Subgroups — C₁₄₉×#11148 #49190097

Order 38144.

894 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#413×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#410×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	#2297×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#339×C₁₄₉	C₂	1	2	yes	maximal, complemented
5	C₂×H(3,ℤ/4)×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₄₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
8	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
9	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
11	#413×C₁₄₉	—	2	4	no	—
12	C₂×#101×C₁₄₉	—	2	1	no	—
13	C₂×#100×C₁₄₉	—	2	1	no	—
14	#410×C₁₄₉	—	2	4	no	—
15	C₂×#99×C₁₄₉	—	2	2	no	—
16	#391×C₁₄₉	—	2	1	no	—
17	#390×C₁₄₉	—	2	1	no	—
18	#386×C₁₄₉	—	2	2	no	—
19	C₄×C₂²⋊C₄×C₁₄₉	C₄	1	4	yes	complemented
20	#339×C₁₄₉	—	2	4	no	—
21	H(3,ℤ/4)×C₁₄₉	—	2	4	no	—
22	C₂×#41×C₁₄₉	—	2	2	no	—
23	C₂×#41×C₁₄₉	—	2	2	no	—
24	C₂×#41×C₁₄₉	—	2	2	no	—
25	C₂×#41×C₁₄₉	—	2	2	no	—
26	C₂×#41×C₁₄₉	—	2	2	no	—
27	C₂×#41×C₁₄₉	—	2	2	no	—
28	C₂²×Q₈×C₁₄₉	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₄₉	D₄	1	2	yes	—
30	C₂²×D₄×C₁₄₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₄₉	—	2	1	no	—
32	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₁₄₉	—	2	2	no	—
35	C₂×M₁₆×C₁₄₉	—	2	2	no	—
36	C₂×M₁₆×C₁₄₉	—	2	2	no	—
37	C₂×M₁₆×C₁₄₉	—	2	2	no	—
38	C₂×M₁₆×C₁₄₉	—	2	2	no	—
39	C₂×M₁₆×C₁₄₉	D₄	1	4	yes	—
40	C₂²×C₈×C₁₄₉	—	2	2	no	—
41	#117×C₁₄₉	—	2	2	no	—
42	#117×C₁₄₉	—	2	2	no	—
43	#117×C₁₄₉	—	2	2	no	—
44	#117×C₁₄₉	—	2	2	no	—
45	#117×C₁₄₉	—	2	2	no	—
46	#117×C₁₄₉	D₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
52	C₂×C₄²×C₁₄₉	—	2	2	no	—
53	C₂×C₄²×C₁₄₉	—	2	2	no	—
54	C₂×C₄²×C₁₄₉	—	2	2	no	—
55	C₂×C₄²×C₁₄₉	—	2	1	no	—
56	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
58	#101×C₁₄₉	—	2	4	no	—
59	#100×C₁₄₉	—	2	4	no	—
60	#99×C₁₄₉	—	2	8	no	—
61	#95×C₁₄₉	—	2	4	no	—
62	C₂⁴×C₁₄₉	C₂²⋊C₄	1	2	yes	—
63	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
64	#41×C₁₄₉	—	4	2	no	—
65	#41×C₁₄₉	—	4	2	no	—
66	#41×C₁₄₉	—	4	2	no	—
67	#41×C₁₄₉	—	4	2	no	—
68	#41×C₁₄₉	—	4	2	no	—
69	#41×C₁₄₉	—	4	2	no	—
70	#41×C₁₄₉	—	4	2	no	—
71	#41×C₁₄₉	—	4	2	no	—
72	C₂×Q₈×C₁₄₉	—	2	1	no	—
73	C₂×Q₈×C₁₄₉	—	2	2	no	—
74	C₂×Q₈×C₁₄₉	—	2	2	no	—
75	C₂×Q₈×C₁₄₉	—	2	1	no	—
76	C₂×D₄×C₁₄₉	—	2	2	no	—
77	C₂×D₄×C₁₄₉	—	2	4	no	—
78	C₂×D₄×C₁₄₉	—	2	4	no	—
79	C₂×D₄×C₁₄₉	—	2	2	no	—
80	C₂×D₄×C₁₄₉	—	2	1	no	—
81	C₂×D₄×C₁₄₉	—	2	2	no	—
82	C₂×D₄×C₁₄₉	—	2	2	no	—
83	C₂×D₄×C₁₄₉	—	2	1	no	—
84	C₂²×C₄×C₁₄₉	—	2	2	no	—
85	C₂²×C₄×C₁₄₉	—	2	2	no	—
86	C₂²×C₄×C₁₄₉	—	2	2	no	—
87	C₂²×C₄×C₁₄₉	—	2	4	no	—
88	C₂²×C₄×C₁₄₉	—	2	4	no	—
89	C₂²×C₄×C₁₄₉	—	2	2	no	—
90	C₂²×C₄×C₁₄₉	—	4	4	no	—
91	C₂²×C₄×C₁₄₉	—	4	2	no	—
92	C₂²×C₄×C₁₄₉	—	4	2	no	—
93	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
99	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
100	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
101	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
102	M₁₆×C₁₄₉	—	2	4	no	—
103	M₁₆×C₁₄₉	—	2	4	no	—
104	M₁₆×C₁₄₉	—	4	2	no	—
105	M₁₆×C₁₄₉	—	4	2	no	—
106	C₂×C₈×C₁₄₉	—	2	4	no	—
107	C₂×C₈×C₁₄₉	—	4	2	no	—
108	C₂×C₈×C₁₄₉	—	4	2	no	—
109	C₄⋊C₄×C₁₄₉	—	2	4	no	—
110	C₄⋊C₄×C₁₄₉	—	4	2	no	—
111	C₄⋊C₄×C₁₄₉	—	4	2	no	—
112	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
113	C₂²⋊C₄×C₁₄₉	—	4	8	no	—
114	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
115	C₂²⋊C₄×C₁₄₉	—	4	2	no	—
116	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
117	C₄²×C₁₄₉	—	2	4	no	—
118	C₄²×C₁₄₉	—	2	4	no	—
119	C₄²×C₁₄₉	—	2	4	no	—
120	C₄²×C₁₄₉	—	4	1	no	—
121	C₄²×C₁₄₉	—	4	2	no	—
122	C₄²×C₁₄₉	—	4	1	no	—
123	C₂³×C₁₄₉	—	2	2	no	—
124	C₂³×C₁₄₉	—	2	2	no	—
125	C₂³×C₁₄₉	—	2	2	no	—
126	C₂³×C₁₄₉	—	4	2	no	—
127	C₂³×C₁₄₉	—	4	4	no	—
128	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂³×C₁₄₉	#120	1	1	yes	characteristic
130	C₂³×C₁₄₉	#121	1	2	yes	—
131	C₂³×C₁₄₉	#123	1	2	yes	—
132	C₂³×C₁₄₉	#123	1	1	yes	characteristic
133	Q₈×C₁₄₉	—	4	2	no	—
134	Q₈×C₁₄₉	—	4	2	no	—
135	D₄×C₁₄₉	—	4	4	no	—
136	D₄×C₁₄₉	—	4	4	no	—
137	D₄×C₁₄₉	—	4	2	no	—
138	D₄×C₁₄₉	—	4	2	no	—
139	C₂×C₄×C₁₄₉	—	2	4	no	—
140	C₂×C₄×C₁₄₉	—	2	2	no	—
141	C₂×C₄×C₁₄₉	—	2	2	no	—
142	C₂×C₄×C₁₄₉	—	2	2	no	—
143	C₂×C₄×C₁₄₉	—	4	2	no	—
144	C₂×C₄×C₁₄₉	—	4	8	no	—
145	C₂×C₄×C₁₄₉	—	4	2	no	—
146	C₂×C₄×C₁₄₉	—	4	4	no	—
147	C₂×C₄×C₁₄₉	—	4	4	no	—
148	C₂×C₄×C₁₄₉	—	4	4	no	—
149	C₂×C₄×C₁₄₉	—	4	2	no	—
150	C₂×C₄×C₁₄₉	—	4	4	no	—
151	C₂×C₄×C₁₄₉	—	8	4	no	—
152	C₂×C₄×C₁₄₉	#117	1	1	yes	characteristic
153	C₂×C₄×C₁₄₉	#117	1	1	yes	characteristic
154	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
157	C₂×C₄×C₁₄₉	#121	1	2	yes	—
158	C₂×C₄×C₁₄₉	#121	1	2	yes	—
159	C₂×C₄×C₁₄₉	#121	1	2	yes	—
160	C₂×C₄×C₁₄₉	#123	1	2	yes	—
161	C₂×C₄×C₁₄₉	#123	1	2	yes	—
162	C₂×C₄×C₁₄₉	#123	1	2	yes	—
163	C₂×C₄×C₁₄₉	#123	1	1	yes	characteristic
164	C₂×C₄×C₁₄₉	#124	1	2	yes	—
165	C₂×C₄×C₁₄₉	#124	1	2	yes	—
166	C₂×C₄×C₁₄₉	#126	1	2	yes	—
167	C₂×C₄×C₁₄₉	#126	1	2	yes	—
168	C₈×C₁₄₉	—	4	4	no	—
169	C₂²×C₁₄₉	—	2	2	no	—
170	C₂²×C₁₄₉	—	2	4	no	—
171	C₂²×C₁₄₉	—	4	2	no	—
172	C₂²×C₁₄₉	—	4	1	no	—
173	C₂²×C₁₄₉	—	4	1	no	—
174	C₂²×C₁₄₉	—	4	4	no	—
175	C₂²×C₁₄₉	—	4	2	no	—
176	C₂²×C₁₄₉	—	8	2	no	—
177	C₂²×C₁₄₉	—	8	2	no	—
178	C₂²×C₁₄₉	#381	1	1	yes	characteristic
179	C₂²×C₁₄₉	#386	1	1	yes	characteristic
180	C₂²×C₁₄₉	#386	1	1	yes	characteristic
181	C₂²×C₁₄₉	#394	1	2	yes	—
182	C₂²×C₁₄₉	#397	1	2	yes	—
183	C₄×C₁₄₉	—	4	4	no	—
184	C₄×C₁₄₉	—	4	2	no	—
185	C₄×C₁₄₉	—	8	2	no	—
186	C₄×C₁₄₉	—	8	4	no	—
187	C₄×C₁₄₉	#388	1	2	yes	—
188	C₄×C₁₄₉	#388	1	2	yes	—
189	C₄×C₁₄₉	#394	1	2	yes	—
190	C₄×C₁₄₉	#397	1	2	yes	—
191	C₂×C₁₄₉	—	2	1	no	—
192	C₂×C₁₄₉	—	2	1	no	—
193	C₂×C₁₄₉	—	2	2	no	—
194	C₂×C₁₄₉	—	2	2	no	—
195	C₂×C₁₄₉	—	8	2	no	—
196	C₂×C₁₄₉	#1440	1	1	yes	characteristic
197	C₂×C₁₄₉	#1827	1	2	yes	—
198	#11148	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₄₉	#11148	1	1	yes	characteristic, direct product factor, Sylow
200	C₂×#413	C₂×C₁₄₉	1	1	yes	characteristic
201	C₂×#410	C₂×C₁₄₉	1	1	yes	characteristic
202	#2297	C₂×C₁₄₉	1	1	yes	characteristic
203	C₂×#339	C₂×C₁₄₉	1	2	yes	complemented
204	C₂×H(3,ℤ/4)	C₂×C₁₄₉	1	2	yes	complemented
205	C₂²×#41	C₂²×C₁₄₉	1	1	yes	characteristic
206	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
207	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
208	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
209	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
210	#413	—	2	4	no	—
211	C₂×#101	—	2	1	no	—
212	C₂×#100	—	2	1	no	—
213	#410	—	2	4	no	—
214	C₂×#99	—	2	2	no	—
215	#391	—	2	1	no	—
216	#390	—	2	1	no	—
217	#386	—	2	2	no	—
218	C₄×C₂²⋊C₄	C₄×C₁₄₉	1	4	yes	complemented
219	#339	—	2	4	no	—
220	H(3,ℤ/4)	—	2	4	no	—
221	C₂×#41	—	2	2	no	—
222	C₂×#41	—	2	2	no	—
223	C₂×#41	—	2	2	no	—
224	C₂×#41	—	2	2	no	—
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂²×Q₈	D₄×C₁₄₉	1	1	yes	characteristic
228	C₂²×D₄	D₄×C₁₄₉	1	2	yes	—
229	C₂²×D₄	D₄×C₁₄₉	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	D₄×C₁₄₉	1	4	yes	—
239	C₂²×C₈	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	D₄×C₁₄₉	1	4	yes	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	4	no	—
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
256	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
257	#101	—	2	4	no	—
258	#100	—	2	4	no	—
259	#99	—	2	8	no	—
260	#95	—	2	4	no	—
261	C₂⁴	C₂²⋊C₄×C₁₄₉	1	2	yes	—
262	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
263	#41	—	4	2	no	—
264	#41	—	4	2	no	—
265	#41	—	4	2	no	—
266	#41	—	4	2	no	—
267	#41	—	4	2	no	—
268	#41	—	4	2	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
297	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
298	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
299	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
300	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
301	M₁₆	—	2	4	no	—
302	M₁₆	—	2	4	no	—
303	M₁₆	—	4	2	no	—
304	M₁₆	—	4	2	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	4	8	no	—
313	C₂²⋊C₄	—	4	1	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	4	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	4	2	no	—
321	C₄²	—	4	1	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	4	no	—
327	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
328	C₂³	#120×C₁₄₉	1	1	yes	characteristic
329	C₂³	#121×C₁₄₉	1	2	yes	—
330	C₂³	#123×C₁₄₉	1	2	yes	—
331	C₂³	#123×C₁₄₉	1	1	yes	characteristic
332	Q₈	—	4	2	no	—
333	Q₈	—	4	2	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	4	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	8	4	no	—
351	C₂×C₄	#117×C₁₄₉	1	1	yes	characteristic
352	C₂×C₄	#117×C₁₄₉	1	1	yes	characteristic
353	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
354	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
355	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
356	C₂×C₄	#121×C₁₄₉	1	2	yes	—
357	C₂×C₄	#121×C₁₄₉	1	2	yes	—
358	C₂×C₄	#121×C₁₄₉	1	2	yes	—
359	C₂×C₄	#123×C₁₄₉	1	2	yes	—
360	C₂×C₄	#123×C₁₄₉	1	2	yes	—
361	C₂×C₄	#123×C₁₄₉	1	2	yes	—
362	C₂×C₄	#123×C₁₄₉	1	1	yes	characteristic
363	C₂×C₄	#124×C₁₄₉	1	2	yes	—
364	C₂×C₄	#124×C₁₄₉	1	2	yes	—
365	C₂×C₄	#126×C₁₄₉	1	2	yes	—
366	C₂×C₄	#126×C₁₄₉	1	2	yes	—
367	C₈	—	4	4	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	#381×C₁₄₉	1	1	yes	characteristic
378	C₂²	#386×C₁₄₉	1	1	yes	characteristic
379	C₂²	#386×C₁₄₉	1	1	yes	characteristic
380	C₂²	#394×C₁₄₉	1	2	yes	—
381	C₂²	#397×C₁₄₉	1	2	yes	—
382	C₄	—	4	4	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	4	no	—
386	C₄	#388×C₁₄₉	1	2	yes	—
387	C₄	#388×C₁₄₉	1	2	yes	—
388	C₄	#394×C₁₄₉	1	2	yes	—
389	C₄	#397×C₁₄₉	1	2	yes	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	2	no	—
393	C₂	—	2	2	no	—
394	C₂	—	8	2	no	—
395	C₂	#1440×C₁₄₉	1	1	yes	characteristic
396	C₂	#1827×C₁₄₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₄₉	#117
commutator	C₂²×C₄	C₂²×C₄×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
socle	C₂²×C₁₄₉	#381
prime radical	C₂²×#41×C₁₄₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₂×#117×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#339×C₁₄₉	C₂	semidirect
5. C₂×H(3,ℤ/4)×C₁₄₉	C₂	semidirect
19. C₄×C₂²⋊C₄×C₁₄₉	C₄	semidirect
198. #11148	C₁₄₉	direct (N × H)
199. C₁₄₉	#11148	direct (N × H)
203. C₂×#339	C₂×C₁₄₉	semidirect
204. C₂×H(3,ℤ/4)	C₂×C₁₄₉	semidirect
218. C₄×C₂²⋊C₄	C₄×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#413×C₁₄₉	2
C₂×#410×C₁₄₉	2
#2297×C₁₄₉	2
C₂×#339×C₁₄₉	2
C₂×H(3,ℤ/4)×C₁₄₉	2
#11148	149

Subgroups — C149×#11148 #49190097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#11148 #49190097