Subgroups — #34058740

Order 19072.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750345	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750330	C₂	1	2	yes	maximal, complemented
3	#23750315	C₂	1	2	yes	maximal, complemented
4	#23750301	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₂₉₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750284	C₂	1	2	yes	maximal, complemented
7	#23750280	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750279	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750269	C₂	1	2	yes	maximal, complemented
10	#23750240	C₂	1	2	yes	maximal, complemented
11	#23750217	C₂	1	4	yes	maximal, complemented
12	#23750182	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750159	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750136	C₂	1	2	yes	maximal, complemented
15	C₂×#18011890	C₂	1	2	yes	maximal, complemented
16	#23750104	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558736	C₂²	1	2	yes	complemented
19	C₂×#14558735	C₂²	1	2	yes	—
20	C₂²×Dic₂₉₈	C₂²	1	2	yes	complemented
21	#18011911	C₂²	1	1	yes	characteristic, complemented
22	#18011911	C₂²	1	1	yes	characteristic, complemented
23	#18011910	C₂²	1	2	yes	complemented
24	#18011905	C₂²	1	2	yes	complemented
25	#18011904	C₂²	1	4	yes	complemented
26	#18011904	C₂²	1	4	yes	complemented
27	#18011903	C₂²	1	1	yes	characteristic, complemented
28	#18011903	C₂²	1	2	yes	complemented
29	#18011901	C₂²	1	4	yes	complemented
30	#18011899	C₂²	1	1	yes	characteristic, complemented
31	#18011898	C₂²	1	2	yes	—
32	#18011897	C₂²	1	4	yes	complemented
33	#18011895	C₂²	1	4	yes	complemented
34	#18011894	C₂²	1	2	yes	—
35	#18011894	C₂²	1	4	yes	complemented
36	#18011893	C₂²	1	4	yes	complemented
37	#18011892	C₂²	1	4	yes	—
38	#18011891	C₂²	1	2	yes	complemented
39	#18011890	C₂²	1	1	yes	characteristic
40	#18011890	C₂²	1	2	yes	—
41	#18011890	C₂²	1	2	yes	—
42	#18011890	C₂²	1	4	yes	—
43	#18011890	C₂²	1	4	yes	complemented
44	#18011890	C₂²	1	2	yes	complemented
45	#18011890	C₂²	1	2	yes	complemented
46	#18011890	C₂²	1	2	yes	complemented
47	#18011889	C₂²	1	4	yes	complemented
48	#18011888	C₂²	1	4	yes	complemented
49	#18011885	C₂²	1	1	yes	characteristic
50	#18011885	C₂²	1	2	yes	complemented
51	#18011883	C₂²	1	4	yes	—
52	#18011882	C₂²	1	2	yes	—
53	#18011880	C₂²	1	4	yes	—
54	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
55	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
56	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
57	#18011876	C₂²	1	2	yes	complemented
58	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
59	D₄×Dic₁₄₉	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	—
62	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
63	#18011871	C₂²	1	4	yes	complemented
64	#18011870	C₂²	1	2	yes	—
65	#18011870	C₂²	1	2	yes	complemented
66	#18011868	C₂²	1	2	yes	complemented
67	#18011867	C₂²	1	4	yes	complemented
68	C₂×C₄⋊Dic₁₄₉	C₂²	1	2	yes	complemented
69	C₂×#14558715	C₂²	1	4	yes	complemented
70	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
71	C₂×C₂²⋊Dic₁₄₉	C₂²	1	4	yes	—
72	C₂²×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
73	C₂³×C₄×C₁₄₉	C₂²	1	2	yes	—
74	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
75	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
77	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
78	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
79	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
83	#14558736	—	4	4	no	—
84	#14558735	—	2	8	no	—
85	C₂×Dic₂₉₈	—	4	4	no	—
86	C₂×Dic₂₉₈	C₂³	1	2	yes	—
87	C₂×Dic₂₉₈	C₂³	1	2	yes	—
88	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
89	C₂×Dic₂₉₈	C₂³	1	4	yes	—
90	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
94	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
95	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
96	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
97	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
98	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
99	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
100	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
101	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
102	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
103	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
105	#14558715	C₂³	1	2	yes	—
106	#14558715	C₂³	1	2	yes	—
107	#14558715	C₂³	1	4	yes	—
108	#14558715	C₂³	1	4	yes	—
109	#14558715	C₂³	1	2	yes	—
110	#14558715	C₂³	1	2	yes	—
111	#14558715	C₂³	1	4	yes	—
112	#14558715	C₂³	1	4	yes	—
113	#14558715	C₂³	1	4	yes	—
114	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
116	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
119	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
120	#14558713	C₂³	1	2	yes	—
121	#14558713	C₂³	1	2	yes	—
122	#14558713	C₂³	1	2	yes	—
123	#14558713	C₂³	1	2	yes	—
124	#14558713	C₂³	1	4	yes	—
125	C₄×Dic₁₄₉	C₂³	1	4	yes	—
126	C₄×Dic₁₄₉	C₂³	1	4	yes	—
127	C₄×Dic₁₄₉	C₂³	1	2	yes	—
128	C₂⁴×C₁₄₉	C₂³	1	2	yes	—
129	C₂×D₄×C₁₄₉	—	2	4	no	—
130	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
132	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₄₉	—	4	4	no	—
134	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
140	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
141	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
149	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
150	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
151	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
152	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
153	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
154	Dic₂₉₈	—	2	4	no	—
155	Dic₂₉₈	—	2	2	no	—
156	Dic₂₉₈	—	2	4	no	—
157	Dic₂₉₈	—	4	4	no	—
158	D₅₉₆	—	2	2	no	—
159	C₂²⋊D₁₄₉	—	2	8	no	—
160	C₂²⋊D₁₄₉	—	2	4	no	—
161	C₂²⋊D₁₄₉	—	4	4	no	—
162	C₂×Dic₁₄₉	—	2	8	no	—
163	C₂×Dic₁₄₉	—	4	4	no	—
164	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
165	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
166	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
167	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
168	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
169	C₄×D₁₄₉	—	2	4	no	—
170	C₄×D₁₄₉	—	4	4	no	—
171	C₂³×C₁₄₉	—	2	4	no	—
172	C₂³×C₁₄₉	—	2	4	no	—
173	C₂³×C₁₄₉	—	4	2	no	—
174	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
175	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
176	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
177	D₄×C₁₄₉	—	2	4	no	—
178	D₄×C₁₄₉	—	2	2	no	—
179	D₄×C₁₄₉	#41	1	4	yes	complemented
180	C₂×C₄×C₁₄₉	—	2	2	no	—
181	C₂×C₄×C₁₄₉	—	2	2	no	—
182	C₂×C₄×C₁₄₉	—	2	4	no	—
183	C₂×C₄×C₁₄₉	—	2	4	no	—
184	C₂×C₄×C₁₄₉	—	2	2	no	—
185	C₂×C₄×C₁₄₉	—	4	2	no	—
186	C₂×C₄×C₁₄₉	—	4	2	no	—
187	C₂×C₄×C₁₄₉	—	4	2	no	—
188	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
189	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
190	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₁₄₉	—	2	1	no	—
197	C₂²×C₁₄₉	—	2	1	no	—
198	C₂²×C₁₄₉	—	2	2	no	—
199	C₂²×C₁₄₉	—	2	2	no	—
200	C₂²×C₁₄₉	—	2	2	no	—
201	C₂²×C₁₄₉	—	2	2	no	—
202	C₂²×C₁₄₉	—	2	2	no	—
203	C₂²×C₁₄₉	—	4	8	no	—
204	C₂²×C₁₄₉	C₂×#41	1	4	yes	—
205	C₂²×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
206	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
207	C₂×D₁₄₉	—	2	2	no	—
208	C₂×D₁₄₉	—	2	2	no	—
209	C₂×D₁₄₉	—	2	2	no	—
210	C₄×C₁₄₉	—	2	1	no	—
211	C₄×C₁₄₉	—	2	1	no	—
212	C₄×C₁₄₉	—	2	2	no	—
213	C₄×C₁₄₉	—	2	2	no	—
214	C₄×C₁₄₉	—	2	1	no	—
215	C₄×C₁₄₉	—	2	1	no	—
216	C₄×C₁₄₉	C₂×#41	1	2	yes	—
217	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
218	Dic₁₄₉	—	2	2	no	—
219	Dic₁₄₉	—	2	4	no	—
220	Dic₁₄₉	—	2	4	no	—
221	Dic₁₄₉	—	2	2	no	—
222	Dic₁₄₉	—	2	2	no	—
223	C₂×C₁₄₉	—	2	2	no	—
224	C₂×C₁₄₉	—	2	4	no	—
225	C₂×C₁₄₉	—	4	2	no	—
226	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
227	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
229	D₁₄₉	—	4	2	no	—
230	C₁₄₉	#3520	1	1	yes	characteristic, complemented, Sylow
231	#3520	—	149	1	no	maximal, Sylow
232	#556	—	149	1	no	—
233	#554	—	149	2	no	—
234	#552	—	149	2	no	—
235	#551	—	149	4	no	—
236	D₄×Q₈	—	149	1	no	—
237	#548	—	149	2	no	—
238	#547	—	149	1	no	—
239	#547	—	149	1	no	—
240	#546	—	149	2	no	—
241	#542	—	149	2	no	—
242	#539	—	149	4	no	—
243	#533	—	149	1	no	—
244	#529	—	149	1	no	—
245	#525	—	149	2	no	—
246	C₂×C₂²⋊Q₈	—	149	2	no	—
247	#520	—	149	2	no	—
248	C₂×C₄×D₄	D₁₄₉	1	1	yes	characteristic, complemented
249	C₂×#41	—	149	2	no	—
250	C₂×#41	—	149	2	no	—
251	C₂²×Q₈	—	149	2	no	—
252	C₂²×D₄	C₂×D₁₄₉	1	1	yes	characteristic
253	C₂³×C₄	C₂×D₁₄₉	1	2	yes	—
254	C₄⋊Q₈	—	149	2	no	—
255	C₄⋊Q₈	—	149	1	no	—
256	C₄⋊Q₈	—	149	1	no	—
257	#126	—	149	4	no	—
258	#126	—	149	4	no	—
259	#126	—	149	2	no	—
260	#125	—	149	4	no	—
261	#125	—	149	1	no	—
262	#125	—	149	2	no	—
263	#124	—	149	2	no	—
264	#124	—	149	4	no	—
265	#124	—	149	1	no	—
266	#123	—	149	4	no	—
267	#123	—	149	4	no	—
268	#123	—	149	2	no	—
269	#123	—	149	4	no	—
270	#123	—	149	4	no	—
271	C₂²⋊Q₈	—	149	1	no	—
272	C₂²⋊Q₈	—	149	2	no	—
273	C₂²⋊Q₈	—	149	4	no	—
274	C₂²⋊Q₈	—	149	2	no	—
275	C₂²⋊Q₈	—	149	2	no	—
276	C₂²⋊Q₈	—	149	4	no	—
277	C₂²⋊Q₈	—	149	2	no	—
278	C₂²⋊Q₈	—	149	2	no	—
279	C₂²⋊Q₈	—	149	4	no	—
280	C₂²⋊Q₈	—	149	2	no	—
281	C₂²⋊Q₈	—	149	4	no	—
282	#121	—	149	4	no	—
283	#121	—	149	2	no	—
284	#121	—	149	1	no	—
285	#121	—	149	2	no	—
286	#120	—	149	4	no	—
287	C₄×Q₈	—	149	2	no	—
288	C₄×Q₈	—	149	2	no	—
289	C₄×Q₈	—	149	1	no	—
290	C₄×Q₈	—	149	2	no	—
291	C₄×D₄	—	149	2	no	—
292	C₄×D₄	—	149	4	no	—
293	C₄×D₄	—	149	4	no	—
294	C₄×D₄	—	149	2	no	—
295	C₄×D₄	—	149	4	no	—
296	C₄×D₄	—	149	1	no	—
297	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
298	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
299	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
300	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
301	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
302	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
303	#117	—	149	2	no	—
304	#117	—	149	2	no	—
305	#117	—	149	4	no	—
306	#117	—	149	2	no	—
307	C₂×C₄⋊C₄	—	149	4	no	—
308	C₂×C₄⋊C₄	—	149	2	no	—
309	C₂×C₄⋊C₄	—	149	2	no	—
310	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	—	149	4	no	—
312	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	2	yes	—
313	C₂×C₄²	C₂×D₁₄₉	1	1	yes	characteristic
314	C₂⁴	C₂²×D₁₄₉	1	2	yes	—
315	#41	—	298	8	no	—
316	#41	—	596	4	no	—
317	C₂×Q₈	—	596	4	no	—
318	C₂×Q₈	—	149	2	no	—
319	C₂×Q₈	—	149	1	no	—
320	C₂×Q₈	—	149	2	no	—
321	C₂×Q₈	—	149	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	149	2	no	—
324	C₂×D₄	—	149	4	no	—
325	C₂×D₄	—	149	4	no	—
326	C₂×D₄	—	149	1	no	—
327	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
328	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
329	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	149	4	no	—
332	C₂²×C₄	—	149	2	no	—
333	C₂²×C₄	—	149	4	no	—
334	C₂²×C₄	—	149	4	no	—
335	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
337	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
338	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
339	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
340	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
341	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
342	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
343	C₄⋊C₄	—	149	2	no	—
344	C₄⋊C₄	—	149	4	no	—
345	C₄⋊C₄	—	149	1	no	—
346	C₄⋊C₄	—	149	2	no	—
347	C₄⋊C₄	—	149	2	no	—
348	C₄⋊C₄	—	149	4	no	—
349	C₄⋊C₄	—	149	4	no	—
350	C₄⋊C₄	—	149	4	no	—
351	C₄⋊C₄	—	149	2	no	—
352	C₄⋊C₄	—	149	1	no	—
353	C₄⋊C₄	—	149	2	no	—
354	C₄⋊C₄	—	149	2	no	—
355	C₄⋊C₄	—	149	4	no	—
356	C₄⋊C₄	—	149	2	no	—
357	C₄⋊C₄	—	149	4	no	—
358	C₄⋊C₄	—	149	2	no	—
359	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
361	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
362	C₂²⋊C₄	—	149	2	no	—
363	C₂²⋊C₄	—	149	4	no	—
364	C₂²⋊C₄	—	149	4	no	—
365	C₂²⋊C₄	—	149	4	no	—
366	C₂²⋊C₄	—	149	4	no	—
367	C₂²⋊C₄	—	149	4	no	—
368	C₂²⋊C₄	—	149	2	no	—
369	C₂²⋊C₄	—	149	2	no	—
370	C₂²⋊C₄	—	149	2	no	—
371	C₂²⋊C₄	—	149	4	no	—
372	C₂²⋊C₄	—	149	2	no	—
373	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
377	C₄²	—	149	4	no	—
378	C₄²	—	149	4	no	—
379	C₄²	—	149	2	no	—
380	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
381	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
382	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
383	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	149	2	no	—
388	C₂³	C₂³×D₁₄₉	1	2	yes	—
389	C₂³	C₂³×D₁₄₉	1	2	yes	—
390	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
391	Q₈	—	298	4	no	—
392	Q₈	—	298	2	no	—
393	Q₈	—	298	4	no	—
394	Q₈	—	596	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	—	298	8	no	—
398	D₄	—	298	4	no	—
399	D₄	—	298	2	no	—
400	D₄	—	596	4	no	—
401	D₄	#14558736	1	4	yes	complemented
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	298	8	no	—
411	C₂×C₄	—	298	4	no	—
412	C₂×C₄	—	596	4	no	—
413	C₂×C₄	—	596	4	no	—
414	C₂×C₄	—	149	2	no	—
415	C₂×C₄	—	149	4	no	—
416	C₂×C₄	—	149	2	no	—
417	C₂×C₄	—	149	4	no	—
418	C₂×C₄	—	149	2	no	—
419	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
421	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
425	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	298	2	no	—
436	C₂²	—	298	2	no	—
437	C₂²	—	298	2	no	—
438	C₂²	C₂×#14558736	1	4	yes	—
439	C₂²	#18011958	1	2	yes	—
440	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	298	2	no	—
448	C₄	—	298	4	no	—
449	C₄	—	298	4	no	—
450	C₄	—	298	2	no	—
451	C₄	—	298	2	no	—
452	C₄	C₂×#14558736	1	2	yes	—
453	C₄	#18011956	1	2	yes	—
454	C₂	—	2	2	no	—
455	C₂	—	2	4	no	—
456	C₂	—	4	2	no	—
457	C₂	—	596	2	no	—
458	C₂	C₂²×#14558736	1	1	yes	characteristic
459	C₂	C₂×#18011956	1	1	yes	characteristic
460	C₂	C₂×#18011958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	C₂×C₄×D₄×C₁₄₉	C₂
hypercenter	C₂×C₄×D₄	D₁₄₉
hypocenter	C₁₄₉	#3520
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #23750345	C₂	semidirect
2. #23750330	C₂	semidirect
3. #23750315	C₂	semidirect
4. #23750301	C₂	semidirect
5. D₄×Dic₂₉₈	C₂	semidirect
6. #23750284	C₂	semidirect
7. #23750280	C₂	semidirect
8. #23750279	C₂	semidirect
9. #23750269	C₂	semidirect
10. #23750240	C₂	semidirect
11. #23750217	C₂	semidirect
12. #23750182	C₂	semidirect
13. #23750159	C₂	semidirect
14. #23750136	C₂	semidirect
15. C₂×#18011890	C₂	semidirect
16. #23750104	C₂	semidirect
17. C₂×C₄×D₄×C₁₄₉	C₂	semidirect
18. C₂×#14558736	C₂²	semidirect
20. C₂²×Dic₂₉₈	C₂²	semidirect
21. #18011911	C₂²	semidirect
22. #18011911	C₂²	semidirect
23. #18011910	C₂²	semidirect
24. #18011905	C₂²	semidirect
25. #18011904	C₂²	semidirect
26. #18011904	C₂²	semidirect
27. #18011903	C₂²	semidirect
28. #18011903	C₂²	semidirect
29. #18011901	C₂²	semidirect
30. #18011899	C₂²	semidirect
32. #18011897	C₂²	semidirect
33. #18011895	C₂²	semidirect
35. #18011894	C₂²	semidirect
36. #18011893	C₂²	semidirect
38. #18011891	C₂²	semidirect
43. #18011890	C₂²	semidirect
44. #18011890	C₂²	semidirect
45. #18011890	C₂²	semidirect
46. #18011890	C₂²	semidirect
47. #18011889	C₂²	semidirect
48. #18011888	C₂²	semidirect
50. #18011885	C₂²	semidirect
54. C₄×Dic₂₉₈	C₂²	semidirect
55. C₄×Dic₂₉₈	C₂²	semidirect
56. C₄×Dic₂₉₈	C₂²	semidirect
57. #18011876	C₂²	semidirect
58. C₄×D₅₉₆	C₂²	semidirect
62. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
63. #18011871	C₂²	semidirect
65. #18011870	C₂²	semidirect
66. #18011868	C₂²	semidirect
67. #18011867	C₂²	semidirect
68. C₂×C₄⋊Dic₁₄₉	C₂²	semidirect
69. C₂×#14558715	C₂²	semidirect
70. C₄⋊C₄×D₁₄₉	C₂²	semidirect
179. D₄×C₁₄₉	#41	semidirect
230. C₁₄₉	#3520	semidirect
248. C₂×C₄×D₄	D₁₄₉	semidirect
401. D₄	#14558736	semidirect

Maximal subgroups

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

subgroup	index
#23750345	2
#23750330	2
#23750315	2
#23750301	2
D₄×Dic₂₉₈	2
#23750284	2
#23750280	2
#23750279	2
#23750269	2
#23750240	2
#23750217	2
#23750182	2
#23750159	2
#23750136	2
C₂×#18011890	2
#23750104	2
C₂×C₄×D₄×C₁₄₉	2
#3520	149