Subgroups — #34058783

Order 19072.

992 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750352	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750352	C₂	1	2	yes	maximal, complemented
3	#23750350	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750346	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750342	C₂	1	2	yes	maximal, complemented
6	#23750313	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750311	C₂	1	2	yes	maximal, complemented
8	#23750309	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750307	C₂	1	2	yes	maximal, complemented
10	#23750290	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750288	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750288	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750234	C₂	1	2	yes	maximal, complemented
14	#23750233	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750232	C₂	1	2	yes	maximal, complemented
16	#23750181	C₂	1	2	yes	maximal, complemented
17	#23750179	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750158	C₂	1	2	yes	maximal
19	#23750153	C₂	1	1	yes	maximal, characteristic
20	#23750102	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750101	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#541×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Dic₂₉₈	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₄₉	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₁₄₉	C₂²	1	1	yes	characteristic
27	#18011910	C₂²	1	1	yes	characteristic
28	#18011910	C₂²	1	2	yes	—
29	#18011910	C₂²	1	2	yes	—
30	#18011910	C₂²	1	2	yes	—
31	#18011910	C₂²	1	2	yes	—
32	#18011909	C₂²	1	1	yes	characteristic
33	#18011909	C₂²	1	1	yes	characteristic
34	#18011906	C₂²	1	1	yes	characteristic
35	#18011906	C₂²	1	2	yes	—
36	#18011906	C₂²	1	2	yes	—
37	#18011906	C₂²	1	2	yes	—
38	#18011905	C₂²	1	2	yes	—
39	#18011904	C₂²	1	1	yes	characteristic
40	#18011904	C₂²	1	2	yes	—
41	#18011904	C₂²	1	2	yes	—
42	#18011903	C₂²	1	2	yes	—
43	#18011902	C₂²	1	2	yes	—
44	#18011902	C₂²	1	1	yes	characteristic
45	#18011902	C₂²	1	2	yes	—
46	#18011901	C₂²	1	1	yes	characteristic
47	#18011901	C₂²	1	2	yes	—
48	#18011901	C₂²	1	2	yes	—
49	#18011901	C₂²	1	2	yes	—
50	#18011901	C₂²	1	2	yes	—
51	#18011901	C₂²	1	2	yes	—
52	#18011901	C₂²	1	2	yes	—
53	#18011901	C₂²	1	2	yes	—
54	#18011897	C₂²	1	1	yes	characteristic
55	#18011897	C₂²	1	2	yes	—
56	#18011896	C₂²	1	1	yes	characteristic
57	#18011896	C₂²	1	2	yes	—
58	#18011893	C₂²	1	1	yes	characteristic
59	#18011893	C₂²	1	2	yes	—
60	#18011891	C₂²	1	1	yes	characteristic
61	#18011891	C₂²	1	1	yes	characteristic
62	#18011889	C₂²	1	1	yes	characteristic
63	#18011889	C₂²	1	2	yes	—
64	#18011889	C₂²	1	2	yes	—
65	#18011889	C₂²	1	2	yes	—
66	#18011889	C₂²	1	2	yes	—
67	#18011889	C₂²	1	2	yes	—
68	#18011888	C₂²	1	2	yes	—
69	#18011888	C₂²	1	2	yes	—
70	#18011887	C₂²	1	1	yes	characteristic
71	#18011887	C₂²	1	1	yes	characteristic
72	#18011884	C₂²	1	1	yes	characteristic
73	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
74	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
75	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
76	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
77	C₄×Dic₂₉₈	C₂²	1	2	yes	—
78	C₄×Dic₂₉₈	C₂²	1	2	yes	—
79	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
80	C₄×Dic₂₉₈	C₂²	1	2	yes	—
81	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
82	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
83	#18011876	C₂²	1	2	yes	—
84	#18011876	C₂²	1	2	yes	—
85	#18011876	C₂²	1	2	yes	—
86	#18011876	C₂²	1	2	yes	—
87	#18011876	C₂²	1	2	yes	—
88	#18011876	C₂²	1	1	yes	characteristic
89	#18011876	C₂²	1	1	yes	characteristic
90	#18011876	C₂²	1	2	yes	—
91	#18011876	C₂²	1	2	yes	—
92	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
93	#18011873	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
96	#18011871	C₂²	1	2	yes	—
97	#18011871	C₂²	1	2	yes	—
98	#18011870	C₂²	1	1	yes	characteristic
99	#18011869	C₂²	1	2	yes	—
100	#18011869	C₂²	1	2	yes	—
101	#18011869	C₂²	1	2	yes	—
102	#18011869	C₂²	1	1	yes	characteristic
103	#18011868	C₂²	1	1	yes	characteristic
104	#18011868	C₂²	1	2	yes	—
105	#18011868	C₂²	1	2	yes	—
106	#18011867	C₂²	1	2	yes	—
107	#18011867	C₂²	1	2	yes	—
108	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
109	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
110	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
111	C₄²×D₁₄₉	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
113	#126×C₁₄₉	C₂²	1	2	yes	—
114	#126×C₁₄₉	C₂²	1	2	yes	—
115	#125×C₁₄₉	C₂²	1	2	yes	—
116	#125×C₁₄₉	C₂²	1	2	yes	—
117	#125×C₁₄₉	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
119	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
121	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
122	#117×C₁₄₉	C₂²	1	1	yes	characteristic
123	C₂×Dic₂₉₈	—	2	4	no	—
124	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
125	C₂×Dic₂₉₈	C₂³	1	2	yes	—
126	C₂×Dic₂₉₈	C₂³	1	2	yes	—
127	C₂×Dic₂₉₈	C₂³	1	2	yes	—
128	C₂×Dic₂₉₈	C₂³	1	2	yes	—
129	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
131	Q₈×D₁₄₉	—	2	4	no	—
132	Q₈×D₁₄₉	—	2	4	no	—
133	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
137	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
138	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
140	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
144	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
145	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
146	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
148	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
150	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
153	#14558715	C₂³	1	2	yes	—
154	#14558715	C₂³	1	2	yes	—
155	#14558715	C₂³	1	2	yes	—
156	#14558715	C₂³	1	2	yes	—
157	#14558715	C₂³	1	1	yes	characteristic
158	#14558715	C₂³	1	1	yes	characteristic
159	#14558715	C₂³	1	2	yes	—
160	#14558715	C₂³	1	2	yes	—
161	#14558715	C₂³	1	2	yes	—
162	#14558715	C₂³	1	2	yes	—
163	#14558715	C₂³	1	1	yes	characteristic
164	#14558715	C₂³	1	2	yes	—
165	#14558715	C₂³	1	2	yes	—
166	#14558715	C₂³	1	1	yes	characteristic
167	#14558715	C₂³	1	2	yes	—
168	#14558715	C₂³	1	2	yes	—
169	#14558715	C₂³	1	2	yes	—
170	#14558715	C₂³	1	2	yes	—
171	#14558715	C₂³	1	2	yes	—
172	#14558715	C₂³	1	1	yes	characteristic
173	#14558715	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
177	#14558713	C₂³	1	1	yes	characteristic
178	#14558713	C₂³	1	2	yes	—
179	#14558713	C₂³	1	2	yes	—
180	#14558713	C₂³	1	1	yes	characteristic
181	#14558713	C₂³	1	1	yes	characteristic
182	#14558713	C₂³	1	1	yes	characteristic
183	#14558713	C₂³	1	2	yes	—
184	#14558713	C₂³	1	2	yes	—
185	#14558713	C₂³	1	2	yes	—
186	#14558713	C₂³	1	1	yes	characteristic
187	#14558713	C₂³	1	1	yes	characteristic
188	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
189	C₄×Dic₁₄₉	C₂³	1	2	yes	—
190	C₄×Dic₁₄₉	C₂³	1	2	yes	—
191	C₄×Dic₁₄₉	C₂³	1	2	yes	—
192	C₄×Dic₁₄₉	C₂³	1	2	yes	—
193	C₄×Dic₁₄₉	C₂³	1	2	yes	—
194	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₄₉	C₂³	1	2	yes	—
197	C₄×Dic₁₄₉	C₂³	1	2	yes	—
198	C₄×Dic₁₄₉	C₂³	1	2	yes	—
199	C₄×Dic₁₄₉	C₂³	1	2	yes	—
200	C₄×Dic₁₄₉	C₂³	1	2	yes	—
201	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
206	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
207	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
209	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
221	C₄²×C₁₄₉	C₂³	1	2	yes	—
222	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
223	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
224	C₄²×C₁₄₉	C₂³	1	2	yes	—
225	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
226	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
227	Dic₂₉₈	—	2	2	no	—
228	Dic₂₉₈	—	2	4	no	—
229	Dic₂₉₈	—	2	4	no	—
230	Dic₂₉₈	—	2	4	no	—
231	Dic₂₉₈	—	2	4	no	—
232	Dic₂₉₈	—	2	2	no	—
233	Dic₂₉₈	#41	1	4	yes	—
234	D₅₉₆	—	2	2	no	—
235	C₂²⋊D₁₄₉	—	2	2	no	—
236	C₂²⋊D₁₄₉	—	2	2	no	—
237	C₂×Dic₁₄₉	—	2	4	no	—
238	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
239	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
240	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
241	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
243	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
246	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
247	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
248	C₄×D₁₄₉	—	2	2	no	—
249	C₄×D₁₄₉	—	2	4	no	—
250	C₄×D₁₄₉	—	2	2	no	—
251	C₄×D₁₄₉	—	2	2	no	—
252	C₄×D₁₄₉	—	2	4	no	—
253	C₄×D₁₄₉	—	2	4	no	—
254	C₄×D₁₄₉	—	2	2	no	—
255	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
256	Q₈×C₁₄₉	—	2	2	no	—
257	Q₈×C₁₄₉	—	2	2	no	—
258	C₂×C₄×C₁₄₉	—	2	2	no	—
259	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
264	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
268	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₁₄₉	—	2	1	no	—
270	C₂²×C₁₄₉	—	2	1	no	—
271	C₂²×C₁₄₉	—	2	1	no	—
272	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
273	C₂×D₁₄₉	—	2	1	no	—
274	C₂×D₁₄₉	—	2	1	no	—
275	C₂×D₁₄₉	—	2	1	no	—
276	C₂×D₁₄₉	—	2	1	no	—
277	C₂×D₁₄₉	—	2	1	no	—
278	C₂×D₁₄₉	2₋¹⁺⁴	1	2	yes	—
279	C₄×C₁₄₉	—	2	1	no	—
280	C₄×C₁₄₉	—	2	2	no	—
281	C₄×C₁₄₉	—	2	2	no	—
282	C₄×C₁₄₉	—	2	1	no	—
283	C₄×C₁₄₉	—	2	2	no	—
284	C₄×C₁₄₉	—	2	1	no	—
285	C₄×C₁₄₉	—	2	1	no	—
286	C₄×C₁₄₉	—	2	1	no	—
287	C₄×C₁₄₉	—	2	2	no	—
288	C₄×C₁₄₉	C₂×#41	1	2	yes	—
289	Dic₁₄₉	—	2	1	no	—
290	Dic₁₄₉	—	2	1	no	—
291	Dic₁₄₉	—	2	2	no	—
292	Dic₁₄₉	—	2	2	no	—
293	Dic₁₄₉	—	2	1	no	—
294	Dic₁₄₉	—	2	1	no	—
295	Dic₁₄₉	—	2	1	no	—
296	Dic₁₄₉	—	2	2	no	—
297	Dic₁₄₉	C₂×#41	1	4	yes	—
298	Dic₁₄₉	2₋¹⁺⁴	1	2	yes	—
299	C₂×C₁₄₉	—	4	1	no	—
300	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
301	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
303	D₁₄₉	—	2	2	no	—
304	D₁₄₉	—	4	1	no	—
305	C₁₄₉	#3523	1	1	yes	characteristic, complemented, Sylow
306	#3523	—	149	1	no	maximal, Sylow
307	#557	—	149	1	no	—
308	#557	—	149	1	no	—
309	#557	—	149	2	no	—
310	#556	—	149	2	no	—
311	#556	—	149	1	no	—
312	#552	—	149	2	no	—
313	#552	—	149	2	no	—
314	#552	—	149	1	no	—
315	#552	—	149	1	no	—
316	D₄×Q₈	—	149	1	no	—
317	D₄×Q₈	—	149	1	no	—
318	D₄×Q₈	—	149	1	no	—
319	#541	—	149	2	no	—
320	#541	—	149	2	no	—
321	#541	—	149	1	no	—
322	#541	D₁₄₉	1	1	yes	characteristic, complemented
323	#533	—	149	2	no	—
324	#533	—	149	1	no	—
325	#529	—	149	2	no	—
326	#529	—	149	1	no	—
327	#519	—	149	1	no	—
328	#519	—	149	1	no	—
329	C₂×C₄×Q₈	—	149	1	no	—
330	C₂²×Q₈	—	149	1	no	—
331	C₂²×Q₈	—	149	1	no	—
332	C₂²×Q₈	—	149	1	no	—
333	C₄⋊Q₈	—	149	1	no	—
334	C₄⋊Q₈	—	149	1	no	—
335	C₄⋊Q₈	—	149	2	no	—
336	C₄⋊Q₈	—	149	2	no	—
337	C₄⋊Q₈	—	149	1	no	—
338	C₄⋊Q₈	—	149	2	no	—
339	C₄⋊Q₈	—	149	2	no	—
340	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
341	#126	—	149	1	no	—
342	#126	—	149	2	no	—
343	#126	—	149	2	no	—
344	#126	—	149	2	no	—
345	#126	—	149	1	no	—
346	#126	—	149	2	no	—
347	#126	—	149	2	no	—
348	#126	—	149	2	no	—
349	#126	C₂×D₁₄₉	1	2	yes	—
350	#126	C₂×D₁₄₉	1	2	yes	—
351	#125	—	149	2	no	—
352	#125	—	149	1	no	—
353	#125	—	149	2	no	—
354	#125	—	149	2	no	—
355	#125	—	149	2	no	—
356	#125	—	149	2	no	—
357	#125	—	149	2	no	—
358	#125	—	149	2	no	—
359	#125	—	149	2	no	—
360	#125	—	149	2	no	—
361	#125	—	149	1	no	—
362	#125	—	149	2	no	—
363	#125	C₂×D₁₄₉	1	2	yes	—
364	#125	C₂×D₁₄₉	1	2	yes	—
365	#125	C₂×D₁₄₉	1	1	yes	characteristic
366	#124	—	149	2	no	—
367	#124	—	149	1	no	—
368	#123	—	149	2	no	—
369	#123	—	149	1	no	—
370	#123	—	149	2	no	—
371	#123	—	149	1	no	—
372	C₂²⋊Q₈	—	149	1	no	—
373	C₂²⋊Q₈	—	149	1	no	—
374	C₂²⋊Q₈	—	149	2	no	—
375	C₂²⋊Q₈	—	149	1	no	—
376	C₂²⋊Q₈	—	149	2	no	—
377	C₂²⋊Q₈	—	149	2	no	—
378	C₂²⋊Q₈	—	149	1	no	—
379	C₂²⋊Q₈	—	149	2	no	—
380	C₂²⋊Q₈	—	149	1	no	—
381	C₂²⋊Q₈	—	149	2	no	—
382	C₂²⋊Q₈	—	149	2	no	—
383	C₂²⋊Q₈	—	149	2	no	—
384	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
385	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
386	#121	—	149	1	no	—
387	C₄×Q₈	—	149	1	no	—
388	C₄×Q₈	—	149	1	no	—
389	C₄×Q₈	—	149	1	no	—
390	C₄×Q₈	—	149	2	no	—
391	C₄×Q₈	—	149	2	no	—
392	C₄×Q₈	—	149	2	no	—
393	C₄×Q₈	—	149	1	no	—
394	C₄×Q₈	—	149	2	no	—
395	C₄×Q₈	—	149	2	no	—
396	C₄×Q₈	—	149	2	no	—
397	C₄×Q₈	—	149	2	no	—
398	C₄×Q₈	—	149	1	no	—
399	C₄×Q₈	—	149	2	no	—
400	C₄×Q₈	—	149	1	no	—
401	C₄×Q₈	—	149	1	no	—
402	C₄×Q₈	—	149	1	no	—
403	C₄×Q₈	—	149	2	no	—
404	C₄×Q₈	—	149	1	no	—
405	C₄×Q₈	—	149	2	no	—
406	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
407	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
408	C₄×D₄	—	149	1	no	—
409	C₄×D₄	—	149	1	no	—
410	C₄×D₄	—	149	2	no	—
411	C₄×D₄	—	149	2	no	—
412	C₄×D₄	—	149	2	no	—
413	C₄×D₄	—	149	1	no	—
414	#117	—	149	1	no	—
415	#117	—	149	2	no	—
416	#117	—	149	1	no	—
417	#117	—	149	2	no	—
418	#117	—	149	2	no	—
419	#117	—	149	2	no	—
420	#117	—	149	2	no	—
421	#117	—	149	1	no	—
422	#117	—	149	2	no	—
423	#117	—	149	2	no	—
424	#117	C₂×D₁₄₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	—	149	2	no	—
426	C₂×C₄⋊C₄	—	149	1	no	—
427	C₂×C₄²	—	149	2	no	—
428	C₂×C₄²	—	149	1	no	—
429	C₂×Q₈	—	298	4	no	—
430	C₂×Q₈	—	298	4	no	—
431	C₂×Q₈	—	298	4	no	—
432	C₂×Q₈	—	149	2	no	—
433	C₂×Q₈	—	149	1	no	—
434	C₂×Q₈	—	149	1	no	—
435	C₂×Q₈	—	149	2	no	—
436	C₂×Q₈	—	149	2	no	—
437	C₂×Q₈	—	149	2	no	—
438	C₂×Q₈	—	149	1	no	—
439	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
440	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
441	C₂×D₄	—	149	1	no	—
442	C₂×D₄	—	149	1	no	—
443	C₂×D₄	—	149	1	no	—
444	C₂²×C₄	—	149	2	no	—
445	C₂²×C₄	—	149	1	no	—
446	C₂²×C₄	—	149	2	no	—
447	C₂²×C₄	—	149	1	no	—
448	C₂²×C₄	—	149	2	no	—
449	C₂²×C₄	—	149	1	no	—
450	C₂²×C₄	—	149	2	no	—
451	C₂²×C₄	—	149	1	no	—
452	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
453	C₄⋊C₄	—	149	2	no	—
454	C₄⋊C₄	—	149	1	no	—
455	C₄⋊C₄	—	149	2	no	—
456	C₄⋊C₄	—	149	2	no	—
457	C₄⋊C₄	—	149	2	no	—
458	C₄⋊C₄	—	149	2	no	—
459	C₄⋊C₄	—	149	2	no	—
460	C₄⋊C₄	—	149	1	no	—
461	C₄⋊C₄	—	149	2	no	—
462	C₄⋊C₄	—	149	1	no	—
463	C₄⋊C₄	—	149	2	no	—
464	C₄⋊C₄	—	149	1	no	—
465	C₄⋊C₄	—	149	2	no	—
466	C₄⋊C₄	—	149	2	no	—
467	C₄⋊C₄	—	149	2	no	—
468	C₄⋊C₄	—	149	2	no	—
469	C₄⋊C₄	—	149	2	no	—
470	C₄⋊C₄	—	149	1	no	—
471	C₄⋊C₄	—	149	2	no	—
472	C₄⋊C₄	—	149	1	no	—
473	C₄⋊C₄	—	149	2	no	—
474	C₄⋊C₄	—	149	1	no	—
475	C₄⋊C₄	—	149	1	no	—
476	C₄⋊C₄	—	149	2	no	—
477	C₄⋊C₄	—	149	2	no	—
478	C₄⋊C₄	—	149	2	no	—
479	C₄⋊C₄	—	149	2	no	—
480	C₄⋊C₄	—	149	2	no	—
481	C₄⋊C₄	—	149	1	no	—
482	C₄⋊C₄	—	149	1	no	—
483	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
485	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
487	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
488	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
489	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
492	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
493	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
494	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
495	C₂²⋊C₄	—	149	2	no	—
496	C₂²⋊C₄	—	149	1	no	—
497	C₂²⋊C₄	—	149	1	no	—
498	C₂²⋊C₄	—	149	1	no	—
499	C₂²⋊C₄	—	149	2	no	—
500	C₂²⋊C₄	—	149	1	no	—
501	C₂²⋊C₄	—	149	1	no	—
502	C₂²⋊C₄	—	149	2	no	—
503	C₂²⋊C₄	—	149	1	no	—
504	C₂²⋊C₄	—	149	2	no	—
505	C₂²⋊C₄	—	149	1	no	—
506	C₂²⋊C₄	—	149	2	no	—
507	C₂²⋊C₄	—	149	2	no	—
508	C₂²⋊C₄	—	149	1	no	—
509	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
510	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
513	C₄²	—	149	2	no	—
514	C₄²	—	149	1	no	—
515	C₄²	—	149	2	no	—
516	C₄²	—	149	2	no	—
517	C₄²	—	149	1	no	—
518	C₄²	—	149	1	no	—
519	C₄²	—	149	2	no	—
520	C₄²	—	149	2	no	—
521	C₄²	—	149	2	no	—
522	C₄²	—	149	2	no	—
523	C₄²	—	149	2	no	—
524	C₄²	—	149	1	no	—
525	C₄²	—	149	2	no	—
526	C₄²	—	149	2	no	—
527	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
528	C₄²	C₂²×D₁₄₉	1	2	yes	—
529	C₄²	C₂²×D₁₄₉	1	2	yes	—
530	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
531	C₂³	—	149	1	no	—
532	C₂³	—	149	1	no	—
533	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	298	4	no	—
537	Q₈	—	298	4	no	—
538	Q₈	—	298	4	no	—
539	Q₈	—	298	4	no	—
540	Q₈	—	298	2	no	—
541	Q₈	—	298	2	no	—
542	Q₈	—	149	4	no	—
543	D₄	—	298	2	no	—
544	D₄	—	298	2	no	—
545	D₄	—	298	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	298	2	no	—
548	C₂×C₄	—	298	4	no	—
549	C₂×C₄	—	298	2	no	—
550	C₂×C₄	—	298	4	no	—
551	C₂×C₄	—	298	4	no	—
552	C₂×C₄	—	298	4	no	—
553	C₂×C₄	—	298	2	no	—
554	C₂×C₄	—	298	2	no	—
555	C₂×C₄	—	149	2	no	—
556	C₂×C₄	—	149	2	no	—
557	C₂×C₄	—	149	1	no	—
558	C₂×C₄	—	149	1	no	—
559	C₂×C₄	—	149	1	no	—
560	C₂×C₄	—	149	1	no	—
561	C₂×C₄	—	149	1	no	—
562	C₂×C₄	—	149	2	no	—
563	C₂×C₄	—	149	1	no	—
564	C₂×C₄	—	149	2	no	—
565	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
569	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
572	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
573	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
574	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	298	1	no	—
579	C₂²	—	298	1	no	—
580	C₂²	—	298	1	no	—
581	C₂²	—	298	1	no	—
582	C₂²	—	298	1	no	—
583	C₂²	—	149	2	no	—
584	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	298	2	no	—
595	C₄	—	298	1	no	—
596	C₄	—	298	1	no	—
597	C₄	—	298	2	no	—
598	C₄	—	298	1	no	—
599	C₄	—	298	1	no	—
600	C₄	—	298	2	no	—
601	C₄	—	298	1	no	—
602	C₄	—	149	4	no	—
603	C₄	—	149	2	no	—
604	C₄	#41×D₁₄₉	1	2	yes	—
605	C₂	—	4	1	no	—
606	C₂	—	298	2	no	—
607	C₂	—	596	1	no	—
608	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
609	C₂	2₋¹⁺⁴×D₁₄₉	1	1	yes	characteristic
610	C₂	2₋¹⁺⁴×D₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#541×C₁₄₉	C₂
prime radical	#18011884	C₂²
hypercenter	#541	D₁₄₉
hypocenter	C₁₄₉	#3523
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #23750352	C₂	semidirect
2. #23750352	C₂	semidirect
3. #23750350	C₂	semidirect
4. #23750346	C₂	semidirect
5. #23750342	C₂	semidirect
6. #23750313	C₂	semidirect
7. #23750311	C₂	semidirect
8. #23750309	C₂	semidirect
9. #23750307	C₂	semidirect
10. #23750290	C₂	semidirect
11. #23750288	C₂	semidirect
12. #23750288	C₂	semidirect
13. #23750234	C₂	semidirect
14. #23750233	C₂	semidirect
15. #23750232	C₂	semidirect
16. #23750181	C₂	semidirect
17. #23750179	C₂	semidirect
20. #23750102	C₂	semidirect
21. #23750101	C₂	semidirect
22. C₄×Q₈×D₁₄₉	C₂	semidirect
23. #541×C₁₄₉	C₂	semidirect
305. C₁₄₉	#3523	semidirect
322. #541	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750352	2
#23750350	2
#23750346	2
#23750342	2
#23750313	2
#23750311	2
#23750309	2
#23750307	2
#23750290	2
#23750288	2
#23750234	2
#23750233	2
#23750232	2
#23750181	2
#23750179	2
#23750158	2
#23750153	2
#23750102	2
#23750101	2
C₄×Q₈×D₁₄₉	2
#541×C₁₄₉	2
#3523	149