Subgroups — #34058734

Order 19072.

1124 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750346	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750329	C₂	1	2	yes	maximal, complemented
3	#23750310	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750309	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750302	C₂	1	2	yes	maximal, complemented
6	#23750301	C₂	1	2	yes	maximal, complemented
7	Q₈×C₂²⋊D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750286	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750285	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750277	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750276	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750265	C₂	1	2	yes	maximal, complemented
13	#23750245	C₂	1	2	yes	maximal, complemented
14	#23750222	C₂	1	2	yes	maximal, complemented
15	#23750221	C₂	1	2	yes	maximal, complemented
16	#23750177	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750161	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750138	C₂	1	1	yes	maximal, characteristic, complemented
19	#23750136	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²⋊Q₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750106	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×C₂²⋊D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂²⋊Q₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558737	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14558736	C₂²	1	2	yes	—
26	C₂×#14558736	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
30	#18011910	C₂²	1	1	yes	characteristic, complemented
31	#18011909	C₂²	1	1	yes	characteristic, complemented
32	#18011909	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	#18011904	C₂²	1	2	yes	complemented
37	#18011904	C₂²	1	2	yes	complemented
38	#18011902	C₂²	1	1	yes	characteristic, complemented
39	#18011901	C₂²	1	2	yes	complemented
40	#18011901	C₂²	1	2	yes	complemented
41	#18011901	C₂²	1	2	yes	complemented
42	#18011900	C₂²	1	1	yes	characteristic, complemented
43	#18011900	C₂²	1	2	yes	complemented
44	#18011897	C₂²	1	2	yes	—
45	#18011897	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	—
50	#18011894	C₂²	1	2	yes	—
51	#18011894	C₂²	1	2	yes	complemented
52	#18011894	C₂²	1	2	yes	complemented
53	#18011893	C₂²	1	2	yes	—
54	#18011893	C₂²	1	2	yes	complemented
55	#18011891	C₂²	1	1	yes	characteristic, complemented
56	#18011890	C₂²	1	1	yes	characteristic
57	#18011890	C₂²	1	2	yes	complemented
58	#18011890	C₂²	1	1	yes	characteristic, complemented
59	#18011889	C₂²	1	2	yes	complemented
60	#18011889	C₂²	1	2	yes	complemented
61	#18011889	C₂²	1	2	yes	complemented
62	#18011888	C₂²	1	2	yes	—
63	#18011888	C₂²	1	2	yes	—
64	#18011887	C₂²	1	2	yes	complemented
65	#18011887	C₂²	1	2	yes	complemented
66	#18011887	C₂²	1	1	yes	characteristic, complemented
67	#18011887	C₂²	1	1	yes	characteristic, complemented
68	#18011886	C₂²	1	1	yes	characteristic, complemented
69	#18011885	C₂²	1	1	yes	characteristic
70	#18011885	C₂²	1	2	yes	—
71	#18011885	C₂²	1	1	yes	characteristic, complemented
72	#18011884	C₂²	1	2	yes	—
73	#18011884	C₂²	1	2	yes	—
74	#18011881	C₂²	1	2	yes	—
75	#18011880	C₂²	1	2	yes	—
76	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
77	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
78	#18011876	C₂²	1	2	yes	complemented
79	#18011876	C₂²	1	1	yes	characteristic, complemented
80	#18011876	C₂²	1	2	yes	complemented
81	#18011873	C₂²	1	1	yes	characteristic, complemented
82	#18011873	C₂²	1	2	yes	complemented
83	#18011873	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
93	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
94	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
96	#18011871	C₂²	1	2	yes	—
97	#18011871	C₂²	1	2	yes	—
98	#18011870	C₂²	1	2	yes	complemented
99	#18011870	C₂²	1	1	yes	characteristic, complemented
100	#18011869	C₂²	1	2	yes	complemented
101	#18011869	C₂²	1	2	yes	complemented
102	#18011869	C₂²	1	1	yes	characteristic, complemented
103	#18011867	C₂²	1	2	yes	—
104	C₂×#14558715	C₂²	1	1	yes	characteristic
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	C₂×C₂²⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
109	C₂×#14558713	C₂²	1	1	yes	characteristic
110	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
111	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
112	C₂²×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
113	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
114	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
115	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
119	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	complemented
121	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
123	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
124	#14558737	—	4	2	no	—
125	#14558736	—	2	8	no	—
126	#14558736	—	4	2	no	—
127	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₉₈	C₂³	1	2	yes	—
129	C₂×Dic₂₉₈	C₂³	1	2	yes	—
130	Q₈×D₁₄₉	—	4	2	no	—
131	C₂×D₅₉₆	C₂³	1	2	yes	—
132	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
133	C₂×D₅₉₆	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₄₉	—	2	4	no	—
135	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
142	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
144	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₄₉	—	4	2	no	—
146	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
149	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
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	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
156	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
157	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
159	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
161	#14558715	C₂³	1	2	yes	—
162	#14558715	C₂³	1	2	yes	—
163	#14558715	C₂³	1	2	yes	—
164	#14558715	C₂³	1	2	yes	—
165	#14558715	C₂³	1	2	yes	—
166	#14558715	C₂³	1	2	yes	—
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	1	yes	characteristic
173	#14558715	C₂³	1	1	yes	characteristic
174	#14558715	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
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	2	yes	—
187	#14558713	C₂³	1	2	yes	—
188	#14558713	C₂³	1	2	yes	—
189	#14558713	C₂³	1	2	yes	—
190	#14558713	C₂³	1	1	yes	characteristic
191	#14558713	C₂³	1	1	yes	characteristic
192	#14558713	C₂³	1	2	yes	—
193	#14558713	C₂³	1	2	yes	—
194	#14558713	C₂³	1	2	yes	—
195	#14558713	C₂³	1	2	yes	—
196	C₄×Dic₁₄₉	C₂³	1	2	yes	—
197	C₄×Dic₁₄₉	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	1	yes	characteristic
202	C₄×Dic₁₄₉	C₂³	1	2	yes	—
203	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
205	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₄₉	—	4	2	no	—
207	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
208	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
210	C₂²×C₄×C₁₄₉	—	4	2	no	—
211	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
213	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
216	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
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	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
224	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
225	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
229	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
230	C₂²×D₁₄₉	—	2	2	no	—
231	C₂²×D₁₄₉	—	2	2	no	—
232	C₂²×D₁₄₉	—	4	1	no	—
233	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
234	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
236	Dic₂₉₈	—	2	2	no	—
237	Dic₂₉₈	—	2	4	no	—
238	Dic₂₉₈	—	4	2	no	—
239	D₅₉₆	—	2	4	no	—
240	D₅₉₆	—	2	2	no	—
241	D₅₉₆	—	4	2	no	—
242	C₂²⋊D₁₄₉	—	2	2	no	—
243	C₂²⋊D₁₄₉	—	2	4	no	—
244	C₂²⋊D₁₄₉	—	2	4	no	—
245	C₂²⋊D₁₄₉	—	2	2	no	—
246	C₂²⋊D₁₄₉	—	2	2	no	—
247	C₂²⋊D₁₄₉	—	4	2	no	—
248	C₂²⋊D₁₄₉	#41	1	4	yes	complemented
249	C₂×Dic₁₄₉	—	2	2	no	—
250	C₂×Dic₁₄₉	—	2	2	no	—
251	C₂×Dic₁₄₉	—	4	1	no	—
252	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
255	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
256	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
260	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
261	C₄×D₁₄₉	—	2	4	no	—
262	C₄×D₁₄₉	—	2	2	no	—
263	C₄×D₁₄₉	—	2	2	no	—
264	C₄×D₁₄₉	—	2	4	no	—
265	C₄×D₁₄₉	—	4	1	no	—
266	C₄×D₁₄₉	—	4	1	no	—
267	C₄×D₁₄₉	—	4	2	no	—
268	C₄×D₁₄₉	—	4	2	no	—
269	C₄×D₁₄₉	—	4	2	no	—
270	C₂³×C₁₄₉	—	2	2	no	—
271	C₂³×C₁₄₉	—	2	2	no	—
272	C₂³×C₁₄₉	—	4	1	no	—
273	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
274	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
275	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
276	Q₈×C₁₄₉	—	2	2	no	—
277	Q₈×C₁₄₉	—	2	2	no	—
278	Q₈×C₁₄₉	—	4	2	no	—
279	C₂×C₄×C₁₄₉	—	2	4	no	—
280	C₂×C₄×C₁₄₉	—	2	2	no	—
281	C₂×C₄×C₁₄₉	—	2	2	no	—
282	C₂×C₄×C₁₄₉	—	2	2	no	—
283	C₂×C₄×C₁₄₉	—	4	1	no	—
284	C₂×C₄×C₁₄₉	—	4	1	no	—
285	C₂×C₄×C₁₄₉	—	4	1	no	—
286	C₂×C₄×C₁₄₉	—	4	2	no	—
287	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
288	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
291	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
292	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
293	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₁₄₉	—	2	1	no	—
296	C₂²×C₁₄₉	—	2	1	no	—
297	C₂²×C₁₄₉	—	2	1	no	—
298	C₂²×C₁₄₉	—	2	1	no	—
299	C₂²×C₁₄₉	—	2	1	no	—
300	C₂²×C₁₄₉	—	2	1	no	—
301	C₂²×C₁₄₉	—	2	1	no	—
302	C₂²×C₁₄₉	—	4	4	no	—
303	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
304	C₂²×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
305	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
306	C₂×D₁₄₉	—	2	1	no	—
307	C₂×D₁₄₉	—	2	1	no	—
308	C₂×D₁₄₉	—	2	2	no	—
309	C₂×D₁₄₉	—	2	1	no	—
310	C₂×D₁₄₉	—	2	1	no	—
311	C₂×D₁₄₉	—	2	2	no	—
312	C₂×D₁₄₉	—	2	2	no	—
313	C₂×D₁₄₉	—	2	1	no	—
314	C₂×D₁₄₉	—	4	4	no	—
315	C₂×D₁₄₉	C₂×#41	1	2	yes	—
316	C₄×C₁₄₉	—	2	2	no	—
317	C₄×C₁₄₉	—	2	2	no	—
318	C₄×C₁₄₉	—	2	1	no	—
319	C₄×C₁₄₉	—	2	1	no	—
320	C₄×C₁₄₉	—	2	1	no	—
321	C₄×C₁₄₉	—	2	2	no	—
322	C₄×C₁₄₉	—	2	2	no	—
323	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
324	Dic₁₄₉	—	2	2	no	—
325	Dic₁₄₉	—	2	1	no	—
326	Dic₁₄₉	—	2	1	no	—
327	Dic₁₄₉	—	2	1	no	—
328	Dic₁₄₉	—	2	2	no	—
329	Dic₁₄₉	—	2	1	no	—
330	Dic₁₄₉	—	2	1	no	—
331	Dic₁₄₉	—	2	2	no	—
332	Dic₁₄₉	C₂×#41	1	2	yes	—
333	C₂×C₁₄₉	—	2	2	no	—
334	C₂×C₁₄₉	—	2	2	no	—
335	C₂×C₁₄₉	—	4	1	no	—
336	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
337	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
339	D₁₄₉	—	2	2	no	—
340	D₁₄₉	—	4	2	no	—
341	D₁₄₉	—	4	1	no	—
342	C₁₄₉	#3520	1	1	yes	characteristic, complemented, Sylow
343	#3520	—	149	1	no	maximal, Sylow
344	#556	—	149	1	no	—
345	#554	—	149	2	no	—
346	#552	—	149	1	no	—
347	#552	—	149	1	no	—
348	#551	—	149	2	no	—
349	#551	—	149	2	no	—
350	D₄×Q₈	—	149	1	no	—
351	#548	—	149	1	no	—
352	#548	—	149	1	no	—
353	#547	—	149	1	no	—
354	#547	—	149	1	no	—
355	#546	—	149	2	no	—
356	#542	—	149	2	no	—
357	#539	—	149	2	no	—
358	#539	—	149	2	no	—
359	#533	—	149	1	no	—
360	#529	—	149	1	no	—
361	#525	—	149	1	no	—
362	#525	—	149	1	no	—
363	C₂×C₂²⋊Q₈	—	149	1	no	—
364	C₂×C₂²⋊Q₈	D₁₄₉	1	1	yes	characteristic, complemented
365	#520	—	149	2	no	—
366	C₂×C₄×D₄	—	149	1	no	—
367	C₂×#41	—	149	1	no	—
368	C₂×#41	—	149	2	no	—
369	C₂×#41	—	149	1	no	—
370	C₂²×Q₈	—	149	1	no	—
371	C₂²×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
372	C₂²×D₄	—	149	1	no	—
373	C₂³×C₄	—	149	1	no	—
374	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic
375	C₄⋊Q₈	—	149	1	no	—
376	C₄⋊Q₈	—	149	2	no	—
377	C₄⋊Q₈	—	149	1	no	—
378	#126	—	149	2	no	—
379	#126	—	149	2	no	—
380	#126	—	149	2	no	—
381	#126	—	149	2	no	—
382	#126	—	149	2	no	—
383	#125	—	149	1	no	—
384	#125	—	149	2	no	—
385	#125	—	149	2	no	—
386	#125	—	149	2	no	—
387	#124	—	149	1	no	—
388	#124	—	149	2	no	—
389	#124	—	149	2	no	—
390	#124	—	149	2	no	—
391	#123	—	149	2	no	—
392	#123	—	149	2	no	—
393	#123	—	149	2	no	—
394	#123	—	149	2	no	—
395	#123	—	149	2	no	—
396	#123	—	149	2	no	—
397	#123	—	149	2	no	—
398	#123	—	149	2	no	—
399	#123	—	149	2	no	—
400	C₂²⋊Q₈	—	149	1	no	—
401	C₂²⋊Q₈	—	149	1	no	—
402	C₂²⋊Q₈	—	149	2	no	—
403	C₂²⋊Q₈	—	149	2	no	—
404	C₂²⋊Q₈	—	149	1	no	—
405	C₂²⋊Q₈	—	149	1	no	—
406	C₂²⋊Q₈	—	149	2	no	—
407	C₂²⋊Q₈	—	149	2	no	—
408	C₂²⋊Q₈	—	149	1	no	—
409	C₂²⋊Q₈	—	149	2	no	—
410	C₂²⋊Q₈	—	149	2	no	—
411	C₂²⋊Q₈	—	149	2	no	—
412	C₂²⋊Q₈	—	149	2	no	—
413	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
414	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
415	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
416	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
417	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
418	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
419	#121	—	149	1	no	—
420	#121	—	149	1	no	—
421	#121	—	149	2	no	—
422	#121	—	149	1	no	—
423	#121	—	149	2	no	—
424	#121	—	149	2	no	—
425	#120	—	149	2	no	—
426	#120	—	149	2	no	—
427	C₄×Q₈	—	149	1	no	—
428	C₄×Q₈	—	149	1	no	—
429	C₄×Q₈	—	149	2	no	—
430	C₄×Q₈	—	149	2	no	—
431	C₄×Q₈	—	149	1	no	—
432	C₄×D₄	—	149	1	no	—
433	C₄×D₄	—	149	1	no	—
434	C₄×D₄	—	149	1	no	—
435	C₄×D₄	—	149	1	no	—
436	C₄×D₄	—	149	1	no	—
437	C₄×D₄	—	149	1	no	—
438	C₄×D₄	—	149	1	no	—
439	C₄×D₄	—	149	1	no	—
440	C₄×D₄	—	149	2	no	—
441	C₄×D₄	—	149	2	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	2	no	—
448	C₄×D₄	—	149	2	no	—
449	#117	—	149	2	no	—
450	#117	—	149	1	no	—
451	#117	—	149	2	no	—
452	#117	—	149	2	no	—
453	#117	—	149	1	no	—
454	#117	—	149	2	no	—
455	C₂×C₄⋊C₄	—	149	1	no	—
456	C₂×C₄⋊C₄	—	149	2	no	—
457	C₂×C₄⋊C₄	—	149	2	no	—
458	C₂×C₄⋊C₄	—	149	1	no	—
459	C₂×C₄⋊C₄	C₂×D₁₄₉	1	2	yes	complemented
460	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
461	C₂×C₂²⋊C₄	—	149	1	no	—
462	C₂×C₂²⋊C₄	—	149	1	no	—
463	C₂×C₂²⋊C₄	—	149	2	no	—
464	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	2	yes	—
465	C₂×C₄²	—	149	1	no	—
466	C₂⁴	—	149	1	no	—
467	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
468	#41	—	298	8	no	—
469	#41	—	596	2	no	—
470	#41	—	596	2	no	—
471	C₂×Q₈	—	4	2	no	—
472	C₂×Q₈	—	596	2	no	—
473	C₂×Q₈	—	149	2	no	—
474	C₂×Q₈	—	149	1	no	—
475	C₂×Q₈	—	149	2	no	—
476	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
477	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
478	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
479	C₂×D₄	—	298	4	no	—
480	C₂×D₄	—	149	2	no	—
481	C₂×D₄	—	149	2	no	—
482	C₂×D₄	—	149	1	no	—
483	C₂×D₄	—	149	1	no	—
484	C₂×D₄	—	149	1	no	—
485	C₂×D₄	—	149	2	no	—
486	C₂×D₄	—	149	1	no	—
487	C₂×D₄	—	149	2	no	—
488	C₂×D₄	—	149	1	no	—
489	C₂×D₄	—	149	2	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	596	2	no	—
492	C₂²×C₄	—	149	1	no	—
493	C₂²×C₄	—	149	1	no	—
494	C₂²×C₄	—	149	2	no	—
495	C₂²×C₄	—	149	2	no	—
496	C₂²×C₄	—	149	1	no	—
497	C₂²×C₄	—	149	1	no	—
498	C₂²×C₄	—	149	1	no	—
499	C₂²×C₄	—	149	2	no	—
500	C₂²×C₄	—	149	1	no	—
501	C₂²×C₄	—	149	2	no	—
502	C₂²×C₄	—	149	2	no	—
503	C₂²×C₄	—	149	1	no	—
504	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
506	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
508	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
509	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
510	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
512	C₄⋊C₄	—	149	1	no	—
513	C₄⋊C₄	—	149	2	no	—
514	C₄⋊C₄	—	149	1	no	—
515	C₄⋊C₄	—	149	1	no	—
516	C₄⋊C₄	—	149	1	no	—
517	C₄⋊C₄	—	149	1	no	—
518	C₄⋊C₄	—	149	2	no	—
519	C₄⋊C₄	—	149	2	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	—	149	2	no	—
526	C₄⋊C₄	—	149	2	no	—
527	C₄⋊C₄	—	149	2	no	—
528	C₄⋊C₄	—	149	2	no	—
529	C₄⋊C₄	—	149	2	no	—
530	C₄⋊C₄	—	149	2	no	—
531	C₄⋊C₄	—	149	2	no	—
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	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
537	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
538	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
539	C₂²⋊C₄	—	149	1	no	—
540	C₂²⋊C₄	—	149	2	no	—
541	C₂²⋊C₄	—	149	1	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	1	no	—
547	C₂²⋊C₄	—	149	1	no	—
548	C₂²⋊C₄	—	149	1	no	—
549	C₂²⋊C₄	—	149	1	no	—
550	C₂²⋊C₄	—	149	2	no	—
551	C₂²⋊C₄	—	149	2	no	—
552	C₂²⋊C₄	—	149	2	no	—
553	C₂²⋊C₄	—	149	2	no	—
554	C₂²⋊C₄	—	149	2	no	—
555	C₂²⋊C₄	—	149	2	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	C₂²×D₁₄₉	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
564	C₄²	—	149	1	no	—
565	C₄²	—	149	1	no	—
566	C₄²	—	149	1	no	—
567	C₄²	—	149	1	no	—
568	C₄²	—	149	2	no	—
569	C₄²	—	149	2	no	—
570	C₄²	—	149	2	no	—
571	C₄²	—	149	2	no	—
572	C₄²	—	149	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	298	2	no	—
577	C₂³	—	298	2	no	—
578	C₂³	—	596	1	no	—
579	C₂³	—	149	1	no	—
580	C₂³	—	149	2	no	—
581	C₂³	—	149	1	no	—
582	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
583	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
584	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	298	4	no	—
589	Q₈	—	298	2	no	—
590	Q₈	—	596	2	no	—
591	D₄	—	298	4	no	—
592	D₄	—	298	2	no	—
593	D₄	—	298	2	no	—
594	D₄	—	298	4	no	—
595	D₄	—	298	4	no	—
596	D₄	—	298	2	no	—
597	D₄	—	298	2	no	—
598	D₄	—	596	2	no	—
599	D₄	—	596	2	no	—
600	D₄	—	149	4	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	298	4	no	—
610	C₂×C₄	—	298	4	no	—
611	C₂×C₄	—	298	2	no	—
612	C₂×C₄	—	298	2	no	—
613	C₂×C₄	—	298	2	no	—
614	C₂×C₄	—	298	2	no	—
615	C₂×C₄	—	596	1	no	—
616	C₂×C₄	—	596	1	no	—
617	C₂×C₄	—	596	2	no	—
618	C₂×C₄	—	596	2	no	—
619	C₂×C₄	—	596	2	no	—
620	C₂×C₄	—	596	1	no	—
621	C₂×C₄	—	149	1	no	—
622	C₂×C₄	—	149	2	no	—
623	C₂×C₄	—	149	1	no	—
624	C₂×C₄	—	149	2	no	—
625	C₂×C₄	—	149	1	no	—
626	C₂×C₄	—	149	1	no	—
627	C₂×C₄	—	149	2	no	—
628	C₂×C₄	—	149	1	no	—
629	C₂×C₄	—	149	1	no	—
630	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
631	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
634	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
635	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
637	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	298	1	no	—
647	C₂²	—	298	1	no	—
648	C₂²	—	298	2	no	—
649	C₂²	—	298	1	no	—
650	C₂²	—	298	1	no	—
651	C₂²	—	298	2	no	—
652	C₂²	—	298	2	no	—
653	C₂²	—	298	1	no	—
654	C₂²	—	596	4	no	—
655	C₂²	—	149	2	no	—
656	C₂²	#41×D₁₄₉	1	2	yes	—
657	C₂²	#18011959	1	2	yes	—
658	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	298	1	no	—
667	C₄	—	298	2	no	—
668	C₄	—	298	1	no	—
669	C₄	—	298	1	no	—
670	C₄	—	298	2	no	—
671	C₄	—	298	1	no	—
672	C₄	—	298	1	no	—
673	C₄	—	298	2	no	—
674	C₄	—	149	2	no	—
675	C₄	#18011956	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	2	2	no	—
678	C₂	—	4	1	no	—
679	C₂	—	298	2	no	—
680	C₂	—	596	1	no	—
681	C₂	—	596	2	no	—
682	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
683	C₂	C₂×#18011956	1	1	yes	characteristic
684	C₂	C₂×#18011959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	C₂×C₂²⋊Q₈×C₁₄₉	C₂
hypercenter	C₂×C₂²⋊Q₈	D₁₄₉
hypocenter	C₁₄₉	#3520
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #23750346	C₂	semidirect
2. #23750329	C₂	semidirect
3. #23750310	C₂	semidirect
4. #23750309	C₂	semidirect
5. #23750302	C₂	semidirect
6. #23750301	C₂	semidirect
7. Q₈×C₂²⋊D₁₄₉	C₂	semidirect
8. #23750286	C₂	semidirect
9. #23750285	C₂	semidirect
10. #23750277	C₂	semidirect
11. #23750276	C₂	semidirect
12. #23750265	C₂	semidirect
13. #23750245	C₂	semidirect
14. #23750222	C₂	semidirect
15. #23750221	C₂	semidirect
16. #23750177	C₂	semidirect
17. #23750161	C₂	semidirect
18. #23750138	C₂	semidirect
19. #23750136	C₂	semidirect
20. C₂²⋊Q₈×D₁₄₉	C₂	semidirect
21. #23750106	C₂	semidirect
22. C₂×C₄×C₂²⋊D₁₄₉	C₂	semidirect
23. C₂×C₂²⋊Q₈×C₁₄₉	C₂	semidirect
24. C₂×#14558737	C₂²	semidirect
26. C₂×#14558736	C₂²	semidirect
27. C₂×Q₈×D₁₄₉	C₂²	semidirect
30. #18011910	C₂²	semidirect
31. #18011909	C₂²	semidirect
32. #18011909	C₂²	semidirect
33. #18011906	C₂²	semidirect
34. #18011906	C₂²	semidirect
35. #18011906	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
42. #18011900	C₂²	semidirect
43. #18011900	C₂²	semidirect
45. #18011897	C₂²	semidirect
46. #18011896	C₂²	semidirect
47. #18011896	C₂²	semidirect
48. #18011896	C₂²	semidirect
51. #18011894	C₂²	semidirect
52. #18011894	C₂²	semidirect
54. #18011893	C₂²	semidirect
55. #18011891	C₂²	semidirect
57. #18011890	C₂²	semidirect
58. #18011890	C₂²	semidirect
59. #18011889	C₂²	semidirect
60. #18011889	C₂²	semidirect
61. #18011889	C₂²	semidirect
64. #18011887	C₂²	semidirect
65. #18011887	C₂²	semidirect
66. #18011887	C₂²	semidirect
67. #18011887	C₂²	semidirect
68. #18011886	C₂²	semidirect
71. #18011885	C₂²	semidirect
76. Q₈×Dic₁₄₉	C₂²	semidirect
77. Q₈×Dic₁₄₉	C₂²	semidirect
78. #18011876	C₂²	semidirect
79. #18011876	C₂²	semidirect
80. #18011876	C₂²	semidirect
81. #18011873	C₂²	semidirect
82. #18011873	C₂²	semidirect
83. #18011873	C₂²	semidirect
94. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
95. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
98. #18011870	C₂²	semidirect
99. #18011870	C₂²	semidirect
100. #18011869	C₂²	semidirect
101. #18011869	C₂²	semidirect
102. #18011869	C₂²	semidirect
105. C₄⋊C₄×D₁₄₉	C₂²	semidirect
106. C₄⋊C₄×D₁₄₉	C₂²	semidirect
107. C₄⋊C₄×D₁₄₉	C₂²	semidirect
112. C₂²×Q₈×C₁₄₉	C₂²	semidirect
117. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
118. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
119. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
120. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
121. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
248. C₂²⋊D₁₄₉	#41	semidirect
342. C₁₄₉	#3520	semidirect
364. C₂×C₂²⋊Q₈	D₁₄₉	semidirect
371. C₂²×Q₈	C₂×D₁₄₉	semidirect
416. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
417. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
418. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
459. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect
460. 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
#23750346	2
#23750329	2
#23750310	2
#23750309	2
#23750302	2
#23750301	2
Q₈×C₂²⋊D₁₄₉	2
#23750286	2
#23750285	2
#23750277	2
#23750276	2
#23750265	2
#23750245	2
#23750222	2
#23750221	2
#23750177	2
#23750161	2
#23750138	2
#23750136	2
C₂²⋊Q₈×D₁₄₉	2
#23750106	2
C₂×C₄×C₂²⋊D₁₄₉	2
C₂×C₂²⋊Q₈×C₁₄₉	2
#3520	149