Subgroups — C₃×#33579 #10652186

Order 768.

718 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×#508	C₂	1	2	yes	maximal, complemented
2	C₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2211	C₂	1	2	yes	maximal, complemented
5	C₃×#2210	C₂	1	2	yes	maximal, complemented
6	C₃×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2138	C₂	1	2	yes	maximal, complemented
12	#33579	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×#135	—	2	1	no	—
14	C₂×C₃×#135	C₂²	1	2	yes	—
15	C₂×C₃×#135	C₂²	1	1	yes	characteristic
16	C₃×#532	—	2	1	no	—
17	C₃×C₄×#41	—	2	1	no	—
18	C₃×#508	—	2	8	no	—
19	C₂×C₃×Q₃₂	C₂²	1	2	yes	—
20	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
22	C₂×C₃×D₁₆	C₂²	1	2	yes	—
23	C₂²×C₃×C₁₆	C₂²	1	2	yes	—
24	C₃×#495	—	2	1	no	—
25	C₃×#495	C₂²	1	2	yes	—
26	C₃×#494	C₂²	1	1	yes	characteristic
27	C₃×#493	C₂²	1	1	yes	characteristic
28	C₃×#492	—	2	1	no	—
29	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
30	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
31	C₃×C₄×SD₁₆	—	2	1	no	—
32	C₃×C₄×SD₁₆	—	2	1	no	—
33	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
34	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
35	C₃×#427	C₂²	1	1	yes	characteristic
36	C₃×#416	—	2	1	no	—
37	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
38	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊C₁₆	C₂²	1	2	yes	—
41	C₃×#358	C₂²	1	2	yes	—
42	C₃×#358	C₂²	1	2	yes	—
43	C₃×#357	C₂²	1	2	yes	—
44	C₃×#357	C₂²	1	2	yes	—
45	C₂×#508	C₂×C₃	1	2	yes	complemented
46	#3147	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×#135	C₂×C₃	1	1	yes	characteristic, complemented
48	#2211	C₂×C₃	1	2	yes	complemented
49	#2210	C₂×C₃	1	2	yes	complemented
50	#2209	C₂×C₃	1	1	yes	characteristic, complemented
51	#2208	C₂×C₃	1	1	yes	characteristic, complemented
52	#2207	C₂×C₃	1	1	yes	characteristic, complemented
53	#2206	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₄⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
55	#2138	C₂×C₃	1	2	yes	complemented
56	C₂×C₃×#41	—	2	1	no	—
57	C₂×C₃×#41	—	2	2	no	—
58	C₃×#135	—	2	4	no	—
59	C₃×#135	—	2	2	no	—
60	C₃×#135	—	2	4	no	—
61	C₃×#135	—	4	4	no	—
62	C₃×#135	D₄	1	4	yes	complemented
63	C₂×C₃×Q₁₆	—	2	1	no	—
64	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
65	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₃×SD₁₆	—	2	1	no	—
67	C₂×C₃×SD₁₆	—	2	2	no	—
68	C₂×C₃×SD₁₆	—	2	2	no	—
69	C₂×C₃×D₈	—	2	1	no	—
70	C₂×C₃×D₈	C₂³	1	2	yes	—
71	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
73	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
74	C₃×C₄⋊Q₈	—	2	1	no	—
75	C₃×#127	—	2	1	no	—
76	C₃×#124	—	2	2	no	—
77	C₃×#121	—	4	1	no	—
78	C₃×#121	—	4	1	no	—
79	C₃×C₄×Q₈	—	2	1	no	—
80	C₃×C₄×Q₈	—	2	1	no	—
81	C₃×C₄×D₄	—	2	1	no	—
82	C₃×C₄×D₄	—	2	1	no	—
83	C₃×C₄×D₄	—	4	1	no	—
84	C₃×C₄×D₄	—	4	1	no	—
85	C₃×C₄×D₄	—	4	1	no	—
86	C₃×C₄×D₄	—	4	1	no	—
87	C₃×#117	—	2	1	no	—
88	C₃×#117	—	4	1	no	—
89	C₂×C₃×C₄²	—	4	1	no	—
90	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
91	C₃×Q₃₂	—	2	4	no	—
92	C₃×SD₃₂	—	2	4	no	—
93	C₃×SD₃₂	—	2	4	no	—
94	C₃×D₁₆	—	2	4	no	—
95	C₂×C₃×C₁₆	—	2	4	no	—
96	C₂×C₃×C₁₆	C₂³	1	2	yes	—
97	C₂×C₃×C₁₆	C₂³	1	2	yes	—
98	C₃×#107	C₂³	1	1	yes	characteristic
99	C₃×#107	C₂³	1	1	yes	characteristic
100	C₃×#106	—	2	1	no	—
101	C₃×#103	—	2	1	no	—
102	C₃×#103	—	2	1	no	—
103	C₃×#102	—	2	1	no	—
104	C₃×#102	—	2	1	no	—
105	C₃×C₄×C₈	D₄	1	1	yes	characteristic
106	C₃×C₄×C₈	D₄	1	1	yes	characteristic
107	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
108	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
109	C₂×#135	—	2	1	no	—
110	C₂×#135	C₂²×C₃	1	2	yes	—
111	C₂×#135	C₂²×C₃	1	1	yes	characteristic
112	#532	—	2	1	no	—
113	C₄×#41	—	2	1	no	—
114	#508	—	2	8	no	—
115	C₂×Q₃₂	C₂²×C₃	1	2	yes	—
116	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
117	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
118	C₂×D₁₆	C₂²×C₃	1	2	yes	—
119	C₂²×C₁₆	C₂²×C₃	1	2	yes	—
120	#495	—	2	1	no	—
121	#495	C₂²×C₃	1	2	yes	—
122	#494	C₂²×C₃	1	1	yes	characteristic
123	#493	C₂²×C₃	1	1	yes	characteristic
124	#492	—	2	1	no	—
125	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
127	C₄×SD₁₆	—	2	1	no	—
128	C₄×SD₁₆	—	2	1	no	—
129	C₄×D₈	C₂²×C₃	1	1	yes	characteristic
130	C₄×D₈	C₂²×C₃	1	1	yes	characteristic
131	#427	C₂²×C₃	1	1	yes	characteristic
132	#416	—	2	1	no	—
133	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
134	C₄⋊C₁₆	C₂²×C₃	1	1	yes	characteristic
135	C₄⋊C₁₆	C₂²×C₃	1	1	yes	characteristic
136	C₄⋊C₁₆	C₂²×C₃	1	2	yes	—
137	#358	C₂²×C₃	1	2	yes	—
138	#358	C₂²×C₃	1	2	yes	—
139	#357	C₂²×C₃	1	2	yes	—
140	#357	C₂²×C₃	1	2	yes	—
141	C₃×#41	—	2	4	no	—
142	C₃×#41	—	4	2	no	—
143	C₃×#41	—	4	4	no	—
144	C₃×#41	—	4	4	no	—
145	C₂×C₃×Q₈	—	2	1	no	—
146	C₂×C₃×Q₈	—	2	2	no	—
147	C₂×C₃×D₄	—	2	1	no	—
148	C₂×C₃×D₄	—	2	2	no	—
149	C₂×C₃×D₄	—	4	1	no	—
150	C₂×C₃×D₄	—	4	2	no	—
151	C₂×C₃×D₄	—	4	1	no	—
152	C₂×C₃×D₄	—	4	1	no	—
153	C₂²×C₃×C₄	—	4	1	no	—
154	C₂²×C₃×C₄	—	4	1	no	—
155	C₂²×C₃×C₄	—	4	1	no	—
156	C₂²×C₃×C₄	—	4	2	no	—
157	C₂²×C₃×C₄	D₈	1	1	yes	characteristic
158	C₂²×C₃×C₄	D₈	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
160	C₃×Q₁₆	—	2	2	no	—
161	C₃×Q₁₆	—	2	1	no	—
162	C₃×Q₁₆	—	2	2	no	—
163	C₃×Q₁₆	—	4	2	no	—
164	C₃×Q₁₆	C₂×D₄	1	2	yes	—
165	C₃×SD₁₆	—	2	4	no	—
166	C₃×SD₁₆	—	4	4	no	—
167	C₃×SD₁₆	—	4	4	no	—
168	C₃×D₈	—	2	2	no	—
169	C₃×D₈	—	2	1	no	—
170	C₃×D₈	—	2	2	no	—
171	C₃×D₈	—	4	2	no	—
172	C₃×D₈	C₂×D₄	1	2	yes	—
173	C₂×C₃×C₈	—	2	2	no	—
174	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
176	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
178	C₂×C₃×C₈	#41	1	2	yes	—
179	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
180	C₃×C₄⋊C₄	—	2	1	no	—
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₄⋊C₄	—	4	1	no	—
183	C₃×C₄⋊C₄	—	4	1	no	—
184	C₃×C₄⋊C₄	—	4	1	no	—
185	C₃×C₄⋊C₄	—	4	1	no	—
186	C₃×C₂²⋊C₄	—	4	1	no	—
187	C₃×C₂²⋊C₄	—	4	1	no	—
188	C₃×C₂²⋊C₄	—	4	1	no	—
189	C₃×C₂²⋊C₄	—	4	2	no	—
190	C₃×C₂²⋊C₄	—	4	2	no	—
191	C₃×C₄²	—	4	1	no	—
192	C₃×C₄²	—	4	1	no	—
193	C₃×C₄²	—	4	1	no	—
194	C₃×C₄²	D₈	1	1	yes	characteristic
195	C₃×C₄²	D₈	1	1	yes	characteristic
196	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
197	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
198	C₃×C₁₆	—	2	2	no	—
199	C₃×C₁₆	—	2	2	no	—
200	C₂×#41	—	2	1	no	—
201	C₂×#41	—	2	2	no	—
202	#135	—	2	4	no	—
203	#135	—	2	2	no	—
204	#135	—	2	4	no	—
205	#135	—	4	4	no	—
206	#135	C₃×D₄	1	4	yes	complemented
207	C₂×Q₁₆	—	2	1	no	—
208	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
209	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
210	C₂×SD₁₆	—	2	1	no	—
211	C₂×SD₁₆	—	2	2	no	—
212	C₂×SD₁₆	—	2	2	no	—
213	C₂×D₈	—	2	1	no	—
214	C₂×D₈	C₂³×C₃	1	2	yes	—
215	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
216	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
218	C₄⋊Q₈	—	2	1	no	—
219	#127	—	2	1	no	—
220	#124	—	2	2	no	—
221	#121	—	4	1	no	—
222	#121	—	4	1	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	4	1	no	—
228	C₄×D₄	—	4	1	no	—
229	C₄×D₄	—	4	1	no	—
230	C₄×D₄	—	4	1	no	—
231	#117	—	2	1	no	—
232	#117	—	4	1	no	—
233	C₂×C₄²	—	4	1	no	—
234	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
235	Q₃₂	—	2	4	no	—
236	SD₃₂	—	2	4	no	—
237	SD₃₂	—	2	4	no	—
238	D₁₆	—	2	4	no	—
239	C₂×C₁₆	—	2	4	no	—
240	C₂×C₁₆	C₂³×C₃	1	2	yes	—
241	C₂×C₁₆	C₂³×C₃	1	2	yes	—
242	#107	C₂³×C₃	1	1	yes	characteristic
243	#107	C₂³×C₃	1	1	yes	characteristic
244	#106	—	2	1	no	—
245	#103	—	2	1	no	—
246	#103	—	2	1	no	—
247	#102	—	2	1	no	—
248	#102	—	2	1	no	—
249	C₄×C₈	C₃×D₄	1	1	yes	characteristic
250	C₄×C₈	C₃×D₄	1	1	yes	characteristic
251	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
252	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
253	C₂³×C₃	—	4	1	no	—
254	C₂³×C₃	—	4	2	no	—
255	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
256	C₃×Q₈	—	2	2	no	—
257	C₃×Q₈	—	4	1	no	—
258	C₃×Q₈	—	4	2	no	—
259	C₃×Q₈	—	4	2	no	—
260	C₃×D₄	—	2	2	no	—
261	C₃×D₄	—	4	4	no	—
262	C₃×D₄	—	4	2	no	—
263	C₃×D₄	—	4	1	no	—
264	C₃×D₄	—	4	2	no	—
265	C₃×D₄	—	8	2	no	—
266	C₃×D₄	—	8	4	no	—
267	C₃×D₄	—	8	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	4	1	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	—	4	4	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	—	4	1	no	—
274	C₂×C₃×C₄	—	4	2	no	—
275	C₂×C₃×C₄	—	8	2	no	—
276	C₂×C₃×C₄	—	8	4	no	—
277	C₂×C₃×C₄	—	8	2	no	—
278	C₂×C₃×C₄	#121	1	2	yes	—
279	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
284	C₂×C₃×C₄	AGL(1,ℤ/8)	1	2	yes	—
285	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
286	C₃×C₈	—	2	1	no	—
287	C₃×C₈	—	2	1	no	—
288	C₃×C₈	#121	1	2	yes	—
289	C₃×C₈	C₂²×D₄	1	1	yes	characteristic
290	C₃×C₈	C₂×#41	1	1	yes	characteristic
291	#41	—	2	4	no	—
292	#41	—	4	2	no	—
293	#41	—	4	4	no	—
294	#41	—	4	4	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	C₃×D₈	1	1	yes	characteristic
308	C₂²×C₄	C₃×D₈	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	2	1	no	—
312	Q₁₆	—	2	2	no	—
313	Q₁₆	—	4	2	no	—
314	Q₁₆	C₂×C₃×D₄	1	2	yes	—
315	SD₁₆	—	2	4	no	—
316	SD₁₆	—	4	4	no	—
317	SD₁₆	—	4	4	no	—
318	D₈	—	2	2	no	—
319	D₈	—	2	1	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	2	no	—
322	D₈	C₂×C₃×D₄	1	2	yes	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
325	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
326	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
327	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
328	C₂×C₈	C₃×#41	1	2	yes	—
329	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	C₃×D₈	1	1	yes	characteristic
345	C₄²	C₃×D₈	1	1	yes	characteristic
346	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
347	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
348	C₁₆	—	2	2	no	—
349	C₁₆	—	2	2	no	—
350	C₂²×C₃	—	2	1	no	—
351	C₂²×C₃	—	2	1	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	8	1	no	—
354	C₂²×C₃	—	8	1	no	—
355	C₂²×C₃	—	8	2	no	—
356	C₂²×C₃	—	8	2	no	—
357	C₂²×C₃	—	8	2	no	—
358	C₂²×C₃	#459	1	2	yes	—
359	C₂²×C₃	C₂²×D₈	1	1	yes	characteristic
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	2	1	no	—
362	C₃×C₄	—	2	1	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	—	8	1	no	—
365	C₃×C₄	—	8	1	no	—
366	C₃×C₄	—	8	2	no	—
367	C₃×C₄	#459	1	2	yes	—
368	C₃×C₄	#508	1	2	yes	complemented
369	C₃×C₄	C₂×#121	1	1	yes	characteristic
370	C₃×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
374	Q₈	—	2	2	no	—
375	Q₈	—	4	1	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	D₄	—	2	2	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	1	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	2	no	—
384	D₄	—	8	4	no	—
385	D₄	—	8	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	8	4	no	—
396	C₂×C₄	C₃×#121	1	2	yes	—
397	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
398	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
399	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
400	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
401	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
402	C₂×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
403	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	C₃×#121	1	2	yes	—
407	C₈	C₂²×C₃×D₄	1	1	yes	characteristic
408	C₈	C₂×C₃×#41	1	1	yes	characteristic
409	C₂×C₃	—	2	2	no	—
410	C₂×C₃	—	8	2	no	—
411	C₂×C₃	—	16	2	no	—
412	C₂×C₃	C₂×#459	1	1	yes	characteristic
413	C₂×C₃	C₂×#508	1	1	yes	characteristic
414	C₂×C₃	#3414	1	1	yes	characteristic
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	C₃×#459	1	2	yes	—
424	C₂²	C₂²×C₃×D₈	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	2	no	—
432	C₄	C₃×#459	1	2	yes	—
433	C₄	C₃×#508	1	2	yes	complemented
434	C₄	C₂×C₃×#121	1	1	yes	characteristic
435	C₄	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
436	C₃	#33579	1	1	yes	characteristic, direct product factor, Sylow
437	C₂	—	2	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂×C₃×#459	1	1	yes	characteristic
441	C₂	C₂×C₃×#508	1	1	yes	characteristic
442	C₂	C₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃
socle	C₂²×C₃	C₂²×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#508	C₂	semidirect
2. C₃×#3147	C₂	semidirect
3. C₃×C₄×#135	C₂	semidirect
4. C₃×#2211	C₂	semidirect
5. C₃×#2210	C₂	semidirect
6. C₃×#2209	C₂	semidirect
7. C₃×#2208	C₂	semidirect
8. C₃×#2207	C₂	semidirect
9. C₃×#2206	C₂	semidirect
10. C₂×C₃×C₄⋊C₁₆	C₂	semidirect
11. C₃×#2138	C₂	semidirect
12. #33579	C₃	direct (N × H)
45. C₂×#508	C₂×C₃	semidirect
46. #3147	C₂×C₃	semidirect
47. C₄×#135	C₂×C₃	semidirect
48. #2211	C₂×C₃	semidirect
49. #2210	C₂×C₃	semidirect
50. #2209	C₂×C₃	semidirect
51. #2208	C₂×C₃	semidirect
52. #2207	C₂×C₃	semidirect
53. #2206	C₂×C₃	semidirect
54. C₂×C₄⋊C₁₆	C₂×C₃	semidirect
55. #2138	C₂×C₃	semidirect
62. C₃×#135	D₄	semidirect
206. #135	C₃×D₄	semidirect
368. C₃×C₄	#508	semidirect
433. C₄	C₃×#508	semidirect
436. C₃	#33579	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×#508	2
C₃×#3147	2
C₃×C₄×#135	2
C₃×#2211	2
C₃×#2210	2
C₃×#2209	2
C₃×#2208	2
C₃×#2207	2
C₃×#2206	2
C₂×C₃×C₄⋊C₁₆	2
C₃×#2138	2
#33579	3

Subgroups — C3×#33579 #10652186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33579 #10652186