Subgroups — C₃×#33777 #10652384

Order 768.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2249	C₂	1	2	yes	maximal, complemented
4	C₃×#2242	C₂	1	2	yes	maximal, complemented
5	C₃×#2211	C₂	1	2	yes	maximal, complemented
6	C₃×#2210	C₂	1	2	yes	maximal, complemented
7	C₃×#2188	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2187	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2185	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2184	C₂	1	1	yes	maximal, characteristic
11	C₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	#33777	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃×SD₁₆	—	2	1	no	—
15	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic
16	C₃×#529	—	2	1	no	—
17	C₂×C₃×#124	—	2	1	no	—
18	C₂×C₃×Q₃₂	C₂²	1	2	yes	complemented
19	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₃×SD₃₂	C₂²	1	2	yes	complemented
21	C₂×C₃×D₁₆	C₂²	1	2	yes	—
22	C₃×#499	C₂²	1	1	yes	characteristic, complemented
23	C₃×#495	—	2	1	no	—
24	C₃×#495	—	2	1	no	—
25	C₃×#495	C₂²	1	2	yes	—
26	C₃×#495	C₂²	1	2	yes	—
27	C₃×#495	C₂²	1	1	yes	characteristic, complemented
28	C₃×#488	—	2	1	no	—
29	C₃×#467	C₂²	1	1	yes	characteristic
30	C₃×#466	C₂²	1	1	yes	characteristic
31	C₃×#465	—	2	1	no	—
32	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₄×SD₁₆	—	2	1	no	—
34	C₃×C₄×D₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
37	C₃×#358	C₂²	1	2	yes	complemented
38	C₃×#358	C₂²	1	2	yes	complemented
39	C₃×#357	C₂²	1	2	yes	—
40	C₃×#357	C₂²	1	2	yes	—
41	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
43	C₃×C₄×C₁₆	C₂²	1	2	yes	complemented
44	#3168	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#495	C₂×C₃	1	1	yes	characteristic, complemented
46	#2249	C₂×C₃	1	2	yes	complemented
47	#2242	C₂×C₃	1	2	yes	complemented
48	#2211	C₂×C₃	1	2	yes	complemented
49	#2210	C₂×C₃	1	2	yes	complemented
50	#2188	C₂×C₃	1	1	yes	characteristic, complemented
51	#2187	C₂×C₃	1	1	yes	characteristic, complemented
52	#2185	C₂×C₃	1	1	yes	characteristic, complemented
53	#2184	C₂×C₃	1	1	yes	characteristic
54	#2162	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂²×C₃×Q₈	—	2	1	no	—
56	C₂²×C₃×D₄	—	2	1	no	—
57	C₂×C₃×Q₁₆	—	2	1	no	—
58	C₂×C₃×Q₁₆	—	4	2	no	—
59	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
61	C₂×C₃×SD₁₆	—	2	2	no	—
62	C₂×C₃×SD₁₆	—	2	2	no	—
63	C₂×C₃×SD₁₆	—	2	1	no	—
64	C₂×C₃×SD₁₆	—	4	4	no	—
65	C₂×C₃×D₈	—	2	1	no	—
66	C₂×C₃×D₈	—	4	2	no	—
67	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
68	C₂×C₃×D₈	C₂³	1	2	yes	—
69	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
70	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
71	C₃×#126	—	4	1	no	—
72	C₃×#125	—	2	1	no	—
73	C₃×#124	—	2	2	no	—
74	C₃×#124	—	2	2	no	—
75	C₃×#124	—	2	1	no	—
76	C₃×#124	—	4	1	no	—
77	C₃×#124	—	4	1	no	—
78	C₃×#123	—	4	1	no	—
79	C₃×C₂²⋊Q₈	—	2	1	no	—
80	C₃×#121	—	2	1	no	—
81	C₃×C₄×Q₈	—	2	1	no	—
82	C₃×C₄×D₄	—	2	1	no	—
83	C₃×C₄×D₄	—	4	1	no	—
84	C₃×#117	—	4	1	no	—
85	C₂×C₃×C₂²⋊C₄	—	4	1	no	—
86	C₂×C₃×C₂²⋊C₄	—	4	1	no	—
87	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
88	C₃×Q₃₂	—	4	2	no	—
89	C₃×SD₃₂	—	4	2	no	—
90	C₃×SD₃₂	—	4	2	no	—
91	C₃×D₁₆	—	4	2	no	—
92	C₂×C₃×C₁₆	C₂³	1	2	yes	—
93	C₂×C₃×C₁₆	C₂³	1	2	yes	—
94	C₃×#107	C₂³	1	1	yes	characteristic
95	C₃×#107	C₂³	1	1	yes	characteristic
96	C₃×#106	—	2	1	no	—
97	C₃×#103	—	2	1	no	—
98	C₃×#103	—	2	1	no	—
99	C₃×#102	—	2	1	no	—
100	C₃×#102	—	2	1	no	—
101	C₃×C₄×C₈	D₄	1	1	yes	characteristic
102	C₃×C₄×C₈	D₄	1	1	yes	characteristic
103	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
104	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
105	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
106	C₂²×SD₁₆	—	2	1	no	—
107	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic
108	#529	—	2	1	no	—
109	C₂×#124	—	2	1	no	—
110	C₂×Q₃₂	C₂²×C₃	1	2	yes	complemented
111	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
112	C₂×SD₃₂	C₂²×C₃	1	2	yes	complemented
113	C₂×D₁₆	C₂²×C₃	1	2	yes	—
114	#499	C₂²×C₃	1	1	yes	characteristic, complemented
115	#495	—	2	1	no	—
116	#495	—	2	1	no	—
117	#495	C₂²×C₃	1	2	yes	—
118	#495	C₂²×C₃	1	2	yes	—
119	#495	C₂²×C₃	1	1	yes	characteristic, complemented
120	#488	—	2	1	no	—
121	#467	C₂²×C₃	1	1	yes	characteristic
122	#466	C₂²×C₃	1	1	yes	characteristic
123	#465	—	2	1	no	—
124	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₄×SD₁₆	—	2	1	no	—
126	C₄×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
128	C₄⋊C₁₆	C₂²×C₃	1	2	yes	complemented
129	#358	C₂²×C₃	1	2	yes	complemented
130	#358	C₂²×C₃	1	2	yes	complemented
131	#357	C₂²×C₃	1	2	yes	—
132	#357	C₂²×C₃	1	2	yes	—
133	C₂²⋊C₁₆	C₂²×C₃	1	1	yes	characteristic
134	C₂²⋊C₁₆	C₂²×C₃	1	1	yes	characteristic
135	C₄×C₁₆	C₂²×C₃	1	2	yes	complemented
136	C₂⁴×C₃	—	4	1	no	—
137	C₂×C₃×Q₈	—	2	1	no	—
138	C₂×C₃×Q₈	—	2	2	no	—
139	C₂×C₃×Q₈	—	4	2	no	—
140	C₂×C₃×Q₈	—	4	2	no	—
141	C₂×C₃×Q₈	—	4	1	no	—
142	C₂×C₃×D₄	—	2	1	no	—
143	C₂×C₃×D₄	—	2	2	no	—
144	C₂×C₃×D₄	—	4	2	no	—
145	C₂×C₃×D₄	—	4	2	no	—
146	C₂×C₃×D₄	—	4	1	no	—
147	C₂×C₃×D₄	—	4	1	no	—
148	C₂²×C₃×C₄	—	4	1	no	—
149	C₂²×C₃×C₄	—	4	1	no	—
150	C₂²×C₃×C₄	D₈	1	1	yes	characteristic
151	C₂²×C₃×C₄	D₈	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
153	C₃×Q₁₆	—	2	2	no	—
154	C₃×Q₁₆	—	2	2	no	—
155	C₃×Q₁₆	—	2	2	no	—
156	C₃×Q₁₆	—	4	2	no	—
157	C₃×SD₁₆	—	4	4	no	—
158	C₃×SD₁₆	—	4	2	no	—
159	C₃×SD₁₆	—	4	4	no	—
160	C₃×D₈	—	2	2	no	—
161	C₃×D₈	—	2	2	no	—
162	C₃×D₈	—	2	2	no	—
163	C₃×D₈	—	4	2	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
170	C₃×C₄⋊C₄	—	2	1	no	—
171	C₃×C₄⋊C₄	—	2	1	no	—
172	C₃×C₄⋊C₄	—	4	1	no	—
173	C₃×C₄⋊C₄	—	4	1	no	—
174	C₃×C₄⋊C₄	—	4	1	no	—
175	C₃×C₄⋊C₄	—	4	1	no	—
176	C₃×C₂²⋊C₄	—	4	1	no	—
177	C₃×C₂²⋊C₄	—	4	2	no	—
178	C₃×C₂²⋊C₄	—	4	2	no	—
179	C₃×C₂²⋊C₄	—	4	2	no	—
180	C₃×C₂²⋊C₄	—	4	2	no	—
181	C₃×C₂²⋊C₄	—	4	1	no	—
182	C₃×C₂²⋊C₄	—	4	1	no	—
183	C₃×C₂²⋊C₄	—	4	1	no	—
184	C₃×C₂²⋊C₄	—	4	1	no	—
185	C₃×C₄²	—	4	1	no	—
186	C₃×C₄²	D₈	1	1	yes	characteristic
187	C₃×C₄²	D₈	1	1	yes	characteristic
188	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
189	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
190	C₃×C₁₆	—	2	2	no	—
191	C₃×C₁₆	—	2	2	no	—
192	C₂²×Q₈	—	2	1	no	—
193	C₂²×D₄	—	2	1	no	—
194	C₂×Q₁₆	—	2	1	no	—
195	C₂×Q₁₆	—	4	2	no	—
196	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
197	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
198	C₂×SD₁₆	—	2	2	no	—
199	C₂×SD₁₆	—	2	2	no	—
200	C₂×SD₁₆	—	2	1	no	—
201	C₂×SD₁₆	—	4	4	no	—
202	C₂×D₈	—	2	1	no	—
203	C₂×D₈	—	4	2	no	—
204	C₂×D₈	C₂³×C₃	1	2	yes	—
205	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
206	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
208	#126	—	4	1	no	—
209	#125	—	2	1	no	—
210	#124	—	2	2	no	—
211	#124	—	2	2	no	—
212	#124	—	2	1	no	—
213	#124	—	4	1	no	—
214	#124	—	4	1	no	—
215	#123	—	4	1	no	—
216	C₂²⋊Q₈	—	2	1	no	—
217	#121	—	2	1	no	—
218	C₄×Q₈	—	2	1	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	—	4	1	no	—
221	#117	—	4	1	no	—
222	C₂×C₂²⋊C₄	—	4	1	no	—
223	C₂×C₂²⋊C₄	—	4	1	no	—
224	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
225	Q₃₂	—	4	2	no	—
226	SD₃₂	—	4	2	no	—
227	SD₃₂	—	4	2	no	—
228	D₁₆	—	4	2	no	—
229	C₂×C₁₆	C₂³×C₃	1	2	yes	—
230	C₂×C₁₆	C₂³×C₃	1	2	yes	—
231	#107	C₂³×C₃	1	1	yes	characteristic
232	#107	C₂³×C₃	1	1	yes	characteristic
233	#106	—	2	1	no	—
234	#103	—	2	1	no	—
235	#103	—	2	1	no	—
236	#102	—	2	1	no	—
237	#102	—	2	1	no	—
238	C₄×C₈	C₃×D₄	1	1	yes	characteristic
239	C₄×C₈	C₃×D₄	1	1	yes	characteristic
240	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
241	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
242	C₂³×C₃	—	4	1	no	—
243	C₂³×C₃	—	4	2	no	—
244	C₂³×C₃	—	8	2	no	—
245	C₂³×C₃	—	8	2	no	—
246	C₂³×C₃	—	8	2	no	—
247	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
248	C₃×Q₈	—	4	2	no	—
249	C₃×Q₈	—	4	1	no	—
250	C₃×Q₈	—	4	2	no	—
251	C₃×Q₈	—	4	1	no	—
252	C₃×Q₈	—	8	2	no	—
253	C₃×D₄	—	4	2	no	—
254	C₃×D₄	—	4	1	no	—
255	C₃×D₄	—	4	2	no	—
256	C₃×D₄	—	4	1	no	—
257	C₃×D₄	—	8	2	no	—
258	C₃×D₄	—	8	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	4	1	no	—
263	C₂×C₃×C₄	—	4	1	no	—
264	C₂×C₃×C₄	—	4	1	no	—
265	C₂×C₃×C₄	—	4	2	no	—
266	C₂×C₃×C₄	—	4	1	no	—
267	C₂×C₃×C₄	—	8	2	no	—
268	C₂×C₃×C₄	—	8	2	no	—
269	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
275	C₃×C₈	—	2	1	no	—
276	C₃×C₈	—	2	1	no	—
277	C₃×C₈	AGL(1,ℤ/8)	1	2	yes	—
278	C₃×C₈	H(5,𝔽₂)	1	2	yes	—
279	C₂⁴	—	4	1	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	C₃×D₈	1	1	yes	characteristic
294	C₂²×C₄	C₃×D₈	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	—	4	2	no	—
300	SD₁₆	—	4	4	no	—
301	SD₁₆	—	4	4	no	—
302	SD₁₆	—	4	2	no	—
303	D₈	—	2	2	no	—
304	D₈	—	2	2	no	—
305	D₈	—	2	2	no	—
306	D₈	—	4	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
310	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
311	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₄²	—	4	1	no	—
329	C₄²	C₃×D₈	1	1	yes	characteristic
330	C₄²	C₃×D₈	1	1	yes	characteristic
331	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
332	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
333	C₁₆	—	2	2	no	—
334	C₁₆	—	2	2	no	—
335	C₂²×C₃	—	2	1	no	—
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	8	1	no	—
338	C₂²×C₃	—	8	2	no	—
339	C₂²×C₃	—	8	1	no	—
340	C₂²×C₃	—	8	2	no	—
341	C₂²×C₃	—	8	2	no	—
342	C₂²×C₃	—	8	1	no	—
343	C₂²×C₃	—	16	4	no	—
344	C₂²×C₃	#508	1	2	yes	—
345	C₂²×C₃	C₂²×D₈	1	1	yes	characteristic
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	8	1	no	—
352	C₃×C₄	—	8	1	no	—
353	C₃×C₄	—	8	2	no	—
354	C₃×C₄	—	8	1	no	—
355	C₃×C₄	#535	1	1	yes	characteristic
356	C₃×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₂³	—	4	1	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	—	8	2	no	—
362	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
363	Q₈	—	4	2	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	8	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	1	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
385	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
386	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
387	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
388	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
389	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	C₃×AGL(1,ℤ/8)	1	2	yes	—
393	C₈	C₃×H(5,𝔽₂)	1	2	yes	—
394	C₂×C₃	—	2	2	no	—
395	C₂×C₃	—	16	1	no	—
396	C₂×C₃	—	16	2	no	—
397	C₂×C₃	#3205	1	1	yes	characteristic
398	C₂×C₃	C₂×#508	1	1	yes	characteristic
399	C₂×C₃	#3414	1	1	yes	characteristic
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	16	4	no	—
409	C₂²	C₃×#508	1	2	yes	—
410	C₂²	C₂²×C₃×D₈	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	8	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	1	no	—
420	C₄	C₃×#535	1	1	yes	characteristic
421	C₄	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
422	C₃	#33777	1	1	yes	characteristic, direct product factor, Sylow
423	C₂	—	2	2	no	—
424	C₂	—	16	2	no	—
425	C₂	—	16	1	no	—
426	C₂	C₃×#3205	1	1	yes	characteristic
427	C₂	C₂×C₃×#508	1	1	yes	characteristic
428	C₂	C₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃
prime radical	C₃×#2184	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ 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. C₃×#3168	C₂	semidirect
2. C₂×C₃×#495	C₂	semidirect
3. C₃×#2249	C₂	semidirect
4. C₃×#2242	C₂	semidirect
5. C₃×#2211	C₂	semidirect
6. C₃×#2210	C₂	semidirect
7. C₃×#2188	C₂	semidirect
8. C₃×#2187	C₂	semidirect
9. C₃×#2185	C₂	semidirect
11. C₃×#2162	C₂	semidirect
12. #33777	C₃	direct (N × H)
18. C₂×C₃×Q₃₂	C₂²	semidirect
20. C₂×C₃×SD₃₂	C₂²	semidirect
22. C₃×#499	C₂²	semidirect
27. C₃×#495	C₂²	semidirect
32. C₃×C₄×Q₁₆	C₂²	semidirect
34. C₃×C₄×D₈	C₂²	semidirect
36. C₃×C₄⋊C₁₆	C₂²	semidirect
37. C₃×#358	C₂²	semidirect
38. C₃×#358	C₂²	semidirect
43. C₃×C₄×C₁₆	C₂²	semidirect
44. #3168	C₂×C₃	semidirect
45. C₂×#495	C₂×C₃	semidirect
46. #2249	C₂×C₃	semidirect
47. #2242	C₂×C₃	semidirect
48. #2211	C₂×C₃	semidirect
49. #2210	C₂×C₃	semidirect
50. #2188	C₂×C₃	semidirect
51. #2187	C₂×C₃	semidirect
52. #2185	C₂×C₃	semidirect
54. #2162	C₂×C₃	semidirect
110. C₂×Q₃₂	C₂²×C₃	semidirect
112. C₂×SD₃₂	C₂²×C₃	semidirect
114. #499	C₂²×C₃	semidirect
119. #495	C₂²×C₃	semidirect
124. C₄×Q₁₆	C₂²×C₃	semidirect
126. C₄×D₈	C₂²×C₃	semidirect
128. C₄⋊C₁₆	C₂²×C₃	semidirect
129. #358	C₂²×C₃	semidirect
130. #358	C₂²×C₃	semidirect
135. C₄×C₁₆	C₂²×C₃	semidirect
422. C₃	#33777	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3168	2
C₂×C₃×#495	2
C₃×#2249	2
C₃×#2242	2
C₃×#2211	2
C₃×#2210	2
C₃×#2188	2
C₃×#2187	2
C₃×#2185	2
C₃×#2184	2
C₃×#2162	2
#33777	3

Subgroups — C3×#33777 #10652384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33777 #10652384