Subgroups — #34058449

Order 19072.

1660 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18011957	C₂	1	2	yes	maximal, complemented
2	#23750278	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750276	C₂	1	2	yes	maximal, complemented
4	#23750267	C₂	1	4	yes	maximal, complemented
5	#23750266	C₂	1	2	yes	maximal, complemented
6	#23750263	C₂	1	2	yes	maximal, complemented
7	D₄×D₅₉₆	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×D₅₉₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750259	C₂	1	2	yes	maximal, complemented
10	#23750205	C₂	1	2	yes	maximal, complemented
11	#23750186	C₂	1	4	yes	maximal, complemented
12	#23750176	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750172	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#18011886	C₂	1	2	yes	maximal, complemented
15	#121×D₁₄₉	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#547×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#18011957	—	2	16	no	—
19	C₂×#14558737	C₂²	1	2	yes	complemented
20	C₂×#14558737	C₂²	1	2	yes	complemented
21	C₂×#14558736	C₂²	1	2	yes	complemented
22	C₂×#14558736	C₂²	1	4	yes	complemented
23	C₂²×D₅₉₆	C₂²	1	4	yes	complemented
24	C₂²×D₅₉₆	C₂²	1	2	yes	complemented
25	C₂²×D₅₉₆	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₄₉	C₂²	1	4	yes	complemented
28	C₂×D₄×D₁₄₉	C₂²	1	4	yes	complemented
29	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
30	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
31	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	complemented
32	#18011910	C₂²	1	1	yes	characteristic, complemented
33	#18011908	C₂²	1	1	yes	characteristic, complemented
34	#18011907	C₂²	1	1	yes	characteristic, complemented
35	#18011900	C₂²	1	2	yes	complemented
36	#18011897	C₂²	1	2	yes	complemented
37	#18011896	C₂²	1	4	yes	complemented
38	#18011896	C₂²	1	4	yes	complemented
39	#18011894	C₂²	1	4	yes	complemented
40	#18011889	C₂²	1	4	yes	complemented
41	#18011887	C₂²	1	2	yes	complemented
42	#18011886	C₂²	1	1	yes	characteristic, complemented
43	#18011886	C₂²	1	2	yes	complemented
44	#18011886	C₂²	1	2	yes	complemented
45	#18011886	C₂²	1	4	yes	complemented
46	#18011886	C₂²	1	2	yes	complemented
47	#18011886	C₂²	1	2	yes	complemented
48	#18011886	C₂²	1	2	yes	complemented
49	#18011886	C₂²	1	4	yes	complemented
50	#18011885	C₂²	1	2	yes	complemented
51	#18011885	C₂²	1	2	yes	complemented
52	#18011884	C₂²	1	2	yes	complemented
53	#18011884	C₂²	1	4	yes	complemented
54	#18011884	C₂²	1	4	yes	complemented
55	#18011883	C₂²	1	4	yes	complemented
56	#18011882	C₂²	1	1	yes	characteristic, complemented
57	#18011881	C₂²	1	4	yes	complemented
58	#18011881	C₂²	1	4	yes	complemented
59	#18011881	C₂²	1	4	yes	complemented
60	#18011879	C₂²	1	4	yes	complemented
61	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
62	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
63	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
64	#18011873	C₂²	1	2	yes	complemented
65	#18011873	C₂²	1	2	yes	complemented
66	#18011873	C₂²	1	1	yes	characteristic, complemented
67	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
69	#18011871	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
71	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
72	C₂×#14558713	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
74	C₂²⋊C₄×D₁₄₉	C₂²	1	4	yes	complemented
75	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
76	C₂×#41×C₁₄₉	C₂²	1	2	yes	complemented
77	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
78	#123×C₁₄₉	C₂²	1	4	yes	complemented
79	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
80	#121×C₁₄₉	C₂²	1	2	yes	complemented
81	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	complemented
84	C₂³×D₁₄₉	C₂³	1	4	yes	—
85	C₂³×D₁₄₉	C₂³	1	4	yes	—
86	C₂³×D₁₄₉	C₂³	1	2	yes	—
87	#14558737	—	2	8	no	—
88	#14558737	—	2	8	no	—
89	#14558736	—	2	16	no	—
90	#14558736	—	2	8	no	—
91	C₂×Dic₂₉₈	C₂³	1	2	yes	—
92	C₂×D₅₉₆	—	2	16	no	—
93	C₂×D₅₉₆	—	2	8	no	—
94	C₂×D₅₉₆	—	4	4	no	—
95	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
96	C₂×D₅₉₆	C₂³	1	2	yes	—
97	C₂×D₅₉₆	C₂³	1	2	yes	—
98	C₂×D₅₉₆	C₂³	1	4	yes	—
99	C₂×D₅₉₆	C₂³	1	4	yes	—
100	C₂×D₅₉₆	C₂³	1	4	yes	—
101	C₂×D₅₉₆	C₂³	1	2	yes	—
102	C₂×D₅₉₆	C₂³	1	2	yes	—
103	C₂×D₅₉₆	C₂³	1	4	yes	—
104	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
106	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
111	D₄×D₁₄₉	—	2	16	no	—
112	D₄×D₁₄₉	—	2	16	no	—
113	D₄×D₁₄₉	—	2	8	no	—
114	D₄×D₁₄₉	—	4	4	no	—
115	D₄×D₁₄₉	D₄	1	8	yes	complemented
116	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
117	C₂×C₄×D₁₄₉	—	4	4	no	—
118	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
119	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
120	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
121	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
122	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
123	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
124	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
125	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
127	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
128	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
129	#14558715	C₂³	1	2	yes	—
130	#14558715	C₂³	1	2	yes	—
131	#14558715	C₂³	1	4	yes	—
132	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
133	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
134	#14558713	C₂³	1	4	yes	—
135	#14558713	C₂³	1	2	yes	—
136	#14558713	C₂³	1	2	yes	—
137	#14558713	C₂³	1	4	yes	—
138	#14558713	C₂³	1	2	yes	—
139	#14558713	C₂³	1	4	yes	—
140	#14558713	C₂³	1	4	yes	—
141	#14558713	C₂³	1	4	yes	—
142	#14558713	C₂³	1	2	yes	—
143	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
144	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
145	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
146	#41×C₁₄₉	—	2	8	no	—
147	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
148	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
149	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
150	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
151	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
152	C₂²×C₄×C₁₄₉	C₂³	1	4	yes	—
153	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
154	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
156	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
157	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
162	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
163	C₂²×D₁₄₉	—	2	8	no	—
164	C₂²×D₁₄₉	—	2	8	no	—
165	C₂²×D₁₄₉	—	4	2	no	—
166	C₂²×D₁₄₉	—	4	2	no	—
167	C₂²×D₁₄₉	—	4	4	no	—
168	C₂²×D₁₄₉	—	4	4	no	—
169	C₂²×D₁₄₉	—	4	4	no	—
170	C₂²×D₁₄₉	—	4	4	no	—
171	C₂²×D₁₄₉	C₂×D₄	1	8	yes	complemented
172	C₂²×D₁₄₉	C₂⁴	1	4	yes	—
173	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
174	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
175	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
176	Dic₂₉₈	—	2	4	no	—
177	D₅₉₆	—	2	8	no	—
178	D₅₉₆	—	2	8	no	—
179	D₅₉₆	—	2	8	no	—
180	D₅₉₆	—	2	4	no	—
181	D₅₉₆	—	2	4	no	—
182	D₅₉₆	—	2	4	no	—
183	D₅₉₆	—	2	2	no	—
184	D₅₉₆	—	4	4	no	—
185	D₅₉₆	—	4	2	no	—
186	D₅₉₆	C₂×D₄	1	4	yes	complemented
187	C₂²⋊D₁₄₉	—	2	8	no	—
188	C₂²⋊D₁₄₉	—	2	4	no	—
189	C₂²⋊D₁₄₉	—	2	4	no	—
190	C₂²⋊D₁₄₉	—	4	4	no	—
191	C₂²⋊D₁₄₉	—	4	2	no	—
192	C₂²⋊D₁₄₉	C₂×D₄	1	8	yes	complemented
193	C₂×Dic₁₄₉	—	4	2	no	—
194	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
195	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
196	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
197	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
198	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
199	C₄×D₁₄₉	—	2	8	no	—
200	C₄×D₁₄₉	—	2	4	no	—
201	C₄×D₁₄₉	—	2	2	no	—
202	C₄×D₁₄₉	—	2	4	no	—
203	C₄×D₁₄₉	—	2	8	no	—
204	C₄×D₁₄₉	—	4	2	no	—
205	C₄×D₁₄₉	—	4	2	no	—
206	C₄×D₁₄₉	—	4	1	no	—
207	C₄×D₁₄₉	C₂×D₄	1	4	yes	complemented
208	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
209	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
210	Q₈×C₁₄₉	—	2	4	no	—
211	D₄×C₁₄₉	—	2	8	no	—
212	D₄×C₁₄₉	—	2	2	no	—
213	D₄×C₁₄₉	C₂×D₄	1	4	yes	complemented
214	C₂×C₄×C₁₄₉	—	2	8	no	—
215	C₂×C₄×C₁₄₉	—	2	4	no	—
216	C₂×C₄×C₁₄₉	—	2	4	no	—
217	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
218	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
219	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
220	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
221	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
222	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₁₄₉	—	2	2	no	—
224	C₂²×C₁₄₉	—	2	2	no	—
225	C₂²×C₁₄₉	—	2	2	no	—
226	C₂²×C₁₄₉	—	2	2	no	—
227	C₂²×C₁₄₉	—	2	2	no	—
228	C₂²×C₁₄₉	C₂²×D₄	1	4	yes	—
229	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
230	C₂×D₁₄₉	—	2	1	no	—
231	C₂×D₁₄₉	—	2	2	no	—
232	C₂×D₁₄₉	—	2	1	no	—
233	C₂×D₁₄₉	—	2	2	no	—
234	C₂×D₁₄₉	—	2	2	no	—
235	C₂×D₁₄₉	—	2	4	no	—
236	C₂×D₁₄₉	—	2	4	no	—
237	C₂×D₁₄₉	—	2	2	no	—
238	C₂×D₁₄₉	—	2	2	no	—
239	C₂×D₁₄₉	—	2	4	no	—
240	C₂×D₁₄₉	—	4	8	no	—
241	C₂×D₁₄₉	—	8	8	no	—
242	C₂×D₁₄₉	—	8	8	no	—
243	C₂×D₁₄₉	C₂²×D₄	1	4	yes	—
244	C₂×D₁₄₉	C₂²×D₄	1	2	yes	—
245	C₄×C₁₄₉	—	2	2	no	—
246	C₄×C₁₄₉	—	2	4	no	—
247	C₄×C₁₄₉	—	2	2	no	—
248	C₄×C₁₄₉	—	2	1	no	—
249	C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
250	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	complemented
251	Dic₁₄₉	—	2	2	no	—
252	Dic₁₄₉	—	2	1	no	—
253	Dic₁₄₉	—	2	2	no	—
254	Dic₁₄₉	—	2	1	no	—
255	Dic₁₄₉	C₂²×D₄	1	2	yes	—
256	C₂×C₁₄₉	—	2	4	no	—
257	C₂×C₁₄₉	—	4	2	no	—
258	C₂×C₁₄₉	C₂³×D₄	1	1	yes	characteristic
259	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×C₁₄₉	#585	1	1	yes	characteristic
261	D₁₄₉	—	2	2	no	—
262	D₁₄₉	—	2	4	no	—
263	D₁₄₉	—	4	4	no	—
264	D₁₄₉	—	4	2	no	—
265	C₁₄₉	#3496	1	1	yes	characteristic, complemented, Sylow
266	#3496	—	149	1	no	maximal, Sylow
267	C₂×H(5,𝔽₂)	—	149	2	no	—
268	#547	—	149	1	no	—
269	#547	—	149	2	no	—
270	#547	D₁₄₉	1	1	yes	characteristic, complemented
271	#546	—	149	2	no	—
272	#546	—	149	4	no	—
273	#546	—	149	2	no	—
274	D₄²	—	149	2	no	—
275	D₄²	—	149	1	no	—
276	D₄²	—	149	1	no	—
277	#537	—	149	2	no	—
278	#534	—	149	4	no	—
279	#532	—	149	1	no	—
280	#532	—	149	1	no	—
281	C₂×#121	—	149	2	no	—
282	C₂×#121	—	149	2	no	—
283	C₂×C₄×D₄	—	149	1	no	—
284	H(5,𝔽₂)	—	298	16	no	—
285	C₂×#41	—	149	2	no	—
286	C₂×#41	—	149	2	no	—
287	C₂×#41	—	149	2	no	—
288	C₂×#41	—	149	4	no	—
289	C₂×#41	C₂×D₁₄₉	1	2	yes	complemented
290	C₂²×D₄	—	149	4	no	—
291	C₂²×D₄	—	149	4	no	—
292	C₂²×D₄	—	149	2	no	—
293	C₂²×D₄	—	149	2	no	—
294	C₂²×D₄	—	149	1	no	—
295	C₂²×D₄	—	149	4	no	—
296	C₂²×D₄	—	149	2	no	—
297	C₂²×D₄	—	149	2	no	—
298	C₂³×C₄	—	149	2	no	—
299	C₄⋊Q₈	—	149	1	no	—
300	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
301	#127	—	149	1	no	—
302	#127	—	149	1	no	—
303	#124	—	149	2	no	—
304	#124	—	149	2	no	—
305	#123	—	149	4	no	—
306	#123	—	149	4	no	—
307	#123	—	149	4	no	—
308	#123	C₂×D₁₄₉	1	4	yes	complemented
309	C₂²⋊Q₈	—	149	2	no	—
310	C₂²⋊Q₈	—	149	4	no	—
311	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
312	#121	—	149	1	no	—
313	#121	—	149	4	no	—
314	#121	—	149	2	no	—
315	#121	—	149	2	no	—
316	#121	—	149	2	no	—
317	#121	—	149	1	no	—
318	#121	—	149	4	no	—
319	#121	—	149	2	no	—
320	#121	—	149	2	no	—
321	#121	—	149	4	no	—
322	#121	—	149	2	no	—
323	#121	—	149	2	no	—
324	#121	—	149	4	no	—
325	#121	—	149	2	no	—
326	#121	—	149	4	no	—
327	#121	C₂×D₁₄₉	1	2	yes	complemented
328	#120	—	149	4	no	—
329	#120	—	149	4	no	—
330	#120	—	149	4	no	—
331	#120	—	149	4	no	—
332	C₄×D₄	—	149	1	no	—
333	C₄×D₄	—	149	2	no	—
334	C₄×D₄	—	149	2	no	—
335	C₄×D₄	—	149	1	no	—
336	C₄×D₄	—	149	2	no	—
337	C₄×D₄	—	149	2	no	—
338	C₄×D₄	—	149	2	no	—
339	C₄×D₄	—	149	1	no	—
340	C₄×D₄	—	149	1	no	—
341	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
342	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
343	C₂×C₄⋊C₄	—	149	1	no	—
344	C₂×C₄⋊C₄	—	149	2	no	—
345	C₂×C₄⋊C₄	C₂×D₁₄₉	1	2	yes	complemented
346	C₂×C₂²⋊C₄	—	149	4	no	—
347	C₂×C₂²⋊C₄	—	149	2	no	—
348	C₂×C₂²⋊C₄	—	149	4	no	—
349	C₂×C₄²	—	149	1	no	—
350	C₂⁴	—	149	4	no	—
351	C₂⁴	—	149	4	no	—
352	C₂⁴	—	149	2	no	—
353	#41	—	2	8	no	—
354	#41	—	298	16	no	—
355	#41	—	298	8	no	—
356	#41	—	298	8	no	—
357	#41	—	298	8	no	—
358	C₂×Q₈	—	149	2	no	—
359	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
360	C₂×D₄	—	298	16	no	—
361	C₂×D₄	—	298	8	no	—
362	C₂×D₄	—	298	16	no	—
363	C₂×D₄	—	298	16	no	—
364	C₂×D₄	—	298	8	no	—
365	C₂×D₄	—	596	4	no	—
366	C₂×D₄	—	596	4	no	—
367	C₂×D₄	—	149	4	no	—
368	C₂×D₄	—	149	2	no	—
369	C₂×D₄	—	149	2	no	—
370	C₂×D₄	—	149	2	no	—
371	C₂×D₄	—	149	4	no	—
372	C₂×D₄	—	149	2	no	—
373	C₂×D₄	—	149	8	no	—
374	C₂×D₄	—	149	1	no	—
375	C₂×D₄	—	149	2	no	—
376	C₂×D₄	—	149	4	no	—
377	C₂×D₄	—	149	4	no	—
378	C₂×D₄	—	149	4	no	—
379	C₂×D₄	—	149	2	no	—
380	C₂×D₄	—	149	2	no	—
381	C₂×D₄	—	149	2	no	—
382	C₂×D₄	—	149	4	no	—
383	C₂×D₄	—	149	1	no	—
384	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
385	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
386	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
387	C₂²×C₄	—	596	4	no	—
388	C₂²×C₄	—	149	1	no	—
389	C₂²×C₄	—	149	4	no	—
390	C₂²×C₄	—	149	2	no	—
391	C₂²×C₄	—	149	4	no	—
392	C₂²×C₄	—	149	2	no	—
393	C₂²×C₄	—	149	2	no	—
394	C₂²×C₄	—	149	1	no	—
395	C₂²×C₄	—	149	2	no	—
396	C₂²×C₄	—	149	2	no	—
397	C₂²×C₄	—	149	1	no	—
398	C₂²×C₄	C₂²×D₁₄₉	1	4	yes	—
399	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
400	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
401	C₄⋊C₄	—	149	1	no	—
402	C₄⋊C₄	—	149	2	no	—
403	C₄⋊C₄	—	149	1	no	—
404	C₄⋊C₄	—	149	4	no	—
405	C₄⋊C₄	—	149	2	no	—
406	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
407	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
408	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
409	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
410	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
411	C₂²⋊C₄	—	149	2	no	—
412	C₂²⋊C₄	—	149	2	no	—
413	C₂²⋊C₄	—	149	4	no	—
414	C₂²⋊C₄	—	149	2	no	—
415	C₂²⋊C₄	—	149	2	no	—
416	C₂²⋊C₄	—	149	2	no	—
417	C₂²⋊C₄	—	149	4	no	—
418	C₂²⋊C₄	—	149	4	no	—
419	C₂²⋊C₄	—	149	4	no	—
420	C₂²⋊C₄	—	149	4	no	—
421	C₂²⋊C₄	—	149	2	no	—
422	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
423	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
424	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
425	C₄²	—	149	1	no	—
426	C₄²	—	149	1	no	—
427	C₄²	—	149	1	no	—
428	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
429	C₂³	—	298	8	no	—
430	C₂³	—	298	8	no	—
431	C₂³	—	596	2	no	—
432	C₂³	—	596	2	no	—
433	C₂³	—	596	4	no	—
434	C₂³	—	596	4	no	—
435	C₂³	—	596	4	no	—
436	C₂³	—	596	4	no	—
437	C₂³	—	149	4	no	—
438	C₂³	—	149	2	no	—
439	C₂³	—	149	2	no	—
440	C₂³	—	149	1	no	—
441	C₂³	—	149	8	no	—
442	C₂³	C₂³×D₁₄₉	1	2	yes	—
443	C₂³	C₂³×D₁₄₉	1	2	yes	—
444	Q₈	—	2	4	no	—
445	Q₈	—	298	4	no	—
446	D₄	—	2	8	no	—
447	D₄	—	2	2	no	—
448	D₄	—	298	8	no	—
449	D₄	—	298	4	no	—
450	D₄	—	298	8	no	—
451	D₄	—	298	8	no	—
452	D₄	—	298	4	no	—
453	D₄	—	298	8	no	—
454	D₄	—	298	4	no	—
455	D₄	—	298	4	no	—
456	D₄	—	298	4	no	—
457	D₄	—	298	2	no	—
458	D₄	—	596	4	no	—
459	D₄	—	596	2	no	—
460	D₄	—	596	4	no	—
461	D₄	—	596	2	no	—
462	D₄	—	149	8	no	—
463	D₄	—	149	4	no	—
464	D₄	D₄×D₁₄₉	1	4	yes	complemented
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	298	8	no	—
469	C₂×C₄	—	298	8	no	—
470	C₂×C₄	—	298	4	no	—
471	C₂×C₄	—	298	2	no	—
472	C₂×C₄	—	298	4	no	—
473	C₂×C₄	—	596	2	no	—
474	C₂×C₄	—	596	2	no	—
475	C₂×C₄	—	596	1	no	—
476	C₂×C₄	—	596	2	no	—
477	C₂×C₄	—	149	1	no	—
478	C₂×C₄	—	149	1	no	—
479	C₂×C₄	—	149	2	no	—
480	C₂×C₄	—	149	2	no	—
481	C₂×C₄	—	149	1	no	—
482	C₂×C₄	—	149	4	no	—
483	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
484	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
485	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
486	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
487	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
488	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	298	1	no	—
495	C₂²	—	298	2	no	—
496	C₂²	—	298	1	no	—
497	C₂²	—	298	2	no	—
498	C₂²	—	298	4	no	—
499	C₂²	—	298	2	no	—
500	C₂²	—	298	2	no	—
501	C₂²	—	298	4	no	—
502	C₂²	—	298	4	no	—
503	C₂²	—	298	2	no	—
504	C₂²	—	596	8	no	—
505	C₂²	—	149	4	no	—
506	C₂²	—	149	2	no	—
507	C₂²	—	1192	8	no	—
508	C₂²	—	1192	8	no	—
509	C₂²	C₂×D₄×D₁₄₉	1	4	yes	—
510	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	4	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	1	no	—
515	C₄	—	298	2	no	—
516	C₄	—	298	1	no	—
517	C₄	—	298	2	no	—
518	C₄	—	298	1	no	—
519	C₄	—	149	2	no	—
520	C₄	C₂×D₄×D₁₄₉	1	2	yes	—
521	C₄	#18011957	1	2	yes	complemented
522	C₂	—	2	4	no	—
523	C₂	—	4	2	no	—
524	C₂	—	298	2	no	—
525	C₂	—	298	4	no	—
526	C₂	—	596	2	no	—
527	C₂	—	596	4	no	—
528	C₂	C₂²×D₄×D₁₄₉	1	1	yes	characteristic
529	C₂	C₂×#18011957	1	1	yes	characteristic
530	C₂	#23750462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#547×C₁₄₉	C₂
hypercenter	#547	D₁₄₉
hypocenter	C₁₄₉	#3496
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₂×#18011957	C₂	semidirect
2. #23750278	C₂	semidirect
3. #23750276	C₂	semidirect
4. #23750267	C₂	semidirect
5. #23750266	C₂	semidirect
6. #23750263	C₂	semidirect
7. D₄×D₅₉₆	C₂	semidirect
8. D₄×D₅₉₆	C₂	semidirect
9. #23750259	C₂	semidirect
10. #23750205	C₂	semidirect
11. #23750186	C₂	semidirect
12. #23750176	C₂	semidirect
13. #23750172	C₂	semidirect
14. C₂×#18011886	C₂	semidirect
15. #121×D₁₄₉	C₂	semidirect
16. C₄×D₄×D₁₄₉	C₂	semidirect
17. #547×C₁₄₉	C₂	semidirect
19. C₂×#14558737	C₂²	semidirect
20. C₂×#14558737	C₂²	semidirect
21. C₂×#14558736	C₂²	semidirect
22. C₂×#14558736	C₂²	semidirect
23. C₂²×D₅₉₆	C₂²	semidirect
24. C₂²×D₅₉₆	C₂²	semidirect
25. C₂²×D₅₉₆	C₂²	semidirect
27. C₂×D₄×D₁₄₉	C₂²	semidirect
28. C₂×D₄×D₁₄₉	C₂²	semidirect
29. C₂×D₄×D₁₄₉	C₂²	semidirect
30. C₂×D₄×D₁₄₉	C₂²	semidirect
31. C₂²×C₄×D₁₄₉	C₂²	semidirect
32. #18011910	C₂²	semidirect
33. #18011908	C₂²	semidirect
34. #18011907	C₂²	semidirect
35. #18011900	C₂²	semidirect
36. #18011897	C₂²	semidirect
37. #18011896	C₂²	semidirect
38. #18011896	C₂²	semidirect
39. #18011894	C₂²	semidirect
40. #18011889	C₂²	semidirect
41. #18011887	C₂²	semidirect
42. #18011886	C₂²	semidirect
43. #18011886	C₂²	semidirect
44. #18011886	C₂²	semidirect
45. #18011886	C₂²	semidirect
46. #18011886	C₂²	semidirect
47. #18011886	C₂²	semidirect
48. #18011886	C₂²	semidirect
49. #18011886	C₂²	semidirect
50. #18011885	C₂²	semidirect
51. #18011885	C₂²	semidirect
52. #18011884	C₂²	semidirect
53. #18011884	C₂²	semidirect
54. #18011884	C₂²	semidirect
55. #18011883	C₂²	semidirect
56. #18011882	C₂²	semidirect
57. #18011881	C₂²	semidirect
58. #18011881	C₂²	semidirect
59. #18011881	C₂²	semidirect
60. #18011879	C₂²	semidirect
61. C₄×D₅₉₆	C₂²	semidirect
62. C₄×D₅₉₆	C₂²	semidirect
63. D₄×Dic₁₄₉	C₂²	semidirect
64. #18011873	C₂²	semidirect
65. #18011873	C₂²	semidirect
66. #18011873	C₂²	semidirect
67. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
68. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
69. #18011871	C₂²	semidirect
70. C₄⋊C₄×D₁₄₉	C₂²	semidirect
71. C₄⋊C₄×D₁₄₉	C₂²	semidirect
72. C₂×#14558713	C₂²	semidirect
73. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
74. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
75. C₄²×D₁₄₉	C₂²	semidirect
76. C₂×#41×C₁₄₉	C₂²	semidirect
77. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
78. #123×C₁₄₉	C₂²	semidirect
79. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
80. #121×C₁₄₉	C₂²	semidirect
81. C₄×D₄×C₁₄₉	C₂²	semidirect
82. C₄×D₄×C₁₄₉	C₂²	semidirect
83. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
115. D₄×D₁₄₉	D₄	semidirect
171. C₂²×D₁₄₉	C₂×D₄	semidirect
186. D₅₉₆	C₂×D₄	semidirect
192. C₂²⋊D₁₄₉	C₂×D₄	semidirect
207. C₄×D₁₄₉	C₂×D₄	semidirect
213. D₄×C₁₄₉	C₂×D₄	semidirect
250. C₄×C₁₄₉	H(5,𝔽₂)	semidirect
265. C₁₄₉	#3496	semidirect
270. #547	D₁₄₉	semidirect
289. C₂×#41	C₂×D₁₄₉	semidirect
300. C₄⋊Q₈	C₂×D₁₄₉	semidirect
308. #123	C₂×D₁₄₉	semidirect
311. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
327. #121	C₂×D₁₄₉	semidirect
341. C₄×D₄	C₂×D₁₄₉	semidirect
342. C₄×D₄	C₂×D₁₄₉	semidirect
345. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect
464. D₄	D₄×D₁₄₉	semidirect
521. C₄	#18011957	semidirect

Maximal subgroups

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

subgroup	index
C₂×#18011957	2
#23750278	2
#23750276	2
#23750267	2
#23750266	2
#23750263	2
D₄×D₅₉₆	2
#23750259	2
#23750205	2
#23750186	2
#23750176	2
#23750172	2
C₂×#18011886	2
#121×D₁₄₉	2
C₄×D₄×D₁₄₉	2
#547×C₁₄₉	2
#3496	149