Subgroups — #34058643

Order 19072.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750361	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750345	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750339	C₂	1	2	yes	maximal, complemented
4	#23750306	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₂₉₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750281	C₂	1	2	yes	maximal, complemented
7	#23750269	C₂	1	2	yes	maximal, complemented
8	#23750269	C₂	1	2	yes	maximal, complemented
9	#23750242	C₂	1	2	yes	maximal, complemented
10	#23750210	C₂	1	4	yes	maximal, complemented
11	#23750173	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750157	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750156	C₂	1	2	yes	maximal, complemented
14	C₂×#18011898	C₂	1	2	yes	maximal, complemented
15	#23750100	C₂	1	2	yes	maximal, complemented
16	C₄×#14558735	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄²×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558735	C₂²	1	1	yes	characteristic
19	C₂×#14558735	C₂²	1	2	yes	complemented
20	C₂²×Dic₂₉₈	C₂²	1	2	yes	complemented
21	#18011911	C₂²	1	1	yes	characteristic, complemented
22	#18011910	C₂²	1	2	yes	complemented
23	#18011904	C₂²	1	4	yes	complemented
24	#18011904	C₂²	1	2	yes	complemented
25	#18011904	C₂²	1	4	yes	complemented
26	#18011902	C₂²	1	1	yes	characteristic, complemented
27	#18011898	C₂²	1	1	yes	characteristic
28	#18011898	C₂²	1	2	yes	—
29	#18011898	C₂²	1	2	yes	complemented
30	#18011898	C₂²	1	4	yes	complemented
31	#18011898	C₂²	1	2	yes	complemented
32	#18011898	C₂²	1	2	yes	complemented
33	#18011898	C₂²	1	4	yes	complemented
34	#18011897	C₂²	1	4	yes	complemented
35	#18011893	C₂²	1	2	yes	complemented
36	#18011892	C₂²	1	4	yes	complemented
37	#18011892	C₂²	1	4	yes	complemented
38	#18011892	C₂²	1	4	yes	complemented
39	#18011891	C₂²	1	1	yes	characteristic, complemented
40	#18011890	C₂²	1	2	yes	complemented
41	#18011890	C₂²	1	2	yes	complemented
42	#18011888	C₂²	1	4	yes	complemented
43	#18011888	C₂²	1	4	yes	complemented
44	#18011883	C₂²	1	4	yes	complemented
45	#18011883	C₂²	1	4	yes	complemented
46	#18011882	C₂²	1	1	yes	characteristic
47	#18011882	C₂²	1	2	yes	complemented
48	#18011882	C₂²	1	2	yes	complemented
49	#18011880	C₂²	1	4	yes	complemented
50	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
51	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
52	#18011876	C₂²	1	2	yes	complemented
53	#18011876	C₂²	1	1	yes	characteristic, complemented
54	D₄×Dic₁₄₉	C₂²	1	2	yes	—
55	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
56	D₄×Dic₁₄₉	C₂²	1	4	yes	complemented
57	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
58	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
59	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
60	D₄×Dic₁₄₉	C₂²	1	4	yes	complemented
61	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
64	#18011871	C₂²	1	2	yes	complemented
65	#18011870	C₂²	1	2	yes	complemented
66	#18011870	C₂²	1	2	yes	complemented
67	#18011869	C₂²	1	1	yes	characteristic, complemented
68	#18011867	C₂²	1	4	yes	complemented
69	#18011867	C₂²	1	2	yes	complemented
70	C₂×C₂²⋊Dic₁₄₉	C₂²	1	4	yes	complemented
71	C₂×C₂²⋊Dic₁₄₉	C₂²	1	4	yes	complemented
72	C₂×C₂²⋊Dic₁₄₉	C₂²	1	4	yes	complemented
73	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	complemented
74	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
75	C₂²×D₄×C₁₄₉	C₂²	1	2	yes	—
76	C₂²×D₄×C₁₄₉	C₂²	1	2	yes	—
77	#127×C₁₄₉	C₂²	1	1	yes	characteristic
78	#121×C₁₄₉	C₂²	1	2	yes	—
79	#121×C₁₄₉	C₂²	1	2	yes	—
80	#120×C₁₄₉	C₂²	1	4	yes	—
81	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
82	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
83	#14558735	—	2	4	no	—
84	#14558735	—	4	4	no	—
85	C₂×Dic₂₉₈	—	4	4	no	—
86	C₂×Dic₂₉₈	C₂³	1	2	yes	—
87	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
88	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
89	C₂×Dic₂₉₈	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
93	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
94	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
95	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
96	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
97	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
98	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
101	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
102	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
103	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
104	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
105	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
107	#14558715	C₂³	1	2	yes	—
108	#14558715	C₂³	1	4	yes	—
109	#14558715	C₂³	1	4	yes	—
110	#14558715	C₂³	1	2	yes	—
111	#14558715	C₂³	1	2	yes	—
112	#14558715	C₂³	1	2	yes	—
113	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
114	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
116	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
119	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
120	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
121	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
123	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
124	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
125	#14558713	C₂³	1	2	yes	—
126	#14558713	C₂³	1	2	yes	—
127	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
128	C₄×Dic₁₄₉	C₂³	1	2	yes	—
129	C₄×Dic₁₄₉	C₂³	1	4	yes	—
130	C₄×Dic₁₄₉	C₂³	1	2	yes	—
131	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
132	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
133	C₄×Dic₁₄₉	C₂³	1	2	yes	—
134	C₄×Dic₁₄₉	C₂³	1	2	yes	—
135	C₂⁴×C₁₄₉	C₂³	1	4	yes	—
136	C₂×D₄×C₁₄₉	—	2	8	no	—
137	C₂×D₄×C₁₄₉	—	4	4	no	—
138	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
139	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
141	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
142	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
143	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
144	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
145	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
146	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
147	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
149	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
151	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
152	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
153	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
154	Dic₂₉₈	—	2	2	no	—
155	Dic₂₉₈	—	2	2	no	—
156	Dic₂₉₈	—	2	4	no	—
157	Dic₂₉₈	—	4	4	no	—
158	C₂²⋊D₁₄₉	—	2	4	no	—
159	C₂²⋊D₁₄₉	—	4	2	no	—
160	C₂²⋊D₁₄₉	—	4	4	no	—
161	C₂×Dic₁₄₉	—	2	4	no	—
162	C₂×Dic₁₄₉	—	4	2	no	—
163	C₂×Dic₁₄₉	—	4	4	no	—
164	C₂×Dic₁₄₉	—	4	4	no	—
165	C₂×Dic₁₄₉	—	4	4	no	—
166	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
167	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
168	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
169	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
170	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
171	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
172	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
173	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
174	C₄×D₁₄₉	—	2	2	no	—
175	C₄×D₁₄₉	—	2	2	no	—
176	C₄×D₁₄₉	—	4	1	no	—
177	C₂³×C₁₄₉	—	2	8	no	—
178	C₂³×C₁₄₉	—	4	4	no	—
179	C₂³×C₁₄₉	—	4	4	no	—
180	C₂³×C₁₄₉	C₂⁴	1	4	yes	—
181	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
182	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
183	D₄×C₁₄₉	—	2	8	no	—
184	D₄×C₁₄₉	—	2	4	no	—
185	D₄×C₁₄₉	—	2	4	no	—
186	D₄×C₁₄₉	—	2	2	no	—
187	D₄×C₁₄₉	—	4	4	no	—
188	D₄×C₁₄₉	—	4	2	no	—
189	D₄×C₁₄₉	#41	1	4	yes	complemented
190	C₂×C₄×C₁₄₉	—	2	4	no	—
191	C₂×C₄×C₁₄₉	—	2	4	no	—
192	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
194	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
195	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
196	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
197	C₂²×C₁₄₉	—	2	2	no	—
198	C₂²×C₁₄₉	—	2	2	no	—
199	C₂²×C₁₄₉	—	2	2	no	—
200	C₂²×C₁₄₉	—	2	4	no	—
201	C₂²×C₁₄₉	—	2	2	no	—
202	C₂²×C₁₄₉	—	2	4	no	—
203	C₂²×C₁₄₉	—	2	4	no	—
204	C₂²×C₁₄₉	—	2	2	no	—
205	C₂²×C₁₄₉	—	8	8	no	—
206	C₂²×C₁₄₉	C₂×#41	1	4	yes	—
207	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
208	C₂×D₁₄₉	—	2	1	no	—
209	C₂×D₁₄₉	—	2	1	no	—
210	C₂×D₁₄₉	—	2	1	no	—
211	C₄×C₁₄₉	—	2	2	no	—
212	C₄×C₁₄₉	—	2	2	no	—
213	C₄×C₁₄₉	—	2	1	no	—
214	C₄×C₁₄₉	C₂×#41	1	2	yes	—
215	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
216	Dic₁₄₉	—	2	1	no	—
217	Dic₁₄₉	—	2	2	no	—
218	Dic₁₄₉	—	2	1	no	—
219	Dic₁₄₉	—	2	4	no	—
220	Dic₁₄₉	—	2	2	no	—
221	Dic₁₄₉	—	2	1	no	—
222	Dic₁₄₉	—	2	2	no	—
223	Dic₁₄₉	—	2	2	no	—
224	C₂×C₁₄₉	—	2	4	no	—
225	C₂×C₁₄₉	—	4	4	no	—
226	C₂×C₁₄₉	—	4	2	no	—
227	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
228	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₁₄₉	#585	1	1	yes	characteristic
230	D₁₄₉	—	4	1	no	—
231	C₁₄₉	#3514	1	1	yes	characteristic, complemented, Sylow
232	#3514	—	149	1	no	maximal, Sylow
233	#559	—	149	1	no	—
234	#556	—	149	1	no	—
235	#555	—	149	2	no	—
236	#551	—	149	4	no	—
237	D₄×Q₈	—	149	1	no	—
238	#548	—	149	2	no	—
239	#546	—	149	2	no	—
240	#546	—	149	2	no	—
241	D₄²	D₁₄₉	1	1	yes	characteristic, complemented
242	#542	—	149	2	no	—
243	#538	—	149	4	no	—
244	#532	—	149	1	no	—
245	#529	—	149	2	no	—
246	#529	—	149	1	no	—
247	C₂×#124	—	149	2	no	—
248	#518	—	149	2	no	—
249	C₄×#41	—	149	1	no	—
250	C₂×#41	—	149	1	no	—
251	C₂×#41	—	149	2	no	—
252	C₂²×Q₈	—	149	2	no	—
253	C₂²×D₄	C₂×D₁₄₉	1	2	yes	—
254	C₂²×D₄	C₂×D₁₄₉	1	2	yes	—
255	C₄⋊Q₈	—	149	2	no	—
256	C₄⋊Q₈	—	149	1	no	—
257	#127	C₂×D₁₄₉	1	1	yes	characteristic
258	#126	—	149	4	no	—
259	#126	—	149	2	no	—
260	#126	—	149	4	no	—
261	#125	—	149	1	no	—
262	#124	—	149	1	no	—
263	#124	—	149	2	no	—
264	#124	—	149	4	no	—
265	#124	—	149	2	no	—
266	#124	—	149	2	no	—
267	#124	—	149	4	no	—
268	#124	—	149	2	no	—
269	#124	—	149	4	no	—
270	#123	—	149	4	no	—
271	#123	—	149	4	no	—
272	#123	—	149	4	no	—
273	#123	—	149	2	no	—
274	C₂²⋊Q₈	—	149	2	no	—
275	C₂²⋊Q₈	—	149	2	no	—
276	C₂²⋊Q₈	—	149	1	no	—
277	C₂²⋊Q₈	—	149	4	no	—
278	C₂²⋊Q₈	—	149	4	no	—
279	#121	—	149	1	no	—
280	#121	—	149	2	no	—
281	#121	—	149	2	no	—
282	#121	—	149	4	no	—
283	#121	—	149	4	no	—
284	#121	C₂×D₁₄₉	1	2	yes	—
285	#121	C₂×D₁₄₉	1	2	yes	—
286	#120	—	149	4	no	—
287	#120	C₂×D₁₄₉	1	4	yes	—
288	C₄×Q₈	—	149	1	no	—
289	C₄×Q₈	—	149	2	no	—
290	C₄×Q₈	—	149	1	no	—
291	C₄×Q₈	—	149	1	no	—
292	C₄×D₄	—	149	1	no	—
293	C₄×D₄	—	149	4	no	—
294	C₄×D₄	—	149	2	no	—
295	C₄×D₄	—	149	2	no	—
296	C₄×D₄	—	149	4	no	—
297	C₄×D₄	—	149	2	no	—
298	C₄×D₄	—	149	2	no	—
299	C₄×D₄	—	149	2	no	—
300	C₄×D₄	—	149	2	no	—
301	C₄×D₄	—	149	2	no	—
302	C₄×D₄	—	149	2	no	—
303	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
304	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
305	#117	—	149	2	no	—
306	#117	—	149	2	no	—
307	#117	—	149	1	no	—
308	#117	—	149	2	no	—
309	#117	—	149	4	no	—
310	C₂×C₂²⋊C₄	—	149	4	no	—
311	C₂×C₂²⋊C₄	—	149	4	no	—
312	C₂×C₂²⋊C₄	—	149	4	no	—
313	C₂×C₄²	—	149	2	no	—
314	C₂×C₄²	—	149	1	no	—
315	C₂⁴	C₂²×D₁₄₉	1	4	yes	—
316	#41	—	298	4	no	—
317	#41	—	596	4	no	—
318	C₂×Q₈	—	596	4	no	—
319	C₂×Q₈	—	149	1	no	—
320	C₂×Q₈	—	149	1	no	—
321	C₂×Q₈	—	149	2	no	—
322	C₂×Q₈	—	149	4	no	—
323	C₂×D₄	—	2	8	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	149	2	no	—
326	C₂×D₄	—	149	2	no	—
327	C₂×D₄	—	149	4	no	—
328	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
329	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
330	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
331	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
332	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
333	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
334	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
335	C₂²×C₄	—	149	2	no	—
336	C₂²×C₄	—	149	1	no	—
337	C₂²×C₄	—	149	1	no	—
338	C₂²×C₄	—	149	2	no	—
339	C₂²×C₄	—	149	4	no	—
340	C₂²×C₄	—	149	4	no	—
341	C₂²×C₄	—	149	4	no	—
342	C₂²×C₄	—	149	1	no	—
343	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
344	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
345	C₄⋊C₄	—	149	1	no	—
346	C₄⋊C₄	—	149	2	no	—
347	C₄⋊C₄	—	149	2	no	—
348	C₄⋊C₄	—	149	2	no	—
349	C₄⋊C₄	—	149	2	no	—
350	C₄⋊C₄	—	149	2	no	—
351	C₄⋊C₄	—	149	2	no	—
352	C₄⋊C₄	—	149	4	no	—
353	C₄⋊C₄	—	149	1	no	—
354	C₄⋊C₄	—	149	2	no	—
355	C₄⋊C₄	—	149	4	no	—
356	C₄⋊C₄	—	149	2	no	—
357	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
358	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
359	C₂²⋊C₄	—	149	2	no	—
360	C₂²⋊C₄	—	149	2	no	—
361	C₂²⋊C₄	—	149	4	no	—
362	C₂²⋊C₄	—	149	2	no	—
363	C₂²⋊C₄	—	149	2	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	4	no	—
369	C₂²⋊C₄	—	149	4	no	—
370	C₂²⋊C₄	—	149	4	no	—
371	C₂²⋊C₄	—	149	2	no	—
372	C₂²⋊C₄	—	149	2	no	—
373	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
375	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
376	C₄²	—	149	1	no	—
377	C₄²	—	149	2	no	—
378	C₄²	—	149	1	no	—
379	C₄²	—	149	1	no	—
380	C₄²	—	149	2	no	—
381	C₄²	—	149	2	no	—
382	C₄²	—	149	4	no	—
383	C₄²	—	149	2	no	—
384	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
385	C₂³	—	2	8	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	149	1	no	—
389	C₂³	C₂³×D₁₄₉	1	2	yes	—
390	C₂³	C₂³×D₁₄₉	1	4	yes	—
391	C₂³	C₂³×D₁₄₉	1	2	yes	—
392	Q₈	—	298	2	no	—
393	Q₈	—	298	2	no	—
394	Q₈	—	298	4	no	—
395	Q₈	—	596	4	no	—
396	D₄	—	2	8	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	298	4	no	—
403	D₄	—	596	2	no	—
404	D₄	—	596	4	no	—
405	D₄	#14558735	1	4	yes	complemented
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	298	4	no	—
409	C₂×C₄	—	298	2	no	—
410	C₂×C₄	—	298	2	no	—
411	C₂×C₄	—	596	1	no	—
412	C₂×C₄	—	596	2	no	—
413	C₂×C₄	—	596	4	no	—
414	C₂×C₄	—	596	4	no	—
415	C₂×C₄	—	596	4	no	—
416	C₂×C₄	—	149	1	no	—
417	C₂×C₄	—	149	1	no	—
418	C₂×C₄	—	149	2	no	—
419	C₂×C₄	—	149	2	no	—
420	C₂×C₄	—	149	1	no	—
421	C₂×C₄	—	149	2	no	—
422	C₂×C₄	—	149	2	no	—
423	C₂×C₄	—	149	4	no	—
424	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
425	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
426	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	8	8	no	—
438	C₂²	—	298	1	no	—
439	C₂²	—	298	1	no	—
440	C₂²	—	298	1	no	—
441	C₂²	C₂×#14558735	1	4	yes	—
442	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	298	1	no	—
447	C₄	—	298	2	no	—
448	C₄	—	298	1	no	—
449	C₄	—	298	4	no	—
450	C₄	—	298	2	no	—
451	C₄	—	298	1	no	—
452	C₄	—	298	2	no	—
453	C₄	—	298	2	no	—
454	C₄	C₂×#14558735	1	2	yes	—
455	C₄	#18011956	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	4	2	no	—
458	C₂	—	4	4	no	—
459	C₂	—	596	1	no	—
460	C₂	C₂²×#14558735	1	1	yes	characteristic
461	C₂	C₂×#18011956	1	1	yes	characteristic
462	C₂	#23750460	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	D₄²×C₁₄₉	C₂
hypercenter	D₄²	D₁₄₉
hypocenter	C₁₄₉	#3514
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. #23750361	C₂	semidirect
2. #23750345	C₂	semidirect
3. #23750339	C₂	semidirect
4. #23750306	C₂	semidirect
5. D₄×Dic₂₉₈	C₂	semidirect
6. #23750281	C₂	semidirect
7. #23750269	C₂	semidirect
8. #23750269	C₂	semidirect
9. #23750242	C₂	semidirect
10. #23750210	C₂	semidirect
11. #23750173	C₂	semidirect
12. #23750157	C₂	semidirect
13. #23750156	C₂	semidirect
14. C₂×#18011898	C₂	semidirect
15. #23750100	C₂	semidirect
16. C₄×#14558735	C₂	semidirect
17. D₄²×C₁₄₉	C₂	semidirect
19. C₂×#14558735	C₂²	semidirect
20. C₂²×Dic₂₉₈	C₂²	semidirect
21. #18011911	C₂²	semidirect
22. #18011910	C₂²	semidirect
23. #18011904	C₂²	semidirect
24. #18011904	C₂²	semidirect
25. #18011904	C₂²	semidirect
26. #18011902	C₂²	semidirect
29. #18011898	C₂²	semidirect
30. #18011898	C₂²	semidirect
31. #18011898	C₂²	semidirect
32. #18011898	C₂²	semidirect
33. #18011898	C₂²	semidirect
34. #18011897	C₂²	semidirect
35. #18011893	C₂²	semidirect
36. #18011892	C₂²	semidirect
37. #18011892	C₂²	semidirect
38. #18011892	C₂²	semidirect
39. #18011891	C₂²	semidirect
40. #18011890	C₂²	semidirect
41. #18011890	C₂²	semidirect
42. #18011888	C₂²	semidirect
43. #18011888	C₂²	semidirect
44. #18011883	C₂²	semidirect
45. #18011883	C₂²	semidirect
47. #18011882	C₂²	semidirect
48. #18011882	C₂²	semidirect
49. #18011880	C₂²	semidirect
50. C₄×Dic₂₉₈	C₂²	semidirect
51. C₄×Dic₂₉₈	C₂²	semidirect
52. #18011876	C₂²	semidirect
53. #18011876	C₂²	semidirect
56. D₄×Dic₁₄₉	C₂²	semidirect
57. D₄×Dic₁₄₉	C₂²	semidirect
58. D₄×Dic₁₄₉	C₂²	semidirect
59. D₄×Dic₁₄₉	C₂²	semidirect
60. D₄×Dic₁₄₉	C₂²	semidirect
61. D₄×Dic₁₄₉	C₂²	semidirect
62. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
63. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
64. #18011871	C₂²	semidirect
65. #18011870	C₂²	semidirect
66. #18011870	C₂²	semidirect
67. #18011869	C₂²	semidirect
68. #18011867	C₂²	semidirect
69. #18011867	C₂²	semidirect
70. C₂×C₂²⋊Dic₁₄₉	C₂²	semidirect
71. C₂×C₂²⋊Dic₁₄₉	C₂²	semidirect
72. C₂×C₂²⋊Dic₁₄₉	C₂²	semidirect
73. C₂×C₄×Dic₁₄₉	C₂²	semidirect
74. C₄²×D₁₄₉	C₂²	semidirect
189. D₄×C₁₄₉	#41	semidirect
231. C₁₄₉	#3514	semidirect
241. D₄²	D₁₄₉	semidirect
405. D₄	#14558735	semidirect

Maximal subgroups

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

subgroup	index
#23750361	2
#23750345	2
#23750339	2
#23750306	2
D₄×Dic₂₉₈	2
#23750281	2
#23750269	2
#23750242	2
#23750210	2
#23750173	2
#23750157	2
#23750156	2
C₂×#18011898	2
#23750100	2
C₄×#14558735	2
D₄²×C₁₄₉	2
#3514	149