Subgroups — #22623964

Order 9344.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989303	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989290	C₂	1	2	yes	maximal, complemented
3	#17989285	C₂	1	2	yes	maximal, complemented
4	#17989259	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989228	C₂	1	4	yes	maximal, complemented
6	#17989228	C₂	1	2	yes	maximal, complemented
7	D₄×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×D₂₉₂	C₂	1	2	yes	maximal, complemented
9	#17989193	C₂	1	2	yes	maximal, complemented
10	#17989177	C₂	1	4	yes	maximal, complemented
11	#17989138	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989124	C₂	1	1	yes	maximal, characteristic, complemented
13	#17989100	C₂	1	2	yes	maximal, complemented
14	C₂×#14556566	C₂	1	2	yes	maximal, complemented
15	#17989059	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#554×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11924029	C₂²	1	2	yes	complemented
19	C₂×#11924029	C₂²	1	2	yes	complemented
20	C₂²×D₂₉₂	C₂²	1	2	yes	complemented
21	C₂²×D₂₉₂	C₂²	1	4	yes	complemented
22	C₂×D₄×D₇₃	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₇₃	C₂²	1	2	yes	—
24	C₂²×C₄×D₇₃	C₂²	1	2	yes	complemented
25	#14556588	C₂²	1	1	yes	characteristic, complemented
26	#14556588	C₂²	1	2	yes	complemented
27	#14556586	C₂²	1	2	yes	complemented
28	#14556586	C₂²	1	4	yes	complemented
29	#14556582	C₂²	1	1	yes	characteristic, complemented
30	#14556580	C₂²	1	1	yes	characteristic, complemented
31	#14556580	C₂²	1	2	yes	complemented
32	#14556580	C₂²	1	4	yes	complemented
33	#14556576	C₂²	1	2	yes	complemented
34	#14556576	C₂²	1	4	yes	complemented
35	#14556576	C₂²	1	4	yes	complemented
36	#14556576	C₂²	1	4	yes	complemented
37	#14556567	C₂²	1	1	yes	characteristic, complemented
38	#14556566	C₂²	1	1	yes	characteristic
39	#14556566	C₂²	1	2	yes	complemented
40	#14556566	C₂²	1	2	yes	complemented
41	#14556566	C₂²	1	4	yes	complemented
42	#14556566	C₂²	1	4	yes	complemented
43	#14556566	C₂²	1	2	yes	complemented
44	#14556566	C₂²	1	2	yes	complemented
45	#14556566	C₂²	1	4	yes	complemented
46	#14556566	C₂²	1	4	yes	complemented
47	#14556566	C₂²	1	2	yes	complemented
48	#14556566	C₂²	1	2	yes	complemented
49	#14556565	C₂²	1	4	yes	complemented
50	#14556565	C₂²	1	2	yes	complemented
51	#14556561	C₂²	1	4	yes	complemented
52	#14556561	C₂²	1	4	yes	complemented
53	#14556561	C₂²	1	4	yes	complemented
54	C₄×D₂₉₂	C₂²	1	2	yes	complemented
55	C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₂₉₂	C₂²	1	2	yes	complemented
57	C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₇₃	C₂²	1	1	yes	characteristic
59	#14556553	C₂²	1	2	yes	complemented
60	#14556553	C₂²	1	2	yes	complemented
61	#14556553	C₂²	1	1	yes	characteristic, complemented
62	#14556553	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₇₃	C₂²	1	4	yes	complemented
65	#14556551	C₂²	1	2	yes	complemented
66	#14556551	C₂²	1	4	yes	complemented
67	#14556549	C₂²	1	2	yes	complemented
68	#14556549	C₂²	1	2	yes	complemented
69	#14556548	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₇₃	C₂²	1	1	yes	characteristic, complemented
71	C₂×#11924005	C₂²	1	4	yes	complemented
72	C₂²⋊C₄×D₇₃	C₂²	1	2	yes	complemented
73	C₂²⋊C₄×D₇₃	C₂²	1	4	yes	complemented
74	C₄²×D₇₃	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
76	#125×C₇₃	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	complemented
78	C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₇₃	C₂²	1	2	yes	—
82	C₂×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
83	C₂³×D₇₃	C₂³	1	2	yes	—
84	C₂³×D₇₃	C₂³	1	4	yes	—
85	#11924029	—	4	4	no	—
86	#11924029	—	4	4	no	—
87	C₂×D₂₉₂	—	4	4	no	—
88	C₂×D₂₉₂	—	4	8	no	—
89	C₂×D₂₉₂	C₂³	1	2	yes	—
90	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
91	C₂×D₂₉₂	C₂³	1	4	yes	—
92	C₂×D₂₉₂	C₂³	1	2	yes	—
93	C₂×D₂₉₂	C₂³	1	2	yes	—
94	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
95	C₂×D₂₉₂	C₂³	1	4	yes	—
96	C₂×D₂₉₂	C₂³	1	2	yes	—
97	C₂×D₂₉₂	C₂³	1	4	yes	—
98	C₂×D₂₉₂	C₂³	1	4	yes	—
99	C₂×D₂₉₂	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
101	C₂×C₂²⋊D₇₃	C₂³	1	4	yes	—
102	D₄×D₇₃	—	2	4	no	—
103	D₄×D₇₃	—	2	8	no	—
104	C₂²×Dic₇₃	C₂³	1	2	yes	—
105	C₂×C₄×D₇₃	—	4	4	no	—
106	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₂³	1	2	yes	—
110	C₂×C₄×D₇₃	C₂³	1	2	yes	—
111	C₂×C₄×D₇₃	C₂³	1	2	yes	—
112	C₂×C₄×D₇₃	C₂³	1	4	yes	—
113	C₂×C₄×D₇₃	C₂³	1	4	yes	—
114	C₂×C₄×D₇₃	C₂³	1	2	yes	—
115	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
117	C₄⋊Dic₇₃	C₂³	1	2	yes	—
118	#11924007	C₂³	1	2	yes	—
119	#11924007	C₂³	1	2	yes	—
120	#11924007	C₂³	1	2	yes	—
121	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
122	#11924005	C₂³	1	2	yes	—
123	#11924005	C₂³	1	4	yes	—
124	#11924005	C₂³	1	2	yes	—
125	#11924005	C₂³	1	2	yes	—
126	#11924005	C₂³	1	2	yes	—
127	#11924005	C₂³	1	4	yes	—
128	#11924005	C₂³	1	4	yes	—
129	#11924005	C₂³	1	4	yes	—
130	#11924005	C₂³	1	2	yes	—
131	#11924005	C₂³	1	4	yes	—
132	#11924005	C₂³	1	4	yes	—
133	#11924005	C₂³	1	2	yes	—
134	#11924005	C₂³	1	2	yes	—
135	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
136	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
137	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
138	C₄×Dic₇₃	C₂³	1	4	yes	—
139	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
140	C₂×Q₈×C₇₃	C₂³	1	2	yes	—
141	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
143	C₂²×C₄×C₇₃	C₂³	1	4	yes	—
144	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
146	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
147	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
149	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
150	C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
151	C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
152	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
153	C₄²×C₇₃	C₂³	1	2	yes	—
154	C₄²×C₇₃	C₂³	1	1	yes	characteristic
155	C₂³×C₇₃	C₂⁴	1	2	yes	—
156	C₂²×D₇₃	—	2	4	no	—
157	C₂²×D₇₃	—	2	8	no	—
158	C₂²×D₇₃	—	2	4	no	—
159	C₂²×D₇₃	—	4	2	no	—
160	C₂²×D₇₃	—	4	4	no	—
161	C₂²×D₇₃	—	4	4	no	—
162	C₂²×D₇₃	C₂⁴	1	2	yes	—
163	C₂²×D₇₃	C₂⁴	1	2	yes	—
164	C₂²×D₇₃	C₂⁴	1	4	yes	—
165	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
166	Q₈×C₇₃	—	2	2	no	—
167	Q₈×C₇₃	—	4	2	no	—
168	D₄×C₇₃	#41	1	4	yes	complemented
169	C₂×C₄×C₇₃	—	2	4	no	—
170	C₂×C₄×C₇₃	—	4	4	no	—
171	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
172	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
175	C₂×C₄×C₇₃	C₂⁴	1	4	yes	—
176	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₇₃	—	2	4	no	—
179	C₂²⋊D₇₃	—	2	8	no	—
180	C₂×Dic₇₃	—	4	2	no	—
181	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₇₃	C₂⁴	1	2	yes	—
183	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₇₃	C₂⁴	1	2	yes	—
185	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
186	D₂₉₂	—	2	4	no	—
187	D₂₉₂	—	2	8	no	—
188	D₂₉₂	—	2	2	no	—
189	D₂₉₂	—	2	4	no	—
190	D₂₉₂	—	2	2	no	—
191	D₂₉₂	—	2	4	no	—
192	D₂₉₂	—	4	4	no	—
193	D₂₉₂	—	4	4	no	—
194	D₂₉₂	—	4	4	no	—
195	D₂₉₂	—	4	2	no	—
196	D₂₉₂	—	4	4	no	—
197	C₄×D₇₃	—	2	2	no	—
198	C₄×D₇₃	—	2	2	no	—
199	C₄×D₇₃	—	2	4	no	—
200	C₄×D₇₃	—	2	2	no	—
201	C₄×D₇₃	—	2	4	no	—
202	C₄×D₇₃	—	4	2	no	—
203	C₄×D₇₃	—	4	2	no	—
204	C₄×D₇₃	—	4	4	no	—
205	C₄×D₇₃	—	4	4	no	—
206	C₂²×C₇₃	—	2	2	no	—
207	C₂²×C₇₃	—	2	2	no	—
208	C₂²×C₇₃	C₂×#41	1	4	yes	—
209	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
210	C₂×D₇₃	—	2	1	no	—
211	C₂×D₇₃	—	2	1	no	—
212	C₂×D₇₃	—	2	2	no	—
213	C₂×D₇₃	—	2	2	no	—
214	C₂×D₇₃	—	2	4	no	—
215	C₂×D₇₃	—	2	2	no	—
216	C₂×D₇₃	—	2	4	no	—
217	C₂×D₇₃	—	2	4	no	—
218	C₂×D₇₃	—	2	2	no	—
219	C₂×D₇₃	—	2	2	no	—
220	C₂×D₇₃	—	2	2	no	—
221	C₂×D₇₃	—	4	8	no	—
222	C₂×D₇₃	—	8	8	no	—
223	C₂×D₇₃	H(5,𝔽₂)	1	2	yes	—
224	C₄×C₇₃	—	2	1	no	—
225	C₄×C₇₃	—	2	2	no	—
226	C₄×C₇₃	—	2	2	no	—
227	C₄×C₇₃	—	2	4	no	—
228	C₄×C₇₃	—	2	2	no	—
229	C₄×C₇₃	C₂×#41	1	2	yes	—
230	C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
231	Dic₇₃	—	2	1	no	—
232	Dic₇₃	—	2	2	no	—
233	Dic₇₃	—	2	1	no	—
234	Dic₇₃	—	2	2	no	—
235	Dic₇₃	—	2	1	no	—
236	C₂×C₇₃	—	2	4	no	—
237	C₂×C₇₃	C₂²×#41	1	1	yes	characteristic
238	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	D₇₃	—	2	2	no	—
241	D₇₃	—	4	2	no	—
242	D₇₃	—	4	4	no	—
243	D₇₃	—	4	2	no	—
244	#3519	—	73	1	no	maximal, Sylow
245	C₇₃	#3519	1	1	yes	characteristic, complemented, Sylow
246	#555	—	73	1	no	—
247	#554	D₇₃	1	1	yes	characteristic, complemented
248	#553	—	73	2	no	—
249	#553	—	73	2	no	—
250	#550	—	73	1	no	—
251	#546	—	73	4	no	—
252	#546	—	73	2	no	—
253	D₄²	—	73	2	no	—
254	D₄²	—	73	1	no	—
255	#540	—	73	2	no	—
256	#538	—	73	4	no	—
257	#532	—	73	1	no	—
258	#529	—	73	1	no	—
259	#525	—	73	2	no	—
260	C₂×#121	—	73	2	no	—
261	#518	—	73	2	no	—
262	C₂×C₄×D₄	—	73	1	no	—
263	C₂×#41	—	73	2	no	—
264	C₂×#41	—	73	2	no	—
265	C₂²×D₄	—	73	1	no	—
266	C₂²×D₄	—	73	2	no	—
267	C₂²×D₄	—	73	2	no	—
268	C₂²×D₄	—	73	4	no	—
269	C₂³×C₄	—	73	2	no	—
270	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
271	#127	—	73	1	no	—
272	#127	—	73	2	no	—
273	#126	—	73	2	no	—
274	#126	—	73	4	no	—
275	#125	—	73	1	no	—
276	#125	C₂×D₇₃	1	2	yes	complemented
277	#124	—	73	1	no	—
278	#124	—	73	2	no	—
279	#124	—	73	4	no	—
280	#123	—	73	4	no	—
281	#123	—	73	2	no	—
282	#123	—	73	4	no	—
283	#123	—	73	4	no	—
284	C₂²⋊Q₈	—	73	1	no	—
285	C₂²⋊Q₈	C₂×D₇₃	1	2	yes	complemented
286	C₂²⋊Q₈	C₂×D₇₃	1	4	yes	complemented
287	#121	—	73	2	no	—
288	#121	—	73	4	no	—
289	#121	—	73	1	no	—
290	#121	—	73	2	no	—
291	#121	—	73	4	no	—
292	#121	—	73	4	no	—
293	#121	—	73	2	no	—
294	#121	—	73	2	no	—
295	#121	—	73	2	no	—
296	#121	—	73	4	no	—
297	#121	—	73	2	no	—
298	#121	—	73	2	no	—
299	#121	—	73	4	no	—
300	#120	—	73	4	no	—
301	#120	—	73	4	no	—
302	#120	—	73	4	no	—
303	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
304	C₄×D₄	—	73	1	no	—
305	C₄×D₄	—	73	2	no	—
306	C₄×D₄	—	73	4	no	—
307	C₄×D₄	—	73	1	no	—
308	C₄×D₄	—	73	2	no	—
309	C₄×D₄	—	73	4	no	—
310	C₄×D₄	—	73	2	no	—
311	C₄×D₄	—	73	2	no	—
312	C₄×D₄	—	73	4	no	—
313	C₄×D₄	—	73	1	no	—
314	C₄×D₄	—	73	2	no	—
315	C₄×D₄	—	73	2	no	—
316	C₄×D₄	—	73	1	no	—
317	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
318	C₄×D₄	C₂×D₇₃	1	2	yes	—
319	#117	—	73	2	no	—
320	#117	—	73	2	no	—
321	#117	—	73	2	no	—
322	C₂×C₄⋊C₄	—	73	1	no	—
323	C₂×C₄⋊C₄	C₂×D₇₃	1	2	yes	complemented
324	C₂×C₂²⋊C₄	—	73	4	no	—
325	C₂×C₂²⋊C₄	—	73	2	no	—
326	C₂×C₂²⋊C₄	—	73	4	no	—
327	C₂×C₄²	—	73	1	no	—
328	C₂⁴	—	73	4	no	—
329	C₂⁴	—	73	2	no	—
330	#41	—	292	4	no	—
331	#41	—	292	4	no	—
332	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
333	C₂×Q₈	C₂²×D₇₃	1	2	yes	—
334	C₂×D₄	—	292	4	no	—
335	C₂×D₄	—	292	8	no	—
336	C₂×D₄	—	73	2	no	—
337	C₂×D₄	—	73	4	no	—
338	C₂×D₄	—	73	4	no	—
339	C₂×D₄	—	73	2	no	—
340	C₂×D₄	—	73	4	no	—
341	C₂×D₄	—	73	4	no	—
342	C₂×D₄	—	73	4	no	—
343	C₂×D₄	—	73	1	no	—
344	C₂×D₄	—	73	2	no	—
345	C₂×D₄	—	73	4	no	—
346	C₂×D₄	—	73	2	no	—
347	C₂×D₄	—	73	1	no	—
348	C₂×D₄	—	73	2	no	—
349	C₂×D₄	—	146	4	no	—
350	C₂×D₄	—	146	8	no	—
351	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
352	C₂²×C₄	—	292	4	no	—
353	C₂²×C₄	—	73	2	no	—
354	C₂²×C₄	—	73	2	no	—
355	C₂²×C₄	—	73	4	no	—
356	C₂²×C₄	—	73	4	no	—
357	C₂²×C₄	—	73	2	no	—
358	C₂²×C₄	—	73	1	no	—
359	C₂²×C₄	—	73	1	no	—
360	C₂²×C₄	—	73	1	no	—
361	C₂²×C₄	—	73	2	no	—
362	C₂²×C₄	—	73	2	no	—
363	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
364	C₂²×C₄	C₂²×D₇₃	1	4	yes	—
365	C₄⋊C₄	—	73	2	no	—
366	C₄⋊C₄	—	73	2	no	—
367	C₄⋊C₄	—	73	2	no	—
368	C₄⋊C₄	—	73	1	no	—
369	C₄⋊C₄	—	73	1	no	—
370	C₄⋊C₄	—	73	2	no	—
371	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
372	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
373	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
374	C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
375	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
376	C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
377	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
378	C₂²⋊C₄	—	73	2	no	—
379	C₂²⋊C₄	—	73	2	no	—
380	C₂²⋊C₄	—	73	4	no	—
381	C₂²⋊C₄	—	73	2	no	—
382	C₂²⋊C₄	—	73	4	no	—
383	C₂²⋊C₄	—	73	2	no	—
384	C₂²⋊C₄	—	73	4	no	—
385	C₂²⋊C₄	—	73	2	no	—
386	C₂²⋊C₄	—	73	4	no	—
387	C₂²⋊C₄	—	73	2	no	—
388	C₂²⋊C₄	—	73	2	no	—
389	C₂²⋊C₄	—	73	2	no	—
390	C₂²⋊C₄	—	73	4	no	—
391	C₂²⋊C₄	—	73	4	no	—
392	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
394	C₄²	—	73	1	no	—
395	C₄²	—	73	1	no	—
396	C₄²	—	73	1	no	—
397	C₄²	—	73	4	no	—
398	C₄²	C₂²×D₇₃	1	1	yes	characteristic
399	C₄²	C₂²×D₇₃	1	2	yes	—
400	C₂³	—	292	2	no	—
401	C₂³	—	292	4	no	—
402	C₂³	—	292	4	no	—
403	C₂³	—	73	1	no	—
404	C₂³	—	73	2	no	—
405	C₂³	—	73	4	no	—
406	C₂³	—	73	2	no	—
407	C₂³	—	146	4	no	—
408	C₂³	—	146	4	no	—
409	C₂³	—	146	8	no	—
410	C₂³	C₂³×D₇₃	1	2	yes	—
411	Q₈	—	2	2	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	292	4	no	—
414	D₄	—	292	4	no	—
415	D₄	—	292	4	no	—
416	D₄	—	292	2	no	—
417	D₄	—	292	4	no	—
418	D₄	—	146	4	no	—
419	D₄	—	146	8	no	—
420	D₄	—	146	4	no	—
421	D₄	—	146	8	no	—
422	D₄	—	146	2	no	—
423	D₄	—	146	4	no	—
424	D₄	—	146	2	no	—
425	D₄	—	146	4	no	—
426	D₄	#11924029	1	4	yes	complemented
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	292	2	no	—
430	C₂×C₄	—	292	2	no	—
431	C₂×C₄	—	292	4	no	—
432	C₂×C₄	—	292	4	no	—
433	C₂×C₄	—	292	2	no	—
434	C₂×C₄	—	73	1	no	—
435	C₂×C₄	—	73	2	no	—
436	C₂×C₄	—	73	1	no	—
437	C₂×C₄	—	73	1	no	—
438	C₂×C₄	—	73	2	no	—
439	C₂×C₄	—	146	2	no	—
440	C₂×C₄	—	146	4	no	—
441	C₂×C₄	—	146	2	no	—
442	C₂×C₄	—	146	2	no	—
443	C₂×C₄	—	146	4	no	—
444	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
445	C₂×C₄	C₂³×D₇₃	1	4	yes	—
446	C₂×C₄	C₂³×D₇₃	1	2	yes	—
447	C₂×C₄	C₂³×D₇₃	1	2	yes	—
448	C₂×C₄	C₂³×D₇₃	1	2	yes	—
449	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	292	8	no	—
454	C₂²	—	584	8	no	—
455	C₂²	—	73	2	no	—
456	C₂²	—	146	2	no	—
457	C₂²	—	146	2	no	—
458	C₂²	—	146	4	no	—
459	C₂²	—	146	4	no	—
460	C₂²	—	146	2	no	—
461	C₂²	—	146	2	no	—
462	C₂²	—	146	2	no	—
463	C₂²	—	146	4	no	—
464	C₂²	—	146	2	no	—
465	C₂²	—	146	1	no	—
466	C₂²	—	146	1	no	—
467	C₂²	C₂×#11924029	1	4	yes	—
468	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	4	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	146	1	no	—
475	C₄	—	146	2	no	—
476	C₄	—	146	1	no	—
477	C₄	—	146	1	no	—
478	C₄	—	146	2	no	—
479	C₄	C₂×#11924029	1	2	yes	—
480	C₄	#14556637	1	2	yes	—
481	C₂	—	2	4	no	—
482	C₂	—	292	2	no	—
483	C₂	—	292	2	no	—
484	C₂	—	292	4	no	—
485	C₂	—	146	2	no	—
486	C₂	C₂²×#11924029	1	1	yes	characteristic
487	C₂	H(5,𝔽₂)×D₇₃	1	1	yes	characteristic
488	C₂	C₂×#14556637	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#554×C₇₃	C₂
hypercenter	#554	D₇₃
hypocenter	C₇₃	#3519
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #17989303	C₂	semidirect
2. #17989290	C₂	semidirect
3. #17989285	C₂	semidirect
4. #17989259	C₂	semidirect
5. #17989228	C₂	semidirect
6. #17989228	C₂	semidirect
7. D₄×D₂₉₂	C₂	semidirect
8. D₄×D₂₉₂	C₂	semidirect
9. #17989193	C₂	semidirect
10. #17989177	C₂	semidirect
11. #17989138	C₂	semidirect
12. #17989124	C₂	semidirect
13. #17989100	C₂	semidirect
14. C₂×#14556566	C₂	semidirect
15. #17989059	C₂	semidirect
16. C₄×D₄×D₇₃	C₂	semidirect
17. #554×C₇₃	C₂	semidirect
18. C₂×#11924029	C₂²	semidirect
19. C₂×#11924029	C₂²	semidirect
20. C₂²×D₂₉₂	C₂²	semidirect
21. C₂²×D₂₉₂	C₂²	semidirect
24. C₂²×C₄×D₇₃	C₂²	semidirect
25. #14556588	C₂²	semidirect
26. #14556588	C₂²	semidirect
27. #14556586	C₂²	semidirect
28. #14556586	C₂²	semidirect
29. #14556582	C₂²	semidirect
30. #14556580	C₂²	semidirect
31. #14556580	C₂²	semidirect
32. #14556580	C₂²	semidirect
33. #14556576	C₂²	semidirect
34. #14556576	C₂²	semidirect
35. #14556576	C₂²	semidirect
36. #14556576	C₂²	semidirect
37. #14556567	C₂²	semidirect
39. #14556566	C₂²	semidirect
40. #14556566	C₂²	semidirect
41. #14556566	C₂²	semidirect
42. #14556566	C₂²	semidirect
43. #14556566	C₂²	semidirect
44. #14556566	C₂²	semidirect
45. #14556566	C₂²	semidirect
46. #14556566	C₂²	semidirect
47. #14556566	C₂²	semidirect
48. #14556566	C₂²	semidirect
49. #14556565	C₂²	semidirect
50. #14556565	C₂²	semidirect
51. #14556561	C₂²	semidirect
52. #14556561	C₂²	semidirect
53. #14556561	C₂²	semidirect
54. C₄×D₂₉₂	C₂²	semidirect
55. C₄×D₂₉₂	C₂²	semidirect
56. C₄×D₂₉₂	C₂²	semidirect
57. C₄×D₂₉₂	C₂²	semidirect
59. #14556553	C₂²	semidirect
60. #14556553	C₂²	semidirect
61. #14556553	C₂²	semidirect
62. #14556553	C₂²	semidirect
63. C₄×C₂²⋊D₇₃	C₂²	semidirect
64. C₄×C₂²⋊D₇₃	C₂²	semidirect
65. #14556551	C₂²	semidirect
66. #14556551	C₂²	semidirect
67. #14556549	C₂²	semidirect
68. #14556549	C₂²	semidirect
69. #14556548	C₂²	semidirect
70. C₄⋊C₄×D₇₃	C₂²	semidirect
71. C₂×#11924005	C₂²	semidirect
72. C₂²⋊C₄×D₇₃	C₂²	semidirect
73. C₂²⋊C₄×D₇₃	C₂²	semidirect
74. C₄²×D₇₃	C₂²	semidirect
75. C₄⋊Q₈×C₇₃	C₂²	semidirect
76. #125×C₇₃	C₂²	semidirect
77. C₂²⋊Q₈×C₇₃	C₂²	semidirect
78. C₂²⋊Q₈×C₇₃	C₂²	semidirect
79. C₄×Q₈×C₇₃	C₂²	semidirect
82. C₂×C₄⋊C₄×C₇₃	C₂²	semidirect
168. D₄×C₇₃	#41	semidirect
245. C₇₃	#3519	semidirect
247. #554	D₇₃	semidirect
270. C₄⋊Q₈	C₂×D₇₃	semidirect
276. #125	C₂×D₇₃	semidirect
285. C₂²⋊Q₈	C₂×D₇₃	semidirect
286. C₂²⋊Q₈	C₂×D₇₃	semidirect
303. C₄×Q₈	C₂×D₇₃	semidirect
323. C₂×C₄⋊C₄	C₂×D₇₃	semidirect
426. D₄	#11924029	semidirect