Subgroups — #34058174

Order 19072.

1648 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14558736	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750293	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750288	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750285	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750281	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750277	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750273	C₂	1	2	yes	maximal, complemented
9	#23750272	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750267	C₂	1	2	yes	maximal, complemented
11	#23750266	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750262	C₂	1	2	yes	maximal, complemented
13	#23750259	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750257	C₂	1	2	yes	maximal, complemented
15	#23750172	C₂	1	2	yes	maximal, complemented
16	#23750171	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750137	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750134	C₂	1	2	yes	maximal, complemented
19	#23750134	C₂	1	2	yes	maximal, complemented
20	#23750093	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×C₂²⋊D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₄₉	C₂	1	2	yes	maximal, complemented
23	#525×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558737	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14558736	—	2	8	no	—
26	C₂×#14558736	C₂²	1	1	yes	characteristic
27	C₂×#14558736	C₂²	1	1	yes	characteristic, complemented
28	C₂×#14558736	C₂²	1	2	yes	complemented
29	C₂×#14558736	C₂²	1	2	yes	complemented
30	C₂×#14558736	C₂²	1	2	yes	complemented
31	C₂×#14558736	C₂²	1	1	yes	characteristic, complemented
32	C₂×#14558736	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14558735	C₂²	1	2	yes	complemented
34	C₂×#14558735	C₂²	1	1	yes	characteristic, complemented
35	#41×D₁₄₉	—	2	8	no	—
36	C₂²×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×Q₈×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
41	C₂×D₄×D₁₄₉	C₂²	1	2	yes	—
42	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
43	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	complemented
45	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	complemented
47	#18011910	C₂²	1	2	yes	complemented
48	#18011909	C₂²	1	1	yes	characteristic, complemented
49	#18011907	C₂²	1	1	yes	characteristic, complemented
50	#18011907	C₂²	1	2	yes	complemented
51	#18011900	C₂²	1	1	yes	characteristic, complemented
52	#18011898	C₂²	1	1	yes	characteristic, complemented
53	#18011897	C₂²	1	2	yes	complemented
54	#18011897	C₂²	1	2	yes	complemented
55	#18011896	C₂²	1	2	yes	complemented
56	#18011896	C₂²	1	2	yes	complemented
57	#18011895	C₂²	1	2	yes	complemented
58	#18011893	C₂²	1	2	yes	complemented
59	#18011893	C₂²	1	2	yes	complemented
60	#18011891	C₂²	1	1	yes	characteristic, complemented
61	#18011891	C₂²	1	1	yes	characteristic, complemented
62	#18011889	C₂²	1	2	yes	complemented
63	#18011889	C₂²	1	2	yes	complemented
64	#18011888	C₂²	1	2	yes	complemented
65	#18011888	C₂²	1	2	yes	complemented
66	#18011886	C₂²	1	2	yes	complemented
67	#18011886	C₂²	1	1	yes	characteristic, complemented
68	#18011886	C₂²	1	1	yes	characteristic, complemented
69	#18011884	C₂²	1	2	yes	complemented
70	#18011884	C₂²	1	2	yes	complemented
71	#18011884	C₂²	1	2	yes	complemented
72	#18011884	C₂²	1	2	yes	complemented
73	#18011883	C₂²	1	2	yes	complemented
74	#18011883	C₂²	1	2	yes	complemented
75	#18011883	C₂²	1	2	yes	complemented
76	#18011883	C₂²	1	2	yes	complemented
77	#18011882	C₂²	1	2	yes	complemented
78	#18011881	C₂²	1	2	yes	complemented
79	#18011881	C₂²	1	2	yes	complemented
80	#18011881	C₂²	1	2	yes	complemented
81	#18011879	C₂²	1	2	yes	complemented
82	#18011879	C₂²	1	2	yes	complemented
83	#18011876	C₂²	1	1	yes	characteristic, complemented
84	#18011876	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₅₉₆	C₂²	1	2	yes	complemented
86	C₄×D₅₉₆	C₂²	1	2	yes	complemented
87	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
88	#18011873	C₂²	1	1	yes	characteristic, complemented
89	#18011873	C₂²	1	1	yes	characteristic, complemented
90	#18011873	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
97	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
101	#18011871	C₂²	1	2	yes	—
102	#18011871	C₂²	1	2	yes	complemented
103	#18011871	C₂²	1	2	yes	complemented
104	#18011871	C₂²	1	2	yes	complemented
105	#18011868	C₂²	1	2	yes	complemented
106	C₂×#14558715	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
108	C₂×C₂²⋊Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
109	C₂×#14558713	C₂²	1	1	yes	characteristic, complemented
110	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
112	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
113	C₄²×D₁₄₉	C₂²	1	2	yes	complemented
114	C₂×#41×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
115	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
116	#123×C₁₄₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
118	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
120	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
121	#120×C₁₄₉	C₂²	1	2	yes	complemented
122	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
123	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
124	#117×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
125	C₂³×D₁₄₉	C₂³	1	2	yes	—
126	C₂³×D₁₄₉	C₂³	1	2	yes	—
127	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
128	#14558737	—	2	4	no	—
129	#14558736	—	2	4	no	—
130	#14558736	—	2	4	no	—
131	#14558736	—	2	8	no	—
132	#14558736	—	2	8	no	—
133	#14558736	—	2	8	no	—
134	#14558736	—	2	4	no	—
135	#14558736	D₄	1	8	yes	complemented
136	#14558735	—	2	4	no	—
137	#14558735	—	2	8	no	—
138	C₂×Dic₂₉₈	—	2	4	no	—
139	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
140	C₂×Dic₂₉₈	C₂³	1	2	yes	—
141	C₂×Dic₂₉₈	C₂³	1	2	yes	—
142	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
143	Q₈×D₁₄₉	—	2	4	no	—
144	C₂×D₅₉₆	—	2	4	no	—
145	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
146	C₂×D₅₉₆	C₂³	1	2	yes	—
147	C₂×D₅₉₆	C₂³	1	2	yes	—
148	C₂×D₅₉₆	C₂³	1	2	yes	—
149	C₂×D₅₉₆	C₂³	1	2	yes	—
150	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊D₁₄₉	—	2	8	no	—
152	C₂×C₂²⋊D₁₄₉	—	2	4	no	—
153	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
165	D₄×D₁₄₉	—	2	4	no	—
166	D₄×D₁₄₉	—	2	8	no	—
167	D₄×D₁₄₉	—	2	8	no	—
168	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
169	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
170	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
171	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
172	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₁₄₉	—	2	8	no	—
174	C₂×C₄×D₁₄₉	—	2	8	no	—
175	C₂×C₄×D₁₄₉	—	2	4	no	—
176	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
177	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
178	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
179	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
180	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
182	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
183	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
185	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
186	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
187	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
188	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
189	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
190	#14558715	C₂³	1	2	yes	—
191	#14558715	C₂³	1	2	yes	—
192	#14558715	C₂³	1	1	yes	characteristic
193	#14558715	C₂³	1	1	yes	characteristic
194	#14558715	C₂³	1	1	yes	characteristic
195	#14558715	C₂³	1	1	yes	characteristic
196	#14558715	C₂³	1	2	yes	—
197	#14558715	C₂³	1	2	yes	—
198	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
199	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
200	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
201	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
202	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
203	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
204	#14558713	C₂³	1	1	yes	characteristic
205	#14558713	C₂³	1	2	yes	—
206	#14558713	C₂³	1	2	yes	—
207	#14558713	C₂³	1	2	yes	—
208	#14558713	C₂³	1	1	yes	characteristic
209	#14558713	C₂³	1	1	yes	characteristic
210	#14558713	C₂³	1	1	yes	characteristic
211	#14558713	C₂³	1	2	yes	—
212	#14558713	C₂³	1	2	yes	—
213	#14558713	C₂³	1	2	yes	—
214	#14558713	C₂³	1	2	yes	—
215	#14558713	C₂³	1	2	yes	—
216	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₄₉	C₂³	1	2	yes	—
218	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₄₉	C₂³	1	2	yes	—
220	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
222	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
223	#41×C₁₄₉	—	2	4	no	—
224	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
225	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
226	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
227	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
228	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
229	C₂²×C₄×C₁₄₉	—	2	4	no	—
230	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
231	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
232	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
233	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
234	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
235	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
236	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
238	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
241	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
242	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
243	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
244	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
245	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
246	C₄²×C₁₄₉	C₂³	1	2	yes	—
247	C₂²×D₁₄₉	—	2	2	no	—
248	C₂²×D₁₄₉	—	2	4	no	—
249	C₂²×D₁₄₉	—	2	4	no	—
250	C₂²×D₁₄₉	—	2	4	no	—
251	C₂²×D₁₄₉	—	2	4	no	—
252	C₂²×D₁₄₉	—	2	2	no	—
253	C₂²×D₁₄₉	—	4	2	no	—
254	C₂²×D₁₄₉	—	4	2	no	—
255	C₂²×D₁₄₉	—	4	1	no	—
256	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
257	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
258	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
259	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
260	Dic₂₉₈	—	2	2	no	—
261	Dic₂₉₈	—	2	4	no	—
262	Dic₂₉₈	—	2	4	no	—
263	Dic₂₉₈	C₂×D₄	1	4	yes	complemented
264	D₅₉₆	—	2	4	no	—
265	D₅₉₆	—	2	4	no	—
266	D₅₉₆	—	2	4	no	—
267	D₅₉₆	—	2	2	no	—
268	D₅₉₆	—	4	2	no	—
269	D₅₉₆	C₂×D₄	1	4	yes	complemented
270	C₂²⋊D₁₄₉	—	2	4	no	—
271	C₂²⋊D₁₄₉	—	2	2	no	—
272	C₂²⋊D₁₄₉	—	2	4	no	—
273	C₂²⋊D₁₄₉	—	2	4	no	—
274	C₂²⋊D₁₄₉	—	2	2	no	—
275	C₂²⋊D₁₄₉	—	2	4	no	—
276	C₂²⋊D₁₄₉	—	2	4	no	—
277	C₂²⋊D₁₄₉	—	2	4	no	—
278	C₂²⋊D₁₄₉	—	2	2	no	—
279	C₂²⋊D₁₄₉	—	4	2	no	—
280	C₂²⋊D₁₄₉	C₂×D₄	1	8	yes	complemented
281	C₂²⋊D₁₄₉	#41	1	4	yes	complemented
282	C₂×Dic₁₄₉	—	2	2	no	—
283	C₂×Dic₁₄₉	—	2	4	no	—
284	C₂×Dic₁₄₉	—	2	4	no	—
285	C₂×Dic₁₄₉	—	2	2	no	—
286	C₂×Dic₁₄₉	—	4	1	no	—
287	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
290	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
294	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
295	C₄×D₁₄₉	—	2	4	no	—
296	C₄×D₁₄₉	—	2	4	no	—
297	C₄×D₁₄₉	—	2	2	no	—
298	C₄×D₁₄₉	—	2	2	no	—
299	C₄×D₁₄₉	—	2	2	no	—
300	C₄×D₁₄₉	—	2	4	no	—
301	C₄×D₁₄₉	—	2	2	no	—
302	C₄×D₁₄₉	—	2	4	no	—
303	C₄×D₁₄₉	—	2	4	no	—
304	C₄×D₁₄₉	—	2	4	no	—
305	C₄×D₁₄₉	—	4	2	no	—
306	C₄×D₁₄₉	C₂×D₄	1	8	yes	complemented
307	C₂³×C₁₄₉	—	2	2	no	—
308	C₂³×C₁₄₉	—	2	2	no	—
309	C₂³×C₁₄₉	—	4	1	no	—
310	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
311	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
312	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
313	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
314	Q₈×C₁₄₉	—	2	2	no	—
315	D₄×C₁₄₉	—	2	4	no	—
316	D₄×C₁₄₉	—	2	4	no	—
317	D₄×C₁₄₉	—	2	2	no	—
318	D₄×C₁₄₉	—	4	2	no	—
319	C₂×C₄×C₁₄₉	—	2	2	no	—
320	C₂×C₄×C₁₄₉	—	2	2	no	—
321	C₂×C₄×C₁₄₉	—	2	4	no	—
322	C₂×C₄×C₁₄₉	—	2	2	no	—
323	C₂×C₄×C₁₄₉	—	2	2	no	—
324	C₂×C₄×C₁₄₉	—	2	2	no	—
325	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	complemented
326	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
327	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
328	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
329	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
330	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
331	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
332	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
333	C₂²×C₁₄₉	—	2	1	no	—
334	C₂²×C₁₄₉	—	2	1	no	—
335	C₂²×C₁₄₉	—	2	1	no	—
336	C₂²×C₁₄₉	—	2	1	no	—
337	C₂²×C₁₄₉	—	2	1	no	—
338	C₂²×C₁₄₉	—	2	2	no	—
339	C₂²×C₁₄₉	—	2	2	no	—
340	C₂²×C₁₄₉	—	2	1	no	—
341	C₂²×C₁₄₉	—	2	1	no	—
342	C₂²×C₁₄₉	—	2	2	no	—
343	C₂²×C₁₄₉	—	4	4	no	—
344	C₂²×C₁₄₉	C₂²×D₄	1	2	yes	—
345	C₂²×C₁₄₉	C₂×#41	1	2	yes	complemented
346	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
347	C₂×D₁₄₉	—	2	1	no	—
348	C₂×D₁₄₉	—	2	2	no	—
349	C₂×D₁₄₉	—	2	2	no	—
350	C₂×D₁₄₉	—	2	1	no	—
351	C₂×D₁₄₉	—	2	1	no	—
352	C₂×D₁₄₉	—	2	2	no	—
353	C₂×D₁₄₉	—	2	1	no	—
354	C₂×D₁₄₉	—	2	2	no	—
355	C₂×D₁₄₉	—	2	2	no	—
356	C₂×D₁₄₉	—	2	1	no	—
357	C₂×D₁₄₉	—	4	8	no	—
358	C₂×D₁₄₉	—	4	4	no	—
359	C₂×D₁₄₉	—	4	8	no	—
360	C₂×D₁₄₉	C₂²×D₄	1	4	yes	—
361	C₂×D₁₄₉	C₂×#41	1	2	yes	complemented
362	C₄×C₁₄₉	—	2	1	no	—
363	C₄×C₁₄₉	—	2	1	no	—
364	C₄×C₁₄₉	—	2	2	no	—
365	C₄×C₁₄₉	—	2	2	no	—
366	C₄×C₁₄₉	—	2	2	no	—
367	C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
368	C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
369	Dic₁₄₉	—	2	1	no	—
370	Dic₁₄₉	—	2	2	no	—
371	Dic₁₄₉	—	2	1	no	—
372	Dic₁₄₉	—	2	1	no	—
373	Dic₁₄₉	—	2	1	no	—
374	Dic₁₄₉	—	2	1	no	—
375	Dic₁₄₉	C₂²×D₄	1	4	yes	—
376	Dic₁₄₉	C₂×#41	1	2	yes	complemented
377	C₂×C₁₄₉	—	2	2	no	—
378	C₂×C₁₄₉	—	2	2	no	—
379	C₂×C₁₄₉	—	4	2	no	—
380	C₂×C₁₄₉	—	4	1	no	—
381	C₂×C₁₄₉	C₂³×D₄	1	1	yes	characteristic
382	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
383	C₂×C₁₄₉	#585	1	1	yes	characteristic
384	D₁₄₉	—	2	2	no	—
385	D₁₄₉	—	2	4	no	—
386	D₁₄₉	—	4	1	no	—
387	D₁₄₉	—	4	2	no	—
388	C₁₄₉	D₄×#41	1	1	yes	characteristic, complemented, Sylow
389	D₄×#41	—	149	1	no	maximal, Sylow
390	C₂²×#41	—	149	1	no	—
391	C₂²×#41	—	149	1	no	—
392	#550	—	149	1	no	—
393	D₄×Q₈	—	149	1	no	—
394	#548	—	149	1	no	—
395	#548	—	149	1	no	—
396	#547	—	149	2	no	—
397	#547	—	149	1	no	—
398	#546	—	149	2	no	—
399	#546	—	149	1	no	—
400	#546	—	149	1	no	—
401	#546	—	149	2	no	—
402	D₄²	—	149	1	no	—
403	D₄²	—	149	2	no	—
404	#532	—	149	1	no	—
405	#532	—	149	2	no	—
406	#525	—	149	2	no	—
407	#525	—	149	2	no	—
408	#525	—	149	1	no	—
409	#525	D₁₄₉	1	1	yes	characteristic, complemented
410	C₄×#41	—	149	1	no	—
411	C₂×C₄×D₄	—	149	1	no	—
412	C₂×C₄×D₄	—	149	2	no	—
413	C₂×#41	—	298	8	no	—
414	C₂×#41	—	298	8	no	—
415	C₂×#41	—	149	1	no	—
416	C₂×#41	—	149	2	no	—
417	C₂×#41	—	149	1	no	—
418	C₂×#41	—	149	1	no	—
419	C₂×#41	—	149	2	no	—
420	C₂×#41	—	149	2	no	—
421	C₂×#41	—	149	1	no	—
422	C₂×#41	—	149	2	no	—
423	C₂×#41	—	149	1	no	—
424	C₂×#41	—	149	1	no	—
425	C₂×#41	C₂×D₁₄₉	1	1	yes	characteristic, complemented
426	C₂²×Q₈	—	149	1	no	—
427	C₂²×Q₈	—	149	1	no	—
428	C₂²×D₄	—	149	1	no	—
429	C₂²×D₄	—	149	2	no	—
430	C₂²×D₄	—	149	2	no	—
431	C₂²×D₄	—	149	1	no	—
432	C₂²×D₄	—	149	2	no	—
433	C₂²×D₄	—	149	1	no	—
434	C₂³×C₄	—	149	2	no	—
435	C₂³×C₄	—	149	2	no	—
436	C₂³×C₄	—	149	1	no	—
437	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
438	C₄⋊Q₈	—	149	1	no	—
439	C₄⋊Q₈	—	149	2	no	—
440	#127	—	149	2	no	—
441	#127	—	149	1	no	—
442	#124	—	149	1	no	—
443	#124	—	149	1	no	—
444	#124	—	149	2	no	—
445	#124	—	149	2	no	—
446	#123	—	149	2	no	—
447	#123	—	149	2	no	—
448	#123	—	149	2	no	—
449	#123	—	149	2	no	—
450	#123	—	149	2	no	—
451	#123	C₂×D₁₄₉	1	2	yes	complemented
452	C₂²⋊Q₈	—	149	2	no	—
453	C₂²⋊Q₈	—	149	1	no	—
454	C₂²⋊Q₈	—	149	2	no	—
455	C₂²⋊Q₈	—	149	1	no	—
456	C₂²⋊Q₈	—	149	2	no	—
457	C₂²⋊Q₈	—	149	2	no	—
458	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
459	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
460	#121	—	149	2	no	—
461	#121	—	149	2	no	—
462	#121	—	149	2	no	—
463	#121	—	149	2	no	—
464	#121	—	149	2	no	—
465	#121	—	149	1	no	—
466	#121	—	149	1	no	—
467	#121	—	149	2	no	—
468	#121	—	149	2	no	—
469	#121	—	149	2	no	—
470	#121	—	149	2	no	—
471	#121	—	149	2	no	—
472	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
473	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
474	#120	—	149	2	no	—
475	#120	—	149	2	no	—
476	#120	—	149	2	no	—
477	#120	—	149	2	no	—
478	#120	—	149	2	no	—
479	#120	C₂×D₁₄₉	1	2	yes	complemented
480	C₄×Q₈	—	149	1	no	—
481	C₄×Q₈	—	149	1	no	—
482	C₄×D₄	—	149	2	no	—
483	C₄×D₄	—	149	1	no	—
484	C₄×D₄	—	149	1	no	—
485	C₄×D₄	—	149	1	no	—
486	C₄×D₄	—	149	2	no	—
487	C₄×D₄	—	149	1	no	—
488	C₄×D₄	—	149	1	no	—
489	C₄×D₄	—	149	1	no	—
490	C₄×D₄	—	149	1	no	—
491	C₄×D₄	—	149	1	no	—
492	C₄×D₄	—	149	2	no	—
493	C₄×D₄	—	149	2	no	—
494	C₄×D₄	—	149	1	no	—
495	C₄×D₄	—	149	1	no	—
496	C₄×D₄	—	149	2	no	—
497	C₄×D₄	—	149	2	no	—
498	C₄×D₄	—	149	2	no	—
499	C₄×D₄	—	149	2	no	—
500	C₄×D₄	—	149	2	no	—
501	C₄×D₄	—	149	2	no	—
502	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
503	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
504	#117	—	149	2	no	—
505	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
506	C₂×C₄⋊C₄	—	149	1	no	—
507	C₂×C₄⋊C₄	—	149	2	no	—
508	C₂×C₂²⋊C₄	—	149	1	no	—
509	C₂×C₂²⋊C₄	—	149	1	no	—
510	C₂×C₂²⋊C₄	—	149	2	no	—
511	C₂×C₂²⋊C₄	—	149	2	no	—
512	C₂×C₄²	—	149	1	no	—
513	C₂×C₄²	—	149	2	no	—
514	C₂⁴	—	149	2	no	—
515	C₂⁴	—	149	2	no	—
516	C₂⁴	—	149	1	no	—
517	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
518	#41	—	2	4	no	—
519	#41	—	298	4	no	—
520	#41	—	298	8	no	—
521	#41	—	298	4	no	—
522	#41	—	298	8	no	—
523	#41	—	298	8	no	—
524	#41	—	298	4	no	—
525	#41	—	298	8	no	—
526	#41	—	298	4	no	—
527	#41	—	298	4	no	—
528	#41	—	149	8	no	—
529	C₂×Q₈	—	298	4	no	—
530	C₂×Q₈	—	298	4	no	—
531	C₂×Q₈	—	149	1	no	—
532	C₂×Q₈	—	149	2	no	—
533	C₂×Q₈	—	149	2	no	—
534	C₂×Q₈	—	149	1	no	—
535	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
536	C₂×D₄	—	298	4	no	—
537	C₂×D₄	—	298	8	no	—
538	C₂×D₄	—	298	8	no	—
539	C₂×D₄	—	298	4	no	—
540	C₂×D₄	—	298	4	no	—
541	C₂×D₄	—	298	8	no	—
542	C₂×D₄	—	149	1	no	—
543	C₂×D₄	—	149	1	no	—
544	C₂×D₄	—	149	2	no	—
545	C₂×D₄	—	149	1	no	—
546	C₂×D₄	—	149	2	no	—
547	C₂×D₄	—	149	2	no	—
548	C₂×D₄	—	149	2	no	—
549	C₂×D₄	—	149	2	no	—
550	C₂×D₄	—	149	2	no	—
551	C₂×D₄	—	149	2	no	—
552	C₂×D₄	—	149	1	no	—
553	C₂×D₄	—	149	2	no	—
554	C₂×D₄	—	149	2	no	—
555	C₂×D₄	—	149	2	no	—
556	C₂×D₄	—	149	2	no	—
557	C₂×D₄	—	149	1	no	—
558	C₂×D₄	—	149	2	no	—
559	C₂×D₄	—	149	1	no	—
560	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
561	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
562	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
563	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	298	8	no	—
566	C₂²×C₄	—	298	8	no	—
567	C₂²×C₄	—	298	4	no	—
568	C₂²×C₄	—	149	1	no	—
569	C₂²×C₄	—	149	1	no	—
570	C₂²×C₄	—	149	2	no	—
571	C₂²×C₄	—	149	2	no	—
572	C₂²×C₄	—	149	2	no	—
573	C₂²×C₄	—	149	2	no	—
574	C₂²×C₄	—	149	2	no	—
575	C₂²×C₄	—	149	2	no	—
576	C₂²×C₄	—	149	1	no	—
577	C₂²×C₄	—	149	2	no	—
578	C₂²×C₄	—	149	1	no	—
579	C₂²×C₄	—	149	1	no	—
580	C₂²×C₄	—	149	1	no	—
581	C₂²×C₄	—	149	2	no	—
582	C₂²×C₄	—	149	1	no	—
583	C₂²×C₄	—	149	2	no	—
584	C₂²×C₄	—	149	2	no	—
585	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
586	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
587	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
588	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
589	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
590	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
591	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
592	C₄⋊C₄	—	149	1	no	—
593	C₄⋊C₄	—	149	2	no	—
594	C₄⋊C₄	—	149	1	no	—
595	C₄⋊C₄	—	149	1	no	—
596	C₄⋊C₄	—	149	1	no	—
597	C₄⋊C₄	—	149	2	no	—
598	C₄⋊C₄	—	149	2	no	—
599	C₄⋊C₄	—	149	2	no	—
600	C₄⋊C₄	—	149	2	no	—
601	C₄⋊C₄	—	149	2	no	—
602	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
603	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
604	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
605	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
606	C₂²⋊C₄	—	149	1	no	—
607	C₂²⋊C₄	—	149	1	no	—
608	C₂²⋊C₄	—	149	1	no	—
609	C₂²⋊C₄	—	149	2	no	—
610	C₂²⋊C₄	—	149	1	no	—
611	C₂²⋊C₄	—	149	2	no	—
612	C₂²⋊C₄	—	149	1	no	—
613	C₂²⋊C₄	—	149	1	no	—
614	C₂²⋊C₄	—	149	2	no	—
615	C₂²⋊C₄	—	149	1	no	—
616	C₂²⋊C₄	—	149	2	no	—
617	C₂²⋊C₄	—	149	2	no	—
618	C₂²⋊C₄	—	149	1	no	—
619	C₂²⋊C₄	—	149	2	no	—
620	C₂²⋊C₄	—	149	2	no	—
621	C₂²⋊C₄	—	149	2	no	—
622	C₂²⋊C₄	—	149	2	no	—
623	C₂²⋊C₄	—	149	2	no	—
624	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
625	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
626	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
627	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
628	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
629	C₄²	—	149	1	no	—
630	C₄²	—	149	2	no	—
631	C₄²	—	149	1	no	—
632	C₄²	—	149	2	no	—
633	C₄²	—	149	1	no	—
634	C₄²	—	149	1	no	—
635	C₄²	C₂²×D₁₄₉	1	2	yes	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	298	4	no	—
640	C₂³	—	298	4	no	—
641	C₂³	—	298	2	no	—
642	C₂³	—	298	4	no	—
643	C₂³	—	298	2	no	—
644	C₂³	—	298	4	no	—
645	C₂³	—	596	1	no	—
646	C₂³	—	596	2	no	—
647	C₂³	—	596	2	no	—
648	C₂³	—	149	1	no	—
649	C₂³	—	149	2	no	—
650	C₂³	—	149	1	no	—
651	C₂³	—	149	2	no	—
652	C₂³	C₂³×D₁₄₉	1	2	yes	—
653	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
654	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
655	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
656	Q₈	—	2	2	no	—
657	Q₈	—	298	4	no	—
658	Q₈	—	298	4	no	—
659	Q₈	—	298	2	no	—
660	Q₈	—	149	4	no	—
661	D₄	—	2	4	no	—
662	D₄	—	2	4	no	—
663	D₄	—	2	2	no	—
664	D₄	—	4	2	no	—
665	D₄	—	298	4	no	—
666	D₄	—	298	4	no	—
667	D₄	—	298	4	no	—
668	D₄	—	298	2	no	—
669	D₄	—	298	4	no	—
670	D₄	—	298	4	no	—
671	D₄	—	298	4	no	—
672	D₄	—	298	2	no	—
673	D₄	—	298	4	no	—
674	D₄	—	298	2	no	—
675	D₄	—	298	4	no	—
676	D₄	—	298	4	no	—
677	D₄	—	298	2	no	—
678	D₄	—	596	2	no	—
679	D₄	—	596	2	no	—
680	D₄	—	149	8	no	—
681	D₄	—	149	4	no	—
682	D₄	—	149	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	298	4	no	—
690	C₂×C₄	—	298	4	no	—
691	C₂×C₄	—	298	4	no	—
692	C₂×C₄	—	298	4	no	—
693	C₂×C₄	—	298	4	no	—
694	C₂×C₄	—	298	2	no	—
695	C₂×C₄	—	298	4	no	—
696	C₂×C₄	—	298	4	no	—
697	C₂×C₄	—	298	2	no	—
698	C₂×C₄	—	298	2	no	—
699	C₂×C₄	—	298	2	no	—
700	C₂×C₄	—	298	2	no	—
701	C₂×C₄	—	298	4	no	—
702	C₂×C₄	—	298	2	no	—
703	C₂×C₄	—	596	2	no	—
704	C₂×C₄	—	596	1	no	—
705	C₂×C₄	—	149	1	no	—
706	C₂×C₄	—	149	1	no	—
707	C₂×C₄	—	149	1	no	—
708	C₂×C₄	—	149	1	no	—
709	C₂×C₄	—	149	1	no	—
710	C₂×C₄	—	149	2	no	—
711	C₂×C₄	—	149	1	no	—
712	C₂×C₄	—	149	2	no	—
713	C₂×C₄	—	149	8	no	—
714	C₂×C₄	D₄×D₁₄₉	1	4	yes	complemented
715	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
716	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
717	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
718	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
719	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
720	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
721	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	298	1	no	—
734	C₂²	—	298	2	no	—
735	C₂²	—	298	2	no	—
736	C₂²	—	298	1	no	—
737	C₂²	—	298	2	no	—
738	C₂²	—	298	1	no	—
739	C₂²	—	298	2	no	—
740	C₂²	—	298	1	no	—
741	C₂²	—	298	1	no	—
742	C₂²	—	298	2	no	—
743	C₂²	—	596	8	no	—
744	C₂²	—	596	4	no	—
745	C₂²	—	596	8	no	—
746	C₂²	—	149	4	no	—
747	C₂²	—	149	2	no	—
748	C₂²	C₂×D₄×D₁₄₉	1	2	yes	—
749	C₂²	#41×D₁₄₉	1	2	yes	complemented
750	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	298	1	no	—
757	C₄	—	298	2	no	—
758	C₄	—	298	1	no	—
759	C₄	—	298	1	no	—
760	C₄	—	298	1	no	—
761	C₄	—	298	1	no	—
762	C₄	—	149	4	no	—
763	C₄	—	149	2	no	—
764	C₄	C₂×D₄×D₁₄₉	1	2	yes	—
765	C₄	C₂×D₄×D₁₄₉	1	2	yes	—
766	C₂	—	2	2	no	—
767	C₂	—	2	2	no	—
768	C₂	—	4	1	no	—
769	C₂	—	4	2	no	—
770	C₂	—	298	2	no	—
771	C₂	—	298	4	no	—
772	C₂	—	596	2	no	—
773	C₂	—	596	1	no	—
774	C₂	C₂²×D₄×D₁₄₉	1	1	yes	characteristic
775	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
776	C₂	#23750461	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₄₉
Fitting	#525×C₁₄₉	C₂
hypercenter	#525	D₁₄₉
hypocenter	C₁₄₉	D₄×#41
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂²×#14558736	C₂	semidirect
2. C₂×#41×D₁₄₉	C₂	semidirect
3. #23750293	C₂	semidirect
4. #23750288	C₂	semidirect
5. #23750285	C₂	semidirect
6. #23750281	C₂	semidirect
7. #23750277	C₂	semidirect
8. #23750273	C₂	semidirect
9. #23750272	C₂	semidirect
10. #23750267	C₂	semidirect
11. #23750266	C₂	semidirect
12. #23750262	C₂	semidirect
13. #23750259	C₂	semidirect
14. #23750257	C₂	semidirect
15. #23750172	C₂	semidirect
16. #23750171	C₂	semidirect
17. #23750137	C₂	semidirect
18. #23750134	C₂	semidirect
19. #23750134	C₂	semidirect
20. #23750093	C₂	semidirect
21. C₂×C₄×C₂²⋊D₁₄₉	C₂	semidirect
22. C₄×D₄×D₁₄₉	C₂	semidirect
23. #525×C₁₄₉	C₂	semidirect
24. C₂×#14558737	C₂²	semidirect
27. C₂×#14558736	C₂²	semidirect
28. C₂×#14558736	C₂²	semidirect
29. C₂×#14558736	C₂²	semidirect
30. C₂×#14558736	C₂²	semidirect
31. C₂×#14558736	C₂²	semidirect
32. C₂×#14558736	C₂²	semidirect
33. C₂×#14558735	C₂²	semidirect
34. C₂×#14558735	C₂²	semidirect
36. C₂²×Dic₂₉₈	C₂²	semidirect
37. C₂×Q₈×D₁₄₉	C₂²	semidirect
38. C₂²×D₅₉₆	C₂²	semidirect
40. C₂²×C₂²⋊D₁₄₉	C₂²	semidirect
42. C₂×D₄×D₁₄₉	C₂²	semidirect
43. C₂×D₄×D₁₄₉	C₂²	semidirect
44. C₂²×C₄×D₁₄₉	C₂²	semidirect
45. C₂²×C₄×D₁₄₉	C₂²	semidirect
46. C₂²×C₄×D₁₄₉	C₂²	semidirect
47. #18011910	C₂²	semidirect
48. #18011909	C₂²	semidirect
49. #18011907	C₂²	semidirect
50. #18011907	C₂²	semidirect
51. #18011900	C₂²	semidirect
52. #18011898	C₂²	semidirect
53. #18011897	C₂²	semidirect
54. #18011897	C₂²	semidirect
55. #18011896	C₂²	semidirect
56. #18011896	C₂²	semidirect
57. #18011895	C₂²	semidirect
58. #18011893	C₂²	semidirect
59. #18011893	C₂²	semidirect
60. #18011891	C₂²	semidirect
61. #18011891	C₂²	semidirect
62. #18011889	C₂²	semidirect
63. #18011889	C₂²	semidirect
64. #18011888	C₂²	semidirect
65. #18011888	C₂²	semidirect
66. #18011886	C₂²	semidirect
67. #18011886	C₂²	semidirect
68. #18011886	C₂²	semidirect
69. #18011884	C₂²	semidirect
70. #18011884	C₂²	semidirect
71. #18011884	C₂²	semidirect
72. #18011884	C₂²	semidirect
73. #18011883	C₂²	semidirect
74. #18011883	C₂²	semidirect
75. #18011883	C₂²	semidirect
76. #18011883	C₂²	semidirect
77. #18011882	C₂²	semidirect
78. #18011881	C₂²	semidirect
79. #18011881	C₂²	semidirect
80. #18011881	C₂²	semidirect
81. #18011879	C₂²	semidirect
82. #18011879	C₂²	semidirect
83. #18011876	C₂²	semidirect
84. #18011876	C₂²	semidirect
85. C₄×D₅₉₆	C₂²	semidirect
86. C₄×D₅₉₆	C₂²	semidirect
87. D₄×Dic₁₄₉	C₂²	semidirect
88. #18011873	C₂²	semidirect
89. #18011873	C₂²	semidirect
90. #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. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
99. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
100. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
102. #18011871	C₂²	semidirect
103. #18011871	C₂²	semidirect
104. #18011871	C₂²	semidirect
105. #18011868	C₂²	semidirect
106. C₂×#14558715	C₂²	semidirect
107. C₄⋊C₄×D₁₄₉	C₂²	semidirect
108. C₂×C₂²⋊Dic₁₄₉	C₂²	semidirect
109. C₂×#14558713	C₂²	semidirect
110. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
111. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
112. C₂×C₄×Dic₁₄₉	C₂²	semidirect
113. C₄²×D₁₄₉	C₂²	semidirect
114. C₂×#41×C₁₄₉	C₂²	semidirect
115. C₂³×C₄×C₁₄₉	C₂²	semidirect
116. #123×C₁₄₉	C₂²	semidirect
117. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
118. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
119. #121×C₁₄₉	C₂²	semidirect
120. #121×C₁₄₉	C₂²	semidirect
121. #120×C₁₄₉	C₂²	semidirect
122. C₄×D₄×C₁₄₉	C₂²	semidirect
123. C₄×D₄×C₁₄₉	C₂²	semidirect
124. #117×C₁₄₉	C₂²	semidirect
135. #14558736	D₄	semidirect
263. Dic₂₉₈	C₂×D₄	semidirect
269. D₅₉₆	C₂×D₄	semidirect
280. C₂²⋊D₁₄₉	C₂×D₄	semidirect
281. C₂²⋊D₁₄₉	#41	semidirect
306. C₄×D₁₄₉	C₂×D₄	semidirect
325. C₂×C₄×C₁₄₉	C₂×D₄	semidirect
345. C₂²×C₁₄₉	C₂×#41	semidirect
361. C₂×D₁₄₉	C₂×#41	semidirect
376. Dic₁₄₉	C₂×#41	semidirect
388. C₁₄₉	D₄×#41	semidirect
409. #525	D₁₄₉	semidirect
425. C₂×#41	C₂×D₁₄₉	semidirect
437. C₂³×C₄	C₂×D₁₄₉	semidirect
451. #123	C₂×D₁₄₉	semidirect
458. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
459. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
472. #121	C₂×D₁₄₉	semidirect
473. #121	C₂×D₁₄₉	semidirect
479. #120	C₂×D₁₄₉	semidirect
502. C₄×D₄	C₂×D₁₄₉	semidirect
503. C₄×D₄	C₂×D₁₄₉	semidirect
505. #117	C₂×D₁₄₉	semidirect
714. C₂×C₄	D₄×D₁₄₉	semidirect
749. C₂²	#41×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14558736	2
C₂×#41×D₁₄₉	2
#23750293	2
#23750288	2
#23750285	2
#23750281	2
#23750277	2
#23750273	2
#23750272	2
#23750267	2
#23750266	2
#23750262	2
#23750259	2
#23750257	2
#23750172	2
#23750171	2
#23750137	2
#23750134	2
#23750093	2
C₂×C₄×C₂²⋊D₁₄₉	2
C₄×D₄×D₁₄₉	2
#525×C₁₄₉	2
D₄×#41	149