Subgroups — #37548323

Order 23168.

912 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₈₁⋊#564	C₂	1	2	yes	maximal, complemented
2	#26042030	C₂	1	2	yes	maximal, complemented
3	#26042006	C₂	1	1	yes	maximal, characteristic, complemented
4	#26042004	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041990	C₂	1	1	yes	maximal, characteristic, complemented
6	#26041984	C₂	1	1	yes	maximal, characteristic, complemented
7	#26041968	C₂	1	1	yes	maximal, characteristic, complemented
8	#26041968	C₂	1	1	yes	maximal, characteristic, complemented
9	#26041967	C₂	1	1	yes	maximal, characteristic, complemented
10	#26041964	C₂	1	1	yes	maximal, characteristic, complemented
11	#26041963	C₂	1	2	yes	maximal, complemented
12	#26041961	C₂	1	2	yes	maximal, complemented
13	#26041906	C₂	1	2	yes	maximal, complemented
14	#26041906	C₂	1	1	yes	maximal, characteristic, complemented
15	#26041892	C₂	1	1	yes	maximal, characteristic, complemented
16	#26041891	C₂	1	1	yes	maximal, characteristic, complemented
17	#26041890	C₂	1	2	yes	maximal, complemented
18	#26041889	C₂	1	2	yes	maximal, complemented
19	#26041875	C₂	1	2	yes	maximal
20	#26041834	C₂	1	1	yes	maximal, characteristic, complemented
21	#26041807	C₂	1	1	yes	maximal, characteristic
22	#125×D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#544×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	#19153816	C₂²	1	1	yes	characteristic
25	#19153815	C₂²	1	1	yes	characteristic
26	#19153815	C₂²	1	2	yes	—
27	#19153814	C₂²	1	2	yes	—
28	#19153814	C₂²	1	2	yes	—
29	#19153811	C₂²	1	2	yes	—
30	#19153811	C₂²	1	1	yes	characteristic
31	#19153811	C₂²	1	2	yes	—
32	#19153811	C₂²	1	2	yes	—
33	#19153811	C₂²	1	2	yes	—
34	#19153809	C₂²	1	2	yes	—
35	#19153809	C₂²	1	1	yes	characteristic
36	#19153809	C₂²	1	2	yes	—
37	#19153809	C₂²	1	2	yes	—
38	#19153809	C₂²	1	2	yes	—
39	#19153808	C₂²	1	2	yes	—
40	#19153808	C₂²	1	1	yes	characteristic
41	#19153808	C₂²	1	2	yes	—
42	#19153807	C₂²	1	2	yes	—
43	#19153807	C₂²	1	2	yes	—
44	#19153807	C₂²	1	2	yes	—
45	#19153807	C₂²	1	2	yes	—
46	#19153807	C₂²	1	1	yes	characteristic
47	#19153807	C₂²	1	1	yes	characteristic
48	#19153807	C₂²	1	1	yes	characteristic
49	#19153807	C₂²	1	2	yes	—
50	#19153806	C₂²	1	2	yes	—
51	#19153806	C₂²	1	2	yes	—
52	#19153806	C₂²	1	2	yes	—
53	#19153806	C₂²	1	2	yes	—
54	#19153806	C₂²	1	2	yes	—
55	#19153806	C₂²	1	2	yes	—
56	#19153806	C₂²	1	2	yes	—
57	#19153806	C₂²	1	2	yes	—
58	#19153806	C₂²	1	2	yes	—
59	#19153806	C₂²	1	2	yes	—
60	#19153806	C₂²	1	2	yes	—
61	#19153806	C₂²	1	1	yes	characteristic
62	#19153802	C₂²	1	1	yes	characteristic
63	#19153801	C₂²	1	2	yes	—
64	#19153801	C₂²	1	1	yes	characteristic
65	#19153799	C₂²	1	2	yes	—
66	#19153798	C₂²	1	2	yes	—
67	#19153798	C₂²	1	2	yes	—
68	#19153798	C₂²	1	1	yes	characteristic
69	#19153796	C₂²	1	1	yes	characteristic
70	#19153796	C₂²	1	1	yes	characteristic
71	#19153796	C₂²	1	1	yes	characteristic
72	#19153796	C₂²	1	1	yes	characteristic
73	#19153795	C₂²	1	2	yes	—
74	#19153795	C₂²	1	1	yes	characteristic
75	#19153795	C₂²	1	1	yes	characteristic
76	#19153794	C₂²	1	1	yes	characteristic
77	#19153794	C₂²	1	2	yes	—
78	#19153794	C₂²	1	2	yes	—
79	#19153792	C₂²	1	2	yes	—
80	#19153792	C₂²	1	2	yes	—
81	#19153792	C₂²	1	2	yes	—
82	#19153792	C₂²	1	2	yes	—
83	#19153789	C₂²	1	1	yes	characteristic
84	Q₈×Dic₁₈₁	C₂²	1	2	yes	—
85	Q₈×Dic₁₈₁	C₂²	1	2	yes	—
86	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic
87	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic
88	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic
89	#19153781	C₂²	1	2	yes	—
90	#19153781	C₂²	1	1	yes	characteristic
91	#19153781	C₂²	1	1	yes	characteristic
92	#19153781	C₂²	1	1	yes	characteristic
93	#19153781	C₂²	1	1	yes	characteristic
94	C₄×D₇₂₄	C₂²	1	1	yes	characteristic
95	#19153778	C₂²	1	2	yes	—
96	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic
99	#19153775	C₂²	1	2	yes	—
100	#19153774	C₂²	1	2	yes	—
101	#19153774	C₂²	1	1	yes	characteristic
102	#19153774	C₂²	1	2	yes	—
103	#19153773	C₂²	1	2	yes	—
104	#19153773	C₂²	1	1	yes	characteristic
105	#19153773	C₂²	1	2	yes	—
106	C₄⋊C₄×D₁₈₁	C₂²	1	2	yes	—
107	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₁₈₁	C₂²	1	2	yes	—
109	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic
111	C₄²×D₁₈₁	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₁₈₁	C₂²	1	2	yes	—
113	C₄⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic
114	C₄⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic
115	#125×C₁₈₁	C₂²	1	1	yes	characteristic
116	#125×C₁₈₁	C₂²	1	2	yes	—
117	#125×C₁₈₁	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₁₈₁	C₂²	1	2	yes	—
119	C₂²⋊Q₈×C₁₈₁	C₂²	1	2	yes	—
120	#117×C₁₈₁	C₂²	1	1	yes	characteristic
121	#117×C₁₈₁	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₈₁	C₂²	1	1	yes	characteristic
123	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
124	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
125	C₂×Dic₃₆₂	C₂³	1	2	yes	—
126	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
127	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
130	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
131	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
133	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
136	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
137	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
140	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
141	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
142	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
143	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
144	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
147	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
148	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
149	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
150	#15668428	C₂³	1	2	yes	—
151	#15668428	C₂³	1	2	yes	—
152	#15668428	C₂³	1	2	yes	—
153	#15668428	C₂³	1	2	yes	—
154	#15668428	C₂³	1	2	yes	—
155	#15668428	C₂³	1	2	yes	—
156	#15668428	C₂³	1	2	yes	—
157	#15668428	C₂³	1	2	yes	—
158	#15668428	C₂³	1	2	yes	—
159	#15668428	C₂³	1	1	yes	characteristic
160	#15668428	C₂³	1	2	yes	—
161	#15668428	C₂³	1	1	yes	characteristic
162	#15668428	C₂³	1	2	yes	—
163	#15668428	C₂³	1	1	yes	characteristic
164	#15668428	C₂³	1	1	yes	characteristic
165	#15668428	C₂³	1	1	yes	characteristic
166	#15668428	C₂³	1	2	yes	—
167	#15668428	C₂³	1	2	yes	—
168	#15668428	C₂³	1	2	yes	—
169	#15668428	C₂³	1	2	yes	—
170	#15668428	C₂³	1	1	yes	characteristic
171	#15668428	C₂³	1	2	yes	—
172	#15668428	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
177	#15668426	C₂³	1	1	yes	characteristic
178	#15668426	C₂³	1	1	yes	characteristic
179	#15668426	C₂³	1	2	yes	—
180	#15668426	C₂³	1	1	yes	characteristic
181	#15668426	C₂³	1	1	yes	characteristic
182	#15668426	C₂³	1	2	yes	—
183	#15668426	C₂³	1	2	yes	—
184	#15668426	C₂³	1	1	yes	characteristic
185	#15668426	C₂³	1	2	yes	—
186	#15668426	C₂³	1	2	yes	—
187	#15668426	C₂³	1	1	yes	characteristic
188	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
189	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
190	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₈₁	C₂³	1	2	yes	—
192	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₈₁	C₂³	1	2	yes	—
194	C₄×Dic₁₈₁	C₂³	1	2	yes	—
195	C₄×Dic₁₈₁	C₂³	1	2	yes	—
196	C₄×Dic₁₈₁	C₂³	1	2	yes	—
197	C₄×Dic₁₈₁	C₂³	1	2	yes	—
198	C₄×Dic₁₈₁	C₂³	1	2	yes	—
199	C₂×Q₈×C₁₈₁	C₂³	1	2	yes	—
200	C₂×Q₈×C₁₈₁	C₂³	1	2	yes	—
201	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
202	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
203	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
204	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
206	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
219	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
220	C₄²×C₁₈₁	C₂³	1	2	yes	—
221	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
222	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
223	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
224	Dic₃₆₂	—	2	2	no	—
225	Dic₃₆₂	—	2	2	no	—
226	Dic₃₆₂	—	4	2	no	—
227	Dic₃₆₂	—	4	1	no	—
228	D₇₂₄	—	2	2	no	—
229	C₂²⋊D₁₈₁	—	2	2	no	—
230	C₂²⋊D₁₈₁	—	4	1	no	—
231	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
232	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
233	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
234	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
235	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
236	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
237	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
238	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
239	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
240	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
241	C₄×D₁₈₁	—	2	2	no	—
242	C₄×D₁₈₁	—	2	4	no	—
243	C₄×D₁₈₁	—	2	2	no	—
244	C₄×D₁₈₁	—	2	2	no	—
245	C₄×D₁₈₁	—	4	2	no	—
246	C₄×D₁₈₁	—	4	2	no	—
247	C₄×D₁₈₁	—	4	1	no	—
248	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
249	Q₈×C₁₈₁	—	4	2	no	—
250	Q₈×C₁₈₁	—	4	2	no	—
251	C₂×C₄×C₁₈₁	—	2	2	no	—
252	C₂×C₄×C₁₈₁	—	4	2	no	—
253	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
262	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₁₈₁	—	2	1	no	—
264	C₂²×C₁₈₁	—	2	1	no	—
265	C₂²×C₁₈₁	—	2	1	no	—
266	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
267	C₂×D₁₈₁	—	2	1	no	—
268	C₂×D₁₈₁	—	2	1	no	—
269	C₂×D₁₈₁	—	2	1	no	—
270	C₂×D₁₈₁	—	2	1	no	—
271	C₂×D₁₈₁	—	2	1	no	—
272	C₂×D₁₈₁	2₋¹⁺⁴	1	2	yes	—
273	C₄×C₁₈₁	—	2	1	no	—
274	C₄×C₁₈₁	—	2	1	no	—
275	C₄×C₁₈₁	—	2	2	no	—
276	C₄×C₁₈₁	—	2	1	no	—
277	C₄×C₁₈₁	—	2	2	no	—
278	C₄×C₁₈₁	—	2	2	no	—
279	C₄×C₁₈₁	—	2	1	no	—
280	C₄×C₁₈₁	—	2	2	no	—
281	C₄×C₁₈₁	—	2	1	no	—
282	C₄×C₁₈₁	2₋¹⁺⁴	1	2	yes	—
283	Dic₁₈₁	—	2	1	no	—
284	Dic₁₈₁	—	2	1	no	—
285	Dic₁₈₁	—	2	1	no	—
286	Dic₁₈₁	—	2	2	no	—
287	Dic₁₈₁	—	2	1	no	—
288	Dic₁₈₁	—	2	2	no	—
289	Dic₁₈₁	—	2	2	no	—
290	Dic₁₈₁	—	2	2	no	—
291	Dic₁₈₁	—	2	1	no	—
292	Dic₁₈₁	—	2	1	no	—
293	C₂×C₁₈₁	—	4	1	no	—
294	C₂×C₁₈₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
295	C₂×C₁₈₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
296	C₂×C₁₈₁	#585	1	1	yes	characteristic
297	D₁₈₁	—	2	2	no	—
298	D₁₈₁	—	4	1	no	—
299	C₁₈₁	#3563	1	1	yes	characteristic, complemented, Sylow
300	#3563	—	181	1	no	maximal, Sylow
301	#564	—	181	2	no	—
302	#563	—	181	2	no	—
303	#557	—	181	1	no	—
304	#557	—	181	1	no	—
305	#554	—	181	1	no	—
306	#554	—	181	1	no	—
307	#552	—	181	2	no	—
308	#552	—	181	1	no	—
309	#552	—	181	2	no	—
310	#552	—	181	1	no	—
311	#552	—	181	1	no	—
312	#552	—	181	1	no	—
313	#544	—	181	2	no	—
314	#544	—	181	1	no	—
315	#544	D₁₈₁	1	1	yes	characteristic, complemented
316	#541	—	181	2	no	—
317	#541	—	181	1	no	—
318	#541	—	181	2	no	—
319	#541	—	181	1	no	—
320	#539	—	181	2	no	—
321	#533	—	181	1	no	—
322	#529	—	181	1	no	—
323	C₂×#125	—	181	1	no	—
324	C₄⋊Q₈	—	181	2	no	—
325	C₄⋊Q₈	—	181	2	no	—
326	C₄⋊Q₈	—	181	1	no	—
327	C₄⋊Q₈	—	181	2	no	—
328	C₄⋊Q₈	—	181	1	no	—
329	C₄⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic
330	C₄⋊Q₈	C₂×D₁₈₁	1	2	yes	—
331	C₄⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic
332	#126	—	181	1	no	—
333	#126	—	181	2	no	—
334	#126	—	181	2	no	—
335	#126	—	181	2	no	—
336	#126	—	181	2	no	—
337	#126	—	181	1	no	—
338	#126	—	181	2	no	—
339	#126	—	181	2	no	—
340	#126	—	181	2	no	—
341	#126	—	181	2	no	—
342	#125	—	181	2	no	—
343	#125	—	181	1	no	—
344	#125	—	181	1	no	—
345	#125	—	181	2	no	—
346	#125	—	181	1	no	—
347	#125	—	181	2	no	—
348	#125	—	181	2	no	—
349	#125	—	181	2	no	—
350	#125	—	181	2	no	—
351	#125	—	181	2	no	—
352	#125	—	181	2	no	—
353	#125	—	181	2	no	—
354	#125	—	181	2	no	—
355	#125	—	181	2	no	—
356	#125	—	181	2	no	—
357	#125	—	181	2	no	—
358	#125	—	181	2	no	—
359	#125	—	181	1	no	—
360	#125	—	181	2	no	—
361	#125	—	181	2	no	—
362	#125	—	181	1	no	—
363	#125	—	181	2	no	—
364	#125	—	181	2	no	—
365	#125	C₂×D₁₈₁	1	1	yes	characteristic
366	#125	C₂×D₁₈₁	1	1	yes	characteristic
367	#125	C₂×D₁₈₁	1	2	yes	—
368	#124	—	181	1	no	—
369	#123	—	181	2	no	—
370	#123	—	181	1	no	—
371	#123	—	181	2	no	—
372	#123	—	181	1	no	—
373	#123	—	181	2	no	—
374	#123	—	181	2	no	—
375	C₂²⋊Q₈	—	181	2	no	—
376	C₂²⋊Q₈	—	181	2	no	—
377	C₂²⋊Q₈	—	181	2	no	—
378	C₂²⋊Q₈	—	181	2	no	—
379	C₂²⋊Q₈	—	181	1	no	—
380	C₂²⋊Q₈	—	181	1	no	—
381	C₂²⋊Q₈	—	181	2	no	—
382	C₂²⋊Q₈	—	181	1	no	—
383	C₂²⋊Q₈	—	181	1	no	—
384	C₂²⋊Q₈	—	181	1	no	—
385	C₂²⋊Q₈	—	181	1	no	—
386	C₂²⋊Q₈	—	181	1	no	—
387	C₂²⋊Q₈	—	181	2	no	—
388	C₂²⋊Q₈	—	181	2	no	—
389	C₂²⋊Q₈	C₂×D₁₈₁	1	2	yes	—
390	C₂²⋊Q₈	C₂×D₁₈₁	1	2	yes	—
391	#121	—	181	1	no	—
392	C₄×Q₈	—	181	2	no	—
393	C₄×Q₈	—	181	2	no	—
394	C₄×Q₈	—	181	1	no	—
395	C₄×Q₈	—	181	1	no	—
396	C₄×Q₈	—	181	2	no	—
397	C₄×Q₈	—	181	1	no	—
398	C₄×Q₈	—	181	1	no	—
399	C₄×Q₈	—	181	1	no	—
400	C₄×Q₈	—	181	1	no	—
401	C₄×Q₈	—	181	1	no	—
402	C₄×D₄	—	181	1	no	—
403	C₄×D₄	—	181	1	no	—
404	C₄×D₄	—	181	2	no	—
405	C₄×D₄	—	181	2	no	—
406	C₄×D₄	—	181	1	no	—
407	#117	—	181	2	no	—
408	#117	—	181	2	no	—
409	#117	—	181	1	no	—
410	#117	—	181	2	no	—
411	#117	—	181	1	no	—
412	#117	—	181	2	no	—
413	#117	—	181	2	no	—
414	#117	C₂×D₁₈₁	1	1	yes	characteristic
415	#117	C₂×D₁₈₁	1	1	yes	characteristic
416	C₂×C₄⋊C₄	—	181	2	no	—
417	C₂×C₄⋊C₄	—	181	1	no	—
418	C₂×C₄⋊C₄	—	181	2	no	—
419	C₂×C₄⋊C₄	—	181	1	no	—
420	C₂×C₄⋊C₄	—	181	1	no	—
421	C₂×C₄⋊C₄	C₂×D₁₈₁	1	1	yes	characteristic
422	C₂×C₄²	—	181	1	no	—
423	C₂×Q₈	—	181	1	no	—
424	C₂×Q₈	—	181	1	no	—
425	C₂×Q₈	—	181	2	no	—
426	C₂×Q₈	—	181	1	no	—
427	C₂×Q₈	C₂²×D₁₈₁	1	2	yes	—
428	C₂×Q₈	C₂²×D₁₈₁	1	2	yes	—
429	C₂×D₄	—	181	1	no	—
430	C₂×D₄	—	181	1	no	—
431	C₂×D₄	—	181	1	no	—
432	C₂²×C₄	—	181	1	no	—
433	C₂²×C₄	—	181	1	no	—
434	C₂²×C₄	—	181	2	no	—
435	C₂²×C₄	—	181	1	no	—
436	C₂²×C₄	—	181	1	no	—
437	C₂²×C₄	—	181	2	no	—
438	C₂²×C₄	—	181	2	no	—
439	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
440	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
441	C₄⋊C₄	—	181	1	no	—
442	C₄⋊C₄	—	181	1	no	—
443	C₄⋊C₄	—	181	2	no	—
444	C₄⋊C₄	—	181	2	no	—
445	C₄⋊C₄	—	181	2	no	—
446	C₄⋊C₄	—	181	2	no	—
447	C₄⋊C₄	—	181	2	no	—
448	C₄⋊C₄	—	181	2	no	—
449	C₄⋊C₄	—	181	2	no	—
450	C₄⋊C₄	—	181	2	no	—
451	C₄⋊C₄	—	181	2	no	—
452	C₄⋊C₄	—	181	2	no	—
453	C₄⋊C₄	—	181	2	no	—
454	C₄⋊C₄	—	181	2	no	—
455	C₄⋊C₄	—	181	2	no	—
456	C₄⋊C₄	—	181	1	no	—
457	C₄⋊C₄	—	181	2	no	—
458	C₄⋊C₄	—	181	1	no	—
459	C₄⋊C₄	—	181	2	no	—
460	C₄⋊C₄	—	181	1	no	—
461	C₄⋊C₄	—	181	2	no	—
462	C₄⋊C₄	—	181	1	no	—
463	C₄⋊C₄	—	181	1	no	—
464	C₄⋊C₄	—	181	1	no	—
465	C₄⋊C₄	—	181	1	no	—
466	C₄⋊C₄	—	181	1	no	—
467	C₄⋊C₄	—	181	2	no	—
468	C₄⋊C₄	—	181	2	no	—
469	C₄⋊C₄	—	181	2	no	—
470	C₄⋊C₄	—	181	2	no	—
471	C₄⋊C₄	—	181	2	no	—
472	C₄⋊C₄	—	181	2	no	—
473	C₄⋊C₄	—	181	2	no	—
474	C₄⋊C₄	—	181	2	no	—
475	C₄⋊C₄	—	181	2	no	—
476	C₄⋊C₄	—	181	2	no	—
477	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
481	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
482	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
484	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
485	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
486	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
489	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
490	C₂²⋊C₄	—	181	1	no	—
491	C₂²⋊C₄	—	181	2	no	—
492	C₂²⋊C₄	—	181	2	no	—
493	C₂²⋊C₄	—	181	1	no	—
494	C₂²⋊C₄	—	181	2	no	—
495	C₂²⋊C₄	—	181	2	no	—
496	C₂²⋊C₄	—	181	1	no	—
497	C₂²⋊C₄	—	181	1	no	—
498	C₂²⋊C₄	—	181	1	no	—
499	C₂²⋊C₄	—	181	1	no	—
500	C₂²⋊C₄	—	181	2	no	—
501	C₂²⋊C₄	—	181	1	no	—
502	C₂²⋊C₄	—	181	2	no	—
503	C₂²⋊C₄	—	181	2	no	—
504	C₂²⋊C₄	—	181	1	no	—
505	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
508	C₄²	—	181	1	no	—
509	C₄²	—	181	1	no	—
510	C₄²	—	181	1	no	—
511	C₄²	—	181	2	no	—
512	C₄²	—	181	2	no	—
513	C₄²	—	181	2	no	—
514	C₄²	—	181	1	no	—
515	C₄²	—	181	2	no	—
516	C₄²	—	181	2	no	—
517	C₄²	—	181	2	no	—
518	C₄²	—	181	2	no	—
519	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
520	C₄²	C₂²×D₁₈₁	1	2	yes	—
521	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
522	C₂³	—	181	1	no	—
523	C₂³	—	181	1	no	—
524	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
525	Q₈	—	4	2	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	362	2	no	—
528	Q₈	—	362	2	no	—
529	Q₈	—	724	2	no	—
530	Q₈	—	724	1	no	—
531	D₄	—	362	2	no	—
532	D₄	—	362	2	no	—
533	D₄	—	724	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	362	2	no	—
537	C₂×C₄	—	362	4	no	—
538	C₂×C₄	—	362	2	no	—
539	C₂×C₄	—	362	2	no	—
540	C₂×C₄	—	181	1	no	—
541	C₂×C₄	—	181	2	no	—
542	C₂×C₄	—	181	2	no	—
543	C₂×C₄	—	181	1	no	—
544	C₂×C₄	—	181	1	no	—
545	C₂×C₄	—	181	1	no	—
546	C₂×C₄	—	181	1	no	—
547	C₂×C₄	—	181	2	no	—
548	C₂×C₄	—	181	1	no	—
549	C₂×C₄	—	181	2	no	—
550	C₂×C₄	—	724	2	no	—
551	C₂×C₄	—	724	2	no	—
552	C₂×C₄	—	724	1	no	—
553	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
555	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
556	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
558	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
559	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
560	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
561	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	362	1	no	—
567	C₂²	—	362	1	no	—
568	C₂²	—	362	1	no	—
569	C₂²	—	362	1	no	—
570	C₂²	—	362	1	no	—
571	C₂²	—	181	2	no	—
572	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	1	no	—
582	C₄	—	362	1	no	—
583	C₄	—	362	1	no	—
584	C₄	—	362	2	no	—
585	C₄	—	362	2	no	—
586	C₄	—	362	2	no	—
587	C₄	—	362	1	no	—
588	C₄	—	362	1	no	—
589	C₄	—	362	1	no	—
590	C₄	—	362	2	no	—
591	C₄	—	362	1	no	—
592	C₄	#19153864	1	2	yes	—
593	C₂	—	4	1	no	—
594	C₂	—	362	2	no	—
595	C₂	—	724	1	no	—
596	C₂	2₋¹⁺⁴×D₁₈₁	1	1	yes	characteristic
597	C₂	C₂×#19153864	1	1	yes	characteristic
598	C₂	#26042114	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#544×C₁₈₁	C₂
prime radical	#19153789	C₂²
hypercenter	#544	D₁₈₁
hypocenter	C₁₈₁	#3563
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #544

Complements

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

N	H ≅ G/N	type
1. C₁₈₁⋊#564	C₂	semidirect
2. #26042030	C₂	semidirect
3. #26042006	C₂	semidirect
4. #26042004	C₂	semidirect
5. #26041990	C₂	semidirect
6. #26041984	C₂	semidirect
7. #26041968	C₂	semidirect
8. #26041968	C₂	semidirect
9. #26041967	C₂	semidirect
10. #26041964	C₂	semidirect
11. #26041963	C₂	semidirect
12. #26041961	C₂	semidirect
13. #26041906	C₂	semidirect
14. #26041906	C₂	semidirect
15. #26041892	C₂	semidirect
16. #26041891	C₂	semidirect
17. #26041890	C₂	semidirect
18. #26041889	C₂	semidirect
20. #26041834	C₂	semidirect
22. #125×D₁₈₁	C₂	semidirect
23. #544×C₁₈₁	C₂	semidirect
299. C₁₈₁	#3563	semidirect
315. #544	D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₈₁⋊#564	2
#26042030	2
#26042006	2
#26042004	2
#26041990	2
#26041984	2
#26041968	2
#26041967	2
#26041964	2
#26041963	2
#26041961	2
#26041906	2
#26041892	2
#26041891	2
#26041890	2
#26041889	2
#26041875	2
#26041834	2
#26041807	2
#125×D₁₈₁	2
#544×C₁₈₁	2
#3563	181