Subgroups — #34058079

Order 19072.

1040 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750248	C₂	1	2	yes	maximal, complemented
2	#23750242	C₂	1	2	yes	maximal, complemented
3	#23750235	C₂	1	2	yes	maximal, complemented
4	#23750228	C₂	1	2	yes	maximal, complemented
5	#23750219	C₂	1	4	yes	maximal, complemented
6	#23750210	C₂	1	4	yes	maximal, complemented
7	#23750178	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750171	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750157	C₂	1	4	yes	maximal, complemented
10	#23750155	C₂	1	4	yes	maximal, complemented
11	#23750136	C₂	1	1	yes	maximal, characteristic, complemented
12	#41×Dic₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#18011870	C₂	1	1	yes	maximal, characteristic, complemented
15	#525×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14558736	C₂²	1	1	yes	characteristic
17	#18011910	C₂²	1	2	yes	complemented
18	#18011909	C₂²	1	1	yes	characteristic, complemented
19	#18011907	C₂²	1	1	yes	characteristic, complemented
20	#18011906	C₂²	1	4	yes	complemented
21	#18011904	C₂²	1	4	yes	—
22	#18011904	C₂²	1	4	yes	—
23	#18011904	C₂²	1	4	yes	complemented
24	#18011902	C₂²	1	4	yes	complemented
25	#18011902	C₂²	1	2	yes	complemented
26	#18011901	C₂²	1	4	yes	complemented
27	#18011900	C₂²	1	1	yes	characteristic, complemented
28	#18011898	C₂²	1	4	yes	—
29	#18011898	C₂²	1	1	yes	characteristic, complemented
30	#18011897	C₂²	1	4	yes	—
31	#18011895	C₂²	1	4	yes	complemented
32	#18011894	C₂²	1	2	yes	—
33	#18011893	C₂²	1	4	yes	—
34	#18011893	C₂²	1	4	yes	complemented
35	#18011892	C₂²	1	4	yes	—
36	#18011891	C₂²	1	4	yes	complemented
37	#18011890	C₂²	1	2	yes	—
38	#18011888	C₂²	1	4	yes	—
39	#18011888	C₂²	1	4	yes	complemented
40	#18011885	C₂²	1	2	yes	—
41	#18011883	C₂²	1	4	yes	—
42	#18011883	C₂²	1	4	yes	—
43	#18011882	C₂²	1	4	yes	—
44	#18011880	C₂²	1	2	yes	—
45	Q₈×Dic₁₄₉	C₂²	1	2	yes	complemented
46	C₄×Dic₂₉₈	C₂²	1	4	yes	complemented
47	#18011876	C₂²	1	2	yes	complemented
48	D₄×Dic₁₄₉	C₂²	1	4	yes	—
49	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
50	#18011873	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	—
52	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
53	#18011871	C₂²	1	4	yes	—
54	#18011870	C₂²	1	2	yes	—
55	#18011870	C₂²	1	2	yes	—
56	#18011870	C₂²	1	1	yes	characteristic
57	#18011870	C₂²	1	2	yes	—
58	#18011870	C₂²	1	2	yes	—
59	#18011870	C₂²	1	2	yes	complemented
60	#18011868	C₂²	1	2	yes	complemented
61	C₂×C₄⋊Dic₁₄₉	C₂²	1	2	yes	—
62	C₂×C₂²⋊Dic₁₄₉	C₂²	1	2	yes	—
63	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
64	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
65	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	complemented
66	C₄²×D₁₄₉	C₂²	1	2	yes	complemented
67	C₂×#41×C₁₄₉	C₂²	1	1	yes	characteristic
68	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
69	#123×C₁₄₉	C₂²	1	2	yes	—
70	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
71	#121×C₁₄₉	C₂²	1	2	yes	—
72	#120×C₁₄₉	C₂²	1	2	yes	—
73	C₄×D₄×C₁₄₉	C₂²	1	4	yes	—
74	#117×C₁₄₉	C₂²	1	1	yes	characteristic
75	#14558736	—	2	4	no	—
76	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
77	C₂×Dic₂₉₈	C₂³	1	4	yes	—
78	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
80	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
81	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
82	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
83	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
84	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
85	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
86	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
87	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
88	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
89	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
90	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
91	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
92	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
93	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
94	#14558715	C₂³	1	4	yes	—
95	#14558715	C₂³	1	4	yes	—
96	#14558715	C₂³	1	4	yes	—
97	#14558715	C₂³	1	4	yes	—
98	#14558715	C₂³	1	4	yes	—
99	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
100	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
101	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
102	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
103	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
104	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
105	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
106	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
107	#14558713	C₂³	1	4	yes	—
108	#14558713	C₂³	1	4	yes	—
109	#14558713	C₂³	1	4	yes	—
110	C₄×Dic₁₄₉	C₂³	1	4	yes	—
111	C₄×Dic₁₄₉	C₂³	1	4	yes	—
112	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
113	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
114	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
115	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
116	C₄×Dic₁₄₉	C₂³	1	2	yes	—
117	C₄×Dic₁₄₉	C₂³	1	2	yes	—
118	C₄×Dic₁₄₉	C₂³	1	2	yes	—
119	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
120	#41×C₁₄₉	—	2	4	no	—
121	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
122	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
123	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
124	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
125	C₂²×C₄×C₁₄₉	—	2	4	no	—
126	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
127	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
131	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
132	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
133	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
134	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
135	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
136	C₄²×C₁₄₉	C₂³	1	2	yes	—
137	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
138	Dic₂₉₈	—	2	2	no	—
139	Dic₂₉₈	—	4	4	no	—
140	D₅₉₆	—	2	2	no	—
141	C₂²⋊D₁₄₉	—	2	4	no	—
142	C₂²⋊D₁₄₉	—	4	4	no	—
143	C₂²⋊D₁₄₉	—	4	4	no	—
144	C₂×Dic₁₄₉	—	4	2	no	—
145	C₂×Dic₁₄₉	—	4	4	no	—
146	C₂×Dic₁₄₉	—	4	2	no	—
147	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
148	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
149	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
150	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
151	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
152	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
153	C₄×D₁₄₉	—	2	4	no	—
154	C₄×D₁₄₉	—	4	4	no	—
155	C₂³×C₁₄₉	—	2	2	no	—
156	C₂³×C₁₄₉	—	4	2	no	—
157	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
158	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
159	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
160	Q₈×C₁₄₉	—	2	2	no	—
161	D₄×C₁₄₉	—	2	4	no	—
162	D₄×C₁₄₉	—	2	2	no	—
163	D₄×C₁₄₉	—	4	4	no	—
164	C₂×C₄×C₁₄₉	—	2	2	no	—
165	C₂×C₄×C₁₄₉	—	2	4	no	—
166	C₂×C₄×C₁₄₉	—	2	4	no	—
167	C₂×C₄×C₁₄₉	—	2	4	no	—
168	C₂×C₄×C₁₄₉	#41	1	4	yes	—
169	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
170	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
174	C₂²×C₁₄₉	—	2	2	no	—
175	C₂²×C₁₄₉	—	2	2	no	—
176	C₂²×C₁₄₉	—	2	2	no	—
177	C₂²×C₁₄₉	—	2	2	no	—
178	C₂²×C₁₄₉	—	2	4	no	—
179	C₂²×C₁₄₉	—	2	2	no	—
180	C₂²×C₁₄₉	—	4	4	no	—
181	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
182	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
183	C₂×D₁₄₉	—	2	2	no	—
184	C₂×D₁₄₉	—	2	4	no	—
185	C₄×C₁₄₉	—	2	2	no	—
186	C₄×C₁₄₉	—	2	2	no	—
187	C₄×C₁₄₉	—	2	4	no	—
188	C₄×C₁₄₉	C₂×#41	1	2	yes	—
189	C₄×C₁₄₉	C₂×#41	1	2	yes	—
190	Dic₁₄₉	—	2	2	no	—
191	Dic₁₄₉	—	2	2	no	—
192	Dic₁₄₉	—	2	2	no	—
193	Dic₁₄₉	—	2	2	no	—
194	Dic₁₄₉	—	2	4	no	—
195	Dic₁₄₉	—	2	2	no	—
196	C₂×C₁₄₉	—	2	2	no	—
197	C₂×C₁₄₉	—	4	2	no	—
198	C₂×C₁₄₉	—	4	2	no	—
199	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
200	C₂×C₁₄₉	#585	1	2	yes	—
201	D₁₄₉	—	4	2	no	—
202	C₁₄₉	#3455	1	1	yes	characteristic, complemented, Sylow
203	#3455	—	149	1	no	maximal, Sylow
204	#542	—	149	2	no	—
205	#542	—	149	2	no	—
206	#541	—	149	2	no	—
207	#540	—	149	2	no	—
208	#539	—	149	4	no	—
209	#538	—	149	4	no	—
210	#533	—	149	1	no	—
211	#532	—	149	1	no	—
212	#529	—	149	4	no	—
213	#529	—	149	4	no	—
214	#525	—	149	1	no	—
215	#525	D₁₄₉	1	1	yes	characteristic, complemented
216	C₄×#41	—	149	1	no	—
217	C₄×#41	—	149	1	no	—
218	C₂×#117	—	149	1	no	—
219	C₂×#41	—	149	1	no	—
220	C₂×#41	C₂×D₁₄₉	1	1	yes	characteristic
221	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic
222	C₄⋊Q₈	—	149	1	no	—
223	C₄⋊Q₈	—	149	2	no	—
224	#127	—	149	1	no	—
225	#126	—	149	4	no	—
226	#126	—	149	4	no	—
227	#126	—	149	4	no	—
228	#126	—	149	4	no	—
229	#125	—	149	4	no	—
230	#125	—	149	4	no	—
231	#125	—	149	2	no	—
232	#124	—	149	1	no	—
233	#124	—	149	4	no	—
234	#124	—	149	1	no	—
235	#124	—	149	4	no	—
236	#123	—	149	4	no	—
237	#123	—	149	2	no	—
238	#123	—	149	4	no	—
239	#123	—	149	4	no	—
240	#123	—	149	4	no	—
241	#123	C₂×D₁₄₉	1	2	yes	—
242	C₂²⋊Q₈	—	149	2	no	—
243	C₂²⋊Q₈	—	149	4	no	—
244	C₂²⋊Q₈	—	149	4	no	—
245	C₂²⋊Q₈	—	149	4	no	—
246	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
247	#121	—	149	4	no	—
248	#121	—	149	4	no	—
249	#121	—	149	4	no	—
250	#121	—	149	2	no	—
251	#121	C₂×D₁₄₉	1	2	yes	—
252	#120	—	149	2	no	—
253	#120	C₂×D₁₄₉	1	2	yes	—
254	C₄×Q₈	—	149	2	no	—
255	C₄×Q₈	—	149	2	no	—
256	C₄×Q₈	—	149	4	no	—
257	C₄×D₄	—	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	4	no	—
263	C₄×D₄	C₂×D₁₄₉	1	4	yes	—
264	#117	—	149	2	no	—
265	#117	—	149	2	no	—
266	#117	—	149	2	no	—
267	#117	—	149	2	no	—
268	#117	—	149	1	no	—
269	#117	—	149	2	no	—
270	#117	—	149	2	no	—
271	#117	C₂×D₁₄₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	—	149	2	no	—
273	C₂×C₂²⋊C₄	—	149	2	no	—
274	C₂×C₄²	—	149	1	no	—
275	C₂×C₄²	—	149	1	no	—
276	C₂×C₄²	—	149	2	no	—
277	C₂×C₄²	—	149	2	no	—
278	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
279	#41	—	2	4	no	—
280	#41	—	298	4	no	—
281	C₂×Q₈	—	149	1	no	—
282	C₂×Q₈	—	149	4	no	—
283	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
284	C₂×D₄	—	149	2	no	—
285	C₂×D₄	—	149	4	no	—
286	C₂×D₄	—	149	4	no	—
287	C₂×D₄	—	149	1	no	—
288	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
289	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
290	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	149	2	no	—
293	C₂²×C₄	—	149	2	no	—
294	C₂²×C₄	—	149	2	no	—
295	C₂²×C₄	—	149	4	no	—
296	C₂²×C₄	—	149	4	no	—
297	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
298	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
299	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
300	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
301	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
302	C₄⋊C₄	—	149	2	no	—
303	C₄⋊C₄	—	149	2	no	—
304	C₄⋊C₄	—	149	2	no	—
305	C₄⋊C₄	—	149	2	no	—
306	C₄⋊C₄	—	149	2	no	—
307	C₄⋊C₄	—	149	4	no	—
308	C₄⋊C₄	—	149	4	no	—
309	C₄⋊C₄	—	149	4	no	—
310	C₄⋊C₄	—	149	4	no	—
311	C₄⋊C₄	—	149	4	no	—
312	C₄⋊C₄	—	149	4	no	—
313	C₄⋊C₄	—	149	4	no	—
314	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
315	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
316	C₂²⋊C₄	—	149	2	no	—
317	C₂²⋊C₄	—	149	2	no	—
318	C₂²⋊C₄	—	149	2	no	—
319	C₂²⋊C₄	—	149	2	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	4	no	—
325	C₂²⋊C₄	—	149	4	no	—
326	C₂²⋊C₄	—	149	4	no	—
327	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
328	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
329	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
330	C₄²	—	149	2	no	—
331	C₄²	—	149	1	no	—
332	C₄²	—	149	1	no	—
333	C₄²	—	149	4	no	—
334	C₄²	—	149	4	no	—
335	C₄²	—	149	1	no	—
336	C₄²	—	149	1	no	—
337	C₄²	—	149	2	no	—
338	C₄²	—	149	2	no	—
339	C₄²	C₂²×D₁₄₉	1	2	yes	—
340	C₂³	—	2	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	149	2	no	—
343	C₂³	C₂³×D₁₄₉	1	2	yes	—
344	C₂³	C₂³×D₁₄₉	1	2	yes	—
345	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
346	Q₈	—	2	2	no	—
347	Q₈	—	298	2	no	—
348	Q₈	—	596	4	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	2	no	—
351	D₄	—	4	4	no	—
352	D₄	—	298	4	no	—
353	D₄	—	298	2	no	—
354	D₄	—	596	4	no	—
355	D₄	—	596	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	298	4	no	—
361	C₂×C₄	—	596	4	no	—
362	C₂×C₄	—	596	2	no	—
363	C₂×C₄	—	596	4	no	—
364	C₂×C₄	—	596	2	no	—
365	C₂×C₄	—	149	2	no	—
366	C₂×C₄	—	149	2	no	—
367	C₂×C₄	—	149	2	no	—
368	C₂×C₄	—	149	2	no	—
369	C₂×C₄	—	149	4	no	—
370	C₂×C₄	—	149	2	no	—
371	C₂×C₄	#14558735	1	4	yes	—
372	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
373	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
374	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
375	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	298	2	no	—
385	C₂²	—	298	4	no	—
386	C₂²	C₂×#14558735	1	2	yes	—
387	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	4	no	—
391	C₄	—	298	2	no	—
392	C₄	—	298	2	no	—
393	C₄	—	298	2	no	—
394	C₄	—	298	2	no	—
395	C₄	—	298	4	no	—
396	C₄	—	298	2	no	—
397	C₄	C₂×#14558735	1	2	yes	—
398	C₄	C₂×#14558735	1	2	yes	—
399	C₂	—	2	2	no	—
400	C₂	—	4	2	no	—
401	C₂	—	4	2	no	—
402	C₂	—	596	2	no	—
403	C₂	C₂²×#14558735	1	1	yes	characteristic
404	C₂	#23750461	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₄₉
Fitting	#525×C₁₄₉	C₂
hypercenter	#525	D₁₄₉
hypocenter	C₁₄₉	#3455
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #23750248	C₂	semidirect
2. #23750242	C₂	semidirect
3. #23750235	C₂	semidirect
4. #23750228	C₂	semidirect
5. #23750219	C₂	semidirect
6. #23750210	C₂	semidirect
7. #23750178	C₂	semidirect
8. #23750171	C₂	semidirect
9. #23750157	C₂	semidirect
10. #23750155	C₂	semidirect
11. #23750136	C₂	semidirect
12. #41×Dic₁₄₉	C₂	semidirect
13. #23750093	C₂	semidirect
14. C₂×#18011870	C₂	semidirect
15. #525×C₁₄₉	C₂	semidirect
17. #18011910	C₂²	semidirect
18. #18011909	C₂²	semidirect
19. #18011907	C₂²	semidirect
20. #18011906	C₂²	semidirect
23. #18011904	C₂²	semidirect
24. #18011902	C₂²	semidirect
25. #18011902	C₂²	semidirect
26. #18011901	C₂²	semidirect
27. #18011900	C₂²	semidirect
29. #18011898	C₂²	semidirect
31. #18011895	C₂²	semidirect
34. #18011893	C₂²	semidirect
36. #18011891	C₂²	semidirect
39. #18011888	C₂²	semidirect
45. Q₈×Dic₁₄₉	C₂²	semidirect
46. C₄×Dic₂₉₈	C₂²	semidirect
47. #18011876	C₂²	semidirect
49. D₄×Dic₁₄₉	C₂²	semidirect
50. #18011873	C₂²	semidirect
52. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
59. #18011870	C₂²	semidirect
60. #18011868	C₂²	semidirect
65. C₂×C₄×Dic₁₄₉	C₂²	semidirect
66. C₄²×D₁₄₉	C₂²	semidirect
202. C₁₄₉	#3455	semidirect
215. #525	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750248	2
#23750242	2
#23750235	2
#23750228	2
#23750219	2
#23750210	2
#23750178	2
#23750171	2
#23750157	2
#23750155	2
#23750136	2
#41×Dic₁₄₉	2
#23750093	2
C₂×#18011870	2
#525×C₁₄₉	2
#3455	149