Subgroups — #34053391

Order 19072.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18011919	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750134	C₂	1	1	yes	maximal, characteristic
4	#23749704	C₂	1	1	yes	maximal, characteristic, complemented
5	#23749701	C₂	1	1	yes	maximal, characteristic, complemented
6	#23749701	C₂	1	1	yes	maximal, characteristic, complemented
7	#23749699	C₂	1	1	yes	maximal, characteristic, complemented
8	#23749697	C₂	1	1	yes	maximal, characteristic, complemented
9	#23749695	C₂	1	1	yes	maximal, characteristic, complemented
10	#23749693	C₂	1	1	yes	maximal, characteristic, complemented
11	#23749650	C₂	1	1	yes	maximal, characteristic, complemented
12	#23749590	C₂	1	1	yes	maximal, characteristic, complemented
13	#23749587	C₂	1	1	yes	maximal, characteristic, complemented
14	#23749579	C₂	1	1	yes	maximal, characteristic, complemented
15	#436×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14558736	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
18	#18011919	—	2	4	no	—
19	C₂×#14558720	C₂²	1	1	yes	characteristic
20	C₂×#14558719	C₂²	1	1	yes	characteristic
21	C₂×#14558719	C₂²	1	1	yes	characteristic
22	C₂×#14558719	C₂²	1	1	yes	characteristic
23	C₂×#14558719	C₂²	1	1	yes	characteristic
24	C₂×#14558719	C₂²	1	1	yes	characteristic, complemented
25	M₁₆×D₁₄₉	—	2	4	no	—
26	C₂²×#11924746	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₈×D₁₄₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₄₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
30	#18011896	C₄	1	1	yes	characteristic
31	#18011893	C₄	1	1	yes	characteristic
32	#18011889	C₄	1	1	yes	characteristic
33	#18011888	C₄	1	1	yes	characteristic
34	#18011884	C₄	1	1	yes	characteristic
35	#18011883	C₄	1	1	yes	characteristic
36	#18011881	C₄	1	1	yes	characteristic
37	#18011879	C₄	1	1	yes	characteristic
38	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
41	#18011868	C₂²	1	1	yes	characteristic
42	C₄⋊#11924746	C₂²	1	1	yes	characteristic, complemented
43	#18011840	C₂²	1	1	yes	characteristic, complemented
44	#18011840	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊#11924746	C₂²	1	1	yes	characteristic
46	C₂²⋊#11924746	C₂²	1	1	yes	characteristic, complemented
47	#18011823	C₂²	1	1	yes	characteristic
48	#18011823	C₂²	1	1	yes	characteristic
49	#18011823	C₂²	1	1	yes	characteristic, complemented
50	#18011823	C₂²	1	1	yes	characteristic, complemented
51	#18011822	C₂²	1	1	yes	characteristic, complemented
52	#18011821	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₁₆×C₁₄₉	C₂²	1	1	yes	characteristic
55	C₂×M₁₆×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₁₄₉	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₄₉	C₂×C₄	1	1	yes	characteristic
62	#14558736	—	2	2	no	—
63	#14558736	—	2	2	no	—
64	C₂×Dic₂₉₈	C₂×C₄	1	1	yes	characteristic
65	C₂×D₅₉₆	C₂×C₄	1	1	yes	characteristic
66	C₂×D₅₉₆	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₄₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₁₄₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊D₁₄₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₄₉	C₂×C₄	1	1	yes	characteristic
71	C₂²×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₁₄₉	—	2	2	no	—
73	C₂×C₄×D₁₄₉	—	2	2	no	—
74	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
79	#14558720	—	2	2	no	—
80	#14558719	—	2	2	no	—
81	#14558719	—	2	2	no	—
82	#14558719	—	2	2	no	—
83	#14558719	—	2	2	no	—
84	#14558719	—	2	2	no	—
85	C₂×#11924746	—	2	2	no	—
86	C₂×#11924746	C₂³	1	1	yes	characteristic
87	C₂×#11924746	C₂³	1	1	yes	characteristic
88	C₂×#11924746	C₂³	1	1	yes	characteristic
89	C₂×#11924746	C₂³	1	1	yes	characteristic
90	C₈×D₁₄₉	—	2	2	no	—
91	C₈×D₁₄₉	—	2	2	no	—
92	C₈×D₁₄₉	D₄	1	4	yes	complemented
93	C₄⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
94	#14558715	C₂×C₄	1	1	yes	characteristic
95	#14558715	C₂×C₄	1	1	yes	characteristic
96	#14558715	C₂×C₄	1	1	yes	characteristic
97	#14558715	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
100	#14558713	C₂×C₄	1	1	yes	characteristic
101	#14558713	C₂×C₄	1	1	yes	characteristic
102	#14558713	C₂×C₄	1	1	yes	characteristic
103	#14558713	C₂×C₄	1	1	yes	characteristic
104	#14558713	C₂×C₄	1	1	yes	characteristic
105	#14558713	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
110	M₁₆×C₁₄₉	—	2	2	no	—
111	M₁₆×C₁₄₉	—	2	2	no	—
112	C₂×C₈×C₁₄₉	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₁₄₉	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₁₄₉	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₄₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
119	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
120	C₂²×D₁₄₉	—	2	2	no	—
121	C₂²×D₁₄₉	—	4	1	no	—
122	C₂²×D₁₄₉	—	4	1	no	—
123	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
126	Dic₂₉₈	—	2	2	no	—
127	D₅₉₆	—	2	2	no	—
128	D₅₉₆	—	4	1	no	—
129	C₂²⋊D₁₄₉	—	2	2	no	—
130	C₂²⋊D₁₄₉	—	2	2	no	—
131	C₂²⋊D₁₄₉	—	4	1	no	—
132	C₂²⋊D₁₄₉	—	4	1	no	—
133	C₂×Dic₁₄₉	—	2	2	no	—
134	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
139	C₄×D₁₄₉	—	2	2	no	—
140	C₄×D₁₄₉	—	2	1	no	—
141	C₄×D₁₄₉	—	2	1	no	—
142	C₄×D₁₄₉	—	2	1	no	—
143	C₄×D₁₄₉	—	2	1	no	—
144	C₄×D₁₄₉	—	2	2	no	—
145	C₄×D₁₄₉	C₂×D₄	1	2	yes	—
146	C₄×D₁₄₉	#41	1	2	yes	—
147	#11924746	—	2	1	no	—
148	#11924746	—	2	1	no	—
149	#11924746	—	2	1	no	—
150	#11924746	C₂×D₄	1	2	yes	—
151	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
152	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
153	D₄×C₁₄₉	—	4	1	no	—
154	C₂×C₄×C₁₄₉	—	2	1	no	—
155	C₂×C₄×C₁₄₉	—	2	1	no	—
156	C₂×C₄×C₁₄₉	—	2	1	no	—
157	C₂×C₄×C₁₄₉	—	2	1	no	—
158	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
163	C₈×C₁₄₉	—	2	1	no	—
164	C₈×C₁₄₉	—	2	1	no	—
165	C₈×C₁₄₉	—	2	1	no	—
166	C₈×C₁₄₉	C₂×D₄	1	2	yes	—
167	C₂²×C₁₄₉	—	2	1	no	—
168	C₂²×C₁₄₉	—	2	1	no	—
169	C₂²×C₁₄₉	—	2	1	no	—
170	C₂²×C₁₄₉	—	2	1	no	—
171	C₂²×C₁₄₉	—	2	1	no	—
172	C₂²×C₁₄₉	—	2	1	no	—
173	C₂²×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₁₄₉	—	2	1	no	—
175	C₂×D₁₄₉	—	2	1	no	—
176	C₂×D₁₄₉	—	2	1	no	—
177	C₂×D₁₄₉	—	2	1	no	—
178	C₂×D₁₄₉	—	2	1	no	—
179	C₂×D₁₄₉	—	2	1	no	—
180	C₂×D₁₄₉	—	2	1	no	—
181	C₂×D₁₄₉	—	2	1	no	—
182	C₂×D₁₄₉	—	4	4	no	—
183	C₂×D₁₄₉	C₄×D₄	1	2	yes	—
184	C₄×C₁₄₉	—	2	1	no	—
185	C₄×C₁₄₉	—	2	1	no	—
186	C₄×C₁₄₉	—	2	1	no	—
187	C₄×C₁₄₉	—	2	1	no	—
188	C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₁₄₉	C₂×#41	1	1	yes	characteristic
190	Dic₁₄₉	—	2	1	no	—
191	Dic₁₄₉	—	2	1	no	—
192	Dic₁₄₉	—	2	1	no	—
193	Dic₁₄₉	—	2	1	no	—
194	Dic₁₄₉	C₄×D₄	1	2	yes	—
195	C₂×C₁₄₉	—	4	1	no	—
196	C₂×C₁₄₉	—	4	1	no	—
197	C₂×C₁₄₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×C₁₄₉	#568	1	1	yes	characteristic
199	C₂×C₁₄₉	#568	1	1	yes	characteristic
200	D₁₄₉	—	2	2	no	—
201	D₁₄₉	—	4	1	no	—
202	D₁₄₉	—	4	1	no	—
203	C₁₄₉	#2930	1	1	yes	characteristic, complemented, Sylow
204	#2930	—	149	1	no	maximal, Sylow
205	C₂×#131	—	149	1	no	—
206	C₂²×M₁₆	—	149	1	no	—
207	#525	—	149	1	no	—
208	#436	—	149	1	no	—
209	#436	—	149	1	no	—
210	#436	—	149	1	no	—
211	#436	D₁₄₉	1	1	yes	characteristic, complemented
212	#435	—	149	1	no	—
213	#435	—	149	1	no	—
214	#435	—	149	1	no	—
215	#435	—	149	1	no	—
216	#424	—	149	1	no	—
217	#408	—	149	1	no	—
218	#407	—	149	1	no	—
219	#405	—	149	1	no	—
220	C₂×#41	—	149	1	no	—
221	C₂³×C₄	—	149	1	no	—
222	#131	—	298	4	no	—
223	C₂×M₁₆	—	298	4	no	—
224	C₂×M₁₆	—	149	1	no	—
225	C₂×M₁₆	—	149	1	no	—
226	C₂×M₁₆	—	149	1	no	—
227	C₂×M₁₆	—	149	1	no	—
228	C₂×M₁₆	—	149	1	no	—
229	C₂×M₁₆	—	149	1	no	—
230	C₂×M₁₆	C₂×D₁₄₉	1	1	yes	characteristic
231	C₂×M₁₆	C₂×D₁₄₉	1	1	yes	characteristic, complemented
232	C₂²×C₈	—	149	1	no	—
233	C₂²×C₈	—	149	1	no	—
234	C₂²×C₈	—	149	1	no	—
235	C₂²×C₈	—	149	1	no	—
236	#123	—	149	1	no	—
237	#123	—	149	1	no	—
238	C₂²⋊Q₈	—	149	1	no	—
239	C₂²⋊Q₈	—	149	1	no	—
240	#121	—	149	1	no	—
241	#121	—	149	1	no	—
242	#120	—	149	1	no	—
243	#120	—	149	1	no	—
244	C₄×D₄	—	149	1	no	—
245	C₄×D₄	—	149	1	no	—
246	C₄×D₄	—	149	1	no	—
247	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
248	#117	—	149	1	no	—
249	C₄⋊C₈	—	149	1	no	—
250	C₄⋊C₈	—	149	1	no	—
251	C₄⋊C₈	—	149	1	no	—
252	C₄⋊C₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
253	C₂²⋊C₈	—	149	1	no	—
254	C₂²⋊C₈	—	149	1	no	—
255	C₂²⋊C₈	—	149	1	no	—
256	C₂²⋊C₈	—	149	1	no	—
257	C₂²⋊C₈	—	149	1	no	—
258	C₂²⋊C₈	—	149	1	no	—
259	C₂²⋊C₈	C₂×D₁₄₉	1	1	yes	characteristic
260	C₂²⋊C₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
261	#97	—	149	1	no	—
262	#97	—	149	1	no	—
263	C₄×C₈	—	149	1	no	—
264	C₄×C₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
265	C₂⁴	—	149	1	no	—
266	#41	—	298	2	no	—
267	#41	—	298	2	no	—
268	C₂×Q₈	—	149	1	no	—
269	C₂×D₄	—	149	1	no	—
270	C₂×D₄	—	149	1	no	—
271	C₂×D₄	—	149	1	no	—
272	C₂×D₄	—	149	1	no	—
273	C₂×D₄	—	149	1	no	—
274	C₂×D₄	—	149	1	no	—
275	C₂×D₄	C₄×D₁₄₉	1	1	yes	characteristic
276	C₂²×C₄	—	298	2	no	—
277	C₂²×C₄	—	298	2	no	—
278	C₂²×C₄	—	149	1	no	—
279	C₂²×C₄	—	149	1	no	—
280	C₂²×C₄	—	149	1	no	—
281	C₂²×C₄	—	149	1	no	—
282	C₂²×C₄	—	149	1	no	—
283	C₂²×C₄	—	149	1	no	—
284	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	298	2	no	—
289	M₁₆	—	298	2	no	—
290	M₁₆	—	298	2	no	—
291	M₁₆	—	298	2	no	—
292	M₁₆	—	298	2	no	—
293	M₁₆	—	298	2	no	—
294	C₂×C₈	—	298	2	no	—
295	C₂×C₈	—	298	2	no	—
296	C₂×C₈	—	298	2	no	—
297	C₂×C₈	—	149	1	no	—
298	C₂×C₈	—	149	1	no	—
299	C₂×C₈	—	149	1	no	—
300	C₂×C₈	—	149	1	no	—
301	C₂×C₈	—	149	4	no	—
302	C₂×C₈	C₂²×D₁₄₉	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₁₄₉	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₁₄₉	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₁₄₉	1	1	yes	characteristic
306	C₄⋊C₄	—	149	1	no	—
307	C₄⋊C₄	—	149	1	no	—
308	C₄⋊C₄	—	149	1	no	—
309	C₄⋊C₄	—	149	1	no	—
310	C₄⋊C₄	—	149	1	no	—
311	C₄⋊C₄	C₄×D₁₄₉	1	1	yes	characteristic
312	C₂²⋊C₄	—	149	1	no	—
313	C₂²⋊C₄	—	149	1	no	—
314	C₂²⋊C₄	—	149	1	no	—
315	C₂²⋊C₄	—	149	1	no	—
316	C₂²⋊C₄	—	149	1	no	—
317	C₂²⋊C₄	—	149	1	no	—
318	C₂²⋊C₄	—	149	1	no	—
319	C₂²⋊C₄	—	149	1	no	—
320	C₂²⋊C₄	C₄×D₁₄₉	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₁₄₉	1	1	yes	characteristic
322	C₄²	—	149	1	no	—
323	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
324	C₂³	—	298	2	no	—
325	C₂³	—	596	1	no	—
326	C₂³	—	596	1	no	—
327	C₂³	—	149	1	no	—
328	C₂³	—	149	1	no	—
329	C₂³	—	149	1	no	—
330	C₂³	C₂×C₄×D₁₄₉	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₁₄₉	1	1	yes	characteristic
332	Q₈	—	298	2	no	—
333	D₄	—	4	1	no	—
334	D₄	—	298	2	no	—
335	D₄	—	298	2	no	—
336	D₄	—	298	2	no	—
337	D₄	—	596	1	no	—
338	D₄	—	596	1	no	—
339	D₄	—	596	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	298	2	no	—
345	C₂×C₄	—	298	2	no	—
346	C₂×C₄	—	298	2	no	—
347	C₂×C₄	—	298	1	no	—
348	C₂×C₄	—	298	1	no	—
349	C₂×C₄	—	298	1	no	—
350	C₂×C₄	—	298	1	no	—
351	C₂×C₄	—	149	1	no	—
352	C₂×C₄	—	149	1	no	—
353	C₂×C₄	—	149	1	no	—
354	C₂×C₄	—	149	1	no	—
355	C₂×C₄	—	149	1	no	—
356	C₂×C₄	—	149	2	no	—
357	C₂×C₄	—	149	2	no	—
358	C₂×C₄	C₂×C₄×D₁₄₉	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₁₄₉	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₁₄₉	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₁₄₉	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	298	1	no	—
367	C₈	—	298	1	no	—
368	C₈	—	298	1	no	—
369	C₈	—	149	2	no	—
370	C₈	D₄×D₁₄₉	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	298	1	no	—
378	C₂²	—	298	1	no	—
379	C₂²	—	298	1	no	—
380	C₂²	—	298	1	no	—
381	C₂²	—	298	1	no	—
382	C₂²	—	298	1	no	—
383	C₂²	—	298	1	no	—
384	C₂²	—	298	1	no	—
385	C₂²	—	596	4	no	—
386	C₂²	—	149	2	no	—
387	C₂²	C₂²×C₄×D₁₄₉	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	298	1	no	—
393	C₄	—	298	1	no	—
394	C₄	—	298	1	no	—
395	C₄	—	298	1	no	—
396	C₄	—	149	2	no	—
397	C₄	C₂×D₄×D₁₄₉	1	1	yes	characteristic
398	C₄	#41×D₁₄₉	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	298	2	no	—
402	C₂	—	596	1	no	—
403	C₂	—	596	1	no	—
404	C₂	C₄×D₄×D₁₄₉	1	1	yes	characteristic
405	C₂	#23750390	1	1	yes	characteristic
406	C₂	#23750391	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₄₉
commutator, socle	C₂²×C₁₄₉	C₂³×C₄
Fitting	#436×C₁₄₉	C₂
prime radical	#23750134	C₂
cosocle	C₂×C₄×C₁₄₉	C₂⁴
hypercenter	#436	D₁₄₉
hypocenter	C₁₄₉	#2930
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ #436

Complements

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

N	H ≅ G/N	type
1. C₂×#18011919	C₂	semidirect
2. C₂×M₁₆×D₁₄₉	C₂	semidirect
4. #23749704	C₂	semidirect
5. #23749701	C₂	semidirect
6. #23749701	C₂	semidirect
7. #23749699	C₂	semidirect
8. #23749697	C₂	semidirect
9. #23749695	C₂	semidirect
10. #23749693	C₂	semidirect
11. #23749650	C₂	semidirect
12. #23749590	C₂	semidirect
13. #23749587	C₂	semidirect
14. #23749579	C₂	semidirect
15. #436×C₁₄₉	C₂	semidirect
24. C₂×#14558719	C₂²	semidirect
26. C₂²×#11924746	C₂²	semidirect
29. C₂×C₈×D₁₄₉	C₂²	semidirect
42. C₄⋊#11924746	C₂²	semidirect
43. #18011840	C₂²	semidirect
44. #18011840	C₂²	semidirect
46. C₂²⋊#11924746	C₂²	semidirect
49. #18011823	C₂²	semidirect
50. #18011823	C₂²	semidirect
51. #18011822	C₂²	semidirect
52. #18011821	C₂²	semidirect
53. C₈×Dic₁₄₉	C₂²	semidirect
55. C₂×M₁₆×C₁₄₉	C₂²	semidirect
57. C₄⋊C₈×C₁₄₉	C₂²	semidirect
59. C₂²⋊C₈×C₁₄₉	C₂²	semidirect
60. C₄×C₈×C₁₄₉	C₂²	semidirect
92. C₈×D₁₄₉	D₄	semidirect
203. C₁₄₉	#2930	semidirect
211. #436	D₁₄₉	semidirect
231. C₂×M₁₆	C₂×D₁₄₉	semidirect
252. C₄⋊C₈	C₂×D₁₄₉	semidirect
260. C₂²⋊C₈	C₂×D₁₄₉	semidirect
264. C₄×C₈	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#18011919	2
C₂×M₁₆×D₁₄₉	2
#23750134	2
#23749704	2
#23749701	2
#23749699	2
#23749697	2
#23749695	2
#23749693	2
#23749650	2
#23749590	2
#23749587	2
#23749579	2
#436×C₁₄₉	2
#2930	149