Subgroups — #2414×C₁₄₉ #34041327

Order 19072.

704 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×#121×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#121×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#117×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#394×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	#392×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	#390×C₁₄₉	C₂	1	2	yes	maximal, complemented
8	#390×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#389×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#388×C₁₄₉	C₂	1	2	yes	maximal, complemented
11	#380×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₁₄₉	C₂²	1	2	yes	—
15	C₂²×D₄×C₁₄₉	C₂²	1	2	yes	—
16	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
18	#121×C₁₄₉	—	2	4	no	—
19	#121×C₁₄₉	—	2	4	no	—
20	C₄×D₄×C₁₄₉	—	2	4	no	—
21	#117×C₁₄₉	—	2	4	no	—
22	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
26	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
35	C₂×C₄²×C₁₄₉	C₂²	1	2	yes	—
36	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
37	#95×C₁₄₉	C₂²	1	2	yes	—
38	#95×C₁₄₉	C₂²	1	2	yes	—
39	C₂⁴×C₁₄₉	C₂³	1	2	yes	—
40	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
41	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
42	C₂×D₄×C₁₄₉	—	2	2	no	—
43	C₂×D₄×C₁₄₉	—	2	2	no	—
44	C₂×D₄×C₁₄₉	—	2	4	no	—
45	C₂×D₄×C₁₄₉	—	2	4	no	—
46	C₂×D₄×C₁₄₉	—	2	4	no	—
47	C₂×D₄×C₁₄₉	—	2	2	no	—
48	C₂×D₄×C₁₄₉	—	2	2	no	—
49	C₂×D₄×C₁₄₉	—	2	2	no	—
50	C₂×D₄×C₁₄₉	—	2	2	no	—
51	C₂×D₄×C₁₄₉	—	4	2	no	—
52	C₂×D₄×C₁₄₉	—	4	2	no	—
53	C₂×D₄×C₁₄₉	—	4	2	no	—
54	C₂²×C₄×C₁₄₉	—	2	2	no	—
55	C₂²×C₄×C₁₄₉	—	2	2	no	—
56	C₂²×C₄×C₁₄₉	—	2	2	no	—
57	C₂²×C₄×C₁₄₉	—	2	2	no	—
58	C₂²×C₄×C₁₄₉	—	2	2	no	—
59	C₂²×C₄×C₁₄₉	D₄	1	4	yes	complemented
60	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
62	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
63	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
65	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
68	C₄⋊C₄×C₁₄₉	—	2	2	no	—
69	C₄⋊C₄×C₁₄₉	—	2	2	no	—
70	C₄⋊C₄×C₁₄₉	—	2	2	no	—
71	C₄⋊C₄×C₁₄₉	—	4	2	no	—
72	C₄⋊C₄×C₁₄₉	D₄	1	4	yes	complemented
73	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
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	—	2	4	no	—
78	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
79	C₂²⋊C₄×C₁₄₉	—	4	2	no	—
80	C₂²⋊C₄×C₁₄₉	—	4	2	no	—
81	C₄²×C₁₄₉	—	2	4	no	—
82	C₄²×C₁₄₉	—	2	2	no	—
83	C₂³×C₁₄₉	—	2	1	no	—
84	C₂³×C₁₄₉	—	2	1	no	—
85	C₂³×C₁₄₉	—	2	1	no	—
86	C₂³×C₁₄₉	—	2	1	no	—
87	C₂³×C₁₄₉	—	2	1	no	—
88	C₂³×C₁₄₉	—	2	1	no	—
89	C₂³×C₁₄₉	—	2	1	no	—
90	C₂³×C₁₄₉	—	2	1	no	—
91	C₂³×C₁₄₉	—	2	1	no	—
92	C₂³×C₁₄₉	—	2	1	no	—
93	C₂³×C₁₄₉	—	2	1	no	—
94	C₂³×C₁₄₉	—	2	1	no	—
95	C₂³×C₁₄₉	—	2	2	no	—
96	C₂³×C₁₄₉	—	2	2	no	—
97	C₂³×C₁₄₉	—	2	2	no	—
98	C₂³×C₁₄₉	—	2	2	no	—
99	C₂³×C₁₄₉	—	2	2	no	—
100	C₂³×C₁₄₉	—	2	2	no	—
101	C₂³×C₁₄₉	—	2	2	no	—
102	C₂³×C₁₄₉	C₂×D₄	1	2	yes	—
103	C₂³×C₁₄₉	#41	1	2	yes	—
104	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
105	D₄×C₁₄₉	—	2	8	no	—
106	D₄×C₁₄₉	—	4	8	no	—
107	D₄×C₁₄₉	—	4	8	no	—
108	D₄×C₁₄₉	—	4	4	no	—
109	C₂×C₄×C₁₄₉	—	2	1	no	—
110	C₂×C₄×C₁₄₉	—	2	1	no	—
111	C₂×C₄×C₁₄₉	—	2	1	no	—
112	C₂×C₄×C₁₄₉	—	2	1	no	—
113	C₂×C₄×C₁₄₉	—	2	2	no	—
114	C₂×C₄×C₁₄₉	—	2	2	no	—
115	C₂×C₄×C₁₄₉	—	2	8	no	—
116	C₂×C₄×C₁₄₉	—	2	1	no	—
117	C₂×C₄×C₁₄₉	—	2	2	no	—
118	C₂×C₄×C₁₄₉	—	2	1	no	—
119	C₂×C₄×C₁₄₉	—	2	1	no	—
120	C₂×C₄×C₁₄₉	—	2	2	no	—
121	C₂×C₄×C₁₄₉	—	2	2	no	—
122	C₂×C₄×C₁₄₉	—	2	1	no	—
123	C₂×C₄×C₁₄₉	—	2	1	no	—
124	C₂×C₄×C₁₄₉	—	2	2	no	—
125	C₂×C₄×C₁₄₉	—	2	2	no	—
126	C₂×C₄×C₁₄₉	—	2	1	no	—
127	C₂×C₄×C₁₄₉	—	2	2	no	—
128	C₂×C₄×C₁₄₉	—	4	4	no	—
129	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
130	C₂×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
131	C₂×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
132	C₂×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
133	C₂×C₄×C₁₄₉	#41	1	2	yes	—
134	C₂×C₄×C₁₄₉	#41	1	2	yes	—
135	C₂²×C₁₄₉	—	2	2	no	—
136	C₂²×C₁₄₉	—	2	2	no	—
137	C₂²×C₁₄₉	—	2	2	no	—
138	C₂²×C₁₄₉	—	2	2	no	—
139	C₂²×C₁₄₉	—	2	2	no	—
140	C₂²×C₁₄₉	—	2	2	no	—
141	C₂²×C₁₄₉	—	4	1	no	—
142	C₂²×C₁₄₉	—	4	1	no	—
143	C₂²×C₁₄₉	—	4	1	no	—
144	C₂²×C₁₄₉	—	4	1	no	—
145	C₂²×C₁₄₉	—	4	1	no	—
146	C₂²×C₁₄₉	—	4	1	no	—
147	C₂²×C₁₄₉	—	4	1	no	—
148	C₂²×C₁₄₉	—	4	1	no	—
149	C₂²×C₁₄₉	—	4	2	no	—
150	C₂²×C₁₄₉	—	4	2	no	—
151	C₂²×C₁₄₉	—	4	2	no	—
152	C₂²×C₁₄₉	—	4	2	no	—
153	C₂²×C₁₄₉	—	4	2	no	—
154	C₂²×C₁₄₉	—	4	2	no	—
155	C₂²×C₁₄₉	—	4	2	no	—
156	C₂²×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
157	C₂²×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
158	C₂²×C₁₄₉	C₂×#41	1	1	yes	characteristic
159	C₂²×C₁₄₉	C₂×#41	1	1	yes	characteristic
160	C₂²×C₁₄₉	C₂×#41	1	1	yes	characteristic
161	C₂²×C₁₄₉	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂²×C₁₄₉	H(5,𝔽₂)	1	1	yes	characteristic
163	C₄×C₁₄₉	—	2	2	no	—
164	C₄×C₁₄₉	—	2	2	no	—
165	C₄×C₁₄₉	—	2	4	no	—
166	C₄×C₁₄₉	—	4	1	no	—
167	C₄×C₁₄₉	—	4	1	no	—
168	C₄×C₁₄₉	—	4	2	no	—
169	C₄×C₁₄₉	—	4	2	no	—
170	C₄×C₁₄₉	#121	1	4	yes	—
171	C₂×C₁₄₉	—	4	2	no	—
172	C₂×C₁₄₉	—	4	2	no	—
173	C₂×C₁₄₉	—	8	2	no	—
174	C₂×C₁₄₉	C₂×#121	1	1	yes	characteristic
175	C₂×C₁₄₉	#525	1	1	yes	characteristic
176	C₂×C₁₄₉	#535	1	1	yes	characteristic
177	C₂×C₁₄₉	#546	1	1	yes	characteristic
178	C₂×C₁₄₉	#550	1	1	yes	characteristic
179	C₂×C₁₄₉	#553	1	1	yes	characteristic
180	C₂×C₁₄₉	#555	1	1	yes	characteristic
181	C₁₄₉	#2414	1	1	yes	characteristic, direct product factor, Sylow
182	#2414	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×#121	C₂×C₁₄₉	1	1	yes	characteristic, complemented
184	C₂×#121	C₂×C₁₄₉	1	1	yes	characteristic, complemented
185	C₂×C₄×D₄	C₂×C₁₄₉	1	1	yes	characteristic, complemented
186	C₂×#117	C₂×C₁₄₉	1	1	yes	characteristic, complemented
187	#394	C₂×C₁₄₉	1	2	yes	complemented
188	#392	C₂×C₁₄₉	1	2	yes	complemented
189	#390	C₂×C₁₄₉	1	2	yes	complemented
190	#390	C₂×C₁₄₉	1	1	yes	characteristic, complemented
191	#389	C₂×C₁₄₉	1	1	yes	characteristic, complemented
192	#388	C₂×C₁₄₉	1	2	yes	complemented
193	#380	C₂×C₁₄₉	1	1	yes	characteristic, complemented
194	C₂²×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
195	C₂²×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
196	C₂²×D₄	C₂²×C₁₄₉	1	2	yes	—
197	C₂²×D₄	C₂²×C₁₄₉	1	2	yes	—
198	C₂³×C₄	C₂²×C₁₄₉	1	1	yes	characteristic
199	C₂³×C₄	C₂²×C₁₄₉	1	1	yes	characteristic
200	#121	—	2	4	no	—
201	#121	—	2	4	no	—
202	C₄×D₄	—	2	4	no	—
203	#117	—	2	4	no	—
204	C₂×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
205	C₂×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₁₄₉	1	2	yes	—
208	C₂×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
209	C₂×C₂²⋊C₄	C₂²×C₁₄₉	1	2	yes	—
210	C₂×C₂²⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
212	C₂×C₂²⋊C₄	C₂²×C₁₄₉	1	2	yes	—
213	C₂×C₂²⋊C₄	C₂²×C₁₄₉	1	2	yes	—
214	C₂×C₂²⋊C₄	C₂²×C₁₄₉	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂²×C₁₄₉	1	2	yes	—
216	C₂×C₂²⋊C₄	C₂²×C₁₄₉	1	2	yes	—
217	C₂×C₄²	C₂²×C₁₄₉	1	2	yes	—
218	C₂×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
219	#95	C₂²×C₁₄₉	1	2	yes	—
220	#95	C₂²×C₁₄₉	1	2	yes	—
221	C₂⁴	C₂³×C₁₄₉	1	2	yes	—
222	C₂⁴	C₂³×C₁₄₉	1	1	yes	characteristic
223	C₂⁴	C₂³×C₁₄₉	1	1	yes	characteristic
224	C₂×D₄	—	2	2	no	—
225	C₂×D₄	—	2	2	no	—
226	C₂×D₄	—	2	4	no	—
227	C₂×D₄	—	2	4	no	—
228	C₂×D₄	—	2	4	no	—
229	C₂×D₄	—	2	2	no	—
230	C₂×D₄	—	2	2	no	—
231	C₂×D₄	—	2	2	no	—
232	C₂×D₄	—	2	2	no	—
233	C₂×D₄	—	4	2	no	—
234	C₂×D₄	—	4	2	no	—
235	C₂×D₄	—	4	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	D₄×C₁₄₉	1	4	yes	complemented
242	C₂²×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
243	C₂²×C₄	C₂³×C₁₄₉	1	2	yes	—
244	C₂²×C₄	C₂³×C₁₄₉	1	2	yes	—
245	C₂²×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
246	C₂²×C₄	C₂³×C₁₄₉	1	2	yes	—
247	C₂²×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
248	C₂²×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
250	C₄⋊C₄	—	2	2	no	—
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	4	2	no	—
254	C₄⋊C₄	D₄×C₁₄₉	1	4	yes	complemented
255	C₂²⋊C₄	—	2	2	no	—
256	C₂²⋊C₄	—	2	4	no	—
257	C₂²⋊C₄	—	2	2	no	—
258	C₂²⋊C₄	—	2	4	no	—
259	C₂²⋊C₄	—	2	4	no	—
260	C₂²⋊C₄	—	2	4	no	—
261	C₂²⋊C₄	—	4	2	no	—
262	C₂²⋊C₄	—	4	2	no	—
263	C₄²	—	2	4	no	—
264	C₄²	—	2	2	no	—
265	C₂³	—	2	1	no	—
266	C₂³	—	2	1	no	—
267	C₂³	—	2	1	no	—
268	C₂³	—	2	1	no	—
269	C₂³	—	2	1	no	—
270	C₂³	—	2	1	no	—
271	C₂³	—	2	1	no	—
272	C₂³	—	2	1	no	—
273	C₂³	—	2	1	no	—
274	C₂³	—	2	1	no	—
275	C₂³	—	2	1	no	—
276	C₂³	—	2	1	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	2	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	C₂×D₄×C₁₄₉	1	2	yes	—
285	C₂³	#41×C₁₄₉	1	2	yes	—
286	C₂³	C₂⁴×C₁₄₉	1	1	yes	characteristic
287	D₄	—	2	8	no	—
288	D₄	—	4	8	no	—
289	D₄	—	4	8	no	—
290	D₄	—	4	4	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
312	C₂×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
313	C₂×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
314	C₂×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
315	C₂×C₄	#41×C₁₄₉	1	2	yes	—
316	C₂×C₄	#41×C₁₄₉	1	2	yes	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	4	1	no	—
324	C₂²	—	4	1	no	—
325	C₂²	—	4	1	no	—
326	C₂²	—	4	1	no	—
327	C₂²	—	4	1	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	1	no	—
330	C₂²	—	4	1	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	2	no	—
338	C₂²	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
339	C₂²	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
340	C₂²	C₂×#41×C₁₄₉	1	1	yes	characteristic
341	C₂²	C₂×#41×C₁₄₉	1	1	yes	characteristic
342	C₂²	C₂×#41×C₁₄₉	1	1	yes	characteristic
343	C₂²	H(5,𝔽₂)×C₁₄₉	1	1	yes	characteristic
344	C₂²	H(5,𝔽₂)×C₁₄₉	1	1	yes	characteristic
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	2	4	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	2	no	—
350	C₄	—	4	1	no	—
351	C₄	—	4	2	no	—
352	C₄	#121×C₁₄₉	1	4	yes	—
353	C₂	—	4	2	no	—
354	C₂	—	4	2	no	—
355	C₂	—	8	2	no	—
356	C₂	C₂×#121×C₁₄₉	1	1	yes	characteristic
357	C₂	#525×C₁₄₉	1	1	yes	characteristic
358	C₂	#535×C₁₄₉	1	1	yes	characteristic
359	C₂	#546×C₁₄₉	1	1	yes	characteristic
360	C₂	#550×C₁₄₉	1	1	yes	characteristic
361	C₂	#553×C₁₄₉	1	1	yes	characteristic
362	C₂	#555×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₄₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₄₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#121×C₁₄₉	C₂	semidirect
2. C₂×#121×C₁₄₉	C₂	semidirect
3. C₂×C₄×D₄×C₁₄₉	C₂	semidirect
4. C₂×#117×C₁₄₉	C₂	semidirect
5. #394×C₁₄₉	C₂	semidirect
6. #392×C₁₄₉	C₂	semidirect
7. #390×C₁₄₉	C₂	semidirect
8. #390×C₁₄₉	C₂	semidirect
9. #389×C₁₄₉	C₂	semidirect
10. #388×C₁₄₉	C₂	semidirect
11. #380×C₁₄₉	C₂	semidirect
59. C₂²×C₄×C₁₄₉	D₄	semidirect
72. C₄⋊C₄×C₁₄₉	D₄	semidirect
181. C₁₄₉	#2414	direct (N × H)
182. #2414	C₁₄₉	direct (N × H)
183. C₂×#121	C₂×C₁₄₉	semidirect
184. C₂×#121	C₂×C₁₄₉	semidirect
185. C₂×C₄×D₄	C₂×C₁₄₉	semidirect
186. C₂×#117	C₂×C₁₄₉	semidirect
187. #394	C₂×C₁₄₉	semidirect
188. #392	C₂×C₁₄₉	semidirect
189. #390	C₂×C₁₄₉	semidirect
190. #390	C₂×C₁₄₉	semidirect
191. #389	C₂×C₁₄₉	semidirect
192. #388	C₂×C₁₄₉	semidirect
193. #380	C₂×C₁₄₉	semidirect
241. C₂²×C₄	D₄×C₁₄₉	semidirect
254. C₄⋊C₄	D₄×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#121×C₁₄₉	2
C₂×C₄×D₄×C₁₄₉	2
C₂×#117×C₁₄₉	2
#394×C₁₄₉	2
#392×C₁₄₉	2
#390×C₁₄₉	2
#389×C₁₄₉	2
#388×C₁₄₉	2
#380×C₁₄₉	2
#2414	149

Subgroups — #2414×C149 #34041327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2414×C₁₄₉ #34041327