Subgroups — #34058584

Order 19072.

1040 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750361	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750358	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750357	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750348	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750347	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750345	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750344	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750305	C₂	1	2	yes	maximal, complemented
9	#23750304	C₂	1	2	yes	maximal, complemented
10	#23750303	C₂	1	2	yes	maximal, complemented
11	#23750298	C₂	1	2	yes	maximal, complemented
12	#23750243	C₂	1	2	yes	maximal, complemented
13	#23750239	C₂	1	2	yes	maximal, complemented
14	#23750195	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750188	C₂	1	1	yes	maximal, characteristic
16	#23750179	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750155	C₂	1	2	yes	maximal, complemented
18	#23750152	C₂	1	2	yes	maximal, complemented
19	#124×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#23750101	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750097	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14558735	C₂	1	1	yes	maximal, characteristic, complemented
23	#559×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558735	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₄₉	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
27	#18011911	C₂²	1	1	yes	characteristic, complemented
28	#18011910	C₂²	1	1	yes	characteristic, complemented
29	#18011909	C₂²	1	1	yes	characteristic, complemented
30	#18011909	C₂²	1	1	yes	characteristic, complemented
31	#18011907	C₂²	1	1	yes	characteristic
32	#18011906	C₂²	1	2	yes	complemented
33	#18011906	C₂²	1	2	yes	complemented
34	#18011906	C₂²	1	2	yes	complemented
35	#18011905	C₂²	1	2	yes	complemented
36	#18011904	C₂²	1	2	yes	complemented
37	#18011904	C₂²	1	2	yes	complemented
38	#18011904	C₂²	1	2	yes	complemented
39	#18011904	C₂²	1	2	yes	complemented
40	#18011901	C₂²	1	1	yes	characteristic, complemented
41	#18011901	C₂²	1	1	yes	characteristic, complemented
42	#18011900	C₂²	1	1	yes	characteristic
43	#18011899	C₂²	1	1	yes	characteristic
44	#18011899	C₂²	1	1	yes	characteristic
45	#18011898	C₂²	1	1	yes	characteristic
46	#18011898	C₂²	1	1	yes	characteristic
47	#18011898	C₂²	1	1	yes	characteristic, complemented
48	#18011898	C₂²	1	2	yes	complemented
49	#18011897	C₂²	1	2	yes	—
50	#18011897	C₂²	1	2	yes	—
51	#18011897	C₂²	1	2	yes	complemented
52	#18011897	C₂²	1	2	yes	complemented
53	#18011895	C₂²	1	2	yes	complemented
54	#18011894	C₂²	1	2	yes	complemented
55	#18011893	C₂²	1	2	yes	—
56	#18011893	C₂²	1	2	yes	—
57	#18011893	C₂²	1	2	yes	complemented
58	#18011893	C₂²	1	2	yes	complemented
59	#18011892	C₂²	1	2	yes	complemented
60	#18011892	C₂²	1	2	yes	complemented
61	#18011891	C₂²	1	1	yes	characteristic
62	#18011890	C₂²	1	2	yes	complemented
63	#18011889	C₂²	1	1	yes	characteristic
64	#18011889	C₂²	1	1	yes	characteristic
65	#18011889	C₂²	1	2	yes	complemented
66	#18011888	C₂²	1	2	yes	complemented
67	#18011888	C₂²	1	2	yes	complemented
68	#18011888	C₂²	1	2	yes	complemented
69	#18011887	C₂²	1	1	yes	characteristic
70	#18011887	C₂²	1	2	yes	complemented
71	#18011883	C₂²	1	2	yes	—
72	#18011883	C₂²	1	2	yes	—
73	#18011879	C₂²	1	2	yes	—
74	#18011879	C₂²	1	2	yes	—
75	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
77	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
78	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
82	#18011876	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	1	yes	characteristic
86	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
87	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
88	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
89	#18011873	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
93	#18011871	C₂²	1	2	yes	—
94	#18011871	C₂²	1	2	yes	—
95	#18011871	C₂²	1	2	yes	complemented
96	#18011870	C₂²	1	2	yes	complemented
97	#18011869	C₂²	1	2	yes	—
98	#18011869	C₂²	1	1	yes	characteristic
99	#18011869	C₂²	1	2	yes	complemented
100	#18011868	C₂²	1	1	yes	characteristic
101	#18011868	C₂²	1	1	yes	characteristic
102	#18011868	C₂²	1	2	yes	—
103	#18011868	C₂²	1	2	yes	complemented
104	#18011867	C₂²	1	2	yes	complemented
105	#18011867	C₂²	1	2	yes	complemented
106	C₂×#14558713	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
110	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	complemented
111	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
112	#127×C₁₄₉	C₂²	1	1	yes	characteristic
113	#124×C₁₄₉	C₂²	1	1	yes	characteristic
114	#124×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
115	#124×C₁₄₉	C₂²	1	2	yes	complemented
116	#123×C₁₄₉	C₂²	1	2	yes	complemented
117	#123×C₁₄₉	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
122	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₄₉	C₂³	1	2	yes	—
124	#14558735	—	2	4	no	—
125	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
126	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
131	Q₈×D₁₄₉	—	2	4	no	—
132	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
137	D₄×D₁₄₉	—	2	4	no	—
138	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
139	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
140	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
141	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
142	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
145	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
149	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
150	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
151	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
154	#14558715	C₂³	1	2	yes	—
155	#14558715	C₂³	1	1	yes	characteristic
156	#14558715	C₂³	1	1	yes	characteristic
157	#14558715	C₂³	1	1	yes	characteristic
158	#14558715	C₂³	1	2	yes	—
159	#14558715	C₂³	1	2	yes	—
160	#14558715	C₂³	1	2	yes	—
161	#14558715	C₂³	1	1	yes	characteristic
162	#14558715	C₂³	1	2	yes	—
163	#14558715	C₂³	1	2	yes	—
164	#14558715	C₂³	1	1	yes	characteristic
165	#14558715	C₂³	1	1	yes	characteristic
166	#14558715	C₂³	1	1	yes	characteristic
167	#14558715	C₂³	1	1	yes	characteristic
168	#14558715	C₂³	1	1	yes	characteristic
169	#14558715	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
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	#14558713	C₂³	1	2	yes	—
179	#14558713	C₂³	1	2	yes	—
180	#14558713	C₂³	1	2	yes	—
181	#14558713	C₂³	1	2	yes	—
182	#14558713	C₂³	1	2	yes	—
183	#14558713	C₂³	1	2	yes	—
184	#14558713	C₂³	1	2	yes	—
185	#14558713	C₂³	1	2	yes	—
186	#14558713	C₂³	1	1	yes	characteristic
187	#14558713	C₂³	1	2	yes	—
188	#14558713	C₂³	1	1	yes	characteristic
189	#14558713	C₂³	1	1	yes	characteristic
190	#14558713	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₄₉	C₂³	1	2	yes	—
192	C₄×Dic₁₄₉	C₂³	1	2	yes	—
193	C₄×Dic₁₄₉	C₂³	1	2	yes	—
194	C₄×Dic₁₄₉	C₂³	1	2	yes	—
195	C₄×Dic₁₄₉	C₂³	1	2	yes	—
196	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
201	C₄×Dic₁₄₉	C₂³	1	2	yes	—
202	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
204	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
207	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
209	C₂²×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	1	yes	characteristic
214	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
221	C₄²×C₁₄₉	C₂³	1	2	yes	—
222	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
223	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
224	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
225	C₂²×D₁₄₉	—	2	4	no	—
226	C₂²×D₁₄₉	—	4	2	no	—
227	C₂²×D₁₄₉	—	4	2	no	—
228	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
229	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
230	Dic₂₉₈	—	2	2	no	—
231	Dic₂₉₈	—	2	2	no	—
232	Dic₂₉₈	—	2	4	no	—
233	Dic₂₉₈	—	4	1	no	—
234	Dic₂₉₈	—	4	1	no	—
235	Dic₂₉₈	—	4	1	no	—
236	D₅₉₆	—	2	2	no	—
237	C₂²⋊D₁₄₉	—	2	4	no	—
238	C₂²⋊D₁₄₉	—	2	4	no	—
239	C₂²⋊D₁₄₉	—	4	2	no	—
240	C₂²⋊D₁₄₉	—	4	2	no	—
241	C₂×Dic₁₄₉	—	2	4	no	—
242	C₂×Dic₁₄₉	—	4	2	no	—
243	C₂×Dic₁₄₉	—	4	2	no	—
244	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
247	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
249	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
251	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
254	C₄×D₁₄₉	—	2	4	no	—
255	C₄×D₁₄₉	—	4	2	no	—
256	C₄×D₁₄₉	—	4	2	no	—
257	C₄×D₁₄₉	—	4	1	no	—
258	C₄×D₁₄₉	—	4	1	no	—
259	C₄×D₁₄₉	#41	1	4	yes	—
260	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
261	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
262	Q₈×C₁₄₉	—	2	2	no	—
263	Q₈×C₁₄₉	—	4	1	no	—
264	D₄×C₁₄₉	—	2	2	no	—
265	D₄×C₁₄₉	—	2	2	no	—
266	D₄×C₁₄₉	—	4	2	no	—
267	D₄×C₁₄₉	—	4	2	no	—
268	C₂×C₄×C₁₄₉	—	4	2	no	—
269	C₂×C₄×C₁₄₉	—	4	2	no	—
270	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
275	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₁₄₉	—	2	2	no	—
280	C₂²×C₁₄₉	—	2	2	no	—
281	C₂²×C₁₄₉	—	2	2	no	—
282	C₂²×C₁₄₉	—	2	2	no	—
283	C₂²×C₁₄₉	—	2	2	no	—
284	C₂²×C₁₄₉	—	2	2	no	—
285	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
286	C₂×D₁₄₉	—	2	1	no	—
287	C₂×D₁₄₉	—	2	1	no	—
288	C₂×D₁₄₉	—	2	2	no	—
289	C₂×D₁₄₉	—	2	2	no	—
290	C₂×D₁₄₉	—	2	2	no	—
291	C₂×D₁₄₉	—	8	4	no	—
292	C₂×D₁₄₉	C₂×#41	1	2	yes	—
293	C₄×C₁₄₉	—	2	2	no	—
294	C₄×C₁₄₉	—	2	1	no	—
295	C₄×C₁₄₉	—	2	2	no	—
296	C₄×C₁₄₉	—	2	1	no	—
297	C₄×C₁₄₉	—	2	1	no	—
298	C₄×C₁₄₉	—	2	1	no	—
299	C₄×C₁₄₉	—	2	1	no	—
300	C₄×C₁₄₉	—	2	1	no	—
301	C₄×C₁₄₉	C₂×#41	1	2	yes	—
302	Dic₁₄₉	—	2	2	no	—
303	Dic₁₄₉	—	2	2	no	—
304	Dic₁₄₉	—	2	1	no	—
305	Dic₁₄₉	—	2	2	no	—
306	Dic₁₄₉	—	2	1	no	—
307	Dic₁₄₉	—	2	1	no	—
308	Dic₁₄₉	—	2	1	no	—
309	Dic₁₄₉	—	2	1	no	—
310	Dic₁₄₉	—	2	1	no	—
311	Dic₁₄₉	C₂×#41	1	2	yes	—
312	C₂×C₁₄₉	—	4	2	no	—
313	C₂×C₁₄₉	—	4	2	no	—
314	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
315	C₂×C₁₄₉	#585	1	1	yes	characteristic
316	C₂×C₁₄₉	#585	1	1	yes	characteristic
317	D₁₄₉	—	2	2	no	—
318	D₁₄₉	—	4	2	no	—
319	C₁₄₉	#3510	1	1	yes	characteristic, complemented, Sylow
320	#3510	—	149	1	no	maximal, Sylow
321	#559	—	149	1	no	—
322	#559	—	149	1	no	—
323	#559	—	149	1	no	—
324	#559	D₁₄₉	1	1	yes	characteristic, complemented
325	#556	—	149	1	no	—
326	#556	—	149	1	no	—
327	#556	—	149	1	no	—
328	#556	—	149	1	no	—
329	#551	—	149	2	no	—
330	#551	—	149	2	no	—
331	#551	—	149	2	no	—
332	#551	—	149	2	no	—
333	#542	—	149	2	no	—
334	#542	—	149	2	no	—
335	#536	—	149	1	no	—
336	#535	—	149	1	no	—
337	#533	—	149	1	no	—
338	#529	—	149	2	no	—
339	#529	—	149	2	no	—
340	C₂×#124	—	149	1	no	—
341	#519	—	149	1	no	—
342	#518	—	149	1	no	—
343	C₄×#41	—	149	1	no	—
344	C₂×#41	—	149	1	no	—
345	C₂²×Q₈	—	149	1	no	—
346	C₂²×D₄	—	149	1	no	—
347	C₄⋊Q₈	—	149	1	no	—
348	C₄⋊Q₈	—	149	1	no	—
349	C₄⋊Q₈	—	149	1	no	—
350	C₄⋊Q₈	—	149	1	no	—
351	#127	—	149	1	no	—
352	#127	C₂×D₁₄₉	1	1	yes	characteristic
353	#126	—	149	2	no	—
354	#126	—	149	2	no	—
355	#126	—	149	2	no	—
356	#126	—	149	2	no	—
357	#126	—	149	2	no	—
358	#126	—	149	2	no	—
359	#126	—	149	2	no	—
360	#126	—	149	2	no	—
361	#125	—	149	1	no	—
362	#125	—	149	1	no	—
363	#124	—	149	1	no	—
364	#124	—	149	1	no	—
365	#124	—	149	1	no	—
366	#124	—	149	1	no	—
367	#124	—	149	2	no	—
368	#124	—	149	2	no	—
369	#124	—	149	2	no	—
370	#124	—	149	2	no	—
371	#124	—	149	2	no	—
372	#124	—	149	1	no	—
373	#124	—	149	1	no	—
374	#124	C₂×D₁₄₉	1	1	yes	characteristic
375	#124	C₂×D₁₄₉	1	1	yes	characteristic, complemented
376	#124	C₂×D₁₄₉	1	2	yes	complemented
377	#123	—	149	2	no	—
378	#123	—	149	2	no	—
379	#123	—	149	2	no	—
380	#123	—	149	2	no	—
381	#123	—	149	2	no	—
382	#123	—	149	2	no	—
383	#123	—	149	2	no	—
384	#123	—	149	2	no	—
385	#123	C₂×D₁₄₉	1	2	yes	complemented
386	#123	C₂×D₁₄₉	1	2	yes	complemented
387	C₂²⋊Q₈	—	149	1	no	—
388	C₂²⋊Q₈	—	149	2	no	—
389	C₂²⋊Q₈	—	149	2	no	—
390	C₂²⋊Q₈	—	149	1	no	—
391	C₂²⋊Q₈	—	149	1	no	—
392	C₂²⋊Q₈	—	149	1	no	—
393	C₂²⋊Q₈	—	149	2	no	—
394	C₂²⋊Q₈	—	149	2	no	—
395	C₂²⋊Q₈	—	149	2	no	—
396	C₂²⋊Q₈	—	149	2	no	—
397	#121	—	149	2	no	—
398	#121	—	149	2	no	—
399	#120	—	149	2	no	—
400	#120	—	149	2	no	—
401	C₄×Q₈	—	149	1	no	—
402	C₄×Q₈	—	149	1	no	—
403	C₄×Q₈	—	149	2	no	—
404	C₄×Q₈	—	149	1	no	—
405	C₄×Q₈	—	149	1	no	—
406	C₄×Q₈	—	149	2	no	—
407	C₄×Q₈	—	149	1	no	—
408	C₄×Q₈	—	149	1	no	—
409	C₄×Q₈	—	149	1	no	—
410	C₄×Q₈	—	149	1	no	—
411	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
412	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
413	C₄×D₄	—	149	1	no	—
414	C₄×D₄	—	149	1	no	—
415	C₄×D₄	—	149	2	no	—
416	C₄×D₄	—	149	2	no	—
417	C₄×D₄	—	149	2	no	—
418	C₄×D₄	—	149	2	no	—
419	C₄×D₄	—	149	1	no	—
420	C₄×D₄	—	149	2	no	—
421	C₄×D₄	—	149	2	no	—
422	C₄×D₄	—	149	2	no	—
423	C₄×D₄	—	149	1	no	—
424	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
425	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
426	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
427	#117	—	149	2	no	—
428	#117	—	149	1	no	—
429	#117	—	149	2	no	—
430	#117	—	149	2	no	—
431	#117	—	149	2	no	—
432	#117	—	149	2	no	—
433	#117	—	149	1	no	—
434	#117	—	149	1	no	—
435	#117	—	149	2	no	—
436	#117	—	149	2	no	—
437	C₂×C₂²⋊C₄	—	149	2	no	—
438	C₂×C₂²⋊C₄	—	149	2	no	—
439	C₂×C₂²⋊C₄	—	149	2	no	—
440	C₂×C₂²⋊C₄	—	149	2	no	—
441	C₂×C₄²	—	149	2	no	—
442	C₂×C₄²	—	149	1	no	—
443	C₂⁴	—	149	2	no	—
444	#41	—	298	4	no	—
445	C₂×Q₈	—	298	4	no	—
446	C₂×Q₈	—	149	2	no	—
447	C₂×Q₈	—	149	1	no	—
448	C₂×Q₈	—	149	1	no	—
449	C₂×Q₈	—	149	1	no	—
450	C₂×Q₈	—	149	1	no	—
451	C₂×Q₈	—	149	1	no	—
452	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
453	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
454	C₂×D₄	—	298	4	no	—
455	C₂×D₄	—	149	2	no	—
456	C₂×D₄	—	149	2	no	—
457	C₂×D₄	—	149	2	no	—
458	C₂×D₄	—	149	2	no	—
459	C₂×D₄	—	149	1	no	—
460	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
461	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
462	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
463	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
464	C₂²×C₄	—	149	2	no	—
465	C₂²×C₄	—	149	2	no	—
466	C₂²×C₄	—	149	2	no	—
467	C₂²×C₄	—	149	2	no	—
468	C₂²×C₄	—	149	1	no	—
469	C₂²×C₄	—	149	1	no	—
470	C₂²×C₄	—	149	2	no	—
471	C₂²×C₄	—	149	2	no	—
472	C₂²×C₄	—	149	1	no	—
473	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
474	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
475	C₄⋊C₄	—	149	1	no	—
476	C₄⋊C₄	—	149	1	no	—
477	C₄⋊C₄	—	149	1	no	—
478	C₄⋊C₄	—	149	1	no	—
479	C₄⋊C₄	—	149	1	no	—
480	C₄⋊C₄	—	149	1	no	—
481	C₄⋊C₄	—	149	2	no	—
482	C₄⋊C₄	—	149	2	no	—
483	C₄⋊C₄	—	149	1	no	—
484	C₄⋊C₄	—	149	1	no	—
485	C₄⋊C₄	—	149	2	no	—
486	C₄⋊C₄	—	149	2	no	—
487	C₄⋊C₄	—	149	2	no	—
488	C₄⋊C₄	—	149	2	no	—
489	C₄⋊C₄	—	149	2	no	—
490	C₄⋊C₄	—	149	2	no	—
491	C₄⋊C₄	—	149	2	no	—
492	C₄⋊C₄	—	149	1	no	—
493	C₄⋊C₄	—	149	1	no	—
494	C₄⋊C₄	—	149	1	no	—
495	C₄⋊C₄	—	149	1	no	—
496	C₄⋊C₄	—	149	1	no	—
497	C₄⋊C₄	—	149	1	no	—
498	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
503	C₂²⋊C₄	—	149	2	no	—
504	C₂²⋊C₄	—	149	2	no	—
505	C₂²⋊C₄	—	149	2	no	—
506	C₂²⋊C₄	—	149	2	no	—
507	C₂²⋊C₄	—	149	2	no	—
508	C₂²⋊C₄	—	149	2	no	—
509	C₂²⋊C₄	—	149	2	no	—
510	C₂²⋊C₄	—	149	2	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	2	no	—
518	C₂²⋊C₄	—	149	2	no	—
519	C₂²⋊C₄	—	149	2	no	—
520	C₂²⋊C₄	—	149	1	no	—
521	C₂²⋊C₄	—	149	1	no	—
522	C₂²⋊C₄	—	149	2	no	—
523	C₂²⋊C₄	—	149	2	no	—
524	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
530	C₄²	—	149	1	no	—
531	C₄²	—	149	2	no	—
532	C₄²	—	149	2	no	—
533	C₄²	—	149	2	no	—
534	C₄²	—	149	1	no	—
535	C₄²	—	149	1	no	—
536	C₄²	—	149	2	no	—
537	C₄²	—	149	2	no	—
538	C₄²	—	149	2	no	—
539	C₄²	—	149	1	no	—
540	C₄²	—	149	1	no	—
541	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
542	C₄²	C₂²×D₁₄₉	1	2	yes	—
543	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
544	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
545	C₂³	—	298	4	no	—
546	C₂³	—	596	2	no	—
547	C₂³	—	596	2	no	—
548	C₂³	—	149	2	no	—
549	C₂³	—	149	1	no	—
550	C₂³	C₂³×D₁₄₉	1	2	yes	—
551	C₂³	C₂³×D₁₄₉	1	2	yes	—
552	Q₈	—	2	2	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	298	4	no	—
555	Q₈	—	298	2	no	—
556	Q₈	—	298	2	no	—
557	Q₈	—	596	1	no	—
558	Q₈	—	596	1	no	—
559	Q₈	—	596	1	no	—
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	298	4	no	—
565	D₄	—	298	4	no	—
566	D₄	—	298	2	no	—
567	D₄	—	596	2	no	—
568	D₄	—	596	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	298	4	no	—
572	C₂×C₄	—	298	4	no	—
573	C₂×C₄	—	596	2	no	—
574	C₂×C₄	—	596	1	no	—
575	C₂×C₄	—	596	2	no	—
576	C₂×C₄	—	596	1	no	—
577	C₂×C₄	—	596	2	no	—
578	C₂×C₄	—	596	2	no	—
579	C₂×C₄	—	149	1	no	—
580	C₂×C₄	—	149	2	no	—
581	C₂×C₄	—	149	1	no	—
582	C₂×C₄	—	149	1	no	—
583	C₂×C₄	—	149	2	no	—
584	C₂×C₄	—	149	1	no	—
585	C₂×C₄	—	149	2	no	—
586	C₂×C₄	—	149	1	no	—
587	C₂×C₄	—	149	1	no	—
588	C₂×C₄	—	149	1	no	—
589	C₂×C₄	—	149	4	no	—
590	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
592	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
594	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	298	1	no	—
606	C₂²	—	298	1	no	—
607	C₂²	—	298	2	no	—
608	C₂²	—	298	2	no	—
609	C₂²	—	298	2	no	—
610	C₂²	—	149	2	no	—
611	C₂²	—	1192	4	no	—
612	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
613	C₄	—	2	2	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	298	2	no	—
622	C₄	—	298	2	no	—
623	C₄	—	298	1	no	—
624	C₄	—	298	1	no	—
625	C₄	—	298	1	no	—
626	C₄	—	298	2	no	—
627	C₄	—	298	1	no	—
628	C₄	—	298	1	no	—
629	C₄	—	298	1	no	—
630	C₄	—	149	2	no	—
631	C₄	#41×D₁₄₉	1	2	yes	—
632	C₂	—	4	2	no	—
633	C₂	—	4	2	no	—
634	C₂	—	298	2	no	—
635	C₂	—	596	2	no	—
636	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
637	C₂	#23750460	1	1	yes	characteristic
638	C₂	#23750461	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#559×C₁₄₉	C₂
prime radical	#23750188	C₂
hypercenter	#559	D₁₄₉
hypocenter	C₁₄₉	#3510
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. #23750361	C₂	semidirect
2. #23750358	C₂	semidirect
3. #23750357	C₂	semidirect
4. #23750348	C₂	semidirect
5. #23750347	C₂	semidirect
6. #23750345	C₂	semidirect
7. #23750344	C₂	semidirect
8. #23750305	C₂	semidirect
9. #23750304	C₂	semidirect
10. #23750303	C₂	semidirect
11. #23750298	C₂	semidirect
12. #23750243	C₂	semidirect
13. #23750239	C₂	semidirect
14. #23750195	C₂	semidirect
16. #23750179	C₂	semidirect
17. #23750155	C₂	semidirect
18. #23750152	C₂	semidirect
19. #124×D₁₄₉	C₂	semidirect
20. #23750101	C₂	semidirect
21. #23750097	C₂	semidirect
22. C₄×#14558735	C₂	semidirect
23. #559×C₁₄₉	C₂	semidirect
27. #18011911	C₂²	semidirect
28. #18011910	C₂²	semidirect
29. #18011909	C₂²	semidirect
30. #18011909	C₂²	semidirect
32. #18011906	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. #18011904	C₂²	semidirect
40. #18011901	C₂²	semidirect
41. #18011901	C₂²	semidirect
47. #18011898	C₂²	semidirect
48. #18011898	C₂²	semidirect
51. #18011897	C₂²	semidirect
52. #18011897	C₂²	semidirect
53. #18011895	C₂²	semidirect
54. #18011894	C₂²	semidirect
57. #18011893	C₂²	semidirect
58. #18011893	C₂²	semidirect
59. #18011892	C₂²	semidirect
60. #18011892	C₂²	semidirect
62. #18011890	C₂²	semidirect
65. #18011889	C₂²	semidirect
66. #18011888	C₂²	semidirect
67. #18011888	C₂²	semidirect
68. #18011888	C₂²	semidirect
70. #18011887	C₂²	semidirect
75. Q₈×Dic₁₄₉	C₂²	semidirect
76. C₄×Dic₂₉₈	C₂²	semidirect
77. C₄×Dic₂₉₈	C₂²	semidirect
78. C₄×Dic₂₉₈	C₂²	semidirect
79. C₄×Dic₂₉₈	C₂²	semidirect
80. C₄×Dic₂₉₈	C₂²	semidirect
81. C₄×Dic₂₉₈	C₂²	semidirect
82. #18011876	C₂²	semidirect
83. #18011876	C₂²	semidirect
84. #18011876	C₂²	semidirect
87. D₄×Dic₁₄₉	C₂²	semidirect
88. D₄×Dic₁₄₉	C₂²	semidirect
92. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
95. #18011871	C₂²	semidirect
96. #18011870	C₂²	semidirect
99. #18011869	C₂²	semidirect
103. #18011868	C₂²	semidirect
104. #18011867	C₂²	semidirect
105. #18011867	C₂²	semidirect
110. C₂×C₄×Dic₁₄₉	C₂²	semidirect
114. #124×C₁₄₉	C₂²	semidirect
115. #124×C₁₄₉	C₂²	semidirect
116. #123×C₁₄₉	C₂²	semidirect
117. #123×C₁₄₉	C₂²	semidirect
118. C₄×Q₈×C₁₄₉	C₂²	semidirect
119. C₄×Q₈×C₁₄₉	C₂²	semidirect
121. C₄×D₄×C₁₄₉	C₂²	semidirect
122. C₄×D₄×C₁₄₉	C₂²	semidirect
319. C₁₄₉	#3510	semidirect
324. #559	D₁₄₉	semidirect
375. #124	C₂×D₁₄₉	semidirect
376. #124	C₂×D₁₄₉	semidirect
385. #123	C₂×D₁₄₉	semidirect
386. #123	C₂×D₁₄₉	semidirect
411. C₄×Q₈	C₂×D₁₄₉	semidirect
412. C₄×Q₈	C₂×D₁₄₉	semidirect
425. C₄×D₄	C₂×D₁₄₉	semidirect
426. C₄×D₄	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750361	2
#23750358	2
#23750357	2
#23750348	2
#23750347	2
#23750345	2
#23750344	2
#23750305	2
#23750304	2
#23750303	2
#23750298	2
#23750243	2
#23750239	2
#23750195	2
#23750188	2
#23750179	2
#23750155	2
#23750152	2
#124×D₁₄₉	2
#23750101	2
#23750097	2
C₄×#14558735	2
#559×C₁₄₉	2
#3510	149