Subgroups — #34058642

Order 19072.

1142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750358	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750343	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750340	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750338	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750304	C₂	1	2	yes	maximal, complemented
6	#23750301	C₂	1	2	yes	maximal, complemented
7	D₄×Dic₂₉₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750284	C₂	1	2	yes	maximal, complemented
9	#23750270	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750269	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750265	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750246	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750240	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750213	C₂	1	2	yes	maximal, complemented
16	#23750208	C₂	1	2	yes	maximal, complemented
17	#23750172	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750155	C₂	1	2	yes	maximal, complemented
19	#23750153	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#18011897	C₂	1	2	yes	maximal, complemented
21	#23750097	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14558735	C₂	1	1	yes	maximal, characteristic, complemented
23	#518×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558736	C₂²	1	2	yes	complemented
25	C₂×#14558735	C₂²	1	1	yes	characteristic
26	C₂²×Dic₂₉₈	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
28	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
29	#18011911	C₂²	1	1	yes	characteristic, complemented
30	#18011910	C₂²	1	1	yes	characteristic, complemented
31	#18011910	C₂²	1	1	yes	characteristic, complemented
32	#18011907	C₂²	1	1	yes	characteristic
33	#18011906	C₂²	1	1	yes	characteristic, complemented
34	#18011906	C₂²	1	2	yes	complemented
35	#18011905	C₂²	1	2	yes	complemented
36	#18011904	C₂²	1	1	yes	characteristic, complemented
37	#18011904	C₂²	1	2	yes	complemented
38	#18011904	C₂²	1	2	yes	complemented
39	#18011901	C₂²	1	1	yes	characteristic, complemented
40	#18011899	C₂²	1	2	yes	complemented
41	#18011899	C₂²	1	1	yes	characteristic, complemented
42	#18011898	C₂²	1	1	yes	characteristic, complemented
43	#18011897	C₂²	1	1	yes	characteristic
44	#18011897	C₂²	1	2	yes	—
45	#18011897	C₂²	1	2	yes	complemented
46	#18011897	C₂²	1	2	yes	complemented
47	#18011897	C₂²	1	2	yes	complemented
48	#18011897	C₂²	1	2	yes	complemented
49	#18011897	C₂²	1	2	yes	complemented
50	#18011897	C₂²	1	2	yes	complemented
51	#18011897	C₂²	1	2	yes	complemented
52	#18011896	C₂²	1	1	yes	characteristic, complemented
53	#18011895	C₂²	1	2	yes	complemented
54	#18011894	C₂²	1	2	yes	complemented
55	#18011894	C₂²	1	2	yes	complemented
56	#18011893	C₂²	1	1	yes	characteristic, complemented
57	#18011893	C₂²	1	2	yes	complemented
58	#18011893	C₂²	1	2	yes	complemented
59	#18011892	C₂²	1	2	yes	complemented
60	#18011891	C₂²	1	1	yes	characteristic, complemented
61	#18011890	C₂²	1	2	yes	complemented
62	#18011890	C₂²	1	2	yes	complemented
63	#18011890	C₂²	1	1	yes	characteristic, complemented
64	#18011889	C₂²	1	1	yes	characteristic, complemented
65	#18011889	C₂²	1	2	yes	complemented
66	#18011888	C₂²	1	2	yes	complemented
67	#18011888	C₂²	1	2	yes	complemented
68	#18011886	C₂²	1	1	yes	characteristic, complemented
69	#18011885	C₂²	1	1	yes	characteristic
70	#18011885	C₂²	1	2	yes	complemented
71	#18011885	C₂²	1	2	yes	complemented
72	#18011884	C₂²	1	1	yes	characteristic
73	#18011884	C₂²	1	2	yes	complemented
74	#18011884	C₂²	1	2	yes	complemented
75	#18011883	C₂²	1	2	yes	—
76	#18011883	C₂²	1	2	yes	complemented
77	#18011882	C₂²	1	1	yes	characteristic
78	#18011882	C₂²	1	1	yes	characteristic, complemented
79	#18011881	C₂²	1	2	yes	complemented
80	#18011880	C₂²	1	2	yes	—
81	#18011880	C₂²	1	2	yes	complemented
82	#18011879	C₂²	1	2	yes	—
83	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
84	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
85	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
86	#18011876	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
88	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
89	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
90	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
91	#18011873	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
98	#18011871	C₂²	1	2	yes	complemented
99	#18011871	C₂²	1	2	yes	complemented
100	#18011870	C₂²	1	2	yes	complemented
101	#18011869	C₂²	1	1	yes	characteristic, complemented
102	#18011869	C₂²	1	1	yes	characteristic, complemented
103	#18011868	C₂²	1	1	yes	characteristic, complemented
104	#18011868	C₂²	1	2	yes	complemented
105	#18011867	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊Dic₁₄₉	C₂²	1	2	yes	complemented
107	C₂×#14558713	C₂²	1	2	yes	complemented
108	C₂×#14558713	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
110	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	complemented
111	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
112	C₂²×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
113	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
114	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
115	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
116	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
118	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
119	#117×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
120	#117×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	complemented
123	C₂³×D₁₄₉	C₂³	1	2	yes	—
124	#14558736	—	4	4	no	—
125	#14558735	—	2	4	no	—
126	C₂×Dic₂₉₈	—	4	4	no	—
127	C₂×Dic₂₉₈	C₂³	1	2	yes	—
128	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₉₈	C₂³	1	2	yes	—
131	C₂×Dic₂₉₈	C₂³	1	2	yes	—
132	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
133	C₂×D₅₉₆	C₂³	1	2	yes	—
134	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₄₉	—	4	4	no	—
136	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
145	D₄×D₁₄₉	—	2	4	no	—
146	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
147	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
148	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
149	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
153	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
155	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
156	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
158	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
161	#14558715	C₂³	1	1	yes	characteristic
162	#14558715	C₂³	1	2	yes	—
163	#14558715	C₂³	1	2	yes	—
164	#14558715	C₂³	1	2	yes	—
165	#14558715	C₂³	1	1	yes	characteristic
166	#14558715	C₂³	1	1	yes	characteristic
167	#14558715	C₂³	1	2	yes	—
168	#14558715	C₂³	1	1	yes	characteristic
169	#14558715	C₂³	1	2	yes	—
170	#14558715	C₂³	1	1	yes	characteristic
171	#14558715	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
181	#14558713	C₂³	1	1	yes	characteristic
182	#14558713	C₂³	1	2	yes	—
183	#14558713	C₂³	1	2	yes	—
184	#14558713	C₂³	1	1	yes	characteristic
185	#14558713	C₂³	1	1	yes	characteristic
186	#14558713	C₂³	1	2	yes	—
187	#14558713	C₂³	1	2	yes	—
188	#14558713	C₂³	1	2	yes	—
189	#14558713	C₂³	1	1	yes	characteristic
190	#14558713	C₂³	1	2	yes	—
191	#14558713	C₂³	1	2	yes	—
192	#14558713	C₂³	1	2	yes	—
193	#14558713	C₂³	1	2	yes	—
194	#14558713	C₂³	1	1	yes	characteristic
195	#14558713	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₄₉	C₂³	1	2	yes	—
198	C₄×Dic₁₄₉	C₂³	1	2	yes	—
199	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₄₉	C₂³	1	2	yes	—
203	C₄×Dic₁₄₉	C₂³	1	2	yes	—
204	C₂⁴×C₁₄₉	C₂³	1	2	yes	—
205	C₂×D₄×C₁₄₉	—	2	4	no	—
206	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
208	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
212	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
213	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
225	C₄²×C₁₄₉	C₂³	1	2	yes	—
226	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
227	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
228	C₂²×D₁₄₉	—	2	4	no	—
229	C₂²×D₁₄₉	—	4	2	no	—
230	C₂²×D₁₄₉	—	4	2	no	—
231	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
233	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
234	Dic₂₉₈	—	2	2	no	—
235	Dic₂₉₈	—	2	2	no	—
236	Dic₂₉₈	—	2	4	no	—
237	Dic₂₉₈	—	4	2	no	—
238	Dic₂₉₈	—	4	2	no	—
239	D₅₉₆	—	2	2	no	—
240	D₅₉₆	—	4	1	no	—
241	D₅₉₆	—	4	2	no	—
242	C₂²⋊D₁₄₉	—	2	4	no	—
243	C₂²⋊D₁₄₉	—	2	4	no	—
244	C₂²⋊D₁₄₉	—	2	2	no	—
245	C₂²⋊D₁₄₉	—	2	4	no	—
246	C₂²⋊D₁₄₉	—	4	2	no	—
247	C₂²⋊D₁₄₉	—	4	2	no	—
248	C₂²⋊D₁₄₉	—	4	1	no	—
249	C₂²⋊D₁₄₉	—	4	2	no	—
250	C₂²⋊D₁₄₉	—	4	2	no	—
251	C₂×Dic₁₄₉	—	2	4	no	—
252	C₂×Dic₁₄₉	—	2	4	no	—
253	C₂×Dic₁₄₉	—	4	2	no	—
254	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
257	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
261	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
262	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
263	C₄×D₁₄₉	—	2	2	no	—
264	C₄×D₁₄₉	—	2	2	no	—
265	C₄×D₁₄₉	—	2	2	no	—
266	C₄×D₁₄₉	—	4	2	no	—
267	C₄×D₁₄₉	—	4	1	no	—
268	C₄×D₁₄₉	—	4	2	no	—
269	C₂³×C₁₄₉	—	2	4	no	—
270	C₂³×C₁₄₉	—	4	2	no	—
271	C₂³×C₁₄₉	—	4	2	no	—
272	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
273	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
274	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
275	D₄×C₁₄₉	—	2	4	no	—
276	D₄×C₁₄₉	—	2	2	no	—
277	D₄×C₁₄₉	#41	1	4	yes	complemented
278	C₂×C₄×C₁₄₉	—	2	2	no	—
279	C₂×C₄×C₁₄₉	—	4	2	no	—
280	C₂×C₄×C₁₄₉	—	4	2	no	—
281	C₂×C₄×C₁₄₉	—	4	2	no	—
282	C₂×C₄×C₁₄₉	—	4	2	no	—
283	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
286	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
287	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₁₄₉	—	2	2	no	—
292	C₂²×C₁₄₉	—	2	2	no	—
293	C₂²×C₁₄₉	—	2	1	no	—
294	C₂²×C₁₄₉	—	2	2	no	—
295	C₂²×C₁₄₉	—	2	2	no	—
296	C₂²×C₁₄₉	—	2	1	no	—
297	C₂²×C₁₄₉	—	2	2	no	—
298	C₂²×C₁₄₉	—	2	1	no	—
299	C₂²×C₁₄₉	—	8	4	no	—
300	C₂²×C₁₄₉	C₂×#41	1	4	yes	—
301	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
302	C₂×D₁₄₉	—	2	1	no	—
303	C₂×D₁₄₉	—	2	1	no	—
304	C₂×D₁₄₉	—	2	2	no	—
305	C₂×D₁₄₉	—	2	1	no	—
306	C₂×D₁₄₉	—	2	2	no	—
307	C₂×D₁₄₉	—	2	1	no	—
308	C₂×D₁₄₉	—	2	1	no	—
309	C₂×D₁₄₉	—	2	2	no	—
310	C₂×D₁₄₉	—	2	1	no	—
311	C₂×D₁₄₉	—	8	4	no	—
312	C₄×C₁₄₉	—	2	1	no	—
313	C₄×C₁₄₉	—	2	1	no	—
314	C₄×C₁₄₉	—	2	2	no	—
315	C₄×C₁₄₉	—	2	1	no	—
316	C₄×C₁₄₉	—	2	1	no	—
317	C₄×C₁₄₉	—	2	2	no	—
318	C₄×C₁₄₉	—	2	1	no	—
319	C₄×C₁₄₉	C₂×#41	1	2	yes	—
320	Dic₁₄₉	—	2	1	no	—
321	Dic₁₄₉	—	2	1	no	—
322	Dic₁₄₉	—	2	2	no	—
323	Dic₁₄₉	—	2	2	no	—
324	Dic₁₄₉	—	2	2	no	—
325	Dic₁₄₉	—	2	1	no	—
326	Dic₁₄₉	—	2	1	no	—
327	Dic₁₄₉	—	2	1	no	—
328	Dic₁₄₉	H(5,𝔽₂)	1	2	yes	—
329	C₂×C₁₄₉	—	2	4	no	—
330	C₂×C₁₄₉	—	4	2	no	—
331	C₂×C₁₄₉	—	4	1	no	—
332	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
333	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₁₄₉	#585	1	1	yes	characteristic
335	D₁₄₉	—	4	1	no	—
336	D₁₄₉	—	4	2	no	—
337	D₁₄₉	—	4	1	no	—
338	C₁₄₉	#3514	1	1	yes	characteristic, complemented, Sylow
339	#3514	—	149	1	no	maximal, Sylow
340	#559	—	149	1	no	—
341	#556	—	149	1	no	—
342	#555	—	149	1	no	—
343	#555	—	149	1	no	—
344	#551	—	149	2	no	—
345	#551	—	149	2	no	—
346	D₄×Q₈	—	149	1	no	—
347	#548	—	149	2	no	—
348	#546	—	149	1	no	—
349	#546	—	149	1	no	—
350	#546	—	149	2	no	—
351	D₄²	—	149	1	no	—
352	#542	—	149	1	no	—
353	#542	—	149	1	no	—
354	#538	—	149	2	no	—
355	#538	—	149	2	no	—
356	#532	—	149	1	no	—
357	#529	—	149	2	no	—
358	#529	—	149	1	no	—
359	C₂×#124	—	149	2	no	—
360	#518	—	149	1	no	—
361	#518	D₁₄₉	1	1	yes	characteristic, complemented
362	C₄×#41	—	149	1	no	—
363	C₂×#41	—	149	1	no	—
364	C₂×#41	—	149	2	no	—
365	C₂²×Q₈	—	149	2	no	—
366	C₂²×D₄	—	149	1	no	—
367	C₂²×D₄	—	149	2	no	—
368	C₂²×D₄	C₂×D₁₄₉	1	1	yes	characteristic
369	C₄⋊Q₈	—	149	1	no	—
370	C₄⋊Q₈	—	149	1	no	—
371	C₄⋊Q₈	—	149	1	no	—
372	#127	—	149	1	no	—
373	#126	—	149	2	no	—
374	#126	—	149	1	no	—
375	#126	—	149	2	no	—
376	#126	—	149	1	no	—
377	#126	—	149	2	no	—
378	#126	—	149	2	no	—
379	#125	—	149	1	no	—
380	#124	—	149	1	no	—
381	#124	—	149	1	no	—
382	#124	—	149	2	no	—
383	#124	—	149	2	no	—
384	#124	—	149	2	no	—
385	#124	—	149	2	no	—
386	#124	—	149	2	no	—
387	#124	—	149	2	no	—
388	#124	—	149	2	no	—
389	#124	—	149	2	no	—
390	#124	—	149	2	no	—
391	#124	—	149	1	no	—
392	#123	—	149	2	no	—
393	#123	—	149	2	no	—
394	#123	—	149	2	no	—
395	#123	—	149	1	no	—
396	#123	—	149	1	no	—
397	#123	—	149	2	no	—
398	#123	—	149	2	no	—
399	#123	—	149	2	no	—
400	C₂²⋊Q₈	—	149	2	no	—
401	C₂²⋊Q₈	—	149	1	no	—
402	C₂²⋊Q₈	—	149	2	no	—
403	C₂²⋊Q₈	—	149	1	no	—
404	C₂²⋊Q₈	—	149	1	no	—
405	C₂²⋊Q₈	—	149	2	no	—
406	C₂²⋊Q₈	—	149	2	no	—
407	C₂²⋊Q₈	—	149	2	no	—
408	#121	—	149	2	no	—
409	#121	—	149	1	no	—
410	#121	—	149	2	no	—
411	#121	—	149	1	no	—
412	#121	—	149	2	no	—
413	#121	—	149	2	no	—
414	#121	—	149	1	no	—
415	#121	—	149	1	no	—
416	#121	—	149	1	no	—
417	#121	—	149	2	no	—
418	#121	—	149	2	no	—
419	#120	—	149	2	no	—
420	#120	—	149	2	no	—
421	#120	—	149	2	no	—
422	#120	—	149	2	no	—
423	C₄×Q₈	—	149	1	no	—
424	C₄×Q₈	—	149	1	no	—
425	C₄×Q₈	—	149	2	no	—
426	C₄×Q₈	—	149	1	no	—
427	C₄×D₄	—	149	1	no	—
428	C₄×D₄	—	149	1	no	—
429	C₄×D₄	—	149	2	no	—
430	C₄×D₄	—	149	2	no	—
431	C₄×D₄	—	149	1	no	—
432	C₄×D₄	—	149	1	no	—
433	C₄×D₄	—	149	2	no	—
434	C₄×D₄	—	149	2	no	—
435	C₄×D₄	—	149	1	no	—
436	C₄×D₄	—	149	2	no	—
437	C₄×D₄	—	149	2	no	—
438	C₄×D₄	—	149	1	no	—
439	C₄×D₄	—	149	1	no	—
440	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
441	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
442	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
443	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
444	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
445	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
446	#117	—	149	2	no	—
447	#117	—	149	1	no	—
448	#117	—	149	1	no	—
449	#117	—	149	2	no	—
450	#117	—	149	1	no	—
451	#117	—	149	2	no	—
452	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
453	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
454	C₂×C₂²⋊C₄	—	149	2	no	—
455	C₂×C₂²⋊C₄	—	149	2	no	—
456	C₂×C₂²⋊C₄	—	149	2	no	—
457	C₂×C₂²⋊C₄	—	149	2	no	—
458	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	2	yes	complemented
459	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	2	yes	complemented
460	C₂×C₄²	—	149	2	no	—
461	C₂×C₄²	—	149	1	no	—
462	C₂⁴	—	149	2	no	—
463	C₂⁴	C₂²×D₁₄₉	1	2	yes	—
464	#41	—	298	4	no	—
465	#41	—	596	4	no	—
466	C₂×Q₈	—	596	4	no	—
467	C₂×Q₈	—	149	1	no	—
468	C₂×Q₈	—	149	1	no	—
469	C₂×Q₈	—	149	2	no	—
470	C₂×Q₈	—	149	2	no	—
471	C₂×Q₈	—	149	2	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	298	4	no	—
474	C₂×D₄	—	596	4	no	—
475	C₂×D₄	—	149	2	no	—
476	C₂×D₄	—	149	2	no	—
477	C₂×D₄	—	149	1	no	—
478	C₂×D₄	—	149	2	no	—
479	C₂×D₄	—	149	1	no	—
480	C₂×D₄	—	149	2	no	—
481	C₂×D₄	—	149	2	no	—
482	C₂×D₄	—	149	2	no	—
483	C₂×D₄	—	149	2	no	—
484	C₂×D₄	—	149	1	no	—
485	C₂×D₄	—	149	1	no	—
486	C₂×D₄	—	149	2	no	—
487	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
488	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
490	C₂²×C₄	—	149	2	no	—
491	C₂²×C₄	—	149	2	no	—
492	C₂²×C₄	—	149	1	no	—
493	C₂²×C₄	—	149	1	no	—
494	C₂²×C₄	—	149	1	no	—
495	C₂²×C₄	—	149	2	no	—
496	C₂²×C₄	—	149	1	no	—
497	C₂²×C₄	—	149	2	no	—
498	C₂²×C₄	—	149	2	no	—
499	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
501	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
502	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
503	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
504	C₄⋊C₄	—	149	1	no	—
505	C₄⋊C₄	—	149	1	no	—
506	C₄⋊C₄	—	149	1	no	—
507	C₄⋊C₄	—	149	1	no	—
508	C₄⋊C₄	—	149	1	no	—
509	C₄⋊C₄	—	149	1	no	—
510	C₄⋊C₄	—	149	2	no	—
511	C₄⋊C₄	—	149	2	no	—
512	C₄⋊C₄	—	149	2	no	—
513	C₄⋊C₄	—	149	2	no	—
514	C₄⋊C₄	—	149	1	no	—
515	C₄⋊C₄	—	149	1	no	—
516	C₄⋊C₄	—	149	2	no	—
517	C₄⋊C₄	—	149	2	no	—
518	C₄⋊C₄	—	149	2	no	—
519	C₄⋊C₄	—	149	1	no	—
520	C₄⋊C₄	—	149	1	no	—
521	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
525	C₂²⋊C₄	—	149	1	no	—
526	C₂²⋊C₄	—	149	2	no	—
527	C₂²⋊C₄	—	149	2	no	—
528	C₂²⋊C₄	—	149	2	no	—
529	C₂²⋊C₄	—	149	2	no	—
530	C₂²⋊C₄	—	149	2	no	—
531	C₂²⋊C₄	—	149	2	no	—
532	C₂²⋊C₄	—	149	1	no	—
533	C₂²⋊C₄	—	149	2	no	—
534	C₂²⋊C₄	—	149	1	no	—
535	C₂²⋊C₄	—	149	2	no	—
536	C₂²⋊C₄	—	149	1	no	—
537	C₂²⋊C₄	—	149	1	no	—
538	C₂²⋊C₄	—	149	2	no	—
539	C₂²⋊C₄	—	149	2	no	—
540	C₂²⋊C₄	—	149	2	no	—
541	C₂²⋊C₄	—	149	2	no	—
542	C₂²⋊C₄	—	149	2	no	—
543	C₂²⋊C₄	—	149	2	no	—
544	C₂²⋊C₄	—	149	2	no	—
545	C₂²⋊C₄	—	149	1	no	—
546	C₂²⋊C₄	—	149	2	no	—
547	C₂²⋊C₄	—	149	1	no	—
548	C₂²⋊C₄	—	149	1	no	—
549	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
556	C₄²	—	149	1	no	—
557	C₄²	—	149	2	no	—
558	C₄²	—	149	1	no	—
559	C₄²	—	149	2	no	—
560	C₄²	—	149	1	no	—
561	C₄²	—	149	2	no	—
562	C₄²	—	149	2	no	—
563	C₄²	—	149	1	no	—
564	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
565	C₄²	C₂²×D₁₄₉	1	2	yes	—
566	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
567	C₂³	—	2	4	no	—
568	C₂³	—	4	2	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	298	4	no	—
571	C₂³	—	596	2	no	—
572	C₂³	—	596	2	no	—
573	C₂³	—	149	1	no	—
574	C₂³	—	149	2	no	—
575	C₂³	—	149	1	no	—
576	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
577	C₂³	C₂³×D₁₄₉	1	2	yes	—
578	C₂³	C₂³×D₁₄₉	1	2	yes	—
579	Q₈	—	298	2	no	—
580	Q₈	—	298	4	no	—
581	Q₈	—	298	2	no	—
582	Q₈	—	596	2	no	—
583	Q₈	—	596	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	2	no	—
586	D₄	—	298	4	no	—
587	D₄	—	298	4	no	—
588	D₄	—	298	2	no	—
589	D₄	—	298	4	no	—
590	D₄	—	298	2	no	—
591	D₄	—	596	1	no	—
592	D₄	—	596	2	no	—
593	D₄	—	596	2	no	—
594	D₄	—	596	2	no	—
595	D₄	—	596	1	no	—
596	D₄	—	596	2	no	—
597	D₄	—	596	2	no	—
598	D₄	#14558736	1	4	yes	complemented
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	298	2	no	—
605	C₂×C₄	—	298	4	no	—
606	C₂×C₄	—	298	4	no	—
607	C₂×C₄	—	298	2	no	—
608	C₂×C₄	—	298	2	no	—
609	C₂×C₄	—	596	2	no	—
610	C₂×C₄	—	596	1	no	—
611	C₂×C₄	—	596	2	no	—
612	C₂×C₄	—	596	2	no	—
613	C₂×C₄	—	149	1	no	—
614	C₂×C₄	—	149	2	no	—
615	C₂×C₄	—	149	1	no	—
616	C₂×C₄	—	149	1	no	—
617	C₂×C₄	—	149	2	no	—
618	C₂×C₄	—	149	1	no	—
619	C₂×C₄	—	149	1	no	—
620	C₂×C₄	—	149	2	no	—
621	C₂×C₄	—	149	1	no	—
622	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
624	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
629	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	8	4	no	—
639	C₂²	—	298	1	no	—
640	C₂²	—	298	1	no	—
641	C₂²	—	298	2	no	—
642	C₂²	—	298	1	no	—
643	C₂²	—	298	2	no	—
644	C₂²	—	298	1	no	—
645	C₂²	—	298	1	no	—
646	C₂²	—	298	2	no	—
647	C₂²	—	298	1	no	—
648	C₂²	—	1192	4	no	—
649	C₂²	C₂×#14558736	1	4	yes	—
650	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	298	1	no	—
659	C₄	—	298	1	no	—
660	C₄	—	298	2	no	—
661	C₄	—	298	2	no	—
662	C₄	—	298	2	no	—
663	C₄	—	298	1	no	—
664	C₄	—	298	1	no	—
665	C₄	—	298	1	no	—
666	C₄	—	149	2	no	—
667	C₄	C₂×#14558736	1	2	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	4	1	no	—
670	C₂	—	4	2	no	—
671	C₂	—	596	1	no	—
672	C₂	—	596	2	no	—
673	C₂	—	596	1	no	—
674	C₂	C₂²×#14558736	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic
676	C₂	#23750460	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#518×C₁₄₉	C₂
hypercenter	#518	D₁₄₉
hypocenter	C₁₄₉	#3514
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. #23750358	C₂	semidirect
2. #23750343	C₂	semidirect
3. #23750340	C₂	semidirect
4. #23750338	C₂	semidirect
5. #23750304	C₂	semidirect
6. #23750301	C₂	semidirect
7. D₄×Dic₂₉₈	C₂	semidirect
8. #23750284	C₂	semidirect
9. #23750270	C₂	semidirect
10. #23750269	C₂	semidirect
11. #23750265	C₂	semidirect
12. D₄×C₂²⋊D₁₄₉	C₂	semidirect
13. #23750246	C₂	semidirect
14. #23750240	C₂	semidirect
15. #23750213	C₂	semidirect
16. #23750208	C₂	semidirect
17. #23750172	C₂	semidirect
18. #23750155	C₂	semidirect
19. #23750153	C₂	semidirect
20. C₂×#18011897	C₂	semidirect
21. #23750097	C₂	semidirect
22. C₄×#14558735	C₂	semidirect
23. #518×C₁₄₉	C₂	semidirect
24. C₂×#14558736	C₂²	semidirect
26. C₂²×Dic₂₉₈	C₂²	semidirect
29. #18011911	C₂²	semidirect
30. #18011910	C₂²	semidirect
31. #18011910	C₂²	semidirect
33. #18011906	C₂²	semidirect
34. #18011906	C₂²	semidirect
35. #18011905	C₂²	semidirect
36. #18011904	C₂²	semidirect
37. #18011904	C₂²	semidirect
38. #18011904	C₂²	semidirect
39. #18011901	C₂²	semidirect
40. #18011899	C₂²	semidirect
41. #18011899	C₂²	semidirect
42. #18011898	C₂²	semidirect
45. #18011897	C₂²	semidirect
46. #18011897	C₂²	semidirect
47. #18011897	C₂²	semidirect
48. #18011897	C₂²	semidirect
49. #18011897	C₂²	semidirect
50. #18011897	C₂²	semidirect
51. #18011897	C₂²	semidirect
52. #18011896	C₂²	semidirect
53. #18011895	C₂²	semidirect
54. #18011894	C₂²	semidirect
55. #18011894	C₂²	semidirect
56. #18011893	C₂²	semidirect
57. #18011893	C₂²	semidirect
58. #18011893	C₂²	semidirect
59. #18011892	C₂²	semidirect
60. #18011891	C₂²	semidirect
61. #18011890	C₂²	semidirect
62. #18011890	C₂²	semidirect
63. #18011890	C₂²	semidirect
64. #18011889	C₂²	semidirect
65. #18011889	C₂²	semidirect
66. #18011888	C₂²	semidirect
67. #18011888	C₂²	semidirect
68. #18011886	C₂²	semidirect
70. #18011885	C₂²	semidirect
71. #18011885	C₂²	semidirect
73. #18011884	C₂²	semidirect
74. #18011884	C₂²	semidirect
76. #18011883	C₂²	semidirect
78. #18011882	C₂²	semidirect
79. #18011881	C₂²	semidirect
81. #18011880	C₂²	semidirect
83. C₄×Dic₂₉₈	C₂²	semidirect
84. C₄×Dic₂₉₈	C₂²	semidirect
85. C₄×Dic₂₉₈	C₂²	semidirect
86. #18011876	C₂²	semidirect
87. C₄×D₅₉₆	C₂²	semidirect
88. C₄×D₅₉₆	C₂²	semidirect
91. #18011873	C₂²	semidirect
93. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
94. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
95. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
96. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
97. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
98. #18011871	C₂²	semidirect
99. #18011871	C₂²	semidirect
100. #18011870	C₂²	semidirect
101. #18011869	C₂²	semidirect
102. #18011869	C₂²	semidirect
103. #18011868	C₂²	semidirect
104. #18011868	C₂²	semidirect
105. #18011867	C₂²	semidirect
106. C₂×C₂²⋊Dic₁₄₉	C₂²	semidirect
107. C₂×#14558713	C₂²	semidirect
108. C₂×#14558713	C₂²	semidirect
109. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
110. C₂×C₄×Dic₁₄₉	C₂²	semidirect
111. C₄²×D₁₄₉	C₂²	semidirect
115. C₄×D₄×C₁₄₉	C₂²	semidirect
116. C₄×D₄×C₁₄₉	C₂²	semidirect
117. C₄×D₄×C₁₄₉	C₂²	semidirect
118. C₄×D₄×C₁₄₉	C₂²	semidirect
119. #117×C₁₄₉	C₂²	semidirect
120. #117×C₁₄₉	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₁₄₉	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₁₄₉	C₂²	semidirect
277. D₄×C₁₄₉	#41	semidirect
338. C₁₄₉	#3514	semidirect
361. #518	D₁₄₉	semidirect
442. C₄×D₄	C₂×D₁₄₉	semidirect
443. C₄×D₄	C₂×D₁₄₉	semidirect
444. C₄×D₄	C₂×D₁₄₉	semidirect
445. C₄×D₄	C₂×D₁₄₉	semidirect
452. #117	C₂×D₁₄₉	semidirect
453. #117	C₂×D₁₄₉	semidirect
458. C₂×C₂²⋊C₄	C₂×D₁₄₉	semidirect
459. C₂×C₂²⋊C₄	C₂×D₁₄₉	semidirect
598. D₄	#14558736	semidirect

Maximal subgroups

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

subgroup	index
#23750358	2
#23750343	2
#23750340	2
#23750338	2
#23750304	2
#23750301	2
D₄×Dic₂₉₈	2
#23750284	2
#23750270	2
#23750269	2
#23750265	2
D₄×C₂²⋊D₁₄₉	2
#23750246	2
#23750240	2
#23750213	2
#23750208	2
#23750172	2
#23750155	2
#23750153	2
C₂×#18011897	2
#23750097	2
C₄×#14558735	2
#518×C₁₄₉	2
#3514	149