Subgroups — #34058665

Order 19072.

1014 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750353	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750331	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750330	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750320	C₂	1	2	yes	maximal, complemented
5	#23750314	C₂	1	2	yes	maximal, complemented
6	#23750314	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750311	C₂	1	2	yes	maximal, complemented
8	#23750307	C₂	1	2	yes	maximal, complemented
9	#23750280	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750277	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750277	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750238	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750235	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750218	C₂	1	2	yes	maximal, complemented
15	#23750216	C₂	1	2	yes	maximal, complemented
16	#23750177	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750155	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750153	C₂	1	2	yes	maximal, complemented
19	#125×D₁₄₉	C₂	1	2	yes	maximal, complemented
20	#23750107	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750106	C₂	1	1	yes	maximal, characteristic, complemented
22	#23750093	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×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×#14558736	C₂²	1	1	yes	characteristic
27	#18011911	C₂²	1	1	yes	characteristic
28	#18011910	C₂²	1	1	yes	characteristic
29	#18011909	C₂²	1	1	yes	characteristic
30	#18011909	C₂²	1	1	yes	characteristic
31	#18011906	C₂²	1	2	yes	—
32	#18011906	C₂²	1	1	yes	characteristic
33	#18011906	C₂²	1	2	yes	—
34	#18011904	C₂²	1	2	yes	—
35	#18011904	C₂²	1	1	yes	characteristic
36	#18011904	C₂²	1	2	yes	—
37	#18011904	C₂²	1	2	yes	—
38	#18011903	C₂²	1	2	yes	—
39	#18011903	C₂²	1	2	yes	—
40	#18011902	C₂²	1	2	yes	—
41	#18011902	C₂²	1	2	yes	—
42	#18011902	C₂²	1	1	yes	characteristic
43	#18011902	C₂²	1	2	yes	—
44	#18011901	C₂²	1	1	yes	characteristic
45	#18011901	C₂²	1	2	yes	—
46	#18011901	C₂²	1	2	yes	—
47	#18011901	C₂²	1	2	yes	—
48	#18011901	C₂²	1	2	yes	—
49	#18011901	C₂²	1	2	yes	—
50	#18011897	C₂²	1	1	yes	characteristic
51	#18011896	C₂²	1	2	yes	—
52	#18011896	C₂²	1	2	yes	—
53	#18011895	C₂²	1	1	yes	characteristic
54	#18011893	C₂²	1	2	yes	—
55	#18011893	C₂²	1	2	yes	—
56	#18011893	C₂²	1	2	yes	—
57	#18011893	C₂²	1	2	yes	—
58	#18011893	C₂²	1	2	yes	—
59	#18011892	C₂²	1	1	yes	characteristic
60	#18011891	C₂²	1	2	yes	—
61	#18011891	C₂²	1	1	yes	characteristic
62	#18011891	C₂²	1	1	yes	characteristic
63	#18011890	C₂²	1	1	yes	characteristic
64	#18011890	C₂²	1	2	yes	—
65	#18011890	C₂²	1	1	yes	characteristic
66	#18011889	C₂²	1	2	yes	—
67	#18011889	C₂²	1	2	yes	—
68	#18011889	C₂²	1	2	yes	—
69	#18011888	C₂²	1	1	yes	characteristic
70	#18011888	C₂²	1	2	yes	—
71	#18011884	C₂²	1	2	yes	—
72	#18011884	C₂²	1	2	yes	—
73	#18011883	C₂²	1	1	yes	characteristic
74	#18011882	C₂²	1	2	yes	—
75	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
76	C₄×Dic₂₉₈	C₂²	1	2	yes	—
77	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
78	#18011876	C₂²	1	1	yes	characteristic
79	#18011876	C₂²	1	2	yes	—
80	#18011876	C₂²	1	1	yes	characteristic
81	#18011876	C₂²	1	1	yes	characteristic
82	#18011876	C₂²	1	1	yes	characteristic
83	C₄×D₅₉₆	C₂²	1	2	yes	—
84	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
85	#18011873	C₂²	1	1	yes	characteristic
86	#18011873	C₂²	1	1	yes	characteristic
87	#18011873	C₂²	1	2	yes	—
88	#18011873	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
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	—
94	#18011871	C₂²	1	2	yes	—
95	#18011871	C₂²	1	2	yes	—
96	#18011870	C₂²	1	1	yes	characteristic
97	#18011869	C₂²	1	2	yes	—
98	#18011868	C₂²	1	2	yes	—
99	#18011868	C₂²	1	1	yes	characteristic
100	#18011868	C₂²	1	2	yes	—
101	#18011868	C₂²	1	2	yes	—
102	#18011867	C₂²	1	2	yes	—
103	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
104	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
105	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
106	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
107	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
108	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
109	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
110	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
111	C₄²×D₁₄₉	C₂²	1	2	yes	—
112	#126×C₁₄₉	C₂²	1	2	yes	—
113	#125×C₁₄₉	C₂²	1	2	yes	—
114	#125×C₁₄₉	C₂²	1	1	yes	characteristic
115	#123×C₁₄₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
120	#117×C₁₄₉	C₂²	1	2	yes	—
121	#117×C₁₄₉	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
123	#14558737	—	2	4	no	—
124	#14558736	—	2	4	no	—
125	#14558736	—	2	4	no	—
126	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₉₈	C₂³	1	2	yes	—
130	C₂×D₅₉₆	C₂³	1	2	yes	—
131	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
139	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
140	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
141	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
143	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
144	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
145	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
147	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
148	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
149	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
150	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
152	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
153	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
157	#14558715	C₂³	1	2	yes	—
158	#14558715	C₂³	1	2	yes	—
159	#14558715	C₂³	1	2	yes	—
160	#14558715	C₂³	1	2	yes	—
161	#14558715	C₂³	1	2	yes	—
162	#14558715	C₂³	1	1	yes	characteristic
163	#14558715	C₂³	1	1	yes	characteristic
164	#14558715	C₂³	1	2	yes	—
165	#14558715	C₂³	1	1	yes	characteristic
166	#14558715	C₂³	1	2	yes	—
167	#14558715	C₂³	1	2	yes	—
168	#14558715	C₂³	1	2	yes	—
169	#14558715	C₂³	1	1	yes	characteristic
170	#14558715	C₂³	1	1	yes	characteristic
171	#14558715	C₂³	1	1	yes	characteristic
172	#14558715	C₂³	1	2	yes	—
173	#14558715	C₂³	1	2	yes	—
174	#14558715	C₂³	1	2	yes	—
175	#14558715	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
182	#14558713	C₂³	1	1	yes	characteristic
183	#14558713	C₂³	1	1	yes	characteristic
184	#14558713	C₂³	1	2	yes	—
185	#14558713	C₂³	1	2	yes	—
186	#14558713	C₂³	1	1	yes	characteristic
187	#14558713	C₂³	1	1	yes	characteristic
188	#14558713	C₂³	1	2	yes	—
189	#14558713	C₂³	1	2	yes	—
190	#14558713	C₂³	1	2	yes	—
191	#14558713	C₂³	1	2	yes	—
192	C₄×Dic₁₄₉	C₂³	1	2	yes	—
193	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₄₉	C₂³	1	2	yes	—
195	C₄×Dic₁₄₉	C₂³	1	2	yes	—
196	C₄×Dic₁₄₉	C₂³	1	2	yes	—
197	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₄₉	C₂³	1	2	yes	—
201	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
207	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
208	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
210	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
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	C₂²⋊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	1	yes	characteristic
221	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
222	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
223	C₄²×C₁₄₉	C₂³	1	2	yes	—
224	C₄²×C₁₄₉	C₂³	1	2	yes	—
225	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
226	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
227	Dic₂₉₈	—	2	2	no	—
228	Dic₂₉₈	—	2	2	no	—
229	Dic₂₉₈	—	2	2	no	—
230	Dic₂₉₈	—	4	2	no	—
231	D₅₉₆	—	2	4	no	—
232	D₅₉₆	#41	1	4	yes	—
233	C₂²⋊D₁₄₉	—	2	4	no	—
234	C₂²⋊D₁₄₉	—	2	4	no	—
235	C₂²⋊D₁₄₉	—	2	2	no	—
236	C₂²⋊D₁₄₉	—	4	1	no	—
237	C₂×Dic₁₄₉	—	2	2	no	—
238	C₂×Dic₁₄₉	—	4	1	no	—
239	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
240	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
241	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
243	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
244	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
245	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
249	C₄×D₁₄₉	—	2	4	no	—
250	C₄×D₁₄₉	—	2	4	no	—
251	C₄×D₁₄₉	—	2	4	no	—
252	C₄×D₁₄₉	—	2	2	no	—
253	C₄×D₁₄₉	—	2	4	no	—
254	C₄×D₁₄₉	—	4	2	no	—
255	C₄×D₁₄₉	—	4	2	no	—
256	C₄×D₁₄₉	—	4	2	no	—
257	C₄×D₁₄₉	—	4	2	no	—
258	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
259	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
260	Q₈×C₁₄₉	—	2	2	no	—
261	D₄×C₁₄₉	—	4	1	no	—
262	C₂×C₄×C₁₄₉	—	2	2	no	—
263	C₂×C₄×C₁₄₉	—	2	2	no	—
264	C₂×C₄×C₁₄₉	—	4	2	no	—
265	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
267	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
270	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
271	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
272	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₁₄₉	—	2	1	no	—
275	C₂²×C₁₄₉	—	2	1	no	—
276	C₂²×C₁₄₉	—	2	1	no	—
277	C₂²×C₁₄₉	—	2	1	no	—
278	C₂²×C₁₄₉	—	2	1	no	—
279	C₂²×C₁₄₉	—	2	1	no	—
280	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
281	C₂×D₁₄₉	—	2	2	no	—
282	C₂×D₁₄₉	—	2	2	no	—
283	C₂×D₁₄₉	—	2	1	no	—
284	C₂×D₁₄₉	—	2	1	no	—
285	C₂×D₁₄₉	—	2	1	no	—
286	C₂×D₁₄₉	C₂×#41	1	4	yes	—
287	C₄×C₁₄₉	—	2	1	no	—
288	C₄×C₁₄₉	—	2	1	no	—
289	C₄×C₁₄₉	—	2	2	no	—
290	C₄×C₁₄₉	—	2	2	no	—
291	C₄×C₁₄₉	—	2	1	no	—
292	C₄×C₁₄₉	—	2	2	no	—
293	C₄×C₁₄₉	—	2	2	no	—
294	C₄×C₁₄₉	—	2	1	no	—
295	C₄×C₁₄₉	C₂×#41	1	2	yes	—
296	Dic₁₄₉	—	2	1	no	—
297	Dic₁₄₉	—	2	2	no	—
298	Dic₁₄₉	—	2	2	no	—
299	Dic₁₄₉	—	2	1	no	—
300	Dic₁₄₉	—	2	1	no	—
301	Dic₁₄₉	—	2	1	no	—
302	Dic₁₄₉	—	2	1	no	—
303	Dic₁₄₉	—	2	2	no	—
304	Dic₁₄₉	—	2	1	no	—
305	Dic₁₄₉	2₋¹⁺⁴	1	2	yes	—
306	C₂×C₁₄₉	—	4	1	no	—
307	C₂×C₁₄₉	—	4	1	no	—
308	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
309	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	C₂×C₁₄₉	#585	1	1	yes	characteristic
311	D₁₄₉	—	2	4	no	—
312	D₁₄₉	—	4	1	no	—
313	C₁₄₉	#3515	1	1	yes	characteristic, complemented, Sylow
314	#3515	—	149	1	no	maximal, Sylow
315	#557	—	149	1	no	—
316	#554	—	149	1	no	—
317	#554	—	149	1	no	—
318	#553	—	149	2	no	—
319	#552	—	149	2	no	—
320	#552	—	149	2	no	—
321	#552	—	149	1	no	—
322	#552	—	149	2	no	—
323	#552	D₁₄₉	1	1	yes	characteristic, complemented
324	#547	—	149	1	no	—
325	#547	—	149	1	no	—
326	#547	—	149	1	no	—
327	#541	—	149	1	no	—
328	#541	—	149	1	no	—
329	#539	—	149	2	no	—
330	#539	—	149	2	no	—
331	#533	—	149	1	no	—
332	#529	—	149	1	no	—
333	#529	—	149	2	no	—
334	C₂×#125	—	149	2	no	—
335	#520	—	149	1	no	—
336	#520	—	149	1	no	—
337	C₄×#41	—	149	1	no	—
338	C₂×#41	—	149	1	no	—
339	C₂×#41	—	149	1	no	—
340	C₂×#41	—	149	1	no	—
341	C₄⋊Q₈	—	149	1	no	—
342	C₄⋊Q₈	—	149	1	no	—
343	C₄⋊Q₈	—	149	1	no	—
344	C₄⋊Q₈	—	149	1	no	—
345	#126	—	149	2	no	—
346	#126	—	149	1	no	—
347	#126	—	149	2	no	—
348	#126	—	149	2	no	—
349	#126	—	149	1	no	—
350	#126	—	149	2	no	—
351	#126	—	149	2	no	—
352	#126	C₂×D₁₄₉	1	2	yes	—
353	#125	—	149	1	no	—
354	#125	—	149	2	no	—
355	#125	—	149	2	no	—
356	#125	—	149	2	no	—
357	#125	—	149	2	no	—
358	#125	—	149	2	no	—
359	#125	—	149	2	no	—
360	#125	—	149	2	no	—
361	#125	—	149	2	no	—
362	#125	—	149	1	no	—
363	#125	—	149	2	no	—
364	#125	—	149	2	no	—
365	#125	C₂×D₁₄₉	1	2	yes	—
366	#125	C₂×D₁₄₉	1	1	yes	characteristic
367	#124	—	149	1	no	—
368	#123	—	149	1	no	—
369	#123	—	149	2	no	—
370	#123	—	149	2	no	—
371	#123	—	149	1	no	—
372	#123	—	149	2	no	—
373	#123	—	149	2	no	—
374	#123	—	149	2	no	—
375	#123	—	149	2	no	—
376	#123	—	149	2	no	—
377	#123	C₂×D₁₄₉	1	2	yes	—
378	C₂²⋊Q₈	—	149	1	no	—
379	C₂²⋊Q₈	—	149	2	no	—
380	C₂²⋊Q₈	—	149	1	no	—
381	C₂²⋊Q₈	—	149	2	no	—
382	C₂²⋊Q₈	—	149	2	no	—
383	C₂²⋊Q₈	—	149	2	no	—
384	C₂²⋊Q₈	—	149	2	no	—
385	C₂²⋊Q₈	—	149	1	no	—
386	C₂²⋊Q₈	—	149	1	no	—
387	C₂²⋊Q₈	—	149	1	no	—
388	C₂²⋊Q₈	—	149	2	no	—
389	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
390	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
391	#121	—	149	1	no	—
392	#121	—	149	2	no	—
393	#121	—	149	2	no	—
394	#121	—	149	2	no	—
395	C₄×Q₈	—	149	1	no	—
396	C₄×Q₈	—	149	1	no	—
397	C₄×Q₈	—	149	1	no	—
398	C₄×Q₈	—	149	1	no	—
399	C₄×Q₈	—	149	1	no	—
400	C₄×Q₈	—	149	2	no	—
401	C₄×Q₈	—	149	2	no	—
402	C₄×Q₈	—	149	1	no	—
403	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
404	C₄×D₄	—	149	2	no	—
405	C₄×D₄	—	149	2	no	—
406	C₄×D₄	—	149	1	no	—
407	C₄×D₄	—	149	1	no	—
408	C₄×D₄	—	149	2	no	—
409	C₄×D₄	—	149	1	no	—
410	C₄×D₄	—	149	1	no	—
411	C₄×D₄	—	149	1	no	—
412	C₄×D₄	—	149	2	no	—
413	C₄×D₄	—	149	2	no	—
414	C₄×D₄	—	149	2	no	—
415	C₄×D₄	—	149	2	no	—
416	C₄×D₄	—	149	1	no	—
417	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
418	#117	—	149	1	no	—
419	#117	—	149	2	no	—
420	#117	—	149	2	no	—
421	#117	—	149	2	no	—
422	#117	—	149	1	no	—
423	#117	—	149	2	no	—
424	#117	—	149	2	no	—
425	#117	C₂×D₁₄₉	1	1	yes	characteristic
426	#117	C₂×D₁₄₉	1	2	yes	—
427	C₂×C₄⋊C₄	—	149	2	no	—
428	C₂×C₄⋊C₄	—	149	2	no	—
429	C₂×C₄⋊C₄	—	149	1	no	—
430	C₂×C₄⋊C₄	—	149	2	no	—
431	C₂×C₄⋊C₄	—	149	2	no	—
432	C₂×C₄⋊C₄	—	149	2	no	—
433	C₂×C₄⋊C₄	—	149	2	no	—
434	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
435	C₂×C₄²	—	149	1	no	—
436	C₂×C₄²	—	149	2	no	—
437	#41	—	298	4	no	—
438	#41	—	298	4	no	—
439	#41	—	298	4	no	—
440	C₂×Q₈	—	149	1	no	—
441	C₂×Q₈	—	149	1	no	—
442	C₂×Q₈	—	149	1	no	—
443	C₂×Q₈	—	149	2	no	—
444	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
445	C₂×D₄	—	149	1	no	—
446	C₂×D₄	—	149	2	no	—
447	C₂×D₄	—	149	2	no	—
448	C₂×D₄	—	149	1	no	—
449	C₂×D₄	—	149	2	no	—
450	C₂×D₄	—	149	1	no	—
451	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
452	C₂²×C₄	—	149	1	no	—
453	C₂²×C₄	—	149	2	no	—
454	C₂²×C₄	—	149	2	no	—
455	C₂²×C₄	—	149	2	no	—
456	C₂²×C₄	—	149	2	no	—
457	C₂²×C₄	—	149	1	no	—
458	C₂²×C₄	—	149	1	no	—
459	C₂²×C₄	—	149	2	no	—
460	C₂²×C₄	—	149	2	no	—
461	C₂²×C₄	—	149	2	no	—
462	C₂²×C₄	—	149	2	no	—
463	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
464	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
465	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
466	C₄⋊C₄	—	149	2	no	—
467	C₄⋊C₄	—	149	1	no	—
468	C₄⋊C₄	—	149	1	no	—
469	C₄⋊C₄	—	149	1	no	—
470	C₄⋊C₄	—	149	1	no	—
471	C₄⋊C₄	—	149	1	no	—
472	C₄⋊C₄	—	149	2	no	—
473	C₄⋊C₄	—	149	2	no	—
474	C₄⋊C₄	—	149	2	no	—
475	C₄⋊C₄	—	149	1	no	—
476	C₄⋊C₄	—	149	2	no	—
477	C₄⋊C₄	—	149	2	no	—
478	C₄⋊C₄	—	149	2	no	—
479	C₄⋊C₄	—	149	2	no	—
480	C₄⋊C₄	—	149	2	no	—
481	C₄⋊C₄	—	149	2	no	—
482	C₄⋊C₄	—	149	2	no	—
483	C₄⋊C₄	—	149	2	no	—
484	C₄⋊C₄	—	149	2	no	—
485	C₄⋊C₄	—	149	1	no	—
486	C₄⋊C₄	—	149	1	no	—
487	C₄⋊C₄	—	149	2	no	—
488	C₄⋊C₄	—	149	2	no	—
489	C₄⋊C₄	—	149	2	no	—
490	C₄⋊C₄	—	149	1	no	—
491	C₄⋊C₄	—	149	1	no	—
492	C₄⋊C₄	—	149	2	no	—
493	C₄⋊C₄	—	149	2	no	—
494	C₄⋊C₄	—	149	2	no	—
495	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
497	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
500	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
505	C₂²⋊C₄	—	149	1	no	—
506	C₂²⋊C₄	—	149	1	no	—
507	C₂²⋊C₄	—	149	2	no	—
508	C₂²⋊C₄	—	149	2	no	—
509	C₂²⋊C₄	—	149	1	no	—
510	C₂²⋊C₄	—	149	1	no	—
511	C₂²⋊C₄	—	149	2	no	—
512	C₂²⋊C₄	—	149	1	no	—
513	C₂²⋊C₄	—	149	1	no	—
514	C₂²⋊C₄	—	149	2	no	—
515	C₂²⋊C₄	—	149	2	no	—
516	C₂²⋊C₄	—	149	2	no	—
517	C₂²⋊C₄	—	149	1	no	—
518	C₂²⋊C₄	—	149	2	no	—
519	C₂²⋊C₄	—	149	2	no	—
520	C₂²⋊C₄	—	149	1	no	—
521	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
523	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
526	C₄²	—	149	1	no	—
527	C₄²	—	149	1	no	—
528	C₄²	—	149	1	no	—
529	C₄²	—	149	2	no	—
530	C₄²	—	149	1	no	—
531	C₄²	—	149	2	no	—
532	C₄²	—	149	2	no	—
533	C₄²	—	149	2	no	—
534	C₄²	—	149	2	no	—
535	C₄²	—	149	1	no	—
536	C₄²	C₂²×D₁₄₉	1	2	yes	—
537	C₄²	C₂²×D₁₄₉	1	2	yes	—
538	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
539	C₂³	—	149	1	no	—
540	C₂³	—	149	2	no	—
541	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
542	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
543	Q₈	—	2	2	no	—
544	Q₈	—	298	2	no	—
545	Q₈	—	298	2	no	—
546	Q₈	—	298	2	no	—
547	Q₈	—	596	2	no	—
548	D₄	—	4	1	no	—
549	D₄	—	298	4	no	—
550	D₄	—	298	4	no	—
551	D₄	—	298	4	no	—
552	D₄	—	298	2	no	—
553	D₄	—	596	1	no	—
554	D₄	—	149	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	298	4	no	—
559	C₂×C₄	—	298	4	no	—
560	C₂×C₄	—	298	4	no	—
561	C₂×C₄	—	298	4	no	—
562	C₂×C₄	—	298	2	no	—
563	C₂×C₄	—	298	2	no	—
564	C₂×C₄	—	596	2	no	—
565	C₂×C₄	—	596	2	no	—
566	C₂×C₄	—	596	2	no	—
567	C₂×C₄	—	596	2	no	—
568	C₂×C₄	—	596	1	no	—
569	C₂×C₄	—	149	1	no	—
570	C₂×C₄	—	149	1	no	—
571	C₂×C₄	—	149	1	no	—
572	C₂×C₄	—	149	1	no	—
573	C₂×C₄	—	149	2	no	—
574	C₂×C₄	—	149	2	no	—
575	C₂×C₄	—	149	2	no	—
576	C₂×C₄	—	149	1	no	—
577	C₂×C₄	—	149	1	no	—
578	C₂×C₄	—	149	1	no	—
579	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
581	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
582	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
583	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
584	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	298	2	no	—
595	C₂²	—	298	2	no	—
596	C₂²	—	298	1	no	—
597	C₂²	—	298	1	no	—
598	C₂²	—	298	1	no	—
599	C₂²	—	149	4	no	—
600	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	1	no	—
609	C₄	—	298	1	no	—
610	C₄	—	298	2	no	—
611	C₄	—	298	2	no	—
612	C₄	—	298	1	no	—
613	C₄	—	298	1	no	—
614	C₄	—	298	1	no	—
615	C₄	—	298	1	no	—
616	C₄	—	298	2	no	—
617	C₄	—	298	1	no	—
618	C₄	—	149	2	no	—
619	C₄	#41×D₁₄₉	1	2	yes	—
620	C₂	—	4	1	no	—
621	C₂	—	4	1	no	—
622	C₂	—	298	4	no	—
623	C₂	—	596	1	no	—
624	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
625	C₂	2₋¹⁺⁴×D₁₄₉	1	1	yes	characteristic
626	C₂	#23750461	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#552×C₁₄₉	C₂
hypercenter	#552	D₁₄₉
hypocenter	C₁₄₉	#3515
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #23750353	C₂	semidirect
2. #23750331	C₂	semidirect
3. #23750330	C₂	semidirect
4. #23750320	C₂	semidirect
5. #23750314	C₂	semidirect
6. #23750314	C₂	semidirect
7. #23750311	C₂	semidirect
8. #23750307	C₂	semidirect
9. #23750280	C₂	semidirect
10. #23750277	C₂	semidirect
11. #23750277	C₂	semidirect
12. #23750238	C₂	semidirect
13. #23750235	C₂	semidirect
14. #23750218	C₂	semidirect
15. #23750216	C₂	semidirect
16. #23750177	C₂	semidirect
17. #23750155	C₂	semidirect
18. #23750153	C₂	semidirect
19. #125×D₁₄₉	C₂	semidirect
20. #23750107	C₂	semidirect
21. #23750106	C₂	semidirect
22. #23750093	C₂	semidirect
23. #552×C₁₄₉	C₂	semidirect
313. C₁₄₉	#3515	semidirect
323. #552	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750353	2
#23750331	2
#23750330	2
#23750320	2
#23750314	2
#23750311	2
#23750307	2
#23750280	2
#23750277	2
#23750238	2
#23750235	2
#23750218	2
#23750216	2
#23750177	2
#23750155	2
#23750153	2
#125×D₁₄₉	2
#23750107	2
#23750106	2
#23750093	2
#552×C₁₄₉	2
#3515	149