Subgroups — D₁₄₉⋊#435 #34061399

Order 19072.

564 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₄₉⋊M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₄₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750657	C₂	1	2	yes	maximal, complemented
4	#23750656	C₂	1	2	yes	maximal, complemented
5	#23750655	C₂	1	2	yes	maximal, complemented
6	#23750654	C₂	1	2	yes	maximal, complemented
7	D₁₄₉⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	D₁₄₉⋊(C₂²⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₄₉⋊(C₂²⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750584	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₄×D₁₄₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#14558746	C₂²	1	2	yes	complemented
13	D₁₄₉⋊M₁₆	—	2	4	no	—
14	C₂×#14558745	C₂²	1	2	yes	complemented
15	C₂×D₁₄₉⋊C₈	—	2	4	no	—
16	C₂×D₁₄₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×D₁₄₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×D₁₄₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×D₁₄₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×D₁₄₉⋊C₈	C₂²	1	2	yes	complemented
21	C₂²×#11924753	C₂²	1	2	yes	complemented
22	#18011978	C₂²	1	2	yes	complemented
23	C₄⋊#11924753	C₂²	1	2	yes	complemented
24	#18011968	C₂²	1	2	yes	complemented
25	#18011968	C₂²	1	2	yes	complemented
26	C₂²⋊#11924753	C₂²	1	2	yes	complemented
27	C₂²⋊#11924753	C₂²	1	2	yes	complemented
28	#18011966	C₂²	1	2	yes	complemented
29	#18011966	C₂²	1	2	yes	complemented
30	C₂×D₄×D₁₄₉	C₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
33	C₄×D₅₉₆	C₄	1	1	yes	characteristic
34	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
35	#18011873	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊D₁₄₉	C₄	1	1	yes	characteristic
37	C₄×C₂²⋊D₁₄₉	C₄	1	1	yes	characteristic
38	#18011871	C₂²	1	1	yes	characteristic
39	#18011871	C₂²	1	1	yes	characteristic
40	C₄⋊C₄×D₁₄₉	C₄	1	1	yes	characteristic
41	C₂²⋊C₄×D₁₄₉	C₄	1	1	yes	characteristic
42	C₂²⋊C₄×D₁₄₉	C₄	1	1	yes	characteristic
43	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
44	C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic
45	#14558746	—	2	4	no	—
46	#14558745	—	2	4	no	—
47	D₁₄₉⋊C₈	—	2	4	no	—
48	D₁₄₉⋊C₈	—	2	2	no	—
49	D₁₄₉⋊C₈	—	2	2	no	—
50	D₁₄₉⋊C₈	—	2	2	no	—
51	D₁₄₉⋊C₈	D₄	1	4	yes	complemented
52	C₂×#11924753	—	2	4	no	—
53	C₂×#11924753	C₂³	1	2	yes	—
54	C₂×#11924753	C₂³	1	2	yes	—
55	C₂×#11924753	C₂³	1	2	yes	—
56	C₂×#11924753	C₂³	1	2	yes	—
57	C₂³×D₁₄₉	C₂×C₄	1	1	yes	characteristic
58	C₂³×D₁₄₉	C₂×C₄	1	1	yes	characteristic
59	C₂×D₅₉₆	C₂×C₄	1	1	yes	characteristic
60	C₂×C₂²⋊D₁₄₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₂²⋊D₁₄₉	C₂×C₄	1	1	yes	characteristic
62	D₄×D₁₄₉	—	2	4	no	—
63	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
64	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
65	C₂×C₄×D₁₄₉	—	2	2	no	—
66	C₂×C₄×D₁₄₉	—	2	2	no	—
67	C₂×C₄×D₁₄₉	—	2	2	no	—
68	C₂×C₄×D₁₄₉	—	2	2	no	—
69	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
76	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
78	C₄⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
79	#14558715	C₂×C₄	1	1	yes	characteristic
80	#14558715	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
83	#14558713	C₂×C₄	1	1	yes	characteristic
84	#14558713	C₂×C₄	1	1	yes	characteristic
85	#14558713	C₂×C₄	1	1	yes	characteristic
86	#14558713	C₂×C₄	1	1	yes	characteristic
87	C₄×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
88	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
89	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
90	C₂×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
93	C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
96	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
97	#11924753	—	2	2	no	—
98	#11924753	—	2	2	no	—
99	#11924753	—	2	2	no	—
100	#11924753	C₂×D₄	1	4	yes	complemented
101	C₂²×D₁₄₉	—	2	2	no	—
102	C₂²×D₁₄₉	—	2	2	no	—
103	C₂²×D₁₄₉	—	2	2	no	—
104	C₂²×D₁₄₉	—	2	2	no	—
105	C₂²×D₁₄₉	—	2	2	no	—
106	C₂²×D₁₄₉	M₁₆	1	4	yes	complemented
107	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
110	D₅₉₆	—	2	2	no	—
111	C₂²⋊D₁₄₉	—	2	2	no	—
112	C₂²⋊D₁₄₉	—	2	2	no	—
113	C₂×Dic₁₄₉	—	2	1	no	—
114	C₂×Dic₁₄₉	—	2	1	no	—
115	C₂×Dic₁₄₉	—	2	1	no	—
116	C₂×Dic₁₄₉	—	2	1	no	—
117	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
122	C₄×D₁₄₉	—	2	2	no	—
123	C₄×D₁₄₉	—	2	2	no	—
124	C₄×D₁₄₉	—	2	2	no	—
125	C₄×D₁₄₉	—	2	2	no	—
126	C₄×D₁₄₉	—	2	2	no	—
127	C₄×D₁₄₉	—	2	2	no	—
128	C₄×D₁₄₉	—	2	1	no	—
129	C₄×D₁₄₉	—	2	1	no	—
130	C₄×D₁₄₉	—	2	1	no	—
131	C₄×D₁₄₉	—	2	1	no	—
132	C₄×D₁₄₉	C₂×D₄	1	2	yes	—
133	C₄×D₁₄₉	#41	1	2	yes	—
134	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
135	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
136	D₄×C₁₄₉	—	2	2	no	—
137	C₂×C₄×C₁₄₉	—	2	2	no	—
138	C₂×C₄×C₁₄₉	—	2	2	no	—
139	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₁₄₉	—	2	1	no	—
145	C₂²×C₁₄₉	—	2	1	no	—
146	C₂²×C₁₄₉	—	2	1	no	—
147	C₂²×C₁₄₉	—	2	1	no	—
148	C₂²×C₁₄₉	—	2	1	no	—
149	C₂²×C₁₄₉	C₂×M₁₆	1	2	yes	complemented
150	C₂²×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
151	C₂×D₁₄₉	—	2	1	no	—
152	C₂×D₁₄₉	—	2	1	no	—
153	C₂×D₁₄₉	—	2	8	no	—
154	C₂×D₁₄₉	—	2	1	no	—
155	C₂×D₁₄₉	—	2	1	no	—
156	C₂×D₁₄₉	—	2	1	no	—
157	C₂×D₁₄₉	—	4	4	no	—
158	C₂×D₁₄₉	C₄×D₄	1	2	yes	—
159	C₂×D₁₄₉	C₂×M₁₆	1	2	yes	—
160	C₂×D₁₄₉	C₂×M₁₆	1	2	yes	complemented
161	C₂×D₁₄₉	#131	1	2	yes	—
162	C₄×C₁₄₉	—	2	1	no	—
163	C₄×C₁₄₉	—	2	1	no	—
164	C₄×C₁₄₉	—	2	1	no	—
165	C₄×C₁₄₉	—	2	1	no	—
166	C₄×C₁₄₉	C₄×D₄	1	2	yes	—
167	Dic₁₄₉	—	2	1	no	—
168	Dic₁₄₉	—	2	1	no	—
169	Dic₁₄₉	—	2	1	no	—
170	Dic₁₄₉	—	2	1	no	—
171	Dic₁₄₉	C₂²×D₄	1	1	yes	characteristic
172	Dic₁₄₉	C₂×#41	1	1	yes	characteristic
173	C₂×C₁₄₉	—	2	2	no	—
174	C₂×C₁₄₉	—	4	1	no	—
175	C₂×C₁₄₉	C₂×C₄×D₄	1	1	yes	characteristic
176	C₂×C₁₄₉	C₂²×M₁₆	1	1	yes	characteristic
177	C₂×C₁₄₉	C₂×#131	1	1	yes	characteristic
178	D₁₄₉	—	2	2	no	—
179	D₁₄₉	—	4	1	no	—
180	D₁₄₉	#435	1	4	yes	complemented
181	C₁₄₉	C₂×#435	1	1	yes	characteristic, complemented, Sylow
182	C₂×#435	—	149	1	no	maximal, Sylow
183	C₂²×M₁₆	—	149	1	no	—
184	C₂³×C₈	—	149	1	no	—
185	C₂×C₄×D₄	—	149	1	no	—
186	#435	—	149	2	no	—
187	#435	—	149	2	no	—
188	#435	—	149	2	no	—
189	#435	—	149	2	no	—
190	C₂×C₄⋊C₈	—	149	1	no	—
191	C₂×C₂²⋊C₈	—	149	1	no	—
192	C₂×C₂²⋊C₈	—	149	1	no	—
193	C₂×#97	—	149	1	no	—
194	C₂²×D₄	—	149	1	no	—
195	C₂³×C₄	—	149	1	no	—
196	C₂³×C₄	—	149	1	no	—
197	C₂×M₁₆	—	298	4	no	—
198	C₂×M₁₆	—	149	2	no	—
199	C₂×M₁₆	—	149	2	no	—
200	C₂²×C₈	—	298	4	no	—
201	C₂²×C₈	—	149	2	no	—
202	C₂²×C₈	—	149	1	no	—
203	C₂²×C₈	—	149	2	no	—
204	C₂²×C₈	—	149	1	no	—
205	C₂²×C₈	—	149	1	no	—
206	C₂²×C₈	—	149	1	no	—
207	C₄×D₄	—	149	1	no	—
208	C₄×D₄	—	149	1	no	—
209	C₄×D₄	—	149	1	no	—
210	C₄×D₄	—	149	1	no	—
211	C₄×D₄	—	149	1	no	—
212	C₄×D₄	—	149	1	no	—
213	C₄×D₄	—	149	1	no	—
214	C₄×D₄	#10597010	1	1	yes	characteristic
215	C₂×C₄⋊C₄	—	149	1	no	—
216	C₂×C₂²⋊C₄	—	149	1	no	—
217	C₂×C₂²⋊C₄	—	149	1	no	—
218	C₂×C₄²	—	149	1	no	—
219	C₄⋊C₈	—	149	2	no	—
220	C₄⋊C₈	—	149	2	no	—
221	C₂²⋊C₈	—	149	2	no	—
222	C₂²⋊C₈	—	149	2	no	—
223	C₂²⋊C₈	—	149	2	no	—
224	C₂²⋊C₈	—	149	2	no	—
225	#97	—	149	2	no	—
226	#97	—	149	2	no	—
227	C₂⁴	—	149	1	no	—
228	C₂⁴	—	149	1	no	—
229	C₂×D₄	—	298	4	no	—
230	C₂×D₄	—	149	1	no	—
231	C₂×D₄	—	149	1	no	—
232	C₂×D₄	—	149	1	no	—
233	C₂×D₄	C₂×#10597010	1	1	yes	characteristic
234	C₂²×C₄	—	298	2	no	—
235	C₂²×C₄	—	298	2	no	—
236	C₂²×C₄	—	298	2	no	—
237	C₂²×C₄	—	298	2	no	—
238	C₂²×C₄	—	149	1	no	—
239	C₂²×C₄	—	149	1	no	—
240	C₂²×C₄	—	149	1	no	—
241	C₂²×C₄	—	149	1	no	—
242	C₂²×C₄	—	149	1	no	—
243	C₂²×C₄	—	149	1	no	—
244	C₂²×C₄	—	149	1	no	—
245	C₂²×C₄	—	149	1	no	—
246	C₂²×C₄	—	149	1	no	—
247	C₂²×C₄	—	149	1	no	—
248	C₂²×C₄	—	149	1	no	—
249	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
250	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
251	M₁₆	—	298	4	no	—
252	M₁₆	—	298	4	no	—
253	C₂×C₈	—	298	2	no	—
254	C₂×C₈	—	298	2	no	—
255	C₂×C₈	—	298	2	no	—
256	C₂×C₈	—	298	4	no	—
257	C₂×C₈	—	298	4	no	—
258	C₂×C₈	—	149	2	no	—
259	C₂×C₈	—	149	2	no	—
260	C₂×C₈	—	149	2	no	—
261	C₂×C₈	—	149	2	no	—
262	C₂×C₈	—	149	4	no	—
263	C₄⋊C₄	—	149	1	no	—
264	C₄⋊C₄	—	149	1	no	—
265	C₄⋊C₄	—	149	1	no	—
266	C₄⋊C₄	C₂×#10597010	1	1	yes	characteristic
267	C₂²⋊C₄	—	149	1	no	—
268	C₂²⋊C₄	—	149	1	no	—
269	C₂²⋊C₄	—	149	1	no	—
270	C₂²⋊C₄	—	149	1	no	—
271	C₂²⋊C₄	—	149	1	no	—
272	C₂²⋊C₄	—	149	1	no	—
273	C₂²⋊C₄	C₂×#10597010	1	1	yes	characteristic
274	C₂²⋊C₄	C₂×#10597010	1	1	yes	characteristic
275	C₄²	—	149	1	no	—
276	C₄²	—	149	1	no	—
277	C₄²	—	149	1	no	—
278	C₄²	C₂×#10597010	1	1	yes	characteristic
279	C₂³	—	298	2	no	—
280	C₂³	—	298	2	no	—
281	C₂³	—	298	2	no	—
282	C₂³	—	298	2	no	—
283	C₂³	—	298	2	no	—
284	C₂³	—	149	1	no	—
285	C₂³	—	149	4	no	—
286	C₂³	—	149	1	no	—
287	C₂³	—	149	1	no	—
288	C₂³	C₂²×#10597010	1	1	yes	characteristic
289	C₂³	C₂²×#10597010	1	1	yes	characteristic
290	D₄	—	2	2	no	—
291	D₄	—	298	2	no	—
292	D₄	—	298	2	no	—
293	D₄	—	298	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	298	2	no	—
297	C₂×C₄	—	298	2	no	—
298	C₂×C₄	—	298	2	no	—
299	C₂×C₄	—	298	2	no	—
300	C₂×C₄	—	298	1	no	—
301	C₂×C₄	—	298	1	no	—
302	C₂×C₄	—	298	1	no	—
303	C₂×C₄	—	298	1	no	—
304	C₂×C₄	—	298	1	no	—
305	C₂×C₄	—	298	1	no	—
306	C₂×C₄	—	298	1	no	—
307	C₂×C₄	—	298	1	no	—
308	C₂×C₄	—	298	2	no	—
309	C₂×C₄	—	298	2	no	—
310	C₂×C₄	—	149	1	no	—
311	C₂×C₄	—	149	1	no	—
312	C₂×C₄	—	149	1	no	—
313	C₂×C₄	—	149	1	no	—
314	C₂×C₄	—	149	1	no	—
315	C₂×C₄	—	149	2	no	—
316	C₂×C₄	—	149	2	no	—
317	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
318	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
319	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
320	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
321	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
322	C₈	—	298	2	no	—
323	C₈	—	298	2	no	—
324	C₈	—	298	2	no	—
325	C₈	—	149	4	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	298	8	no	—
332	C₂²	—	298	1	no	—
333	C₂²	—	298	1	no	—
334	C₂²	—	298	1	no	—
335	C₂²	—	298	1	no	—
336	C₂²	—	298	1	no	—
337	C₂²	—	596	4	no	—
338	C₂²	—	149	2	no	—
339	C₂²	—	149	2	no	—
340	C₂²	—	149	2	no	—
341	C₂²	—	149	2	no	—
342	C₂²	D₁₄₉⋊M₁₆	1	2	yes	complemented
343	C₂²	C₂³×#10597010	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	298	1	no	—
349	C₄	—	298	1	no	—
350	C₄	—	298	1	no	—
351	C₄	—	298	1	no	—
352	C₄	—	149	1	no	—
353	C₄	—	149	1	no	—
354	C₄	D₄×#10597010	1	2	yes	—
355	C₂	—	2	2	no	—
356	C₂	—	4	1	no	—
357	C₂	—	298	2	no	—
358	C₂	—	596	1	no	—
359	C₂	—	149	4	no	—
360	C₂	C₂×D₄×#10597010	1	1	yes	characteristic
361	C₂	C₂×D₁₄₉⋊M₁₆	1	1	yes	characteristic
362	C₂	D₁₄₉⋊#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#10597010
commutator, socle	C₂²×C₁₄₉	C₂³×C₄
Frattini	C₂²	C₂³×#10597010
Fitting	C₄×D₄×C₁₄₉	C₄
prime radical	C₂×D₄×D₁₄₉	C₄
cosocle	C₂×Dic₁₄₉	C₂⁴
hypercenter	C₄×D₄	#10597010
hypocenter	C₁₄₉	C₂×#435
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₄₉⋊M₁₆	C₂	semidirect
2. C₂²×D₁₄₉⋊C₈	C₂	semidirect
3. #23750657	C₂	semidirect
4. #23750656	C₂	semidirect
5. #23750655	C₂	semidirect
6. #23750654	C₂	semidirect
7. D₁₄₉⋊(C₄⋊C₈)	C₂	semidirect
8. D₁₄₉⋊(C₂²⋊C₈)	C₂	semidirect
9. D₁₄₉⋊(C₂²⋊C₈)	C₂	semidirect
10. #23750584	C₂	semidirect
12. C₂×#14558746	C₂²	semidirect
14. C₂×#14558745	C₂²	semidirect
20. C₂×D₁₄₉⋊C₈	C₂²	semidirect
21. C₂²×#11924753	C₂²	semidirect
22. #18011978	C₂²	semidirect
23. C₄⋊#11924753	C₂²	semidirect
24. #18011968	C₂²	semidirect
25. #18011968	C₂²	semidirect
26. C₂²⋊#11924753	C₂²	semidirect
27. C₂²⋊#11924753	C₂²	semidirect
28. #18011966	C₂²	semidirect
29. #18011966	C₂²	semidirect
51. D₁₄₉⋊C₈	D₄	semidirect
100. #11924753	C₂×D₄	semidirect
106. C₂²×D₁₄₉	M₁₆	semidirect
149. C₂²×C₁₄₉	C₂×M₁₆	semidirect
160. C₂×D₁₄₉	C₂×M₁₆	semidirect
180. D₁₄₉	#435	semidirect
181. C₁₄₉	C₂×#435	semidirect
342. C₂²	D₁₄₉⋊M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₄₉⋊M₁₆	2
C₂²×D₁₄₉⋊C₈	2
#23750657	2
#23750656	2
#23750655	2
#23750654	2
D₁₄₉⋊(C₄⋊C₈)	2
D₁₄₉⋊(C₂²⋊C₈)	2
#23750584	2
C₄×D₄×D₁₄₉	2
C₂×#435	149

Subgroups — D149⋊#435 #34061399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₄₉⋊#435 #34061399