Subgroups — C₃×#33722 #10652329

Order 768.

826 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2251	C₂	1	2	yes	maximal, complemented
8	C₃×#2250	C₂	1	2	yes	maximal, complemented
9	C₃×#2249	C₂	1	2	yes	maximal, complemented
10	C₃×#2248	C₂	1	2	yes	maximal, complemented
11	C₃×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	#33722	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×#137	—	2	1	no	—
14	C₂×C₃×AGL(1,ℤ/8)	—	2	1	no	—
15	C₂×C₃×#135	C₂²	1	1	yes	characteristic
16	C₂×C₃×#135	C₂²	1	1	yes	characteristic
17	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic
19	C₃×#536	—	2	1	no	—
20	C₃×#535	—	2	1	no	—
21	C₃×#510	—	2	4	no	—
22	C₃×#509	—	2	4	no	—
23	C₃×#508	—	2	4	no	—
24	C₂×C₃×Q₃₂	C₂²	1	2	yes	complemented
25	C₂×C₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×SD₃₂	—	2	4	no	—
27	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
28	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
29	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
30	C₂×C₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×SD₃₂	C₂²	1	2	yes	complemented
32	C₂×C₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×D₁₆	C₂²	1	2	yes	—
34	C₂×C₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×M₃₂	C₂²	1	1	yes	characteristic
36	C₂²×C₃×C₁₆	C₂²	1	1	yes	characteristic
37	C₃×#497	—	2	2	no	—
38	C₃×#496	—	2	2	no	—
39	C₃×#495	C₂²	1	2	yes	—
40	C₃×#495	C₂²	1	2	yes	complemented
41	C₃×#494	C₂²	1	2	yes	complemented
42	C₃×#493	C₂²	1	2	yes	—
43	C₃×#405	C₂²	1	1	yes	characteristic
44	C₃×#346	C₂²	1	2	yes	complemented
45	C₃×C₄×C₁₆	C₂²	1	2	yes	complemented
46	C₂×#510	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#509	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#508	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂²×SD₃₂	C₂×C₃	1	1	yes	characteristic, complemented
50	#3156	C₂×C₃	1	1	yes	characteristic, complemented
51	#3155	C₂×C₃	1	1	yes	characteristic, complemented
52	#2251	C₂×C₃	1	2	yes	complemented
53	#2250	C₂×C₃	1	2	yes	complemented
54	#2249	C₂×C₃	1	2	yes	complemented
55	#2248	C₂×C₃	1	2	yes	complemented
56	#2108	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×C₃×#41	—	2	1	no	—
58	C₂×C₃×#41	—	2	1	no	—
59	C₂²×C₃×Q₈	—	2	1	no	—
60	C₂²×C₃×D₄	—	2	1	no	—
61	C₃×#137	—	4	4	no	—
62	C₃×AGL(1,ℤ/8)	—	4	4	no	—
63	C₃×#135	—	2	2	no	—
64	C₃×#135	—	2	2	no	—
65	C₃×#135	—	2	2	no	—
66	C₃×#135	—	2	2	no	—
67	C₂×C₃×Q₁₆	—	2	2	no	—
68	C₂×C₃×Q₁₆	—	2	2	no	—
69	C₂×C₃×Q₁₆	—	2	1	no	—
70	C₂×C₃×Q₁₆	—	2	2	no	—
71	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
72	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₃×SD₁₆	—	2	1	no	—
75	C₂×C₃×SD₁₆	—	2	1	no	—
76	C₂×C₃×SD₁₆	—	2	2	no	—
77	C₂×C₃×SD₁₆	—	2	2	no	—
78	C₂×C₃×D₈	—	2	2	no	—
79	C₂×C₃×D₈	—	2	2	no	—
80	C₂×C₃×D₈	—	2	1	no	—
81	C₂×C₃×D₈	—	2	2	no	—
82	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×D₈	C₂³	1	2	yes	—
84	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
86	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
87	C₃×C₄⋊Q₈	—	2	2	no	—
88	C₃×#127	—	2	2	no	—
89	C₃×#124	—	2	2	no	—
90	C₃×#124	—	2	2	no	—
91	C₃×#123	—	4	2	no	—
92	C₃×C₂²⋊Q₈	—	4	2	no	—
93	C₃×#121	—	4	2	no	—
94	C₃×#120	—	4	2	no	—
95	C₃×#117	D₄	1	1	yes	characteristic
96	C₃×Q₃₂	—	2	2	no	—
97	C₃×Q₃₂	—	2	4	no	—
98	C₃×SD₃₂	—	2	4	no	—
99	C₃×SD₃₂	—	2	4	no	—
100	C₃×SD₃₂	—	2	4	no	—
101	C₃×SD₃₂	—	2	2	no	—
102	C₃×SD₃₂	—	2	2	no	—
103	C₃×SD₃₂	—	2	4	no	—
104	C₃×D₁₆	—	2	4	no	—
105	C₃×D₁₆	—	2	2	no	—
106	C₃×M₃₂	D₄	1	4	yes	complemented
107	C₂×C₃×C₁₆	D₄	1	4	yes	complemented
108	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₁₆	C₂³	1	2	yes	—
111	C₃×#97	D₄	1	2	yes	—
112	C₃×C₄×C₈	C₂³	1	2	yes	—
113	C₂×#137	—	2	1	no	—
114	C₂×AGL(1,ℤ/8)	—	2	1	no	—
115	C₂×#135	C₂²×C₃	1	1	yes	characteristic
116	C₂×#135	C₂²×C₃	1	1	yes	characteristic
117	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
118	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic
119	#536	—	2	1	no	—
120	#535	—	2	1	no	—
121	#510	—	2	4	no	—
122	#509	—	2	4	no	—
123	#508	—	2	4	no	—
124	C₂×Q₃₂	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×Q₃₂	C₂²×C₃	1	2	yes	complemented
126	C₂×SD₃₂	—	2	4	no	—
127	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
128	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
129	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
130	C₂×SD₃₂	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₂×SD₃₂	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₂×SD₃₂	C₂²×C₃	1	2	yes	complemented
133	C₂×D₁₆	C₂²×C₃	1	2	yes	—
134	C₂×D₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
135	C₂×M₃₂	C₂²×C₃	1	1	yes	characteristic
136	C₂²×C₁₆	C₂²×C₃	1	1	yes	characteristic
137	#497	—	2	2	no	—
138	#496	—	2	2	no	—
139	#495	C₂²×C₃	1	2	yes	—
140	#495	C₂²×C₃	1	2	yes	complemented
141	#494	C₂²×C₃	1	2	yes	complemented
142	#493	C₂²×C₃	1	2	yes	—
143	#405	C₂²×C₃	1	1	yes	characteristic
144	#346	C₂²×C₃	1	2	yes	complemented
145	C₄×C₁₆	C₂²×C₃	1	2	yes	complemented
146	C₂⁴×C₃	—	4	1	no	—
147	C₃×#41	—	4	2	no	—
148	C₃×#41	—	4	2	no	—
149	C₃×#41	—	4	2	no	—
150	C₃×#41	—	4	2	no	—
151	C₂×C₃×Q₈	—	2	1	no	—
152	C₂×C₃×Q₈	—	2	2	no	—
153	C₂×C₃×Q₈	—	2	1	no	—
154	C₂×C₃×Q₈	—	4	1	no	—
155	C₂×C₃×Q₈	—	4	2	no	—
156	C₂×C₃×Q₈	—	4	2	no	—
157	C₂×C₃×D₄	—	2	1	no	—
158	C₂×C₃×D₄	—	2	2	no	—
159	C₂×C₃×D₄	—	2	1	no	—
160	C₂×C₃×D₄	—	4	1	no	—
161	C₂×C₃×D₄	—	4	1	no	—
162	C₂×C₃×D₄	—	4	2	no	—
163	C₂×C₃×D₄	—	4	2	no	—
164	C₂×C₃×D₄	—	4	1	no	—
165	C₂×C₃×D₄	—	4	4	no	—
166	C₂²×C₃×C₄	—	4	1	no	—
167	C₂²×C₃×C₄	—	4	1	no	—
168	C₂²×C₃×C₄	—	4	1	no	—
169	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
170	C₃×Q₁₆	—	2	2	no	—
171	C₃×Q₁₆	—	2	1	no	—
172	C₃×Q₁₆	—	2	2	no	—
173	C₃×Q₁₆	—	2	1	no	—
174	C₃×Q₁₆	—	2	1	no	—
175	C₃×Q₁₆	—	2	1	no	—
176	C₃×Q₁₆	—	4	2	no	—
177	C₃×Q₁₆	—	4	4	no	—
178	C₃×SD₁₆	—	4	2	no	—
179	C₃×SD₁₆	—	4	2	no	—
180	C₃×SD₁₆	—	4	4	no	—
181	C₃×SD₁₆	—	4	4	no	—
182	C₃×D₈	—	2	1	no	—
183	C₃×D₈	—	2	2	no	—
184	C₃×D₈	—	2	1	no	—
185	C₃×D₈	—	2	1	no	—
186	C₃×D₈	—	2	2	no	—
187	C₃×D₈	—	2	1	no	—
188	C₃×D₈	—	4	2	no	—
189	C₃×D₈	—	4	4	no	—
190	C₃×M₁₆	D₈	1	4	yes	—
191	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
193	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
194	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
195	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
196	C₃×C₄⋊C₄	—	4	4	no	—
197	C₃×C₄⋊C₄	D₈	1	2	yes	—
198	C₃×C₂²⋊C₄	—	4	4	no	—
199	C₃×C₂²⋊C₄	—	4	4	no	—
200	C₃×C₂²⋊C₄	D₈	1	2	yes	—
201	C₃×C₄²	C₂×D₄	1	2	yes	—
202	C₃×C₁₆	C₂×D₄	1	2	yes	—
203	C₃×C₁₆	C₂×D₄	1	2	yes	—
204	C₃×C₁₆	C₂×D₄	1	4	yes	—
205	C₂×#41	—	2	1	no	—
206	C₂×#41	—	2	1	no	—
207	C₂²×Q₈	—	2	1	no	—
208	C₂²×D₄	—	2	1	no	—
209	#137	—	4	4	no	—
210	AGL(1,ℤ/8)	—	4	4	no	—
211	#135	—	2	2	no	—
212	#135	—	2	2	no	—
213	#135	—	2	2	no	—
214	#135	—	2	2	no	—
215	C₂×Q₁₆	—	2	2	no	—
216	C₂×Q₁₆	—	2	2	no	—
217	C₂×Q₁₆	—	2	1	no	—
218	C₂×Q₁₆	—	2	2	no	—
219	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
220	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
221	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
222	C₂×SD₁₆	—	2	1	no	—
223	C₂×SD₁₆	—	2	1	no	—
224	C₂×SD₁₆	—	2	2	no	—
225	C₂×SD₁₆	—	2	2	no	—
226	C₂×D₈	—	2	2	no	—
227	C₂×D₈	—	2	2	no	—
228	C₂×D₈	—	2	1	no	—
229	C₂×D₈	—	2	2	no	—
230	C₂×D₈	C₂³×C₃	1	2	yes	—
231	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
232	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
233	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
235	C₄⋊Q₈	—	2	2	no	—
236	#127	—	2	2	no	—
237	#124	—	2	2	no	—
238	#124	—	2	2	no	—
239	#123	—	4	2	no	—
240	C₂²⋊Q₈	—	4	2	no	—
241	#121	—	4	2	no	—
242	#120	—	4	2	no	—
243	#117	C₃×D₄	1	1	yes	characteristic
244	Q₃₂	—	2	2	no	—
245	Q₃₂	—	2	4	no	—
246	SD₃₂	—	2	4	no	—
247	SD₃₂	—	2	4	no	—
248	SD₃₂	—	2	4	no	—
249	SD₃₂	—	2	2	no	—
250	SD₃₂	—	2	2	no	—
251	SD₃₂	—	2	4	no	—
252	D₁₆	—	2	4	no	—
253	D₁₆	—	2	2	no	—
254	M₃₂	C₃×D₄	1	4	yes	complemented
255	C₂×C₁₆	C₃×D₄	1	4	yes	complemented
256	C₂×C₁₆	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₁₆	C₂³×C₃	1	2	yes	—
258	C₂×C₁₆	C₂³×C₃	1	1	yes	characteristic
259	#97	C₃×D₄	1	2	yes	—
260	C₄×C₈	C₂³×C₃	1	2	yes	—
261	C₂³×C₃	—	4	1	no	—
262	C₂³×C₃	—	4	2	no	—
263	C₂³×C₃	—	4	1	no	—
264	C₂³×C₃	—	8	2	no	—
265	C₂³×C₃	—	16	2	no	—
266	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
267	C₃×Q₈	—	4	1	no	—
268	C₃×Q₈	—	4	1	no	—
269	C₃×Q₈	—	4	2	no	—
270	C₃×Q₈	—	4	1	no	—
271	C₃×Q₈	—	4	2	no	—
272	C₃×Q₈	—	4	1	no	—
273	C₃×Q₈	—	8	2	no	—
274	C₃×D₄	—	4	2	no	—
275	C₃×D₄	—	4	1	no	—
276	C₃×D₄	—	4	1	no	—
277	C₃×D₄	—	4	1	no	—
278	C₃×D₄	—	4	2	no	—
279	C₃×D₄	—	4	1	no	—
280	C₃×D₄	—	8	2	no	—
281	C₃×D₄	—	8	2	no	—
282	C₃×D₄	—	8	2	no	—
283	C₃×D₄	—	16	4	no	—
284	C₂×C₃×C₄	—	4	1	no	—
285	C₂×C₃×C₄	—	4	2	no	—
286	C₂×C₃×C₄	—	4	1	no	—
287	C₂×C₃×C₄	—	8	2	no	—
288	C₂×C₃×C₄	—	8	2	no	—
289	C₂×C₃×C₄	—	8	2	no	—
290	C₂×C₃×C₄	#127	1	2	yes	—
291	C₂×C₃×C₄	C₂×D₈	1	4	yes	—
292	C₂×C₃×C₄	C₂×D₈	1	2	yes	—
293	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
295	C₃×C₈	#127	1	2	yes	—
296	C₃×C₈	C₂×D₈	1	4	yes	—
297	C₃×C₈	C₂²×D₄	1	1	yes	characteristic
298	C₃×C₈	C₂²×D₄	1	1	yes	characteristic
299	C₂⁴	—	4	1	no	—
300	#41	—	4	2	no	—
301	#41	—	4	2	no	—
302	#41	—	4	2	no	—
303	#41	—	4	2	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	4	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
323	Q₁₆	—	2	2	no	—
324	Q₁₆	—	2	1	no	—
325	Q₁₆	—	2	2	no	—
326	Q₁₆	—	2	1	no	—
327	Q₁₆	—	2	1	no	—
328	Q₁₆	—	2	1	no	—
329	Q₁₆	—	4	2	no	—
330	Q₁₆	—	4	4	no	—
331	SD₁₆	—	4	2	no	—
332	SD₁₆	—	4	2	no	—
333	SD₁₆	—	4	4	no	—
334	SD₁₆	—	4	4	no	—
335	D₈	—	2	1	no	—
336	D₈	—	2	2	no	—
337	D₈	—	2	1	no	—
338	D₈	—	2	1	no	—
339	D₈	—	2	2	no	—
340	D₈	—	2	1	no	—
341	D₈	—	4	2	no	—
342	D₈	—	4	4	no	—
343	M₁₆	C₃×D₈	1	4	yes	—
344	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
345	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
346	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
347	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
348	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	C₃×D₈	1	2	yes	—
351	C₂²⋊C₄	—	4	4	no	—
352	C₂²⋊C₄	—	4	4	no	—
353	C₂²⋊C₄	C₃×D₈	1	2	yes	—
354	C₄²	C₂×C₃×D₄	1	2	yes	—
355	C₁₆	C₂×C₃×D₄	1	2	yes	—
356	C₁₆	C₂×C₃×D₄	1	2	yes	—
357	C₁₆	C₂×C₃×D₄	1	4	yes	—
358	C₂²×C₃	—	2	2	no	—
359	C₂²×C₃	—	8	1	no	—
360	C₂²×C₃	—	8	1	no	—
361	C₂²×C₃	—	8	2	no	—
362	C₂²×C₃	—	8	2	no	—
363	C₂²×C₃	—	8	4	no	—
364	C₂²×C₃	—	8	2	no	—
365	C₂²×C₃	—	16	4	no	—
366	C₂²×C₃	#493	1	2	yes	—
367	C₂²×C₃	C₂²×D₈	1	1	yes	characteristic
368	C₃×C₄	—	2	4	no	—
369	C₃×C₄	—	8	1	no	—
370	C₃×C₄	—	8	1	no	—
371	C₃×C₄	—	8	2	no	—
372	C₃×C₄	#493	1	2	yes	—
373	C₃×C₄	C₂×#127	1	1	yes	characteristic
374	C₃×C₄	C₂²×D₈	1	1	yes	characteristic
375	C₂³	—	4	1	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	16	2	no	—
380	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
381	Q₈	—	4	1	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	1	no	—
384	Q₈	—	4	1	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	8	2	no	—
388	D₄	—	4	1	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	1	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	16	4	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	C₃×#127	1	2	yes	—
405	C₂×C₄	C₂×C₃×D₈	1	4	yes	—
406	C₂×C₄	C₂×C₃×D₈	1	2	yes	—
407	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
409	C₈	C₃×#127	1	2	yes	—
410	C₈	C₂×C₃×D₈	1	4	yes	—
411	C₈	C₂²×C₃×D₄	1	1	yes	characteristic
412	C₈	C₂²×C₃×D₄	1	1	yes	characteristic
413	C₂×C₃	—	2	2	no	—
414	C₂×C₃	—	16	1	no	—
415	C₂×C₃	—	16	1	no	—
416	C₂×C₃	—	16	2	no	—
417	C₂×C₃	C₂×#493	1	1	yes	characteristic
418	C₂×C₃	#3416	1	2	yes	—
419	C₂²	—	2	2	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	4	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	16	4	no	—
427	C₂²	C₃×#493	1	2	yes	—
428	C₂²	C₂²×C₃×D₈	1	1	yes	characteristic
429	C₄	—	2	4	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	2	no	—
433	C₄	C₃×#493	1	2	yes	—
434	C₄	C₂×C₃×#127	1	1	yes	characteristic
435	C₄	C₂²×C₃×D₈	1	1	yes	characteristic
436	C₃	#33722	1	1	yes	characteristic, direct product factor, Sylow
437	C₂	—	2	2	no	—
438	C₂	—	16	2	no	—
439	C₂	—	16	1	no	—
440	C₂	—	16	1	no	—
441	C₂	C₂×C₃×#493	1	1	yes	characteristic
442	C₂	C₃×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#510	C₂	semidirect
2. C₂×C₃×#509	C₂	semidirect
3. C₂×C₃×#508	C₂	semidirect
4. C₂²×C₃×SD₃₂	C₂	semidirect
5. C₃×#3156	C₂	semidirect
6. C₃×#3155	C₂	semidirect
7. C₃×#2251	C₂	semidirect
8. C₃×#2250	C₂	semidirect
9. C₃×#2249	C₂	semidirect
10. C₃×#2248	C₂	semidirect
11. C₃×#2108	C₂	semidirect
12. #33722	C₃	direct (N × H)
24. C₂×C₃×Q₃₂	C₂²	semidirect
25. C₂×C₃×Q₃₂	C₂²	semidirect
30. C₂×C₃×SD₃₂	C₂²	semidirect
31. C₂×C₃×SD₃₂	C₂²	semidirect
32. C₂×C₃×SD₃₂	C₂²	semidirect
34. C₂×C₃×D₁₆	C₂²	semidirect
40. C₃×#495	C₂²	semidirect
41. C₃×#494	C₂²	semidirect
44. C₃×#346	C₂²	semidirect
45. C₃×C₄×C₁₆	C₂²	semidirect
46. C₂×#510	C₂×C₃	semidirect
47. C₂×#509	C₂×C₃	semidirect
48. C₂×#508	C₂×C₃	semidirect
49. C₂²×SD₃₂	C₂×C₃	semidirect
50. #3156	C₂×C₃	semidirect
51. #3155	C₂×C₃	semidirect
52. #2251	C₂×C₃	semidirect
53. #2250	C₂×C₃	semidirect
54. #2249	C₂×C₃	semidirect
55. #2248	C₂×C₃	semidirect
56. #2108	C₂×C₃	semidirect
106. C₃×M₃₂	D₄	semidirect
107. C₂×C₃×C₁₆	D₄	semidirect
124. C₂×Q₃₂	C₂²×C₃	semidirect
125. C₂×Q₃₂	C₂²×C₃	semidirect
130. C₂×SD₃₂	C₂²×C₃	semidirect
131. C₂×SD₃₂	C₂²×C₃	semidirect
132. C₂×SD₃₂	C₂²×C₃	semidirect
134. C₂×D₁₆	C₂²×C₃	semidirect
140. #495	C₂²×C₃	semidirect
141. #494	C₂²×C₃	semidirect
144. #346	C₂²×C₃	semidirect
145. C₄×C₁₆	C₂²×C₃	semidirect
254. M₃₂	C₃×D₄	semidirect
255. C₂×C₁₆	C₃×D₄	semidirect
436. C₃	#33722	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#510	2
C₂×C₃×#509	2
C₂×C₃×#508	2
C₂²×C₃×SD₃₂	2
C₃×#3156	2
C₃×#3155	2
C₃×#2251	2
C₃×#2250	2
C₃×#2249	2
C₃×#2248	2
C₃×#2108	2
#33722	3

Subgroups — C3×#33722 #10652329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33722 #10652329