Subgroups — #34058077

Order 19072.

1040 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750245	C₂	1	2	yes	maximal, complemented
2	#23750241	C₂	1	2	yes	maximal, complemented
3	#23750234	C₂	1	2	yes	maximal, complemented
4	#23750227	C₂	1	2	yes	maximal, complemented
5	#23750222	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750219	C₂	1	2	yes	maximal, complemented
7	#23750215	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750212	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750208	C₂	1	2	yes	maximal, complemented
10	#23750177	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750170	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750161	C₂	1	2	yes	maximal, complemented
13	#23750160	C₂	1	2	yes	maximal, complemented
14	#23750158	C₂	1	2	yes	maximal, complemented
15	#23750152	C₂	1	2	yes	maximal, complemented
16	#23750133	C₂	1	2	yes	maximal, complemented
17	C₄×#14558735	C₂	1	2	yes	maximal, complemented
18	C₂×#18011869	C₂	1	1	yes	maximal, characteristic, complemented
19	#539×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14558735	C₂²	1	2	yes	—
21	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
22	#18011910	C₂²	1	1	yes	characteristic, complemented
23	#18011910	C₂²	1	1	yes	characteristic, complemented
24	#18011909	C₂²	1	1	yes	characteristic, complemented
25	#18011907	C₂²	1	1	yes	characteristic, complemented
26	#18011906	C₂²	1	2	yes	—
27	#18011906	C₂²	1	2	yes	—
28	#18011906	C₂²	1	2	yes	—
29	#18011906	C₂²	1	2	yes	complemented
30	#18011906	C₂²	1	2	yes	complemented
31	#18011905	C₂²	1	2	yes	—
32	#18011904	C₂²	1	2	yes	complemented
33	#18011902	C₂²	1	2	yes	complemented
34	#18011901	C₂²	1	2	yes	complemented
35	#18011901	C₂²	1	2	yes	complemented
36	#18011901	C₂²	1	2	yes	complemented
37	#18011900	C₂²	1	2	yes	—
38	#18011899	C₂²	1	2	yes	—
39	#18011897	C₂²	1	2	yes	—
40	#18011897	C₂²	1	2	yes	—
41	#18011897	C₂²	1	2	yes	complemented
42	#18011896	C₂²	1	2	yes	—
43	#18011896	C₂²	1	2	yes	—
44	#18011896	C₂²	1	2	yes	complemented
45	#18011895	C₂²	1	2	yes	—
46	#18011895	C₂²	1	2	yes	complemented
47	#18011894	C₂²	1	2	yes	—
48	#18011894	C₂²	1	2	yes	—
49	#18011893	C₂²	1	2	yes	complemented
50	#18011891	C₂²	1	2	yes	complemented
51	#18011890	C₂²	1	1	yes	characteristic
52	#18011889	C₂²	1	2	yes	—
53	#18011889	C₂²	1	2	yes	—
54	#18011889	C₂²	1	2	yes	complemented
55	#18011888	C₂²	1	2	yes	—
56	#18011888	C₂²	1	2	yes	complemented
57	#18011886	C₂²	1	2	yes	—
58	#18011885	C₂²	1	2	yes	—
59	#18011885	C₂²	1	1	yes	characteristic
60	#18011884	C₂²	1	2	yes	—
61	#18011884	C₂²	1	2	yes	—
62	#18011884	C₂²	1	2	yes	—
63	#18011883	C₂²	1	2	yes	—
64	#18011883	C₂²	1	2	yes	—
65	#18011881	C₂²	1	2	yes	—
66	#18011879	C₂²	1	2	yes	—
67	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
68	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
69	#18011876	C₂²	1	2	yes	complemented
70	#18011876	C₂²	1	1	yes	characteristic, complemented
71	#18011876	C₂²	1	2	yes	complemented
72	D₄×Dic₁₄₉	C₂²	1	2	yes	—
73	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
74	#18011873	C₂²	1	2	yes	—
75	#18011873	C₂²	1	2	yes	—
76	#18011873	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
78	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
79	#18011871	C₂²	1	2	yes	—
80	#18011871	C₂²	1	2	yes	—
81	#18011871	C₂²	1	2	yes	—
82	#18011871	C₂²	1	2	yes	complemented
83	#18011871	C₂²	1	2	yes	complemented
84	#18011869	C₂²	1	2	yes	—
85	#18011869	C₂²	1	2	yes	—
86	#18011869	C₂²	1	2	yes	—
87	#18011869	C₂²	1	2	yes	—
88	#18011869	C₂²	1	2	yes	complemented
89	#18011867	C₂²	1	2	yes	—
90	#18011867	C₂²	1	2	yes	complemented
91	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
92	C₂×#14558713	C₂²	1	1	yes	characteristic
93	C₂×#14558713	C₂²	1	1	yes	characteristic
94	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
95	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
96	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	complemented
97	C₄²×D₁₄₉	C₂²	1	2	yes	complemented
98	#126×C₁₄₉	C₂²	1	2	yes	complemented
99	#125×C₁₄₉	C₂²	1	2	yes	complemented
100	#123×C₁₄₉	C₂²	1	2	yes	—
101	#123×C₁₄₉	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
103	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
104	#121×C₁₄₉	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
107	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
108	#14558735	—	2	8	no	—
109	C₂×Dic₂₉₈	C₂³	1	2	yes	—
110	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
111	C₂×Dic₂₉₈	C₂³	1	2	yes	—
112	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
113	C₂×D₅₉₆	C₂³	1	2	yes	—
114	C₂×D₅₉₆	C₂³	1	2	yes	—
115	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
120	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
121	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
122	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
123	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
124	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
125	C₂×C₄×D₁₄₉	—	2	4	no	—
126	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
127	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
128	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
129	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
130	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
131	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
132	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
134	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
135	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
136	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
137	#14558715	C₂³	1	2	yes	—
138	#14558715	C₂³	1	2	yes	—
139	#14558715	C₂³	1	2	yes	—
140	#14558715	C₂³	1	2	yes	—
141	#14558715	C₂³	1	2	yes	—
142	#14558715	C₂³	1	2	yes	—
143	#14558715	C₂³	1	2	yes	—
144	#14558715	C₂³	1	2	yes	—
145	#14558715	C₂³	1	2	yes	—
146	#14558715	C₂³	1	2	yes	—
147	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
148	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
149	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
150	#14558713	C₂³	1	2	yes	—
151	#14558713	C₂³	1	2	yes	—
152	#14558713	C₂³	1	2	yes	—
153	#14558713	C₂³	1	2	yes	—
154	#14558713	C₂³	1	2	yes	—
155	#14558713	C₂³	1	2	yes	—
156	#14558713	C₂³	1	2	yes	—
157	#14558713	C₂³	1	2	yes	—
158	#14558713	C₂³	1	2	yes	—
159	#14558713	C₂³	1	2	yes	—
160	#14558713	C₂³	1	2	yes	—
161	#14558713	C₂³	1	2	yes	—
162	#14558713	C₂³	1	2	yes	—
163	#14558713	C₂³	1	2	yes	—
164	C₄×Dic₁₄₉	C₂³	1	2	yes	—
165	C₄×Dic₁₄₉	C₂³	1	2	yes	—
166	C₄×Dic₁₄₉	C₂³	1	2	yes	—
167	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
168	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
169	C₄×Dic₁₄₉	C₂³	1	2	yes	—
170	C₄×Dic₁₄₉	C₂³	1	2	yes	—
171	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
172	C₄×Dic₁₄₉	C₂³	1	2	yes	—
173	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
174	C₄×Dic₁₄₉	C₂³	1	2	yes	—
175	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
176	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
177	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
178	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
179	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
180	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
181	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
182	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
183	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
184	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
185	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
186	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
187	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
195	C₄²×C₁₄₉	C₂³	1	2	yes	—
196	C₂²×D₁₄₉	—	2	2	no	—
197	C₂²×D₁₄₉	—	4	1	no	—
198	C₂²×D₁₄₉	—	4	1	no	—
199	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
200	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
201	Dic₂₉₈	—	2	4	no	—
202	Dic₂₉₈	—	4	1	no	—
203	Dic₂₉₈	—	4	2	no	—
204	D₅₉₆	—	4	1	no	—
205	D₅₉₆	—	4	2	no	—
206	D₅₉₆	—	4	2	no	—
207	C₂²⋊D₁₄₉	—	2	4	no	—
208	C₂²⋊D₁₄₉	—	2	4	no	—
209	C₂²⋊D₁₄₉	—	4	2	no	—
210	C₂²⋊D₁₄₉	—	4	2	no	—
211	C₂²⋊D₁₄₉	—	4	2	no	—
212	C₂×Dic₁₄₉	—	2	4	no	—
213	C₂×Dic₁₄₉	—	4	1	no	—
214	C₂×Dic₁₄₉	—	4	2	no	—
215	C₂×Dic₁₄₉	—	4	1	no	—
216	C₂×Dic₁₄₉	#41	1	4	yes	—
217	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
218	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
219	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
220	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
221	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
222	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
223	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
224	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
225	C₄×D₁₄₉	—	2	4	no	—
226	C₄×D₁₄₉	—	2	4	no	—
227	C₄×D₁₄₉	—	2	4	no	—
228	C₄×D₁₄₉	—	4	2	no	—
229	C₄×D₁₄₉	—	4	2	no	—
230	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
231	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
232	Q₈×C₁₄₉	—	4	1	no	—
233	D₄×C₁₄₉	—	2	4	no	—
234	D₄×C₁₄₉	—	4	1	no	—
235	C₂×C₄×C₁₄₉	—	2	2	no	—
236	C₂×C₄×C₁₄₉	—	4	1	no	—
237	C₂×C₄×C₁₄₉	—	4	2	no	—
238	C₂×C₄×C₁₄₉	—	4	1	no	—
239	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
240	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
241	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₁₄₉	—	2	1	no	—
247	C₂²×C₁₄₉	—	2	1	no	—
248	C₂²×C₁₄₉	—	2	2	no	—
249	C₂²×C₁₄₉	—	2	2	no	—
250	C₂²×C₁₄₉	—	2	2	no	—
251	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
252	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
253	C₂×D₁₄₉	—	2	2	no	—
254	C₂×D₁₄₉	—	2	2	no	—
255	C₂×D₁₄₉	—	2	2	no	—
256	C₂×D₁₄₉	—	2	2	no	—
257	C₂×D₁₄₉	—	2	2	no	—
258	C₂×D₁₄₉	—	2	2	no	—
259	C₂×D₁₄₉	—	4	4	no	—
260	C₄×C₁₄₉	—	2	2	no	—
261	C₄×C₁₄₉	—	2	2	no	—
262	C₄×C₁₄₉	—	2	2	no	—
263	C₄×C₁₄₉	—	2	1	no	—
264	C₄×C₁₄₉	—	2	2	no	—
265	C₄×C₁₄₉	—	2	1	no	—
266	C₄×C₁₄₉	—	2	2	no	—
267	Dic₁₄₉	—	2	2	no	—
268	Dic₁₄₉	—	2	2	no	—
269	Dic₁₄₉	—	2	2	no	—
270	Dic₁₄₉	—	2	1	no	—
271	Dic₁₄₉	—	2	2	no	—
272	Dic₁₄₉	—	2	1	no	—
273	Dic₁₄₉	C₂×#41	1	2	yes	—
274	Dic₁₄₉	C₂×#41	1	2	yes	—
275	C₂×C₁₄₉	—	2	2	no	—
276	C₂×C₁₄₉	—	4	2	no	—
277	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
278	C₂×C₁₄₉	#585	1	1	yes	characteristic
279	C₂×C₁₄₉	#585	1	1	yes	characteristic
280	D₁₄₉	—	4	2	no	—
281	D₁₄₉	—	4	2	no	—
282	C₁₄₉	#3455	1	1	yes	characteristic, complemented, Sylow
283	#3455	—	149	1	no	maximal, Sylow
284	#542	—	149	2	no	—
285	#542	—	149	2	no	—
286	#541	—	149	2	no	—
287	#540	—	149	2	no	—
288	#539	—	149	2	no	—
289	#539	—	149	1	no	—
290	#539	D₁₄₉	1	1	yes	characteristic, complemented
291	#538	—	149	1	no	—
292	#538	—	149	1	no	—
293	#538	—	149	2	no	—
294	#533	—	149	1	no	—
295	#532	—	149	1	no	—
296	#529	—	149	2	no	—
297	#529	—	149	2	no	—
298	#529	—	149	2	no	—
299	#529	—	149	2	no	—
300	#525	—	149	2	no	—
301	C₄×#41	—	149	2	no	—
302	C₂×#117	—	149	1	no	—
303	C₂×#41	—	149	2	no	—
304	C₂³×C₄	—	149	1	no	—
305	C₄⋊Q₈	—	149	1	no	—
306	C₄⋊Q₈	—	149	1	no	—
307	C₄⋊Q₈	—	149	1	no	—
308	#127	—	149	1	no	—
309	#126	—	149	2	no	—
310	#126	—	149	2	no	—
311	#126	—	149	2	no	—
312	#126	—	149	2	no	—
313	#126	—	149	2	no	—
314	#126	—	149	2	no	—
315	#126	—	149	2	no	—
316	#126	C₂×D₁₄₉	1	2	yes	complemented
317	#125	—	149	2	no	—
318	#125	—	149	2	no	—
319	#125	—	149	2	no	—
320	#125	—	149	2	no	—
321	#125	C₂×D₁₄₉	1	2	yes	complemented
322	#124	—	149	2	no	—
323	#124	—	149	2	no	—
324	#124	—	149	2	no	—
325	#124	—	149	2	no	—
326	#124	—	149	2	no	—
327	#123	—	149	2	no	—
328	#123	—	149	2	no	—
329	#123	—	149	2	no	—
330	#123	—	149	2	no	—
331	#123	—	149	2	no	—
332	#123	—	149	2	no	—
333	#123	—	149	2	no	—
334	#123	—	149	2	no	—
335	#123	C₂×D₁₄₉	1	2	yes	—
336	#123	C₂×D₁₄₉	1	2	yes	complemented
337	C₂²⋊Q₈	—	149	1	no	—
338	C₂²⋊Q₈	—	149	2	no	—
339	C₂²⋊Q₈	—	149	2	no	—
340	C₂²⋊Q₈	—	149	2	no	—
341	C₂²⋊Q₈	—	149	2	no	—
342	C₂²⋊Q₈	—	149	2	no	—
343	C₂²⋊Q₈	—	149	2	no	—
344	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
345	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
346	#121	—	149	2	no	—
347	#121	—	149	2	no	—
348	#121	—	149	2	no	—
349	#121	—	149	1	no	—
350	#121	—	149	2	no	—
351	#121	—	149	2	no	—
352	#121	—	149	2	no	—
353	#121	—	149	2	no	—
354	#121	C₂×D₁₄₉	1	1	yes	characteristic
355	#120	—	149	2	no	—
356	#120	—	149	2	no	—
357	C₄×Q₈	—	149	1	no	—
358	C₄×Q₈	—	149	2	no	—
359	C₄×Q₈	—	149	1	no	—
360	C₄×Q₈	—	149	2	no	—
361	C₄×Q₈	—	149	2	no	—
362	C₄×D₄	—	149	2	no	—
363	C₄×D₄	—	149	1	no	—
364	C₄×D₄	—	149	2	no	—
365	C₄×D₄	—	149	2	no	—
366	C₄×D₄	—	149	2	no	—
367	C₄×D₄	—	149	2	no	—
368	C₄×D₄	—	149	1	no	—
369	C₄×D₄	—	149	2	no	—
370	C₄×D₄	—	149	2	no	—
371	C₄×D₄	—	149	2	no	—
372	C₄×D₄	—	149	2	no	—
373	C₄×D₄	—	149	2	no	—
374	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
375	#117	—	149	2	no	—
376	#117	—	149	2	no	—
377	#117	—	149	2	no	—
378	#117	—	149	2	no	—
379	#117	—	149	2	no	—
380	#117	—	149	2	no	—
381	#117	—	149	2	no	—
382	C₂×C₄⋊C₄	—	149	1	no	—
383	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	149	1	no	—
385	C₂×C₂²⋊C₄	—	149	1	no	—
386	C₂×C₄²	—	149	1	no	—
387	C₂×C₄²	—	149	1	no	—
388	C₂×C₄²	—	149	2	no	—
389	C₂×C₄²	—	149	2	no	—
390	C₂⁴	—	149	1	no	—
391	#41	—	298	8	no	—
392	C₂×Q₈	—	149	2	no	—
393	C₂×Q₈	—	149	2	no	—
394	C₂×Q₈	—	149	1	no	—
395	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
396	C₂×D₄	—	149	2	no	—
397	C₂×D₄	—	149	2	no	—
398	C₂×D₄	—	149	2	no	—
399	C₂×D₄	—	149	2	no	—
400	C₂×D₄	—	149	2	no	—
401	C₂×D₄	—	149	2	no	—
402	C₂×D₄	—	149	2	no	—
403	C₂×D₄	—	149	1	no	—
404	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
405	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
406	C₂²×C₄	—	298	4	no	—
407	C₂²×C₄	—	149	2	no	—
408	C₂²×C₄	—	149	2	no	—
409	C₂²×C₄	—	149	2	no	—
410	C₂²×C₄	—	149	2	no	—
411	C₂²×C₄	—	149	1	no	—
412	C₂²×C₄	—	149	1	no	—
413	C₂²×C₄	—	149	2	no	—
414	C₂²×C₄	—	149	2	no	—
415	C₂²×C₄	—	149	2	no	—
416	C₂²×C₄	—	149	1	no	—
417	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
418	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
419	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
420	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
421	C₄⋊C₄	—	149	2	no	—
422	C₄⋊C₄	—	149	2	no	—
423	C₄⋊C₄	—	149	2	no	—
424	C₄⋊C₄	—	149	2	no	—
425	C₄⋊C₄	—	149	2	no	—
426	C₄⋊C₄	—	149	2	no	—
427	C₄⋊C₄	—	149	2	no	—
428	C₄⋊C₄	—	149	2	no	—
429	C₄⋊C₄	—	149	1	no	—
430	C₄⋊C₄	—	149	2	no	—
431	C₄⋊C₄	—	149	2	no	—
432	C₄⋊C₄	—	149	2	no	—
433	C₄⋊C₄	—	149	2	no	—
434	C₄⋊C₄	—	149	2	no	—
435	C₄⋊C₄	—	149	2	no	—
436	C₄⋊C₄	—	149	1	no	—
437	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
438	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
439	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
440	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
441	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
442	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
443	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
444	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
445	C₂²⋊C₄	—	149	2	no	—
446	C₂²⋊C₄	—	149	2	no	—
447	C₂²⋊C₄	—	149	2	no	—
448	C₂²⋊C₄	—	149	2	no	—
449	C₂²⋊C₄	—	149	2	no	—
450	C₂²⋊C₄	—	149	2	no	—
451	C₂²⋊C₄	—	149	2	no	—
452	C₂²⋊C₄	—	149	2	no	—
453	C₂²⋊C₄	—	149	2	no	—
454	C₂²⋊C₄	—	149	2	no	—
455	C₂²⋊C₄	—	149	2	no	—
456	C₂²⋊C₄	—	149	2	no	—
457	C₂²⋊C₄	—	149	2	no	—
458	C₂²⋊C₄	—	149	2	no	—
459	C₂²⋊C₄	—	149	2	no	—
460	C₂²⋊C₄	—	149	2	no	—
461	C₂²⋊C₄	—	149	2	no	—
462	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
463	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
464	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
465	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
466	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
467	C₄²	—	149	2	no	—
468	C₄²	—	149	2	no	—
469	C₄²	—	149	1	no	—
470	C₄²	—	149	2	no	—
471	C₄²	—	149	2	no	—
472	C₄²	—	149	1	no	—
473	C₄²	—	149	1	no	—
474	C₄²	—	149	1	no	—
475	C₄²	—	149	2	no	—
476	C₄²	—	149	2	no	—
477	C₄²	—	149	2	no	—
478	C₄²	C₂²×D₁₄₉	1	2	yes	—
479	C₂³	—	298	2	no	—
480	C₂³	—	596	1	no	—
481	C₂³	—	596	1	no	—
482	C₂³	—	149	2	no	—
483	C₂³	—	149	2	no	—
484	C₂³	C₂³×D₁₄₉	1	2	yes	—
485	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
486	Q₈	—	4	1	no	—
487	Q₈	—	298	4	no	—
488	Q₈	—	596	1	no	—
489	Q₈	—	596	2	no	—
490	D₄	—	2	4	no	—
491	D₄	—	4	1	no	—
492	D₄	—	298	4	no	—
493	D₄	—	298	4	no	—
494	D₄	—	596	1	no	—
495	D₄	—	596	2	no	—
496	D₄	—	596	2	no	—
497	D₄	—	596	2	no	—
498	D₄	—	596	2	no	—
499	D₄	—	596	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	298	4	no	—
505	C₂×C₄	—	298	4	no	—
506	C₂×C₄	—	298	4	no	—
507	C₂×C₄	—	298	4	no	—
508	C₂×C₄	—	596	2	no	—
509	C₂×C₄	—	596	2	no	—
510	C₂×C₄	—	596	1	no	—
511	C₂×C₄	—	596	2	no	—
512	C₂×C₄	—	596	1	no	—
513	C₂×C₄	—	149	2	no	—
514	C₂×C₄	—	149	1	no	—
515	C₂×C₄	—	149	2	no	—
516	C₂×C₄	—	149	2	no	—
517	C₂×C₄	—	149	2	no	—
518	C₂×C₄	—	149	1	no	—
519	C₂×C₄	—	149	4	no	—
520	C₂×C₄	—	149	1	no	—
521	C₂×C₄	—	149	1	no	—
522	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
523	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
524	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
525	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
526	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
527	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
528	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	298	2	no	—
535	C₂²	—	298	2	no	—
536	C₂²	—	298	2	no	—
537	C₂²	—	298	2	no	—
538	C₂²	—	298	2	no	—
539	C₂²	—	298	2	no	—
540	C₂²	—	596	4	no	—
541	C₂²	#41×D₁₄₉	1	2	yes	—
542	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	2	no	—
550	C₄	—	298	2	no	—
551	C₄	—	298	2	no	—
552	C₄	—	298	2	no	—
553	C₄	—	298	1	no	—
554	C₄	—	298	2	no	—
555	C₄	—	298	1	no	—
556	C₄	—	149	2	no	—
557	C₄	—	149	2	no	—
558	C₂	—	2	2	no	—
559	C₂	—	4	2	no	—
560	C₂	—	596	2	no	—
561	C₂	—	596	2	no	—
562	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
563	C₂	#23750460	1	1	yes	characteristic
564	C₂	#23750462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#539×C₁₄₉	C₂
hypercenter	#539	D₁₄₉
hypocenter	C₁₄₉	#3455
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #23750245	C₂	semidirect
2. #23750241	C₂	semidirect
3. #23750234	C₂	semidirect
4. #23750227	C₂	semidirect
5. #23750222	C₂	semidirect
6. #23750219	C₂	semidirect
7. #23750215	C₂	semidirect
8. #23750212	C₂	semidirect
9. #23750208	C₂	semidirect
10. #23750177	C₂	semidirect
11. #23750170	C₂	semidirect
12. #23750161	C₂	semidirect
13. #23750160	C₂	semidirect
14. #23750158	C₂	semidirect
15. #23750152	C₂	semidirect
16. #23750133	C₂	semidirect
17. C₄×#14558735	C₂	semidirect
18. C₂×#18011869	C₂	semidirect
19. #539×C₁₄₉	C₂	semidirect
22. #18011910	C₂²	semidirect
23. #18011910	C₂²	semidirect
24. #18011909	C₂²	semidirect
25. #18011907	C₂²	semidirect
29. #18011906	C₂²	semidirect
30. #18011906	C₂²	semidirect
32. #18011904	C₂²	semidirect
33. #18011902	C₂²	semidirect
34. #18011901	C₂²	semidirect
35. #18011901	C₂²	semidirect
36. #18011901	C₂²	semidirect
41. #18011897	C₂²	semidirect
44. #18011896	C₂²	semidirect
46. #18011895	C₂²	semidirect
49. #18011893	C₂²	semidirect
50. #18011891	C₂²	semidirect
54. #18011889	C₂²	semidirect
56. #18011888	C₂²	semidirect
67. Q₈×Dic₁₄₉	C₂²	semidirect
68. C₄×Dic₂₉₈	C₂²	semidirect
69. #18011876	C₂²	semidirect
70. #18011876	C₂²	semidirect
71. #18011876	C₂²	semidirect
73. D₄×Dic₁₄₉	C₂²	semidirect
76. #18011873	C₂²	semidirect
78. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
82. #18011871	C₂²	semidirect
83. #18011871	C₂²	semidirect
88. #18011869	C₂²	semidirect
90. #18011867	C₂²	semidirect
96. C₂×C₄×Dic₁₄₉	C₂²	semidirect
97. C₄²×D₁₄₉	C₂²	semidirect
98. #126×C₁₄₉	C₂²	semidirect
99. #125×C₁₄₉	C₂²	semidirect
101. #123×C₁₄₉	C₂²	semidirect
103. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
282. C₁₄₉	#3455	semidirect
290. #539	D₁₄₉	semidirect
316. #126	C₂×D₁₄₉	semidirect
321. #125	C₂×D₁₄₉	semidirect
336. #123	C₂×D₁₄₉	semidirect
345. C₂²⋊Q₈	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750245	2
#23750241	2
#23750234	2
#23750227	2
#23750222	2
#23750219	2
#23750215	2
#23750212	2
#23750208	2
#23750177	2
#23750170	2
#23750161	2
#23750160	2
#23750158	2
#23750152	2
#23750133	2
C₄×#14558735	2
C₂×#18011869	2
#539×C₁₄₉	2
#3455	149