Subgroups — C₄×#18011879 #34047191

Order 19072.

1224 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#18011879	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊D₁₄₉	C₂	1	2	yes	maximal, complemented
4	#23749505	C₂	1	1	yes	maximal, characteristic, complemented
5	#23749501	C₂	1	2	yes	maximal, complemented
6	#23749497	C₂	1	1	yes	maximal, characteristic, complemented
7	#23749496	C₂	1	2	yes	maximal, complemented
8	#23749480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#14558713	C₂	1	2	yes	maximal, complemented
10	C₄×C₂²⋊Dic₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×D₁₄₉	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
14	C₂³×Dic₁₄₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄×D₁₄₉	—	2	4	no	—
16	C₂²×C₄×D₁₄₉	—	2	8	no	—
17	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	—
18	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	—
19	#18011879	C₄	1	8	yes	direct product factor
20	C₄×C₂²⋊D₁₄₉	—	2	8	no	—
21	C₂×#14558715	C₂²	1	2	yes	complemented
22	C₂×C₂²⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Dic₁₄₉	C₂²	1	2	yes	complemented
25	C₂×#14558713	C₂²	1	2	yes	—
26	C₂×#14558713	C₂²	1	2	yes	—
27	C₂×#14558713	C₂²	1	2	yes	—
28	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	complemented
29	#18011818	C₂²	1	2	yes	complemented
30	#18011818	C₂²	1	2	yes	complemented
31	#18011818	C₂²	1	2	yes	complemented
32	C₂²×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
33	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
34	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄×C₁₄₉	—	2	4	no	—
36	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
40	C₂³×D₁₄₉	—	2	4	no	—
41	C₂³×D₁₄₉	—	2	4	no	—
42	C₂³×D₁₄₉	—	2	2	no	—
43	C₂³×D₁₄₉	—	2	2	no	—
44	C₂³×D₁₄₉	C₂×C₄	1	4	yes	complemented
45	C₂³×D₁₄₉	C₂³	1	2	yes	—
46	C₂×C₂²⋊D₁₄₉	—	2	4	no	—
47	C₂×C₂²⋊D₁₄₉	—	2	4	no	—
48	C₂×C₂²⋊D₁₄₉	C₂×C₄	1	8	yes	complemented
49	C₂²×Dic₁₄₉	—	2	4	no	—
50	C₂²×Dic₁₄₉	—	2	2	no	—
51	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
52	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
53	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
54	C₂×C₄×D₁₄₉	—	2	32	no	—
55	C₂×C₄×D₁₄₉	—	2	4	no	—
56	C₂×C₄×D₁₄₉	—	2	4	no	—
57	C₂×C₄×D₁₄₉	—	2	4	no	—
58	C₂×C₄×D₁₄₉	—	2	4	no	—
59	C₂×C₄×D₁₄₉	—	2	4	no	—
60	C₂×C₄×D₁₄₉	D₄	1	8	yes	complemented
61	#14558715	—	2	4	no	—
62	C₂²⋊Dic₁₄₉	—	2	4	no	—
63	C₂²⋊Dic₁₄₉	—	2	2	no	—
64	C₂²⋊Dic₁₄₉	C₂×C₄	1	4	yes	complemented
65	#14558713	—	2	4	no	—
66	#14558713	—	2	4	no	—
67	#14558713	C₂×C₄	1	8	yes	complemented
68	C₄×Dic₁₄₉	—	2	4	no	—
69	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
70	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₁₄₉	—	2	2	no	—
72	C₂×D₄×C₁₄₉	—	2	2	no	—
73	C₂×D₄×C₁₄₉	C₂×C₄	1	4	yes	complemented
74	C₂²×C₄×C₁₄₉	—	2	4	no	—
75	C₂²×C₄×C₁₄₉	—	2	2	no	—
76	C₂²×C₄×C₁₄₉	—	2	4	no	—
77	C₂²×C₄×C₁₄₉	D₄	1	4	yes	complemented
78	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₄×C₁₄₉	—	2	2	no	—
84	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
85	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
86	C₄²×C₁₄₉	—	2	2	no	—
87	C₂²×D₁₄₉	—	2	8	no	—
88	C₂²×D₁₄₉	—	2	16	no	—
89	C₂²×D₁₄₉	—	2	8	no	—
90	C₂²×D₁₄₉	—	2	8	no	—
91	C₂²×D₁₄₉	—	2	2	no	—
92	C₂²×D₁₄₉	—	2	2	no	—
93	C₂²×D₁₄₉	—	2	2	no	—
94	C₂²×D₁₄₉	—	2	2	no	—
95	C₂²×D₁₄₉	—	2	16	no	—
96	C₂²×D₁₄₉	C₂²×C₄	1	4	yes	—
97	C₂²×D₁₄₉	C₂×D₄	1	4	yes	—
98	C₂²×D₁₄₉	#41	1	4	yes	—
99	C₂²⋊D₁₄₉	—	2	16	no	—
100	C₂×Dic₁₄₉	—	2	8	no	—
101	C₂×Dic₁₄₉	—	2	2	no	—
102	C₂×Dic₁₄₉	—	2	2	no	—
103	C₂×Dic₁₄₉	—	2	2	no	—
104	C₂×Dic₁₄₉	—	2	2	no	—
105	C₂×Dic₁₄₉	—	2	2	no	—
106	C₂×Dic₁₄₉	—	2	2	no	—
107	C₂×Dic₁₄₉	—	2	2	no	—
108	C₂×Dic₁₄₉	C₂²×C₄	1	4	yes	complemented
109	C₂×Dic₁₄₉	C₂×D₄	1	4	yes	—
110	C₄×D₁₄₉	—	2	16	no	—
111	C₄×D₁₄₉	—	2	16	no	—
112	C₂³×C₁₄₉	—	2	2	no	—
113	C₂³×C₁₄₉	—	2	2	no	—
114	C₂³×C₁₄₉	—	2	2	no	—
115	C₂³×C₁₄₉	—	2	1	no	—
116	C₂³×C₁₄₉	—	2	2	no	—
117	C₂³×C₁₄₉	—	2	1	no	—
118	C₂³×C₁₄₉	C₂²×C₄	1	2	yes	—
119	C₂³×C₁₄₉	C₂²×C₄	1	2	yes	complemented
120	C₂³×C₁₄₉	C₂×D₄	1	2	yes	—
121	C₂³×C₁₄₉	#41	1	2	yes	—
122	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
123	D₄×C₁₄₉	—	2	8	no	—
124	C₂×C₄×C₁₄₉	—	2	2	no	—
125	C₂×C₄×C₁₄₉	—	2	1	no	—
126	C₂×C₄×C₁₄₉	—	2	1	no	—
127	C₂×C₄×C₁₄₉	—	2	8	no	—
128	C₂×C₄×C₁₄₉	—	2	1	no	—
129	C₂×C₄×C₁₄₉	—	2	1	no	—
130	C₂×C₄×C₁₄₉	—	2	2	no	—
131	C₂×C₄×C₁₄₉	—	2	2	no	—
132	C₂×C₄×C₁₄₉	—	4	4	no	—
133	C₂×C₄×C₁₄₉	C₂²×C₄	1	2	yes	complemented
134	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
135	C₂×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
136	C₂×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
137	C₂²×C₁₄₉	—	2	4	no	—
138	C₂²×C₁₄₉	—	2	2	no	—
139	C₂²×C₁₄₉	—	2	2	no	—
140	C₂²×C₁₄₉	—	2	4	no	—
141	C₂²×C₁₄₉	—	2	2	no	—
142	C₂²×C₁₄₉	—	2	4	no	—
143	C₂²×C₁₄₉	—	4	1	no	—
144	C₂²×C₁₄₉	—	4	1	no	—
145	C₂²×C₁₄₉	—	4	2	no	—
146	C₂²×C₁₄₉	C₄×D₄	1	4	yes	complemented
147	C₂²×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
148	C₂²×C₁₄₉	C₂²×D₄	1	2	yes	—
149	C₂²×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
150	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
151	C₂²×C₁₄₉	C₂×#41	1	1	yes	characteristic
152	C₂×D₁₄₉	—	2	32	no	—
153	C₂×D₁₄₉	—	2	4	no	—
154	C₂×D₁₄₉	—	2	4	no	—
155	C₂×D₁₄₉	—	2	4	no	—
156	C₂×D₁₄₉	—	2	4	no	—
157	C₂×D₁₄₉	—	2	4	no	—
158	C₂×D₁₄₉	—	2	4	no	—
159	C₂×D₁₄₉	C₄×D₄	1	8	yes	complemented
160	C₄×C₁₄₉	—	2	2	no	—
161	C₄×C₁₄₉	—	2	2	no	—
162	C₄×C₁₄₉	—	4	1	no	—
163	C₄×C₁₄₉	—	4	1	no	—
164	C₄×C₁₄₉	#120	1	4	yes	complemented
165	Dic₁₄₉	—	2	4	no	—
166	Dic₁₄₉	—	2	4	no	—
167	Dic₁₄₉	—	4	2	no	—
168	C₂×C₁₄₉	—	2	4	no	—
169	C₂×C₁₄₉	—	4	2	no	—
170	C₂×C₁₄₉	C₂×C₄×D₄	1	2	yes	—
171	C₂×C₁₄₉	C₂×C₄×D₄	1	1	yes	characteristic
172	C₂×C₁₄₉	C₂×#120	1	1	yes	characteristic
173	C₂×C₁₄₉	#525	1	1	yes	characteristic
174	C₂×C₁₄₉	#525	1	2	yes	—
175	D₁₄₉	—	2	8	no	—
176	C₁₄₉	C₄×#120	1	1	yes	characteristic, complemented, Sylow
177	C₄×#120	—	149	1	no	maximal, Sylow
178	C₂⁴×C₄	—	149	1	no	—
179	C₂×#120	—	149	1	no	—
180	C₂×C₄×D₄	—	149	2	no	—
181	C₂×C₄×D₄	D₁₄₉	1	1	yes	characteristic, complemented
182	#386	—	149	1	no	—
183	#386	—	149	2	no	—
184	#385	—	149	2	no	—
185	#385	—	149	1	no	—
186	#379	—	149	1	no	—
187	C₄×C₂²⋊C₄	—	149	1	no	—
188	C₄×C₂²⋊C₄	—	149	2	no	—
189	C₂⁵	—	149	1	no	—
190	C₂²×D₄	—	149	2	no	—
191	C₂²×D₄	C₂×D₁₄₉	1	1	yes	characteristic
192	C₂³×C₄	—	298	8	no	—
193	C₂³×C₄	—	298	4	no	—
194	C₂³×C₄	—	149	1	no	—
195	C₂³×C₄	—	149	2	no	—
196	C₂³×C₄	—	149	2	no	—
197	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic
198	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
199	#120	—	149	8	no	—
200	C₄×D₄	—	2	4	no	—
201	C₄×D₄	—	298	8	no	—
202	C₂×C₄⋊C₄	—	149	2	no	—
203	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
204	C₂×C₂²⋊C₄	—	149	2	no	—
205	C₂×C₂²⋊C₄	—	149	1	no	—
206	C₂×C₂²⋊C₄	—	149	2	no	—
207	C₂×C₂²⋊C₄	—	149	2	no	—
208	C₂×C₂²⋊C₄	—	149	1	no	—
209	C₂×C₂²⋊C₄	—	149	2	no	—
210	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
212	C₂×C₄²	—	149	2	no	—
213	C₂×C₄²	C₂×D₁₄₉	1	1	yes	characteristic, complemented
214	#95	—	149	2	no	—
215	#95	—	149	2	no	—
216	#95	—	149	2	no	—
217	C₂⁴	—	298	4	no	—
218	C₂⁴	—	298	4	no	—
219	C₂⁴	—	298	2	no	—
220	C₂⁴	—	298	2	no	—
221	C₂⁴	—	149	4	no	—
222	C₂⁴	—	149	2	no	—
223	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
224	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
225	C₂×D₄	—	2	2	no	—
226	C₂×D₄	—	2	2	no	—
227	C₂×D₄	—	298	4	no	—
228	C₂×D₄	—	298	4	no	—
229	C₂×D₄	—	149	8	no	—
230	C₂×D₄	C₄×D₁₄₉	1	4	yes	complemented
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	298	32	no	—
235	C₂²×C₄	—	298	4	no	—
236	C₂²×C₄	—	298	4	no	—
237	C₂²×C₄	—	298	2	no	—
238	C₂²×C₄	—	298	4	no	—
239	C₂²×C₄	—	298	4	no	—
240	C₂²×C₄	—	298	4	no	—
241	C₂²×C₄	—	298	4	no	—
242	C₂²×C₄	—	149	2	no	—
243	C₂²×C₄	—	149	2	no	—
244	C₂²×C₄	—	149	2	no	—
245	C₂²×C₄	—	149	8	no	—
246	C₂²×C₄	C₂²⋊D₁₄₉	1	4	yes	complemented
247	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
248	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
249	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
250	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
251	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	298	4	no	—
254	C₂²⋊C₄	—	2	2	no	—
255	C₂²⋊C₄	—	2	2	no	—
256	C₂²⋊C₄	—	298	4	no	—
257	C₂²⋊C₄	—	298	4	no	—
258	C₂²⋊C₄	—	298	2	no	—
259	C₂²⋊C₄	—	298	4	no	—
260	C₂²⋊C₄	—	149	4	no	—
261	C₂²⋊C₄	—	149	8	no	—
262	C₄²	—	2	2	no	—
263	C₄²	—	298	4	no	—
264	C₂³	—	2	2	no	—
265	C₂³	—	2	2	no	—
266	C₂³	—	2	2	no	—
267	C₂³	—	2	1	no	—
268	C₂³	—	2	2	no	—
269	C₂³	—	2	1	no	—
270	C₂³	—	298	8	no	—
271	C₂³	—	298	8	no	—
272	C₂³	—	298	16	no	—
273	C₂³	—	298	16	no	—
274	C₂³	—	298	2	no	—
275	C₂³	—	298	2	no	—
276	C₂³	—	298	2	no	—
277	C₂³	—	298	2	no	—
278	C₂³	—	298	8	no	—
279	C₂³	—	149	4	no	—
280	C₂³	—	149	4	no	—
281	C₂³	—	149	4	no	—
282	C₂³	C₂×C₄×D₁₄₉	1	2	yes	—
283	C₂³	C₂×C₄×D₁₄₉	1	2	yes	complemented
284	C₂³	C₂×C₂²⋊D₁₄₉	1	2	yes	—
285	C₂³	#14558736	1	2	yes	—
286	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
287	D₄	—	2	8	no	—
288	D₄	—	298	16	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	—	298	16	no	—
299	C₂×C₄	—	298	8	no	—
300	C₂×C₄	—	298	2	no	—
301	C₂×C₄	—	298	2	no	—
302	C₂×C₄	—	298	2	no	—
303	C₂×C₄	—	298	2	no	—
304	C₂×C₄	—	298	16	no	—
305	C₂×C₄	—	298	2	no	—
306	C₂×C₄	—	298	2	no	—
307	C₂×C₄	—	298	2	no	—
308	C₂×C₄	—	149	4	no	—
309	C₂×C₄	—	149	4	no	—
310	C₂×C₄	C₂×C₄×D₁₄₉	1	2	yes	complemented
311	C₂×C₄	D₄×D₁₄₉	1	4	yes	—
312	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	2	yes	—
313	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	2	yes	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	2	no	—
317	C₂²	—	2	4	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	4	1	no	—
321	C₂²	—	4	1	no	—
322	C₂²	—	4	2	no	—
323	C₂²	—	298	32	no	—
324	C₂²	—	298	4	no	—
325	C₂²	—	298	4	no	—
326	C₂²	—	298	4	no	—
327	C₂²	—	298	4	no	—
328	C₂²	—	298	4	no	—
329	C₂²	—	298	4	no	—
330	C₂²	—	149	8	no	—
331	C₂²	C₄×C₂²⋊D₁₄₉	1	4	yes	complemented
332	C₂²	C₂²×C₄×D₁₄₉	1	1	yes	characteristic
333	C₂²	C₂×D₄×D₁₄₉	1	2	yes	—
334	C₂²	C₂²×C₂²⋊D₁₄₉	1	1	yes	characteristic
335	C₂²	#41×D₁₄₉	1	2	yes	—
336	C₂²	C₂×#14558736	1	1	yes	characteristic
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	4	1	no	—
340	C₄	—	4	1	no	—
341	C₄	—	298	4	no	—
342	C₄	—	298	4	no	—
343	C₄	—	596	2	no	—
344	C₄	#18011879	1	4	yes	direct product factor
345	C₂	—	2	4	no	—
346	C₂	—	4	2	no	—
347	C₂	—	298	8	no	—
348	C₂	C₄×D₄×D₁₄₉	1	2	yes	—
349	C₂	C₂×C₄×C₂²⋊D₁₄₉	1	1	yes	characteristic
350	C₂	C₂×#18011879	1	1	yes	characteristic
351	C₂	#23750132	1	1	yes	characteristic
352	C₂	#23750134	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₄₉
commutator	C₂²×C₁₄₉	C₂³×C₄
Frattini	C₂³	C₂³×D₁₄₉
Fitting	C₂×C₄×D₄×C₁₄₉	C₂
socle, cosocle	C₂³×C₁₄₉	C₂⁴
prime radical	C₂×#18011879	C₂
hypercenter	C₂×C₄×D₄	D₁₄₉
hypocenter	C₁₄₉	C₄×#120
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄×D₁₄₉	C₂	semidirect
3. C₂×C₄×C₂²⋊D₁₄₉	C₂	semidirect
4. #23749505	C₂	semidirect
5. #23749501	C₂	semidirect
6. #23749497	C₂	semidirect
7. #23749496	C₂	semidirect
8. #23749480	C₂	semidirect
9. C₄×#14558713	C₂	semidirect
10. C₄×C₂²⋊Dic₁₄₉	C₂	semidirect
11. C₂×C₄×D₄×C₁₄₉	C₂	semidirect
19. #18011879	C₄	direct (N × H)
21. C₂×#14558715	C₂²	semidirect
24. C₂×C₂²⋊Dic₁₄₉	C₂²	semidirect
28. C₂×C₄×Dic₁₄₉	C₂²	semidirect
29. #18011818	C₂²	semidirect
30. #18011818	C₂²	semidirect
31. #18011818	C₂²	semidirect
34. C₂³×C₄×C₁₄₉	C₂²	semidirect
36. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
38. C₂×C₂²⋊C₄×C₁₄₉	C₂²	semidirect
39. C₂×C₄²×C₁₄₉	C₂²	semidirect
44. C₂³×D₁₄₉	C₂×C₄	semidirect
48. C₂×C₂²⋊D₁₄₉	C₂×C₄	semidirect
60. C₂×C₄×D₁₄₉	D₄	semidirect
64. C₂²⋊Dic₁₄₉	C₂×C₄	semidirect
67. #14558713	C₂×C₄	semidirect
73. C₂×D₄×C₁₄₉	C₂×C₄	semidirect
77. C₂²×C₄×C₁₄₉	D₄	semidirect
108. C₂×Dic₁₄₉	C₂²×C₄	semidirect
119. C₂³×C₁₄₉	C₂²×C₄	semidirect
133. C₂×C₄×C₁₄₉	C₂²×C₄	semidirect
146. C₂²×C₁₄₉	C₄×D₄	semidirect
159. C₂×D₁₄₉	C₄×D₄	semidirect
164. C₄×C₁₄₉	#120	semidirect
176. C₁₄₉	C₄×#120	semidirect
181. C₂×C₄×D₄	D₁₄₉	semidirect
198. C₂³×C₄	C₂×D₁₄₉	semidirect
203. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect
211. C₂×C₂²⋊C₄	C₂×D₁₄₉	semidirect
213. C₂×C₄²	C₂×D₁₄₉	semidirect
230. C₂×D₄	C₄×D₁₄₉	semidirect
246. C₂²×C₄	C₂²⋊D₁₄₉	semidirect
283. C₂³	C₂×C₄×D₁₄₉	semidirect
310. C₂×C₄	C₂×C₄×D₁₄₉	semidirect
331. C₂²	C₄×C₂²⋊D₁₄₉	semidirect
344. C₄	#18011879	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×D₁₄₉	2
C₂×#18011879	2
C₂×C₄×C₂²⋊D₁₄₉	2
#23749505	2
#23749501	2
#23749497	2
#23749496	2
#23749480	2
C₄×#14558713	2
C₄×C₂²⋊Dic₁₄₉	2
C₂×C₄×D₄×C₁₄₉	2
C₄×#120	149

Subgroups — C4×#18011879 #34047191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#18011879 #34047191