Subgroups — #37548499

Order 23168.

1464 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042116	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#26042088	C₂	1	3	yes	maximal, complemented
4	#26042087	C₂	1	1	yes	maximal, characteristic, complemented
5	#26042085	C₂	1	3	yes	maximal, complemented
6	#26042084	C₂	1	1	yes	maximal, characteristic, complemented
7	#26042083	C₂	1	3	yes	maximal, complemented
8	#26042082	C₂	1	1	yes	maximal, characteristic, complemented
9	#26042081	C₂	1	3	yes	maximal, complemented
10	#26042078	C₂	1	3	yes	maximal, complemented
11	#26042076	C₂	1	3	yes	maximal, complemented
12	C₂×#19153843	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₁₈₁	C₂	1	3	yes	maximal, complemented
14	#26042044	C₂	1	1	yes	maximal, characteristic, complemented
15	#577×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#19153864	—	2	1	no	—
17	#19153864	C₂²	1	3	yes	complemented
18	#19153862	—	2	1	no	—
19	#19153862	—	2	3	no	—
20	#19153862	C₂²	1	1	yes	characteristic, complemented
21	#19153862	C₂²	1	1	yes	characteristic, complemented
22	#19153862	C₂²	1	3	yes	complemented
23	#19153862	C₂²	1	3	yes	complemented
24	#19153861	—	2	3	no	—
25	#19153861	C₂²	1	3	yes	complemented
26	C₂×#15668450	—	2	1	no	—
27	C₂×#15668450	C₂²	1	3	yes	complemented
28	#41×D₁₈₁	—	2	3	no	—
29	#41×D₁₈₁	—	2	1	no	—
30	#41×D₁₈₁	C₂²	1	1	yes	characteristic
31	#41×D₁₈₁	C₂²	1	3	yes	complemented
32	#41×D₁₈₁	C₂²	1	3	yes	complemented
33	C₂×D₄×D₁₈₁	—	2	3	no	—
34	C₂×D₄×D₁₈₁	C₂²	1	3	yes	complemented
35	#19153848	C₂²	1	3	yes	complemented
36	#19153848	C₂²	1	3	yes	complemented
37	#19153847	C₂²	1	3	yes	complemented
38	#19153845	C₂²	1	1	yes	characteristic, complemented
39	#19153845	C₂²	1	3	yes	complemented
40	#19153844	C₂²	1	3	yes	complemented
41	#19153844	C₂²	1	3	yes	complemented
42	#19153843	C₂²	1	6	yes	complemented
43	#19153843	C₂²	1	3	yes	complemented
44	#19153843	C₂²	1	6	yes	complemented
45	#19153843	C₂²	1	6	yes	complemented
46	#19153843	C₂²	1	3	yes	complemented
47	#19153842	C₂²	1	3	yes	complemented
48	#19153841	C₂²	1	3	yes	complemented
49	#19153841	C₂²	1	3	yes	complemented
50	#19153840	C₂²	1	3	yes	complemented
51	#19153840	C₂²	1	3	yes	complemented
52	#19153839	C₂²	1	6	yes	complemented
53	#19153838	C₂²	1	3	yes	complemented
54	#19153837	C₂²	1	6	yes	complemented
55	#19153836	C₂²	1	3	yes	complemented
56	#19153836	C₂²	1	3	yes	complemented
57	C₂×#15668436	C₂²	1	3	yes	complemented
58	SD₁₆×D₁₈₁	C₂²	1	6	yes	complemented
59	C₂×D₁₄₄₈	C₂²	1	3	yes	complemented
60	C₂×#15668434	C₂²	1	3	yes	complemented
61	D₈×D₁₈₁	C₂²	1	6	yes	complemented
62	#19153824	C₂²	1	3	yes	complemented
63	#19153823	C₂²	1	1	yes	characteristic, complemented
64	#19153822	C₂²	1	3	yes	complemented
65	C₂×#15668432	C₂²	1	3	yes	complemented
66	M₁₆×D₁₈₁	C₂²	1	3	yes	complemented
67	2₋¹⁺⁴×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
69	#137×C₁₈₁	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₁₈₁	C₂²	1	3	yes	complemented
71	#135×C₁₈₁	C₂²	1	3	yes	complemented
72	C₂×SD₁₆×C₁₈₁	C₂²	1	3	yes	complemented
73	#131×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₁₈₁	—	2	3	no	—
75	#15668450	—	2	3	no	—
76	#15668450	—	2	3	no	—
77	#15668450	—	2	3	no	—
78	#15668450	—	2	1	no	—
79	#15668450	—	2	1	no	—
80	#15668450	D₄	1	1	yes	characteristic
81	#15668450	C₂³	1	3	yes	—
82	#15668450	C₂³	1	3	yes	—
83	#15668450	C₂³	1	6	yes	complemented
84	#15668449	—	2	3	no	—
85	#15668449	—	2	3	no	—
86	#15668449	—	2	6	no	—
87	#15668449	—	2	3	no	—
88	#15668449	—	2	3	no	—
89	#15668449	C₂³	1	3	yes	—
90	#15668449	C₂³	1	3	yes	—
91	#15668449	C₂³	1	3	yes	complemented
92	#15668448	—	2	3	no	—
93	#15668448	—	2	3	no	—
94	#15668448	—	2	3	no	—
95	#15668448	D₄	1	3	yes	—
96	#15668448	C₂³	1	3	yes	—
97	#15668448	C₂³	1	1	yes	characteristic
98	Q₈×D₁₈₁	—	2	3	no	—
99	Q₈×D₁₈₁	D₄	1	1	yes	characteristic
100	Q₈×D₁₈₁	C₂³	1	1	yes	characteristic
101	Q₈×D₁₈₁	C₂³	1	3	yes	complemented
102	C₂×D₇₂₄	—	2	3	no	—
103	C₂×D₇₂₄	—	2	3	no	—
104	C₂×D₇₂₄	—	2	3	no	—
105	C₂×D₇₂₄	C₂³	1	3	yes	—
106	C₂×D₇₂₄	C₂³	1	3	yes	complemented
107	C₂×C₂²⋊D₁₈₁	—	2	6	no	—
108	C₂×C₂²⋊D₁₈₁	—	2	3	no	—
109	D₄×D₁₈₁	—	2	3	no	—
110	D₄×D₁₈₁	—	2	3	no	—
111	D₄×D₁₈₁	—	2	3	no	—
112	D₄×D₁₈₁	—	2	6	no	—
113	D₄×D₁₈₁	—	2	6	no	—
114	D₄×D₁₈₁	—	2	3	no	—
115	D₄×D₁₈₁	—	2	3	no	—
116	D₄×D₁₈₁	—	2	3	no	—
117	D₄×D₁₈₁	—	2	3	no	—
118	D₄×D₁₈₁	D₄	1	3	yes	—
119	D₄×D₁₈₁	C₂³	1	6	yes	—
120	D₄×D₁₈₁	C₂³	1	3	yes	—
121	D₄×D₁₈₁	C₂³	1	3	yes	complemented
122	C₂×C₄×D₁₈₁	—	2	3	no	—
123	C₂×C₄×D₁₈₁	—	2	3	no	—
124	C₂×C₄×D₁₈₁	—	2	3	no	—
125	C₂×C₄×D₁₈₁	C₂³	1	3	yes	—
126	Dic₇₂₄	C₂³	1	1	yes	characteristic, complemented
127	#15668439	C₂³	1	1	yes	characteristic, complemented
128	#15668439	C₂³	1	3	yes	complemented
129	#15668438	C₂³	1	3	yes	complemented
130	#15668438	C₂³	1	3	yes	complemented
131	#15668437	C₂³	1	3	yes	complemented
132	#15668437	C₂³	1	1	yes	characteristic, complemented
133	#15668436	C₂³	1	6	yes	complemented
134	#15668436	C₂³	1	3	yes	complemented
135	#15668436	C₂³	1	3	yes	complemented
136	D₁₄₄₈	C₂³	1	6	yes	complemented
137	D₁₄₄₈	C₂³	1	3	yes	complemented
138	#15668434	C₂³	1	3	yes	complemented
139	#15668434	C₂³	1	6	yes	complemented
140	#15668434	C₂³	1	3	yes	complemented
141	#15668433	C₂³	1	3	yes	complemented
142	#15668432	C₂³	1	3	yes	—
143	#15668432	C₂³	1	1	yes	characteristic
144	#15668432	C₂³	1	3	yes	complemented
145	#15668432	C₂³	1	3	yes	complemented
146	C₂×#13089678	C₂³	1	3	yes	complemented
147	C₈×D₁₈₁	C₂³	1	6	yes	complemented
148	#41×C₁₈₁	—	2	1	no	—
149	#41×C₁₈₁	—	2	3	no	—
150	#41×C₁₈₁	C₂³	1	3	yes	—
151	#41×C₁₈₁	C₂³	1	1	yes	characteristic
152	#41×C₁₈₁	C₂³	1	3	yes	complemented
153	C₂×Q₈×C₁₈₁	—	2	1	no	—
154	C₂×Q₈×C₁₈₁	C₂³	1	3	yes	complemented
155	C₂×D₄×C₁₈₁	—	2	3	no	—
156	C₂×D₄×C₁₈₁	C₂³	1	3	yes	—
157	Q₁₆×C₁₈₁	C₂³	1	3	yes	complemented
158	SD₁₆×C₁₈₁	C₂³	1	3	yes	complemented
159	SD₁₆×C₁₈₁	C₂³	1	6	yes	complemented
160	SD₁₆×C₁₈₁	C₂³	1	1	yes	characteristic, complemented
161	D₈×C₁₈₁	C₂³	1	3	yes	complemented
162	M₁₆×C₁₈₁	C₂³	1	3	yes	complemented
163	C₂×C₈×C₁₈₁	C₂³	1	3	yes	complemented
164	C₂²×D₁₈₁	—	2	3	no	—
165	C₂²×D₁₈₁	—	2	3	no	—
166	C₂²×D₁₈₁	—	2	3	no	—
167	C₂²×D₁₈₁	—	2	3	no	—
168	C₂²×D₁₈₁	—	2	6	no	—
169	C₂²×D₁₈₁	—	8	6	no	—
170	C₂²×D₁₈₁	C₂×D₄	1	3	yes	—
171	Dic₃₆₂	—	2	3	no	—
172	Dic₃₆₂	—	2	1	no	—
173	Dic₃₆₂	C₂×D₄	1	3	yes	—
174	Dic₃₆₂	C₂⁴	1	1	yes	characteristic
175	Dic₃₆₂	C₂⁴	1	1	yes	characteristic
176	D₇₂₄	—	2	3	no	—
177	D₇₂₄	—	2	3	no	—
178	D₇₂₄	—	2	6	no	—
179	D₇₂₄	—	2	3	no	—
180	D₇₂₄	—	2	3	no	—
181	D₇₂₄	C₂×D₄	1	3	yes	—
182	D₇₂₄	C₂⁴	1	3	yes	—
183	D₇₂₄	C₂⁴	1	3	yes	—
184	C₂²⋊D₁₈₁	—	2	3	no	—
185	C₂²⋊D₁₈₁	—	2	3	no	—
186	C₂²⋊D₁₈₁	—	2	3	no	—
187	C₂²⋊D₁₈₁	—	2	1	no	—
188	C₂²⋊D₁₈₁	—	2	3	no	—
189	C₂²⋊D₁₈₁	—	2	6	no	—
190	C₂²⋊D₁₈₁	—	2	3	no	—
191	C₂²⋊D₁₈₁	C₂×D₄	1	6	yes	—
192	C₂×Dic₁₈₁	—	2	1	no	—
193	C₂×Dic₁₈₁	—	2	3	no	—
194	C₂×Dic₁₈₁	C₂×D₄	1	3	yes	—
195	C₄×D₁₈₁	—	2	1	no	—
196	C₄×D₁₈₁	—	2	3	no	—
197	C₄×D₁₈₁	—	2	3	no	—
198	C₄×D₁₈₁	—	2	3	no	—
199	C₄×D₁₈₁	—	2	3	no	—
200	C₄×D₁₈₁	—	2	3	no	—
201	C₄×D₁₈₁	—	2	6	no	—
202	C₄×D₁₈₁	C₂×D₄	1	3	yes	—
203	C₄×D₁₈₁	C₂×D₄	1	3	yes	—
204	C₄×D₁₈₁	C₂⁴	1	3	yes	—
205	C₄×D₁₈₁	C₂⁴	1	1	yes	characteristic
206	#13089678	C₂⁴	1	3	yes	—
207	#13089678	C₂⁴	1	1	yes	characteristic
208	C₂³×C₁₈₁	—	2	3	no	—
209	Q₈×C₁₈₁	—	2	3	no	—
210	Q₈×C₁₈₁	C₂×D₄	1	1	yes	characteristic
211	Q₈×C₁₈₁	C₂⁴	1	3	yes	—
212	Q₈×C₁₈₁	C₂⁴	1	1	yes	characteristic
213	D₄×C₁₈₁	—	2	3	no	—
214	D₄×C₁₈₁	—	2	3	no	—
215	D₄×C₁₈₁	—	2	3	no	—
216	D₄×C₁₈₁	C₂×D₄	1	3	yes	—
217	D₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
218	D₄×C₁₈₁	C₂⁴	1	3	yes	—
219	C₂×C₄×C₁₈₁	—	2	3	no	—
220	C₂×C₄×C₁₈₁	—	2	3	no	—
221	C₂×C₄×C₁₈₁	—	2	3	no	—
222	C₂×C₄×C₁₈₁	C₂⁴	1	3	yes	—
223	C₈×C₁₈₁	C₂⁴	1	1	yes	characteristic
224	C₈×C₁₈₁	C₂⁴	1	3	yes	—
225	C₂²×C₁₈₁	—	2	1	no	—
226	C₂²×C₁₈₁	—	2	3	no	—
227	C₂²×C₁₈₁	—	8	3	no	—
228	C₂²×C₁₈₁	C₂²×D₄	1	3	yes	—
229	C₂×D₁₈₁	—	2	3	no	—
230	C₂×D₁₈₁	—	2	3	no	—
231	C₂×D₁₈₁	—	4	3	no	—
232	C₂×D₁₈₁	—	4	6	no	—
233	C₂×D₁₈₁	—	8	3	no	—
234	C₂×D₁₈₁	—	8	6	no	—
235	C₂×D₁₈₁	—	8	3	no	—
236	C₂×D₁₈₁	—	8	3	no	—
237	C₂×D₁₈₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₁₈₁	C₂²×D₄	1	3	yes	—
239	C₄×C₁₈₁	—	2	1	no	—
240	C₄×C₁₈₁	—	2	3	no	—
241	C₄×C₁₈₁	C₂²×D₄	1	3	yes	—
242	C₄×C₁₈₁	C₂⁵	1	1	yes	characteristic
243	Dic₁₈₁	—	2	1	no	—
244	Dic₁₈₁	—	2	1	no	—
245	Dic₁₈₁	C₂²×D₄	1	1	yes	characteristic
246	Dic₁₈₁	C₂²×D₄	1	3	yes	—
247	C₂×C₁₈₁	—	2	3	no	—
248	C₂×C₁₈₁	—	4	3	no	—
249	C₂×C₁₈₁	—	4	1	no	—
250	C₂×C₁₈₁	C₂³×D₄	1	1	yes	characteristic
251	D₁₈₁	—	2	1	no	—
252	D₁₈₁	—	2	3	no	—
253	D₁₈₁	—	4	3	no	—
254	D₁₈₁	—	4	3	no	—
255	C₁₈₁	#3585	1	1	yes	characteristic, complemented, Sylow
256	#3585	—	181	1	no	maximal, Sylow
257	#585	—	181	1	no	—
258	C₂×H(5,𝔽₂)	—	181	1	no	—
259	#577	—	181	1	no	—
260	#577	—	181	3	no	—
261	#577	—	181	3	no	—
262	#577	D₁₈₁	1	1	yes	characteristic, complemented
263	#576	—	181	1	no	—
264	#576	—	181	3	no	—
265	#576	—	181	3	no	—
266	#576	—	181	1	no	—
267	#575	—	181	3	no	—
268	#575	—	181	3	no	—
269	C₂×AGL(1,ℤ/8)	—	181	3	no	—
270	C₂×AGL(1,ℤ/8)	—	181	3	no	—
271	#568	—	181	1	no	—
272	2₋¹⁺⁴	—	362	1	no	—
273	2₋¹⁺⁴	—	181	3	no	—
274	2₋¹⁺⁴	C₂×D₁₈₁	1	1	yes	characteristic, complemented
275	H(5,𝔽₂)	—	362	3	no	—
276	H(5,𝔽₂)	—	362	1	no	—
277	H(5,𝔽₂)	—	362	3	no	—
278	H(5,𝔽₂)	—	181	3	no	—
279	H(5,𝔽₂)	—	181	1	no	—
280	H(5,𝔽₂)	—	181	1	no	—
281	H(5,𝔽₂)	—	181	3	no	—
282	H(5,𝔽₂)	—	181	3	no	—
283	H(5,𝔽₂)	C₂×D₁₈₁	1	1	yes	characteristic, complemented
284	C₂×#41	—	362	1	no	—
285	C₂×#41	—	362	3	no	—
286	C₂×#41	—	362	1	no	—
287	C₂×#41	—	181	3	no	—
288	C₂×#41	—	181	3	no	—
289	C₂×#41	—	181	3	no	—
290	C₂×#41	—	181	1	no	—
291	C₂²×D₄	—	362	3	no	—
292	C₂²×D₄	—	181	3	no	—
293	#137	—	181	3	no	—
294	#137	—	181	3	no	—
295	#137	—	181	3	no	—
296	#137	—	181	1	no	—
297	#137	—	181	3	no	—
298	#137	C₂×D₁₈₁	1	3	yes	complemented
299	AGL(1,ℤ/8)	—	181	3	no	—
300	AGL(1,ℤ/8)	—	181	3	no	—
301	AGL(1,ℤ/8)	—	181	3	no	—
302	AGL(1,ℤ/8)	—	181	6	no	—
303	AGL(1,ℤ/8)	—	181	3	no	—
304	AGL(1,ℤ/8)	—	181	6	no	—
305	AGL(1,ℤ/8)	—	181	6	no	—
306	AGL(1,ℤ/8)	—	181	3	no	—
307	AGL(1,ℤ/8)	—	181	3	no	—
308	AGL(1,ℤ/8)	—	181	3	no	—
309	AGL(1,ℤ/8)	—	181	3	no	—
310	AGL(1,ℤ/8)	—	181	3	no	—
311	AGL(1,ℤ/8)	C₂×D₁₈₁	1	3	yes	complemented
312	#135	—	181	3	no	—
313	#135	—	181	3	no	—
314	#135	—	181	6	no	—
315	#135	—	181	6	no	—
316	#135	—	181	3	no	—
317	#135	C₂×D₁₈₁	1	3	yes	complemented
318	C₂×SD₁₆	—	181	3	no	—
319	C₂×SD₁₆	—	181	6	no	—
320	C₂×SD₁₆	C₂×D₁₈₁	1	3	yes	complemented
321	C₂×D₈	—	181	3	no	—
322	C₂×D₈	—	181	6	no	—
323	C₂×D₈	—	181	3	no	—
324	#131	—	181	1	no	—
325	#131	—	181	3	no	—
326	#131	—	181	3	no	—
327	#131	C₂×D₁₈₁	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	181	3	no	—
329	C₂×M₁₆	—	181	3	no	—
330	C₂⁴	—	362	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	3	no	—
333	#41	—	362	3	no	—
334	#41	—	362	3	no	—
335	#41	—	362	6	no	—
336	#41	—	362	3	no	—
337	#41	—	362	3	no	—
338	#41	—	362	3	no	—
339	#41	—	362	1	no	—
340	#41	—	362	1	no	—
341	#41	—	362	3	no	—
342	#41	—	362	3	no	—
343	#41	—	362	3	no	—
344	#41	—	362	3	no	—
345	#41	—	362	3	no	—
346	#41	—	181	6	no	—
347	#41	—	181	3	no	—
348	#41	—	181	3	no	—
349	#41	—	181	3	no	—
350	#41	—	181	1	no	—
351	#41	—	181	3	no	—
352	#41	—	181	3	no	—
353	#41	—	181	1	no	—
354	#41	—	181	3	no	—
355	#41	—	181	3	no	—
356	#41	C₂²×D₁₈₁	1	3	yes	—
357	#41	C₂²×D₁₈₁	1	1	yes	characteristic
358	#41	C₂²×D₁₈₁	1	3	yes	complemented
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	362	3	no	—
361	C₂×Q₈	—	181	3	no	—
362	C₂×Q₈	—	181	1	no	—
363	C₂×Q₈	—	181	1	no	—
364	C₂×Q₈	C₂²×D₁₈₁	1	3	yes	complemented
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	362	3	no	—
367	C₂×D₄	—	362	3	no	—
368	C₂×D₄	—	362	3	no	—
369	C₂×D₄	—	362	3	no	—
370	C₂×D₄	—	362	3	no	—
371	C₂×D₄	—	362	6	no	—
372	C₂×D₄	—	362	3	no	—
373	C₂×D₄	—	362	6	no	—
374	C₂×D₄	—	362	6	no	—
375	C₂×D₄	—	362	3	no	—
376	C₂×D₄	—	362	3	no	—
377	C₂×D₄	—	362	3	no	—
378	C₂×D₄	—	362	3	no	—
379	C₂×D₄	—	362	3	no	—
380	C₂×D₄	—	181	3	no	—
381	C₂×D₄	—	181	6	no	—
382	C₂×D₄	—	181	3	no	—
383	C₂×D₄	—	181	3	no	—
384	C₂×D₄	—	181	3	no	—
385	C₂×D₄	—	181	3	no	—
386	C₂×D₄	C₂²×D₁₈₁	1	3	yes	—
387	C₂²×C₄	—	362	3	no	—
388	C₂²×C₄	—	362	3	no	—
389	C₂²×C₄	—	362	3	no	—
390	C₂²×C₄	—	181	3	no	—
391	Q₁₆	—	181	1	no	—
392	Q₁₆	—	181	3	no	—
393	Q₁₆	—	181	1	no	—
394	Q₁₆	C₂²×D₁₈₁	1	3	yes	complemented
395	SD₁₆	—	181	3	no	—
396	SD₁₆	—	181	6	no	—
397	SD₁₆	—	181	3	no	—
398	SD₁₆	—	181	3	no	—
399	SD₁₆	—	181	1	no	—
400	SD₁₆	—	181	3	no	—
401	SD₁₆	—	181	3	no	—
402	SD₁₆	C₂²×D₁₈₁	1	6	yes	complemented
403	SD₁₆	C₂²×D₁₈₁	1	3	yes	complemented
404	SD₁₆	C₂²×D₁₈₁	1	1	yes	characteristic, complemented
405	D₈	—	181	3	no	—
406	D₈	—	181	6	no	—
407	D₈	—	181	3	no	—
408	D₈	—	181	6	no	—
409	D₈	—	181	3	no	—
410	D₈	C₂²×D₁₈₁	1	3	yes	complemented
411	M₁₆	—	181	3	no	—
412	M₁₆	—	181	3	no	—
413	M₁₆	—	181	1	no	—
414	M₁₆	—	181	3	no	—
415	M₁₆	—	181	3	no	—
416	M₁₆	C₂²×D₁₈₁	1	3	yes	complemented
417	C₂×C₈	—	181	3	no	—
418	C₂×C₈	—	181	6	no	—
419	C₂×C₈	C₂²×D₁₈₁	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	362	3	no	—
422	C₂³	—	362	6	no	—
423	C₂³	—	362	3	no	—
424	C₂³	—	362	3	no	—
425	C₂³	—	362	3	no	—
426	C₂³	—	1448	6	no	—
427	C₂³	—	181	3	no	—
428	Q₈	—	2	3	no	—
429	Q₈	—	362	3	no	—
430	Q₈	—	362	1	no	—
431	Q₈	—	181	1	no	—
432	Q₈	—	181	1	no	—
433	Q₈	—	181	3	no	—
434	Q₈	D₄×D₁₈₁	1	1	yes	characteristic
435	Q₈	C₂³×D₁₈₁	1	3	yes	—
436	Q₈	C₂³×D₁₈₁	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	362	3	no	—
441	D₄	—	362	3	no	—
442	D₄	—	362	6	no	—
443	D₄	—	362	3	no	—
444	D₄	—	362	1	no	—
445	D₄	—	362	3	no	—
446	D₄	—	362	3	no	—
447	D₄	—	362	3	no	—
448	D₄	—	362	6	no	—
449	D₄	—	362	3	no	—
450	D₄	—	362	3	no	—
451	D₄	—	362	3	no	—
452	D₄	—	181	6	no	—
453	D₄	—	181	3	no	—
454	D₄	—	181	3	no	—
455	D₄	—	181	3	no	—
456	D₄	D₄×D₁₈₁	1	3	yes	—
457	D₄	C₂³×D₁₈₁	1	1	yes	characteristic
458	D₄	C₂³×D₁₈₁	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	2	3	no	—
462	C₂×C₄	—	362	1	no	—
463	C₂×C₄	—	362	3	no	—
464	C₂×C₄	—	362	3	no	—
465	C₂×C₄	—	362	3	no	—
466	C₂×C₄	—	362	6	no	—
467	C₂×C₄	—	362	1	no	—
468	C₂×C₄	—	362	3	no	—
469	C₂×C₄	—	362	3	no	—
470	C₂×C₄	—	362	3	no	—
471	C₂×C₄	—	181	3	no	—
472	C₂×C₄	—	181	3	no	—
473	C₂×C₄	—	181	3	no	—
474	C₂×C₄	—	181	3	no	—
475	C₂×C₄	—	181	1	no	—
476	C₂×C₄	C₂³×D₁₈₁	1	3	yes	—
477	C₈	—	181	1	no	—
478	C₈	—	181	3	no	—
479	C₈	C₂³×D₁₈₁	1	3	yes	—
480	C₈	C₂³×D₁₈₁	1	1	yes	characteristic
481	C₂²	—	2	1	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	362	3	no	—
485	C₂²	—	362	3	no	—
486	C₂²	—	1448	3	no	—
487	C₂²	—	1448	3	no	—
488	C₂²	—	1448	6	no	—
489	C₂²	—	1448	3	no	—
490	C₂²	—	181	1	no	—
491	C₂²	—	181	3	no	—
492	C₂²	—	724	3	no	—
493	C₂²	—	724	6	no	—
494	C₂²	C₂×D₄×D₁₈₁	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	3	no	—
497	C₄	—	362	1	no	—
498	C₄	—	362	1	no	—
499	C₄	—	181	1	no	—
500	C₄	—	181	3	no	—
501	C₄	C₂×D₄×D₁₈₁	1	3	yes	—
502	C₄	C₂⁴×D₁₈₁	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	1	no	—
506	C₂	—	362	3	no	—
507	C₂	—	362	1	no	—
508	C₂	—	724	3	no	—
509	C₂	—	724	3	no	—
510	C₂	C₂²×D₄×D₁₈₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₁₈₁
commutator, cosocle	C₄×C₁₈₁	C₂⁵
Frattini	C₄	C₂⁴×D₁₈₁
Fitting	#577×C₁₈₁	C₂
socle	C₂×C₁₈₁	C₂³×D₄
hypercenter	#577	D₁₈₁
hypocenter	C₁₈₁	#3585
LCS	G ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #577

Complements

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

N	H ≅ G/N	type
1. #26042116	C₂	semidirect
2. H(5,𝔽₂)×D₁₈₁	C₂	semidirect
3. #26042088	C₂	semidirect
4. #26042087	C₂	semidirect
5. #26042085	C₂	semidirect
6. #26042084	C₂	semidirect
7. #26042083	C₂	semidirect
8. #26042082	C₂	semidirect
9. #26042081	C₂	semidirect
10. #26042078	C₂	semidirect
11. #26042076	C₂	semidirect
12. C₂×#19153843	C₂	semidirect
13. AGL(1,ℤ/8)×D₁₈₁	C₂	semidirect
14. #26042044	C₂	semidirect
15. #577×C₁₈₁	C₂	semidirect
17. #19153864	C₂²	semidirect
20. #19153862	C₂²	semidirect
21. #19153862	C₂²	semidirect
22. #19153862	C₂²	semidirect
23. #19153862	C₂²	semidirect
25. #19153861	C₂²	semidirect
27. C₂×#15668450	C₂²	semidirect
31. #41×D₁₈₁	C₂²	semidirect
32. #41×D₁₈₁	C₂²	semidirect
34. C₂×D₄×D₁₈₁	C₂²	semidirect
35. #19153848	C₂²	semidirect
36. #19153848	C₂²	semidirect
37. #19153847	C₂²	semidirect
38. #19153845	C₂²	semidirect
39. #19153845	C₂²	semidirect
40. #19153844	C₂²	semidirect
41. #19153844	C₂²	semidirect
42. #19153843	C₂²	semidirect
43. #19153843	C₂²	semidirect
44. #19153843	C₂²	semidirect
45. #19153843	C₂²	semidirect
46. #19153843	C₂²	semidirect
47. #19153842	C₂²	semidirect
48. #19153841	C₂²	semidirect
49. #19153841	C₂²	semidirect
50. #19153840	C₂²	semidirect
51. #19153840	C₂²	semidirect
52. #19153839	C₂²	semidirect
53. #19153838	C₂²	semidirect
54. #19153837	C₂²	semidirect
55. #19153836	C₂²	semidirect
56. #19153836	C₂²	semidirect
57. C₂×#15668436	C₂²	semidirect
58. SD₁₆×D₁₈₁	C₂²	semidirect
59. C₂×D₁₄₄₈	C₂²	semidirect
60. C₂×#15668434	C₂²	semidirect
61. D₈×D₁₈₁	C₂²	semidirect
62. #19153824	C₂²	semidirect
63. #19153823	C₂²	semidirect
64. #19153822	C₂²	semidirect
65. C₂×#15668432	C₂²	semidirect
66. M₁₆×D₁₈₁	C₂²	semidirect
67. 2₋¹⁺⁴×C₁₈₁	C₂²	semidirect
68. H(5,𝔽₂)×C₁₈₁	C₂²	semidirect
69. #137×C₁₈₁	C₂²	semidirect
70. AGL(1,ℤ/8)×C₁₈₁	C₂²	semidirect
71. #135×C₁₈₁	C₂²	semidirect
72. C₂×SD₁₆×C₁₈₁	C₂²	semidirect
73. #131×C₁₈₁	C₂²	semidirect
83. #15668450	C₂³	semidirect
91. #15668449	C₂³	semidirect
101. Q₈×D₁₈₁	C₂³	semidirect
106. C₂×D₇₂₄	C₂³	semidirect
121. D₄×D₁₈₁	C₂³	semidirect
126. Dic₇₂₄	C₂³	semidirect
127. #15668439	C₂³	semidirect
128. #15668439	C₂³	semidirect
129. #15668438	C₂³	semidirect
130. #15668438	C₂³	semidirect
131. #15668437	C₂³	semidirect
132. #15668437	C₂³	semidirect
133. #15668436	C₂³	semidirect
134. #15668436	C₂³	semidirect
135. #15668436	C₂³	semidirect
136. D₁₄₄₈	C₂³	semidirect
137. D₁₄₄₈	C₂³	semidirect
138. #15668434	C₂³	semidirect
139. #15668434	C₂³	semidirect
140. #15668434	C₂³	semidirect
141. #15668433	C₂³	semidirect
144. #15668432	C₂³	semidirect
145. #15668432	C₂³	semidirect
146. C₂×#13089678	C₂³	semidirect
147. C₈×D₁₈₁	C₂³	semidirect
152. #41×C₁₈₁	C₂³	semidirect
154. C₂×Q₈×C₁₈₁	C₂³	semidirect
157. Q₁₆×C₁₈₁	C₂³	semidirect
158. SD₁₆×C₁₈₁	C₂³	semidirect
159. SD₁₆×C₁₈₁	C₂³	semidirect
160. SD₁₆×C₁₈₁	C₂³	semidirect
161. D₈×C₁₈₁	C₂³	semidirect
162. M₁₆×C₁₈₁	C₂³	semidirect
163. C₂×C₈×C₁₈₁	C₂³	semidirect
255. C₁₈₁	#3585	semidirect
262. #577	D₁₈₁	semidirect
274. 2₋¹⁺⁴	C₂×D₁₈₁	semidirect
283. H(5,𝔽₂)	C₂×D₁₈₁	semidirect
298. #137	C₂×D₁₈₁	semidirect
311. AGL(1,ℤ/8)	C₂×D₁₈₁	semidirect
317. #135	C₂×D₁₈₁	semidirect
320. C₂×SD₁₆	C₂×D₁₈₁	semidirect
327. #131	C₂×D₁₈₁	semidirect
358. #41	C₂²×D₁₈₁	semidirect
364. C₂×Q₈	C₂²×D₁₈₁	semidirect
394. Q₁₆	C₂²×D₁₈₁	semidirect
402. SD₁₆	C₂²×D₁₈₁	semidirect
403. SD₁₆	C₂²×D₁₈₁	semidirect
404. SD₁₆	C₂²×D₁₈₁	semidirect
410. D₈	C₂²×D₁₈₁	semidirect
416. M₁₆	C₂²×D₁₈₁	semidirect
419. C₂×C₈	C₂²×D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
#26042116	2
H(5,𝔽₂)×D₁₈₁	2
#26042088	2
#26042087	2
#26042085	2
#26042084	2
#26042083	2
#26042082	2
#26042081	2
#26042078	2
#26042076	2
C₂×#19153843	2
AGL(1,ℤ/8)×D₁₈₁	2
#26042044	2
#577×C₁₈₁	2
#3585	181