Subgroups — #34058774

Order 19072.

1104 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750360	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750357	C₂	1	2	yes	maximal, complemented
3	Q₈×Dic₂₉₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750332	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750331	C₂	1	2	yes	maximal, complemented
6	#23750296	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750284	C₂	1	2	yes	maximal, complemented
8	#23750279	C₂	1	2	yes	maximal, complemented
9	#23750273	C₂	1	4	yes	maximal, complemented
10	#23750246	C₂	1	2	yes	maximal, complemented
11	#23750241	C₂	1	4	yes	maximal, complemented
12	#23750175	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750170	C₂	1	2	yes	maximal, complemented
14	#23750161	C₂	1	2	yes	maximal, complemented
15	#23750105	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×Dic₂₉₈	C₂	1	1	yes	maximal, characteristic, complemented
17	#529×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558736	C₂²	1	2	yes	—
19	C₂×#14558736	C₂²	1	2	yes	—
20	C₂×#14558735	C₂²	1	4	yes	—
21	C₂²×Dic₂₉₈	C₂²	1	1	yes	characteristic
22	#18011911	C₂²	1	1	yes	characteristic
23	#18011911	C₂²	1	2	yes	—
24	#18011910	C₂²	1	2	yes	—
25	#18011910	C₂²	1	4	yes	—
26	#18011908	C₂²	1	1	yes	characteristic
27	#18011907	C₂²	1	2	yes	—
28	#18011906	C₂²	1	4	yes	—
29	#18011902	C₂²	1	2	yes	—
30	#18011900	C₂²	1	2	yes	—
31	#18011899	C₂²	1	2	yes	—
32	#18011899	C₂²	1	2	yes	—
33	#18011897	C₂²	1	4	yes	—
34	#18011897	C₂²	1	4	yes	—
35	#18011896	C₂²	1	4	yes	—
36	#18011895	C₂²	1	4	yes	—
37	#18011895	C₂²	1	4	yes	—
38	#18011893	C₂²	1	4	yes	—
39	#18011891	C₂²	1	4	yes	—
40	#18011890	C₂²	1	2	yes	—
41	#18011889	C₂²	1	4	yes	—
42	#18011889	C₂²	1	4	yes	—
43	#18011888	C₂²	1	4	yes	—
44	#18011885	C₂²	1	2	yes	—
45	#18011885	C₂²	1	2	yes	—
46	#18011885	C₂²	1	2	yes	—
47	#18011884	C₂²	1	4	yes	—
48	#18011883	C₂²	1	4	yes	—
49	Q₈×Dic₁₄₉	C₂²	1	2	yes	—
50	C₄×Dic₂₉₈	C₂²	1	2	yes	—
51	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
52	C₄×Dic₂₉₈	C₂²	1	2	yes	—
53	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
54	C₄×Dic₂₉₈	C₂²	1	2	yes	—
55	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
56	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
57	C₄×D₅₉₆	C₂²	1	2	yes	—
58	C₄×D₅₉₆	C₂²	1	2	yes	—
59	C₄×D₅₉₆	C₂²	1	2	yes	—
60	D₄×Dic₁₄₉	C₂²	1	2	yes	—
61	#18011873	C₂²	1	2	yes	—
62	#18011873	C₂²	1	2	yes	—
63	#18011871	C₂²	1	4	yes	—
64	#18011871	C₂²	1	4	yes	—
65	#18011871	C₂²	1	4	yes	—
66	#18011869	C₂²	1	4	yes	—
67	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
68	C₂×C₄⋊Dic₁₄₉	C₂²	1	2	yes	—
69	C₂×#14558715	C₂²	1	2	yes	—
70	C₄⋊C₄×D₁₄₉	C₂²	1	4	yes	—
71	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	—
72	#126×C₁₄₉	C₂²	1	2	yes	—
73	#125×C₁₄₉	C₂²	1	1	yes	characteristic
74	#124×C₁₄₉	C₂²	1	1	yes	characteristic
75	#123×C₁₄₉	C₂²	1	2	yes	—
76	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
77	#121×C₁₄₉	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
79	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
80	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
81	#117×C₁₄₉	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
83	#14558736	—	2	8	no	—
84	#14558736	—	4	4	no	—
85	#14558735	—	4	8	no	—
86	C₂×Dic₂₉₈	—	2	4	no	—
87	C₂×Dic₂₉₈	C₂³	1	2	yes	—
88	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
89	C₂×Dic₂₉₈	C₂³	1	4	yes	—
90	C₂×Dic₂₉₈	C₂³	1	2	yes	—
91	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
92	C₂×D₅₉₆	C₂³	1	2	yes	—
93	C₂×D₅₉₆	C₂³	1	2	yes	—
94	C₂×D₅₉₆	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
98	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
99	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
100	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
101	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
102	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
103	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
104	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
105	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
106	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
107	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
109	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
111	#14558715	C₂³	1	4	yes	—
112	#14558715	C₂³	1	4	yes	—
113	#14558715	C₂³	1	2	yes	—
114	#14558715	C₂³	1	2	yes	—
115	#14558715	C₂³	1	2	yes	—
116	#14558715	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
118	#14558713	C₂³	1	4	yes	—
119	#14558713	C₂³	1	4	yes	—
120	#14558713	C₂³	1	4	yes	—
121	#14558713	C₂³	1	4	yes	—
122	#14558713	C₂³	1	4	yes	—
123	#14558713	C₂³	1	4	yes	—
124	C₄×Dic₁₄₉	C₂³	1	2	yes	—
125	C₄×Dic₁₄₉	C₂³	1	2	yes	—
126	C₄×Dic₁₄₉	C₂³	1	4	yes	—
127	C₄×Dic₁₄₉	C₂³	1	2	yes	—
128	C₄×Dic₁₄₉	C₂³	1	2	yes	—
129	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
137	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
139	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
140	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
147	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
148	C₄²×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	C₂²×D₁₄₉	C₂⁴	1	4	yes	—
153	Dic₂₉₈	—	2	2	no	—
154	Dic₂₉₈	—	2	4	no	—
155	Dic₂₉₈	—	4	4	no	—
156	Dic₂₉₈	—	4	2	no	—
157	Dic₂₉₈	#41	1	4	yes	complemented
158	D₅₉₆	—	2	4	no	—
159	D₅₉₆	—	2	4	no	—
160	D₅₉₆	—	4	2	no	—
161	C₂²⋊D₁₄₉	—	2	8	no	—
162	C₂²⋊D₁₄₉	—	2	8	no	—
163	C₂²⋊D₁₄₉	—	4	4	no	—
164	C₂×Dic₁₄₉	—	2	4	no	—
165	C₂×Dic₁₄₉	—	2	4	no	—
166	C₂×Dic₁₄₉	—	4	4	no	—
167	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
168	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
169	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
170	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
171	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
172	C₄×D₁₄₉	—	2	8	no	—
173	C₄×D₁₄₉	—	4	4	no	—
174	C₄×D₁₄₉	—	4	4	no	—
175	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
176	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
177	Q₈×C₁₄₉	—	2	2	no	—
178	D₄×C₁₄₉	—	2	4	no	—
179	D₄×C₁₄₉	—	2	2	no	—
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	2	no	—
184	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
185	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
186	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
187	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
191	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
193	C₂²×C₁₄₉	—	2	1	no	—
194	C₂²×C₁₄₉	—	2	1	no	—
195	C₂²×C₁₄₉	—	2	2	no	—
196	C₂²×C₁₄₉	—	2	2	no	—
197	C₂²×C₁₄₉	—	2	2	no	—
198	C₂²×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
199	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
200	C₂×D₁₄₉	—	2	4	no	—
201	C₂×D₁₄₉	—	2	4	no	—
202	C₂×D₁₄₉	—	2	4	no	—
203	C₄×C₁₄₉	—	2	2	no	—
204	C₄×C₁₄₉	—	2	1	no	—
205	C₄×C₁₄₉	—	2	1	no	—
206	C₄×C₁₄₉	—	2	1	no	—
207	C₄×C₁₄₉	—	2	2	no	—
208	C₄×C₁₄₉	—	2	1	no	—
209	C₄×C₁₄₉	—	2	2	no	—
210	C₄×C₁₄₉	C₂×#41	1	2	yes	—
211	C₄×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
212	Dic₁₄₉	—	2	2	no	—
213	Dic₁₄₉	—	2	2	no	—
214	Dic₁₄₉	—	2	4	no	—
215	Dic₁₄₉	—	2	2	no	—
216	Dic₁₄₉	C₂×#41	1	4	yes	—
217	C₂×C₁₄₉	—	2	2	no	—
218	C₂×C₁₄₉	—	4	2	no	—
219	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
220	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
222	D₁₄₉	—	4	4	no	—
223	C₁₄₉	#3522	1	1	yes	characteristic, complemented, Sylow
224	#3522	—	149	1	no	maximal, Sylow
225	#559	—	149	2	no	—
226	#559	—	149	1	no	—
227	Q₈²	—	149	1	no	—
228	#554	—	149	2	no	—
229	#554	—	149	1	no	—
230	#550	—	149	1	no	—
231	#548	—	149	2	no	—
232	#547	—	149	4	no	—
233	#547	—	149	2	no	—
234	#542	—	149	4	no	—
235	#542	—	149	2	no	—
236	#532	—	149	2	no	—
237	#532	—	149	1	no	—
238	#529	—	149	2	no	—
239	#529	D₁₄₉	1	1	yes	characteristic, complemented
240	#520	—	149	2	no	—
241	C₂×C₄×Q₈	—	149	1	no	—
242	C₂×#41	—	149	4	no	—
243	C₂×#41	—	149	2	no	—
244	C₂×#41	—	149	2	no	—
245	C₂²×Q₈	—	149	1	no	—
246	C₄⋊Q₈	—	149	2	no	—
247	C₄⋊Q₈	—	149	4	no	—
248	C₄⋊Q₈	—	149	1	no	—
249	C₄⋊Q₈	—	149	2	no	—
250	#127	—	149	2	no	—
251	#127	—	149	1	no	—
252	#126	—	149	4	no	—
253	#126	C₂×D₁₄₉	1	2	yes	—
254	#125	—	149	2	no	—
255	#125	C₂×D₁₄₉	1	1	yes	characteristic
256	#124	—	149	2	no	—
257	#124	—	149	4	no	—
258	#124	—	149	4	no	—
259	#124	—	149	2	no	—
260	#124	—	149	2	no	—
261	#124	C₂×D₁₄₉	1	1	yes	characteristic
262	#123	—	149	4	no	—
263	#123	—	149	4	no	—
264	#123	—	149	4	no	—
265	#123	—	149	4	no	—
266	#123	C₂×D₁₄₉	1	2	yes	—
267	C₂²⋊Q₈	—	149	2	no	—
268	C₂²⋊Q₈	—	149	4	no	—
269	C₂²⋊Q₈	—	149	4	no	—
270	C₂²⋊Q₈	—	149	4	no	—
271	C₂²⋊Q₈	—	149	4	no	—
272	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
273	#121	—	149	4	no	—
274	#121	—	149	2	no	—
275	#121	—	149	2	no	—
276	#121	—	149	2	no	—
277	#121	—	149	4	no	—
278	#121	C₂×D₁₄₉	1	1	yes	characteristic
279	C₄×Q₈	—	149	2	no	—
280	C₄×Q₈	—	149	1	no	—
281	C₄×Q₈	—	149	2	no	—
282	C₄×Q₈	—	149	1	no	—
283	C₄×Q₈	—	149	1	no	—
284	C₄×Q₈	—	149	1	no	—
285	C₄×Q₈	—	149	2	no	—
286	C₄×Q₈	—	149	2	no	—
287	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
288	C₄×D₄	—	149	2	no	—
289	C₄×D₄	—	149	2	no	—
290	C₄×D₄	—	149	2	no	—
291	C₄×D₄	—	149	4	no	—
292	C₄×D₄	—	149	4	no	—
293	C₄×D₄	—	149	4	no	—
294	C₄×D₄	—	149	2	no	—
295	C₄×D₄	—	149	2	no	—
296	C₄×D₄	—	149	2	no	—
297	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
298	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
299	#117	—	149	4	no	—
300	#117	C₂×D₁₄₉	1	2	yes	—
301	C₂×C₄⋊C₄	—	149	2	no	—
302	C₂×C₄⋊C₄	—	149	1	no	—
303	C₂×C₄⋊C₄	—	149	2	no	—
304	C₂×C₄⋊C₄	—	149	4	no	—
305	C₂×C₄²	—	149	2	no	—
306	C₂×C₄²	C₂×D₁₄₉	1	1	yes	characteristic
307	#41	—	298	8	no	—
308	#41	—	596	4	no	—
309	#41	—	596	8	no	—
310	C₂×Q₈	—	298	4	no	—
311	C₂×Q₈	—	149	1	no	—
312	C₂×Q₈	—	149	2	no	—
313	C₂×Q₈	—	149	4	no	—
314	C₂×Q₈	—	149	2	no	—
315	C₂×Q₈	—	149	1	no	—
316	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
317	C₂×D₄	—	149	4	no	—
318	C₂×D₄	—	149	4	no	—
319	C₂×D₄	—	149	4	no	—
320	C₂×D₄	—	149	2	no	—
321	C₂×D₄	—	149	2	no	—
322	C₂×D₄	—	149	2	no	—
323	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
324	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
325	C₂²×C₄	—	149	2	no	—
326	C₂²×C₄	—	149	2	no	—
327	C₂²×C₄	—	149	4	no	—
328	C₂²×C₄	—	149	4	no	—
329	C₂²×C₄	—	149	4	no	—
330	C₂²×C₄	—	149	4	no	—
331	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
332	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
333	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
335	C₄⋊C₄	—	149	2	no	—
336	C₄⋊C₄	—	149	1	no	—
337	C₄⋊C₄	—	149	4	no	—
338	C₄⋊C₄	—	149	4	no	—
339	C₄⋊C₄	—	149	2	no	—
340	C₄⋊C₄	—	149	2	no	—
341	C₄⋊C₄	—	149	1	no	—
342	C₄⋊C₄	—	149	2	no	—
343	C₄⋊C₄	—	149	2	no	—
344	C₄⋊C₄	—	149	2	no	—
345	C₄⋊C₄	—	149	2	no	—
346	C₄⋊C₄	—	149	4	no	—
347	C₄⋊C₄	—	149	4	no	—
348	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
349	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
350	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
351	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
352	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
353	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
354	C₂²⋊C₄	—	149	4	no	—
355	C₂²⋊C₄	—	149	4	no	—
356	C₂²⋊C₄	—	149	4	no	—
357	C₂²⋊C₄	—	149	4	no	—
358	C₂²⋊C₄	—	149	4	no	—
359	C₂²⋊C₄	—	149	4	no	—
360	C₂²⋊C₄	—	149	4	no	—
361	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
362	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
363	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
364	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
365	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
366	C₄²	—	149	2	no	—
367	C₄²	—	149	2	no	—
368	C₄²	—	149	2	no	—
369	C₄²	—	149	2	no	—
370	C₄²	—	149	4	no	—
371	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
372	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
373	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
374	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
375	C₄²	C₂²×D₁₄₉	1	2	yes	—
376	C₂³	—	149	4	no	—
377	C₂³	C₂³×D₁₄₉	1	2	yes	—
378	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	298	4	no	—
381	Q₈	—	298	2	no	—
382	Q₈	—	596	2	no	—
383	Q₈	—	596	4	no	—
384	Q₈	—	149	4	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	2	no	—
387	D₄	—	298	8	no	—
388	D₄	—	298	8	no	—
389	D₄	—	298	4	no	—
390	D₄	—	298	4	no	—
391	D₄	—	596	2	no	—
392	D₄	—	596	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	298	8	no	—
398	C₂×C₄	—	298	4	no	—
399	C₂×C₄	—	298	4	no	—
400	C₂×C₄	—	596	4	no	—
401	C₂×C₄	—	596	4	no	—
402	C₂×C₄	—	596	4	no	—
403	C₂×C₄	—	149	2	no	—
404	C₂×C₄	—	149	2	no	—
405	C₂×C₄	—	149	2	no	—
406	C₂×C₄	—	149	4	no	—
407	C₂×C₄	—	149	2	no	—
408	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
409	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
410	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
411	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
413	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
414	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
415	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	298	4	no	—
423	C₂²	—	298	4	no	—
424	C₂²	—	298	4	no	—
425	C₂²	#18011957	1	2	yes	—
426	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	2	no	—
434	C₄	—	298	2	no	—
435	C₄	—	298	2	no	—
436	C₄	—	298	2	no	—
437	C₄	—	298	4	no	—
438	C₄	—	149	4	no	—
439	C₄	#41×D₁₄₉	1	2	yes	—
440	C₄	#18011958	1	2	yes	—
441	C₂	—	2	2	no	—
442	C₂	—	4	2	no	—
443	C₂	—	596	4	no	—
444	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
445	C₂	C₂×#18011957	1	1	yes	characteristic
446	C₂	C₂×#18011958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#529×C₁₄₉	C₂
hypercenter	#529	D₁₄₉
hypocenter	C₁₄₉	#3522
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #23750360	C₂	semidirect
2. #23750357	C₂	semidirect
3. Q₈×Dic₂₉₈	C₂	semidirect
4. #23750332	C₂	semidirect
5. #23750331	C₂	semidirect
6. #23750296	C₂	semidirect
7. #23750284	C₂	semidirect
8. #23750279	C₂	semidirect
9. #23750273	C₂	semidirect
10. #23750246	C₂	semidirect
11. #23750241	C₂	semidirect
12. #23750175	C₂	semidirect
13. #23750170	C₂	semidirect
14. #23750161	C₂	semidirect
15. #23750105	C₂	semidirect
16. C₂×C₄×Dic₂₉₈	C₂	semidirect
17. #529×C₁₄₉	C₂	semidirect
157. Dic₂₉₈	#41	semidirect
223. C₁₄₉	#3522	semidirect
239. #529	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750360	2
#23750357	2
Q₈×Dic₂₉₈	2
#23750332	2
#23750331	2
#23750296	2
#23750284	2
#23750279	2
#23750273	2
#23750246	2
#23750241	2
#23750175	2
#23750170	2
#23750161	2
#23750105	2
C₂×C₄×Dic₂₉₈	2
#529×C₁₄₉	2
#3522	149