Subgroups — C₃×#34253 #10652860

Order 768.

2426 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#520	C₂	1	1	yes	maximal, characteristic
2	C₃×#2353	C₂	1	4	yes	maximal, complemented
3	C₃×#2352	C₂	1	4	yes	maximal, complemented
4	C₃×#2347	C₂	1	2	yes	maximal, complemented
5	C₃×#2346	C₂	1	2	yes	maximal, complemented
6	C₃×#2345	C₂	1	2	yes	maximal, complemented
7	C₃×#2344	C₂	1	2	yes	maximal, complemented
8	C₃×#2320	C₂	1	2	yes	maximal, complemented
9	C₃×#2319	C₂	1	2	yes	maximal, complemented
10	C₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2311	C₂	1	1	yes	maximal, characteristic
12	C₃×#2297	C₂	1	1	yes	maximal, characteristic
13	C₃×#2295	C₂	1	2	yes	maximal, complemented
14	C₃×#2293	C₂	1	2	yes	maximal, complemented
15	C₂×C₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	#34253	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
20	C₃×#520	C₄	1	16	yes	complemented
21	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
22	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
23	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
24	C₂×C₃×#117	C₂²	1	1	yes	characteristic
25	C₂×C₃×#117	C₂²	1	1	yes	characteristic
26	C₂×C₃×#117	C₂²	1	4	yes	—
27	C₂×C₃×#117	C₂²	1	1	yes	characteristic
28	C₂×C₃×#117	C₂²	1	2	yes	—
29	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
34	C₃×#391	C₂²	1	1	yes	characteristic
35	C₃×#391	C₂²	1	2	yes	—
36	C₃×#391	C₂²	1	1	yes	characteristic
37	C₃×#390	C₂²	1	1	yes	characteristic
38	C₃×#390	C₂²	1	2	yes	—
39	C₃×#390	C₂²	1	1	yes	characteristic
40	C₃×#389	C₂²	1	2	yes	—
41	C₃×#389	C₂²	1	2	yes	—
42	C₃×#389	C₂²	1	2	yes	—
43	C₃×#389	C₂²	1	2	yes	—
44	C₃×#389	C₂²	1	2	yes	—
45	C₃×#389	C₂²	1	2	yes	—
46	C₃×#389	C₂²	1	2	yes	—
47	C₃×#389	C₂²	1	2	yes	—
48	C₃×#388	C₂²	1	4	yes	—
49	C₃×#388	C₂²	1	4	yes	—
50	C₃×#388	C₂²	1	4	yes	—
51	C₃×#388	C₂²	1	4	yes	—
52	C₃×#387	C₂²	1	4	yes	—
53	C₃×#387	C₂²	1	4	yes	—
54	C₃×#387	C₂²	1	4	yes	—
55	C₃×#387	C₂²	1	4	yes	—
56	C₃×#386	C₂²	1	2	yes	—
57	C₃×#386	C₂²	1	2	yes	—
58	C₃×#386	C₂²	1	4	yes	—
59	C₃×#383	C₂²	1	4	yes	—
60	C₃×#382	C₂²	1	4	yes	—
61	C₃×#381	C₂²	1	4	yes	—
62	C₃×#380	C₂²	1	2	yes	—
63	C₃×#380	C₂²	1	2	yes	—
64	C₃×#380	C₂²	1	4	yes	—
65	C₃×#380	C₂²	1	4	yes	—
66	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
71	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
72	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
73	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
74	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
75	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
77	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
78	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
79	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₃×#376	C₂²	1	2	yes	—
82	C₃×#376	C₂²	1	4	yes	—
83	C₂×C₃×#95	C₂²	1	2	yes	—
84	C₃×C₄³	C₂²	1	2	yes	—
85	C₂×#520	C₂×C₃	1	1	yes	characteristic
86	#2353	C₂×C₃	1	4	yes	complemented
87	#2352	C₂×C₃	1	4	yes	complemented
88	#2347	C₂×C₃	1	2	yes	complemented
89	#2346	C₂×C₃	1	2	yes	complemented
90	#2345	C₂×C₃	1	2	yes	complemented
91	#2344	C₂×C₃	1	2	yes	complemented
92	#2320	C₂×C₃	1	2	yes	complemented
93	#2319	C₂×C₃	1	2	yes	complemented
94	#2316	C₂×C₃	1	1	yes	characteristic, complemented
95	#2311	C₂×C₃	1	1	yes	characteristic
96	#2297	C₂×C₃	1	1	yes	characteristic
97	#2295	C₂×C₃	1	2	yes	complemented
98	#2293	C₂×C₃	1	2	yes	complemented
99	C₂×#389	C₂×C₃	1	1	yes	characteristic, complemented
100	#2274	C₂×C₃	1	1	yes	characteristic, complemented
101	C₄×#117	C₂×C₃	1	1	yes	characteristic, complemented
102	C₂×C₃×#41	—	2	4	no	—
103	C₂×C₃×#41	—	2	4	no	—
104	C₂×C₃×#41	C₂×C₄	1	8	yes	—
105	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂²×C₃×D₄	C₂³	1	2	yes	—
107	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
108	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
109	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
110	C₂³×C₃×C₄	C₂³	1	2	yes	—
111	C₂³×C₃×C₄	C₂³	1	2	yes	—
112	C₂³×C₃×C₄	C₂³	1	2	yes	—
113	C₂³×C₃×C₄	C₂³	1	4	yes	—
114	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
115	C₃×C₄×Q₈	C₂×C₄	1	16	yes	complemented
116	C₃×C₄×D₄	C₂×C₄	1	32	yes	—
117	C₃×C₄×D₄	C₂×C₄	1	16	yes	complemented
118	C₃×#117	—	2	4	no	—
119	C₃×#117	—	2	4	no	—
120	C₃×#117	—	4	8	no	—
121	C₃×#117	C₂×C₄	1	8	yes	—
122	C₃×#117	C₂×C₄	1	16	yes	complemented
123	C₂×C₃×C₄⋊C₄	—	2	4	no	—
124	C₂×C₃×C₄⋊C₄	—	4	4	no	—
125	C₂×C₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
126	C₂×C₃×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
127	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
134	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₃×C₄²	—	2	4	no	—
153	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₄²	C₂³	1	2	yes	—
155	C₂×C₃×C₄²	C₂³	1	2	yes	—
156	C₂×C₃×C₄²	C₂³	1	2	yes	—
157	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₄²	C₂³	1	2	yes	—
161	C₂×C₃×C₄²	C₂³	1	2	yes	—
162	C₂×C₃×C₄²	C₂³	1	2	yes	—
163	C₂×C₃×C₄²	C₂³	1	4	yes	—
164	C₂×C₃×C₄²	C₂³	1	4	yes	—
165	C₂×C₃×C₄²	C₂³	1	2	yes	—
166	C₂×C₃×C₄²	C₂³	1	4	yes	—
167	C₃×#95	C₂³	1	4	yes	—
168	C₃×#95	C₂³	1	4	yes	—
169	C₃×#95	C₂³	1	2	yes	—
170	C₃×#95	C₂³	1	2	yes	—
171	C₃×#95	C₂³	1	2	yes	—
172	C₃×#95	C₂³	1	2	yes	—
173	C₃×#95	C₂³	1	2	yes	—
174	C₃×#95	C₂³	1	4	yes	—
175	C₃×#95	C₂³	1	4	yes	—
176	C₃×#95	C₂³	1	4	yes	—
177	C₃×#95	C₂³	1	4	yes	—
178	C₃×#95	C₂³	1	2	yes	—
179	C₃×#95	C₂³	1	4	yes	—
180	C₃×#95	C₂³	1	2	yes	—
181	C₃×#95	C₂³	1	2	yes	—
182	C₃×#95	C₂³	1	4	yes	—
183	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
184	#520	C₃×C₄	1	16	yes	complemented
185	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
186	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
187	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
188	C₂×#117	C₂²×C₃	1	1	yes	characteristic
189	C₂×#117	C₂²×C₃	1	1	yes	characteristic
190	C₂×#117	C₂²×C₃	1	4	yes	—
191	C₂×#117	C₂²×C₃	1	1	yes	characteristic
192	C₂×#117	C₂²×C₃	1	2	yes	—
193	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
194	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
196	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
197	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
198	#391	C₂²×C₃	1	2	yes	—
199	#391	C₂²×C₃	1	1	yes	characteristic
200	#391	C₂²×C₃	1	1	yes	characteristic
201	#390	C₂²×C₃	1	2	yes	—
202	#390	C₂²×C₃	1	1	yes	characteristic
203	#390	C₂²×C₃	1	1	yes	characteristic
204	#389	C₂²×C₃	1	2	yes	—
205	#389	C₂²×C₃	1	2	yes	—
206	#389	C₂²×C₃	1	2	yes	—
207	#389	C₂²×C₃	1	2	yes	—
208	#389	C₂²×C₃	1	2	yes	—
209	#389	C₂²×C₃	1	2	yes	—
210	#389	C₂²×C₃	1	2	yes	—
211	#389	C₂²×C₃	1	2	yes	—
212	#388	C₂²×C₃	1	4	yes	—
213	#388	C₂²×C₃	1	4	yes	—
214	#388	C₂²×C₃	1	4	yes	—
215	#388	C₂²×C₃	1	4	yes	—
216	#387	C₂²×C₃	1	4	yes	—
217	#387	C₂²×C₃	1	4	yes	—
218	#387	C₂²×C₃	1	4	yes	—
219	#387	C₂²×C₃	1	4	yes	—
220	#386	C₂²×C₃	1	4	yes	—
221	#386	C₂²×C₃	1	2	yes	—
222	#386	C₂²×C₃	1	2	yes	—
223	#383	C₂²×C₃	1	4	yes	—
224	#382	C₂²×C₃	1	4	yes	—
225	#381	C₂²×C₃	1	4	yes	—
226	#380	C₂²×C₃	1	2	yes	—
227	#380	C₂²×C₃	1	2	yes	—
228	#380	C₂²×C₃	1	4	yes	—
229	#380	C₂²×C₃	1	4	yes	—
230	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
231	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
233	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
234	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
235	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
236	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
237	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
239	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
241	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
242	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
243	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
244	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
245	#376	C₂²×C₃	1	2	yes	—
246	#376	C₂²×C₃	1	4	yes	—
247	C₂×#95	C₂²×C₃	1	2	yes	—
248	C₄³	C₂²×C₃	1	2	yes	—
249	C₂⁴×C₃	C₂⁴	1	2	yes	—
250	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
251	C₃×#41	—	2	32	no	—
252	C₂×C₃×Q₈	—	2	2	no	—
253	C₂×C₃×Q₈	—	2	2	no	—
254	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
255	C₂×C₃×D₄	—	2	4	no	—
256	C₂×C₃×D₄	—	2	4	no	—
257	C₂×C₃×D₄	—	2	2	no	—
258	C₂×C₃×D₄	—	2	2	no	—
259	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
260	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
261	C₂²×C₃×C₄	—	2	4	no	—
262	C₂²×C₃×C₄	—	2	4	no	—
263	C₂²×C₃×C₄	—	2	2	no	—
264	C₂²×C₃×C₄	—	2	2	no	—
265	C₂²×C₃×C₄	—	2	4	no	—
266	C₂²×C₃×C₄	—	2	2	no	—
267	C₂²×C₃×C₄	—	2	2	no	—
268	C₂²×C₃×C₄	—	4	2	no	—
269	C₂²×C₃×C₄	—	4	4	no	—
270	C₂²×C₃×C₄	—	4	1	no	—
271	C₂²×C₃×C₄	—	4	1	no	—
272	C₂²×C₃×C₄	—	4	4	no	—
273	C₂²×C₃×C₄	—	4	2	no	—
274	C₂²×C₃×C₄	—	4	2	no	—
275	C₂²×C₃×C₄	—	4	2	no	—
276	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
277	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
278	C₂²×C₃×C₄	C₂²×C₄	1	16	yes	—
279	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
280	C₂²×C₃×C₄	#41	1	4	yes	—
281	C₂²×C₃×C₄	#41	1	4	yes	—
282	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
283	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
284	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
285	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
286	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
287	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
288	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
289	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
290	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
291	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
292	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
293	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
294	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
295	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
296	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
297	C₃×C₄⋊C₄	—	2	4	no	—
298	C₃×C₄⋊C₄	—	2	4	no	—
299	C₃×C₄⋊C₄	—	2	2	no	—
300	C₃×C₄⋊C₄	—	2	2	no	—
301	C₃×C₄⋊C₄	—	2	2	no	—
302	C₃×C₄⋊C₄	—	2	2	no	—
303	C₃×C₄⋊C₄	—	2	8	no	—
304	C₃×C₄⋊C₄	—	4	4	no	—
305	C₃×C₄⋊C₄	—	4	4	no	—
306	C₃×C₄⋊C₄	—	4	4	no	—
307	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
308	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
309	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
310	C₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
311	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
312	C₃×C₂²⋊C₄	—	2	4	no	—
313	C₃×C₂²⋊C₄	—	2	4	no	—
314	C₃×C₂²⋊C₄	—	2	4	no	—
315	C₃×C₂²⋊C₄	—	2	4	no	—
316	C₃×C₂²⋊C₄	—	4	2	no	—
317	C₃×C₂²⋊C₄	—	4	4	no	—
318	C₃×C₂²⋊C₄	—	4	2	no	—
319	C₃×C₂²⋊C₄	—	4	4	no	—
320	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
321	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
322	C₃×C₄²	—	2	2	no	—
323	C₃×C₄²	—	2	2	no	—
324	C₃×C₄²	—	2	2	no	—
325	C₃×C₄²	—	2	2	no	—
326	C₃×C₄²	—	2	4	no	—
327	C₃×C₄²	—	2	4	no	—
328	C₃×C₄²	—	2	4	no	—
329	C₃×C₄²	—	2	4	no	—
330	C₃×C₄²	—	4	2	no	—
331	C₃×C₄²	—	4	4	no	—
332	C₃×C₄²	—	4	2	no	—
333	C₃×C₄²	—	4	4	no	—
334	C₃×C₄²	C₂²×C₄	1	8	yes	—
335	C₃×C₄²	C₂²×C₄	1	16	yes	—
336	C₂×#41	—	2	4	no	—
337	C₂×#41	—	2	4	no	—
338	C₂×#41	C₂×C₃×C₄	1	8	yes	—
339	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
340	C₂²×D₄	C₂³×C₃	1	2	yes	—
341	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₃	1	2	yes	—
345	C₂³×C₄	C₂³×C₃	1	2	yes	—
346	C₂³×C₄	C₂³×C₃	1	2	yes	—
347	C₂³×C₄	C₂³×C₃	1	4	yes	—
348	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
349	C₄×Q₈	C₂×C₃×C₄	1	16	yes	complemented
350	C₄×D₄	C₂×C₃×C₄	1	32	yes	—
351	C₄×D₄	C₂×C₃×C₄	1	16	yes	complemented
352	#117	—	2	4	no	—
353	#117	—	2	4	no	—
354	#117	—	4	8	no	—
355	#117	C₂×C₃×C₄	1	8	yes	—
356	#117	C₂×C₃×C₄	1	16	yes	complemented
357	C₂×C₄⋊C₄	—	2	4	no	—
358	C₂×C₄⋊C₄	—	4	4	no	—
359	C₂×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
360	C₂×C₄⋊C₄	C₂×C₃×C₄	1	16	yes	complemented
361	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
386	C₂×C₄²	—	2	4	no	—
387	C₂×C₄²	C₂³×C₃	1	2	yes	—
388	C₂×C₄²	C₂³×C₃	1	2	yes	—
389	C₂×C₄²	C₂³×C₃	1	2	yes	—
390	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₃	1	2	yes	—
392	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₃	1	4	yes	—
396	C₂×C₄²	C₂³×C₃	1	2	yes	—
397	C₂×C₄²	C₂³×C₃	1	2	yes	—
398	C₂×C₄²	C₂³×C₃	1	4	yes	—
399	C₂×C₄²	C₂³×C₃	1	2	yes	—
400	C₂×C₄²	C₂³×C₃	1	4	yes	—
401	#95	C₂³×C₃	1	4	yes	—
402	#95	C₂³×C₃	1	4	yes	—
403	#95	C₂³×C₃	1	2	yes	—
404	#95	C₂³×C₃	1	2	yes	—
405	#95	C₂³×C₃	1	2	yes	—
406	#95	C₂³×C₃	1	2	yes	—
407	#95	C₂³×C₃	1	2	yes	—
408	#95	C₂³×C₃	1	4	yes	—
409	#95	C₂³×C₃	1	4	yes	—
410	#95	C₂³×C₃	1	4	yes	—
411	#95	C₂³×C₃	1	4	yes	—
412	#95	C₂³×C₃	1	2	yes	—
413	#95	C₂³×C₃	1	4	yes	—
414	#95	C₂³×C₃	1	2	yes	—
415	#95	C₂³×C₃	1	2	yes	—
416	#95	C₂³×C₃	1	4	yes	—
417	C₂³×C₃	—	2	1	no	—
418	C₂³×C₃	—	2	1	no	—
419	C₂³×C₃	—	2	1	no	—
420	C₂³×C₃	—	2	1	no	—
421	C₂³×C₃	—	2	2	no	—
422	C₂³×C₃	—	2	2	no	—
423	C₂³×C₃	—	2	2	no	—
424	C₂³×C₃	—	2	2	no	—
425	C₂³×C₃	—	2	2	no	—
426	C₂³×C₃	—	2	2	no	—
427	C₂³×C₃	C₂³×C₄	1	4	yes	—
428	C₂³×C₃	C₂³×C₄	1	2	yes	—
429	C₂³×C₃	C₂×#41	1	2	yes	—
430	C₂³×C₃	C₂×#41	1	2	yes	—
431	C₂³×C₃	C₂⁵	1	1	yes	characteristic
432	C₃×Q₈	—	2	8	no	—
433	C₃×D₄	—	2	16	no	—
434	C₃×D₄	—	2	8	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	2	1	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	2	2	no	—
439	C₂×C₃×C₄	—	2	2	no	—
440	C₂×C₃×C₄	—	2	4	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	2	no	—
446	C₂×C₃×C₄	—	2	4	no	—
447	C₂×C₃×C₄	—	2	16	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	2	no	—
453	C₂×C₃×C₄	—	2	2	no	—
454	C₂×C₃×C₄	—	2	4	no	—
455	C₂×C₃×C₄	—	2	2	no	—
456	C₂×C₃×C₄	—	2	2	no	—
457	C₂×C₃×C₄	—	2	4	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	2	no	—
460	C₂×C₃×C₄	—	2	2	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	2	no	—
463	C₂×C₃×C₄	—	2	2	no	—
464	C₂×C₃×C₄	—	2	4	no	—
465	C₂×C₃×C₄	—	2	2	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	2	no	—
469	C₂×C₃×C₄	—	4	8	no	—
470	C₂×C₃×C₄	—	4	16	no	—
471	C₂×C₃×C₄	—	4	4	no	—
472	C₂×C₃×C₄	—	4	4	no	—
473	C₂×C₃×C₄	—	8	4	no	—
474	C₂×C₃×C₄	#117	1	16	yes	complemented
475	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
476	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
477	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
478	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
479	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
480	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
481	C₂×C₃×C₄	C₂×#41	1	2	yes	—
482	C₂×C₃×C₄	C₂×#41	1	2	yes	—
483	C₂×C₃×C₄	C₂×#41	1	2	yes	—
484	C₂×C₃×C₄	C₂×#41	1	2	yes	—
485	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
486	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
487	C₂⁴	C₂⁴×C₃	1	2	yes	—
488	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
489	#41	—	2	32	no	—
490	C₂×Q₈	—	2	2	no	—
491	C₂×Q₈	—	2	2	no	—
492	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
498	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	4	no	—
508	C₂²×C₄	—	4	1	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	—	4	4	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
515	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
516	C₂²×C₄	C₂²×C₃×C₄	1	16	yes	—
517	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
518	C₂²×C₄	C₃×#41	1	4	yes	—
519	C₂²×C₄	C₃×#41	1	4	yes	—
520	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
521	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
527	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	8	no	—
542	C₄⋊C₄	—	4	4	no	—
543	C₄⋊C₄	—	4	4	no	—
544	C₄⋊C₄	—	4	4	no	—
545	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
546	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
547	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
548	C₄⋊C₄	C₂²×C₃×C₄	1	16	yes	—
549	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	4	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	4	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
559	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
560	C₄²	—	2	2	no	—
561	C₄²	—	2	2	no	—
562	C₄²	—	2	2	no	—
563	C₄²	—	2	2	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	4	no	—
568	C₄²	—	4	4	no	—
569	C₄²	—	4	2	no	—
570	C₄²	—	4	4	no	—
571	C₄²	—	4	2	no	—
572	C₄²	C₂²×C₃×C₄	1	8	yes	—
573	C₄²	C₂²×C₃×C₄	1	16	yes	—
574	C₂²×C₃	—	2	2	no	—
575	C₂²×C₃	—	2	2	no	—
576	C₂²×C₃	—	2	2	no	—
577	C₂²×C₃	—	2	2	no	—
578	C₂²×C₃	—	2	2	no	—
579	C₂²×C₃	—	2	2	no	—
580	C₂²×C₃	—	2	4	no	—
581	C₂²×C₃	—	2	4	no	—
582	C₂²×C₃	—	2	4	no	—
583	C₂²×C₃	—	4	2	no	—
584	C₂²×C₃	—	4	2	no	—
585	C₂²×C₃	—	4	2	no	—
586	C₂²×C₃	—	4	2	no	—
587	C₂²×C₃	C₂×#117	1	4	yes	—
588	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
589	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
590	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
591	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
593	C₂²×C₃	#585	1	1	yes	characteristic
594	C₂²×C₃	#585	1	1	yes	characteristic
595	C₃×C₄	—	2	4	no	—
596	C₃×C₄	—	2	4	no	—
597	C₃×C₄	—	2	8	no	—
598	C₃×C₄	—	2	4	no	—
599	C₃×C₄	—	2	2	no	—
600	C₃×C₄	—	2	2	no	—
601	C₃×C₄	—	4	1	no	—
602	C₃×C₄	—	4	4	no	—
603	C₃×C₄	—	4	1	no	—
604	C₃×C₄	—	4	2	no	—
605	C₃×C₄	—	4	2	no	—
606	C₃×C₄	—	4	2	no	—
607	C₃×C₄	—	4	2	no	—
608	C₃×C₄	C₂×#117	1	4	yes	—
609	C₃×C₄	C₂×#117	1	4	yes	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	C₂³×C₃×C₄	1	4	yes	—
621	C₂³	C₂³×C₃×C₄	1	2	yes	—
622	C₂³	C₂×C₃×#41	1	2	yes	—
623	C₂³	C₂×C₃×#41	1	2	yes	—
624	C₂³	C₂⁵×C₃	1	1	yes	characteristic
625	Q₈	—	2	8	no	—
626	D₄	—	2	16	no	—
627	D₄	—	2	8	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	16	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	4	8	no	—
663	C₂×C₄	—	4	16	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	8	4	no	—
667	C₂×C₄	C₃×#117	1	16	yes	complemented
668	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
669	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
670	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
671	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
672	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
673	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
674	C₂×C₄	C₂×C₃×#41	1	2	yes	—
675	C₂×C₄	C₂×C₃×#41	1	2	yes	—
676	C₂×C₄	C₂×C₃×#41	1	2	yes	—
677	C₂×C₄	C₂×C₃×#41	1	2	yes	—
678	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
679	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
680	C₂×C₃	—	2	4	no	—
681	C₂×C₃	—	4	4	no	—
682	C₂×C₃	C₂²×#117	1	1	yes	characteristic
683	C₂×C₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
684	C₂×C₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
685	C₂×C₃	#3494	1	1	yes	characteristic
686	C₂×C₃	#3495	1	1	yes	characteristic
687	C₂×C₃	#3511	1	1	yes	characteristic
688	C₂×C₃	#3512	1	1	yes	characteristic
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	C₂×C₃×#117	1	4	yes	—
703	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
704	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
705	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
706	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
708	C₂²	C₃×#585	1	1	yes	characteristic
709	C₂²	C₃×#585	1	1	yes	characteristic
710	C₄	—	2	4	no	—
711	C₄	—	2	4	no	—
712	C₄	—	2	8	no	—
713	C₄	—	2	4	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	4	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	C₂×C₃×#117	1	4	yes	—
724	C₄	C₂×C₃×#117	1	4	yes	—
725	C₃	#34253	1	1	yes	characteristic, direct product factor, Sylow
726	C₂	—	2	4	no	—
727	C₂	—	4	4	no	—
728	C₂	C₂²×C₃×#117	1	1	yes	characteristic
729	C₂	C₃×C₄×H(5,𝔽₂)	1	1	yes	characteristic
730	C₂	C₃×C₄×2₋¹⁺⁴	1	1	yes	characteristic
731	C₂	C₃×#3494	1	1	yes	characteristic
732	C₂	C₃×#3495	1	1	yes	characteristic
733	C₂	C₃×#3511	1	1	yes	characteristic
734	C₂	C₃×#3512	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2353	C₂	semidirect
3. C₃×#2352	C₂	semidirect
4. C₃×#2347	C₂	semidirect
5. C₃×#2346	C₂	semidirect
6. C₃×#2345	C₂	semidirect
7. C₃×#2344	C₂	semidirect
8. C₃×#2320	C₂	semidirect
9. C₃×#2319	C₂	semidirect
10. C₃×#2316	C₂	semidirect
13. C₃×#2295	C₂	semidirect
14. C₃×#2293	C₂	semidirect
15. C₂×C₃×#389	C₂	semidirect
16. C₃×#2274	C₂	semidirect
17. C₃×C₄×#117	C₂	semidirect
18. #34253	C₃	direct (N × H)
20. C₃×#520	C₄	semidirect
86. #2353	C₂×C₃	semidirect
87. #2352	C₂×C₃	semidirect
88. #2347	C₂×C₃	semidirect
89. #2346	C₂×C₃	semidirect
90. #2345	C₂×C₃	semidirect
91. #2344	C₂×C₃	semidirect
92. #2320	C₂×C₃	semidirect
93. #2319	C₂×C₃	semidirect
94. #2316	C₂×C₃	semidirect
97. #2295	C₂×C₃	semidirect
98. #2293	C₂×C₃	semidirect
99. C₂×#389	C₂×C₃	semidirect
100. #2274	C₂×C₃	semidirect
101. C₄×#117	C₂×C₃	semidirect
115. C₃×C₄×Q₈	C₂×C₄	semidirect
117. C₃×C₄×D₄	C₂×C₄	semidirect
122. C₃×#117	C₂×C₄	semidirect
126. C₂×C₃×C₄⋊C₄	C₂×C₄	semidirect
184. #520	C₃×C₄	semidirect
349. C₄×Q₈	C₂×C₃×C₄	semidirect
351. C₄×D₄	C₂×C₃×C₄	semidirect
356. #117	C₂×C₃×C₄	semidirect
360. C₂×C₄⋊C₄	C₂×C₃×C₄	semidirect
474. C₂×C₃×C₄	#117	semidirect
667. C₂×C₄	C₃×#117	semidirect
725. C₃	#34253	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×#520	2
C₃×#2353	2
C₃×#2352	2
C₃×#2347	2
C₃×#2346	2
C₃×#2345	2
C₃×#2344	2
C₃×#2320	2
C₃×#2319	2
C₃×#2316	2
C₃×#2311	2
C₃×#2297	2
C₃×#2295	2
C₃×#2293	2
C₂×C₃×#389	2
C₃×#2274	2
C₃×C₄×#117	2
#34253	3

Subgroups — C3×#34253 #10652860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34253 #10652860