Subgroups — #34058446

Order 19072.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750349	C₂	1	2	yes	maximal, complemented
2	#23750336	C₂	1	2	yes	maximal, complemented
3	#23750317	C₂	1	4	yes	maximal, complemented
4	#23750313	C₂	1	2	yes	maximal, complemented
5	#23750313	C₂	1	2	yes	maximal, complemented
6	#23750302	C₂	1	4	yes	maximal, complemented
7	#23750249	C₂	1	2	yes	maximal, complemented
8	#23750238	C₂	1	2	yes	maximal, complemented
9	#23750201	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750180	C₂	1	2	yes	maximal, complemented
11	#23750160	C₂	1	2	yes	maximal, complemented
12	#23750137	C₂	1	1	yes	maximal, characteristic
13	C₂×#18011891	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750106	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750102	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#544×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558736	C₂²	1	1	yes	characteristic
19	C₂²×Dic₂₉₈	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
21	#18011911	C₂²	1	2	yes	complemented
22	#18011906	C₂²	1	4	yes	—
23	#18011906	C₂²	1	4	yes	—
24	#18011906	C₂²	1	4	yes	complemented
25	#18011906	C₂²	1	4	yes	complemented
26	#18011902	C₂²	1	4	yes	complemented
27	#18011902	C₂²	1	4	yes	complemented
28	#18011902	C₂²	1	4	yes	complemented
29	#18011900	C₂²	1	4	yes	—
30	#18011899	C₂²	1	2	yes	complemented
31	#18011896	C₂²	1	4	yes	—
32	#18011896	C₂²	1	4	yes	—
33	#18011895	C₂²	1	4	yes	—
34	#18011895	C₂²	1	2	yes	—
35	#18011891	C₂²	1	2	yes	—
36	#18011891	C₂²	1	1	yes	characteristic
37	#18011891	C₂²	1	1	yes	characteristic
38	#18011891	C₂²	1	2	yes	—
39	#18011891	C₂²	1	2	yes	—
40	#18011891	C₂²	1	2	yes	—
41	#18011891	C₂²	1	2	yes	complemented
42	#18011891	C₂²	1	2	yes	complemented
43	#18011887	C₂²	1	4	yes	—
44	#18011887	C₂²	1	4	yes	complemented
45	#18011886	C₂²	1	1	yes	characteristic
46	#18011886	C₂²	1	1	yes	characteristic
47	#18011881	C₂²	1	2	yes	—
48	Q₈×Dic₁₄₉	C₂²	1	4	yes	complemented
49	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
50	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
51	#18011876	C₂²	1	2	yes	complemented
52	#18011876	C₂²	1	2	yes	complemented
53	#18011876	C₂²	1	2	yes	complemented
54	C₄×D₅₉₆	C₂²	1	2	yes	—
55	C₄×D₅₉₆	C₂²	1	2	yes	—
56	#18011873	C₂²	1	4	yes	—
57	#18011873	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	—
59	#18011870	C₂²	1	1	yes	characteristic
60	#18011869	C₂²	1	4	yes	—
61	#18011869	C₂²	1	1	yes	characteristic
62	#18011869	C₂²	1	1	yes	characteristic
63	#18011869	C₂²	1	4	yes	complemented
64	#18011869	C₂²	1	2	yes	complemented
65	#18011868	C₂²	1	2	yes	—
66	#18011867	C₂²	1	4	yes	—
67	#18011867	C₂²	1	2	yes	—
68	C₂×C₄⋊Dic₁₄₉	C₂²	1	2	yes	—
69	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
70	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
71	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
72	C₂×#14558713	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
74	C₄²×D₁₄₉	C₂²	1	2	yes	—
75	C₄⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
76	C₄⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
77	#125×C₁₄₉	C₂²	1	2	yes	complemented
78	#125×C₁₄₉	C₂²	1	2	yes	complemented
79	C₂²⋊Q₈×C₁₄₉	C₂²	1	4	yes	—
80	#117×C₁₄₉	C₂²	1	1	yes	characteristic
81	#117×C₁₄₉	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
83	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
84	#14558736	—	2	4	no	—
85	C₂×Dic₂₉₈	—	2	4	no	—
86	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
87	C₂×Dic₂₉₈	C₂³	1	2	yes	—
88	C₂×Dic₂₉₈	C₂³	1	2	yes	—
89	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
90	C₂×D₅₉₆	C₂³	1	2	yes	—
91	C₂×D₅₉₆	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
93	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
94	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
95	C₂×C₄×D₁₄₉	—	2	4	no	—
96	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
101	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
102	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
103	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
104	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
105	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
106	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
107	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
108	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
109	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
111	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
112	#14558715	C₂³	1	4	yes	—
113	#14558715	C₂³	1	4	yes	—
114	#14558715	C₂³	1	2	yes	—
115	#14558715	C₂³	1	2	yes	—
116	#14558715	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
118	#14558713	C₂³	1	2	yes	—
119	#14558713	C₂³	1	2	yes	—
120	#14558713	C₂³	1	2	yes	—
121	#14558713	C₂³	1	4	yes	—
122	#14558713	C₂³	1	2	yes	—
123	#14558713	C₂³	1	4	yes	—
124	#14558713	C₂³	1	2	yes	—
125	#14558713	C₂³	1	4	yes	—
126	#14558713	C₂³	1	4	yes	—
127	#14558713	C₂³	1	4	yes	—
128	#14558713	C₂³	1	2	yes	—
129	C₄×Dic₁₄₉	C₂³	1	4	yes	—
130	C₄×Dic₁₄₉	C₂³	1	4	yes	—
131	C₄×Dic₁₄₉	C₂³	1	2	yes	—
132	C₄×Dic₁₄₉	C₂³	1	4	yes	—
133	C₄×Dic₁₄₉	C₂³	1	2	yes	—
134	C₄×Dic₁₄₉	C₂³	1	2	yes	—
135	C₂×Q₈×C₁₄₉	C₂³	1	4	yes	—
136	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
139	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
140	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
141	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
143	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
147	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
149	C₄²×C₁₄₉	C₂³	1	2	yes	—
150	C₄²×C₁₄₉	C₂³	1	2	yes	—
151	C₂²×D₁₄₉	—	2	2	no	—
152	C₂²×D₁₄₉	—	2	2	no	—
153	C₂²×D₁₄₉	—	4	1	no	—
154	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
155	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
156	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
157	Dic₂₉₈	—	2	4	no	—
158	Dic₂₉₈	—	2	4	no	—
159	Dic₂₉₈	—	2	2	no	—
160	D₅₉₆	—	2	4	no	—
161	D₅₉₆	—	2	2	no	—
162	D₅₉₆	—	4	2	no	—
163	C₂²⋊D₁₄₉	—	2	4	no	—
164	C₂×Dic₁₄₉	—	2	2	no	—
165	C₂×Dic₁₄₉	—	2	4	no	—
166	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
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	2	yes	—
171	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
172	C₄×D₁₄₉	—	2	4	no	—
173	C₄×D₁₄₉	—	2	2	no	—
174	C₄×D₁₄₉	—	2	2	no	—
175	C₄×D₁₄₉	—	2	2	no	—
176	C₄×D₁₄₉	—	2	2	no	—
177	C₄×D₁₄₉	—	2	4	no	—
178	C₄×D₁₄₉	—	4	4	no	—
179	C₄×D₁₄₉	—	4	2	no	—
180	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
181	Q₈×C₁₄₉	—	4	4	no	—
182	C₂×C₄×C₁₄₉	—	4	2	no	—
183	C₂×C₄×C₁₄₉	#41	1	4	yes	—
184	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
185	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
186	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
187	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
188	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
189	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₁₄₉	—	2	1	no	—
192	C₂²×C₁₄₉	—	2	1	no	—
193	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
194	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
195	C₂×D₁₄₉	—	2	1	no	—
196	C₂×D₁₄₉	—	2	1	no	—
197	C₂×D₁₄₉	—	2	1	no	—
198	C₂×D₁₄₉	—	2	2	no	—
199	C₂×D₁₄₉	—	2	2	no	—
200	C₂×D₁₄₉	—	2	1	no	—
201	C₂×D₁₄₉	—	2	2	no	—
202	C₂×D₁₄₉	—	2	1	no	—
203	C₂×D₁₄₉	—	4	4	no	—
204	C₂×D₁₄₉	2₋¹⁺⁴	1	2	yes	—
205	C₄×C₁₄₉	—	2	2	no	—
206	C₄×C₁₄₉	—	2	2	no	—
207	C₄×C₁₄₉	—	2	4	no	—
208	C₄×C₁₄₉	—	2	2	no	—
209	C₄×C₁₄₉	—	2	2	no	—
210	C₄×C₁₄₉	C₂×#41	1	2	yes	—
211	C₄×C₁₄₉	C₂×#41	1	2	yes	—
212	Dic₁₄₉	—	2	1	no	—
213	Dic₁₄₉	—	2	1	no	—
214	Dic₁₄₉	—	2	2	no	—
215	Dic₁₄₉	—	2	4	no	—
216	Dic₁₄₉	—	2	2	no	—
217	Dic₁₄₉	—	2	2	no	—
218	C₂×C₁₄₉	—	2	2	no	—
219	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
220	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
221	C₂×C₁₄₉	#585	1	1	yes	characteristic
222	D₁₄₉	—	2	2	no	—
223	D₁₄₉	—	4	2	no	—
224	D₁₄₉	—	4	1	no	—
225	C₁₄₉	#3495	1	1	yes	characteristic, complemented, Sylow
226	#3495	—	149	1	no	maximal, Sylow
227	#556	—	149	2	no	—
228	#554	—	149	2	no	—
229	#552	—	149	2	no	—
230	#552	—	149	2	no	—
231	#552	—	149	4	no	—
232	#551	—	149	4	no	—
233	#544	D₁₄₉	1	1	yes	characteristic, complemented
234	#542	—	149	2	no	—
235	#541	—	149	2	no	—
236	#536	—	149	1	no	—
237	#533	—	149	2	no	—
238	#529	—	149	2	no	—
239	#525	—	149	1	no	—
240	C₂×C₂²⋊Q₈	—	149	1	no	—
241	#520	—	149	1	no	—
242	#519	—	149	1	no	—
243	C₂×#117	—	149	1	no	—
244	C₂×#41	—	149	1	no	—
245	C₂²×Q₈	—	149	1	no	—
246	C₂³×C₄	—	149	1	no	—
247	C₄⋊Q₈	—	149	2	no	—
248	C₄⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
249	C₄⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
250	#126	—	149	4	no	—
251	#126	—	149	4	no	—
252	#126	—	149	4	no	—
253	#126	—	149	4	no	—
254	#125	—	149	4	no	—
255	#125	—	149	4	no	—
256	#125	—	149	4	no	—
257	#125	C₂×D₁₄₉	1	2	yes	complemented
258	#125	C₂×D₁₄₉	1	2	yes	complemented
259	#124	—	149	4	no	—
260	#124	—	149	2	no	—
261	#123	—	149	4	no	—
262	#123	—	149	4	no	—
263	#123	—	149	2	no	—
264	#123	—	149	4	no	—
265	C₂²⋊Q₈	—	149	4	no	—
266	C₂²⋊Q₈	—	149	4	no	—
267	C₂²⋊Q₈	—	149	2	no	—
268	C₂²⋊Q₈	—	149	2	no	—
269	C₂²⋊Q₈	—	149	2	no	—
270	C₂²⋊Q₈	—	149	2	no	—
271	C₂²⋊Q₈	—	149	1	no	—
272	C₂²⋊Q₈	—	149	1	no	—
273	C₂²⋊Q₈	—	149	2	no	—
274	C₂²⋊Q₈	—	149	2	no	—
275	C₂²⋊Q₈	C₂×D₁₄₉	1	4	yes	—
276	#121	—	149	1	no	—
277	#121	—	149	1	no	—
278	#120	—	149	2	no	—
279	C₄×Q₈	—	149	4	no	—
280	C₄×Q₈	—	149	2	no	—
281	C₄×Q₈	—	149	2	no	—
282	C₄×Q₈	—	149	2	no	—
283	C₄×Q₈	—	149	2	no	—
284	C₄×Q₈	—	149	2	no	—
285	C₄×D₄	—	149	4	no	—
286	C₄×D₄	—	149	2	no	—
287	C₄×D₄	—	149	4	no	—
288	C₄×D₄	—	149	2	no	—
289	C₄×D₄	—	149	2	no	—
290	#117	—	149	1	no	—
291	#117	—	149	1	no	—
292	#117	—	149	1	no	—
293	#117	—	149	2	no	—
294	#117	—	149	4	no	—
295	#117	—	149	4	no	—
296	#117	—	149	2	no	—
297	#117	—	149	4	no	—
298	#117	—	149	2	no	—
299	#117	C₂×D₁₄₉	1	1	yes	characteristic
300	#117	C₂×D₁₄₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	—	149	2	no	—
302	C₂×C₄⋊C₄	—	149	1	no	—
303	C₂×C₄⋊C₄	—	149	1	no	—
304	C₂×C₄⋊C₄	—	149	2	no	—
305	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	149	2	no	—
307	C₂×C₂²⋊C₄	—	149	2	no	—
308	C₂×C₄²	—	149	2	no	—
309	C₂⁴	—	149	1	no	—
310	#41	—	298	4	no	—
311	C₂×Q₈	—	298	4	no	—
312	C₂×Q₈	—	149	2	no	—
313	C₂×Q₈	—	149	2	no	—
314	C₂×Q₈	—	149	1	no	—
315	C₂×Q₈	C₂²×D₁₄₉	1	4	yes	—
316	C₂×D₄	—	149	2	no	—
317	C₂×D₄	—	149	2	no	—
318	C₂×D₄	—	149	1	no	—
319	C₂×D₄	—	149	2	no	—
320	C₂²×C₄	—	298	4	no	—
321	C₂²×C₄	—	149	2	no	—
322	C₂²×C₄	—	149	1	no	—
323	C₂²×C₄	—	149	1	no	—
324	C₂²×C₄	—	149	2	no	—
325	C₂²×C₄	—	149	1	no	—
326	C₂²×C₄	—	149	2	no	—
327	C₂²×C₄	—	149	1	no	—
328	C₂²×C₄	—	149	1	no	—
329	C₂²×C₄	—	149	2	no	—
330	C₂²×C₄	—	149	4	no	—
331	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
332	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
333	C₄⋊C₄	—	149	1	no	—
334	C₄⋊C₄	—	149	1	no	—
335	C₄⋊C₄	—	149	2	no	—
336	C₄⋊C₄	—	149	2	no	—
337	C₄⋊C₄	—	149	4	no	—
338	C₄⋊C₄	—	149	4	no	—
339	C₄⋊C₄	—	149	4	no	—
340	C₄⋊C₄	—	149	4	no	—
341	C₄⋊C₄	—	149	4	no	—
342	C₄⋊C₄	—	149	4	no	—
343	C₄⋊C₄	—	149	2	no	—
344	C₄⋊C₄	—	149	2	no	—
345	C₄⋊C₄	—	149	4	no	—
346	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
347	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
348	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
349	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
350	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
351	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
352	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
353	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
354	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
355	C₂²⋊C₄	—	149	2	no	—
356	C₂²⋊C₄	—	149	2	no	—
357	C₂²⋊C₄	—	149	2	no	—
358	C₂²⋊C₄	—	149	4	no	—
359	C₂²⋊C₄	—	149	4	no	—
360	C₂²⋊C₄	—	149	2	no	—
361	C₂²⋊C₄	—	149	2	no	—
362	C₂²⋊C₄	—	149	4	no	—
363	C₂²⋊C₄	—	149	4	no	—
364	C₂²⋊C₄	—	149	2	no	—
365	C₂²⋊C₄	—	149	2	no	—
366	C₂²⋊C₄	—	149	4	no	—
367	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
368	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
369	C₄²	—	149	2	no	—
370	C₄²	—	149	2	no	—
371	C₄²	—	149	2	no	—
372	C₄²	—	149	4	no	—
373	C₄²	—	149	4	no	—
374	C₄²	—	149	4	no	—
375	C₄²	C₂²×D₁₄₉	1	2	yes	—
376	C₄²	C₂²×D₁₄₉	1	2	yes	—
377	C₂³	—	298	2	no	—
378	C₂³	—	298	2	no	—
379	C₂³	—	596	1	no	—
380	C₂³	—	149	1	no	—
381	C₂³	—	149	2	no	—
382	C₂³	—	149	1	no	—
383	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
384	Q₈	—	4	4	no	—
385	Q₈	—	298	4	no	—
386	Q₈	—	298	4	no	—
387	Q₈	—	298	2	no	—
388	D₄	—	298	4	no	—
389	D₄	—	298	4	no	—
390	D₄	—	298	2	no	—
391	D₄	—	596	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	298	4	no	—
394	C₂×C₄	—	298	2	no	—
395	C₂×C₄	—	298	4	no	—
396	C₂×C₄	—	298	2	no	—
397	C₂×C₄	—	298	2	no	—
398	C₂×C₄	—	298	2	no	—
399	C₂×C₄	—	298	2	no	—
400	C₂×C₄	—	298	4	no	—
401	C₂×C₄	—	596	4	no	—
402	C₂×C₄	—	596	2	no	—
403	C₂×C₄	—	149	2	no	—
404	C₂×C₄	—	149	1	no	—
405	C₂×C₄	—	149	2	no	—
406	C₂×C₄	—	149	4	no	—
407	C₂×C₄	—	149	2	no	—
408	C₂×C₄	—	149	1	no	—
409	C₂×C₄	#14558737	1	4	yes	—
410	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
411	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
412	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
413	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
414	C₂×C₄	C₂³×D₁₄₉	1	4	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	—	298	1	no	—
420	C₂²	—	298	1	no	—
421	C₂²	—	298	1	no	—
422	C₂²	—	298	2	no	—
423	C₂²	—	298	2	no	—
424	C₂²	—	298	1	no	—
425	C₂²	—	298	2	no	—
426	C₂²	—	298	1	no	—
427	C₂²	—	596	4	no	—
428	C₂²	—	149	2	no	—
429	C₂²	C₂×#14558737	1	2	yes	—
430	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	298	1	no	—
437	C₄	—	298	1	no	—
438	C₄	—	298	2	no	—
439	C₄	—	298	4	no	—
440	C₄	—	298	2	no	—
441	C₄	—	298	2	no	—
442	C₄	C₂×#14558737	1	2	yes	—
443	C₄	C₂×#14558737	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	298	2	no	—
446	C₂	—	596	1	no	—
447	C₂	—	596	2	no	—
448	C₂	C₂²×#14558737	1	1	yes	characteristic
449	C₂	2₋¹⁺⁴×D₁₄₉	1	1	yes	characteristic
450	C₂	#23750460	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#544×C₁₄₉	C₂
prime radical	#23750137	C₂
hypercenter	#544	D₁₄₉
hypocenter	C₁₄₉	#3495
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #544

Complements

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

N	H ≅ G/N	type
1. #23750349	C₂	semidirect
2. #23750336	C₂	semidirect
3. #23750317	C₂	semidirect
4. #23750313	C₂	semidirect
5. #23750313	C₂	semidirect
6. #23750302	C₂	semidirect
7. #23750249	C₂	semidirect
8. #23750238	C₂	semidirect
9. #23750201	C₂	semidirect
10. #23750180	C₂	semidirect
11. #23750160	C₂	semidirect
13. C₂×#18011891	C₂	semidirect
14. #23750106	C₂	semidirect
15. #23750102	C₂	semidirect
16. #117×D₁₄₉	C₂	semidirect
17. #544×C₁₄₉	C₂	semidirect
21. #18011911	C₂²	semidirect
24. #18011906	C₂²	semidirect
25. #18011906	C₂²	semidirect
26. #18011902	C₂²	semidirect
27. #18011902	C₂²	semidirect
28. #18011902	C₂²	semidirect
30. #18011899	C₂²	semidirect
41. #18011891	C₂²	semidirect
42. #18011891	C₂²	semidirect
44. #18011887	C₂²	semidirect
48. Q₈×Dic₁₄₉	C₂²	semidirect
49. C₄×Dic₂₉₈	C₂²	semidirect
50. C₄×Dic₂₉₈	C₂²	semidirect
51. #18011876	C₂²	semidirect
52. #18011876	C₂²	semidirect
53. #18011876	C₂²	semidirect
57. #18011873	C₂²	semidirect
63. #18011869	C₂²	semidirect
64. #18011869	C₂²	semidirect
71. C₄⋊C₄×D₁₄₉	C₂²	semidirect
75. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
76. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
77. #125×C₁₄₉	C₂²	semidirect
78. #125×C₁₄₉	C₂²	semidirect
225. C₁₄₉	#3495	semidirect
233. #544	D₁₄₉	semidirect
248. C₄⋊Q₈	C₂×D₁₄₉	semidirect
249. C₄⋊Q₈	C₂×D₁₄₉	semidirect
257. #125	C₂×D₁₄₉	semidirect
258. #125	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750349	2
#23750336	2
#23750317	2
#23750313	2
#23750302	2
#23750249	2
#23750238	2
#23750201	2
#23750180	2
#23750160	2
#23750137	2
C₂×#18011891	2
#23750106	2
#23750102	2
#117×D₁₄₉	2
#544×C₁₄₉	2
#3495	149