Subgroups — C₃×#83928 #11868003

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5822	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5237	C₂	1	2	yes	maximal, complemented
5	C₃×#5192	C₂	1	2	yes	maximal, complemented
6	C₃×#5177	C₂	1	4	yes	maximal, complemented
7	C₃×#5160	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3067	—	3	1	no	maximal
10	#83928	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃²×#41	C₂²	1	2	yes	—
12	C₂×C₃×#235	C₂²	1	1	yes	characteristic
13	C₃²×#135	—	2	1	no	—
14	C₃²×#135	—	2	1	no	—
15	C₃²×#135	—	2	1	no	—
16	C₃²×#135	—	2	1	no	—
17	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
21	C₃×#951	—	2	2	no	—
22	C₃×#950	—	2	4	no	—
23	C₃×#949	—	2	2	no	—
24	C₃×#942	C₂²	1	4	yes	—
25	C₃×#932	C₂²	1	4	yes	—
26	C₂×C₃×#208	C₂²	1	1	yes	characteristic
27	C₂×C₃×#208	C₂²	1	2	yes	—
28	C₃×#901	—	2	1	no	—
29	C₃×#901	—	2	1	no	—
30	C₃×#901	C₂²	1	2	yes	—
31	C₃×#901	C₂²	1	2	yes	—
32	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
33	C₂×C₃×D₃×C₈	—	2	1	no	—
34	C₃×#836	C₂²	1	4	yes	complemented
35	C₃×#833	C₂²	1	4	yes	complemented
36	C₃×#819	C₂²	1	2	yes	complemented
37	C₃×#819	C₂²	1	2	yes	complemented
38	C₃×#575	—	3	2	no	—
39	C₂×C₃×#135	—	2	1	no	—
40	C₂×C₃×#135	D₃	1	1	yes	characteristic, complemented
41	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₃×#131	—	3	1	no	—
43	#5822	C₂×C₃	1	2	yes	complemented
44	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃×#473	—	3	2	no	—
46	C₃×#472	—	3	2	no	—
47	C₃×#471	—	3	4	no	—
48	C₂×C₃×#108	—	3	1	no	—
49	C₃×#413	—	3	2	no	—
50	#5237	C₂×C₃	1	2	yes	complemented
51	#5192	C₂×C₃	1	2	yes	complemented
52	#5177	C₂×C₃	1	4	yes	complemented
53	#5160	C₂×C₃	1	2	yes	complemented
54	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃²×#41	—	2	2	no	—
56	C₃²×#41	—	2	2	no	—
57	C₃²×#41	—	2	2	no	—
58	C₃²×#41	—	2	2	no	—
59	C₂×C₃²×Q₈	C₂³	1	2	yes	—
60	C₂×C₃²×D₄	—	2	2	no	—
61	C₂×C₃²×D₄	C₂³	1	2	yes	—
62	C₂²×C₃²×C₄	—	2	2	no	—
63	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
64	C₂×C₃×#67	—	2	1	no	—
65	C₃×#235	—	2	1	no	—
66	C₃×#235	—	2	1	no	—
67	C₃×#235	D₄	1	2	yes	—
68	C₃×#235	C₂³	1	2	yes	—
69	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
70	C₂×C₃×C₄×D₃	—	2	1	no	—
71	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
72	C₃²×Q₁₆	—	2	1	no	—
73	C₃²×Q₁₆	—	2	1	no	—
74	C₃²×SD₁₆	—	2	2	no	—
75	C₃²×SD₁₆	—	2	2	no	—
76	C₃²×D₈	—	2	1	no	—
77	C₃²×D₈	—	2	1	no	—
78	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
79	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
80	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
81	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
82	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
83	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
84	C₃×#216	—	2	4	no	—
85	C₃×#215	—	2	4	no	—
86	C₃×#214	—	2	4	no	—
87	C₃×#213	—	2	4	no	—
88	C₃×#208	—	2	1	no	—
89	C₃×#208	—	2	2	no	—
90	C₃×#208	C₂³	1	2	yes	—
91	C₃×#208	C₂³	1	4	yes	—
92	C₂×C₃×C₃⋊C₈	—	2	1	no	—
93	C₂×C₃×C₃⋊C₈	—	2	2	no	—
94	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
95	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
96	C₃×D₃×C₈	—	2	2	no	—
97	C₃×D₃×C₈	—	2	2	no	—
98	#3067	—	3	1	no	Sylow
99	C₂×C₃×#41	—	2	2	no	—
100	C₂×C₃×#41	—	3	1	no	—
101	C₂×C₃×#41	C₂×D₃	1	2	yes	—
102	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
103	C₂×#235	C₂²×C₃	1	1	yes	characteristic
104	C₃×#137	—	3	4	no	—
105	C₃×#137	—	6	2	no	—
106	C₃×AGL(1,ℤ/8)	—	3	4	no	—
107	C₃×AGL(1,ℤ/8)	—	6	2	no	—
108	C₃×#135	—	2	2	no	—
109	C₃×#135	—	2	2	no	—
110	C₃×#135	—	2	2	no	—
111	C₃×#135	—	2	2	no	—
112	C₃×#135	—	2	1	no	—
113	C₃×#135	—	2	1	no	—
114	C₃×#135	—	2	1	no	—
115	C₃×#135	—	2	1	no	—
116	C₃×#135	—	2	1	no	—
117	C₃×#135	—	2	1	no	—
118	C₃×#135	—	2	1	no	—
119	C₃×#135	—	2	1	no	—
120	C₃×#135	—	6	4	no	—
121	C₂×C₃×Q₁₆	—	2	1	no	—
122	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
123	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₂×C₃×SD₁₆	—	2	2	no	—
125	C₂×C₃×SD₁₆	C₂×D₃	1	2	yes	complemented
126	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	complemented
127	C₂×C₃×D₈	—	2	1	no	—
128	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic, complemented
129	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₃×#131	—	3	2	no	—
131	C₃×#131	—	3	2	no	—
132	C₃×#131	—	6	1	no	—
133	C₃×#131	—	6	1	no	—
134	C₂×C₃×M₁₆	—	3	1	no	—
135	C₂×C₃×M₁₆	—	3	2	no	—
136	C₂×C₃×M₁₆	—	6	1	no	—
137	C₂²×C₃×C₈	—	2	1	no	—
138	C₂²×C₃×C₈	—	6	1	no	—
139	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
140	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
141	#951	—	2	2	no	—
142	#950	—	2	4	no	—
143	#949	—	2	2	no	—
144	#942	C₂²×C₃	1	4	yes	—
145	#932	C₂²×C₃	1	4	yes	—
146	C₂×#208	C₂²×C₃	1	1	yes	characteristic
147	C₂×#208	C₂²×C₃	1	2	yes	—
148	#901	—	2	1	no	—
149	#901	—	2	1	no	—
150	#901	C₂²×C₃	1	2	yes	—
151	#901	C₂²×C₃	1	2	yes	—
152	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
153	C₂×D₃×C₈	—	2	1	no	—
154	C₃×#108	—	3	2	no	—
155	C₃×#108	—	3	2	no	—
156	C₃×#101	—	3	4	no	—
157	C₃×#100	—	3	4	no	—
158	#836	C₂²×C₃	1	4	yes	complemented
159	#833	C₂²×C₃	1	4	yes	complemented
160	#819	C₂²×C₃	1	2	yes	complemented
161	#819	C₂²×C₃	1	2	yes	complemented
162	C₂³×C₃²	—	2	2	no	—
163	C₂³×C₃²	#41	1	1	yes	characteristic
164	C₂²×C₃×D₃	—	2	1	no	—
165	C₃²×Q₈	—	2	2	no	—
166	C₃²×Q₈	—	2	2	no	—
167	C₃²×D₄	—	2	2	no	—
168	C₃²×D₄	—	2	2	no	—
169	C₃²×D₄	—	4	2	no	—
170	C₃²×D₄	—	4	2	no	—
171	C₂×C₃²×C₄	—	2	2	no	—
172	C₂×C₃²×C₄	—	4	2	no	—
173	C₂×C₃²×C₄	—	4	2	no	—
174	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
175	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
176	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
178	C₂×C₃²×C₄	#41	1	1	yes	characteristic
179	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
180	C₃×#67	—	2	2	no	—
181	C₃×#67	—	2	2	no	—
182	C₂×C₃×Dic₃	—	2	1	no	—
183	C₃×D₁₂	—	2	1	no	—
184	C₃×D₁₂	C₂×D₄	1	2	yes	—
185	C₃×C₄×D₃	—	2	2	no	—
186	C₃×C₄×D₃	—	2	2	no	—
187	C₃×Dic₆	—	2	1	no	—
188	C₃×Dic₆	C₂×D₄	1	2	yes	—
189	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
190	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
191	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
192	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
193	C₃×C₃⋊C₈	—	2	2	no	—
194	C₃×C₃⋊C₈	—	2	4	no	—
195	#575	—	3	2	no	—
196	C₂×#135	C₃×D₃	1	1	yes	characteristic, complemented
197	C₂×#131	—	3	1	no	—
198	#473	—	3	2	no	—
199	#472	—	3	2	no	—
200	#471	—	3	4	no	—
201	C₂×#108	—	3	1	no	—
202	#413	—	3	2	no	—
203	C₃×#41	—	2	4	no	—
204	C₃×#41	—	2	4	no	—
205	C₃×#41	—	2	2	no	—
206	C₃×#41	—	2	2	no	—
207	C₃×#41	—	2	2	no	—
208	C₃×#41	—	2	2	no	—
209	C₃×#41	—	2	2	no	—
210	C₃×#41	—	2	2	no	—
211	C₃×#41	—	2	2	no	—
212	C₃×#41	—	2	2	no	—
213	C₃×#41	—	3	2	no	—
214	C₃×#41	—	3	2	no	—
215	C₃×#41	—	4	2	no	—
216	C₃×#41	—	4	2	no	—
217	C₃×#41	—	6	1	no	—
218	C₃×#41	—	6	1	no	—
219	C₂×C₃×Q₈	—	2	2	no	—
220	C₂×C₃×Q₈	—	3	1	no	—
221	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
222	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
223	C₂×C₃×D₄	—	2	2	no	—
224	C₂×C₃×D₄	—	2	2	no	—
225	C₂×C₃×D₄	—	2	2	no	—
226	C₂×C₃×D₄	—	3	1	no	—
227	C₂×C₃×D₄	—	4	2	no	—
228	C₂×C₃×D₄	—	6	1	no	—
229	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
230	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
231	C₂²×C₃×C₄	—	2	2	no	—
232	C₂²×C₃×C₄	—	2	2	no	—
233	C₂²×C₃×C₄	—	2	1	no	—
234	C₂²×C₃×C₄	—	4	2	no	—
235	C₂²×C₃×C₄	—	6	1	no	—
236	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
238	C₂×#67	—	2	1	no	—
239	#235	—	2	1	no	—
240	#235	—	2	1	no	—
241	#235	C₃×D₄	1	2	yes	—
242	#235	C₂³×C₃	1	2	yes	—
243	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
244	C₂×C₄×D₃	—	2	1	no	—
245	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
246	C₃×Q₁₆	—	2	2	no	—
247	C₃×Q₁₆	—	2	2	no	—
248	C₃×Q₁₆	—	2	1	no	—
249	C₃×Q₁₆	—	2	1	no	—
250	C₃×Q₁₆	—	2	1	no	—
251	C₃×Q₁₆	—	2	1	no	—
252	C₃×Q₁₆	—	6	4	no	—
253	C₃×SD₁₆	—	2	4	no	—
254	C₃×SD₁₆	—	2	4	no	—
255	C₃×SD₁₆	—	2	2	no	—
256	C₃×SD₁₆	—	2	2	no	—
257	C₃×SD₁₆	—	2	2	no	—
258	C₃×SD₁₆	—	2	2	no	—
259	C₃×SD₁₆	—	6	4	no	—
260	C₃×SD₁₆	—	6	4	no	—
261	C₃×D₈	—	2	2	no	—
262	C₃×D₈	—	2	2	no	—
263	C₃×D₈	—	2	1	no	—
264	C₃×D₈	—	2	1	no	—
265	C₃×D₈	—	2	1	no	—
266	C₃×D₈	—	2	1	no	—
267	C₃×D₈	—	6	4	no	—
268	C₃×M₁₆	—	3	2	no	—
269	C₃×M₁₆	—	3	4	no	—
270	C₃×M₁₆	—	6	2	no	—
271	C₃×M₁₆	—	6	1	no	—
272	C₃×M₁₆	—	6	2	no	—
273	C₃×M₁₆	—	6	2	no	—
274	C₂×C₃×C₈	—	2	1	no	—
275	C₂×C₃×C₈	—	2	1	no	—
276	C₂×C₃×C₈	—	2	1	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	—	6	2	no	—
281	C₂×C₃×C₈	—	6	1	no	—
282	C₂×C₃×C₈	—	6	2	no	—
283	C₂×C₃×C₈	—	6	2	no	—
284	C₂×C₃×C₈	#67	1	1	yes	characteristic
285	C₂×C₃×C₈	#67	1	1	yes	characteristic
286	C₂×C₃×C₈	#67	1	1	yes	characteristic
287	C₂×C₃×C₈	#67	1	1	yes	characteristic
288	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
289	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
290	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
291	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
292	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
293	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
294	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
295	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
296	#216	—	2	4	no	—
297	#215	—	2	4	no	—
298	#214	—	2	4	no	—
299	#213	—	2	4	no	—
300	#208	—	2	1	no	—
301	#208	—	2	2	no	—
302	#208	C₂³×C₃	1	4	yes	—
303	#208	C₂³×C₃	1	2	yes	—
304	C₂×C₃⋊C₈	—	2	1	no	—
305	C₂×C₃⋊C₈	—	2	2	no	—
306	ΓL(1,𝔽₂₅)	—	2	2	no	—
307	ΓL(1,𝔽₂₅)	—	2	2	no	—
308	D₃×C₈	—	2	2	no	—
309	D₃×C₈	—	2	2	no	—
310	C₂²×C₃²	—	4	1	no	—
311	C₂²×C₃²	—	4	2	no	—
312	C₂²×C₃²	—	8	2	no	—
313	C₂²×C₃²	#121	1	1	yes	characteristic
314	C₂²×C₃²	#121	1	1	yes	characteristic
315	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
316	C₂×C₃×D₃	—	2	2	no	—
317	C₂×C₃×D₃	—	4	2	no	—
318	C₃²×C₄	—	4	2	no	—
319	C₃²×C₄	#121	1	1	yes	characteristic
320	C₃²×C₄	#121	1	1	yes	characteristic
321	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
322	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
323	C₃×Dic₃	—	2	2	no	—
324	C₂×#41	—	3	1	no	—
325	C₂×#41	C₂×C₃×D₃	1	2	yes	—
326	#137	—	3	4	no	—
327	#137	—	6	2	no	—
328	AGL(1,ℤ/8)	—	3	4	no	—
329	AGL(1,ℤ/8)	—	6	2	no	—
330	#135	—	2	1	no	—
331	#135	—	2	1	no	—
332	#135	—	2	1	no	—
333	#135	—	2	1	no	—
334	#135	—	6	4	no	—
335	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
336	C₂×SD₁₆	C₂×C₃×D₃	1	2	yes	complemented
337	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
338	#131	—	3	2	no	—
339	#131	—	3	2	no	—
340	#131	—	6	1	no	—
341	#131	—	6	1	no	—
342	C₂×M₁₆	—	3	1	no	—
343	C₂×M₁₆	—	3	2	no	—
344	C₂×M₁₆	—	6	1	no	—
345	C₂²×C₈	—	6	1	no	—
346	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
347	#108	—	3	2	no	—
348	#108	—	3	2	no	—
349	#101	—	3	4	no	—
350	#100	—	3	4	no	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	2	2	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	—	4	2	no	—
355	C₂³×C₃	—	6	1	no	—
356	C₂³×C₃	#237	1	1	yes	characteristic
357	C₂³×C₃	C₃×#41	1	1	yes	characteristic
358	C₂²×D₃	—	2	1	no	—
359	C₃×Q₈	—	2	4	no	—
360	C₃×Q₈	—	2	2	no	—
361	C₃×Q₈	—	2	2	no	—
362	C₃×Q₈	—	2	2	no	—
363	C₃×Q₈	—	2	2	no	—
364	C₃×Q₈	—	3	2	no	—
365	C₃×Q₈	—	4	2	no	—
366	C₃×Q₈	—	6	1	no	—
367	C₃×D₄	—	2	4	no	—
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	2	2	no	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	3	2	no	—
373	C₃×D₄	—	4	2	no	—
374	C₃×D₄	—	4	4	no	—
375	C₃×D₄	—	4	4	no	—
376	C₃×D₄	—	4	2	no	—
377	C₃×D₄	—	4	2	no	—
378	C₃×D₄	—	4	2	no	—
379	C₃×D₄	—	4	2	no	—
380	C₃×D₄	—	6	2	no	—
381	C₃×D₄	—	6	2	no	—
382	C₃×D₄	—	6	1	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	4	2	no	—
392	C₂×C₃×C₄	—	4	4	no	—
393	C₂×C₃×C₄	—	4	4	no	—
394	C₂×C₃×C₄	—	4	2	no	—
395	C₂×C₃×C₄	—	4	2	no	—
396	C₂×C₃×C₄	—	4	2	no	—
397	C₂×C₃×C₄	—	4	2	no	—
398	C₂×C₃×C₄	—	6	1	no	—
399	C₂×C₃×C₄	—	6	2	no	—
400	C₂×C₃×C₄	—	6	2	no	—
401	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
402	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
403	C₂×C₃×C₄	#237	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
407	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
408	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
410	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
413	#67	—	2	2	no	—
414	#67	—	2	2	no	—
415	C₂×Dic₃	—	2	1	no	—
416	D₁₂	—	2	1	no	—
417	D₁₂	C₂×C₃×D₄	1	2	yes	—
418	C₄×D₃	—	2	2	no	—
419	C₄×D₃	—	2	2	no	—
420	Dic₆	—	2	1	no	—
421	Dic₆	C₂×C₃×D₄	1	2	yes	—
422	C₃×C₈	—	2	1	no	—
423	C₃×C₈	—	2	1	no	—
424	C₃×C₈	—	2	1	no	—
425	C₃×C₈	—	2	1	no	—
426	C₃×C₈	—	6	4	no	—
427	C₃×C₈	—	6	2	no	—
428	C₃×C₈	C₂×#67	1	1	yes	characteristic
429	C₃×C₈	C₂×#67	1	1	yes	characteristic
430	C₃×C₈	C₂×#67	1	1	yes	characteristic
431	C₃×C₈	C₂×#67	1	1	yes	characteristic
432	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
433	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
434	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
435	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
436	C₃⋊C₈	—	2	2	no	—
437	C₃⋊C₈	—	2	4	no	—
438	C₂×C₃²	—	2	1	no	—
439	C₂×C₃²	—	2	1	no	—
440	C₂×C₃²	—	2	1	no	—
441	C₂×C₃²	—	8	2	no	—
442	C₂×C₃²	C₂×#121	1	1	yes	characteristic
443	C₃×D₃	—	4	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	3	2	no	—
449	#41	—	3	2	no	—
450	#41	—	6	1	no	—
451	#41	—	6	1	no	—
452	C₂×Q₈	—	3	1	no	—
453	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	3	1	no	—
456	C₂×D₄	—	6	1	no	—
457	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	6	1	no	—
460	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
461	Q₁₆	—	2	1	no	—
462	Q₁₆	—	2	1	no	—
463	Q₁₆	—	6	4	no	—
464	SD₁₆	—	2	2	no	—
465	SD₁₆	—	2	2	no	—
466	SD₁₆	—	6	4	no	—
467	SD₁₆	—	6	4	no	—
468	D₈	—	2	1	no	—
469	D₈	—	2	1	no	—
470	D₈	—	6	4	no	—
471	M₁₆	—	3	2	no	—
472	M₁₆	—	3	4	no	—
473	M₁₆	—	6	2	no	—
474	M₁₆	—	6	1	no	—
475	M₁₆	—	6	2	no	—
476	M₁₆	—	6	2	no	—
477	C₂×C₈	—	6	2	no	—
478	C₂×C₈	—	6	1	no	—
479	C₂×C₈	—	6	2	no	—
480	C₂×C₈	—	6	2	no	—
481	C₂×C₈	C₃×#67	1	1	yes	characteristic
482	C₂×C₈	C₃×#67	1	1	yes	characteristic
483	C₂×C₈	C₃×#67	1	1	yes	characteristic
484	C₂×C₈	C₃×#67	1	1	yes	characteristic
485	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
486	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
487	C₂²×C₃	—	2	1	no	—
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	—	4	1	no	—
491	C₂²×C₃	—	4	1	no	—
492	C₂²×C₃	—	4	2	no	—
493	C₂²×C₃	—	4	4	no	—
494	C₂²×C₃	—	4	2	no	—
495	C₂²×C₃	—	4	2	no	—
496	C₂²×C₃	—	6	2	no	—
497	C₂²×C₃	—	8	2	no	—
498	C₂²×C₃	—	8	2	no	—
499	C₂²×C₃	—	8	4	no	—
500	C₂²×C₃	—	12	2	no	—
501	C₂²×C₃	#938	1	1	yes	characteristic
502	C₂²×C₃	#938	1	1	yes	characteristic
503	C₂²×C₃	C₃×#121	1	1	yes	characteristic
504	C₂²×C₃	C₃×#121	1	1	yes	characteristic
505	C₂²×C₃	C₂×#237	1	1	yes	characteristic
506	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
507	C₂×D₃	—	2	2	no	—
508	C₂×D₃	—	4	2	no	—
509	C₃×C₄	—	2	1	no	—
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	1	no	—
512	C₃×C₄	—	2	1	no	—
513	C₃×C₄	—	4	4	no	—
514	C₃×C₄	—	4	2	no	—
515	C₃×C₄	—	4	2	no	—
516	C₃×C₄	—	6	2	no	—
517	C₃×C₄	#938	1	1	yes	characteristic
518	C₃×C₄	#938	1	1	yes	characteristic
519	C₃×C₄	C₃×#121	1	1	yes	characteristic
520	C₃×C₄	C₃×#121	1	1	yes	characteristic
521	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
522	C₃×C₄	C₂²×#67	1	1	yes	characteristic
523	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
524	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
525	Dic₃	—	2	2	no	—
526	C₃²	#3067	1	1	yes	characteristic, complemented, Sylow
527	C₂³	—	2	2	no	—
528	C₂³	—	6	1	no	—
529	C₂³	C₃×#237	1	1	yes	characteristic
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	3	2	no	—
533	Q₈	—	6	1	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	2	no	—
536	D₄	—	3	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	6	2	no	—
540	D₄	—	6	2	no	—
541	D₄	—	6	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	6	1	no	—
546	C₂×C₄	—	6	2	no	—
547	C₂×C₄	—	6	2	no	—
548	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
549	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
550	C₂×C₄	C₃×#237	1	1	yes	characteristic
551	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
552	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
553	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
554	C₈	—	6	4	no	—
555	C₈	—	6	2	no	—
556	C₈	C₂×C₃×#67	1	1	yes	characteristic
557	C₈	C₂×C₃×#67	1	1	yes	characteristic
558	C₈	C₂×C₃×#67	1	1	yes	characteristic
559	C₈	C₂×C₃×#67	1	1	yes	characteristic
560	C₂×C₃	—	2	2	no	—
561	C₂×C₃	—	2	1	no	—
562	C₂×C₃	—	2	1	no	—
563	C₂×C₃	—	2	1	no	—
564	C₂×C₃	—	2	1	no	—
565	C₂×C₃	—	2	1	no	—
566	C₂×C₃	—	2	1	no	—
567	C₂×C₃	—	2	1	no	—
568	C₂×C₃	—	4	1	no	—
569	C₂×C₃	—	4	1	no	—
570	C₂×C₃	—	8	4	no	—
571	C₂×C₃	—	8	2	no	—
572	C₂×C₃	—	8	2	no	—
573	C₂×C₃	—	12	2	no	—
574	C₂×C₃	C₂×#938	1	1	yes	characteristic
575	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
576	D₃	—	4	2	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	6	2	no	—
580	C₂²	—	8	2	no	—
581	C₂²	—	12	2	no	—
582	C₂²	C₃×#938	1	1	yes	characteristic
583	C₂²	C₃×#938	1	1	yes	characteristic
584	C₂²	C₂×C₃×#237	1	1	yes	characteristic
585	C₄	—	4	2	no	—
586	C₄	—	6	2	no	—
587	C₄	C₃×#938	1	1	yes	characteristic
588	C₄	C₃×#938	1	1	yes	characteristic
589	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
590	C₄	C₂²×C₃×#67	1	1	yes	characteristic
591	C₃	—	2	1	no	—
592	C₃	#83928	1	1	yes	characteristic, direct product factor
593	C₃	C₃×#3067	1	1	yes	characteristic, complemented
594	C₂	—	2	1	no	—
595	C₂	—	2	1	no	—
596	C₂	—	2	1	no	—
597	C₂	—	8	2	no	—
598	C₂	—	12	2	no	—
599	C₂	C₂×C₃×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#938
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#135	C₂
socle	C₂×C₃²	C₂×#121
hypercenter	C₂×C₃×#135	D₃
hypocenter	C₃	C₃×#3067
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#135	C₂	semidirect
2. C₃×#5822	C₂	semidirect
3. C₂×C₃×#901	C₂	semidirect
4. C₃×#5237	C₂	semidirect
5. C₃×#5192	C₂	semidirect
6. C₃×#5177	C₂	semidirect
7. C₃×#5160	C₂	semidirect
8. C₂×C₃×#819	C₂	semidirect
10. #83928	C₃	direct (N × H)
17. C₂×C₃²×Q₁₆	C₂²	semidirect
18. C₂×C₃²×SD₁₆	C₂²	semidirect
19. C₂×C₃²×D₈	C₂²	semidirect
34. C₃×#836	C₂²	semidirect
35. C₃×#833	C₂²	semidirect
36. C₃×#819	C₂²	semidirect
37. C₃×#819	C₂²	semidirect
40. C₂×C₃×#135	D₃	semidirect
41. C₂×C₃×#135	C₂×C₃	semidirect
43. #5822	C₂×C₃	semidirect
44. C₂×#901	C₂×C₃	semidirect
50. #5237	C₂×C₃	semidirect
51. #5192	C₂×C₃	semidirect
52. #5177	C₂×C₃	semidirect
53. #5160	C₂×C₃	semidirect
54. C₂×#819	C₂×C₃	semidirect
122. C₂×C₃×Q₁₆	C₂×D₃	semidirect
123. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
125. C₂×C₃×SD₁₆	C₂×D₃	semidirect
126. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
128. C₂×C₃×D₈	C₂×D₃	semidirect
129. C₂×C₃×D₈	C₂²×C₃	semidirect
158. #836	C₂²×C₃	semidirect
159. #833	C₂²×C₃	semidirect
160. #819	C₂²×C₃	semidirect
161. #819	C₂²×C₃	semidirect
196. C₂×#135	C₃×D₃	semidirect
335. C₂×Q₁₆	C₂×C₃×D₃	semidirect
336. C₂×SD₁₆	C₂×C₃×D₃	semidirect
337. C₂×D₈	C₂×C₃×D₃	semidirect
526. C₃²	#3067	semidirect
592. C₃	#83928	direct (N × H)
593. C₃	C₃×#3067	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#135	2
C₃×#5822	2
C₂×C₃×#901	2
C₃×#5237	2
C₃×#5192	2
C₃×#5177	2
C₃×#5160	2
C₂×C₃×#819	2
C₃×#3067	3
#83928	3

Subgroups — C3×#83928 #11868003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83928 #11868003