Subgroups — #34058405

Order 19072.

1040 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750347	C₂	1	2	yes	maximal, complemented
2	#23750346	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750341	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750338	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750337	C₂	1	2	yes	maximal, complemented
6	#23750326	C₂	1	2	yes	maximal, complemented
7	#23750321	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750319	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750317	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750316	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750311	C₂	1	2	yes	maximal, complemented
12	#23750252	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750214	C₂	1	2	yes	maximal, complemented
14	#23750209	C₂	1	2	yes	maximal, complemented
15	#23750205	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750162	C₂	1	2	yes	maximal, complemented
17	#23750158	C₂	1	2	yes	maximal, complemented
18	#23750138	C₂	1	1	yes	maximal, characteristic, complemented
19	#23750134	C₂	1	1	yes	maximal, characteristic, complemented
20	#23750107	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750105	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558737	C₂²	1	1	yes	characteristic
25	C₂×#14558736	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
27	#18011910	C₂²	1	1	yes	characteristic, complemented
28	#18011909	C₂²	1	2	yes	complemented
29	#18011906	C₂²	1	2	yes	—
30	#18011906	C₂²	1	2	yes	complemented
31	#18011906	C₂²	1	2	yes	complemented
32	#18011905	C₂²	1	2	yes	—
33	#18011905	C₂²	1	2	yes	complemented
34	#18011904	C₂²	1	2	yes	—
35	#18011903	C₂²	1	1	yes	characteristic, complemented
36	#18011902	C₂²	1	2	yes	complemented
37	#18011902	C₂²	1	1	yes	characteristic, complemented
38	#18011901	C₂²	1	2	yes	complemented
39	#18011901	C₂²	1	2	yes	complemented
40	#18011900	C₂²	1	2	yes	—
41	#18011900	C₂²	1	2	yes	complemented
42	#18011899	C₂²	1	2	yes	—
43	#18011897	C₂²	1	2	yes	—
44	#18011897	C₂²	1	2	yes	complemented
45	#18011896	C₂²	1	2	yes	—
46	#18011896	C₂²	1	1	yes	characteristic
47	#18011896	C₂²	1	2	yes	—
48	#18011895	C₂²	1	2	yes	—
49	#18011893	C₂²	1	1	yes	characteristic
50	#18011893	C₂²	1	2	yes	—
51	#18011893	C₂²	1	2	yes	—
52	#18011889	C₂²	1	2	yes	—
53	#18011889	C₂²	1	1	yes	characteristic
54	#18011889	C₂²	1	2	yes	complemented
55	#18011888	C₂²	1	1	yes	characteristic
56	#18011887	C₂²	1	2	yes	—
57	#18011887	C₂²	1	1	yes	characteristic
58	#18011887	C₂²	1	1	yes	characteristic, complemented
59	#18011886	C₂²	1	2	yes	—
60	#18011886	C₂²	1	2	yes	—
61	#18011886	C₂²	1	1	yes	characteristic
62	#18011886	C₂²	1	1	yes	characteristic, complemented
63	#18011885	C₂²	1	1	yes	characteristic
64	#18011885	C₂²	1	1	yes	characteristic, complemented
65	#18011884	C₂²	1	2	yes	—
66	#18011884	C₂²	1	2	yes	—
67	#18011884	C₂²	1	2	yes	—
68	#18011884	C₂²	1	1	yes	characteristic
69	#18011884	C₂²	1	2	yes	complemented
70	#18011883	C₂²	1	2	yes	—
71	#18011883	C₂²	1	1	yes	characteristic
72	#18011881	C₂²	1	2	yes	—
73	#18011881	C₂²	1	1	yes	characteristic
74	#18011879	C₂²	1	1	yes	characteristic
75	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
77	#18011876	C₂²	1	2	yes	complemented
78	C₄×D₅₉₆	C₂²	1	2	yes	—
79	C₄×D₅₉₆	C₂²	1	2	yes	—
80	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
81	C₄×D₅₉₆	C₂²	1	2	yes	complemented
82	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
83	#18011873	C₂²	1	2	yes	—
84	#18011873	C₂²	1	2	yes	—
85	#18011873	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
88	#18011871	C₂²	1	2	yes	—
89	#18011871	C₂²	1	2	yes	—
90	#18011871	C₂²	1	2	yes	complemented
91	#18011871	C₂²	1	2	yes	complemented
92	#18011870	C₂²	1	1	yes	characteristic
93	#18011869	C₂²	1	1	yes	characteristic
94	#18011869	C₂²	1	1	yes	characteristic
95	#18011869	C₂²	1	1	yes	characteristic
96	#18011869	C₂²	1	2	yes	complemented
97	#18011869	C₂²	1	1	yes	characteristic, complemented
98	#18011868	C₂²	1	1	yes	characteristic
99	#18011868	C₂²	1	2	yes	—
100	#18011868	C₂²	1	2	yes	complemented
101	#18011868	C₂²	1	2	yes	complemented
102	#18011868	C₂²	1	2	yes	complemented
103	#18011867	C₂²	1	2	yes	—
104	#18011867	C₂²	1	2	yes	complemented
105	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
106	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
109	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
110	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
111	C₄²×D₁₄₉	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
113	#126×C₁₄₉	C₂²	1	2	yes	—
114	#126×C₁₄₉	C₂²	1	2	yes	complemented
115	#124×C₁₄₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₁₄₉	C₂²	1	2	yes	complemented
119	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
121	#117×C₁₄₉	C₂²	1	1	yes	characteristic
122	#117×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
124	#14558737	—	2	4	no	—
125	#14558736	—	2	4	no	—
126	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₉₈	C₂³	1	2	yes	—
128	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
129	C₂×D₅₉₆	C₂³	1	2	yes	—
130	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
131	C₂×D₅₉₆	C₂³	1	2	yes	—
132	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
133	C₂×D₅₉₆	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
142	C₂×C₄×D₁₄₉	—	2	4	no	—
143	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
148	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
149	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
150	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
151	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
152	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
153	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
155	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
156	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
161	#14558715	C₂³	1	2	yes	—
162	#14558715	C₂³	1	2	yes	—
163	#14558715	C₂³	1	2	yes	—
164	#14558715	C₂³	1	2	yes	—
165	#14558715	C₂³	1	1	yes	characteristic
166	#14558715	C₂³	1	2	yes	—
167	#14558715	C₂³	1	1	yes	characteristic
168	#14558715	C₂³	1	2	yes	—
169	#14558715	C₂³	1	2	yes	—
170	#14558715	C₂³	1	1	yes	characteristic
171	#14558715	C₂³	1	2	yes	—
172	#14558715	C₂³	1	1	yes	characteristic
173	#14558715	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
177	#14558713	C₂³	1	1	yes	characteristic
178	#14558713	C₂³	1	2	yes	—
179	#14558713	C₂³	1	2	yes	—
180	#14558713	C₂³	1	2	yes	—
181	#14558713	C₂³	1	2	yes	—
182	#14558713	C₂³	1	2	yes	—
183	#14558713	C₂³	1	1	yes	characteristic
184	#14558713	C₂³	1	2	yes	—
185	#14558713	C₂³	1	1	yes	characteristic
186	#14558713	C₂³	1	2	yes	—
187	#14558713	C₂³	1	2	yes	—
188	#14558713	C₂³	1	2	yes	—
189	#14558713	C₂³	1	2	yes	—
190	#14558713	C₂³	1	1	yes	characteristic
191	#14558713	C₂³	1	1	yes	characteristic
192	#14558713	C₂³	1	1	yes	characteristic
193	#14558713	C₂³	1	2	yes	—
194	#14558713	C₂³	1	2	yes	—
195	C₄×Dic₁₄₉	C₂³	1	2	yes	—
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	1	yes	characteristic
200	C₄×Dic₁₄₉	C₂³	1	2	yes	—
201	C₄×Dic₁₄₉	C₂³	1	2	yes	—
202	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
204	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
208	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
210	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
221	C₄²×C₁₄₉	C₂³	1	2	yes	—
222	C₄²×C₁₄₉	C₂³	1	2	yes	—
223	C₄²×C₁₄₉	C₂³	1	2	yes	—
224	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
225	C₂²×D₁₄₉	—	2	2	no	—
226	C₂²×D₁₄₉	—	4	1	no	—
227	C₂²×D₁₄₉	—	4	1	no	—
228	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
230	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
232	Dic₂₉₈	—	2	2	no	—
233	Dic₂₉₈	—	4	2	no	—
234	D₅₉₆	—	2	2	no	—
235	D₅₉₆	—	2	4	no	—
236	D₅₉₆	—	2	2	no	—
237	D₅₉₆	—	4	2	no	—
238	D₅₉₆	—	4	2	no	—
239	D₅₉₆	—	4	1	no	—
240	C₂²⋊D₁₄₉	—	2	2	no	—
241	C₂²⋊D₁₄₉	—	2	2	no	—
242	C₂²⋊D₁₄₉	—	4	1	no	—
243	C₂²⋊D₁₄₉	—	4	2	no	—
244	C₂²⋊D₁₄₉	—	4	2	no	—
245	C₂²⋊D₁₄₉	—	4	1	no	—
246	C₂×Dic₁₄₉	—	2	2	no	—
247	C₂×Dic₁₄₉	—	4	2	no	—
248	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
250	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
252	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
254	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
256	C₄×D₁₄₉	—	2	2	no	—
257	C₄×D₁₄₉	—	2	2	no	—
258	C₄×D₁₄₉	—	2	2	no	—
259	C₄×D₁₄₉	—	2	2	no	—
260	C₄×D₁₄₉	—	2	4	no	—
261	C₄×D₁₄₉	—	4	2	no	—
262	C₄×D₁₄₉	—	4	2	no	—
263	C₄×D₁₄₉	—	4	2	no	—
264	C₄×D₁₄₉	—	4	2	no	—
265	C₄×D₁₄₉	—	4	2	no	—
266	C₄×D₁₄₉	#41	1	4	yes	—
267	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
268	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
269	Q₈×C₁₄₉	—	2	2	no	—
270	Q₈×C₁₄₉	—	4	2	no	—
271	D₄×C₁₄₉	—	4	1	no	—
272	C₂×C₄×C₁₄₉	—	2	2	no	—
273	C₂×C₄×C₁₄₉	—	2	2	no	—
274	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
275	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
278	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
279	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
281	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₁₄₉	—	2	1	no	—
284	C₂²×C₁₄₉	—	2	1	no	—
285	C₂²×C₁₄₉	—	2	1	no	—
286	C₂²×C₁₄₉	—	2	1	no	—
287	C₂²×C₁₄₉	—	2	1	no	—
288	C₂²×C₁₄₉	—	2	1	no	—
289	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
290	C₂×D₁₄₉	—	2	1	no	—
291	C₂×D₁₄₉	—	2	1	no	—
292	C₂×D₁₄₉	—	2	1	no	—
293	C₂×D₁₄₉	—	2	1	no	—
294	C₂×D₁₄₉	—	2	2	no	—
295	C₂×D₁₄₉	—	2	2	no	—
296	C₂×D₁₄₉	—	2	1	no	—
297	C₂×D₁₄₉	—	2	1	no	—
298	C₂×D₁₄₉	—	2	2	no	—
299	C₂×D₁₄₉	—	2	1	no	—
300	C₂×D₁₄₉	—	2	1	no	—
301	C₂×D₁₄₉	—	4	4	no	—
302	C₂×D₁₄₉	C₂×#41	1	2	yes	—
303	C₄×C₁₄₉	—	2	1	no	—
304	C₄×C₁₄₉	—	2	1	no	—
305	C₄×C₁₄₉	—	2	2	no	—
306	C₄×C₁₄₉	—	2	1	no	—
307	C₄×C₁₄₉	—	2	2	no	—
308	C₄×C₁₄₉	—	2	2	no	—
309	C₄×C₁₄₉	—	2	2	no	—
310	C₄×C₁₄₉	—	2	1	no	—
311	C₄×C₁₄₉	C₂×#41	1	2	yes	—
312	Dic₁₄₉	—	2	1	no	—
313	Dic₁₄₉	—	2	1	no	—
314	Dic₁₄₉	—	2	2	no	—
315	Dic₁₄₉	—	2	1	no	—
316	Dic₁₄₉	—	2	2	no	—
317	Dic₁₄₉	—	2	2	no	—
318	Dic₁₄₉	—	2	1	no	—
319	Dic₁₄₉	C₂×#41	1	2	yes	—
320	C₂×C₁₄₉	—	4	1	no	—
321	C₂×C₁₄₉	—	4	1	no	—
322	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
323	C₂×C₁₄₉	#585	1	1	yes	characteristic
324	C₂×C₁₄₉	#585	1	1	yes	characteristic
325	D₁₄₉	—	2	2	no	—
326	D₁₄₉	—	4	1	no	—
327	D₁₄₉	—	4	2	no	—
328	D₁₄₉	—	4	1	no	—
329	C₁₄₉	#3493	1	1	yes	characteristic, complemented, Sylow
330	#3493	—	149	1	no	maximal, Sylow
331	#556	—	149	1	no	—
332	#556	—	149	2	no	—
333	#556	D₁₄₉	1	1	yes	characteristic, complemented
334	#555	—	149	1	no	—
335	#555	—	149	2	no	—
336	#555	—	149	1	no	—
337	#553	—	149	2	no	—
338	#553	—	149	1	no	—
339	#553	—	149	1	no	—
340	#552	—	149	2	no	—
341	#552	—	149	1	no	—
342	#552	—	149	1	no	—
343	#544	—	149	1	no	—
344	#538	—	149	2	no	—
345	#538	—	149	2	no	—
346	#537	—	149	1	no	—
347	#529	—	149	2	no	—
348	#529	—	149	2	no	—
349	#525	—	149	1	no	—
350	#525	—	149	1	no	—
351	#520	—	149	1	no	—
352	#520	—	149	1	no	—
353	C₂×#117	—	149	1	no	—
354	C₂×#41	—	149	1	no	—
355	C₂×#41	—	149	1	no	—
356	C₂³×C₄	—	149	1	no	—
357	C₄⋊Q₈	—	149	2	no	—
358	C₄⋊Q₈	—	149	1	no	—
359	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
360	#126	—	149	2	no	—
361	#126	—	149	2	no	—
362	#126	—	149	2	no	—
363	#126	—	149	2	no	—
364	#126	—	149	2	no	—
365	#126	—	149	2	no	—
366	#126	C₂×D₁₄₉	1	2	yes	—
367	#126	C₂×D₁₄₉	1	2	yes	complemented
368	#125	—	149	2	no	—
369	#125	—	149	2	no	—
370	#125	—	149	2	no	—
371	#125	—	149	1	no	—
372	#125	—	149	1	no	—
373	#124	—	149	2	no	—
374	#124	—	149	2	no	—
375	#124	—	149	2	no	—
376	#124	—	149	2	no	—
377	#124	—	149	2	no	—
378	#124	C₂×D₁₄₉	1	2	yes	—
379	#123	—	149	2	no	—
380	#123	—	149	1	no	—
381	#123	—	149	2	no	—
382	#123	—	149	1	no	—
383	#123	—	149	2	no	—
384	#123	—	149	2	no	—
385	#123	—	149	2	no	—
386	C₂²⋊Q₈	—	149	1	no	—
387	C₂²⋊Q₈	—	149	2	no	—
388	C₂²⋊Q₈	—	149	1	no	—
389	C₂²⋊Q₈	—	149	1	no	—
390	C₂²⋊Q₈	—	149	2	no	—
391	C₂²⋊Q₈	—	149	2	no	—
392	C₂²⋊Q₈	—	149	1	no	—
393	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
394	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
395	#121	—	149	1	no	—
396	#121	—	149	2	no	—
397	#121	—	149	1	no	—
398	#121	—	149	1	no	—
399	#121	—	149	1	no	—
400	#121	—	149	2	no	—
401	#121	—	149	1	no	—
402	#121	—	149	2	no	—
403	#121	—	149	1	no	—
404	#121	—	149	2	no	—
405	#121	—	149	2	no	—
406	#121	—	149	2	no	—
407	#121	—	149	2	no	—
408	#120	—	149	1	no	—
409	#120	—	149	2	no	—
410	#120	—	149	1	no	—
411	C₄×Q₈	—	149	1	no	—
412	C₄×Q₈	—	149	2	no	—
413	C₄×Q₈	—	149	2	no	—
414	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
415	C₄×Q₈	C₂×D₁₄₉	1	2	yes	complemented
416	C₄×D₄	—	149	1	no	—
417	C₄×D₄	—	149	1	no	—
418	C₄×D₄	—	149	2	no	—
419	C₄×D₄	—	149	1	no	—
420	C₄×D₄	—	149	2	no	—
421	C₄×D₄	—	149	2	no	—
422	C₄×D₄	—	149	2	no	—
423	C₄×D₄	—	149	2	no	—
424	C₄×D₄	—	149	2	no	—
425	C₄×D₄	—	149	2	no	—
426	C₄×D₄	—	149	2	no	—
427	C₄×D₄	—	149	1	no	—
428	C₄×D₄	—	149	1	no	—
429	C₄×D₄	—	149	2	no	—
430	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
431	#117	—	149	1	no	—
432	#117	—	149	1	no	—
433	#117	—	149	1	no	—
434	#117	—	149	1	no	—
435	#117	—	149	1	no	—
436	#117	—	149	2	no	—
437	#117	—	149	2	no	—
438	#117	—	149	2	no	—
439	#117	—	149	2	no	—
440	#117	—	149	1	no	—
441	#117	—	149	2	no	—
442	#117	—	149	2	no	—
443	#117	—	149	2	no	—
444	#117	C₂×D₁₄₉	1	1	yes	characteristic
445	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
446	C₂×C₄⋊C₄	—	149	1	no	—
447	C₂×C₄⋊C₄	—	149	1	no	—
448	C₂×C₄⋊C₄	—	149	1	no	—
449	C₂×C₄⋊C₄	—	149	2	no	—
450	C₂×C₄⋊C₄	—	149	1	no	—
451	C₂×C₂²⋊C₄	—	149	2	no	—
452	C₂×C₄²	—	149	2	no	—
453	C₂⁴	—	149	1	no	—
454	#41	—	298	4	no	—
455	#41	—	298	4	no	—
456	C₂×Q₈	—	149	1	no	—
457	C₂×Q₈	—	149	2	no	—
458	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
459	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
460	C₂×D₄	—	149	1	no	—
461	C₂×D₄	—	149	1	no	—
462	C₂×D₄	—	149	1	no	—
463	C₂×D₄	—	149	2	no	—
464	C₂×D₄	—	149	1	no	—
465	C₂×D₄	—	149	2	no	—
466	C₂×D₄	—	149	2	no	—
467	C₂×D₄	—	149	1	no	—
468	C₂×D₄	—	149	1	no	—
469	C₂×D₄	—	149	1	no	—
470	C₂×D₄	—	149	2	no	—
471	C₂×D₄	—	149	2	no	—
472	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
473	C₂²×C₄	—	298	4	no	—
474	C₂²×C₄	—	149	1	no	—
475	C₂²×C₄	—	149	1	no	—
476	C₂²×C₄	—	149	2	no	—
477	C₂²×C₄	—	149	1	no	—
478	C₂²×C₄	—	149	1	no	—
479	C₂²×C₄	—	149	1	no	—
480	C₂²×C₄	—	149	2	no	—
481	C₂²×C₄	—	149	2	no	—
482	C₂²×C₄	—	149	2	no	—
483	C₂²×C₄	—	149	2	no	—
484	C₂²×C₄	—	149	2	no	—
485	C₂²×C₄	—	149	2	no	—
486	C₂²×C₄	—	149	1	no	—
487	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
489	C₄⋊C₄	—	149	2	no	—
490	C₄⋊C₄	—	149	1	no	—
491	C₄⋊C₄	—	149	1	no	—
492	C₄⋊C₄	—	149	1	no	—
493	C₄⋊C₄	—	149	2	no	—
494	C₄⋊C₄	—	149	1	no	—
495	C₄⋊C₄	—	149	2	no	—
496	C₄⋊C₄	—	149	2	no	—
497	C₄⋊C₄	—	149	2	no	—
498	C₄⋊C₄	—	149	1	no	—
499	C₄⋊C₄	—	149	2	no	—
500	C₄⋊C₄	—	149	1	no	—
501	C₄⋊C₄	—	149	1	no	—
502	C₄⋊C₄	—	149	2	no	—
503	C₄⋊C₄	—	149	2	no	—
504	C₄⋊C₄	—	149	2	no	—
505	C₄⋊C₄	—	149	1	no	—
506	C₄⋊C₄	—	149	2	no	—
507	C₄⋊C₄	—	149	2	no	—
508	C₄⋊C₄	—	149	2	no	—
509	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
512	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
514	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
517	C₂²⋊C₄	—	149	2	no	—
518	C₂²⋊C₄	—	149	1	no	—
519	C₂²⋊C₄	—	149	1	no	—
520	C₂²⋊C₄	—	149	2	no	—
521	C₂²⋊C₄	—	149	2	no	—
522	C₂²⋊C₄	—	149	2	no	—
523	C₂²⋊C₄	—	149	1	no	—
524	C₂²⋊C₄	—	149	1	no	—
525	C₂²⋊C₄	—	149	2	no	—
526	C₂²⋊C₄	—	149	1	no	—
527	C₂²⋊C₄	—	149	2	no	—
528	C₂²⋊C₄	—	149	2	no	—
529	C₂²⋊C₄	—	149	2	no	—
530	C₂²⋊C₄	—	149	2	no	—
531	C₂²⋊C₄	—	149	2	no	—
532	C₂²⋊C₄	—	149	2	no	—
533	C₂²⋊C₄	—	149	1	no	—
534	C₂²⋊C₄	—	149	2	no	—
535	C₂²⋊C₄	—	149	2	no	—
536	C₂²⋊C₄	—	149	1	no	—
537	C₂²⋊C₄	—	149	1	no	—
538	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
540	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
542	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
544	C₄²	—	149	2	no	—
545	C₄²	—	149	2	no	—
546	C₄²	—	149	2	no	—
547	C₄²	—	149	2	no	—
548	C₄²	—	149	2	no	—
549	C₄²	—	149	1	no	—
550	C₄²	—	149	2	no	—
551	C₄²	C₂²×D₁₄₉	1	2	yes	—
552	C₄²	C₂²×D₁₄₉	1	2	yes	—
553	C₄²	C₂²×D₁₄₉	1	2	yes	—
554	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
555	C₂³	—	298	2	no	—
556	C₂³	—	596	1	no	—
557	C₂³	—	596	1	no	—
558	C₂³	—	149	1	no	—
559	C₂³	—	149	1	no	—
560	C₂³	—	149	2	no	—
561	C₂³	—	149	1	no	—
562	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
563	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	4	2	no	—
566	Q₈	—	298	2	no	—
567	Q₈	—	596	2	no	—
568	D₄	—	4	1	no	—
569	D₄	—	298	2	no	—
570	D₄	—	298	4	no	—
571	D₄	—	298	2	no	—
572	D₄	—	298	2	no	—
573	D₄	—	298	2	no	—
574	D₄	—	596	2	no	—
575	D₄	—	596	2	no	—
576	D₄	—	596	1	no	—
577	D₄	—	596	2	no	—
578	D₄	—	596	1	no	—
579	D₄	—	596	1	no	—
580	D₄	—	596	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	298	2	no	—
584	C₂×C₄	—	298	2	no	—
585	C₂×C₄	—	298	4	no	—
586	C₂×C₄	—	298	2	no	—
587	C₂×C₄	—	298	2	no	—
588	C₂×C₄	—	298	2	no	—
589	C₂×C₄	—	596	2	no	—
590	C₂×C₄	—	596	2	no	—
591	C₂×C₄	—	596	2	no	—
592	C₂×C₄	—	596	2	no	—
593	C₂×C₄	—	596	2	no	—
594	C₂×C₄	—	596	2	no	—
595	C₂×C₄	—	149	1	no	—
596	C₂×C₄	—	149	2	no	—
597	C₂×C₄	—	149	1	no	—
598	C₂×C₄	—	149	1	no	—
599	C₂×C₄	—	149	2	no	—
600	C₂×C₄	—	149	1	no	—
601	C₂×C₄	—	149	2	no	—
602	C₂×C₄	—	149	1	no	—
603	C₂×C₄	—	149	4	no	—
604	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
606	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
607	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
608	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
609	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	298	1	no	—
620	C₂²	—	298	1	no	—
621	C₂²	—	298	1	no	—
622	C₂²	—	298	2	no	—
623	C₂²	—	298	1	no	—
624	C₂²	—	298	1	no	—
625	C₂²	—	298	2	no	—
626	C₂²	—	298	1	no	—
627	C₂²	—	298	1	no	—
628	C₂²	—	298	2	no	—
629	C₂²	—	298	1	no	—
630	C₂²	—	596	4	no	—
631	C₂²	—	149	2	no	—
632	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	1	no	—
641	C₄	—	298	1	no	—
642	C₄	—	298	1	no	—
643	C₄	—	298	2	no	—
644	C₄	—	298	1	no	—
645	C₄	—	298	2	no	—
646	C₄	—	298	1	no	—
647	C₄	—	298	2	no	—
648	C₄	—	149	2	no	—
649	C₄	#41×D₁₄₉	1	2	yes	—
650	C₂	—	4	1	no	—
651	C₂	—	4	1	no	—
652	C₂	—	298	2	no	—
653	C₂	—	596	1	no	—
654	C₂	—	596	2	no	—
655	C₂	—	596	1	no	—
656	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
657	C₂	#23750461	1	1	yes	characteristic
658	C₂	#23750462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#556×C₁₄₉	C₂
hypercenter	#556	D₁₄₉
hypocenter	C₁₄₉	#3493
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #23750347	C₂	semidirect
2. #23750346	C₂	semidirect
3. #23750341	C₂	semidirect
4. #23750338	C₂	semidirect
5. #23750337	C₂	semidirect
6. #23750326	C₂	semidirect
7. #23750321	C₂	semidirect
8. #23750319	C₂	semidirect
9. #23750317	C₂	semidirect
10. #23750316	C₂	semidirect
11. #23750311	C₂	semidirect
12. #23750252	C₂	semidirect
13. #23750214	C₂	semidirect
14. #23750209	C₂	semidirect
15. #23750205	C₂	semidirect
16. #23750162	C₂	semidirect
17. #23750158	C₂	semidirect
18. #23750138	C₂	semidirect
19. #23750134	C₂	semidirect
20. #23750107	C₂	semidirect
21. #23750105	C₂	semidirect
22. #117×D₁₄₉	C₂	semidirect
23. #556×C₁₄₉	C₂	semidirect
27. #18011910	C₂²	semidirect
28. #18011909	C₂²	semidirect
30. #18011906	C₂²	semidirect
31. #18011906	C₂²	semidirect
33. #18011905	C₂²	semidirect
35. #18011903	C₂²	semidirect
36. #18011902	C₂²	semidirect
37. #18011902	C₂²	semidirect
38. #18011901	C₂²	semidirect
39. #18011901	C₂²	semidirect
41. #18011900	C₂²	semidirect
44. #18011897	C₂²	semidirect
54. #18011889	C₂²	semidirect
58. #18011887	C₂²	semidirect
62. #18011886	C₂²	semidirect
64. #18011885	C₂²	semidirect
69. #18011884	C₂²	semidirect
75. Q₈×Dic₁₄₉	C₂²	semidirect
76. C₄×Dic₂₉₈	C₂²	semidirect
77. #18011876	C₂²	semidirect
81. C₄×D₅₉₆	C₂²	semidirect
82. C₄×D₅₉₆	C₂²	semidirect
85. #18011873	C₂²	semidirect
90. #18011871	C₂²	semidirect
91. #18011871	C₂²	semidirect
96. #18011869	C₂²	semidirect
97. #18011869	C₂²	semidirect
100. #18011868	C₂²	semidirect
101. #18011868	C₂²	semidirect
102. #18011868	C₂²	semidirect
104. #18011867	C₂²	semidirect
105. C₂×C₄⋊Dic₁₄₉	C₂²	semidirect
108. C₄⋊C₄×D₁₄₉	C₂²	semidirect
109. C₄⋊C₄×D₁₄₉	C₂²	semidirect
112. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
114. #126×C₁₄₉	C₂²	semidirect
117. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
118. C₄×Q₈×C₁₄₉	C₂²	semidirect
119. C₄×Q₈×C₁₄₉	C₂²	semidirect
122. #117×C₁₄₉	C₂²	semidirect
329. C₁₄₉	#3493	semidirect
333. #556	D₁₄₉	semidirect
359. C₄⋊Q₈	C₂×D₁₄₉	semidirect
367. #126	C₂×D₁₄₉	semidirect
394. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
414. C₄×Q₈	C₂×D₁₄₉	semidirect
415. C₄×Q₈	C₂×D₁₄₉	semidirect
445. #117	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750347	2
#23750346	2
#23750341	2
#23750338	2
#23750337	2
#23750326	2
#23750321	2
#23750319	2
#23750317	2
#23750316	2
#23750311	2
#23750252	2
#23750214	2
#23750209	2
#23750205	2
#23750162	2
#23750158	2
#23750138	2
#23750134	2
#23750107	2
#23750105	2
#117×D₁₄₉	2
#556×C₁₄₉	2
#3493	149