Subgroups — #34058531

Order 19072.

1152 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750328	C₂	1	2	yes	maximal, complemented
2	#23750328	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750326	C₂	1	2	yes	maximal, complemented
4	#23750319	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750310	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750299	C₂	1	2	yes	maximal, complemented
7	#23750298	C₂	1	2	yes	maximal, complemented
8	#23750287	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750285	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750271	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750266	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750223	C₂	1	2	yes	maximal, complemented
13	#23750214	C₂	1	2	yes	maximal, complemented
14	#23750186	C₂	1	2	yes	maximal, complemented
15	#23750162	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750160	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750138	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750137	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²⋊Q₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#18011886	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750099	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₁₄₉	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, complemented
25	C₂×#14558736	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₅₉₆	C₂²	1	2	yes	—
28	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
32	#18011906	C₂²	1	2	yes	complemented
33	#18011906	C₂²	1	2	yes	complemented
34	#18011906	C₂²	1	2	yes	complemented
35	#18011906	C₂²	1	2	yes	complemented
36	#18011905	C₂²	1	2	yes	complemented
37	#18011902	C₂²	1	1	yes	characteristic, complemented
38	#18011901	C₂²	1	2	yes	complemented
39	#18011900	C₂²	1	1	yes	characteristic, complemented
40	#18011899	C₂²	1	1	yes	characteristic, complemented
41	#18011899	C₂²	1	2	yes	complemented
42	#18011897	C₂²	1	2	yes	complemented
43	#18011896	C₂²	1	2	yes	complemented
44	#18011896	C₂²	1	2	yes	complemented
45	#18011896	C₂²	1	2	yes	complemented
46	#18011896	C₂²	1	2	yes	complemented
47	#18011896	C₂²	1	2	yes	complemented
48	#18011896	C₂²	1	2	yes	complemented
49	#18011895	C₂²	1	2	yes	complemented
50	#18011894	C₂²	1	2	yes	—
51	#18011893	C₂²	1	2	yes	complemented
52	#18011891	C₂²	1	1	yes	characteristic, complemented
53	#18011891	C₂²	1	2	yes	complemented
54	#18011891	C₂²	1	1	yes	characteristic, complemented
55	#18011890	C₂²	1	1	yes	characteristic, complemented
56	#18011889	C₂²	1	2	yes	complemented
57	#18011889	C₂²	1	2	yes	complemented
58	#18011888	C₂²	1	2	yes	complemented
59	#18011887	C₂²	1	1	yes	characteristic, complemented
60	#18011886	C₂²	1	1	yes	characteristic
61	#18011886	C₂²	1	1	yes	characteristic
62	#18011886	C₂²	1	2	yes	—
63	#18011886	C₂²	1	2	yes	complemented
64	#18011886	C₂²	1	2	yes	complemented
65	#18011886	C₂²	1	2	yes	complemented
66	#18011886	C₂²	1	1	yes	characteristic, complemented
67	#18011886	C₂²	1	1	yes	characteristic, complemented
68	#18011886	C₂²	1	1	yes	characteristic, complemented
69	#18011886	C₂²	1	2	yes	complemented
70	#18011885	C₂²	1	1	yes	characteristic, complemented
71	#18011884	C₂²	1	2	yes	complemented
72	#18011884	C₂²	1	2	yes	complemented
73	#18011884	C₂²	1	2	yes	complemented
74	#18011881	C₂²	1	2	yes	—
75	#18011881	C₂²	1	2	yes	complemented
76	#18011881	C₂²	1	2	yes	complemented
77	#18011879	C₂²	1	2	yes	—
78	#18011876	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₅₉₆	C₂²	1	2	yes	complemented
80	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₅₉₆	C₂²	1	2	yes	complemented
82	C₄×D₅₉₆	C₂²	1	2	yes	complemented
83	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₅₉₆	C₂²	1	2	yes	complemented
85	C₄×D₅₉₆	C₂²	1	2	yes	complemented
86	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
87	#18011873	C₂²	1	2	yes	complemented
88	#18011873	C₂²	1	1	yes	characteristic, complemented
89	#18011873	C₂²	1	2	yes	complemented
90	#18011873	C₂²	1	2	yes	complemented
91	#18011873	C₂²	1	2	yes	complemented
92	#18011873	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
94	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
95	#18011871	C₂²	1	1	yes	characteristic
96	#18011871	C₂²	1	2	yes	complemented
97	#18011871	C₂²	1	1	yes	characteristic, complemented
98	#18011870	C₂²	1	2	yes	complemented
99	#18011869	C₂²	1	2	yes	complemented
100	#18011869	C₂²	1	1	yes	characteristic, complemented
101	#18011868	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
105	C₂×#14558713	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
109	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
111	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
112	#126×C₁₄₉	C₂²	1	2	yes	complemented
113	#125×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
114	#125×C₁₄₉	C₂²	1	2	yes	complemented
115	#123×C₁₄₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
120	#117×C₁₄₉	C₂²	1	2	yes	complemented
121	#117×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
124	C₂³×D₁₄₉	C₂³	1	2	yes	—
125	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
126	#14558737	—	4	2	no	—
127	#14558736	—	4	2	no	—
128	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₉₈	C₂³	1	2	yes	—
130	Q₈×D₁₄₉	—	4	2	no	—
131	C₂×D₅₉₆	—	2	8	no	—
132	C₂×D₅₉₆	—	4	2	no	—
133	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
134	C₂×D₅₉₆	C₂³	1	2	yes	—
135	C₂×D₅₉₆	C₂³	1	2	yes	—
136	C₂×D₅₉₆	C₂³	1	2	yes	—
137	C₂×D₅₉₆	C₂³	1	2	yes	—
138	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
139	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
140	C₂×D₅₉₆	C₂³	1	2	yes	—
141	C₂×D₅₉₆	C₂³	1	2	yes	—
142	C₂×D₅₉₆	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
147	D₄×D₁₄₉	—	2	4	no	—
148	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
149	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₄₉	—	4	2	no	—
151	C₂×C₄×D₁₄₉	—	4	2	no	—
152	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
161	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
162	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
163	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
165	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
166	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
167	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
169	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
170	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
172	#14558715	C₂³	1	1	yes	characteristic
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	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	2	yes	—
183	#14558713	C₂³	1	2	yes	—
184	#14558713	C₂³	1	2	yes	—
185	#14558713	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
197	#14558713	C₂³	1	2	yes	—
198	#14558713	C₂³	1	2	yes	—
199	#14558713	C₂³	1	1	yes	characteristic
200	#14558713	C₂³	1	2	yes	—
201	#14558713	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	2	yes	—
205	C₄×Dic₁₄₉	C₂³	1	2	yes	—
206	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
207	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
220	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
221	C₄⋊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	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
226	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
227	C₄²×C₁₄₉	C₂³	1	2	yes	—
228	C₄²×C₁₄₉	C₂³	1	2	yes	—
229	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
230	C₂²×D₁₄₉	—	2	4	no	—
231	C₂²×D₁₄₉	—	2	2	no	—
232	C₂²×D₁₄₉	—	4	1	no	—
233	C₂²×D₁₄₉	—	4	1	no	—
234	C₂²×D₁₄₉	—	4	1	no	—
235	C₂²×D₁₄₉	—	4	1	no	—
236	C₂²×D₁₄₉	—	4	2	no	—
237	C₂²×D₁₄₉	—	4	2	no	—
238	C₂²×D₁₄₉	#41	1	4	yes	complemented
239	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
241	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
242	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
243	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
244	Dic₂₉₈	—	2	2	no	—
245	Dic₂₉₈	—	4	2	no	—
246	D₅₉₆	—	2	2	no	—
247	D₅₉₆	—	2	4	no	—
248	D₅₉₆	—	2	4	no	—
249	D₅₉₆	—	2	4	no	—
250	D₅₉₆	—	2	4	no	—
251	D₅₉₆	—	2	2	no	—
252	D₅₉₆	—	2	2	no	—
253	D₅₉₆	—	4	2	no	—
254	D₅₉₆	—	4	2	no	—
255	D₅₉₆	—	4	2	no	—
256	C₂²⋊D₁₄₉	—	2	2	no	—
257	C₂²⋊D₁₄₉	—	2	2	no	—
258	C₂²⋊D₁₄₉	—	4	2	no	—
259	C₂²⋊D₁₄₉	—	4	2	no	—
260	C₂×Dic₁₄₉	—	4	1	no	—
261	C₂×Dic₁₄₉	—	4	1	no	—
262	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
267	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
268	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
269	C₄×D₁₄₉	—	2	2	no	—
270	C₄×D₁₄₉	—	2	2	no	—
271	C₄×D₁₄₉	—	2	2	no	—
272	C₄×D₁₄₉	—	2	2	no	—
273	C₄×D₁₄₉	—	4	1	no	—
274	C₄×D₁₄₉	—	4	1	no	—
275	C₄×D₁₄₉	—	4	1	no	—
276	C₄×D₁₄₉	—	4	1	no	—
277	C₄×D₁₄₉	—	4	1	no	—
278	C₄×D₁₄₉	—	4	2	no	—
279	C₄×D₁₄₉	—	4	2	no	—
280	C₄×D₁₄₉	—	4	2	no	—
281	C₄×D₁₄₉	—	4	2	no	—
282	C₄×D₁₄₉	—	4	2	no	—
283	C₄×D₁₄₉	—	4	2	no	—
284	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
285	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
286	Q₈×C₁₄₉	—	2	2	no	—
287	D₄×C₁₄₉	—	2	2	no	—
288	C₂×C₄×C₁₄₉	—	2	4	no	—
289	C₂×C₄×C₁₄₉	—	2	2	no	—
290	C₂×C₄×C₁₄₉	—	2	2	no	—
291	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
293	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
295	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
296	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
298	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
299	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₁₄₉	—	2	1	no	—
301	C₂²×C₁₄₉	—	2	1	no	—
302	C₂²×C₁₄₉	—	2	1	no	—
303	C₂²×C₁₄₉	—	2	1	no	—
304	C₂²×C₁₄₉	—	2	1	no	—
305	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
306	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
307	C₂×D₁₄₉	—	2	1	no	—
308	C₂×D₁₄₉	—	2	1	no	—
309	C₂×D₁₄₉	—	2	1	no	—
310	C₂×D₁₄₉	—	2	1	no	—
311	C₂×D₁₄₉	—	2	1	no	—
312	C₂×D₁₄₉	—	2	2	no	—
313	C₂×D₁₄₉	—	2	2	no	—
314	C₂×D₁₄₉	—	2	1	no	—
315	C₂×D₁₄₉	—	2	2	no	—
316	C₂×D₁₄₉	—	2	2	no	—
317	C₂×D₁₄₉	—	2	2	no	—
318	C₂×D₁₄₉	—	2	2	no	—
319	C₂×D₁₄₉	—	2	1	no	—
320	C₂×D₁₄₉	—	4	4	no	—
321	C₂×D₁₄₉	—	4	4	no	—
322	C₂×D₁₄₉	—	8	4	no	—
323	C₂×D₁₄₉	C₂×#41	1	2	yes	—
324	C₂×D₁₄₉	C₂×#41	1	2	yes	—
325	C₄×C₁₄₉	—	2	2	no	—
326	C₄×C₁₄₉	—	2	2	no	—
327	C₄×C₁₄₉	—	2	1	no	—
328	C₄×C₁₄₉	—	2	1	no	—
329	C₄×C₁₄₉	—	2	1	no	—
330	C₄×C₁₄₉	—	2	2	no	—
331	C₄×C₁₄₉	—	2	1	no	—
332	C₄×C₁₄₉	—	2	2	no	—
333	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
334	Dic₁₄₉	—	2	1	no	—
335	Dic₁₄₉	—	2	1	no	—
336	Dic₁₄₉	—	2	1	no	—
337	Dic₁₄₉	—	2	1	no	—
338	Dic₁₄₉	—	2	2	no	—
339	Dic₁₄₉	—	2	1	no	—
340	Dic₁₄₉	—	2	2	no	—
341	C₂×C₁₄₉	—	2	2	no	—
342	C₂×C₁₄₉	—	4	1	no	—
343	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
344	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₁₄₉	#585	1	1	yes	characteristic
346	D₁₄₉	—	2	2	no	—
347	D₁₄₉	—	2	2	no	—
348	D₁₄₉	—	4	1	no	—
349	D₁₄₉	—	4	2	no	—
350	D₁₄₉	—	4	2	no	—
351	C₁₄₉	#3505	1	1	yes	characteristic, complemented, Sylow
352	#3505	—	149	1	no	maximal, Sylow
353	#553	—	149	2	no	—
354	#553	—	149	1	no	—
355	#553	—	149	2	no	—
356	#553	—	149	1	no	—
357	#552	—	149	1	no	—
358	#552	D₁₄₉	1	1	yes	characteristic, complemented
359	#551	—	149	2	no	—
360	#551	—	149	2	no	—
361	#548	—	149	1	no	—
362	#548	—	149	1	no	—
363	#546	—	149	1	no	—
364	#546	—	149	1	no	—
365	#539	—	149	2	no	—
366	#538	—	149	2	no	—
367	#534	—	149	2	no	—
368	#529	—	149	1	no	—
369	#529	—	149	1	no	—
370	#525	—	149	1	no	—
371	#525	—	149	1	no	—
372	C₂×C₂²⋊Q₈	—	149	1	no	—
373	C₂×#121	—	149	1	no	—
374	#518	—	149	2	no	—
375	C₂×C₄×D₄	—	149	1	no	—
376	C₂×#41	—	149	1	no	—
377	C₂×#41	—	149	1	no	—
378	C₂²×Q₈	—	149	1	no	—
379	C₂²×D₄	—	149	1	no	—
380	C₂²×D₄	—	149	2	no	—
381	C₂²×D₄	—	149	1	no	—
382	C₂³×C₄	—	149	1	no	—
383	C₂³×C₄	—	149	1	no	—
384	#126	—	149	2	no	—
385	#126	—	149	2	no	—
386	#126	—	149	2	no	—
387	#126	—	149	2	no	—
388	#126	—	149	2	no	—
389	#126	C₂×D₁₄₉	1	2	yes	complemented
390	#125	—	149	1	no	—
391	#125	—	149	2	no	—
392	#125	C₂×D₁₄₉	1	1	yes	characteristic, complemented
393	#125	C₂×D₁₄₉	1	2	yes	complemented
394	#124	—	149	1	no	—
395	#124	—	149	2	no	—
396	#124	—	149	1	no	—
397	#124	—	149	2	no	—
398	#123	—	149	2	no	—
399	#123	—	149	2	no	—
400	#123	—	149	2	no	—
401	#123	—	149	2	no	—
402	#123	—	149	2	no	—
403	#123	—	149	2	no	—
404	#123	—	149	2	no	—
405	#123	—	149	2	no	—
406	#123	—	149	2	no	—
407	#123	C₂×D₁₄₉	1	2	yes	—
408	C₂²⋊Q₈	—	149	1	no	—
409	C₂²⋊Q₈	—	149	1	no	—
410	C₂²⋊Q₈	—	149	1	no	—
411	C₂²⋊Q₈	—	149	2	no	—
412	C₂²⋊Q₈	—	149	1	no	—
413	C₂²⋊Q₈	—	149	2	no	—
414	C₂²⋊Q₈	—	149	2	no	—
415	C₂²⋊Q₈	—	149	2	no	—
416	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
417	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
418	#121	—	149	1	no	—
419	#121	—	149	1	no	—
420	#121	—	149	1	no	—
421	#121	—	149	2	no	—
422	#121	—	149	1	no	—
423	#121	—	149	1	no	—
424	#121	—	149	2	no	—
425	#121	—	149	1	no	—
426	#121	—	149	2	no	—
427	#121	—	149	2	no	—
428	#121	—	149	2	no	—
429	#121	—	149	2	no	—
430	#121	—	149	2	no	—
431	#121	—	149	2	no	—
432	#120	—	149	2	no	—
433	#120	—	149	2	no	—
434	#120	—	149	2	no	—
435	#120	—	149	2	no	—
436	C₄×Q₈	—	149	1	no	—
437	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
438	C₄×D₄	—	149	1	no	—
439	C₄×D₄	—	149	1	no	—
440	C₄×D₄	—	149	1	no	—
441	C₄×D₄	—	149	1	no	—
442	C₄×D₄	—	149	2	no	—
443	C₄×D₄	—	149	2	no	—
444	C₄×D₄	—	149	2	no	—
445	C₄×D₄	—	149	2	no	—
446	C₄×D₄	—	149	1	no	—
447	C₄×D₄	—	149	1	no	—
448	C₄×D₄	—	149	1	no	—
449	C₄×D₄	—	149	2	no	—
450	C₄×D₄	—	149	1	no	—
451	C₄×D₄	—	149	2	no	—
452	C₄×D₄	—	149	2	no	—
453	C₄×D₄	—	149	2	no	—
454	C₄×D₄	—	149	2	no	—
455	C₄×D₄	—	149	2	no	—
456	C₄×D₄	—	149	1	no	—
457	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
458	#117	—	149	2	no	—
459	#117	—	149	1	no	—
460	#117	—	149	2	no	—
461	#117	—	149	2	no	—
462	#117	C₂×D₁₄₉	1	2	yes	complemented
463	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
464	C₂×C₄⋊C₄	—	149	1	no	—
465	C₂×C₄⋊C₄	—	149	1	no	—
466	C₂×C₄⋊C₄	—	149	2	no	—
467	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
468	C₂×C₂²⋊C₄	—	149	2	no	—
469	C₂×C₂²⋊C₄	—	149	1	no	—
470	C₂×C₂²⋊C₄	—	149	1	no	—
471	C₂×C₂²⋊C₄	—	149	2	no	—
472	C₂×C₂²⋊C₄	—	149	2	no	—
473	C₂×C₂²⋊C₄	—	149	2	no	—
474	C₂×C₄²	—	149	1	no	—
475	C₂⁴	—	149	2	no	—
476	C₂⁴	—	149	1	no	—
477	C₂⁴	—	149	1	no	—
478	#41	—	596	2	no	—
479	#41	—	596	2	no	—
480	C₂×Q₈	—	596	2	no	—
481	C₂×Q₈	—	149	1	no	—
482	C₂×Q₈	—	149	2	no	—
483	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
484	C₂×D₄	—	298	8	no	—
485	C₂×D₄	—	298	4	no	—
486	C₂×D₄	—	596	2	no	—
487	C₂×D₄	—	149	1	no	—
488	C₂×D₄	—	149	1	no	—
489	C₂×D₄	—	149	2	no	—
490	C₂×D₄	—	149	2	no	—
491	C₂×D₄	—	149	2	no	—
492	C₂×D₄	—	149	2	no	—
493	C₂×D₄	—	149	2	no	—
494	C₂×D₄	—	149	1	no	—
495	C₂×D₄	—	149	2	no	—
496	C₂×D₄	—	149	1	no	—
497	C₂×D₄	—	149	1	no	—
498	C₂×D₄	—	149	2	no	—
499	C₂×D₄	—	149	2	no	—
500	C₂×D₄	—	149	2	no	—
501	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
502	C₂²×C₄	—	596	2	no	—
503	C₂²×C₄	—	596	2	no	—
504	C₂²×C₄	—	149	1	no	—
505	C₂²×C₄	—	149	1	no	—
506	C₂²×C₄	—	149	1	no	—
507	C₂²×C₄	—	149	1	no	—
508	C₂²×C₄	—	149	1	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	2	no	—
514	C₂²×C₄	—	149	1	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	1	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	1	yes	characteristic
524	C₄⋊C₄	—	149	1	no	—
525	C₄⋊C₄	—	149	2	no	—
526	C₄⋊C₄	—	149	2	no	—
527	C₄⋊C₄	—	149	1	no	—
528	C₄⋊C₄	—	149	1	no	—
529	C₄⋊C₄	—	149	1	no	—
530	C₄⋊C₄	—	149	2	no	—
531	C₄⋊C₄	—	149	2	no	—
532	C₄⋊C₄	—	149	2	no	—
533	C₄⋊C₄	—	149	2	no	—
534	C₄⋊C₄	—	149	2	no	—
535	C₄⋊C₄	—	149	2	no	—
536	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
537	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
538	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
539	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
540	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
541	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
542	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
543	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
544	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
545	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
546	C₂²⋊C₄	—	149	1	no	—
547	C₂²⋊C₄	—	149	2	no	—
548	C₂²⋊C₄	—	149	1	no	—
549	C₂²⋊C₄	—	149	2	no	—
550	C₂²⋊C₄	—	149	2	no	—
551	C₂²⋊C₄	—	149	1	no	—
552	C₂²⋊C₄	—	149	1	no	—
553	C₂²⋊C₄	—	149	2	no	—
554	C₂²⋊C₄	—	149	2	no	—
555	C₂²⋊C₄	—	149	1	no	—
556	C₂²⋊C₄	—	149	2	no	—
557	C₂²⋊C₄	—	149	2	no	—
558	C₂²⋊C₄	—	149	2	no	—
559	C₂²⋊C₄	—	149	2	no	—
560	C₂²⋊C₄	—	149	1	no	—
561	C₂²⋊C₄	—	149	2	no	—
562	C₂²⋊C₄	—	149	2	no	—
563	C₂²⋊C₄	—	149	2	no	—
564	C₂²⋊C₄	—	149	2	no	—
565	C₂²⋊C₄	—	149	2	no	—
566	C₂²⋊C₄	—	149	2	no	—
567	C₂²⋊C₄	—	149	2	no	—
568	C₂²⋊C₄	—	149	2	no	—
569	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
570	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
572	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
574	C₄²	—	149	1	no	—
575	C₄²	—	149	1	no	—
576	C₄²	—	149	1	no	—
577	C₄²	—	149	2	no	—
578	C₄²	—	149	2	no	—
579	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
580	C₄²	C₂²×D₁₄₉	1	2	yes	—
581	C₄²	C₂²×D₁₄₉	1	2	yes	—
582	C₂³	—	298	2	no	—
583	C₂³	—	298	4	no	—
584	C₂³	—	596	1	no	—
585	C₂³	—	596	1	no	—
586	C₂³	—	596	1	no	—
587	C₂³	—	596	1	no	—
588	C₂³	—	596	2	no	—
589	C₂³	—	596	2	no	—
590	C₂³	—	149	1	no	—
591	C₂³	—	149	2	no	—
592	C₂³	—	149	2	no	—
593	C₂³	—	149	1	no	—
594	C₂³	—	149	1	no	—
595	C₂³	—	149	4	no	—
596	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
597	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	298	2	no	—
600	Q₈	—	596	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	298	4	no	—
603	D₄	—	298	4	no	—
604	D₄	—	298	4	no	—
605	D₄	—	298	4	no	—
606	D₄	—	298	2	no	—
607	D₄	—	298	2	no	—
608	D₄	—	298	2	no	—
609	D₄	—	298	2	no	—
610	D₄	—	298	2	no	—
611	D₄	—	596	2	no	—
612	D₄	—	596	2	no	—
613	D₄	—	596	2	no	—
614	D₄	—	596	2	no	—
615	D₄	—	596	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	298	2	no	—
620	C₂×C₄	—	298	2	no	—
621	C₂×C₄	—	298	2	no	—
622	C₂×C₄	—	298	2	no	—
623	C₂×C₄	—	596	1	no	—
624	C₂×C₄	—	596	1	no	—
625	C₂×C₄	—	596	1	no	—
626	C₂×C₄	—	596	1	no	—
627	C₂×C₄	—	596	1	no	—
628	C₂×C₄	—	596	2	no	—
629	C₂×C₄	—	596	2	no	—
630	C₂×C₄	—	596	2	no	—
631	C₂×C₄	—	596	2	no	—
632	C₂×C₄	—	596	2	no	—
633	C₂×C₄	—	596	2	no	—
634	C₂×C₄	—	596	1	no	—
635	C₂×C₄	—	596	1	no	—
636	C₂×C₄	—	149	1	no	—
637	C₂×C₄	—	149	1	no	—
638	C₂×C₄	—	149	1	no	—
639	C₂×C₄	—	149	1	no	—
640	C₂×C₄	—	149	2	no	—
641	C₂×C₄	—	149	2	no	—
642	C₂×C₄	—	149	1	no	—
643	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
644	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
645	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
647	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
649	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
650	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	298	1	no	—
658	C₂²	—	298	1	no	—
659	C₂²	—	298	1	no	—
660	C₂²	—	298	1	no	—
661	C₂²	—	298	1	no	—
662	C₂²	—	298	2	no	—
663	C₂²	—	298	2	no	—
664	C₂²	—	298	1	no	—
665	C₂²	—	298	2	no	—
666	C₂²	—	298	2	no	—
667	C₂²	—	298	2	no	—
668	C₂²	—	298	2	no	—
669	C₂²	—	298	1	no	—
670	C₂²	—	596	4	no	—
671	C₂²	—	596	4	no	—
672	C₂²	—	149	2	no	—
673	C₂²	—	149	2	no	—
674	C₂²	—	1192	4	no	—
675	C₂²	#41×D₁₄₉	1	2	yes	—
676	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	298	1	no	—
686	C₄	—	298	1	no	—
687	C₄	—	298	1	no	—
688	C₄	—	298	1	no	—
689	C₄	—	298	2	no	—
690	C₄	—	298	1	no	—
691	C₄	—	298	2	no	—
692	C₄	#18011957	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	298	2	no	—
696	C₂	—	298	2	no	—
697	C₂	—	596	1	no	—
698	C₂	—	596	2	no	—
699	C₂	—	596	2	no	—
700	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
701	C₂	C₂×#18011957	1	1	yes	characteristic
702	C₂	#23750462	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	#3505
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. #23750328	C₂	semidirect
2. #23750328	C₂	semidirect
3. #23750326	C₂	semidirect
4. #23750319	C₂	semidirect
5. #23750310	C₂	semidirect
6. #23750299	C₂	semidirect
7. #23750298	C₂	semidirect
8. #23750287	C₂	semidirect
9. #23750285	C₂	semidirect
10. #23750271	C₂	semidirect
11. #23750266	C₂	semidirect
12. #23750223	C₂	semidirect
13. #23750214	C₂	semidirect
14. #23750186	C₂	semidirect
15. #23750162	C₂	semidirect
16. #23750160	C₂	semidirect
17. #23750138	C₂	semidirect
18. #23750137	C₂	semidirect
19. C₂²⋊Q₈×D₁₄₉	C₂	semidirect
20. C₂×#18011886	C₂	semidirect
21. #23750099	C₂	semidirect
22. C₄×D₄×D₁₄₉	C₂	semidirect
23. #552×C₁₄₉	C₂	semidirect
24. C₂×#14558737	C₂²	semidirect
25. C₂×#14558736	C₂²	semidirect
26. C₂×Q₈×D₁₄₉	C₂²	semidirect
28. C₂²×D₅₉₆	C₂²	semidirect
31. C₂²×C₄×D₁₄₉	C₂²	semidirect
32. #18011906	C₂²	semidirect
33. #18011906	C₂²	semidirect
34. #18011906	C₂²	semidirect
35. #18011906	C₂²	semidirect
36. #18011905	C₂²	semidirect
37. #18011902	C₂²	semidirect
38. #18011901	C₂²	semidirect
39. #18011900	C₂²	semidirect
40. #18011899	C₂²	semidirect
41. #18011899	C₂²	semidirect
42. #18011897	C₂²	semidirect
43. #18011896	C₂²	semidirect
44. #18011896	C₂²	semidirect
45. #18011896	C₂²	semidirect
46. #18011896	C₂²	semidirect
47. #18011896	C₂²	semidirect
48. #18011896	C₂²	semidirect
49. #18011895	C₂²	semidirect
51. #18011893	C₂²	semidirect
52. #18011891	C₂²	semidirect
53. #18011891	C₂²	semidirect
54. #18011891	C₂²	semidirect
55. #18011890	C₂²	semidirect
56. #18011889	C₂²	semidirect
57. #18011889	C₂²	semidirect
58. #18011888	C₂²	semidirect
59. #18011887	C₂²	semidirect
63. #18011886	C₂²	semidirect
64. #18011886	C₂²	semidirect
65. #18011886	C₂²	semidirect
66. #18011886	C₂²	semidirect
67. #18011886	C₂²	semidirect
68. #18011886	C₂²	semidirect
69. #18011886	C₂²	semidirect
70. #18011885	C₂²	semidirect
71. #18011884	C₂²	semidirect
72. #18011884	C₂²	semidirect
73. #18011884	C₂²	semidirect
75. #18011881	C₂²	semidirect
76. #18011881	C₂²	semidirect
78. #18011876	C₂²	semidirect
79. C₄×D₅₉₆	C₂²	semidirect
80. C₄×D₅₉₆	C₂²	semidirect
81. C₄×D₅₉₆	C₂²	semidirect
82. C₄×D₅₉₆	C₂²	semidirect
83. C₄×D₅₉₆	C₂²	semidirect
84. C₄×D₅₉₆	C₂²	semidirect
85. C₄×D₅₉₆	C₂²	semidirect
87. #18011873	C₂²	semidirect
88. #18011873	C₂²	semidirect
89. #18011873	C₂²	semidirect
90. #18011873	C₂²	semidirect
91. #18011873	C₂²	semidirect
92. #18011873	C₂²	semidirect
94. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
96. #18011871	C₂²	semidirect
97. #18011871	C₂²	semidirect
98. #18011870	C₂²	semidirect
99. #18011869	C₂²	semidirect
100. #18011869	C₂²	semidirect
101. #18011868	C₂²	semidirect
102. C₄⋊C₄×D₁₄₉	C₂²	semidirect
103. C₄⋊C₄×D₁₄₉	C₂²	semidirect
104. C₄⋊C₄×D₁₄₉	C₂²	semidirect
105. C₂×#14558713	C₂²	semidirect
108. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
109. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
110. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
111. C₄²×D₁₄₉	C₂²	semidirect
112. #126×C₁₄₉	C₂²	semidirect
113. #125×C₁₄₉	C₂²	semidirect
114. #125×C₁₄₉	C₂²	semidirect
116. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
117. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
118. C₄×Q₈×C₁₄₉	C₂²	semidirect
120. #117×C₁₄₉	C₂²	semidirect
121. #117×C₁₄₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
238. C₂²×D₁₄₉	#41	semidirect
351. C₁₄₉	#3505	semidirect
358. #552	D₁₄₉	semidirect
389. #126	C₂×D₁₄₉	semidirect
392. #125	C₂×D₁₄₉	semidirect
393. #125	C₂×D₁₄₉	semidirect
416. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
417. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
437. C₄×Q₈	C₂×D₁₄₉	semidirect
462. #117	C₂×D₁₄₉	semidirect
463. #117	C₂×D₁₄₉	semidirect
467. 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
#23750328	2
#23750326	2
#23750319	2
#23750310	2
#23750299	2
#23750298	2
#23750287	2
#23750285	2
#23750271	2
#23750266	2
#23750223	2
#23750214	2
#23750186	2
#23750162	2
#23750160	2
#23750138	2
#23750137	2
C₂²⋊Q₈×D₁₄₉	2
C₂×#18011886	2
#23750099	2
C₄×D₄×D₁₄₉	2
#552×C₁₄₉	2
#3505	149