Subgroups — #34083399

Order 19328.

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	#23752964	C₂	1	2	yes	maximal, complemented
2	#23752958	C₂	1	2	yes	maximal, complemented
3	#23752936	C₂	1	1	yes	maximal, characteristic, complemented
4	#23752923	C₂	1	1	yes	maximal, characteristic, complemented
5	#23752920	C₂	1	2	yes	maximal, complemented
6	#23752913	C₂	1	2	yes	maximal, complemented
7	#23752912	C₂	1	1	yes	maximal, characteristic, complemented
8	#23752903	C₂	1	1	yes	maximal, characteristic, complemented
9	Q₈×D₆₀₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#23752870	C₂	1	1	yes	maximal, characteristic, complemented
11	#23752870	C₂	1	1	yes	maximal, characteristic, complemented
12	#23752866	C₂	1	1	yes	maximal, characteristic, complemented
13	#23752831	C₂	1	2	yes	maximal, complemented
14	#23752824	C₂	1	1	yes	maximal, characteristic, complemented
15	#23752806	C₂	1	2	yes	maximal, complemented
16	#23752798	C₂	1	2	yes	maximal, complemented
17	#23752796	C₂	1	2	yes	maximal, complemented
18	#23752791	C₂	1	1	yes	maximal, characteristic, complemented
19	#23752785	C₂	1	1	yes	maximal, characteristic, complemented
20	#23752724	C₂	1	1	yes	maximal, characteristic, complemented
21	#23752722	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14559004	C₂²	1	1	yes	characteristic
25	C₂×#14559003	C₂²	1	1	yes	characteristic
26	C₂×#14559003	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₁₅₁	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₁₅₁	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic
30	#18012739	C₂²	1	2	yes	complemented
31	#18012739	C₂²	1	1	yes	characteristic, complemented
32	#18012738	C₂²	1	2	yes	complemented
33	#18012734	C₂²	1	2	yes	—
34	#18012734	C₂²	1	2	yes	complemented
35	#18012733	C₂²	1	2	yes	—
36	#18012732	C₂²	1	2	yes	—
37	#18012732	C₂²	1	2	yes	—
38	#18012732	C₂²	1	2	yes	complemented
39	#18012731	C₂²	1	1	yes	characteristic, complemented
40	#18012730	C₂²	1	2	yes	complemented
41	#18012729	C₂²	1	2	yes	complemented
42	#18012729	C₂²	1	2	yes	complemented
43	#18012729	C₂²	1	2	yes	complemented
44	#18012728	C₂²	1	2	yes	—
45	#18012725	C₂²	1	2	yes	—
46	#18012725	C₂²	1	2	yes	—
47	#18012725	C₂²	1	2	yes	complemented
48	#18012724	C₂²	1	2	yes	—
49	#18012724	C₂²	1	2	yes	complemented
50	#18012723	C₂²	1	2	yes	—
51	#18012723	C₂²	1	1	yes	characteristic
52	#18012723	C₂²	1	1	yes	characteristic
53	#18012723	C₂²	1	2	yes	complemented
54	#18012722	C₂²	1	2	yes	complemented
55	#18012721	C₂²	1	2	yes	—
56	#18012721	C₂²	1	2	yes	—
57	#18012719	C₂²	1	1	yes	characteristic
58	#18012719	C₂²	1	1	yes	characteristic
59	#18012719	C₂²	1	1	yes	characteristic
60	#18012719	C₂²	1	1	yes	characteristic
61	#18012719	C₂²	1	2	yes	—
62	#18012719	C₂²	1	1	yes	characteristic, complemented
63	#18012719	C₂²	1	1	yes	characteristic, complemented
64	#18012719	C₂²	1	2	yes	complemented
65	#18012718	C₂²	1	1	yes	characteristic
66	#18012718	C₂²	1	1	yes	characteristic
67	#18012717	C₂²	1	2	yes	—
68	#18012716	C₂²	1	2	yes	—
69	#18012716	C₂²	1	2	yes	complemented
70	#18012716	C₂²	1	2	yes	complemented
71	#18012716	C₂²	1	2	yes	complemented
72	#18012715	C₂²	1	1	yes	characteristic
73	#18012715	C₂²	1	2	yes	—
74	#18012715	C₂²	1	1	yes	characteristic, complemented
75	#18012715	C₂²	1	2	yes	complemented
76	#18012714	C₂²	1	1	yes	characteristic
77	#18012714	C₂²	1	1	yes	characteristic
78	#18012713	C₂²	1	2	yes	—
79	#18012712	C₂²	1	2	yes	—
80	#18012712	C₂²	1	2	yes	—
81	#18012712	C₂²	1	2	yes	—
82	#18012712	C₂²	1	2	yes	complemented
83	#18012711	C₂²	1	2	yes	—
84	#18012710	C₂²	1	1	yes	characteristic
85	#18012710	C₂²	1	2	yes	—
86	#18012710	C₂²	1	1	yes	characteristic, complemented
87	#18012709	C₂²	1	1	yes	characteristic
88	#18012709	C₂²	1	1	yes	characteristic
89	#18012707	C₂²	1	2	yes	—
90	Q₈×Dic₁₅₁	C₂²	1	2	yes	complemented
91	C₄×Dic₃₀₂	C₂²	1	1	yes	characteristic, complemented
92	C₄×Dic₃₀₂	C₂²	1	1	yes	characteristic, complemented
93	C₄×D₆₀₄	C₂²	1	1	yes	characteristic
94	C₄×D₆₀₄	C₂²	1	1	yes	characteristic
95	C₄×D₆₀₄	C₂²	1	1	yes	characteristic
96	C₄×D₆₀₄	C₂²	1	1	yes	characteristic
97	C₄×D₆₀₄	C₂²	1	2	yes	—
98	D₄×Dic₁₅₁	C₂²	1	2	yes	—
99	#18012701	C₂²	1	2	yes	—
100	C₄×C₂²⋊D₁₅₁	C₂²	1	2	yes	—
101	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	2	yes	—
102	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	2	yes	—
103	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	2	yes	complemented
104	#18012697	C₂²	1	1	yes	characteristic
105	#18012697	C₂²	1	1	yes	characteristic, complemented
106	#18012696	C₂²	1	2	yes	complemented
107	C₂×C₄⋊Dic₁₅₁	C₂²	1	2	yes	complemented
108	C₄⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₁₅₁	C₂²	1	2	yes	—
110	C₄⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic, complemented
111	C₂²⋊C₄×D₁₅₁	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
113	#126×C₁₅₁	C₂²	1	2	yes	complemented
114	#124×C₁₅₁	C₂²	1	2	yes	—
115	#124×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
116	#123×C₁₅₁	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₁₅₁	C₂²	1	2	yes	complemented
119	#121×C₁₅₁	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
122	#117×C₁₅₁	C₂²	1	1	yes	characteristic
123	C₂³×D₁₅₁	C₂³	1	1	yes	characteristic
124	#14559004	—	4	2	no	—
125	#14559003	—	4	2	no	—
126	#14559003	—	4	2	no	—
127	C₂×Dic₃₀₂	C₂³	1	1	yes	characteristic
128	C₂×Dic₃₀₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₃₀₂	C₂³	1	2	yes	—
130	C₂×Dic₃₀₂	C₂³	1	1	yes	characteristic
131	C₂×Dic₃₀₂	C₂³	1	2	yes	—
132	Q₈×D₁₅₁	—	4	2	no	—
133	Q₈×D₁₅₁	—	4	2	no	—
134	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
135	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
136	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
137	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
138	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₅₁	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₅₁	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
145	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
146	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
147	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₅₁	—	4	2	no	—
149	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
154	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
155	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
157	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
158	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
161	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
163	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
164	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
166	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
170	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
171	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
172	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
173	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
174	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
175	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
176	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
177	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
178	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
179	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
180	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
185	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₅₁	C₂³	1	2	yes	—
202	C₄×Dic₁₅₁	C₂³	1	2	yes	—
203	C₄×Dic₁₅₁	C₂³	1	2	yes	—
204	C₄×Dic₁₅₁	C₂³	1	2	yes	—
205	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₅₁	C₂³	1	2	yes	—
207	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₅₁	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
225	C₄²×C₁₅₁	C₂³	1	2	yes	—
226	C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
227	C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
228	C₂²×D₁₅₁	—	2	2	no	—
229	C₂²×D₁₅₁	—	4	1	no	—
230	C₂²×D₁₅₁	—	4	1	no	—
231	C₂²×D₁₅₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₅₁	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₅₁	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₅₁	C₂⁴	1	1	yes	characteristic
235	Dic₃₀₂	—	2	2	no	—
236	Dic₃₀₂	—	2	2	no	—
237	Dic₃₀₂	—	4	2	no	—
238	Dic₃₀₂	—	4	2	no	—
239	Dic₃₀₂	—	4	1	no	—
240	D₆₀₄	—	2	2	no	—
241	D₆₀₄	—	2	2	no	—
242	D₆₀₄	—	4	1	no	—
243	D₆₀₄	—	4	1	no	—
244	D₆₀₄	—	4	1	no	—
245	C₂²⋊D₁₅₁	—	2	4	no	—
246	C₂²⋊D₁₅₁	—	4	2	no	—
247	C₂²⋊D₁₅₁	—	4	2	no	—
248	C₂²⋊D₁₅₁	—	4	2	no	—
249	C₂²⋊D₁₅₁	—	4	1	no	—
250	C₂²⋊D₁₅₁	—	4	1	no	—
251	C₂×Dic₁₅₁	—	4	1	no	—
252	C₂×Dic₁₅₁	—	4	2	no	—
253	C₂×Dic₁₅₁	—	4	2	no	—
254	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
255	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
258	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
259	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
260	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
262	C₄×D₁₅₁	—	2	2	no	—
263	C₄×D₁₅₁	—	2	2	no	—
264	C₄×D₁₅₁	—	2	2	no	—
265	C₄×D₁₅₁	—	2	2	no	—
266	C₄×D₁₅₁	—	4	1	no	—
267	C₄×D₁₅₁	—	4	1	no	—
268	C₄×D₁₅₁	—	4	2	no	—
269	C₄×D₁₅₁	—	4	2	no	—
270	C₄×D₁₅₁	—	4	2	no	—
271	C₄×D₁₅₁	—	4	2	no	—
272	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
273	C₂³×C₁₅₁	C₂⁴	1	2	yes	—
274	Q₈×C₁₅₁	—	2	2	no	—
275	Q₈×C₁₅₁	—	4	2	no	—
276	D₄×C₁₅₁	—	2	2	no	—
277	D₄×C₁₅₁	—	4	2	no	—
278	C₂×C₄×C₁₅₁	—	2	2	no	—
279	C₂×C₄×C₁₅₁	—	4	2	no	—
280	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
282	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
283	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
284	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₁₅₁	—	2	1	no	—
290	C₂²×C₁₅₁	—	2	2	no	—
291	C₂²×C₁₅₁	—	2	2	no	—
292	C₂²×C₁₅₁	—	2	1	no	—
293	C₂²×C₁₅₁	—	2	2	no	—
294	C₂²×C₁₅₁	—	2	1	no	—
295	C₂²×C₁₅₁	C₂⁵	1	1	yes	characteristic
296	C₂×D₁₅₁	—	2	1	no	—
297	C₂×D₁₅₁	—	2	1	no	—
298	C₂×D₁₅₁	—	2	1	no	—
299	C₂×D₁₅₁	—	2	1	no	—
300	C₂×D₁₅₁	—	2	1	no	—
301	C₂×D₁₅₁	—	2	1	no	—
302	C₂×D₁₅₁	—	2	1	no	—
303	C₂×D₁₅₁	—	2	1	no	—
304	C₂×D₁₅₁	—	2	1	no	—
305	C₂×D₁₅₁	—	2	1	no	—
306	C₂×D₁₅₁	—	2	1	no	—
307	C₂×D₁₅₁	—	4	4	no	—
308	C₂×D₁₅₁	2₋¹⁺⁴	1	2	yes	—
309	C₄×C₁₅₁	—	2	1	no	—
310	C₄×C₁₅₁	—	2	2	no	—
311	C₄×C₁₅₁	—	2	1	no	—
312	C₄×C₁₅₁	—	2	1	no	—
313	C₄×C₁₅₁	—	2	1	no	—
314	C₄×C₁₅₁	—	2	2	no	—
315	C₄×C₁₅₁	—	2	2	no	—
316	C₄×C₁₅₁	—	2	1	no	—
317	C₄×C₁₅₁	H(5,𝔽₂)	1	2	yes	—
318	Dic₁₅₁	—	2	1	no	—
319	Dic₁₅₁	—	2	1	no	—
320	Dic₁₅₁	—	2	1	no	—
321	Dic₁₅₁	—	2	1	no	—
322	Dic₁₅₁	—	2	2	no	—
323	Dic₁₅₁	—	2	2	no	—
324	Dic₁₅₁	—	2	2	no	—
325	Dic₁₅₁	—	2	2	no	—
326	C₂×C₁₅₁	—	4	1	no	—
327	C₂×C₁₅₁	—	4	2	no	—
328	C₂×C₁₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
329	C₂×C₁₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
330	C₂×C₁₅₁	#585	1	1	yes	characteristic
331	D₁₅₁	—	2	2	no	—
332	D₁₅₁	—	4	1	no	—
333	D₁₅₁	—	4	1	no	—
334	D₁₅₁	—	4	1	no	—
335	C₁₅₁	#3541	1	1	yes	characteristic, complemented, Sylow
336	#3541	—	151	1	no	maximal, Sylow
337	#563	—	151	2	no	—
338	#562	—	151	2	no	—
339	#556	—	151	1	no	—
340	#554	—	151	1	no	—
341	#554	—	151	2	no	—
342	#553	—	151	2	no	—
343	#553	—	151	1	no	—
344	#552	—	151	1	no	—
345	D₄×Q₈	—	151	1	no	—
346	#548	—	151	1	no	—
347	#548	—	151	1	no	—
348	#547	—	151	1	no	—
349	#542	—	151	2	no	—
350	#542	D₁₅₁	1	1	yes	characteristic, complemented
351	#541	—	151	1	no	—
352	#539	—	151	2	no	—
353	#538	—	151	2	no	—
354	#538	—	151	2	no	—
355	#537	—	151	1	no	—
356	#536	—	151	1	no	—
357	#525	—	151	1	no	—
358	#525	—	151	1	no	—
359	C₂×C₂²⋊Q₈	—	151	1	no	—
360	C₂×#41	—	151	1	no	—
361	C₂×#41	—	151	1	no	—
362	C₂×#41	—	151	1	no	—
363	C₂²×Q₈	—	151	1	no	—
364	C₂²×Q₈	—	151	1	no	—
365	C₂³×C₄	—	151	1	no	—
366	C₄⋊Q₈	—	151	2	no	—
367	C₄⋊Q₈	—	151	1	no	—
368	C₄⋊Q₈	—	151	2	no	—
369	C₄⋊Q₈	C₂×D₁₅₁	1	1	yes	characteristic, complemented
370	#126	—	151	2	no	—
371	#126	—	151	2	no	—
372	#126	—	151	2	no	—
373	#126	—	151	2	no	—
374	#126	—	151	2	no	—
375	#126	—	151	2	no	—
376	#126	C₂×D₁₅₁	1	2	yes	complemented
377	#125	—	151	2	no	—
378	#125	—	151	2	no	—
379	#125	—	151	2	no	—
380	#125	—	151	2	no	—
381	#125	—	151	1	no	—
382	#124	—	151	2	no	—
383	#124	—	151	2	no	—
384	#124	—	151	2	no	—
385	#124	—	151	2	no	—
386	#124	C₂×D₁₅₁	1	2	yes	—
387	#124	C₂×D₁₅₁	1	1	yes	characteristic, complemented
388	#123	—	151	2	no	—
389	#123	—	151	2	no	—
390	#123	—	151	2	no	—
391	#123	—	151	1	no	—
392	#123	—	151	1	no	—
393	#123	—	151	2	no	—
394	#123	—	151	2	no	—
395	#123	—	151	2	no	—
396	#123	—	151	2	no	—
397	#123	C₂×D₁₅₁	1	2	yes	—
398	C₂²⋊Q₈	—	151	1	no	—
399	C₂²⋊Q₈	—	151	1	no	—
400	C₂²⋊Q₈	—	151	2	no	—
401	C₂²⋊Q₈	—	151	2	no	—
402	C₂²⋊Q₈	—	151	1	no	—
403	C₂²⋊Q₈	—	151	1	no	—
404	C₂²⋊Q₈	—	151	1	no	—
405	C₂²⋊Q₈	—	151	2	no	—
406	C₂²⋊Q₈	—	151	1	no	—
407	C₂²⋊Q₈	—	151	1	no	—
408	C₂²⋊Q₈	—	151	1	no	—
409	C₂²⋊Q₈	—	151	1	no	—
410	C₂²⋊Q₈	—	151	1	no	—
411	C₂²⋊Q₈	—	151	2	no	—
412	C₂²⋊Q₈	—	151	2	no	—
413	C₂²⋊Q₈	—	151	2	no	—
414	C₂²⋊Q₈	—	151	2	no	—
415	C₂²⋊Q₈	—	151	2	no	—
416	C₂²⋊Q₈	—	151	2	no	—
417	C₂²⋊Q₈	C₂×D₁₅₁	1	1	yes	characteristic
418	C₂²⋊Q₈	C₂×D₁₅₁	1	2	yes	complemented
419	#121	—	151	1	no	—
420	#121	—	151	2	no	—
421	#121	—	151	2	no	—
422	#121	—	151	1	no	—
423	#121	—	151	2	no	—
424	#121	—	151	1	no	—
425	#121	—	151	1	no	—
426	#121	—	151	2	no	—
427	#121	—	151	2	no	—
428	#121	—	151	2	no	—
429	#121	—	151	2	no	—
430	#121	C₂×D₁₅₁	1	1	yes	characteristic
431	#120	—	151	2	no	—
432	#120	—	151	1	no	—
433	#120	—	151	1	no	—
434	C₄×Q₈	—	151	2	no	—
435	C₄×Q₈	—	151	1	no	—
436	C₄×Q₈	—	151	1	no	—
437	C₄×Q₈	C₂×D₁₅₁	1	1	yes	characteristic, complemented
438	C₄×D₄	—	151	2	no	—
439	C₄×D₄	—	151	2	no	—
440	C₄×D₄	—	151	2	no	—
441	C₄×D₄	—	151	2	no	—
442	C₄×D₄	—	151	2	no	—
443	C₄×D₄	—	151	2	no	—
444	C₄×D₄	—	151	1	no	—
445	C₄×D₄	—	151	1	no	—
446	C₄×D₄	—	151	1	no	—
447	C₄×D₄	—	151	1	no	—
448	C₄×D₄	—	151	2	no	—
449	C₄×D₄	C₂×D₁₅₁	1	1	yes	characteristic, complemented
450	#117	—	151	1	no	—
451	#117	—	151	1	no	—
452	#117	—	151	2	no	—
453	#117	C₂×D₁₅₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	—	151	2	no	—
455	C₂×C₄⋊C₄	—	151	2	no	—
456	C₂×C₄⋊C₄	—	151	1	no	—
457	C₂×C₄⋊C₄	—	151	1	no	—
458	C₂×C₂²⋊C₄	—	151	2	no	—
459	C₂⁴	—	151	1	no	—
460	#41	—	604	2	no	—
461	#41	—	604	2	no	—
462	#41	—	604	2	no	—
463	C₂×Q₈	—	604	2	no	—
464	C₂×Q₈	—	604	2	no	—
465	C₂×Q₈	—	151	1	no	—
466	C₂×Q₈	—	151	1	no	—
467	C₂×Q₈	—	151	2	no	—
468	C₂×Q₈	—	151	1	no	—
469	C₂×Q₈	—	151	2	no	—
470	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₁₅₁	1	2	yes	—
472	C₂×D₄	—	151	2	no	—
473	C₂×D₄	—	151	2	no	—
474	C₂×D₄	—	151	1	no	—
475	C₂×D₄	—	151	2	no	—
476	C₂×D₄	—	151	1	no	—
477	C₂×D₄	—	151	2	no	—
478	C₂×D₄	—	151	1	no	—
479	C₂×D₄	—	151	1	no	—
480	C₂×D₄	—	151	1	no	—
481	C₂×D₄	—	151	1	no	—
482	C₂×D₄	—	151	1	no	—
483	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₁₅₁	1	2	yes	—
485	C₂²×C₄	—	604	2	no	—
486	C₂²×C₄	—	151	1	no	—
487	C₂²×C₄	—	151	1	no	—
488	C₂²×C₄	—	151	1	no	—
489	C₂²×C₄	—	151	1	no	—
490	C₂²×C₄	—	151	2	no	—
491	C₂²×C₄	—	151	2	no	—
492	C₂²×C₄	—	151	1	no	—
493	C₂²×C₄	—	151	2	no	—
494	C₂²×C₄	—	151	2	no	—
495	C₂²×C₄	—	151	1	no	—
496	C₂²×C₄	—	151	2	no	—
497	C₂²×C₄	—	151	2	no	—
498	C₂²×C₄	—	151	1	no	—
499	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
501	C₄⋊C₄	—	151	2	no	—
502	C₄⋊C₄	—	151	2	no	—
503	C₄⋊C₄	—	151	2	no	—
504	C₄⋊C₄	—	151	2	no	—
505	C₄⋊C₄	—	151	2	no	—
506	C₄⋊C₄	—	151	2	no	—
507	C₄⋊C₄	—	151	2	no	—
508	C₄⋊C₄	—	151	2	no	—
509	C₄⋊C₄	—	151	2	no	—
510	C₄⋊C₄	—	151	2	no	—
511	C₄⋊C₄	—	151	1	no	—
512	C₄⋊C₄	—	151	1	no	—
513	C₄⋊C₄	—	151	2	no	—
514	C₄⋊C₄	—	151	2	no	—
515	C₄⋊C₄	—	151	2	no	—
516	C₄⋊C₄	—	151	1	no	—
517	C₄⋊C₄	—	151	1	no	—
518	C₄⋊C₄	—	151	1	no	—
519	C₄⋊C₄	—	151	2	no	—
520	C₄⋊C₄	—	151	1	no	—
521	C₄⋊C₄	—	151	2	no	—
522	C₄⋊C₄	—	151	2	no	—
523	C₄⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₅₁	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₅₁	1	2	yes	—
529	C₄⋊C₄	C₂²×D₁₅₁	1	2	yes	—
530	C₂²⋊C₄	—	151	2	no	—
531	C₂²⋊C₄	—	151	2	no	—
532	C₂²⋊C₄	—	151	2	no	—
533	C₂²⋊C₄	—	151	2	no	—
534	C₂²⋊C₄	—	151	2	no	—
535	C₂²⋊C₄	—	151	2	no	—
536	C₂²⋊C₄	—	151	1	no	—
537	C₂²⋊C₄	—	151	2	no	—
538	C₂²⋊C₄	—	151	2	no	—
539	C₂²⋊C₄	—	151	2	no	—
540	C₂²⋊C₄	—	151	1	no	—
541	C₂²⋊C₄	—	151	2	no	—
542	C₂²⋊C₄	—	151	1	no	—
543	C₂²⋊C₄	—	151	1	no	—
544	C₂²⋊C₄	—	151	1	no	—
545	C₂²⋊C₄	—	151	1	no	—
546	C₂²⋊C₄	—	151	2	no	—
547	C₂²⋊C₄	—	151	1	no	—
548	C₂²⋊C₄	—	151	2	no	—
549	C₂²⋊C₄	—	151	1	no	—
550	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
557	C₄²	—	151	2	no	—
558	C₄²	—	151	2	no	—
559	C₄²	—	151	2	no	—
560	C₄²	—	151	2	no	—
561	C₄²	C₂²×D₁₅₁	1	2	yes	—
562	C₄²	C₂²×D₁₅₁	1	1	yes	characteristic
563	C₄²	C₂²×D₁₅₁	1	1	yes	characteristic
564	C₂³	—	302	2	no	—
565	C₂³	—	604	1	no	—
566	C₂³	—	604	1	no	—
567	C₂³	—	151	1	no	—
568	C₂³	—	151	1	no	—
569	C₂³	—	151	1	no	—
570	C₂³	—	151	1	no	—
571	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
572	C₂³	C₂³×D₁₅₁	1	2	yes	—
573	Q₈	—	2	2	no	—
574	Q₈	—	4	2	no	—
575	Q₈	—	302	2	no	—
576	Q₈	—	302	2	no	—
577	Q₈	—	604	2	no	—
578	Q₈	—	604	2	no	—
579	Q₈	—	604	1	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	302	2	no	—
583	D₄	—	302	2	no	—
584	D₄	—	302	4	no	—
585	D₄	—	604	1	no	—
586	D₄	—	604	1	no	—
587	D₄	—	604	1	no	—
588	D₄	—	604	1	no	—
589	D₄	—	604	1	no	—
590	D₄	—	604	2	no	—
591	D₄	—	604	2	no	—
592	D₄	—	604	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	302	2	no	—
596	C₂×C₄	—	302	2	no	—
597	C₂×C₄	—	302	2	no	—
598	C₂×C₄	—	302	2	no	—
599	C₂×C₄	—	604	1	no	—
600	C₂×C₄	—	604	1	no	—
601	C₂×C₄	—	604	2	no	—
602	C₂×C₄	—	604	2	no	—
603	C₂×C₄	—	604	2	no	—
604	C₂×C₄	—	604	2	no	—
605	C₂×C₄	—	604	1	no	—
606	C₂×C₄	—	604	2	no	—
607	C₂×C₄	—	604	2	no	—
608	C₂×C₄	—	151	2	no	—
609	C₂×C₄	—	151	1	no	—
610	C₂×C₄	—	151	1	no	—
611	C₂×C₄	—	151	2	no	—
612	C₂×C₄	—	151	2	no	—
613	C₂×C₄	—	151	2	no	—
614	C₂×C₄	—	151	1	no	—
615	C₂×C₄	—	151	1	no	—
616	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
619	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
620	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
622	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	302	1	no	—
632	C₂²	—	302	1	no	—
633	C₂²	—	302	1	no	—
634	C₂²	—	302	1	no	—
635	C₂²	—	302	1	no	—
636	C₂²	—	302	1	no	—
637	C₂²	—	302	1	no	—
638	C₂²	—	302	1	no	—
639	C₂²	—	302	1	no	—
640	C₂²	—	302	1	no	—
641	C₂²	—	302	1	no	—
642	C₂²	—	604	4	no	—
643	C₂²	—	151	2	no	—
644	C₂²	C₂⁴×D₁₅₁	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	2	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	302	1	no	—
654	C₄	—	302	1	no	—
655	C₄	—	302	1	no	—
656	C₄	—	302	1	no	—
657	C₄	—	302	2	no	—
658	C₄	—	302	2	no	—
659	C₄	—	302	2	no	—
660	C₄	—	302	2	no	—
661	C₄	#18012785	1	2	yes	—
662	C₂	—	4	1	no	—
663	C₂	—	4	2	no	—
664	C₂	—	302	2	no	—
665	C₂	—	604	1	no	—
666	C₂	—	604	1	no	—
667	C₂	—	604	1	no	—
668	C₂	C₂×#18012785	1	1	yes	characteristic
669	C₂	2₋¹⁺⁴×D₁₅₁	1	1	yes	characteristic
670	C₂	#23753047	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₅₁
commutator, socle, cosocle	C₂²×C₁₅₁	C₂⁵
Fitting	#542×C₁₅₁	C₂
hypercenter	#542	D₁₅₁
hypocenter	C₁₅₁	#3541
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #23752964	C₂	semidirect
2. #23752958	C₂	semidirect
3. #23752936	C₂	semidirect
4. #23752923	C₂	semidirect
5. #23752920	C₂	semidirect
6. #23752913	C₂	semidirect
7. #23752912	C₂	semidirect
8. #23752903	C₂	semidirect
9. Q₈×D₆₀₄	C₂	semidirect
10. #23752870	C₂	semidirect
11. #23752870	C₂	semidirect
12. #23752866	C₂	semidirect
13. #23752831	C₂	semidirect
14. #23752824	C₂	semidirect
15. #23752806	C₂	semidirect
16. #23752798	C₂	semidirect
17. #23752796	C₂	semidirect
18. #23752791	C₂	semidirect
19. #23752785	C₂	semidirect
20. #23752724	C₂	semidirect
21. #23752722	C₂	semidirect
22. C₂²⋊Q₈×D₁₅₁	C₂	semidirect
23. #542×C₁₅₁	C₂	semidirect
26. C₂×#14559003	C₂²	semidirect
28. C₂×Q₈×D₁₅₁	C₂²	semidirect
30. #18012739	C₂²	semidirect
31. #18012739	C₂²	semidirect
32. #18012738	C₂²	semidirect
34. #18012734	C₂²	semidirect
38. #18012732	C₂²	semidirect
39. #18012731	C₂²	semidirect
40. #18012730	C₂²	semidirect
41. #18012729	C₂²	semidirect
42. #18012729	C₂²	semidirect
43. #18012729	C₂²	semidirect
47. #18012725	C₂²	semidirect
49. #18012724	C₂²	semidirect
53. #18012723	C₂²	semidirect
54. #18012722	C₂²	semidirect
62. #18012719	C₂²	semidirect
63. #18012719	C₂²	semidirect
64. #18012719	C₂²	semidirect
69. #18012716	C₂²	semidirect
70. #18012716	C₂²	semidirect
71. #18012716	C₂²	semidirect
74. #18012715	C₂²	semidirect
75. #18012715	C₂²	semidirect
82. #18012712	C₂²	semidirect
86. #18012710	C₂²	semidirect
90. Q₈×Dic₁₅₁	C₂²	semidirect
91. C₄×Dic₃₀₂	C₂²	semidirect
92. C₄×Dic₃₀₂	C₂²	semidirect
103. (C₂²⋊D₁₅₁)⋊C₄	C₂²	semidirect
105. #18012697	C₂²	semidirect
106. #18012696	C₂²	semidirect
107. C₂×C₄⋊Dic₁₅₁	C₂²	semidirect
110. C₄⋊C₄×D₁₅₁	C₂²	semidirect
112. C₄⋊Q₈×C₁₅₁	C₂²	semidirect
113. #126×C₁₅₁	C₂²	semidirect
115. #124×C₁₅₁	C₂²	semidirect
118. C₂²⋊Q₈×C₁₅₁	C₂²	semidirect
120. C₄×Q₈×C₁₅₁	C₂²	semidirect
121. C₄×D₄×C₁₅₁	C₂²	semidirect
335. C₁₅₁	#3541	semidirect
350. #542	D₁₅₁	semidirect
369. C₄⋊Q₈	C₂×D₁₅₁	semidirect
376. #126	C₂×D₁₅₁	semidirect
387. #124	C₂×D₁₅₁	semidirect
418. C₂²⋊Q₈	C₂×D₁₅₁	semidirect
437. C₄×Q₈	C₂×D₁₅₁	semidirect
449. C₄×D₄	C₂×D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#23752964	2
#23752958	2
#23752936	2
#23752923	2
#23752920	2
#23752913	2
#23752912	2
#23752903	2
Q₈×D₆₀₄	2
#23752870	2
#23752866	2
#23752831	2
#23752824	2
#23752806	2
#23752798	2
#23752796	2
#23752791	2
#23752785	2
#23752724	2
#23752722	2
C₂²⋊Q₈×D₁₅₁	2
#542×C₁₅₁	2
#3541	151