Subgroups — #34083389

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	#23752963	C₂	1	2	yes	maximal, complemented
2	#23752956	C₂	1	2	yes	maximal, complemented
3	#23752935	C₂	1	1	yes	maximal, characteristic, complemented
4	#23752921	C₂	1	2	yes	maximal, complemented
5	#23752919	C₂	1	1	yes	maximal, characteristic, complemented
6	#23752914	C₂	1	1	yes	maximal, characteristic, complemented
7	#23752905	C₂	1	2	yes	maximal, complemented
8	#23752904	C₂	1	1	yes	maximal, characteristic, complemented
9	Q₈×C₂²⋊D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#23752870	C₂	1	1	yes	maximal, characteristic, complemented
11	#23752861	C₂	1	1	yes	maximal, characteristic, complemented
12	#23752831	C₂	1	1	yes	maximal, characteristic, complemented
13	#23752826	C₂	1	2	yes	maximal, complemented
14	#23752820	C₂	1	1	yes	maximal, characteristic, complemented
15	#23752811	C₂	1	2	yes	maximal, complemented
16	#23752799	C₂	1	2	yes	maximal, complemented
17	#23752795	C₂	1	2	yes	maximal, complemented
18	#23752790	C₂	1	1	yes	maximal, characteristic, complemented
19	#23752785	C₂	1	1	yes	maximal, characteristic, complemented
20	#23752722	C₂	1	1	yes	maximal, characteristic, complemented
21	#23752721	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#18012715	C₂	1	1	yes	maximal, characteristic, complemented
23	#548×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×Q₈×D₁₅₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic
28	#18012739	C₂²	1	1	yes	characteristic, complemented
29	#18012738	C₂²	1	2	yes	complemented
30	#18012737	C₂²	1	2	yes	complemented
31	#18012737	C₂²	1	1	yes	characteristic, complemented
32	#18012734	C₂²	1	2	yes	—
33	#18012734	C₂²	1	2	yes	—
34	#18012734	C₂²	1	2	yes	—
35	#18012734	C₂²	1	2	yes	complemented
36	#18012733	C₂²	1	2	yes	—
37	#18012732	C₂²	1	2	yes	complemented
38	#18012732	C₂²	1	2	yes	complemented
39	#18012731	C₂²	1	2	yes	complemented
40	#18012730	C₂²	1	2	yes	complemented
41	#18012730	C₂²	1	2	yes	complemented
42	#18012730	C₂²	1	1	yes	characteristic, complemented
43	#18012729	C₂²	1	2	yes	complemented
44	#18012727	C₂²	1	2	yes	—
45	#18012725	C₂²	1	2	yes	—
46	#18012725	C₂²	1	2	yes	—
47	#18012725	C₂²	1	2	yes	—
48	#18012724	C₂²	1	1	yes	characteristic
49	#18012724	C₂²	1	2	yes	—
50	#18012723	C₂²	1	2	yes	—
51	#18012723	C₂²	1	2	yes	—
52	#18012723	C₂²	1	2	yes	complemented
53	#18012722	C₂²	1	2	yes	—
54	#18012721	C₂²	1	2	yes	—
55	#18012721	C₂²	1	1	yes	characteristic
56	#18012721	C₂²	1	2	yes	complemented
57	#18012720	C₂²	1	2	yes	complemented
58	#18012719	C₂²	1	1	yes	characteristic
59	#18012718	C₂²	1	1	yes	characteristic
60	#18012718	C₂²	1	2	yes	—
61	#18012718	C₂²	1	2	yes	complemented
62	#18012718	C₂²	1	1	yes	characteristic, complemented
63	#18012717	C₂²	1	1	yes	characteristic
64	#18012716	C₂²	1	1	yes	characteristic
65	#18012716	C₂²	1	2	yes	—
66	#18012716	C₂²	1	2	yes	complemented
67	#18012716	C₂²	1	2	yes	complemented
68	#18012716	C₂²	1	2	yes	complemented
69	#18012715	C₂²	1	2	yes	—
70	#18012715	C₂²	1	1	yes	characteristic
71	#18012715	C₂²	1	1	yes	characteristic
72	#18012715	C₂²	1	2	yes	—
73	#18012715	C₂²	1	1	yes	characteristic
74	#18012715	C₂²	1	1	yes	characteristic
75	#18012715	C₂²	1	1	yes	characteristic, complemented
76	#18012715	C₂²	1	2	yes	complemented
77	#18012713	C₂²	1	2	yes	—
78	#18012712	C₂²	1	1	yes	characteristic
79	#18012712	C₂²	1	2	yes	—
80	#18012711	C₂²	1	1	yes	characteristic
81	#18012711	C₂²	1	2	yes	—
82	#18012711	C₂²	1	2	yes	—
83	#18012711	C₂²	1	2	yes	—
84	#18012711	C₂²	1	2	yes	complemented
85	#18012710	C₂²	1	1	yes	characteristic
86	#18012710	C₂²	1	1	yes	characteristic, complemented
87	#18012709	C₂²	1	1	yes	characteristic
88	#18012707	C₂²	1	1	yes	characteristic
89	#18012707	C₂²	1	2	yes	—
90	Q₈×Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
91	C₄×Dic₃₀₂	C₂²	1	1	yes	characteristic, complemented
92	C₄×Dic₃₀₂	C₂²	1	2	yes	complemented
93	C₄×D₆₀₄	C₂²	1	1	yes	characteristic
94	D₄×Dic₁₅₁	C₂²	1	2	yes	—
95	D₄×Dic₁₅₁	C₂²	1	2	yes	—
96	D₄×Dic₁₅₁	C₂²	1	2	yes	—
97	D₄×Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊D₁₅₁	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₁₅₁	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊D₁₅₁	C₂²	1	2	yes	—
101	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	2	yes	—
102	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	2	yes	complemented
103	#18012697	C₂²	1	1	yes	characteristic
104	#18012697	C₂²	1	1	yes	characteristic, complemented
105	#18012696	C₂²	1	1	yes	characteristic
106	#18012695	C₂²	1	2	yes	complemented
107	C₂×C₄⋊Dic₁₅₁	C₂²	1	1	yes	characteristic
108	C₂×C₄⋊Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
109	C₂×Dic₁₅₁⋊C₄	C₂²	1	2	yes	—
110	C₂×Dic₁₅₁⋊C₄	C₂²	1	2	yes	complemented
111	C₂×(C₂×D₁₅₁)⋊C₄	C₂²	1	2	yes	—
112	C₂×#41×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
113	C₂²×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
114	#124×C₁₅₁	C₂²	1	2	yes	complemented
115	#124×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₁₅₁	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
118	#121×C₁₅₁	C₂²	1	1	yes	characteristic
119	#121×C₁₅₁	C₂²	1	2	yes	—
120	C₄×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
122	C₄×D₄×C₁₅₁	C₂²	1	2	yes	—
123	C₂³×D₁₅₁	C₂³	1	1	yes	characteristic
124	#14559004	—	4	2	no	—
125	#14559003	—	4	2	no	—
126	C₂×Dic₃₀₂	C₂³	1	1	yes	characteristic
127	C₂×Dic₃₀₂	C₂³	1	2	yes	—
128	C₂×Dic₃₀₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₃₀₂	C₂³	1	2	yes	—
130	Q₈×D₁₅₁	—	4	2	no	—
131	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
132	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₅₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₅₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₅₁	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₅₁	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
141	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
142	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
143	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
144	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
145	C₂×C₄×D₁₅₁	—	4	2	no	—
146	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
151	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
155	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
157	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
158	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
159	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
160	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
162	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
163	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
164	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
165	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
166	Dic₁₅₁⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
168	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
169	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
170	Dic₁₅₁⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₁₅₁⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
173	Dic₁₅₁⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
175	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
176	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₅₁	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	(C₂×D₁₅₁)⋊C₄	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	2	yes	—
188	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
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	C₄×Dic₁₅₁	C₂³	1	2	yes	—
199	C₄×Dic₁₅₁	C₂³	1	2	yes	—
200	C₄×Dic₁₅₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₅₁	C₂³	1	2	yes	—
202	C₄×Dic₁₅₁	C₂³	1	2	yes	—
203	#41×C₁₅₁	—	4	2	no	—
204	C₂×Q₈×C₁₅₁	—	4	2	no	—
205	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
207	C₂×Q₈×C₁₅₁	C₂³	1	2	yes	—
208	C₂×D₄×C₁₅₁	C₂³	1	2	yes	—
209	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₁₅₁	C₂³	1	2	yes	—
212	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
215	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
219	C₄⋊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	2	yes	—
223	C₂²⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
226	C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
227	C₄²×C₁₅₁	C₂³	1	2	yes	—
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	Dic₃₀₂	—	2	2	no	—
235	Dic₃₀₂	—	4	2	no	—
236	Dic₃₀₂	—	4	2	no	—
237	Dic₃₀₂	—	4	1	no	—
238	D₆₀₄	—	4	1	no	—
239	D₆₀₄	—	4	1	no	—
240	C₂²⋊D₁₅₁	—	2	2	no	—
241	C₂²⋊D₁₅₁	—	4	2	no	—
242	C₂²⋊D₁₅₁	—	4	1	no	—
243	C₂²⋊D₁₅₁	—	4	2	no	—
244	C₂²⋊D₁₅₁	—	4	2	no	—
245	C₂²⋊D₁₅₁	—	4	1	no	—
246	C₂²⋊D₁₅₁	—	4	1	no	—
247	C₂×Dic₁₅₁	—	4	1	no	—
248	C₂×Dic₁₅₁	—	4	2	no	—
249	C₂×Dic₁₅₁	—	4	2	no	—
250	C₂×Dic₁₅₁	—	4	2	no	—
251	C₂×Dic₁₅₁	—	4	2	no	—
252	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
254	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
257	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
259	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
260	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
261	C₄×D₁₅₁	—	2	2	no	—
262	C₄×D₁₅₁	—	2	2	no	—
263	C₄×D₁₅₁	—	2	2	no	—
264	C₄×D₁₅₁	—	4	1	no	—
265	C₄×D₁₅₁	—	4	1	no	—
266	C₄×D₁₅₁	—	4	2	no	—
267	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
268	C₂³×C₁₅₁	C₂⁴	1	2	yes	—
269	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
270	Q₈×C₁₅₁	—	2	2	no	—
271	Q₈×C₁₅₁	—	2	2	no	—
272	Q₈×C₁₅₁	—	4	2	no	—
273	D₄×C₁₅₁	—	2	4	no	—
274	D₄×C₁₅₁	—	2	2	no	—
275	D₄×C₁₅₁	—	2	2	no	—
276	D₄×C₁₅₁	—	4	2	no	—
277	C₂×C₄×C₁₅₁	—	2	2	no	—
278	C₂×C₄×C₁₅₁	—	2	2	no	—
279	C₂×C₄×C₁₅₁	—	4	2	no	—
280	C₂×C₄×C₁₅₁	—	4	2	no	—
281	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
282	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
283	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
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	1	no	—
291	C₂²×C₁₅₁	—	2	1	no	—
292	C₂²×C₁₅₁	—	2	2	no	—
293	C₂²×C₁₅₁	—	2	1	no	—
294	C₂²×C₁₅₁	—	2	2	no	—
295	C₂²×C₁₅₁	—	2	1	no	—
296	C₂²×C₁₅₁	—	2	2	no	—
297	C₂²×C₁₅₁	2₋¹⁺⁴	1	2	yes	—
298	C₂²×C₁₅₁	C₂⁵	1	1	yes	characteristic
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	—	2	1	no	—
308	C₂×D₁₅₁	—	4	4	no	—
309	C₄×C₁₅₁	—	2	1	no	—
310	C₄×C₁₅₁	—	2	1	no	—
311	C₄×C₁₅₁	—	2	2	no	—
312	C₄×C₁₅₁	—	2	2	no	—
313	C₄×C₁₅₁	—	2	2	no	—
314	C₄×C₁₅₁	—	2	1	no	—
315	C₄×C₁₅₁	—	2	1	no	—
316	C₄×C₁₅₁	H(5,𝔽₂)	1	2	yes	—
317	Dic₁₅₁	—	2	1	no	—
318	Dic₁₅₁	—	2	1	no	—
319	Dic₁₅₁	—	2	1	no	—
320	Dic₁₅₁	—	2	2	no	—
321	Dic₁₅₁	—	2	1	no	—
322	Dic₁₅₁	—	2	2	no	—
323	Dic₁₅₁	—	2	1	no	—
324	Dic₁₅₁	—	2	2	no	—
325	Dic₁₅₁	—	2	2	no	—
326	C₂×C₁₅₁	—	2	2	no	—
327	C₂×C₁₅₁	—	4	1	no	—
328	C₂×C₁₅₁	—	4	2	no	—
329	C₂×C₁₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₁₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
331	C₂×C₁₅₁	#585	1	1	yes	characteristic
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	D₁₅₁	1	1	yes	characteristic, complemented
348	#547	—	151	1	no	—
349	#542	—	151	2	no	—
350	#542	—	151	1	no	—
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	C₂×D₁₅₁	1	1	yes	characteristic, complemented
363	C₂²×Q₈	—	151	1	no	—
364	C₂²×Q₈	C₂×D₁₅₁	1	1	yes	characteristic
365	C₂³×C₄	—	151	1	no	—
366	C₄⋊Q₈	—	151	1	no	—
367	C₄⋊Q₈	—	151	2	no	—
368	C₄⋊Q₈	—	151	2	no	—
369	C₄⋊Q₈	—	151	1	no	—
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	—	151	2	no	—
377	#125	—	151	2	no	—
378	#125	—	151	2	no	—
379	#125	—	151	1	no	—
380	#125	—	151	2	no	—
381	#125	—	151	2	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	1	yes	characteristic, complemented
387	#124	C₂×D₁₅₁	1	2	yes	complemented
388	#123	—	151	2	no	—
389	#123	—	151	2	no	—
390	#123	—	151	1	no	—
391	#123	—	151	2	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	—	151	2	no	—
398	C₂²⋊Q₈	—	151	1	no	—
399	C₂²⋊Q₈	—	151	1	no	—
400	C₂²⋊Q₈	—	151	2	no	—
401	C₂²⋊Q₈	—	151	1	no	—
402	C₂²⋊Q₈	—	151	1	no	—
403	C₂²⋊Q₈	—	151	2	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	2	no	—
409	C₂²⋊Q₈	—	151	2	no	—
410	C₂²⋊Q₈	—	151	1	no	—
411	C₂²⋊Q₈	—	151	1	no	—
412	C₂²⋊Q₈	—	151	1	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, complemented
418	C₂²⋊Q₈	C₂×D₁₅₁	1	2	yes	complemented
419	#121	—	151	1	no	—
420	#121	—	151	1	no	—
421	#121	—	151	2	no	—
422	#121	—	151	1	no	—
423	#121	—	151	2	no	—
424	#121	—	151	2	no	—
425	#121	—	151	2	no	—
426	#121	—	151	2	no	—
427	#121	—	151	1	no	—
428	#121	—	151	2	no	—
429	#121	C₂×D₁₅₁	1	1	yes	characteristic
430	#121	C₂×D₁₅₁	1	2	yes	—
431	#120	—	151	1	no	—
432	#120	—	151	2	no	—
433	#120	—	151	1	no	—
434	C₄×Q₈	—	151	1	no	—
435	C₄×Q₈	—	151	1	no	—
436	C₄×Q₈	—	151	2	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	1	no	—
442	C₄×D₄	—	151	1	no	—
443	C₄×D₄	—	151	1	no	—
444	C₄×D₄	—	151	2	no	—
445	C₄×D₄	—	151	2	no	—
446	C₄×D₄	—	151	2	no	—
447	C₄×D₄	—	151	1	no	—
448	C₄×D₄	C₂×D₁₅₁	1	1	yes	characteristic
449	C₄×D₄	C₂×D₁₅₁	1	2	yes	—
450	#117	—	151	1	no	—
451	#117	—	151	1	no	—
452	#117	—	151	2	no	—
453	#117	—	151	1	no	—
454	C₂×C₄⋊C₄	—	151	2	no	—
455	C₂×C₄⋊C₄	—	151	1	no	—
456	C₂×C₄⋊C₄	—	151	2	no	—
457	C₂×C₄⋊C₄	—	151	1	no	—
458	C₂×C₂²⋊C₄	—	151	2	no	—
459	C₂⁴	—	151	1	no	—
460	#41	—	4	2	no	—
461	#41	—	604	2	no	—
462	#41	—	604	2	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	604	2	no	—
465	C₂×Q₈	—	151	1	no	—
466	C₂×Q₈	—	151	2	no	—
467	C₂×Q₈	—	151	1	no	—
468	C₂×Q₈	—	151	2	no	—
469	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
470	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₁₅₁	1	2	yes	—
472	C₂×D₄	—	151	1	no	—
473	C₂×D₄	—	151	1	no	—
474	C₂×D₄	—	151	2	no	—
475	C₂×D₄	—	151	2	no	—
476	C₂×D₄	—	151	2	no	—
477	C₂×D₄	—	151	1	no	—
478	C₂×D₄	—	151	1	no	—
479	C₂×D₄	—	151	1	no	—
480	C₂×D₄	—	151	1	no	—
481	C₂×D₄	C₂²×D₁₅₁	1	2	yes	—
482	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
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	2	no	—
490	C₂²×C₄	—	151	1	no	—
491	C₂²×C₄	—	151	2	no	—
492	C₂²×C₄	—	151	2	no	—
493	C₂²×C₄	—	151	2	no	—
494	C₂²×C₄	—	151	2	no	—
495	C₂²×C₄	—	151	1	no	—
496	C₂²×C₄	—	151	1	no	—
497	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
500	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
501	C₄⋊C₄	—	151	1	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	1	no	—
509	C₄⋊C₄	—	151	1	no	—
510	C₄⋊C₄	—	151	2	no	—
511	C₄⋊C₄	—	151	2	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	2	no	—
521	C₄⋊C₄	—	151	1	no	—
522	C₄⋊C₄	—	151	2	no	—
523	C₄⋊C₄	—	151	2	no	—
524	C₄⋊C₄	—	151	2	no	—
525	C₄⋊C₄	—	151	2	no	—
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	1	no	—
531	C₂²⋊C₄	—	151	2	no	—
532	C₂²⋊C₄	—	151	1	no	—
533	C₂²⋊C₄	—	151	2	no	—
534	C₂²⋊C₄	—	151	2	no	—
535	C₂²⋊C₄	—	151	2	no	—
536	C₂²⋊C₄	—	151	2	no	—
537	C₂²⋊C₄	—	151	2	no	—
538	C₂²⋊C₄	—	151	2	no	—
539	C₂²⋊C₄	—	151	2	no	—
540	C₂²⋊C₄	—	151	2	no	—
541	C₂²⋊C₄	—	151	1	no	—
542	C₂²⋊C₄	—	151	2	no	—
543	C₂²⋊C₄	—	151	1	no	—
544	C₂²⋊C₄	—	151	2	no	—
545	C₂²⋊C₄	—	151	1	no	—
546	C₂²⋊C₄	—	151	1	no	—
547	C₂²⋊C₄	—	151	2	no	—
548	C₂²⋊C₄	—	151	1	no	—
549	C₂²⋊C₄	—	151	2	no	—
550	C₂²⋊C₄	—	151	1	no	—
551	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
557	C₄²	—	151	2	no	—
558	C₄²	—	151	1	no	—
559	C₄²	—	151	2	no	—
560	C₄²	—	151	2	no	—
561	C₄²	—	151	2	no	—
562	C₄²	C₂²×D₁₅₁	1	1	yes	characteristic
563	C₄²	C₂²×D₁₅₁	1	2	yes	—
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	C₂³×D₁₅₁	1	1	yes	characteristic
571	C₂³	C₂³×D₁₅₁	1	2	yes	—
572	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	2	no	—
576	Q₈	—	302	2	no	—
577	Q₈	—	604	2	no	—
578	Q₈	—	604	1	no	—
579	Q₈	—	604	2	no	—
580	D₄	—	2	4	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	302	2	no	—
585	D₄	—	604	1	no	—
586	D₄	—	604	1	no	—
587	D₄	—	604	1	no	—
588	D₄	—	604	1	no	—
589	D₄	—	604	2	no	—
590	D₄	—	604	1	no	—
591	D₄	—	604	2	no	—
592	D₄	—	604	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	302	2	no	—
598	C₂×C₄	—	302	2	no	—
599	C₂×C₄	—	302	2	no	—
600	C₂×C₄	—	604	1	no	—
601	C₂×C₄	—	604	1	no	—
602	C₂×C₄	—	604	2	no	—
603	C₂×C₄	—	604	1	no	—
604	C₂×C₄	—	604	2	no	—
605	C₂×C₄	—	604	2	no	—
606	C₂×C₄	—	604	2	no	—
607	C₂×C₄	—	604	2	no	—
608	C₂×C₄	—	151	1	no	—
609	C₂×C₄	—	151	2	no	—
610	C₂×C₄	—	151	1	no	—
611	C₂×C₄	—	151	1	no	—
612	C₂×C₄	—	151	2	no	—
613	C₂×C₄	—	151	1	no	—
614	C₂×C₄	—	151	2	no	—
615	C₂×C₄	—	151	2	no	—
616	C₂×C₄	—	151	1	no	—
617	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
618	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
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	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	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	#18012786	1	2	yes	—
644	C₂²	C₂⁴×D₁₅₁	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	302	1	no	—
653	C₄	—	302	1	no	—
654	C₄	—	302	1	no	—
655	C₄	—	302	2	no	—
656	C₄	—	302	1	no	—
657	C₄	—	302	2	no	—
658	C₄	—	302	1	no	—
659	C₄	—	302	2	no	—
660	C₄	—	302	2	no	—
661	C₄	#18012784	1	2	yes	—
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	2	no	—
665	C₂	—	604	1	no	—
666	C₂	—	604	1	no	—
667	C₂	—	604	1	no	—
668	C₂	C₂×#18012784	1	1	yes	characteristic
669	C₂	C₂×#18012786	1	1	yes	characteristic
670	C₂	#23753049	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₅₁
commutator, socle, cosocle	C₂²×C₁₅₁	C₂⁵
Fitting	#548×C₁₅₁	C₂
hypercenter	#548	D₁₅₁
hypocenter	C₁₅₁	#3541
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. #23752963	C₂	semidirect
2. #23752956	C₂	semidirect
3. #23752935	C₂	semidirect
4. #23752921	C₂	semidirect
5. #23752919	C₂	semidirect
6. #23752914	C₂	semidirect
7. #23752905	C₂	semidirect
8. #23752904	C₂	semidirect
9. Q₈×C₂²⋊D₁₅₁	C₂	semidirect
10. #23752870	C₂	semidirect
11. #23752861	C₂	semidirect
12. #23752831	C₂	semidirect
13. #23752826	C₂	semidirect
14. #23752820	C₂	semidirect
15. #23752811	C₂	semidirect
16. #23752799	C₂	semidirect
17. #23752795	C₂	semidirect
18. #23752790	C₂	semidirect
19. #23752785	C₂	semidirect
20. #23752722	C₂	semidirect
21. #23752721	C₂	semidirect
22. C₂×#18012715	C₂	semidirect
23. #548×C₁₅₁	C₂	semidirect
26. C₂×Q₈×D₁₅₁	C₂²	semidirect
28. #18012739	C₂²	semidirect
29. #18012738	C₂²	semidirect
30. #18012737	C₂²	semidirect
31. #18012737	C₂²	semidirect
35. #18012734	C₂²	semidirect
37. #18012732	C₂²	semidirect
38. #18012732	C₂²	semidirect
39. #18012731	C₂²	semidirect
40. #18012730	C₂²	semidirect
41. #18012730	C₂²	semidirect
42. #18012730	C₂²	semidirect
43. #18012729	C₂²	semidirect
52. #18012723	C₂²	semidirect
56. #18012721	C₂²	semidirect
57. #18012720	C₂²	semidirect
61. #18012718	C₂²	semidirect
62. #18012718	C₂²	semidirect
66. #18012716	C₂²	semidirect
67. #18012716	C₂²	semidirect
68. #18012716	C₂²	semidirect
75. #18012715	C₂²	semidirect
76. #18012715	C₂²	semidirect
84. #18012711	C₂²	semidirect
86. #18012710	C₂²	semidirect
90. Q₈×Dic₁₅₁	C₂²	semidirect
91. C₄×Dic₃₀₂	C₂²	semidirect
92. C₄×Dic₃₀₂	C₂²	semidirect
97. D₄×Dic₁₅₁	C₂²	semidirect
102. (C₂²⋊D₁₅₁)⋊C₄	C₂²	semidirect
104. #18012697	C₂²	semidirect
106. #18012695	C₂²	semidirect
108. C₂×C₄⋊Dic₁₅₁	C₂²	semidirect
110. C₂×Dic₁₅₁⋊C₄	C₂²	semidirect
112. C₂×#41×C₁₅₁	C₂²	semidirect
114. #124×C₁₅₁	C₂²	semidirect
115. #124×C₁₅₁	C₂²	semidirect
116. C₂²⋊Q₈×C₁₅₁	C₂²	semidirect
117. C₂²⋊Q₈×C₁₅₁	C₂²	semidirect
120. C₄×Q₈×C₁₅₁	C₂²	semidirect
335. C₁₅₁	#3541	semidirect
347. #548	D₁₅₁	semidirect
362. C₂×#41	C₂×D₁₅₁	semidirect
386. #124	C₂×D₁₅₁	semidirect
387. #124	C₂×D₁₅₁	semidirect
417. C₂²⋊Q₈	C₂×D₁₅₁	semidirect
418. C₂²⋊Q₈	C₂×D₁₅₁	semidirect
437. C₄×Q₈	C₂×D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#23752963	2
#23752956	2
#23752935	2
#23752921	2
#23752919	2
#23752914	2
#23752905	2
#23752904	2
Q₈×C₂²⋊D₁₅₁	2
#23752870	2
#23752861	2
#23752831	2
#23752826	2
#23752820	2
#23752811	2
#23752799	2
#23752795	2
#23752790	2
#23752785	2
#23752722	2
#23752721	2
C₂×#18012715	2
#548×C₁₅₁	2
#3541	151