Subgroups — #34058399

Order 19072.

1124 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750333	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750329	C₂	1	2	yes	maximal, complemented
3	#23750324	C₂	1	2	yes	maximal, complemented
4	#23750323	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750321	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750316	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750309	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750307	C₂	1	2	yes	maximal, complemented
9	#23750278	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750277	C₂	1	2	yes	maximal, complemented
11	#23750276	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750252	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750223	C₂	1	2	yes	maximal, complemented
14	#23750221	C₂	1	2	yes	maximal, complemented
15	#23750205	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750138	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750138	C₂	1	2	yes	maximal, complemented
18	#23750134	C₂	1	1	yes	maximal, characteristic, complemented
19	#23750134	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	C₂×C₄⋊C₄×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#554×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558737	C₂²	1	1	yes	characteristic
25	C₂×#14558737	C₂²	1	2	yes	—
26	C₂×#14558736	C₂²	1	1	yes	characteristic
27	C₂×#14558736	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	—
30	#18011910	C₂²	1	1	yes	characteristic, complemented
31	#18011909	C₂²	1	2	yes	complemented
32	#18011906	C₂²	1	2	yes	complemented
33	#18011906	C₂²	1	2	yes	complemented
34	#18011905	C₂²	1	2	yes	complemented
35	#18011904	C₂²	1	2	yes	complemented
36	#18011903	C₂²	1	1	yes	characteristic, complemented
37	#18011902	C₂²	1	1	yes	characteristic, complemented
38	#18011901	C₂²	1	2	yes	complemented
39	#18011901	C₂²	1	2	yes	complemented
40	#18011901	C₂²	1	2	yes	complemented
41	#18011901	C₂²	1	2	yes	complemented
42	#18011896	C₂²	1	2	yes	—
43	#18011896	C₂²	1	1	yes	characteristic
44	#18011896	C₂²	1	2	yes	—
45	#18011896	C₂²	1	2	yes	—
46	#18011896	C₂²	1	2	yes	—
47	#18011896	C₂²	1	2	yes	complemented
48	#18011896	C₂²	1	2	yes	complemented
49	#18011894	C₂²	1	2	yes	complemented
50	#18011893	C₂²	1	1	yes	characteristic
51	#18011893	C₂²	1	2	yes	—
52	#18011893	C₂²	1	2	yes	complemented
53	#18011891	C₂²	1	2	yes	complemented
54	#18011889	C₂²	1	2	yes	—
55	#18011889	C₂²	1	1	yes	characteristic
56	#18011889	C₂²	1	2	yes	complemented
57	#18011889	C₂²	1	2	yes	complemented
58	#18011888	C₂²	1	1	yes	characteristic
59	#18011888	C₂²	1	2	yes	—
60	#18011887	C₂²	1	2	yes	—
61	#18011887	C₂²	1	1	yes	characteristic
62	#18011887	C₂²	1	1	yes	characteristic, complemented
63	#18011887	C₂²	1	2	yes	complemented
64	#18011886	C₂²	1	2	yes	—
65	#18011886	C₂²	1	1	yes	characteristic
66	#18011886	C₂²	1	1	yes	characteristic, complemented
67	#18011885	C₂²	1	1	yes	characteristic
68	#18011885	C₂²	1	2	yes	—
69	#18011885	C₂²	1	1	yes	characteristic, complemented
70	#18011884	C₂²	1	2	yes	—
71	#18011884	C₂²	1	1	yes	characteristic
72	#18011884	C₂²	1	2	yes	complemented
73	#18011883	C₂²	1	2	yes	—
74	#18011883	C₂²	1	1	yes	characteristic
75	#18011881	C₂²	1	2	yes	—
76	#18011881	C₂²	1	1	yes	characteristic
77	#18011879	C₂²	1	1	yes	characteristic
78	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
79	#18011876	C₂²	1	2	yes	complemented
80	C₄×D₅₉₆	C₂²	1	2	yes	—
81	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
82	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
83	#18011873	C₂²	1	2	yes	—
84	#18011873	C₂²	1	2	yes	—
85	#18011873	C₂²	1	2	yes	—
86	#18011873	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
92	#18011871	C₂²	1	2	yes	—
93	#18011871	C₂²	1	2	yes	—
94	#18011871	C₂²	1	2	yes	—
95	#18011870	C₂²	1	1	yes	characteristic, complemented
96	#18011869	C₂²	1	1	yes	characteristic
97	#18011869	C₂²	1	2	yes	—
98	#18011869	C₂²	1	1	yes	characteristic, complemented
99	#18011868	C₂²	1	1	yes	characteristic
100	#18011868	C₂²	1	2	yes	—
101	#18011868	C₂²	1	2	yes	complemented
102	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
103	C₂×#14558715	C₂²	1	2	yes	—
104	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
105	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
106	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
108	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
111	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
112	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
113	#125×C₁₄₉	C₂²	1	2	yes	complemented
114	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
124	#14558737	—	2	4	no	—
125	#14558737	—	4	4	no	—
126	#14558736	—	2	4	no	—
127	#14558736	—	4	4	no	—
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×D₅₉₆	C₂³	1	1	yes	characteristic
133	C₂×D₅₉₆	C₂³	1	2	yes	—
134	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
135	C₂×D₅₉₆	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
142	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
144	C₂×C₄×D₁₄₉	—	2	4	no	—
145	C₂×C₄×D₁₄₉	—	4	4	no	—
146	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
147	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
148	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
153	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
155	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
156	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
157	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
158	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
160	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
161	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
164	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₄₉	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	2	yes	—
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	#14558715	C₂³	1	2	yes	—
177	#14558715	C₂³	1	2	yes	—
178	#14558715	C₂³	1	1	yes	characteristic
179	#14558715	C₂³	1	2	yes	—
180	#14558715	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
184	#14558713	C₂³	1	1	yes	characteristic
185	#14558713	C₂³	1	2	yes	—
186	#14558713	C₂³	1	2	yes	—
187	#14558713	C₂³	1	2	yes	—
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	#14558713	C₂³	1	1	yes	characteristic
193	#14558713	C₂³	1	2	yes	—
194	#14558713	C₂³	1	1	yes	characteristic
195	#14558713	C₂³	1	1	yes	characteristic
196	#14558713	C₂³	1	1	yes	characteristic
197	#14558713	C₂³	1	2	yes	—
198	#14558713	C₂³	1	2	yes	—
199	#14558713	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₄₉	C₂³	1	2	yes	—
201	C₄×Dic₁₄₉	C₂³	1	2	yes	—
202	C₄×Dic₁₄₉	C₂³	1	2	yes	—
203	C₄×Dic₁₄₉	C₂³	1	2	yes	—
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	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
220	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
226	C₄²×C₁₄₉	C₂³	1	2	yes	—
227	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
228	C₂²×D₁₄₉	—	2	2	no	—
229	C₂²×D₁₄₉	—	2	2	no	—
230	C₂²×D₁₄₉	—	2	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	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
235	Dic₂₉₈	—	2	2	no	—
236	Dic₂₉₈	—	4	2	no	—
237	D₅₉₆	—	2	2	no	—
238	D₅₉₆	—	2	4	no	—
239	D₅₉₆	—	2	4	no	—
240	D₅₉₆	—	2	2	no	—
241	D₅₉₆	—	2	2	no	—
242	D₅₉₆	—	4	2	no	—
243	C₂²⋊D₁₄₉	—	2	4	no	—
244	C₂²⋊D₁₄₉	—	2	2	no	—
245	C₂²⋊D₁₄₉	—	2	2	no	—
246	C₂²⋊D₁₄₉	—	2	2	no	—
247	C₂²⋊D₁₄₉	—	2	2	no	—
248	C₂²⋊D₁₄₉	—	4	2	no	—
249	C₂×Dic₁₄₉	—	2	2	no	—
250	C₂×Dic₁₄₉	—	4	2	no	—
251	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
252	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
253	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
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	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
258	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
259	C₄×D₁₄₉	—	2	2	no	—
260	C₄×D₁₄₉	—	2	4	no	—
261	C₄×D₁₄₉	—	2	4	no	—
262	C₄×D₁₄₉	—	2	2	no	—
263	C₄×D₁₄₉	—	2	2	no	—
264	C₄×D₁₄₉	—	2	2	no	—
265	C₄×D₁₄₉	—	2	4	no	—
266	C₄×D₁₄₉	—	4	2	no	—
267	C₄×D₁₄₉	—	4	2	no	—
268	C₄×D₁₄₉	—	4	2	no	—
269	C₄×D₁₄₉	—	4	2	no	—
270	C₄×D₁₄₉	—	4	2	no	—
271	C₄×D₁₄₉	#41	1	4	yes	complemented
272	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
273	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
274	Q₈×C₁₄₉	—	2	2	no	—
275	Q₈×C₁₄₉	—	4	2	no	—
276	D₄×C₁₄₉	—	2	2	no	—
277	C₂×C₄×C₁₄₉	—	2	2	no	—
278	C₂×C₄×C₁₄₉	—	2	2	no	—
279	C₂×C₄×C₁₄₉	—	4	2	no	—
280	C₂×C₄×C₁₄₉	—	4	2	no	—
281	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
282	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
284	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
286	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
287	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₁₄₉	—	2	1	no	—
291	C₂²×C₁₄₉	—	2	1	no	—
292	C₂²×C₁₄₉	—	2	1	no	—
293	C₂²×C₁₄₉	—	2	1	no	—
294	C₂²×C₁₄₉	—	2	1	no	—
295	C₂²×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
296	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
297	C₂×D₁₄₉	—	2	8	no	—
298	C₂×D₁₄₉	—	2	1	no	—
299	C₂×D₁₄₉	—	2	1	no	—
300	C₂×D₁₄₉	—	2	1	no	—
301	C₂×D₁₄₉	—	2	1	no	—
302	C₂×D₁₄₉	—	2	1	no	—
303	C₂×D₁₄₉	—	2	2	no	—
304	C₂×D₁₄₉	—	2	2	no	—
305	C₂×D₁₄₉	—	2	1	no	—
306	C₂×D₁₄₉	—	2	1	no	—
307	C₂×D₁₄₉	—	2	2	no	—
308	C₂×D₁₄₉	C₂×#41	1	2	yes	—
309	C₂×D₁₄₉	H(5,𝔽₂)	1	2	yes	—
310	C₄×C₁₄₉	—	2	1	no	—
311	C₄×C₁₄₉	—	2	1	no	—
312	C₄×C₁₄₉	—	2	2	no	—
313	C₄×C₁₄₉	—	2	2	no	—
314	C₄×C₁₄₉	—	2	2	no	—
315	C₄×C₁₄₉	—	2	2	no	—
316	C₄×C₁₄₉	—	2	1	no	—
317	C₄×C₁₄₉	—	2	1	no	—
318	C₄×C₁₄₉	C₂×#41	1	2	yes	—
319	Dic₁₄₉	—	2	1	no	—
320	Dic₁₄₉	—	2	1	no	—
321	Dic₁₄₉	—	2	2	no	—
322	Dic₁₄₉	—	2	2	no	—
323	Dic₁₄₉	—	2	1	no	—
324	Dic₁₄₉	—	2	1	no	—
325	Dic₁₄₉	—	2	2	no	—
326	Dic₁₄₉	C₂×#41	1	2	yes	—
327	C₂×C₁₄₉	—	2	2	no	—
328	C₂×C₁₄₉	—	4	1	no	—
329	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
330	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
332	D₁₄₉	—	2	2	no	—
333	D₁₄₉	—	2	2	no	—
334	D₁₄₉	—	4	1	no	—
335	D₁₄₉	—	4	2	no	—
336	C₁₄₉	#3492	1	1	yes	characteristic, complemented, Sylow
337	#3492	—	149	1	no	maximal, Sylow
338	#554	—	149	2	no	—
339	#554	—	149	1	no	—
340	#554	D₁₄₉	1	1	yes	characteristic, complemented
341	#553	—	149	1	no	—
342	#553	—	149	2	no	—
343	#553	—	149	1	no	—
344	#552	—	149	2	no	—
345	#552	—	149	1	no	—
346	#552	—	149	1	no	—
347	#547	—	149	1	no	—
348	#547	—	149	2	no	—
349	#547	—	149	1	no	—
350	#544	—	149	1	no	—
351	#539	—	149	2	no	—
352	#539	—	149	2	no	—
353	#537	—	149	1	no	—
354	#525	—	149	1	no	—
355	#525	—	149	2	no	—
356	#525	—	149	1	no	—
357	#525	—	149	2	no	—
358	#520	—	149	1	no	—
359	#520	—	149	1	no	—
360	C₂²×C₄⋊C₄	—	149	1	no	—
361	C₂×#41	—	149	1	no	—
362	C₂×#41	—	149	2	no	—
363	C₂×#41	—	149	1	no	—
364	C₂×#41	—	149	2	no	—
365	C₂³×C₄	—	149	1	no	—
366	C₂³×C₄	—	149	2	no	—
367	C₄⋊Q₈	—	149	2	no	—
368	C₄⋊Q₈	—	149	1	no	—
369	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
370	#126	—	149	2	no	—
371	#126	—	149	2	no	—
372	#126	—	149	2	no	—
373	#126	—	149	2	no	—
374	#125	—	149	2	no	—
375	#125	—	149	2	no	—
376	#125	—	149	2	no	—
377	#125	—	149	2	no	—
378	#125	—	149	1	no	—
379	#125	—	149	1	no	—
380	#125	C₂×D₁₄₉	1	2	yes	complemented
381	#123	—	149	2	no	—
382	#123	—	149	1	no	—
383	#123	—	149	2	no	—
384	#123	—	149	2	no	—
385	#123	—	149	2	no	—
386	#123	—	149	2	no	—
387	#123	—	149	2	no	—
388	#123	—	149	2	no	—
389	#123	—	149	1	no	—
390	#123	—	149	2	no	—
391	#123	—	149	2	no	—
392	C₂²⋊Q₈	—	149	2	no	—
393	C₂²⋊Q₈	—	149	1	no	—
394	C₂²⋊Q₈	—	149	1	no	—
395	C₂²⋊Q₈	—	149	2	no	—
396	C₂²⋊Q₈	—	149	2	no	—
397	C₂²⋊Q₈	—	149	1	no	—
398	C₂²⋊Q₈	—	149	2	no	—
399	C₂²⋊Q₈	—	149	2	no	—
400	C₂²⋊Q₈	—	149	2	no	—
401	C₂²⋊Q₈	—	149	1	no	—
402	C₂²⋊Q₈	—	149	2	no	—
403	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
404	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
405	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
406	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
407	#121	—	149	2	no	—
408	#121	—	149	1	no	—
409	#121	—	149	2	no	—
410	#121	—	149	1	no	—
411	#121	—	149	1	no	—
412	#121	—	149	2	no	—
413	#121	—	149	1	no	—
414	#121	—	149	1	no	—
415	#121	—	149	2	no	—
416	#121	—	149	1	no	—
417	#121	—	149	2	no	—
418	#120	—	149	1	no	—
419	#120	—	149	1	no	—
420	#120	—	149	2	no	—
421	C₄×Q₈	—	149	1	no	—
422	C₄×Q₈	—	149	2	no	—
423	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
424	C₄×D₄	—	149	2	no	—
425	C₄×D₄	—	149	2	no	—
426	C₄×D₄	—	149	1	no	—
427	C₄×D₄	—	149	2	no	—
428	C₄×D₄	—	149	1	no	—
429	C₄×D₄	—	149	2	no	—
430	C₄×D₄	—	149	2	no	—
431	C₄×D₄	—	149	1	no	—
432	C₄×D₄	—	149	2	no	—
433	C₄×D₄	—	149	2	no	—
434	C₄×D₄	—	149	2	no	—
435	C₄×D₄	—	149	2	no	—
436	C₄×D₄	—	149	2	no	—
437	C₄×D₄	—	149	1	no	—
438	C₄×D₄	—	149	1	no	—
439	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
440	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
441	#117	—	149	1	no	—
442	#117	—	149	1	no	—
443	#117	—	149	1	no	—
444	#117	—	149	2	no	—
445	#117	—	149	1	no	—
446	#117	—	149	2	no	—
447	#117	—	149	2	no	—
448	C₂×C₄⋊C₄	—	149	2	no	—
449	C₂×C₄⋊C₄	—	149	1	no	—
450	C₂×C₄⋊C₄	—	149	1	no	—
451	C₂×C₄⋊C₄	—	149	1	no	—
452	C₂×C₄⋊C₄	—	149	2	no	—
453	C₂×C₄⋊C₄	—	149	2	no	—
454	C₂×C₄⋊C₄	—	149	1	no	—
455	C₂×C₄⋊C₄	—	149	1	no	—
456	C₂×C₄⋊C₄	—	149	2	no	—
457	C₂×C₄⋊C₄	—	149	1	no	—
458	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
460	C₂⁴	—	149	1	no	—
461	#41	—	298	4	no	—
462	#41	—	298	4	no	—
463	#41	—	596	4	no	—
464	#41	—	596	4	no	—
465	C₂×Q₈	—	149	1	no	—
466	C₂×Q₈	—	149	2	no	—
467	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
468	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
469	C₂×D₄	—	149	2	no	—
470	C₂×D₄	—	149	1	no	—
471	C₂×D₄	—	149	1	no	—
472	C₂×D₄	—	149	1	no	—
473	C₂×D₄	—	149	1	no	—
474	C₂×D₄	—	149	2	no	—
475	C₂×D₄	—	149	1	no	—
476	C₂×D₄	—	149	2	no	—
477	C₂×D₄	—	149	1	no	—
478	C₂×D₄	—	149	2	no	—
479	C₂×D₄	—	149	1	no	—
480	C₂×D₄	—	149	2	no	—
481	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
482	C₂²×C₄	—	298	4	no	—
483	C₂²×C₄	—	596	4	no	—
484	C₂²×C₄	—	149	1	no	—
485	C₂²×C₄	—	149	2	no	—
486	C₂²×C₄	—	149	2	no	—
487	C₂²×C₄	—	149	1	no	—
488	C₂²×C₄	—	149	1	no	—
489	C₂²×C₄	—	149	1	no	—
490	C₂²×C₄	—	149	2	no	—
491	C₂²×C₄	—	149	1	no	—
492	C₂²×C₄	—	149	2	no	—
493	C₂²×C₄	—	149	2	no	—
494	C₂²×C₄	—	149	2	no	—
495	C₂²×C₄	—	149	2	no	—
496	C₂²×C₄	—	149	2	no	—
497	C₂²×C₄	—	149	2	no	—
498	C₂²×C₄	—	149	1	no	—
499	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
502	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
503	C₄⋊C₄	—	149	2	no	—
504	C₄⋊C₄	—	149	1	no	—
505	C₄⋊C₄	—	149	2	no	—
506	C₄⋊C₄	—	149	1	no	—
507	C₄⋊C₄	—	149	2	no	—
508	C₄⋊C₄	—	149	2	no	—
509	C₄⋊C₄	—	149	2	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	—	149	2	no	—
516	C₄⋊C₄	—	149	2	no	—
517	C₄⋊C₄	—	149	2	no	—
518	C₄⋊C₄	—	149	1	no	—
519	C₄⋊C₄	—	149	1	no	—
520	C₄⋊C₄	—	149	2	no	—
521	C₄⋊C₄	—	149	2	no	—
522	C₄⋊C₄	—	149	2	no	—
523	C₄⋊C₄	—	149	1	no	—
524	C₄⋊C₄	—	149	2	no	—
525	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
528	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
530	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
531	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
532	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
533	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
534	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
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	—	149	2	no	—
542	C₂²⋊C₄	—	149	1	no	—
543	C₂²⋊C₄	—	149	1	no	—
544	C₂²⋊C₄	—	149	2	no	—
545	C₂²⋊C₄	—	149	2	no	—
546	C₂²⋊C₄	—	149	2	no	—
547	C₂²⋊C₄	—	149	2	no	—
548	C₂²⋊C₄	—	149	2	no	—
549	C₂²⋊C₄	—	149	2	no	—
550	C₂²⋊C₄	—	149	1	no	—
551	C₂²⋊C₄	—	149	2	no	—
552	C₂²⋊C₄	—	149	2	no	—
553	C₂²⋊C₄	—	149	1	no	—
554	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
558	C₄²	—	149	2	no	—
559	C₄²	—	149	2	no	—
560	C₄²	—	149	2	no	—
561	C₄²	—	149	1	no	—
562	C₄²	—	149	2	no	—
563	C₄²	C₂²×D₁₄₉	1	2	yes	—
564	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
565	C₂³	—	298	2	no	—
566	C₂³	—	298	2	no	—
567	C₂³	—	298	2	no	—
568	C₂³	—	149	1	no	—
569	C₂³	—	149	2	no	—
570	C₂³	—	149	1	no	—
571	C₂³	—	149	1	no	—
572	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
573	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	4	2	no	—
576	Q₈	—	298	2	no	—
577	Q₈	—	596	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	298	2	no	—
580	D₄	—	298	4	no	—
581	D₄	—	298	4	no	—
582	D₄	—	298	2	no	—
583	D₄	—	298	2	no	—
584	D₄	—	298	2	no	—
585	D₄	—	298	4	no	—
586	D₄	—	298	2	no	—
587	D₄	—	298	2	no	—
588	D₄	—	298	2	no	—
589	D₄	—	596	2	no	—
590	D₄	—	596	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	298	2	no	—
596	C₂×C₄	—	298	4	no	—
597	C₂×C₄	—	298	4	no	—
598	C₂×C₄	—	298	2	no	—
599	C₂×C₄	—	298	4	no	—
600	C₂×C₄	—	298	2	no	—
601	C₂×C₄	—	298	2	no	—
602	C₂×C₄	—	298	2	no	—
603	C₂×C₄	—	596	2	no	—
604	C₂×C₄	—	596	2	no	—
605	C₂×C₄	—	596	2	no	—
606	C₂×C₄	—	596	2	no	—
607	C₂×C₄	—	596	2	no	—
608	C₂×C₄	—	596	2	no	—
609	C₂×C₄	—	149	2	no	—
610	C₂×C₄	—	149	1	no	—
611	C₂×C₄	—	149	1	no	—
612	C₂×C₄	—	149	2	no	—
613	C₂×C₄	—	149	1	no	—
614	C₂×C₄	—	149	1	no	—
615	C₂×C₄	—	149	2	no	—
616	C₂×C₄	—	149	1	no	—
617	C₂×C₄	—	149	4	no	—
618	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
620	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
621	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
622	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
626	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	298	8	no	—
633	C₂²	—	298	1	no	—
634	C₂²	—	298	1	no	—
635	C₂²	—	298	1	no	—
636	C₂²	—	298	1	no	—
637	C₂²	—	298	2	no	—
638	C₂²	—	298	1	no	—
639	C₂²	—	298	1	no	—
640	C₂²	—	298	2	no	—
641	C₂²	—	298	1	no	—
642	C₂²	—	298	2	no	—
643	C₂²	—	149	2	no	—
644	C₂²	—	149	2	no	—
645	C₂²	#18011959	1	2	yes	—
646	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	298	1	no	—
656	C₄	—	298	1	no	—
657	C₄	—	298	2	no	—
658	C₄	—	298	2	no	—
659	C₄	—	298	1	no	—
660	C₄	—	298	2	no	—
661	C₄	—	298	1	no	—
662	C₄	—	149	2	no	—
663	C₄	#41×D₁₄₉	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	298	2	no	—
667	C₂	—	298	2	no	—
668	C₂	—	596	2	no	—
669	C₂	—	596	1	no	—
670	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
671	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic
672	C₂	C₂×#18011959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#554×C₁₄₉	C₂
hypercenter	#554	D₁₄₉
hypocenter	C₁₄₉	#3492
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #23750333	C₂	semidirect
2. #23750329	C₂	semidirect
3. #23750324	C₂	semidirect
4. #23750323	C₂	semidirect
5. #23750321	C₂	semidirect
6. #23750316	C₂	semidirect
7. #23750309	C₂	semidirect
8. #23750307	C₂	semidirect
9. #23750278	C₂	semidirect
10. #23750277	C₂	semidirect
11. #23750276	C₂	semidirect
12. #23750252	C₂	semidirect
13. #23750223	C₂	semidirect
14. #23750221	C₂	semidirect
15. #23750205	C₂	semidirect
16. #23750138	C₂	semidirect
17. #23750138	C₂	semidirect
18. #23750134	C₂	semidirect
19. #23750134	C₂	semidirect
20. #23750107	C₂	semidirect
21. #23750106	C₂	semidirect
22. C₂×C₄⋊C₄×D₁₄₉	C₂	semidirect
23. #554×C₁₄₉	C₂	semidirect
30. #18011910	C₂²	semidirect
31. #18011909	C₂²	semidirect
32. #18011906	C₂²	semidirect
33. #18011906	C₂²	semidirect
34. #18011905	C₂²	semidirect
35. #18011904	C₂²	semidirect
36. #18011903	C₂²	semidirect
37. #18011902	C₂²	semidirect
38. #18011901	C₂²	semidirect
39. #18011901	C₂²	semidirect
40. #18011901	C₂²	semidirect
41. #18011901	C₂²	semidirect
47. #18011896	C₂²	semidirect
48. #18011896	C₂²	semidirect
49. #18011894	C₂²	semidirect
52. #18011893	C₂²	semidirect
53. #18011891	C₂²	semidirect
56. #18011889	C₂²	semidirect
57. #18011889	C₂²	semidirect
62. #18011887	C₂²	semidirect
63. #18011887	C₂²	semidirect
66. #18011886	C₂²	semidirect
69. #18011885	C₂²	semidirect
72. #18011884	C₂²	semidirect
78. Q₈×Dic₁₄₉	C₂²	semidirect
79. #18011876	C₂²	semidirect
82. C₄×D₅₉₆	C₂²	semidirect
86. #18011873	C₂²	semidirect
91. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
95. #18011870	C₂²	semidirect
98. #18011869	C₂²	semidirect
101. #18011868	C₂²	semidirect
110. C₄⋊C₄×D₁₄₉	C₂²	semidirect
111. C₄⋊C₄×D₁₄₉	C₂²	semidirect
112. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
113. #125×C₁₄₉	C₂²	semidirect
116. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
117. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
118. C₄×Q₈×C₁₄₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
271. C₄×D₁₄₉	#41	semidirect
336. C₁₄₉	#3492	semidirect
340. #554	D₁₄₉	semidirect
369. C₄⋊Q₈	C₂×D₁₄₉	semidirect
380. #125	C₂×D₁₄₉	semidirect
405. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
406. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
423. C₄×Q₈	C₂×D₁₄₉	semidirect
459. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750333	2
#23750329	2
#23750324	2
#23750323	2
#23750321	2
#23750316	2
#23750309	2
#23750307	2
#23750278	2
#23750277	2
#23750276	2
#23750252	2
#23750223	2
#23750221	2
#23750205	2
#23750138	2
#23750134	2
#23750107	2
#23750106	2
C₂×C₄⋊C₄×D₁₄₉	2
#554×C₁₄₉	2
#3492	149