Subgroups — #34058020

Order 19072.

1556 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14558736	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750203	C₂	1	4	yes	maximal, complemented
3	#23750199	C₂	1	2	yes	maximal, complemented
4	#23750196	C₂	1	2	yes	maximal, complemented
5	#23750192	C₂	1	2	yes	maximal, complemented
6	#23750189	C₂	1	2	yes	maximal, complemented
7	#23750184	C₂	1	4	yes	maximal, complemented
8	#23750171	C₂	1	4	yes	maximal, complemented
9	#23750136	C₂	1	4	yes	maximal, complemented
10	#23750132	C₂	1	4	yes	maximal, complemented
11	C₂×#18011870	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14558736	—	2	8	no	—
14	C₂×#14558736	C₂²	1	2	yes	—
15	C₂×#14558736	C₂²	1	2	yes	—
16	C₂×#14558736	C₂²	1	2	yes	complemented
17	C₂×#14558736	C₂²	1	2	yes	complemented
18	C₂²×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
21	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	complemented
22	#18011909	C₂²	1	4	yes	complemented
23	#18011907	C₂²	1	4	yes	complemented
24	#18011900	C₂²	1	4	yes	complemented
25	#18011898	C₂²	1	4	yes	complemented
26	#18011894	C₂²	1	8	yes	complemented
27	#18011892	C₂²	1	8	yes	complemented
28	#18011890	C₂²	1	8	yes	complemented
29	#18011887	C₂²	1	8	yes	complemented
30	#18011885	C₂²	1	8	yes	complemented
31	#18011883	C₂²	1	16	yes	complemented
32	#18011882	C₂²	1	8	yes	complemented
33	#18011880	C₂²	1	8	yes	complemented
34	#18011879	C₂²	1	8	yes	complemented
35	C₄×C₂²⋊D₁₄₉	C₂²	1	16	yes	complemented
36	#18011870	C₂²	1	2	yes	complemented
37	#18011870	C₂²	1	2	yes	complemented
38	#18011870	C₂²	1	2	yes	complemented
39	#18011870	C₂²	1	2	yes	complemented
40	C₂×C₄⋊Dic₁₄₉	C₂²	1	2	yes	complemented
41	C₂×C₂²⋊Dic₁₄₉	C₂²	1	2	yes	—
42	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	complemented
43	C₂×#41×C₁₄₉	—	2	8	no	—
44	C₂×#41×C₁₄₉	C₂²	1	2	yes	—
45	C₂×#41×C₁₄₉	C₂²	1	2	yes	—
46	C₂×#41×C₁₄₉	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₄₉	C₂²	1	2	yes	complemented
48	C₂²×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
49	C₂²×D₄×C₁₄₉	C₂²	1	2	yes	—
50	C₂²×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
51	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
52	C₂³×C₄×C₁₄₉	C₂²	1	2	yes	complemented
53	C₂³×D₁₄₉	C₂³	1	2	yes	—
54	#14558736	—	2	8	no	—
55	#14558736	—	2	8	no	—
56	#14558736	—	2	8	no	—
57	#14558736	—	2	8	no	—
58	C₂×Dic₂₉₈	—	2	4	no	—
59	C₂×Dic₂₉₈	C₂³	1	2	yes	—
60	C₂×Dic₂₉₈	C₂³	1	2	yes	—
61	C₂×D₅₉₆	—	2	4	no	—
62	C₂×D₅₉₆	C₂³	1	2	yes	—
63	C₂×D₅₉₆	C₂³	1	2	yes	—
64	C₂×C₂²⋊D₁₄₉	—	2	8	no	—
65	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
66	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
67	C₂×C₂²⋊D₁₄₉	C₂³	1	16	yes	—
68	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
69	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
70	C₂×C₄×D₁₄₉	—	2	8	no	—
71	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
72	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
73	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
74	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
75	#14558715	C₂³	1	16	yes	—
76	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
77	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
78	C₂²⋊Dic₁₄₉	C₂³	1	16	yes	—
79	#14558713	C₂³	1	16	yes	—
80	C₄×Dic₁₄₉	C₂³	1	4	yes	—
81	C₄×Dic₁₄₉	C₂³	1	4	yes	—
82	C₂⁴×C₁₄₉	C₂³	1	2	yes	—
83	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
84	#41×C₁₄₉	—	2	8	no	—
85	#41×C₁₄₉	—	2	8	no	—
86	#41×C₁₄₉	—	2	8	no	—
87	#41×C₁₄₉	—	2	8	no	—
88	C₂×Q₈×C₁₄₉	—	2	4	no	—
89	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
90	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
91	C₂×D₄×C₁₄₉	—	2	8	no	—
92	C₂×D₄×C₁₄₉	—	2	4	no	—
93	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
94	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
95	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
96	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
97	C₂²×C₄×C₁₄₉	—	2	8	no	—
98	C₂²×C₄×C₁₄₉	D₄	1	8	yes	complemented
99	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
100	C₂²×C₄×C₁₄₉	C₂³	1	4	yes	—
101	C₂²×C₄×C₁₄₉	C₂³	1	4	yes	—
102	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
106	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
108	C₂²×D₁₄₉	—	2	4	no	—
109	C₂²×D₁₄₉	—	4	4	no	—
110	C₂²×D₁₄₉	C₂⁴	1	4	yes	—
111	Dic₂₉₈	—	2	4	no	—
112	Dic₂₉₈	—	2	4	no	—
113	D₅₉₆	—	2	4	no	—
114	D₅₉₆	—	2	4	no	—
115	C₂²⋊D₁₄₉	—	2	8	no	—
116	C₂²⋊D₁₄₉	—	2	8	no	—
117	C₂²⋊D₁₄₉	—	4	16	no	—
118	C₂×Dic₁₄₉	—	2	4	no	—
119	C₂×Dic₁₄₉	—	4	4	no	—
120	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
121	C₂×Dic₁₄₉	C₂⁴	1	8	yes	—
122	C₄×D₁₄₉	—	2	8	no	—
123	C₄×D₁₄₉	—	2	8	no	—
124	C₂³×C₁₄₉	—	2	4	no	—
125	C₂³×C₁₄₉	—	4	2	no	—
126	C₂³×C₁₄₉	—	4	4	no	—
127	C₂³×C₁₄₉	C₂×D₄	1	4	yes	—
128	C₂³×C₁₄₉	C₂⁴	1	4	yes	—
129	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
130	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
131	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
132	Q₈×C₁₄₉	—	2	4	no	—
133	Q₈×C₁₄₉	—	2	4	no	—
134	D₄×C₁₄₉	—	2	8	no	—
135	D₄×C₁₄₉	—	2	8	no	—
136	D₄×C₁₄₉	—	2	4	no	—
137	D₄×C₁₄₉	—	2	4	no	—
138	C₂×C₄×C₁₄₉	—	2	4	no	—
139	C₂×C₄×C₁₄₉	—	2	8	no	—
140	C₂×C₄×C₁₄₉	—	2	8	no	—
141	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
142	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
143	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
144	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
145	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
146	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
147	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
148	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
149	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
151	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
152	C₂²×C₁₄₉	—	2	2	no	—
153	C₂²×C₁₄₉	—	2	2	no	—
154	C₂²×C₁₄₉	—	2	2	no	—
155	C₂²×C₁₄₉	—	2	4	no	—
156	C₂²×C₁₄₉	—	2	8	no	—
157	C₂²×C₁₄₉	—	4	4	no	—
158	C₂²×C₁₄₉	—	4	8	no	—
159	C₂²×C₁₄₉	C₂²×D₄	1	2	yes	—
160	C₂²×C₁₄₉	C₂²×D₄	1	2	yes	—
161	C₂²×C₁₄₉	C₂²×D₄	1	2	yes	—
162	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
163	C₂×D₁₄₉	—	2	4	no	—
164	C₂×D₁₄₉	—	2	8	no	—
165	C₂×D₁₄₉	—	4	8	no	—
166	C₄×C₁₄₉	—	2	4	no	—
167	C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
168	C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
169	C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
170	C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
171	Dic₁₄₉	—	2	4	no	—
172	Dic₁₄₉	—	2	8	no	—
173	C₂×C₁₄₉	—	2	2	no	—
174	C₂×C₁₄₉	—	2	2	no	—
175	C₂×C₁₄₉	—	2	2	no	—
176	C₂×C₁₄₉	—	4	4	no	—
177	C₂×C₁₄₉	C₂³×D₄	1	1	yes	characteristic
178	C₂×C₁₄₉	#585	1	2	yes	—
179	D₁₄₉	—	4	4	no	—
180	C₁₄₉	#3449	1	1	yes	characteristic, complemented, Sylow
181	#3449	—	149	1	no	maximal, Sylow
182	C₂²×#41	—	149	1	no	—
183	C₂²×#41	D₁₄₉	1	1	yes	characteristic, complemented
184	#537	—	149	4	no	—
185	#536	—	149	2	no	—
186	#536	—	149	2	no	—
187	#535	—	149	2	no	—
188	#535	—	149	2	no	—
189	#534	—	149	4	no	—
190	#532	—	149	4	no	—
191	#525	—	149	4	no	—
192	#525	—	149	4	no	—
193	C₂×#117	—	149	1	no	—
194	C₂×#41	—	2	8	no	—
195	C₂×#41	—	298	8	no	—
196	C₂×#41	—	149	2	no	—
197	C₂×#41	—	149	2	no	—
198	C₂×#41	—	149	2	no	—
199	C₂×#41	—	149	2	no	—
200	C₂×#41	C₂×D₁₄₉	1	2	yes	—
201	C₂×#41	C₂×D₁₄₉	1	2	yes	—
202	C₂×#41	C₂×D₁₄₉	1	2	yes	complemented
203	C₂×#41	C₂×D₁₄₉	1	2	yes	complemented
204	C₂²×Q₈	—	149	1	no	—
205	C₂²×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
206	C₂²×D₄	—	149	2	no	—
207	C₂²×D₄	—	149	1	no	—
208	C₂²×D₄	C₂×D₁₄₉	1	2	yes	—
209	C₂²×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
210	C₂³×C₄	—	149	2	no	—
211	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic
212	C₂³×C₄	C₂×D₁₄₉	1	2	yes	complemented
213	C₄⋊Q₈	—	149	4	no	—
214	#127	—	149	4	no	—
215	#124	—	149	4	no	—
216	#124	—	149	4	no	—
217	#123	—	149	8	no	—
218	#123	—	149	8	no	—
219	C₂²⋊Q₈	—	149	8	no	—
220	C₂²⋊Q₈	—	149	8	no	—
221	#121	—	149	8	no	—
222	#121	—	149	16	no	—
223	#121	—	149	8	no	—
224	#120	—	149	8	no	—
225	#120	—	149	8	no	—
226	C₄×D₄	—	149	16	no	—
227	#117	—	149	2	no	—
228	#117	—	149	2	no	—
229	#117	—	149	2	no	—
230	#117	—	149	2	no	—
231	C₂×C₄⋊C₄	—	149	2	no	—
232	C₂×C₂²⋊C₄	—	149	2	no	—
233	C₂×C₄²	—	149	2	no	—
234	C₂⁴	—	149	2	no	—
235	C₂⁴	C₂²×D₁₄₉	1	2	yes	—
236	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
237	#41	—	2	8	no	—
238	#41	—	2	8	no	—
239	#41	—	2	8	no	—
240	#41	—	2	8	no	—
241	#41	—	298	8	no	—
242	#41	—	298	8	no	—
243	#41	—	298	8	no	—
244	#41	—	298	8	no	—
245	C₂×Q₈	—	2	4	no	—
246	C₂×Q₈	—	298	4	no	—
247	C₂×Q₈	—	149	2	no	—
248	C₂×Q₈	—	149	2	no	—
249	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
250	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	298	8	no	—
254	C₂×D₄	—	298	4	no	—
255	C₂×D₄	—	149	4	no	—
256	C₂×D₄	—	149	4	no	—
257	C₂×D₄	—	149	16	no	—
258	C₂×D₄	—	149	2	no	—
259	C₂×D₄	—	149	2	no	—
260	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
261	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
262	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
263	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	298	8	no	—
266	C₂²×C₄	—	149	2	no	—
267	C₂²×C₄	—	149	4	no	—
268	C₂²×C₄	—	149	4	no	—
269	C₂²×C₄	—	149	4	no	—
270	C₂²×C₄	C₂²⋊D₁₄₉	1	8	yes	complemented
271	C₂²×C₄	C₂²×D₁₄₉	1	4	yes	—
272	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
273	C₂²×C₄	C₂²×D₁₄₉	1	4	yes	—
274	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
279	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
280	C₄⋊C₄	—	149	4	no	—
281	C₄⋊C₄	—	149	4	no	—
282	C₄⋊C₄	—	149	16	no	—
283	C₂²⋊C₄	—	149	4	no	—
284	C₂²⋊C₄	—	149	4	no	—
285	C₂²⋊C₄	—	149	16	no	—
286	C₂²⋊C₄	—	149	16	no	—
287	C₄²	—	149	4	no	—
288	C₄²	—	149	4	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	4	2	no	—
291	C₂³	—	4	4	no	—
292	C₂³	—	298	4	no	—
293	C₂³	—	596	4	no	—
294	C₂³	—	149	4	no	—
295	C₂³	C₂×C₂²⋊D₁₄₉	1	4	yes	—
296	C₂³	C₂³×D₁₄₉	1	4	yes	—
297	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
298	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
299	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
300	Q₈	—	2	4	no	—
301	Q₈	—	2	4	no	—
302	Q₈	—	298	4	no	—
303	Q₈	—	298	4	no	—
304	D₄	—	2	8	no	—
305	D₄	—	2	8	no	—
306	D₄	—	2	4	no	—
307	D₄	—	2	4	no	—
308	D₄	—	298	8	no	—
309	D₄	—	298	8	no	—
310	D₄	—	298	4	no	—
311	D₄	—	298	4	no	—
312	D₄	—	596	16	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	298	4	no	—
317	C₂×C₄	—	298	8	no	—
318	C₂×C₄	—	298	8	no	—
319	C₂×C₄	—	596	4	no	—
320	C₂×C₄	—	149	8	no	—
321	C₂×C₄	—	149	4	no	—
322	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	4	yes	—
323	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	4	yes	—
324	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	4	yes	—
325	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	4	yes	—
326	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	4	yes	—
328	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
329	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
330	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
331	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
332	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	8	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	4	8	no	—
340	C₂²	—	298	4	no	—
341	C₂²	—	298	8	no	—
342	C₂²	—	596	8	no	—
343	C₂²	C₂²×C₂²⋊D₁₄₉	1	2	yes	—
344	C₂²	C₂²×C₂²⋊D₁₄₉	1	2	yes	—
345	C₂²	C₂²×C₂²⋊D₁₄₉	1	2	yes	—
346	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	298	4	no	—
349	C₄	—	298	8	no	—
350	C₄	C₂²×C₂²⋊D₁₄₉	1	2	yes	—
351	C₄	C₂²×C₂²⋊D₁₄₉	1	2	yes	—
352	C₄	C₂²×C₂²⋊D₁₄₉	1	2	yes	—
353	C₄	C₂²×C₂²⋊D₁₄₉	1	2	yes	—
354	C₂	—	2	2	no	—
355	C₂	—	2	2	no	—
356	C₂	—	2	2	no	—
357	C₂	—	4	4	no	—
358	C₂	—	596	4	no	—
359	C₂	C₂³×C₂²⋊D₁₄₉	1	1	yes	characteristic
360	C₂	#23750461	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₄₉
Fitting	C₂²×#41×C₁₄₉	C₂
hypercenter	C₂²×#41	D₁₄₉
hypocenter	C₁₄₉	#3449
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×#14558736	C₂	semidirect
2. #23750203	C₂	semidirect
3. #23750199	C₂	semidirect
4. #23750196	C₂	semidirect
5. #23750192	C₂	semidirect
6. #23750189	C₂	semidirect
7. #23750184	C₂	semidirect
8. #23750171	C₂	semidirect
9. #23750136	C₂	semidirect
10. #23750132	C₂	semidirect
11. C₂×#18011870	C₂	semidirect
12. C₂²×#41×C₁₄₉	C₂	semidirect
16. C₂×#14558736	C₂²	semidirect
17. C₂×#14558736	C₂²	semidirect
18. C₂²×Dic₂₉₈	C₂²	semidirect
19. C₂²×D₅₉₆	C₂²	semidirect
21. C₂²×C₄×D₁₄₉	C₂²	semidirect
22. #18011909	C₂²	semidirect
23. #18011907	C₂²	semidirect
24. #18011900	C₂²	semidirect
25. #18011898	C₂²	semidirect
26. #18011894	C₂²	semidirect
27. #18011892	C₂²	semidirect
28. #18011890	C₂²	semidirect
29. #18011887	C₂²	semidirect
30. #18011885	C₂²	semidirect
31. #18011883	C₂²	semidirect
32. #18011882	C₂²	semidirect
33. #18011880	C₂²	semidirect
34. #18011879	C₂²	semidirect
35. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
36. #18011870	C₂²	semidirect
37. #18011870	C₂²	semidirect
38. #18011870	C₂²	semidirect
39. #18011870	C₂²	semidirect
40. C₂×C₄⋊Dic₁₄₉	C₂²	semidirect
42. C₂×C₄×Dic₁₄₉	C₂²	semidirect
46. C₂×#41×C₁₄₉	C₂²	semidirect
47. C₂×#41×C₁₄₉	C₂²	semidirect
48. C₂²×Q₈×C₁₄₉	C₂²	semidirect
50. C₂²×D₄×C₁₄₉	C₂²	semidirect
52. C₂³×C₄×C₁₄₉	C₂²	semidirect
98. C₂²×C₄×C₁₄₉	D₄	semidirect
180. C₁₄₉	#3449	semidirect
183. C₂²×#41	D₁₄₉	semidirect
202. C₂×#41	C₂×D₁₄₉	semidirect
203. C₂×#41	C₂×D₁₄₉	semidirect
205. C₂²×Q₈	C₂×D₁₄₉	semidirect
209. C₂²×D₄	C₂×D₁₄₉	semidirect
212. C₂³×C₄	C₂×D₁₄₉	semidirect
270. C₂²×C₄	C₂²⋊D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14558736	2
#23750203	2
#23750199	2
#23750196	2
#23750192	2
#23750189	2
#23750184	2
#23750171	2
#23750136	2
#23750132	2
C₂×#18011870	2
C₂²×#41×C₁₄₉	2
#3449	149