Subgroups — #34058439

Order 19072.

1022 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750349	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750346	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750330	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750317	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750316	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750315	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750310	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750309	C₂	1	2	yes	maximal, complemented
9	#23750307	C₂	1	2	yes	maximal, complemented
10	#23750304	C₂	1	2	yes	maximal, complemented
11	#23750302	C₂	1	2	yes	maximal, complemented
12	#23750252	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750245	C₂	1	2	yes	maximal, complemented
14	#23750234	C₂	1	2	yes	maximal, complemented
15	#23750198	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750177	C₂	1	2	yes	maximal, complemented
17	#23750155	C₂	1	2	yes	maximal, complemented
18	#23750134	C₂	1	1	yes	maximal, characteristic
19	C₂²⋊Q₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#23750106	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750101	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#18011869	C₂	1	1	yes	maximal, characteristic, complemented
23	#554×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558736	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₄₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
27	#18011910	C₂²	1	2	yes	complemented
28	#18011910	C₂²	1	1	yes	characteristic, complemented
29	#18011909	C₂²	1	2	yes	complemented
30	#18011906	C₂²	1	2	yes	—
31	#18011906	C₂²	1	2	yes	—
32	#18011906	C₂²	1	2	yes	—
33	#18011906	C₂²	1	2	yes	complemented
34	#18011906	C₂²	1	2	yes	complemented
35	#18011905	C₂²	1	2	yes	—
36	#18011904	C₂²	1	2	yes	complemented
37	#18011904	C₂²	1	2	yes	complemented
38	#18011903	C₂²	1	1	yes	characteristic, complemented
39	#18011902	C₂²	1	2	yes	complemented
40	#18011902	C₂²	1	1	yes	characteristic, complemented
41	#18011901	C₂²	1	2	yes	complemented
42	#18011901	C₂²	1	2	yes	complemented
43	#18011901	C₂²	1	2	yes	complemented
44	#18011901	C₂²	1	2	yes	complemented
45	#18011901	C₂²	1	2	yes	complemented
46	#18011900	C₂²	1	2	yes	—
47	#18011897	C₂²	1	2	yes	—
48	#18011897	C₂²	1	2	yes	complemented
49	#18011896	C₂²	1	2	yes	—
50	#18011896	C₂²	1	2	yes	—
51	#18011896	C₂²	1	1	yes	characteristic
52	#18011895	C₂²	1	2	yes	—
53	#18011894	C₂²	1	2	yes	—
54	#18011893	C₂²	1	2	yes	—
55	#18011893	C₂²	1	1	yes	characteristic
56	#18011892	C₂²	1	2	yes	—
57	#18011891	C₂²	1	1	yes	characteristic
58	#18011891	C₂²	1	1	yes	characteristic, complemented
59	#18011890	C₂²	1	2	yes	—
60	#18011890	C₂²	1	1	yes	characteristic
61	#18011890	C₂²	1	1	yes	characteristic, complemented
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	complemented
66	#18011888	C₂²	1	2	yes	—
67	#18011888	C₂²	1	1	yes	characteristic
68	#18011887	C₂²	1	2	yes	—
69	#18011887	C₂²	1	1	yes	characteristic
70	#18011887	C₂²	1	1	yes	characteristic, complemented
71	#18011884	C₂²	1	1	yes	characteristic
72	#18011883	C₂²	1	1	yes	characteristic
73	#18011881	C₂²	1	1	yes	characteristic
74	#18011879	C₂²	1	1	yes	characteristic
75	Q₈×Dic₁₄₉	C₂²	1	2	yes	complemented
76	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
78	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
79	#18011876	C₂²	1	2	yes	complemented
80	#18011876	C₂²	1	2	yes	complemented
81	#18011876	C₂²	1	2	yes	complemented
82	#18011876	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
84	#18011873	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
86	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
90	#18011870	C₂²	1	2	yes	complemented
91	#18011870	C₂²	1	1	yes	characteristic, complemented
92	#18011869	C₂²	1	1	yes	characteristic
93	#18011869	C₂²	1	2	yes	—
94	#18011869	C₂²	1	2	yes	—
95	#18011869	C₂²	1	2	yes	—
96	#18011869	C₂²	1	1	yes	characteristic
97	#18011869	C₂²	1	1	yes	characteristic
98	#18011869	C₂²	1	1	yes	characteristic
99	#18011869	C₂²	1	1	yes	characteristic, complemented
100	#18011868	C₂²	1	1	yes	characteristic
101	#18011868	C₂²	1	2	yes	—
102	#18011868	C₂²	1	2	yes	complemented
103	#18011867	C₂²	1	2	yes	—
104	#18011867	C₂²	1	2	yes	—
105	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
108	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
109	C₂×#14558713	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
111	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
113	#125×C₁₄₉	C₂²	1	2	yes	complemented
114	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
120	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
124	#14558736	—	2	4	no	—
125	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
126	C₂×Dic₂₉₈	C₂³	1	2	yes	—
127	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₉₈	C₂³	1	2	yes	—
129	Q₈×D₁₄₉	—	2	4	no	—
130	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
131	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₄₉	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	1	yes	characteristic
137	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
138	C₂×C₄×D₁₄₉	—	2	4	no	—
139	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
143	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
145	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
148	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
149	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
150	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
151	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
152	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
156	#14558715	C₂³	1	2	yes	—
157	#14558715	C₂³	1	2	yes	—
158	#14558715	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
170	#14558715	C₂³	1	1	yes	characteristic
171	#14558715	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	C₄×Dic₁₄₉	C₂³	1	2	yes	—
193	C₄×Dic₁₄₉	C₂³	1	2	yes	—
194	C₄×Dic₁₄₉	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	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
209	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
210	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
223	C₄²×C₁₄₉	C₂³	1	2	yes	—
224	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
225	C₂²×D₁₄₉	—	2	2	no	—
226	C₂²×D₁₄₉	—	2	2	no	—
227	C₂²×D₁₄₉	—	4	1	no	—
228	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
231	Dic₂₉₈	—	2	2	no	—
232	Dic₂₉₈	—	2	4	no	—
233	Dic₂₉₈	—	2	2	no	—
234	Dic₂₉₈	—	4	2	no	—
235	D₅₉₆	—	2	2	no	—
236	D₅₉₆	—	4	1	no	—
237	C₂²⋊D₁₄₉	—	2	2	no	—
238	C₂²⋊D₁₄₉	—	2	2	no	—
239	C₂²⋊D₁₄₉	—	2	2	no	—
240	C₂²⋊D₁₄₉	—	4	1	no	—
241	C₂×Dic₁₄₉	—	2	4	no	—
242	C₂×Dic₁₄₉	—	2	2	no	—
243	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
245	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
247	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
248	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
249	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
252	C₄×D₁₄₉	—	2	2	no	—
253	C₄×D₁₄₉	—	2	4	no	—
254	C₄×D₁₄₉	—	2	2	no	—
255	C₄×D₁₄₉	—	2	2	no	—
256	C₄×D₁₄₉	—	2	2	no	—
257	C₄×D₁₄₉	—	4	2	no	—
258	C₄×D₁₄₉	—	4	2	no	—
259	C₄×D₁₄₉	#41	1	4	yes	—
260	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
261	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
262	Q₈×C₁₄₉	—	2	2	no	—
263	Q₈×C₁₄₉	—	4	2	no	—
264	D₄×C₁₄₉	—	2	2	no	—
265	C₂×C₄×C₁₄₉	—	2	2	no	—
266	C₂×C₄×C₁₄₉	—	2	2	no	—
267	C₂×C₄×C₁₄₉	—	4	2	no	—
268	C₂×C₄×C₁₄₉	—	4	2	no	—
269	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
271	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
272	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
273	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
276	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₁₄₉	—	2	1	no	—
279	C₂²×C₁₄₉	—	2	1	no	—
280	C₂²×C₁₄₉	—	2	1	no	—
281	C₂²×C₁₄₉	—	2	1	no	—
282	C₂²×C₁₄₉	—	2	1	no	—
283	C₂²×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
284	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
285	C₂×D₁₄₉	—	2	1	no	—
286	C₂×D₁₄₉	—	2	1	no	—
287	C₂×D₁₄₉	—	2	1	no	—
288	C₂×D₁₄₉	—	2	1	no	—
289	C₂×D₁₄₉	—	2	1	no	—
290	C₂×D₁₄₉	—	2	1	no	—
291	C₂×D₁₄₉	—	2	1	no	—
292	C₂×D₁₄₉	—	2	1	no	—
293	C₂×D₁₄₉	—	4	4	no	—
294	C₂×D₁₄₉	C₂×#41	1	2	yes	—
295	C₄×C₁₄₉	—	2	1	no	—
296	C₄×C₁₄₉	—	2	1	no	—
297	C₄×C₁₄₉	—	2	2	no	—
298	C₄×C₁₄₉	—	2	1	no	—
299	C₄×C₁₄₉	—	2	2	no	—
300	C₄×C₁₄₉	—	2	2	no	—
301	C₄×C₁₄₉	—	2	2	no	—
302	C₄×C₁₄₉	—	2	1	no	—
303	C₄×C₁₄₉	C₂×#41	1	2	yes	—
304	Dic₁₄₉	—	2	1	no	—
305	Dic₁₄₉	—	2	1	no	—
306	Dic₁₄₉	—	2	2	no	—
307	Dic₁₄₉	—	2	2	no	—
308	Dic₁₄₉	—	2	2	no	—
309	Dic₁₄₉	—	2	1	no	—
310	Dic₁₄₉	—	2	2	no	—
311	Dic₁₄₉	—	2	1	no	—
312	Dic₁₄₉	C₂×#41	1	2	yes	—
313	C₂×C₁₄₉	—	2	2	no	—
314	C₂×C₁₄₉	—	4	1	no	—
315	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
316	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂×C₁₄₉	#585	1	1	yes	characteristic
318	D₁₄₉	—	2	2	no	—
319	D₁₄₉	—	4	1	no	—
320	D₁₄₉	—	4	1	no	—
321	C₁₄₉	#3495	1	1	yes	characteristic, complemented, Sylow
322	#3495	—	149	1	no	maximal, Sylow
323	#556	—	149	1	no	—
324	#556	—	149	1	no	—
325	#554	—	149	1	no	—
326	#554	D₁₄₉	1	1	yes	characteristic, complemented
327	#552	—	149	2	no	—
328	#552	—	149	1	no	—
329	#552	—	149	2	no	—
330	#552	—	149	1	no	—
331	#552	—	149	1	no	—
332	#552	—	149	1	no	—
333	#551	—	149	2	no	—
334	#551	—	149	2	no	—
335	#544	—	149	1	no	—
336	#542	—	149	2	no	—
337	#541	—	149	2	no	—
338	#536	—	149	1	no	—
339	#533	—	149	2	no	—
340	#529	—	149	2	no	—
341	#525	—	149	1	no	—
342	C₂×C₂²⋊Q₈	—	149	1	no	—
343	#520	—	149	1	no	—
344	#519	—	149	1	no	—
345	C₂×#117	—	149	1	no	—
346	C₂×#41	—	149	1	no	—
347	C₂²×Q₈	—	149	1	no	—
348	C₂³×C₄	—	149	1	no	—
349	C₄⋊Q₈	—	149	2	no	—
350	C₄⋊Q₈	—	149	2	no	—
351	C₄⋊Q₈	—	149	1	no	—
352	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
353	#126	—	149	2	no	—
354	#126	—	149	2	no	—
355	#126	—	149	2	no	—
356	#126	—	149	2	no	—
357	#126	—	149	2	no	—
358	#126	—	149	2	no	—
359	#126	—	149	2	no	—
360	#126	—	149	2	no	—
361	#125	—	149	2	no	—
362	#125	—	149	2	no	—
363	#125	—	149	2	no	—
364	#125	—	149	2	no	—
365	#125	—	149	2	no	—
366	#125	—	149	2	no	—
367	#125	—	149	1	no	—
368	#125	—	149	1	no	—
369	#125	C₂×D₁₄₉	1	2	yes	complemented
370	#124	—	149	2	no	—
371	#124	—	149	2	no	—
372	#124	—	149	2	no	—
373	#123	—	149	2	no	—
374	#123	—	149	2	no	—
375	#123	—	149	1	no	—
376	#123	—	149	2	no	—
377	#123	—	149	2	no	—
378	#123	—	149	1	no	—
379	#123	—	149	2	no	—
380	#123	—	149	2	no	—
381	C₂²⋊Q₈	—	149	1	no	—
382	C₂²⋊Q₈	—	149	1	no	—
383	C₂²⋊Q₈	—	149	2	no	—
384	C₂²⋊Q₈	—	149	1	no	—
385	C₂²⋊Q₈	—	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	1	no	—
391	C₂²⋊Q₈	—	149	2	no	—
392	C₂²⋊Q₈	—	149	2	no	—
393	C₂²⋊Q₈	—	149	2	no	—
394	C₂²⋊Q₈	—	149	1	no	—
395	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
396	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
397	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
398	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
399	#121	—	149	1	no	—
400	#121	—	149	1	no	—
401	#120	—	149	1	no	—
402	#120	—	149	1	no	—
403	C₄×Q₈	—	149	1	no	—
404	C₄×Q₈	—	149	2	no	—
405	C₄×Q₈	—	149	2	no	—
406	C₄×Q₈	—	149	1	no	—
407	C₄×Q₈	—	149	2	no	—
408	C₄×Q₈	—	149	2	no	—
409	C₄×Q₈	—	149	2	no	—
410	C₄×Q₈	—	149	1	no	—
411	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
412	C₄×D₄	—	149	2	no	—
413	C₄×D₄	—	149	2	no	—
414	C₄×D₄	—	149	1	no	—
415	C₄×D₄	—	149	1	no	—
416	C₄×D₄	—	149	2	no	—
417	C₄×D₄	—	149	2	no	—
418	C₄×D₄	—	149	1	no	—
419	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
420	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
421	#117	—	149	1	no	—
422	#117	—	149	2	no	—
423	#117	—	149	1	no	—
424	#117	—	149	1	no	—
425	#117	—	149	2	no	—
426	#117	—	149	1	no	—
427	#117	—	149	2	no	—
428	#117	—	149	1	no	—
429	#117	—	149	2	no	—
430	#117	—	149	1	no	—
431	#117	—	149	2	no	—
432	#117	—	149	2	no	—
433	#117	—	149	1	no	—
434	#117	—	149	2	no	—
435	#117	—	149	2	no	—
436	C₂×C₄⋊C₄	—	149	1	no	—
437	C₂×C₄⋊C₄	—	149	1	no	—
438	C₂×C₄⋊C₄	—	149	1	no	—
439	C₂×C₄⋊C₄	—	149	2	no	—
440	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
442	C₂×C₂²⋊C₄	—	149	2	no	—
443	C₂×C₂²⋊C₄	—	149	2	no	—
444	C₂×C₄²	—	149	2	no	—
445	C₂⁴	—	149	1	no	—
446	#41	—	298	4	no	—
447	C₂×Q₈	—	298	4	no	—
448	C₂×Q₈	—	149	1	no	—
449	C₂×Q₈	—	149	2	no	—
450	C₂×Q₈	—	149	1	no	—
451	C₂×Q₈	—	149	2	no	—
452	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
453	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
454	C₂×D₄	—	149	1	no	—
455	C₂×D₄	—	149	1	no	—
456	C₂×D₄	—	149	1	no	—
457	C₂×D₄	—	149	1	no	—
458	C₂×D₄	—	149	1	no	—
459	C₂×D₄	—	149	1	no	—
460	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
461	C₂²×C₄	—	298	4	no	—
462	C₂²×C₄	—	149	1	no	—
463	C₂²×C₄	—	149	2	no	—
464	C₂²×C₄	—	149	2	no	—
465	C₂²×C₄	—	149	1	no	—
466	C₂²×C₄	—	149	1	no	—
467	C₂²×C₄	—	149	1	no	—
468	C₂²×C₄	—	149	1	no	—
469	C₂²×C₄	—	149	2	no	—
470	C₂²×C₄	—	149	2	no	—
471	C₂²×C₄	—	149	1	no	—
472	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
476	C₄⋊C₄	—	149	1	no	—
477	C₄⋊C₄	—	149	1	no	—
478	C₄⋊C₄	—	149	1	no	—
479	C₄⋊C₄	—	149	2	no	—
480	C₄⋊C₄	—	149	2	no	—
481	C₄⋊C₄	—	149	2	no	—
482	C₄⋊C₄	—	149	2	no	—
483	C₄⋊C₄	—	149	2	no	—
484	C₄⋊C₄	—	149	2	no	—
485	C₄⋊C₄	—	149	1	no	—
486	C₄⋊C₄	—	149	1	no	—
487	C₄⋊C₄	—	149	2	no	—
488	C₄⋊C₄	—	149	2	no	—
489	C₄⋊C₄	—	149	2	no	—
490	C₄⋊C₄	—	149	2	no	—
491	C₄⋊C₄	—	149	2	no	—
492	C₄⋊C₄	—	149	2	no	—
493	C₄⋊C₄	—	149	2	no	—
494	C₄⋊C₄	—	149	2	no	—
495	C₄⋊C₄	—	149	2	no	—
496	C₄⋊C₄	—	149	1	no	—
497	C₄⋊C₄	—	149	1	no	—
498	C₄⋊C₄	—	149	1	no	—
499	C₄⋊C₄	—	149	2	no	—
500	C₄⋊C₄	—	149	2	no	—
501	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
504	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
505	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
508	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
510	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
511	C₂²⋊C₄	—	149	2	no	—
512	C₂²⋊C₄	—	149	1	no	—
513	C₂²⋊C₄	—	149	1	no	—
514	C₂²⋊C₄	—	149	2	no	—
515	C₂²⋊C₄	—	149	2	no	—
516	C₂²⋊C₄	—	149	2	no	—
517	C₂²⋊C₄	—	149	2	no	—
518	C₂²⋊C₄	—	149	2	no	—
519	C₂²⋊C₄	—	149	2	no	—
520	C₂²⋊C₄	—	149	2	no	—
521	C₂²⋊C₄	—	149	2	no	—
522	C₂²⋊C₄	—	149	1	no	—
523	C₂²⋊C₄	—	149	1	no	—
524	C₂²⋊C₄	—	149	1	no	—
525	C₂²⋊C₄	—	149	2	no	—
526	C₂²⋊C₄	—	149	2	no	—
527	C₂²⋊C₄	—	149	1	no	—
528	C₂²⋊C₄	—	149	1	no	—
529	C₂²⋊C₄	—	149	1	no	—
530	C₂²⋊C₄	—	149	2	no	—
531	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
533	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
534	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
535	C₄²	—	149	2	no	—
536	C₄²	—	149	2	no	—
537	C₄²	—	149	2	no	—
538	C₄²	—	149	2	no	—
539	C₄²	—	149	2	no	—
540	C₄²	—	149	2	no	—
541	C₄²	—	149	2	no	—
542	C₄²	—	149	2	no	—
543	C₄²	—	149	2	no	—
544	C₄²	—	149	1	no	—
545	C₄²	C₂²×D₁₄₉	1	2	yes	—
546	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
547	C₂³	—	298	2	no	—
548	C₂³	—	298	2	no	—
549	C₂³	—	596	1	no	—
550	C₂³	—	149	1	no	—
551	C₂³	—	149	1	no	—
552	C₂³	—	149	1	no	—
553	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
554	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	298	4	no	—
558	Q₈	—	298	2	no	—
559	Q₈	—	298	2	no	—
560	Q₈	—	596	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	298	2	no	—
563	D₄	—	298	2	no	—
564	D₄	—	298	2	no	—
565	D₄	—	298	2	no	—
566	D₄	—	596	1	no	—
567	D₄	—	596	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	298	2	no	—
573	C₂×C₄	—	298	4	no	—
574	C₂×C₄	—	298	2	no	—
575	C₂×C₄	—	298	4	no	—
576	C₂×C₄	—	298	2	no	—
577	C₂×C₄	—	298	2	no	—
578	C₂×C₄	—	298	2	no	—
579	C₂×C₄	—	596	2	no	—
580	C₂×C₄	—	596	2	no	—
581	C₂×C₄	—	149	2	no	—
582	C₂×C₄	—	149	1	no	—
583	C₂×C₄	—	149	1	no	—
584	C₂×C₄	—	149	1	no	—
585	C₂×C₄	—	149	2	no	—
586	C₂×C₄	—	149	2	no	—
587	C₂×C₄	—	149	1	no	—
588	C₂×C₄	—	149	2	no	—
589	C₂×C₄	—	149	1	no	—
590	C₂×C₄	—	149	4	no	—
591	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
592	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
594	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
596	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
597	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	298	1	no	—
606	C₂²	—	298	1	no	—
607	C₂²	—	298	1	no	—
608	C₂²	—	298	1	no	—
609	C₂²	—	298	1	no	—
610	C₂²	—	298	1	no	—
611	C₂²	—	298	1	no	—
612	C₂²	—	298	1	no	—
613	C₂²	—	596	4	no	—
614	C₂²	—	149	2	no	—
615	C₂²	#18011959	1	2	yes	—
616	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	298	1	no	—
626	C₄	—	298	1	no	—
627	C₄	—	298	2	no	—
628	C₄	—	298	2	no	—
629	C₄	—	298	2	no	—
630	C₄	—	298	1	no	—
631	C₄	—	298	2	no	—
632	C₄	—	298	1	no	—
633	C₄	—	149	2	no	—
634	C₄	#41×D₁₄₉	1	2	yes	—
635	C₂	—	2	2	no	—
636	C₂	—	4	1	no	—
637	C₂	—	298	2	no	—
638	C₂	—	596	1	no	—
639	C₂	—	596	1	no	—
640	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
641	C₂	C₂×#18011959	1	1	yes	characteristic
642	C₂	#23750460	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#554×C₁₄₉	C₂
prime radical	#23750134	C₂
hypercenter	#554	D₁₄₉
hypocenter	C₁₄₉	#3495
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #23750349	C₂	semidirect
2. #23750346	C₂	semidirect
3. #23750330	C₂	semidirect
4. #23750317	C₂	semidirect
5. #23750316	C₂	semidirect
6. #23750315	C₂	semidirect
7. #23750310	C₂	semidirect
8. #23750309	C₂	semidirect
9. #23750307	C₂	semidirect
10. #23750304	C₂	semidirect
11. #23750302	C₂	semidirect
12. #23750252	C₂	semidirect
13. #23750245	C₂	semidirect
14. #23750234	C₂	semidirect
15. #23750198	C₂	semidirect
16. #23750177	C₂	semidirect
17. #23750155	C₂	semidirect
19. C₂²⋊Q₈×D₁₄₉	C₂	semidirect
20. #23750106	C₂	semidirect
21. #23750101	C₂	semidirect
22. C₂×#18011869	C₂	semidirect
23. #554×C₁₄₉	C₂	semidirect
27. #18011910	C₂²	semidirect
28. #18011910	C₂²	semidirect
29. #18011909	C₂²	semidirect
33. #18011906	C₂²	semidirect
34. #18011906	C₂²	semidirect
36. #18011904	C₂²	semidirect
37. #18011904	C₂²	semidirect
38. #18011903	C₂²	semidirect
39. #18011902	C₂²	semidirect
40. #18011902	C₂²	semidirect
41. #18011901	C₂²	semidirect
42. #18011901	C₂²	semidirect
43. #18011901	C₂²	semidirect
44. #18011901	C₂²	semidirect
45. #18011901	C₂²	semidirect
48. #18011897	C₂²	semidirect
58. #18011891	C₂²	semidirect
61. #18011890	C₂²	semidirect
65. #18011889	C₂²	semidirect
70. #18011887	C₂²	semidirect
75. Q₈×Dic₁₄₉	C₂²	semidirect
76. Q₈×Dic₁₄₉	C₂²	semidirect
77. C₄×Dic₂₉₈	C₂²	semidirect
78. C₄×Dic₂₉₈	C₂²	semidirect
79. #18011876	C₂²	semidirect
80. #18011876	C₂²	semidirect
81. #18011876	C₂²	semidirect
82. #18011876	C₂²	semidirect
89. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
90. #18011870	C₂²	semidirect
91. #18011870	C₂²	semidirect
99. #18011869	C₂²	semidirect
102. #18011868	C₂²	semidirect
108. C₄⋊C₄×D₁₄₉	C₂²	semidirect
112. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
113. #125×C₁₄₉	C₂²	semidirect
116. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
117. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
118. C₄×Q₈×C₁₄₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
321. C₁₄₉	#3495	semidirect
326. #554	D₁₄₉	semidirect
352. C₄⋊Q₈	C₂×D₁₄₉	semidirect
369. #125	C₂×D₁₄₉	semidirect
397. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
398. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
411. C₄×Q₈	C₂×D₁₄₉	semidirect
441. C₂×C₄⋊C₄	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
#23750346	2
#23750330	2
#23750317	2
#23750316	2
#23750315	2
#23750310	2
#23750309	2
#23750307	2
#23750304	2
#23750302	2
#23750252	2
#23750245	2
#23750234	2
#23750198	2
#23750177	2
#23750155	2
#23750134	2
C₂²⋊Q₈×D₁₄₉	2
#23750106	2
#23750101	2
C₂×#18011869	2
#554×C₁₄₉	2
#3495	149