358	#525	—	73	1	no	—
359	C₂×C₂²⋊Q₈	—	73	1	no	—
360	C₂×#41	—	73	1	no	—
361	C₂×#41	—	73	1	no	—
362	C₂×#41	—	73	1	no	—
363	C₂²×Q₈	—	73	1	no	—
364	C₂²×Q₈	—	73	1	no	—
365	C₂³×C₄	—	73	1	no	—
366	C₄⋊Q₈	—	73	1	no	—
367	C₄⋊Q₈	—	73	2	no	—
368	C₄⋊Q₈	—	73	2	no	—
369	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
370	#126	—	73	2	no	—
371	#126	—	73	2	no	—
372	#126	—	73	2	no	—
373	#126	—	73	2	no	—
374	#126	—	73	2	no	—
375	#126	C₂×D₇₃	1	2	yes	—
376	#126	C₂×D₇₃	1	2	yes	complemented
377	#125	—	73	2	no	—
378	#125	—	73	1	no	—
379	#125	—	73	2	no	—
380	#125	—	73	2	no	—
381	#125	—	73	2	no	—
382	#124	—	73	2	no	—
383	#124	—	73	2	no	—
384	#124	—	73	2	no	—
385	#124	—	73	1	no	—
386	#124	—	73	2	no	—
387	#124	C₂×D₇₃	1	2	yes	—
388	#123	—	73	1	no	—
389	#123	—	73	2	no	—
390	#123	—	73	2	no	—
391	#123	—	73	1	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	C₂²⋊Q₈	—	73	1	no	—
399	C₂²⋊Q₈	—	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	1	no	—
404	C₂²⋊Q₈	—	73	2	no	—
405	C₂²⋊Q₈	—	73	1	no	—
406	C₂²⋊Q₈	—	73	1	no	—
407	C₂²⋊Q₈	—	73	1	no	—
408	C₂²⋊Q₈	—	73	1	no	—
409	C₂²⋊Q₈	—	73	1	no	—
410	C₂²⋊Q₈	—	73	2	no	—
411	C₂²⋊Q₈	—	73	2	no	—
412	C₂²⋊Q₈	—	73	2	no	—
413	C₂²⋊Q₈	—	73	2	no	—
414	C₂²⋊Q₈	—	73	2	no	—
415	C₂²⋊Q₈	—	73	1	no	—
416	C₂²⋊Q₈	—	73	2	no	—
417	C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
418	C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
419	#121	—	73	1	no	—
420	#121	—	73	2	no	—
421	#121	—	73	1	no	—
422	#121	—	73	1	no	—
423	#121	—	73	1	no	—
424	#121	—	73	2	no	—
425	#121	—	73	2	no	—
426	#121	—	73	1	no	—
427	#121	—	73	2	no	—
428	#121	—	73	2	no	—
429	#121	—	73	2	no	—
430	#121	—	73	2	no	—
431	#120	—	73	1	no	—
432	#120	—	73	1	no	—
433	#120	—	73	2	no	—
434	C₄×Q₈	—	73	1	no	—
435	C₄×Q₈	—	73	1	no	—
436	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
437	C₄×Q₈	C₂×D₇₃	1	2	yes	complemented
438	C₄×D₄	—	73	1	no	—
439	C₄×D₄	—	73	1	no	—
440	C₄×D₄	—	73	2	no	—
441	C₄×D₄	—	73	1	no	—
442	C₄×D₄	—	73	2	no	—
443	C₄×D₄	—	73	2	no	—
444	C₄×D₄	—	73	2	no	—
445	C₄×D₄	—	73	1	no	—
446	C₄×D₄	—	73	2	no	—
447	C₄×D₄	—	73	2	no	—
448	C₄×D₄	—	73	2	no	—
449	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
450	#117	—	73	1	no	—
451	#117	—	73	2	no	—
452	#117	C₂×D₇₃	1	1	yes	characteristic
453	#117	C₂×D₇₃	1	1	yes	characteristic, complemented
454	C₂×C₄⋊C₄	—	73	2	no	—
455	C₂×C₄⋊C₄	—	73	1	no	—
456	C₂×C₄⋊C₄	—	73	1	no	—
457	C₂×C₄⋊C₄	—	73	2	no	—
458	C₂×C₂²⋊C₄	—	73	2	no	—
459	C₂⁴	—	73	1	no	—
460	#41	—	292	2	no	—
461	#41	—	292	2	no	—
462	#41	—	292	2	no	—
463	C₂×Q₈	—	292	2	no	—
464	C₂×Q₈	—	292	2	no	—
465	C₂×Q₈	—	73	2	no	—
466	C₂×Q₈	—	73	1	no	—
467	C₂×Q₈	—	73	2	no	—
468	C₂×Q₈	—	73	1	no	—
469	C₂×Q₈	—	73	1	no	—
470	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₇₃	1	2	yes	—
472	C₂×D₄	—	73	1	no	—
473	C₂×D₄	—	73	2	no	—
474	C₂×D₄	—	73	1	no	—
475	C₂×D₄	—	73	2	no	—
476	C₂×D₄	—	73	1	no	—
477	C₂×D₄	—	73	1	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	2	no	—
483	C₂×D₄	—	73	1	no	—
484	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
485	C₂²×C₄	—	292	2	no	—
486	C₂²×C₄	—	73	2	no	—
487	C₂²×C₄	—	73	1	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	1	no	—
498	C₂²×C₄	—	73	1	no	—
499	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
501	C₄⋊C₄	—	73	1	no	—
502	C₄⋊C₄	—	73	2	no	—
503	C₄⋊C₄	—	73	2	no	—
504	C₄⋊C₄	—	73	2	no	—
505	C₄⋊C₄	—	73	2	no	—
506	C₄⋊C₄	—	73	2	no	—
507	C₄⋊C₄	—	73	1	no	—
508	C₄⋊C₄	—	73	1	no	—
509	C₄⋊C₄	—	73	2	no	—
510	C₄⋊C₄	—	73	1	no	—
511	C₄⋊C₄	—	73	2	no	—
512	C₄⋊C₄	—	73	2	no	—
513	C₄⋊C₄	—	73	2	no	—
514	C₄⋊C₄	—	73	1	no	—
515	C₄⋊C₄	—	73	2	no	—
516	C₄⋊C₄	—	73	2	no	—
517	C₄⋊C₄	—	73	1	no	—
518	C₄⋊C₄	—	73	2	no	—
519	C₄⋊C₄	—	73	2	no	—
520	C₄⋊C₄	—	73	2	no	—
521	C₄⋊C₄	—	73	2	no	—
522	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
523	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
527	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
529	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
530	C₂²⋊C₄	—	73	2	no	—
531	C₂²⋊C₄	—	73	1	no	—
532	C₂²⋊C₄	—	73	1	no	—
533	C₂²⋊C₄	—	73	2	no	—
534	C₂²⋊C₄	—	73	2	no	—
535	C₂²⋊C₄	—	73	1	no	—
536	C₂²⋊C₄	—	73	1	no	—
537	C₂²⋊C₄	—	73	1	no	—
538	C₂²⋊C₄	—	73	2	no	—
539	C₂²⋊C₄	—	73	1	no	—
540	C₂²⋊C₄	—	73	2	no	—
541	C₂²⋊C₄	—	73	1	no	—
542	C₂²⋊C₄	—	73	2	no	—
543	C₂²⋊C₄	—	73	2	no	—
544	C₂²⋊C₄	—	73	2	no	—
545	C₂²⋊C₄	—	73	2	no	—
546	C₂²⋊C₄	—	73	1	no	—
547	C₂²⋊C₄	—	73	2	no	—
548	C₂²⋊C₄	—	73	2	no	—
549	C₂²⋊C₄	—	73	2	no	—
550	C₂²⋊C₄	—	73	2	no	—
551	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
557	C₄²	—	73	1	no	—
558	C₄²	—	73	2	no	—
559	C₄²	—	73	2	no	—
560	C₄²	C₂²×D₇₃	1	2	yes	—
561	C₄²	C₂²×D₇₃	1	1	yes	characteristic
562	C₄²	C₂²×D₇₃	1	2	yes	—
563	C₄²	C₂²×D₇₃	1	2	yes	—
564	C₂³	—	292	1	no	—
565	C₂³	—	292	1	no	—
566	C₂³	—	73	1	no	—
567	C₂³	—	73	1	no	—
568	C₂³	—	73	2	no	—
569	C₂³	—	73	1	no	—
570	C₂³	—	146	2	no	—
571	C₂³	C₂³×D₇₃	1	1	yes	characteristic
572	C₂³	C₂³×D₇₃	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	4	2	no	—
575	Q₈	—	292	2	no	—
576	Q₈	—	292	2	no	—
577	Q₈	—	292	1	no	—
578	Q₈	—	146	2	no	—
579	Q₈	—	146	2	no	—
580	D₄	—	4	1	no	—
581	D₄	—	292	1	no	—
582	D₄	—	292	2	no	—
583	D₄	—	292	2	no	—
584	D₄	—	292	1	no	—
585	D₄	—	292	1	no	—
586	D₄	—	292	2	no	—
587	D₄	—	292	2	no	—
588	D₄	—	292	1	no	—
589	D₄	—	146	2	no	—
590	D₄	—	146	4	no	—
591	D₄	—	146	2	no	—
592	D₄	—	146	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	292	1	no	—
596	C₂×C₄	—	292	1	no	—
597	C₂×C₄	—	292	2	no	—
598	C₂×C₄	—	292	2	no	—
599	C₂×C₄	—	292	2	no	—
600	C₂×C₄	—	292	2	no	—
601	C₂×C₄	—	292	2	no	—
602	C₂×C₄	—	292	2	no	—
603	C₂×C₄	—	292	1	no	—
604	C₂×C₄	—	292	2	no	—
605	C₂×C₄	—	73	1	no	—
606	C₂×C₄	—	73	2	no	—
607	C₂×C₄	—	73	1	no	—
608	C₂×C₄	—	73	2	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	—	146	2	no	—
614	C₂×C₄	—	146	2	no	—
615	C₂×C₄	—	146	2	no	—
616	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₇₃	1	2	yes	—
618	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₇₃	1	2	yes	—
620	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₇₃	1	2	yes	—
623	C₂×C₄	C₂³×D₇₃	1	2	yes	—
624	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	292	4	no	—
632	C₂²	—	73	2	no	—
633	C₂²	—	146	2	no	—
634	C₂²	—	146	1	no	—
635	C₂²	—	146	1	no	—
636	C₂²	—	146	2	no	—
637	C₂²	—	146	1	no	—
638	C₂²	—	146	1	no	—
639	C₂²	—	146	1	no	—
640	C₂²	—	146	2	no	—
641	C₂²	—	146	1	no	—
642	C₂²	—	146	1	no	—
643	C₂²	—	146	1	no	—
644	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	146	1	no	—
654	C₄	—	146	1	no	—
655	C₄	—	146	1	no	—
656	C₄	—	146	2	no	—
657	C₄	—	146	2	no	—
658	C₄	—	146	1	no	—
659	C₄	—	146	1	no	—
660	C₄	—	146	2	no	—
661	C₄	#14556637	1	2	yes	—
662	C₂	—	4	1	no	—
663	C₂	—	4	1	no	—
664	C₂	—	292	1	no	—
665	C₂	—	292	2	no	—
666	C₂	—	292	1	no	—
667	C₂	—	146	2	no	—
668	C₂	C₂×#14556637	1	1	yes	characteristic
669	C₂	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
670	C₂	#17989423	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#556×C₇₃	C₂
hypercenter	#556	D₇₃
hypocenter	C₇₃	#3541
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #17989339	C₂	semidirect
2. #17989331	C₂	semidirect
3. #17989298	C₂	semidirect
4. #17989297	C₂	semidirect
5. #17989288	C₂	semidirect
6. #17989281	C₂	semidirect
7. #17989276	C₂	semidirect
8. #17989250	C₂	semidirect
9. #17989249	C₂	semidirect
10. #17989246	C₂	semidirect
11. #17989239	C₂	semidirect
12. #17989211	C₂	semidirect
13. #17989209	C₂	semidirect
14. #17989195	C₂	semidirect
15. #17989178	C₂	semidirect
16. #17989176	C₂	semidirect
17. #17989171	C₂	semidirect
18. #17989167	C₂	semidirect
19. #17989163	C₂	semidirect
20. #17989099	C₂	semidirect
21. #17989096	C₂	semidirect
22. C₂²⋊Q₈×D₇₃	C₂	semidirect
23. #556×C₇₃	C₂	semidirect
24. C₂×#11924029	C₂²	semidirect
27. C₂²×Dic₁₄₆	C₂²	semidirect
30. #14556591	C₂²	semidirect
31. #14556590	C₂²	semidirect
32. #14556589	C₂²	semidirect
34. #14556586	C₂²	semidirect
36. #14556585	C₂²	semidirect
38. #14556583	C₂²	semidirect
39. #14556583	C₂²	semidirect
40. #14556582	C₂²	semidirect
41. #14556582	C₂²	semidirect
42. #14556581	C₂²	semidirect
45. #14556579	C₂²	semidirect
46. #14556579	C₂²	semidirect
50. #14556576	C₂²	semidirect
53. #14556575	C₂²	semidirect
57. #14556573	C₂²	semidirect
61. #14556571	C₂²	semidirect
62. #14556571	C₂²	semidirect
63. #14556571	C₂²	semidirect
68. #14556569	C₂²	semidirect
69. #14556569	C₂²	semidirect
72. #14556568	C₂²	semidirect
75. #14556567	C₂²	semidirect
76. #14556567	C₂²	semidirect
81. #14556565	C₂²	semidirect
86. #14556564	C₂²	semidirect
92. C₄×Dic₁₄₆	C₂²	semidirect
93. #14556556	C₂²	semidirect
100. #14556553	C₂²	semidirect
104. #14556551	C₂²	semidirect
106. #14556548	C₂²	semidirect
109. C₄⋊C₄×D₇₃	C₂²	semidirect
110. C₄⋊C₄×D₇₃	C₂²	semidirect
112. C₄⋊Q₈×C₇₃	C₂²	semidirect
114. #126×C₇₃	C₂²	semidirect
117. C₂²⋊Q₈×C₇₃	C₂²	semidirect
118. C₄×Q₈×C₇₃	C₂²	semidirect
119. C₄×Q₈×C₇₃	C₂²	semidirect
122. #117×C₇₃	C₂²	semidirect
336. C₇₃	#3541	semidirect
339. #556	D₇₃	semidirect
369. C₄⋊Q₈	C₂×D₇₃	semidirect
376. #126	C₂×D₇₃	semidirect
418. C₂²⋊Q₈	C₂×D₇₃	semidirect
436. C₄×Q₈	C₂×D₇₃	semidirect
437. C₄×Q₈	C₂×D₇₃	semidirect
453. #117	C₂×D₇₃	semidirect