Subgroups — #34058563

Order 19072.

1232 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750359	C₂	1	4	yes	maximal, complemented
2	#23750293	C₂	1	4	yes	maximal, complemented
3	#23750267	C₂	1	4	yes	maximal, complemented
4	#23750264	C₂	1	4	yes	maximal, complemented
5	#23750231	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750230	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750229	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750191	C₂	1	2	yes	maximal, complemented
9	#23750181	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750172	C₂	1	2	yes	maximal, complemented
11	#23750170	C₂	1	2	yes	maximal, complemented
12	#127×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750097	C₂	1	2	yes	maximal, complemented
14	#23750093	C₂	1	1	yes	maximal, characteristic, complemented
15	#540×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14558736	C₂²	1	1	yes	characteristic
17	C₂×#14558736	C₂²	1	4	yes	complemented
18	C₂×#14558735	C₂²	1	4	yes	complemented
19	C₂×D₄×D₁₄₉	C₂²	1	2	yes	—
20	C₂×D₄×D₁₄₉	C₂²	1	4	yes	—
21	#18011910	C₂²	1	2	yes	complemented
22	#18011908	C₂²	1	1	yes	characteristic
23	#18011907	C₂²	1	2	yes	—
24	#18011907	C₂²	1	4	yes	—
25	#18011907	C₂²	1	4	yes	complemented
26	#18011903	C₂²	1	1	yes	characteristic, complemented
27	#18011897	C₂²	1	4	yes	complemented
28	#18011897	C₂²	1	4	yes	complemented
29	#18011897	C₂²	1	4	yes	complemented
30	#18011896	C₂²	1	4	yes	complemented
31	#18011896	C₂²	1	4	yes	complemented
32	#18011892	C₂²	1	4	yes	complemented
33	#18011889	C₂²	1	4	yes	—
34	#18011886	C₂²	1	2	yes	complemented
35	#18011886	C₂²	1	4	yes	complemented
36	#18011885	C₂²	1	2	yes	complemented
37	#18011884	C₂²	1	4	yes	complemented
38	#18011884	C₂²	1	4	yes	complemented
39	#18011883	C₂²	1	4	yes	complemented
40	#18011883	C₂²	1	4	yes	complemented
41	#18011882	C₂²	1	2	yes	complemented
42	#18011881	C₂²	1	4	yes	—
43	#18011879	C₂²	1	4	yes	—
44	#18011876	C₂²	1	4	yes	complemented
45	#18011876	C₂²	1	2	yes	complemented
46	C₄×D₅₉₆	C₂²	1	2	yes	complemented
47	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
48	#18011873	C₂²	1	2	yes	—
49	#18011873	C₂²	1	2	yes	complemented
50	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
51	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
52	#18011871	C₂²	1	2	yes	—
53	#18011871	C₂²	1	4	yes	complemented
54	#18011871	C₂²	1	2	yes	complemented
55	#18011871	C₂²	1	4	yes	complemented
56	#18011869	C₂²	1	2	yes	—
57	#18011868	C₂²	1	1	yes	characteristic
58	#18011868	C₂²	1	1	yes	characteristic, complemented
59	C₂×#14558713	C₂²	1	4	yes	—
60	C₂²⋊C₄×D₁₄₉	C₂²	1	4	yes	—
61	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
62	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
63	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
64	#127×C₁₄₉	C₂²	1	1	yes	characteristic
65	#125×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
66	#123×C₁₄₉	C₂²	1	4	yes	complemented
67	#121×C₁₄₉	C₂²	1	2	yes	complemented
68	#121×C₁₄₉	C₂²	1	4	yes	complemented
69	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
70	#117×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
71	C₂³×D₁₄₉	C₂³	1	4	yes	—
72	#14558736	—	2	4	no	—
73	#14558736	—	4	8	no	—
74	#14558735	—	4	8	no	—
75	C₂×Dic₂₉₈	C₂³	1	4	yes	—
76	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
77	C₂×D₅₉₆	C₂³	1	2	yes	—
78	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
79	C₂×D₅₉₆	C₂³	1	4	yes	—
80	C₂×D₅₉₆	C₂³	1	4	yes	—
81	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
83	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
85	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
88	D₄×D₁₄₉	—	2	8	no	—
89	D₄×D₁₄₉	—	4	8	no	—
90	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
91	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
92	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
93	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
95	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
96	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
97	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
99	#14558715	C₂³	1	4	yes	—
100	#14558715	C₂³	1	2	yes	—
101	#14558715	C₂³	1	2	yes	—
102	#14558715	C₂³	1	4	yes	—
103	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
104	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
105	#14558713	C₂³	1	2	yes	—
106	#14558713	C₂³	1	4	yes	—
107	#14558713	C₂³	1	4	yes	—
108	#14558713	C₂³	1	4	yes	—
109	#14558713	C₂³	1	2	yes	—
110	#14558713	C₂³	1	4	yes	—
111	#14558713	C₂³	1	4	yes	—
112	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
113	C₄×Dic₁₄₉	C₂³	1	2	yes	—
114	C₄×Dic₁₄₉	C₂³	1	4	yes	—
115	C₄×Dic₁₄₉	C₂³	1	2	yes	—
116	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
117	C₄×Dic₁₄₉	C₂³	1	2	yes	—
118	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
119	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
120	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
121	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₁₄₉	C₂³	1	4	yes	—
123	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
124	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
125	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
126	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
127	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
128	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
129	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
130	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
131	C₂²×D₁₄₉	—	2	8	no	—
132	C₂²×D₁₄₉	—	4	4	no	—
133	C₂²×D₁₄₉	—	4	4	no	—
134	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
135	C₂²×D₁₄₉	C₂⁴	1	4	yes	—
136	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
137	Dic₂₉₈	—	2	2	no	—
138	Dic₂₉₈	—	2	8	no	—
139	D₅₉₆	—	2	2	no	—
140	D₅₉₆	—	2	4	no	—
141	D₅₉₆	—	4	4	no	—
142	D₅₉₆	—	4	4	no	—
143	C₂²⋊D₁₄₉	—	2	2	no	—
144	C₂²⋊D₁₄₉	—	2	8	no	—
145	C₂²⋊D₁₄₉	—	2	2	no	—
146	C₂²⋊D₁₄₉	—	2	8	no	—
147	C₂²⋊D₁₄₉	—	2	8	no	—
148	C₂²⋊D₁₄₉	—	4	4	no	—
149	C₂²⋊D₁₄₉	—	4	4	no	—
150	C₂×Dic₁₄₉	—	2	4	no	—
151	C₂×Dic₁₄₉	—	4	4	no	—
152	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
153	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
154	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
155	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
156	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
157	C₄×D₁₄₉	—	2	2	no	—
158	C₄×D₁₄₉	—	2	4	no	—
159	C₄×D₁₄₉	—	2	4	no	—
160	C₄×D₁₄₉	—	4	4	no	—
161	C₄×D₁₄₉	—	4	4	no	—
162	C₄×D₁₄₉	#41	1	4	yes	complemented
163	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
164	C₂³×C₁₄₉	C₂⁴	1	4	yes	—
165	D₄×C₁₄₉	—	2	4	no	—
166	D₄×C₁₄₉	—	4	4	no	—
167	D₄×C₁₄₉	—	4	4	no	—
168	C₂×C₄×C₁₄₉	—	2	2	no	—
169	C₂×C₄×C₁₄₉	—	4	4	no	—
170	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
173	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
175	C₂²×C₁₄₉	—	2	1	no	—
176	C₂²×C₁₄₉	—	2	4	no	—
177	C₂²×C₁₄₉	—	2	4	no	—
178	C₂²×C₁₄₉	—	2	2	no	—
179	C₂²×C₁₄₉	—	2	4	no	—
180	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
181	C₂×D₁₄₉	—	2	2	no	—
182	C₂×D₁₄₉	—	2	1	no	—
183	C₂×D₁₄₉	—	2	4	no	—
184	C₂×D₁₄₉	—	2	2	no	—
185	C₂×D₁₄₉	—	2	4	no	—
186	C₂×D₁₄₉	—	2	4	no	—
187	C₂×D₁₄₉	—	8	8	no	—
188	C₂×D₁₄₉	C₂×#41	1	2	yes	—
189	C₄×C₁₄₉	—	2	1	no	—
190	C₄×C₁₄₉	—	2	2	no	—
191	C₄×C₁₄₉	—	2	4	no	—
192	C₄×C₁₄₉	—	2	2	no	—
193	C₄×C₁₄₉	C₂×#41	1	2	yes	—
194	Dic₁₄₉	—	2	1	no	—
195	Dic₁₄₉	—	2	2	no	—
196	Dic₁₄₉	—	2	4	no	—
197	Dic₁₄₉	C₂×#41	1	2	yes	—
198	Dic₁₄₉	H(5,𝔽₂)	1	4	yes	—
199	C₂×C₁₄₉	—	4	4	no	—
200	C₂×C₁₄₉	—	4	1	no	—
201	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
202	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	2	yes	—
203	D₁₄₉	—	2	2	no	—
204	D₁₄₉	—	4	1	no	—
205	D₁₄₉	—	4	4	no	—
206	C₁₄₉	#3508	1	1	yes	characteristic, complemented, Sylow
207	#3508	—	149	1	no	maximal, Sylow
208	#559	—	149	4	no	—
209	#550	—	149	4	no	—
210	#546	—	149	4	no	—
211	#546	—	149	4	no	—
212	#540	—	149	1	no	—
213	#540	—	149	1	no	—
214	#540	—	149	1	no	—
215	#540	D₁₄₉	1	1	yes	characteristic, complemented
216	#535	—	149	2	no	—
217	#533	—	149	1	no	—
218	#532	—	149	2	no	—
219	#532	—	149	2	no	—
220	C₂×#127	—	149	1	no	—
221	#518	—	149	2	no	—
222	C₄×#41	—	149	1	no	—
223	C₂×#41	—	149	4	no	—
224	C₂×#41	—	149	1	no	—
225	C₂×#41	—	149	4	no	—
226	C₂²×D₄	—	149	2	no	—
227	C₂²×D₄	—	149	4	no	—
228	C₄⋊Q₈	—	149	2	no	—
229	#127	—	149	2	no	—
230	#127	—	149	4	no	—
231	#127	—	149	4	no	—
232	#127	—	149	1	no	—
233	#127	C₂×D₁₄₉	1	1	yes	characteristic
234	#125	—	149	1	no	—
235	#125	C₂×D₁₄₉	1	1	yes	characteristic, complemented
236	#124	—	149	4	no	—
237	#124	—	149	4	no	—
238	#124	—	149	4	no	—
239	#123	—	149	4	no	—
240	#123	—	149	4	no	—
241	#123	—	149	4	no	—
242	#123	C₂×D₁₄₉	1	4	yes	complemented
243	C₂²⋊Q₈	—	149	4	no	—
244	#121	—	149	2	no	—
245	#121	—	149	4	no	—
246	#121	—	149	4	no	—
247	#121	—	149	2	no	—
248	#121	—	149	2	no	—
249	#121	—	149	4	no	—
250	#121	—	149	4	no	—
251	#121	—	149	4	no	—
252	#121	C₂×D₁₄₉	1	2	yes	complemented
253	#121	C₂×D₁₄₉	1	4	yes	complemented
254	#120	—	149	4	no	—
255	#120	—	149	4	no	—
256	C₄×Q₈	—	149	2	no	—
257	C₄×Q₈	—	149	4	no	—
258	C₄×D₄	—	149	2	no	—
259	C₄×D₄	—	149	4	no	—
260	C₄×D₄	—	149	4	no	—
261	C₄×D₄	—	149	2	no	—
262	C₄×D₄	—	149	2	no	—
263	C₄×D₄	—	149	2	no	—
264	C₄×D₄	—	149	2	no	—
265	C₄×D₄	—	149	4	no	—
266	C₄×D₄	—	149	4	no	—
267	C₄×D₄	—	149	2	no	—
268	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
269	#117	—	149	2	no	—
270	#117	—	149	1	no	—
271	#117	—	149	1	no	—
272	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
273	C₂×C₂²⋊C₄	—	149	4	no	—
274	C₂×C₂²⋊C₄	—	149	4	no	—
275	C₂×C₄²	—	149	1	no	—
276	C₂×C₄²	—	149	1	no	—
277	C₂×C₄²	—	149	1	no	—
278	C₂⁴	—	149	4	no	—
279	#41	—	298	4	no	—
280	#41	—	596	8	no	—
281	#41	—	596	8	no	—
282	C₂×Q₈	—	149	1	no	—
283	C₂×Q₈	—	149	4	no	—
284	C₂×D₄	—	298	8	no	—
285	C₂×D₄	—	596	8	no	—
286	C₂×D₄	—	149	1	no	—
287	C₂×D₄	—	149	4	no	—
288	C₂×D₄	—	149	1	no	—
289	C₂×D₄	—	149	4	no	—
290	C₂×D₄	—	149	4	no	—
291	C₂×D₄	—	149	4	no	—
292	C₂×D₄	—	149	4	no	—
293	C₂×D₄	—	149	1	no	—
294	C₂×D₄	—	149	2	no	—
295	C₂×D₄	—	149	4	no	—
296	C₂×D₄	—	149	4	no	—
297	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
298	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
299	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
300	C₂²×C₄	—	149	2	no	—
301	C₂²×C₄	—	149	1	no	—
302	C₂²×C₄	—	149	2	no	—
303	C₂²×C₄	—	149	2	no	—
304	C₂²×C₄	—	149	4	no	—
305	C₂²×C₄	—	149	4	no	—
306	C₂²×C₄	—	149	4	no	—
307	C₂²×C₄	—	149	1	no	—
308	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
309	C₂²×C₄	C₂²×D₁₄₉	1	4	yes	—
310	C₄⋊C₄	—	149	2	no	—
311	C₄⋊C₄	—	149	2	no	—
312	C₄⋊C₄	—	149	2	no	—
313	C₄⋊C₄	—	149	4	no	—
314	C₄⋊C₄	—	149	4	no	—
315	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
316	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
317	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
318	C₂²⋊C₄	—	149	4	no	—
319	C₂²⋊C₄	—	149	4	no	—
320	C₂²⋊C₄	—	149	2	no	—
321	C₂²⋊C₄	—	149	4	no	—
322	C₂²⋊C₄	—	149	4	no	—
323	C₂²⋊C₄	—	149	4	no	—
324	C₂²⋊C₄	—	149	2	no	—
325	C₂²⋊C₄	—	149	4	no	—
326	C₂²⋊C₄	—	149	4	no	—
327	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
328	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
329	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
330	C₄²	—	149	1	no	—
331	C₄²	—	149	1	no	—
332	C₄²	—	149	2	no	—
333	C₄²	—	149	2	no	—
334	C₄²	—	149	2	no	—
335	C₄²	—	149	4	no	—
336	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
337	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
338	C₂³	—	298	8	no	—
339	C₂³	—	596	4	no	—
340	C₂³	—	596	4	no	—
341	C₂³	—	149	4	no	—
342	C₂³	—	149	1	no	—
343	C₂³	—	149	1	no	—
344	C₂³	C₂³×D₁₄₉	1	4	yes	—
345	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
346	Q₈	—	298	2	no	—
347	Q₈	—	298	8	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	298	2	no	—
352	D₄	—	298	2	no	—
353	D₄	—	298	8	no	—
354	D₄	—	298	8	no	—
355	D₄	—	298	8	no	—
356	D₄	—	298	2	no	—
357	D₄	—	298	4	no	—
358	D₄	—	596	4	no	—
359	D₄	—	596	4	no	—
360	D₄	—	596	4	no	—
361	D₄	—	596	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	298	4	no	—
365	C₂×C₄	—	298	4	no	—
366	C₂×C₄	—	298	4	no	—
367	C₂×C₄	—	298	2	no	—
368	C₂×C₄	—	596	4	no	—
369	C₂×C₄	—	596	4	no	—
370	C₂×C₄	—	596	4	no	—
371	C₂×C₄	—	149	1	no	—
372	C₂×C₄	—	149	2	no	—
373	C₂×C₄	—	149	4	no	—
374	C₂×C₄	—	149	1	no	—
375	C₂×C₄	—	149	2	no	—
376	C₂×C₄	—	149	4	no	—
377	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
379	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
380	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
381	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
382	C₂²	—	2	1	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	298	2	no	—
388	C₂²	—	298	1	no	—
389	C₂²	—	298	4	no	—
390	C₂²	—	298	2	no	—
391	C₂²	—	298	4	no	—
392	C₂²	—	298	4	no	—
393	C₂²	—	149	2	no	—
394	C₂²	—	1192	8	no	—
395	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	298	1	no	—
401	C₄	—	298	2	no	—
402	C₄	—	298	4	no	—
403	C₄	—	149	2	no	—
404	C₄	—	149	4	no	—
405	C₄	#41×D₁₄₉	1	2	yes	—
406	C₂	—	4	4	no	—
407	C₂	—	4	1	no	—
408	C₂	—	298	2	no	—
409	C₂	—	596	4	no	—
410	C₂	—	596	1	no	—
411	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
412	C₂	H(5,𝔽₂)×D₁₄₉	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#540×C₁₄₉	C₂
hypercenter	#540	D₁₄₉
hypocenter	C₁₄₉	#3508
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #23750359	C₂	semidirect
2. #23750293	C₂	semidirect
3. #23750267	C₂	semidirect
4. #23750264	C₂	semidirect
5. #23750231	C₂	semidirect
6. #23750230	C₂	semidirect
7. #23750229	C₂	semidirect
8. #23750191	C₂	semidirect
9. #23750181	C₂	semidirect
10. #23750172	C₂	semidirect
11. #23750170	C₂	semidirect
12. #127×D₁₄₉	C₂	semidirect
13. #23750097	C₂	semidirect
14. #23750093	C₂	semidirect
15. #540×C₁₄₉	C₂	semidirect
17. C₂×#14558736	C₂²	semidirect
18. C₂×#14558735	C₂²	semidirect
21. #18011910	C₂²	semidirect
25. #18011907	C₂²	semidirect
26. #18011903	C₂²	semidirect
27. #18011897	C₂²	semidirect
28. #18011897	C₂²	semidirect
29. #18011897	C₂²	semidirect
30. #18011896	C₂²	semidirect
31. #18011896	C₂²	semidirect
32. #18011892	C₂²	semidirect
34. #18011886	C₂²	semidirect
35. #18011886	C₂²	semidirect
36. #18011885	C₂²	semidirect
37. #18011884	C₂²	semidirect
38. #18011884	C₂²	semidirect
39. #18011883	C₂²	semidirect
40. #18011883	C₂²	semidirect
41. #18011882	C₂²	semidirect
44. #18011876	C₂²	semidirect
45. #18011876	C₂²	semidirect
46. C₄×D₅₉₆	C₂²	semidirect
47. D₄×Dic₁₄₉	C₂²	semidirect
49. #18011873	C₂²	semidirect
50. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
51. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
53. #18011871	C₂²	semidirect
54. #18011871	C₂²	semidirect
55. #18011871	C₂²	semidirect
58. #18011868	C₂²	semidirect
61. C₂×C₄×Dic₁₄₉	C₂²	semidirect
63. C₄²×D₁₄₉	C₂²	semidirect
65. #125×C₁₄₉	C₂²	semidirect
66. #123×C₁₄₉	C₂²	semidirect
67. #121×C₁₄₉	C₂²	semidirect
68. #121×C₁₄₉	C₂²	semidirect
69. C₄×D₄×C₁₄₉	C₂²	semidirect
70. #117×C₁₄₉	C₂²	semidirect
162. C₄×D₁₄₉	#41	semidirect
206. C₁₄₉	#3508	semidirect
215. #540	D₁₄₉	semidirect
235. #125	C₂×D₁₄₉	semidirect
242. #123	C₂×D₁₄₉	semidirect
252. #121	C₂×D₁₄₉	semidirect
253. #121	C₂×D₁₄₉	semidirect
268. C₄×D₄	C₂×D₁₄₉	semidirect
272. #117	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750359	2
#23750293	2
#23750267	2
#23750264	2
#23750231	2
#23750230	2
#23750229	2
#23750191	2
#23750181	2
#23750172	2
#23750170	2
#127×D₁₄₉	2
#23750097	2
#23750093	2
#540×C₁₄₉	2
#3508	149