Subgroups — #34058738

Order 19072.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750344	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750336	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750333	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750311	C₂	1	2	yes	maximal, complemented
5	#23750305	C₂	1	2	yes	maximal, complemented
6	#23750300	C₂	1	2	yes	maximal, complemented
7	#23750290	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750283	C₂	1	2	yes	maximal, complemented
9	#23750277	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750275	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750272	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750268	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750240	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750221	C₂	1	2	yes	maximal, complemented
15	#23750218	C₂	1	2	yes	maximal, complemented
16	#23750179	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750153	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750133	C₂	1	2	yes	maximal, complemented
19	C₂²⋊Q₈×D₁₄₉	C₂	1	2	yes	maximal, complemented
20	#23750107	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558737	C₂²	1	1	yes	characteristic
25	C₂×#14558736	C₂²	1	1	yes	characteristic
26	C₂×#14558735	C₂²	1	2	yes	complemented
27	C₂×Q₈×D₁₄₉	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	—
30	#18011910	C₂²	1	1	yes	characteristic, complemented
31	#18011910	C₂²	1	1	yes	characteristic, complemented
32	#18011909	C₂²	1	1	yes	characteristic, complemented
33	#18011906	C₂²	1	1	yes	characteristic, complemented
34	#18011904	C₂²	1	1	yes	characteristic, complemented
35	#18011904	C₂²	1	2	yes	complemented
36	#18011904	C₂²	1	2	yes	complemented
37	#18011904	C₂²	1	2	yes	complemented
38	#18011902	C₂²	1	2	yes	complemented
39	#18011901	C₂²	1	1	yes	characteristic, complemented
40	#18011901	C₂²	1	2	yes	complemented
41	#18011901	C₂²	1	2	yes	complemented
42	#18011898	C₂²	1	1	yes	characteristic
43	#18011897	C₂²	1	1	yes	characteristic, complemented
44	#18011897	C₂²	1	2	yes	complemented
45	#18011896	C₂²	1	1	yes	characteristic
46	#18011896	C₂²	1	2	yes	complemented
47	#18011894	C₂²	1	2	yes	complemented
48	#18011893	C₂²	1	1	yes	characteristic
49	#18011893	C₂²	1	2	yes	—
50	#18011893	C₂²	1	2	yes	—
51	#18011893	C₂²	1	2	yes	complemented
52	#18011893	C₂²	1	2	yes	complemented
53	#18011892	C₂²	1	2	yes	complemented
54	#18011891	C₂²	1	1	yes	characteristic
55	#18011891	C₂²	1	2	yes	—
56	#18011891	C₂²	1	1	yes	characteristic, complemented
57	#18011890	C₂²	1	2	yes	complemented
58	#18011889	C₂²	1	1	yes	characteristic
59	#18011889	C₂²	1	2	yes	—
60	#18011889	C₂²	1	2	yes	complemented
61	#18011889	C₂²	1	2	yes	complemented
62	#18011888	C₂²	1	2	yes	complemented
63	#18011888	C₂²	1	2	yes	complemented
64	#18011888	C₂²	1	2	yes	complemented
65	#18011887	C₂²	1	1	yes	characteristic
66	#18011887	C₂²	1	2	yes	—
67	#18011887	C₂²	1	2	yes	complemented
68	#18011887	C₂²	1	2	yes	complemented
69	#18011884	C₂²	1	1	yes	characteristic
70	#18011884	C₂²	1	2	yes	—
71	#18011884	C₂²	1	2	yes	complemented
72	#18011882	C₂²	1	2	yes	—
73	#18011882	C₂²	1	1	yes	characteristic
74	#18011881	C₂²	1	2	yes	—
75	#18011879	C₂²	1	2	yes	—
76	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
78	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
80	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
82	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
83	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
84	C₄×D₅₉₆	C₂²	1	2	yes	complemented
85	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
86	#18011873	C₂²	1	1	yes	characteristic
87	#18011873	C₂²	1	1	yes	characteristic
88	#18011873	C₂²	1	2	yes	—
89	#18011873	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
93	#18011871	C₂²	1	2	yes	—
94	#18011871	C₂²	1	2	yes	—
95	#18011871	C₂²	1	2	yes	complemented
96	#18011871	C₂²	1	2	yes	complemented
97	#18011869	C₂²	1	2	yes	complemented
98	#18011868	C₂²	1	2	yes	—
99	#18011868	C₂²	1	1	yes	characteristic, complemented
100	#18011868	C₂²	1	2	yes	complemented
101	#18011867	C₂²	1	2	yes	complemented
102	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
104	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
111	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
113	#126×C₁₄₉	C₂²	1	2	yes	complemented
114	#124×C₁₄₉	C₂²	1	1	yes	characteristic
115	#124×C₁₄₉	C₂²	1	2	yes	complemented
116	#123×C₁₄₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₄₉	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
122	#117×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₄₉	C₂³	1	2	yes	—
124	#14558737	—	2	4	no	—
125	#14558736	—	2	4	no	—
126	#14558735	—	4	4	no	—
127	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₉₈	C₂³	1	2	yes	—
129	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₉₈	C₂³	1	2	yes	—
131	Q₈×D₁₄₉	—	4	4	no	—
132	C₂×D₅₉₆	C₂³	1	2	yes	—
133	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
134	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
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	D₄×D₁₄₉	—	2	4	no	—
141	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
142	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
143	C₂×C₄×D₁₄₉	—	4	4	no	—
144	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
148	C₂×C₄×D₁₄₉	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	2	yes	—
152	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
153	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
155	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
156	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
158	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
159	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
163	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
164	#14558715	C₂³	1	1	yes	characteristic
165	#14558715	C₂³	1	2	yes	—
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	2	yes	—
172	#14558715	C₂³	1	2	yes	—
173	#14558715	C₂³	1	2	yes	—
174	#14558715	C₂³	1	2	yes	—
175	#14558715	C₂³	1	1	yes	characteristic
176	#14558715	C₂³	1	2	yes	—
177	#14558715	C₂³	1	1	yes	characteristic
178	#14558715	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
185	#14558713	C₂³	1	1	yes	characteristic
186	#14558713	C₂³	1	1	yes	characteristic
187	#14558713	C₂³	1	1	yes	characteristic
188	#14558713	C₂³	1	1	yes	characteristic
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	2	yes	—
195	#14558713	C₂³	1	1	yes	characteristic
196	#14558713	C₂³	1	2	yes	—
197	#14558713	C₂³	1	2	yes	—
198	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₄₉	C₂³	1	2	yes	—
200	C₄×Dic₁₄₉	C₂³	1	2	yes	—
201	C₄×Dic₁₄₉	C₂³	1	2	yes	—
202	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
205	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
207	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
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	2	yes	—
222	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
225	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
226	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
227	C₄²×C₁₄₉	C₂³	1	2	yes	—
228	C₂²×D₁₄₉	—	2	4	no	—
229	C₂²×D₁₄₉	—	2	4	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	D₅₉₆	—	2	4	no	—
239	D₅₉₆	—	2	2	no	—
240	D₅₉₆	#41	1	4	yes	complemented
241	C₂²⋊D₁₄₉	—	2	4	no	—
242	C₂²⋊D₁₄₉	—	2	4	no	—
243	C₂²⋊D₁₄₉	—	2	2	no	—
244	C₂²⋊D₁₄₉	—	2	2	no	—
245	C₂²⋊D₁₄₉	—	4	2	no	—
246	C₂×Dic₁₄₉	—	2	4	no	—
247	C₂×Dic₁₄₉	—	4	2	no	—
248	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
249	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
252	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
254	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
257	C₄×D₁₄₉	—	2	4	no	—
258	C₄×D₁₄₉	—	2	4	no	—
259	C₄×D₁₄₉	—	2	2	no	—
260	C₄×D₁₄₉	—	2	2	no	—
261	C₄×D₁₄₉	—	2	2	no	—
262	C₄×D₁₄₉	—	2	2	no	—
263	C₄×D₁₄₉	—	2	4	no	—
264	C₄×D₁₄₉	—	4	2	no	—
265	C₄×D₁₄₉	—	4	2	no	—
266	C₄×D₁₄₉	—	4	2	no	—
267	C₄×D₁₄₉	—	4	2	no	—
268	C₄×D₁₄₉	—	4	2	no	—
269	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
270	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
271	Q₈×C₁₄₉	—	2	2	no	—
272	Q₈×C₁₄₉	—	4	2	no	—
273	D₄×C₁₄₉	—	2	2	no	—
274	D₄×C₁₄₉	—	4	2	no	—
275	C₂×C₄×C₁₄₉	—	2	2	no	—
276	C₂×C₄×C₁₄₉	—	4	2	no	—
277	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
280	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
281	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
283	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₁₄₉	—	2	1	no	—
287	C₂²×C₁₄₉	—	2	2	no	—
288	C₂²×C₁₄₉	—	2	2	no	—
289	C₂²×C₁₄₉	—	2	1	no	—
290	C₂²×C₁₄₉	—	2	1	no	—
291	C₂²×C₁₄₉	—	2	2	no	—
292	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
293	C₂×D₁₄₉	—	2	1	no	—
294	C₂×D₁₄₉	—	2	2	no	—
295	C₂×D₁₄₉	—	2	1	no	—
296	C₂×D₁₄₉	—	2	2	no	—
297	C₂×D₁₄₉	—	2	1	no	—
298	C₂×D₁₄₉	—	2	1	no	—
299	C₂×D₁₄₉	—	2	1	no	—
300	C₂×D₁₄₉	—	4	8	no	—
301	C₂×D₁₄₉	C₂×#41	1	4	yes	—
302	C₂×D₁₄₉	2₋¹⁺⁴	1	2	yes	—
303	C₄×C₁₄₉	—	2	1	no	—
304	C₄×C₁₄₉	—	2	2	no	—
305	C₄×C₁₄₉	—	2	1	no	—
306	C₄×C₁₄₉	—	2	2	no	—
307	C₄×C₁₄₉	—	2	2	no	—
308	C₄×C₁₄₉	—	2	1	no	—
309	C₄×C₁₄₉	—	2	1	no	—
310	C₄×C₁₄₉	—	2	1	no	—
311	C₄×C₁₄₉	C₂×#41	1	2	yes	—
312	Dic₁₄₉	—	2	1	no	—
313	Dic₁₄₉	—	2	1	no	—
314	Dic₁₄₉	—	2	2	no	—
315	Dic₁₄₉	—	2	2	no	—
316	Dic₁₄₉	—	2	1	no	—
317	Dic₁₄₉	—	2	2	no	—
318	Dic₁₄₉	—	2	1	no	—
319	Dic₁₄₉	—	2	1	no	—
320	Dic₁₄₉	H(5,𝔽₂)	1	2	yes	—
321	C₂×C₁₄₉	—	4	2	no	—
322	C₂×C₁₄₉	—	4	1	no	—
323	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
324	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
326	D₁₄₉	—	2	2	no	—
327	D₁₄₉	—	2	4	no	—
328	D₁₄₉	—	4	1	no	—
329	C₁₄₉	#3520	1	1	yes	characteristic, complemented, Sylow
330	#3520	—	149	1	no	maximal, Sylow
331	#556	—	149	1	no	—
332	#554	—	149	1	no	—
333	#554	—	149	1	no	—
334	#552	—	149	2	no	—
335	#551	—	149	2	no	—
336	#551	—	149	2	no	—
337	D₄×Q₈	—	149	1	no	—
338	#548	—	149	2	no	—
339	#547	—	149	1	no	—
340	#547	—	149	1	no	—
341	#546	—	149	1	no	—
342	#546	—	149	1	no	—
343	#542	—	149	1	no	—
344	#542	D₁₄₉	1	1	yes	characteristic, complemented
345	#539	—	149	2	no	—
346	#539	—	149	2	no	—
347	#533	—	149	1	no	—
348	#529	—	149	1	no	—
349	#525	—	149	2	no	—
350	C₂×C₂²⋊Q₈	—	149	2	no	—
351	#520	—	149	1	no	—
352	#520	—	149	1	no	—
353	C₂×C₄×D₄	—	149	1	no	—
354	C₂×#41	—	149	1	no	—
355	C₂×#41	—	149	2	no	—
356	C₂×#41	—	149	1	no	—
357	C₂²×Q₈	—	149	2	no	—
358	C₂²×D₄	—	149	1	no	—
359	C₂³×C₄	—	149	2	no	—
360	C₄⋊Q₈	—	149	1	no	—
361	C₄⋊Q₈	—	149	1	no	—
362	C₄⋊Q₈	—	149	1	no	—
363	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
364	#126	—	149	1	no	—
365	#126	—	149	1	no	—
366	#126	—	149	2	no	—
367	#126	—	149	2	no	—
368	#126	—	149	2	no	—
369	#126	C₂×D₁₄₉	1	2	yes	complemented
370	#125	—	149	1	no	—
371	#125	—	149	2	no	—
372	#125	—	149	2	no	—
373	#125	—	149	2	no	—
374	#124	—	149	1	no	—
375	#124	—	149	1	no	—
376	#124	—	149	2	no	—
377	#124	C₂×D₁₄₉	1	1	yes	characteristic
378	#124	C₂×D₁₄₉	1	2	yes	complemented
379	#123	—	149	2	no	—
380	#123	—	149	2	no	—
381	#123	—	149	1	no	—
382	#123	—	149	2	no	—
383	#123	—	149	1	no	—
384	#123	—	149	2	no	—
385	#123	—	149	2	no	—
386	#123	—	149	2	no	—
387	#123	—	149	2	no	—
388	#123	C₂×D₁₄₉	1	2	yes	complemented
389	C₂²⋊Q₈	—	149	2	no	—
390	C₂²⋊Q₈	—	149	1	no	—
391	C₂²⋊Q₈	—	149	2	no	—
392	C₂²⋊Q₈	—	149	2	no	—
393	C₂²⋊Q₈	—	149	2	no	—
394	C₂²⋊Q₈	—	149	1	no	—
395	C₂²⋊Q₈	—	149	2	no	—
396	C₂²⋊Q₈	—	149	2	no	—
397	C₂²⋊Q₈	—	149	2	no	—
398	C₂²⋊Q₈	—	149	1	no	—
399	C₂²⋊Q₈	—	149	2	no	—
400	C₂²⋊Q₈	—	149	1	no	—
401	C₂²⋊Q₈	—	149	2	no	—
402	C₂²⋊Q₈	—	149	2	no	—
403	C₂²⋊Q₈	—	149	2	no	—
404	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
405	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
406	#121	—	149	2	no	—
407	#121	—	149	1	no	—
408	#121	—	149	1	no	—
409	#121	—	149	2	no	—
410	#121	—	149	2	no	—
411	#121	C₂×D₁₄₉	1	1	yes	characteristic
412	#120	—	149	2	no	—
413	#120	—	149	2	no	—
414	C₄×Q₈	—	149	1	no	—
415	C₄×Q₈	—	149	1	no	—
416	C₄×Q₈	—	149	1	no	—
417	C₄×Q₈	—	149	1	no	—
418	C₄×Q₈	—	149	2	no	—
419	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
420	C₄×D₄	—	149	1	no	—
421	C₄×D₄	—	149	2	no	—
422	C₄×D₄	—	149	1	no	—
423	C₄×D₄	—	149	1	no	—
424	C₄×D₄	—	149	1	no	—
425	C₄×D₄	—	149	2	no	—
426	C₄×D₄	—	149	1	no	—
427	C₄×D₄	—	149	2	no	—
428	C₄×D₄	—	149	2	no	—
429	C₄×D₄	—	149	2	no	—
430	C₄×D₄	—	149	2	no	—
431	C₄×D₄	—	149	2	no	—
432	C₄×D₄	—	149	1	no	—
433	C₄×D₄	—	149	1	no	—
434	C₄×D₄	—	149	2	no	—
435	C₄×D₄	—	149	1	no	—
436	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
437	#117	—	149	2	no	—
438	#117	—	149	2	no	—
439	#117	—	149	1	no	—
440	#117	—	149	2	no	—
441	#117	—	149	2	no	—
442	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
443	C₂×C₄⋊C₄	—	149	1	no	—
444	C₂×C₄⋊C₄	—	149	1	no	—
445	C₂×C₄⋊C₄	—	149	2	no	—
446	C₂×C₄⋊C₄	—	149	2	no	—
447	C₂×C₄⋊C₄	—	149	1	no	—
448	C₂×C₄⋊C₄	—	149	2	no	—
449	C₂×C₂²⋊C₄	—	149	2	no	—
450	C₂×C₂²⋊C₄	—	149	2	no	—
451	C₂×C₂²⋊C₄	—	149	2	no	—
452	C₂×C₄²	—	149	1	no	—
453	C₂⁴	—	149	2	no	—
454	#41	—	298	4	no	—
455	#41	—	298	4	no	—
456	#41	—	596	4	no	—
457	C₂×Q₈	—	596	4	no	—
458	C₂×Q₈	—	149	1	no	—
459	C₂×Q₈	—	149	1	no	—
460	C₂×Q₈	—	149	2	no	—
461	C₂×Q₈	—	149	2	no	—
462	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
464	C₂×D₄	—	298	4	no	—
465	C₂×D₄	—	149	1	no	—
466	C₂×D₄	—	149	2	no	—
467	C₂×D₄	—	149	2	no	—
468	C₂×D₄	—	149	1	no	—
469	C₂×D₄	—	149	2	no	—
470	C₂×D₄	—	149	1	no	—
471	C₂×D₄	—	149	2	no	—
472	C₂×D₄	—	149	1	no	—
473	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
474	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
475	C₂²×C₄	—	596	4	no	—
476	C₂²×C₄	—	149	2	no	—
477	C₂²×C₄	—	149	1	no	—
478	C₂²×C₄	—	149	1	no	—
479	C₂²×C₄	—	149	1	no	—
480	C₂²×C₄	—	149	2	no	—
481	C₂²×C₄	—	149	2	no	—
482	C₂²×C₄	—	149	1	no	—
483	C₂²×C₄	—	149	2	no	—
484	C₂²×C₄	—	149	2	no	—
485	C₂²×C₄	—	149	2	no	—
486	C₂²×C₄	—	149	2	no	—
487	C₂²×C₄	—	149	2	no	—
488	C₂²×C₄	—	149	2	no	—
489	C₂²×C₄	—	149	2	no	—
490	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
491	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
492	C₄⋊C₄	—	149	1	no	—
493	C₄⋊C₄	—	149	1	no	—
494	C₄⋊C₄	—	149	2	no	—
495	C₄⋊C₄	—	149	2	no	—
496	C₄⋊C₄	—	149	1	no	—
497	C₄⋊C₄	—	149	2	no	—
498	C₄⋊C₄	—	149	2	no	—
499	C₄⋊C₄	—	149	1	no	—
500	C₄⋊C₄	—	149	2	no	—
501	C₄⋊C₄	—	149	2	no	—
502	C₄⋊C₄	—	149	2	no	—
503	C₄⋊C₄	—	149	2	no	—
504	C₄⋊C₄	—	149	1	no	—
505	C₄⋊C₄	—	149	1	no	—
506	C₄⋊C₄	—	149	2	no	—
507	C₄⋊C₄	—	149	2	no	—
508	C₄⋊C₄	—	149	2	no	—
509	C₄⋊C₄	—	149	1	no	—
510	C₄⋊C₄	—	149	1	no	—
511	C₄⋊C₄	—	149	2	no	—
512	C₄⋊C₄	—	149	2	no	—
513	C₄⋊C₄	—	149	1	no	—
514	C₄⋊C₄	—	149	1	no	—
515	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
522	C₂²⋊C₄	—	149	2	no	—
523	C₂²⋊C₄	—	149	2	no	—
524	C₂²⋊C₄	—	149	2	no	—
525	C₂²⋊C₄	—	149	2	no	—
526	C₂²⋊C₄	—	149	1	no	—
527	C₂²⋊C₄	—	149	1	no	—
528	C₂²⋊C₄	—	149	1	no	—
529	C₂²⋊C₄	—	149	1	no	—
530	C₂²⋊C₄	—	149	2	no	—
531	C₂²⋊C₄	—	149	2	no	—
532	C₂²⋊C₄	—	149	2	no	—
533	C₂²⋊C₄	—	149	2	no	—
534	C₂²⋊C₄	—	149	2	no	—
535	C₂²⋊C₄	—	149	2	no	—
536	C₂²⋊C₄	—	149	1	no	—
537	C₂²⋊C₄	—	149	1	no	—
538	C₂²⋊C₄	—	149	1	no	—
539	C₂²⋊C₄	—	149	2	no	—
540	C₂²⋊C₄	—	149	1	no	—
541	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
548	C₄²	—	149	1	no	—
549	C₄²	—	149	1	no	—
550	C₄²	—	149	1	no	—
551	C₄²	—	149	2	no	—
552	C₄²	—	149	2	no	—
553	C₄²	—	149	2	no	—
554	C₄²	—	149	1	no	—
555	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
556	C₄²	C₂²×D₁₄₉	1	2	yes	—
557	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
558	C₂³	—	298	4	no	—
559	C₂³	—	298	4	no	—
560	C₂³	—	596	2	no	—
561	C₂³	—	149	1	no	—
562	C₂³	—	149	1	no	—
563	C₂³	—	149	2	no	—
564	C₂³	C₂³×D₁₄₉	1	2	yes	—
565	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	298	2	no	—
569	Q₈	—	298	4	no	—
570	Q₈	—	298	2	no	—
571	Q₈	—	596	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	298	2	no	—
575	D₄	—	298	4	no	—
576	D₄	—	298	4	no	—
577	D₄	—	298	2	no	—
578	D₄	—	298	4	no	—
579	D₄	—	298	2	no	—
580	D₄	—	596	2	no	—
581	D₄	—	149	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	298	2	no	—
585	C₂×C₄	—	298	4	no	—
586	C₂×C₄	—	298	4	no	—
587	C₂×C₄	—	298	2	no	—
588	C₂×C₄	—	298	4	no	—
589	C₂×C₄	—	298	4	no	—
590	C₂×C₄	—	298	2	no	—
591	C₂×C₄	—	298	2	no	—
592	C₂×C₄	—	596	2	no	—
593	C₂×C₄	—	596	2	no	—
594	C₂×C₄	—	596	2	no	—
595	C₂×C₄	—	596	2	no	—
596	C₂×C₄	—	596	2	no	—
597	C₂×C₄	—	596	2	no	—
598	C₂×C₄	—	149	1	no	—
599	C₂×C₄	—	149	1	no	—
600	C₂×C₄	—	149	2	no	—
601	C₂×C₄	—	149	1	no	—
602	C₂×C₄	—	149	2	no	—
603	C₂×C₄	—	149	1	no	—
604	C₂×C₄	—	149	2	no	—
605	C₂×C₄	—	149	1	no	—
606	C₂×C₄	—	149	1	no	—
607	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
610	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
613	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
615	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	298	1	no	—
623	C₂²	—	298	2	no	—
624	C₂²	—	298	1	no	—
625	C₂²	—	298	2	no	—
626	C₂²	—	298	1	no	—
627	C₂²	—	298	1	no	—
628	C₂²	—	298	1	no	—
629	C₂²	—	596	8	no	—
630	C₂²	—	149	4	no	—
631	C₂²	—	149	2	no	—
632	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	298	1	no	—
642	C₄	—	298	1	no	—
643	C₄	—	298	2	no	—
644	C₄	—	298	2	no	—
645	C₄	—	298	2	no	—
646	C₄	—	298	1	no	—
647	C₄	—	298	1	no	—
648	C₄	—	298	1	no	—
649	C₄	—	149	2	no	—
650	C₄	#41×D₁₄₉	1	2	yes	—
651	C₂	—	4	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	298	2	no	—
654	C₂	—	298	4	no	—
655	C₂	—	596	1	no	—
656	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
657	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic
658	C₂	2₋¹⁺⁴×D₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#542×C₁₄₉	C₂
hypercenter	#542	D₁₄₉
hypocenter	C₁₄₉	#3520
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #23750344	C₂	semidirect
2. #23750336	C₂	semidirect
3. #23750333	C₂	semidirect
4. #23750311	C₂	semidirect
5. #23750305	C₂	semidirect
6. #23750300	C₂	semidirect
7. #23750290	C₂	semidirect
8. #23750283	C₂	semidirect
9. #23750277	C₂	semidirect
10. #23750275	C₂	semidirect
11. #23750272	C₂	semidirect
12. #23750268	C₂	semidirect
13. #23750240	C₂	semidirect
14. #23750221	C₂	semidirect
15. #23750218	C₂	semidirect
16. #23750179	C₂	semidirect
17. #23750153	C₂	semidirect
18. #23750133	C₂	semidirect
19. C₂²⋊Q₈×D₁₄₉	C₂	semidirect
20. #23750107	C₂	semidirect
21. #23750105	C₂	semidirect
22. C₄×D₄×D₁₄₉	C₂	semidirect
23. #542×C₁₄₉	C₂	semidirect
26. C₂×#14558735	C₂²	semidirect
27. C₂×Q₈×D₁₄₉	C₂²	semidirect
30. #18011910	C₂²	semidirect
31. #18011910	C₂²	semidirect
32. #18011909	C₂²	semidirect
33. #18011906	C₂²	semidirect
34. #18011904	C₂²	semidirect
35. #18011904	C₂²	semidirect
36. #18011904	C₂²	semidirect
37. #18011904	C₂²	semidirect
38. #18011902	C₂²	semidirect
39. #18011901	C₂²	semidirect
40. #18011901	C₂²	semidirect
41. #18011901	C₂²	semidirect
43. #18011897	C₂²	semidirect
44. #18011897	C₂²	semidirect
46. #18011896	C₂²	semidirect
47. #18011894	C₂²	semidirect
51. #18011893	C₂²	semidirect
52. #18011893	C₂²	semidirect
53. #18011892	C₂²	semidirect
56. #18011891	C₂²	semidirect
57. #18011890	C₂²	semidirect
60. #18011889	C₂²	semidirect
61. #18011889	C₂²	semidirect
62. #18011888	C₂²	semidirect
63. #18011888	C₂²	semidirect
64. #18011888	C₂²	semidirect
67. #18011887	C₂²	semidirect
68. #18011887	C₂²	semidirect
71. #18011884	C₂²	semidirect
76. Q₈×Dic₁₄₉	C₂²	semidirect
77. C₄×Dic₂₉₈	C₂²	semidirect
78. C₄×Dic₂₉₈	C₂²	semidirect
79. C₄×Dic₂₉₈	C₂²	semidirect
80. C₄×Dic₂₉₈	C₂²	semidirect
84. C₄×D₅₉₆	C₂²	semidirect
89. #18011873	C₂²	semidirect
92. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
95. #18011871	C₂²	semidirect
96. #18011871	C₂²	semidirect
97. #18011869	C₂²	semidirect
99. #18011868	C₂²	semidirect
100. #18011868	C₂²	semidirect
101. #18011867	C₂²	semidirect
102. C₂×C₄⋊Dic₁₄₉	C₂²	semidirect
104. C₄⋊C₄×D₁₄₉	C₂²	semidirect
105. C₄⋊C₄×D₁₄₉	C₂²	semidirect
106. C₄⋊C₄×D₁₄₉	C₂²	semidirect
107. C₄⋊C₄×D₁₄₉	C₂²	semidirect
112. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
113. #126×C₁₄₉	C₂²	semidirect
115. #124×C₁₄₉	C₂²	semidirect
116. #123×C₁₄₉	C₂²	semidirect
117. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
118. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
120. C₄×Q₈×C₁₄₉	C₂²	semidirect
122. #117×C₁₄₉	C₂²	semidirect
240. D₅₉₆	#41	semidirect
329. C₁₄₉	#3520	semidirect
344. #542	D₁₄₉	semidirect
363. C₄⋊Q₈	C₂×D₁₄₉	semidirect
369. #126	C₂×D₁₄₉	semidirect
378. #124	C₂×D₁₄₉	semidirect
388. #123	C₂×D₁₄₉	semidirect
404. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
405. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
419. C₄×Q₈	C₂×D₁₄₉	semidirect
442. #117	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750344	2
#23750336	2
#23750333	2
#23750311	2
#23750305	2
#23750300	2
#23750290	2
#23750283	2
#23750277	2
#23750275	2
#23750272	2
#23750268	2
#23750240	2
#23750221	2
#23750218	2
#23750179	2
#23750153	2
#23750133	2
C₂²⋊Q₈×D₁₄₉	2
#23750107	2
#23750105	2
C₄×D₄×D₁₄₉	2
#542×C₁₄₉	2
#3520	149