Subgroups — C₃×#78596 #11859563

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5791	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5110	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5101	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4730	C₂	1	2	yes	maximal, complemented
9	C₃×#4729	C₂	1	2	yes	maximal, complemented
10	C₃×#4728	C₂	1	2	yes	maximal, complemented
11	C₃×#67⋊C₈	C₂	1	2	yes	maximal, complemented
12	C₃×#2933	—	3	1	no	maximal
13	#78596	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×#235	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
18	C₃×#953	C₄	1	2	yes	—
19	C₃×#930	C₄	1	1	yes	characteristic
20	C₃×#930	C₄	1	1	yes	characteristic
21	C₃×#929	C₄	1	2	yes	—
22	C₃×C₄×#67	C₂²	1	2	yes	—
23	C₃×C₄×#67	C₂²	1	2	yes	—
24	C₃×#926	C₂²	1	1	yes	characteristic
25	C₃×#924	C₄	1	1	yes	characteristic
26	C₃×#924	C₄	1	1	yes	characteristic
27	C₂×C₃×#208	—	2	4	no	—
28	C₂×C₃×#208	C₂²	1	2	yes	—
29	C₂×C₃×#208	C₂²	1	1	yes	characteristic
30	C₂×C₃×#208	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
32	C₃×#901	—	2	4	no	—
33	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
34	C₂×C₃×D₃×C₈	C₂²	1	2	yes	complemented
35	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
40	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
41	C₃×#815	C₂²	1	2	yes	complemented
42	C₃×Dic₃⋊C₈	C₂²	1	2	yes	complemented
43	C₃×Dic₃⋊C₈	C₂²	1	2	yes	complemented
44	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
45	C₂×C₃×#131	—	3	1	no	—
46	C₂²×C₃×M₁₆	—	3	1	no	—
47	C₃×#525	—	3	1	no	—
48	#5791	C₂×C₃	1	1	yes	characteristic
49	C₂²×#208	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
51	C₃×#436	—	3	2	no	—
52	C₃×#435	—	3	2	no	—
53	C₃×#435	—	3	2	no	—
54	C₃×C₈×D₄	—	3	2	no	—
55	C₃×#424	—	3	1	no	—
56	C₃×#408	—	3	1	no	—
57	C₂×C₃×C₂²⋊C₈	—	2	1	no	—
58	C₂×C₃×C₂²⋊C₈	D₃	1	1	yes	characteristic, complemented
59	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
60	C₃×#405	—	3	1	no	—
61	#5110	C₂×C₃	1	1	yes	characteristic, complemented
62	#5102	C₂×C₃	1	1	yes	characteristic, complemented
63	#5101	C₂×C₃	1	1	yes	characteristic, complemented
64	#4730	C₂×C₃	1	2	yes	complemented
65	#4729	C₂×C₃	1	2	yes	complemented
66	#4728	C₂×C₃	1	2	yes	complemented
67	#67⋊C₈	C₂×C₃	1	2	yes	complemented
68	C₂⁴×C₃²	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₃²×C₄	—	2	2	no	—
70	C₂²×C₃²×C₄	—	2	2	no	—
71	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
75	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
76	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
77	C₂×C₃×#67	C₂×C₄	1	2	yes	—
78	C₂×C₃×#67	C₂×C₄	1	2	yes	—
79	C₂×C₃×#67	C₂×C₄	1	2	yes	—
80	C₃×#235	—	2	2	no	—
81	C₃×#235	—	2	2	no	—
82	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
84	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃²×C₈	—	2	2	no	—
86	C₂×C₃²×C₈	—	2	2	no	—
87	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
88	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
89	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
90	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
91	C₃×#217	C₂×C₄	1	2	yes	—
92	C₃×#217	C₂×C₄	1	2	yes	—
93	C₃×#217	C₂×C₄	1	2	yes	—
94	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
95	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
96	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
97	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
98	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
99	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
100	C₃×C₄×Dic₃	C₂³	1	2	yes	—
101	C₃×#208	—	2	2	no	—
102	C₃×#208	—	2	4	no	—
103	C₃×#208	D₄	1	4	yes	complemented
104	C₂×C₃×C₃⋊C₈	—	2	4	no	—
105	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
106	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
107	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
108	C₃×D₃×C₈	—	2	4	no	—
109	#2933	—	3	1	no	Sylow
110	C₂×C₃×#41	—	3	1	no	—
111	C₂³×C₃×C₄	—	2	1	no	—
112	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
113	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
114	C₂×#235	C₂²×C₃	1	1	yes	characteristic
115	C₃×#131	—	6	4	no	—
116	C₂×C₃×M₁₆	—	3	1	no	—
117	C₂×C₃×M₁₆	—	3	1	no	—
118	C₂×C₃×M₁₆	—	3	2	no	—
119	C₂×C₃×M₁₆	—	3	2	no	—
120	C₂×C₃×M₁₆	—	6	4	no	—
121	C₂²×C₃×C₈	—	2	1	no	—
122	C₂²×C₃×C₈	—	2	1	no	—
123	C₂²×C₃×C₈	—	3	2	no	—
124	C₂²×C₃×C₈	—	3	2	no	—
125	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
126	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
127	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
128	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
129	C₃×#123	—	3	2	no	—
130	C₃×C₂²⋊Q₈	—	3	1	no	—
131	C₃×C₂²⋊Q₈	—	3	1	no	—
132	C₃×#121	—	3	1	no	—
133	C₃×#121	—	3	1	no	—
134	C₃×#120	—	3	2	no	—
135	C₃×C₄×D₄	—	3	2	no	—
136	C₃×C₄×D₄	—	3	2	no	—
137	C₃×#117	—	3	1	no	—
138	#953	C₃×C₄	1	2	yes	—
139	#930	C₃×C₄	1	1	yes	characteristic
140	#930	C₃×C₄	1	1	yes	characteristic
141	#929	C₃×C₄	1	2	yes	—
142	C₄×#67	C₂²×C₃	1	2	yes	—
143	C₄×#67	C₂²×C₃	1	2	yes	—
144	#926	C₂²×C₃	1	1	yes	characteristic
145	#924	C₃×C₄	1	1	yes	characteristic
146	#924	C₃×C₄	1	1	yes	characteristic
147	C₂×#208	—	2	4	no	—
148	C₂×#208	C₂²×C₃	1	2	yes	—
149	C₂×#208	C₂²×C₃	1	1	yes	characteristic
150	C₂×#208	C₂²×C₃	1	1	yes	characteristic
151	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
152	#901	—	2	4	no	—
153	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	complemented
154	C₂×D₃×C₈	C₂²×C₃	1	2	yes	complemented
155	C₃×C₄⋊C₈	—	3	2	no	—
156	C₃×C₄⋊C₈	—	3	2	no	—
157	C₃×C₂²⋊C₈	—	2	1	no	—
158	C₃×C₂²⋊C₈	—	2	1	no	—
159	C₃×C₂²⋊C₈	—	2	1	no	—
160	C₃×C₂²⋊C₈	—	2	1	no	—
161	C₃×C₂²⋊C₈	—	3	2	no	—
162	C₃×C₂²⋊C₈	—	3	2	no	—
163	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
164	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
165	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
166	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
167	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
168	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
169	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
170	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
171	C₃×#97	—	3	2	no	—
172	C₃×C₄×C₈	—	3	2	no	—
173	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	complemented
174	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	complemented
175	#815	C₂²×C₃	1	2	yes	complemented
176	Dic₃⋊C₈	C₂²×C₃	1	2	yes	complemented
177	Dic₃⋊C₈	C₂²×C₃	1	2	yes	complemented
178	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
179	C₂³×C₃²	—	2	2	no	—
180	C₂³×C₃²	—	2	2	no	—
181	C₂³×C₃²	—	4	1	no	—
182	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
183	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
184	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
186	C₂×C₃²×C₄	—	2	2	no	—
187	C₂×C₃²×C₄	—	2	2	no	—
188	C₂×C₃²×C₄	—	2	2	no	—
189	C₂×C₃²×C₄	—	2	1	no	—
190	C₂×C₃²×C₄	—	2	1	no	—
191	C₂×C₃²×C₄	—	2	1	no	—
192	C₂×C₃²×C₄	—	2	1	no	—
193	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
197	C₂×C₃²×C₄	#41	1	2	yes	—
198	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
199	C₃×#67	—	2	4	no	—
200	C₃×#67	—	2	4	no	—
201	C₃×#67	—	4	2	no	—
202	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
203	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
204	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
205	C₃×D₁₂	—	2	2	no	—
206	C₃×C₄×D₃	—	2	2	no	—
207	C₃×C₄×D₃	—	2	2	no	—
208	C₃×Dic₆	—	2	2	no	—
209	C₃²×C₈	—	2	1	no	—
210	C₃²×C₈	—	2	1	no	—
211	C₃²×C₈	—	2	1	no	—
212	C₃²×C₈	—	2	1	no	—
213	C₃×C₃⋊C₈	—	2	2	no	—
214	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	—
215	C₂×#131	—	3	1	no	—
216	C₂²×M₁₆	—	3	1	no	—
217	#525	—	3	1	no	—
218	#436	—	3	2	no	—
219	#435	—	3	2	no	—
220	#435	—	3	2	no	—
221	C₈×D₄	—	3	2	no	—
222	#424	—	3	1	no	—
223	#408	—	3	1	no	—
224	C₂×C₂²⋊C₈	C₃×D₃	1	1	yes	characteristic, complemented
225	#405	—	3	1	no	—
226	C₂⁴×C₃	—	2	1	no	—
227	C₂⁴×C₃	C₄×D₃	1	1	yes	characteristic
228	C₂⁴×C₃	C₂×C₃×C₄	1	1	yes	characteristic
229	C₃×#41	—	6	2	no	—
230	C₃×#41	—	6	2	no	—
231	C₂×C₃×Q₈	—	3	1	no	—
232	C₂×C₃×D₄	—	3	2	no	—
233	C₂×C₃×D₄	—	3	2	no	—
234	C₂×C₃×D₄	—	3	2	no	—
235	C₂×C₃×D₄	—	3	1	no	—
236	C₂²×C₃×C₄	—	2	2	no	—
237	C₂²×C₃×C₄	—	2	2	no	—
238	C₂²×C₃×C₄	—	2	2	no	—
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	2	1	no	—
241	C₂²×C₃×C₄	—	2	1	no	—
242	C₂²×C₃×C₄	—	2	1	no	—
243	C₂²×C₃×C₄	—	2	1	no	—
244	C₂²×C₃×C₄	—	2	1	no	—
245	C₂²×C₃×C₄	—	2	1	no	—
246	C₂²×C₃×C₄	—	3	2	no	—
247	C₂²×C₃×C₄	—	4	2	no	—
248	C₂²×C₃×C₄	—	4	2	no	—
249	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
254	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
255	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
256	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
257	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
258	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
261	C₂×#67	C₂×C₃×C₄	1	2	yes	—
262	C₂×#67	C₂×C₃×C₄	1	2	yes	—
263	C₂×#67	C₂×C₃×C₄	1	2	yes	—
264	#235	—	2	2	no	—
265	#235	—	2	2	no	—
266	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
267	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
268	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
269	C₃×M₁₆	—	3	4	no	—
270	C₃×M₁₆	—	6	4	no	—
271	C₃×M₁₆	—	6	4	no	—
272	C₃×M₁₆	—	6	2	no	—
273	C₂×C₃×C₈	—	2	2	no	—
274	C₂×C₃×C₈	—	2	2	no	—
275	C₂×C₃×C₈	—	2	2	no	—
276	C₂×C₃×C₈	—	2	2	no	—
277	C₂×C₃×C₈	—	2	1	no	—
278	C₂×C₃×C₈	—	2	1	no	—
279	C₂×C₃×C₈	—	2	1	no	—
280	C₂×C₃×C₈	—	2	1	no	—
281	C₂×C₃×C₈	—	3	2	no	—
282	C₂×C₃×C₈	—	3	2	no	—
283	C₂×C₃×C₈	—	4	2	no	—
284	C₂×C₃×C₈	—	4	2	no	—
285	C₂×C₃×C₈	—	6	4	no	—
286	C₂×C₃×C₈	—	6	4	no	—
287	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
288	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
289	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
290	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
291	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
295	C₃×C₄⋊C₄	—	3	2	no	—
296	C₃×C₄⋊C₄	—	3	2	no	—
297	C₃×C₄⋊C₄	—	3	1	no	—
298	C₃×C₄⋊C₄	—	3	1	no	—
299	C₃×C₂²⋊C₄	—	3	2	no	—
300	C₃×C₂²⋊C₄	—	3	2	no	—
301	C₃×C₂²⋊C₄	—	3	2	no	—
302	C₃×C₂²⋊C₄	—	3	2	no	—
303	C₃×C₂²⋊C₄	—	3	2	no	—
304	C₃×C₄²	—	3	2	no	—
305	#217	C₂×C₃×C₄	1	2	yes	—
306	#217	C₂×C₃×C₄	1	2	yes	—
307	#217	C₂×C₃×C₄	1	2	yes	—
308	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
309	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
310	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
311	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
312	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
313	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
314	C₄×Dic₃	C₂³×C₃	1	2	yes	—
315	#208	—	2	2	no	—
316	#208	—	2	4	no	—
317	#208	C₃×D₄	1	4	yes	complemented
318	C₂×C₃⋊C₈	—	2	4	no	—
319	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
320	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
321	ΓL(1,𝔽₂₅)	—	2	4	no	—
322	D₃×C₈	—	2	4	no	—
323	C₂²×C₃²	—	2	1	no	—
324	C₂²×C₃²	—	2	1	no	—
325	C₂²×C₃²	—	2	1	no	—
326	C₂²×C₃²	—	2	1	no	—
327	C₂²×C₃²	—	2	1	no	—
328	C₂²×C₃²	—	2	1	no	—
329	C₂²×C₃²	—	2	1	no	—
330	C₂²×C₃²	—	4	4	no	—
331	C₂²×C₃²	C₄×D₄	1	2	yes	—
332	C₂²×C₃²	#131	1	2	yes	complemented
333	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
334	C₂×C₃×D₃	—	2	2	no	—
335	C₂×C₃×D₃	—	2	2	no	—
336	C₂×C₃×D₃	—	2	2	no	—
337	C₃²×C₄	—	2	1	no	—
338	C₃²×C₄	—	2	1	no	—
339	C₃²×C₄	C₄×D₄	1	2	yes	—
340	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
341	C₃²×C₄	C₂×#41	1	1	yes	characteristic
342	C₃×Dic₃	—	2	2	no	—
343	C₃×Dic₃	—	2	2	no	—
344	C₃×Dic₃	—	2	2	no	—
345	C₂×#41	—	3	1	no	—
346	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
347	#131	—	6	4	no	—
348	C₂×M₁₆	—	3	1	no	—
349	C₂×M₁₆	—	3	1	no	—
350	C₂×M₁₆	—	3	2	no	—
351	C₂×M₁₆	—	3	2	no	—
352	C₂×M₁₆	—	6	4	no	—
353	C₂²×C₈	—	3	2	no	—
354	C₂²×C₈	—	3	2	no	—
355	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
356	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
357	#123	—	3	2	no	—
358	C₂²⋊Q₈	—	3	1	no	—
359	C₂²⋊Q₈	—	3	1	no	—
360	#121	—	3	1	no	—
361	#121	—	3	1	no	—
362	#120	—	3	2	no	—
363	C₄×D₄	—	3	2	no	—
364	C₄×D₄	—	3	2	no	—
365	#117	—	3	1	no	—
366	C₄⋊C₈	—	3	2	no	—
367	C₄⋊C₈	—	3	2	no	—
368	C₂²⋊C₈	—	3	2	no	—
369	C₂²⋊C₈	—	3	2	no	—
370	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
371	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
372	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
373	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
374	#97	—	3	2	no	—
375	C₄×C₈	—	3	2	no	—
376	C₂³×C₃	—	2	4	no	—
377	C₂³×C₃	—	2	2	no	—
378	C₂³×C₃	—	2	2	no	—
379	C₂³×C₃	—	2	2	no	—
380	C₂³×C₃	—	2	2	no	—
381	C₂³×C₃	—	2	1	no	—
382	C₂³×C₃	—	2	1	no	—
383	C₂³×C₃	—	2	1	no	—
384	C₂³×C₃	—	3	2	no	—
385	C₂³×C₃	—	4	2	no	—
386	C₂³×C₃	—	4	1	no	—
387	C₂³×C₃	—	4	1	no	—
388	C₂³×C₃	—	4	2	no	—
389	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
390	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
391	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
392	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
393	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
394	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
395	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
396	C₃×Q₈	—	6	2	no	—
397	C₃×D₄	—	6	4	no	—
398	C₃×D₄	—	6	4	no	—
399	C₃×D₄	—	6	2	no	—
400	C₃×D₄	—	12	2	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	1	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	2	1	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	2	1	no	—
419	C₂×C₃×C₄	—	2	2	no	—
420	C₂×C₃×C₄	—	2	2	no	—
421	C₂×C₃×C₄	—	3	2	no	—
422	C₂×C₃×C₄	—	3	2	no	—
423	C₂×C₃×C₄	—	3	2	no	—
424	C₂×C₃×C₄	—	4	2	no	—
425	C₂×C₃×C₄	—	4	2	no	—
426	C₂×C₃×C₄	—	4	1	no	—
427	C₂×C₃×C₄	—	4	1	no	—
428	C₂×C₃×C₄	—	4	1	no	—
429	C₂×C₃×C₄	—	4	1	no	—
430	C₂×C₃×C₄	—	4	2	no	—
431	C₂×C₃×C₄	—	6	2	no	—
432	C₂×C₃×C₄	—	6	2	no	—
433	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
434	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
435	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
436	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
437	C₂×C₃×C₄	#237	1	2	yes	—
438	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
439	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
440	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
441	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
442	C₂×C₃×C₄	C₃×#41	1	2	yes	—
443	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
444	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
445	#67	—	2	4	no	—
446	#67	—	2	4	no	—
447	#67	—	4	2	no	—
448	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
449	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
450	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
451	D₁₂	—	2	2	no	—
452	C₄×D₃	—	2	2	no	—
453	C₄×D₃	—	2	2	no	—
454	Dic₆	—	2	2	no	—
455	C₃×C₈	—	2	1	no	—
456	C₃×C₈	—	2	1	no	—
457	C₃×C₈	—	2	1	no	—
458	C₃×C₈	—	2	1	no	—
459	C₃×C₈	—	2	1	no	—
460	C₃×C₈	—	2	1	no	—
461	C₃×C₈	—	2	1	no	—
462	C₃×C₈	—	2	1	no	—
463	C₃×C₈	—	3	4	no	—
464	C₃×C₈	—	4	1	no	—
465	C₃×C₈	—	4	1	no	—
466	C₃×C₈	—	4	1	no	—
467	C₃×C₈	—	4	1	no	—
468	C₃×C₈	—	6	2	no	—
469	C₃⋊C₈	—	2	2	no	—
470	C₃⋊C₈	C₂×C₃×D₄	1	4	yes	—
471	C₂×C₃²	—	2	2	no	—
472	C₂×C₃²	—	2	2	no	—
473	C₂×C₃²	—	4	1	no	—
474	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
475	C₂×C₃²	C₂×#131	1	1	yes	characteristic
476	C₂×C₃²	#568	1	1	yes	characteristic
477	C₃×D₃	—	4	2	no	—
478	C₂⁴	C₃×C₄×D₃	1	1	yes	characteristic
479	#41	—	6	2	no	—
480	#41	—	6	2	no	—
481	C₂×Q₈	—	3	1	no	—
482	C₂×D₄	—	3	2	no	—
483	C₂×D₄	—	3	2	no	—
484	C₂×D₄	—	3	2	no	—
485	C₂×D₄	—	3	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	3	2	no	—
489	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
490	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
491	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
492	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
493	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
494	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
495	M₁₆	—	3	4	no	—
496	M₁₆	—	6	4	no	—
497	M₁₆	—	6	4	no	—
498	M₁₆	—	6	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	3	2	no	—
502	C₂×C₈	—	3	2	no	—
503	C₂×C₈	—	6	4	no	—
504	C₂×C₈	—	6	4	no	—
505	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
506	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
507	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
508	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
509	C₄⋊C₄	—	3	1	no	—
510	C₄⋊C₄	—	3	1	no	—
511	C₄⋊C₄	—	3	2	no	—
512	C₄⋊C₄	—	3	2	no	—
513	C₂²⋊C₄	—	3	2	no	—
514	C₂²⋊C₄	—	3	2	no	—
515	C₂²⋊C₄	—	3	2	no	—
516	C₂²⋊C₄	—	3	2	no	—
517	C₂²⋊C₄	—	3	2	no	—
518	C₄²	—	3	2	no	—
519	C₂²×C₃	—	2	2	no	—
520	C₂²×C₃	—	2	2	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	2	1	no	—
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	2	1	no	—
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	2	1	no	—
531	C₂²×C₃	—	2	1	no	—
532	C₂²×C₃	—	2	1	no	—
533	C₂²×C₃	—	2	1	no	—
534	C₂²×C₃	—	2	1	no	—
535	C₂²×C₃	—	2	1	no	—
536	C₂²×C₃	—	2	2	no	—
537	C₂²×C₃	—	2	2	no	—
538	C₂²×C₃	—	2	1	no	—
539	C₂²×C₃	—	4	1	no	—
540	C₂²×C₃	—	4	1	no	—
541	C₂²×C₃	—	4	1	no	—
542	C₂²×C₃	—	4	1	no	—
543	C₂²×C₃	—	4	4	no	—
544	C₂²×C₃	—	4	4	no	—
545	C₂²×C₃	—	4	8	no	—
546	C₂²×C₃	—	6	2	no	—
547	C₂²×C₃	—	6	2	no	—
548	C₂²×C₃	—	6	2	no	—
549	C₂²×C₃	#67⋊C₄	1	2	yes	—
550	C₂²×C₃	#901	1	2	yes	complemented
551	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
552	C₂²×C₃	C₃×#131	1	2	yes	complemented
553	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
554	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
555	C₂×D₃	—	2	2	no	—
556	C₂×D₃	—	2	2	no	—
557	C₂×D₃	—	2	2	no	—
558	C₃×C₄	—	2	1	no	—
559	C₃×C₄	—	2	1	no	—
560	C₃×C₄	—	2	1	no	—
561	C₃×C₄	—	2	1	no	—
562	C₃×C₄	—	2	2	no	—
563	C₃×C₄	—	2	1	no	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	4	1	no	—
566	C₃×C₄	—	4	1	no	—
567	C₃×C₄	—	6	2	no	—
568	C₃×C₄	—	6	2	no	—
569	C₃×C₄	—	6	2	no	—
570	C₃×C₄	#67⋊C₄	1	2	yes	—
571	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
572	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
573	C₃×C₄	C₂×#237	1	1	yes	characteristic
574	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
575	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
576	Dic₃	—	2	2	no	—
577	Dic₃	—	2	2	no	—
578	Dic₃	—	2	2	no	—
579	C₃²	#2933	1	1	yes	characteristic, complemented, Sylow
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	3	2	no	—
583	C₂³	—	4	1	no	—
584	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
585	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
586	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
587	Q₈	—	6	2	no	—
588	D₄	—	6	4	no	—
589	D₄	—	6	4	no	—
590	D₄	—	6	2	no	—
591	D₄	—	12	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	3	2	no	—
600	C₂×C₄	—	3	2	no	—
601	C₂×C₄	—	3	2	no	—
602	C₂×C₄	—	6	2	no	—
603	C₂×C₄	—	6	2	no	—
604	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
605	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
606	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
607	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
608	C₂×C₄	C₃×#237	1	2	yes	—
609	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
610	C₈	—	2	1	no	—
611	C₈	—	2	1	no	—
612	C₈	—	2	1	no	—
613	C₈	—	2	1	no	—
614	C₈	—	3	4	no	—
615	C₈	—	6	2	no	—
616	C₂×C₃	—	2	4	no	—
617	C₂×C₃	—	2	2	no	—
618	C₂×C₃	—	2	2	no	—
619	C₂×C₃	—	2	2	no	—
620	C₂×C₃	—	2	2	no	—
621	C₂×C₃	—	2	1	no	—
622	C₂×C₃	—	2	1	no	—
623	C₂×C₃	—	2	1	no	—
624	C₂×C₃	—	4	2	no	—
625	C₂×C₃	—	4	2	no	—
626	C₂×C₃	—	4	1	no	—
627	C₂×C₃	—	4	1	no	—
628	C₂×C₃	—	12	2	no	—
629	C₂×C₃	C₂×#67⋊C₄	1	1	yes	characteristic
630	C₂×C₃	C₂×#901	1	1	yes	characteristic
631	C₂×C₃	#5745	1	1	yes	characteristic
632	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
633	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
634	C₂×C₃	C₃×#568	1	1	yes	characteristic
635	D₃	—	4	2	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	4	4	no	—
644	C₂²	—	6	2	no	—
645	C₂²	—	6	2	no	—
646	C₂²	—	6	2	no	—
647	C₂²	C₃×#67⋊C₄	1	2	yes	—
648	C₂²	C₃×#901	1	2	yes	complemented
649	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	6	2	no	—
653	C₄	—	6	2	no	—
654	C₄	—	6	2	no	—
655	C₄	C₃×#67⋊C₄	1	2	yes	—
656	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
657	C₄	C₂×C₃×#237	1	1	yes	characteristic
658	C₃	—	2	1	no	—
659	C₃	#78596	1	1	yes	characteristic, direct product factor
660	C₃	C₃×#2933	1	1	yes	characteristic, complemented
661	C₂	—	2	2	no	—
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	12	2	no	—
665	C₂	C₂×C₃×#67⋊C₄	1	1	yes	characteristic
666	C₂	C₂×C₃×#901	1	1	yes	characteristic
667	C₂	C₃×#5745	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₂²⋊C₈	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₃×#5791	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₂²⋊C₈	D₃
hypocenter	C₃	C₃×#2933
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×#208	C₂	semidirect
3. C₂×C₃×#901	C₂	semidirect
4. C₂×C₃²×C₂²⋊C₈	C₂	semidirect
5. C₃×#5110	C₂	semidirect
6. C₃×#5102	C₂	semidirect
7. C₃×#5101	C₂	semidirect
8. C₃×#4730	C₂	semidirect
9. C₃×#4729	C₂	semidirect
10. C₃×#4728	C₂	semidirect
11. C₃×#67⋊C₈	C₂	semidirect
13. #78596	C₃	direct (N × H)
33. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
34. C₂×C₃×D₃×C₈	C₂²	semidirect
39. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
40. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
41. C₃×#815	C₂²	semidirect
42. C₃×Dic₃⋊C₈	C₂²	semidirect
43. C₃×Dic₃⋊C₈	C₂²	semidirect
44. C₃×C₈×Dic₃	C₂²	semidirect
49. C₂²×#208	C₂×C₃	semidirect
50. C₂×#901	C₂×C₃	semidirect
58. C₂×C₃×C₂²⋊C₈	D₃	semidirect
59. C₂×C₃×C₂²⋊C₈	C₂×C₃	semidirect
61. #5110	C₂×C₃	semidirect
62. #5102	C₂×C₃	semidirect
63. #5101	C₂×C₃	semidirect
64. #4730	C₂×C₃	semidirect
65. #4729	C₂×C₃	semidirect
66. #4728	C₂×C₃	semidirect
67. #67⋊C₈	C₂×C₃	semidirect
103. C₃×#208	D₄	semidirect
153. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
154. C₂×D₃×C₈	C₂²×C₃	semidirect
173. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
174. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
175. #815	C₂²×C₃	semidirect
176. Dic₃⋊C₈	C₂²×C₃	semidirect
177. Dic₃⋊C₈	C₂²×C₃	semidirect
178. C₈×Dic₃	C₂²×C₃	semidirect
224. C₂×C₂²⋊C₈	C₃×D₃	semidirect
317. #208	C₃×D₄	semidirect
332. C₂²×C₃²	#131	semidirect
550. C₂²×C₃	#901	semidirect
552. C₂²×C₃	C₃×#131	semidirect
579. C₃²	#2933	semidirect
648. C₂²	C₃×#901	semidirect
659. C₃	#78596	direct (N × H)
660. C₃	C₃×#2933	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5791	2
C₂²×C₃×#208	2
C₂×C₃×#901	2
C₂×C₃²×C₂²⋊C₈	2
C₃×#5110	2
C₃×#5102	2
C₃×#5101	2
C₃×#4730	2
C₃×#4729	2
C₃×#4728	2
C₃×#67⋊C₈	2
C₃×#2933	3
#78596	3

Subgroups — C3×#78596 #11859563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78596 #11859563