Subgroups — C₃×#37168 #10655775

Order 768.

1450 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2855	C₂	1	1	yes	maximal, characteristic
2	C₃×#2851	C₂	1	1	yes	maximal, characteristic
3	C₃×#2806	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2805	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2805	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2791	C₂	1	2	yes	maximal, complemented
7	C₃×#2770	C₂	1	2	yes	maximal
8	C₃×#2758	C₂	1	2	yes	maximal, complemented
9	C₃×#2739	C₂	1	2	yes	maximal
10	C₃×#2738	C₂	1	2	yes	maximal
11	C₃×#2726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2720	C₂	1	2	yes	maximal
13	C₃×#2634	C₂	1	2	yes	maximal, complemented
14	C₃×#2577	C₂	1	2	yes	maximal
15	C₃×#2556	C₂	1	2	yes	maximal
16	C₃×#2524	C₂	1	2	yes	maximal, complemented
17	C₃×#2506	C₂	1	2	yes	maximal, complemented
18	C₃×#2336	C₂	1	2	yes	maximal, complemented
19	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
20	#37168	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×#125	C₂²	1	2	yes	—
22	C₂×C₃×#125	C₂²	1	2	yes	—
23	C₂×C₃×#125	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
28	C₃×#400	C₂²	1	2	yes	—
29	C₃×#400	C₂²	1	2	yes	—
30	C₃×#400	C₂²	1	2	yes	—
31	C₃×#400	C₂²	1	2	yes	—
32	C₃×#400	C₂²	1	2	yes	—
33	C₃×#400	C₂²	1	2	yes	—
34	C₃×#400	C₂²	1	2	yes	—
35	C₃×#400	C₂²	1	2	yes	—
36	C₃×#400	C₂²	1	2	yes	—
37	C₃×#399	C₂²	1	2	yes	—
38	C₃×#398	C₂²	1	2	yes	—
39	C₃×#398	C₂²	1	2	yes	—
40	C₃×#398	C₂²	1	2	yes	—
41	C₃×#398	C₂²	1	2	yes	—
42	C₃×#398	C₂²	1	2	yes	—
43	C₃×#398	C₂²	1	2	yes	—
44	C₃×#398	C₂²	1	2	yes	—
45	C₃×#398	C₂²	1	2	yes	—
46	C₃×#397	C₂²	1	2	yes	—
47	C₃×#397	C₂²	1	2	yes	—
48	C₃×#396	C₂²	1	2	yes	—
49	C₃×#395	C₂²	1	2	yes	—
50	C₃×#395	C₂²	1	2	yes	—
51	C₃×#395	C₂²	1	2	yes	—
52	C₃×#391	C₂²	1	1	yes	characteristic
53	C₃×#391	C₂²	1	2	yes	—
54	C₃×#391	C₂²	1	1	yes	characteristic
55	C₃×#391	C₂²	1	1	yes	characteristic
56	C₃×#389	C₂²	1	2	yes	—
57	C₃×#389	C₂²	1	2	yes	—
58	C₃×#389	C₂²	1	1	yes	characteristic
59	C₃×#389	C₂²	1	1	yes	characteristic
60	C₃×#389	C₂²	1	1	yes	characteristic
61	C₃×#389	C₂²	1	2	yes	—
62	C₃×#389	C₂²	1	2	yes	—
63	C₃×#389	C₂²	1	2	yes	—
64	C₃×#389	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	2	yes	—
66	C₃×#389	C₂²	1	1	yes	characteristic
67	C₃×#388	C₂²	1	2	yes	—
68	C₃×#388	C₂²	1	2	yes	—
69	C₃×#388	C₂²	1	2	yes	—
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#387	C₂²	1	2	yes	—
72	C₃×#387	C₂²	1	2	yes	—
73	C₃×#387	C₂²	1	2	yes	—
74	C₃×#387	C₂²	1	2	yes	—
75	C₃×#387	C₂²	1	2	yes	—
76	C₃×#387	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	2	yes	—
87	C₃×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#385	C₂²	1	2	yes	—
90	C₃×#385	C₂²	1	2	yes	—
91	C₃×#385	C₂²	1	2	yes	—
92	C₃×#385	C₂²	1	2	yes	—
93	C₃×#384	C₂²	1	2	yes	—
94	C₃×#383	C₂²	1	2	yes	—
95	C₃×#383	C₂²	1	2	yes	—
96	C₃×#383	C₂²	1	2	yes	—
97	C₃×#382	C₂²	1	1	yes	characteristic
98	C₃×#381	C₂²	1	2	yes	—
99	C₃×#380	C₂²	1	1	yes	characteristic
100	C₃×#380	C₂²	1	1	yes	characteristic
101	C₃×#380	C₂²	1	1	yes	characteristic
102	C₃×#380	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
104	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
105	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
108	#2855	C₂×C₃	1	1	yes	characteristic
109	#2851	C₂×C₃	1	1	yes	characteristic
110	#2806	C₂×C₃	1	1	yes	characteristic, complemented
111	#2805	C₂×C₃	1	1	yes	characteristic, complemented
112	#2805	C₂×C₃	1	1	yes	characteristic, complemented
113	#2791	C₂×C₃	1	2	yes	complemented
114	#2770	C₂×C₃	1	2	yes	—
115	#2758	C₂×C₃	1	2	yes	complemented
116	#2739	C₂×C₃	1	2	yes	—
117	#2738	C₂×C₃	1	2	yes	—
118	#2726	C₂×C₃	1	1	yes	characteristic, complemented
119	#2720	C₂×C₃	1	2	yes	—
120	#2634	C₂×C₃	1	2	yes	complemented
121	#2577	C₂×C₃	1	2	yes	—
122	#2556	C₂×C₃	1	2	yes	—
123	#2524	C₂×C₃	1	2	yes	complemented
124	#2506	C₂×C₃	1	2	yes	complemented
125	#2336	C₂×C₃	1	2	yes	complemented
126	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
127	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
129	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
130	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
131	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
132	C₃×#125	—	2	8	no	—
133	C₃×#125	—	4	2	no	—
134	C₃×#125	—	4	4	no	—
135	C₃×C₂²⋊Q₈	—	2	4	no	—
136	C₃×C₂²⋊Q₈	—	4	2	no	—
137	C₃×C₄×Q₈	—	4	2	no	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₄²	—	4	2	no	—
177	C₂×C₃×C₄²	C₂³	1	2	yes	—
178	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄²	C₂³	1	2	yes	—
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄²	C₂³	1	2	yes	—
182	C₂×C₃×C₄²	C₂³	1	2	yes	—
183	C₂×C₃×C₄²	C₂³	1	2	yes	—
184	C₂×C₃×C₄²	C₂³	1	2	yes	—
185	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
187	C₃×#95	C₂³	1	2	yes	—
188	C₃×#95	C₂³	1	2	yes	—
189	C₃×#95	C₂³	1	2	yes	—
190	C₃×#95	C₂³	1	2	yes	—
191	C₃×#95	C₂³	1	2	yes	—
192	C₃×#95	C₂³	1	2	yes	—
193	C₃×#95	C₂³	1	2	yes	—
194	C₃×#95	C₂³	1	2	yes	—
195	C₃×#95	C₂³	1	2	yes	—
196	C₃×#95	C₂³	1	2	yes	—
197	C₃×#95	C₂³	1	2	yes	—
198	C₃×#95	C₂³	1	2	yes	—
199	C₃×#95	C₂³	1	2	yes	—
200	C₃×#95	C₂³	1	2	yes	—
201	C₃×#95	C₂³	1	2	yes	—
202	C₃×#95	C₂³	1	2	yes	—
203	C₃×#95	C₂³	1	2	yes	—
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	2	yes	—
206	C₃×#95	C₂³	1	2	yes	—
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	2	yes	—
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₂×#125	C₂²×C₃	1	2	yes	—
222	C₂×#125	C₂²×C₃	1	1	yes	characteristic
223	C₂×#125	C₂²×C₃	1	2	yes	—
224	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
225	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
227	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
228	#400	C₂²×C₃	1	2	yes	—
229	#400	C₂²×C₃	1	2	yes	—
230	#400	C₂²×C₃	1	2	yes	—
231	#400	C₂²×C₃	1	2	yes	—
232	#400	C₂²×C₃	1	2	yes	—
233	#400	C₂²×C₃	1	2	yes	—
234	#400	C₂²×C₃	1	2	yes	—
235	#400	C₂²×C₃	1	2	yes	—
236	#400	C₂²×C₃	1	2	yes	—
237	#399	C₂²×C₃	1	2	yes	—
238	#398	C₂²×C₃	1	2	yes	—
239	#398	C₂²×C₃	1	2	yes	—
240	#398	C₂²×C₃	1	2	yes	—
241	#398	C₂²×C₃	1	2	yes	—
242	#398	C₂²×C₃	1	2	yes	—
243	#398	C₂²×C₃	1	2	yes	—
244	#398	C₂²×C₃	1	2	yes	—
245	#398	C₂²×C₃	1	2	yes	—
246	#397	C₂²×C₃	1	2	yes	—
247	#397	C₂²×C₃	1	2	yes	—
248	#396	C₂²×C₃	1	2	yes	—
249	#395	C₂²×C₃	1	2	yes	—
250	#395	C₂²×C₃	1	2	yes	—
251	#395	C₂²×C₃	1	2	yes	—
252	#391	C₂²×C₃	1	1	yes	characteristic
253	#391	C₂²×C₃	1	1	yes	characteristic
254	#391	C₂²×C₃	1	2	yes	—
255	#391	C₂²×C₃	1	1	yes	characteristic
256	#389	C₂²×C₃	1	2	yes	—
257	#389	C₂²×C₃	1	2	yes	—
258	#389	C₂²×C₃	1	1	yes	characteristic
259	#389	C₂²×C₃	1	1	yes	characteristic
260	#389	C₂²×C₃	1	1	yes	characteristic
261	#389	C₂²×C₃	1	1	yes	characteristic
262	#389	C₂²×C₃	1	2	yes	—
263	#389	C₂²×C₃	1	2	yes	—
264	#389	C₂²×C₃	1	1	yes	characteristic
265	#389	C₂²×C₃	1	2	yes	—
266	#389	C₂²×C₃	1	2	yes	—
267	#388	C₂²×C₃	1	2	yes	—
268	#388	C₂²×C₃	1	2	yes	—
269	#388	C₂²×C₃	1	2	yes	—
270	#388	C₂²×C₃	1	2	yes	—
271	#387	C₂²×C₃	1	2	yes	—
272	#387	C₂²×C₃	1	2	yes	—
273	#387	C₂²×C₃	1	2	yes	—
274	#387	C₂²×C₃	1	2	yes	—
275	#387	C₂²×C₃	1	2	yes	—
276	#387	C₂²×C₃	1	2	yes	—
277	#387	C₂²×C₃	1	2	yes	—
278	#387	C₂²×C₃	1	2	yes	—
279	#387	C₂²×C₃	1	2	yes	—
280	#387	C₂²×C₃	1	2	yes	—
281	#387	C₂²×C₃	1	2	yes	—
282	#387	C₂²×C₃	1	2	yes	—
283	#387	C₂²×C₃	1	2	yes	—
284	#387	C₂²×C₃	1	2	yes	—
285	#387	C₂²×C₃	1	2	yes	—
286	#387	C₂²×C₃	1	2	yes	—
287	#387	C₂²×C₃	1	2	yes	—
288	#387	C₂²×C₃	1	2	yes	—
289	#385	C₂²×C₃	1	2	yes	—
290	#385	C₂²×C₃	1	2	yes	—
291	#385	C₂²×C₃	1	2	yes	—
292	#385	C₂²×C₃	1	2	yes	—
293	#384	C₂²×C₃	1	2	yes	—
294	#383	C₂²×C₃	1	2	yes	—
295	#383	C₂²×C₃	1	2	yes	—
296	#383	C₂²×C₃	1	2	yes	—
297	#382	C₂²×C₃	1	1	yes	characteristic
298	#381	C₂²×C₃	1	2	yes	—
299	#380	C₂²×C₃	1	1	yes	characteristic
300	#380	C₂²×C₃	1	1	yes	characteristic
301	#380	C₂²×C₃	1	1	yes	characteristic
302	#380	C₂²×C₃	1	1	yes	characteristic
303	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
304	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
305	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
306	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
307	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
308	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
309	C₂×C₃×Q₈	—	2	2	no	—
310	C₂×C₃×Q₈	—	2	2	no	—
311	C₂×C₃×Q₈	—	4	1	no	—
312	C₂×C₃×Q₈	—	4	1	no	—
313	C₂×C₃×Q₈	—	4	1	no	—
314	C₂×C₃×Q₈	—	4	1	no	—
315	C₂²×C₃×C₄	—	2	2	no	—
316	C₂²×C₃×C₄	—	2	2	no	—
317	C₂²×C₃×C₄	—	2	2	no	—
318	C₂²×C₃×C₄	—	2	2	no	—
319	C₂²×C₃×C₄	—	2	2	no	—
320	C₂²×C₃×C₄	—	4	1	no	—
321	C₂²×C₃×C₄	—	4	1	no	—
322	C₂²×C₃×C₄	—	4	1	no	—
323	C₂²×C₃×C₄	—	4	1	no	—
324	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
325	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
326	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
327	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
328	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
329	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
330	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
331	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
332	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
334	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
335	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
336	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
337	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
338	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
340	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
341	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
342	C₃×C₄⋊C₄	—	2	4	no	—
343	C₃×C₄⋊C₄	—	2	4	no	—
344	C₃×C₄⋊C₄	—	2	4	no	—
345	C₃×C₄⋊C₄	—	2	4	no	—
346	C₃×C₄⋊C₄	—	2	4	no	—
347	C₃×C₄⋊C₄	—	2	4	no	—
348	C₃×C₄⋊C₄	—	2	4	no	—
349	C₃×C₄⋊C₄	—	2	4	no	—
350	C₃×C₄⋊C₄	—	2	4	no	—
351	C₃×C₄⋊C₄	—	2	2	no	—
352	C₃×C₄⋊C₄	—	2	2	no	—
353	C₃×C₄⋊C₄	—	2	2	no	—
354	C₃×C₄⋊C₄	—	2	4	no	—
355	C₃×C₄⋊C₄	—	4	2	no	—
356	C₃×C₄⋊C₄	—	4	1	no	—
357	C₃×C₄⋊C₄	—	4	1	no	—
358	C₃×C₄⋊C₄	—	4	2	no	—
359	C₃×C₄⋊C₄	—	4	2	no	—
360	C₃×C₄⋊C₄	—	4	2	no	—
361	C₃×C₄⋊C₄	—	4	2	no	—
362	C₃×C₄⋊C₄	—	4	2	no	—
363	C₃×C₄⋊C₄	—	4	1	no	—
364	C₃×C₄⋊C₄	—	4	2	no	—
365	C₃×C₄⋊C₄	—	4	1	no	—
366	C₃×C₄⋊C₄	—	4	1	no	—
367	C₃×C₄⋊C₄	—	4	1	no	—
368	C₃×C₄⋊C₄	—	4	2	no	—
369	C₃×C₄⋊C₄	—	4	2	no	—
370	C₃×C₄⋊C₄	—	4	2	no	—
371	C₃×C₄⋊C₄	—	4	2	no	—
372	C₃×C₄⋊C₄	—	4	2	no	—
373	C₃×C₄⋊C₄	#41	1	4	yes	—
374	C₃×C₂²⋊C₄	—	2	4	no	—
375	C₃×C₂²⋊C₄	—	2	4	no	—
376	C₃×C₂²⋊C₄	—	2	4	no	—
377	C₃×C₂²⋊C₄	—	4	2	no	—
378	C₃×C₂²⋊C₄	—	4	2	no	—
379	C₃×C₂²⋊C₄	—	4	2	no	—
380	C₃×C₄²	—	2	4	no	—
381	C₃×C₄²	—	2	2	no	—
382	C₃×C₄²	—	2	2	no	—
383	C₃×C₄²	—	2	4	no	—
384	C₃×C₄²	—	4	1	no	—
385	C₃×C₄²	—	4	1	no	—
386	C₃×C₄²	—	4	2	no	—
387	C₃×C₄²	—	4	2	no	—
388	C₃×C₄²	—	4	2	no	—
389	C₃×C₄²	—	4	2	no	—
390	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
391	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
395	#125	—	2	8	no	—
396	#125	—	4	2	no	—
397	#125	—	4	4	no	—
398	C₂²⋊Q₈	—	2	4	no	—
399	C₂²⋊Q₈	—	4	2	no	—
400	C₄×Q₈	—	4	2	no	—
401	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₄²	—	4	2	no	—
440	C₂×C₄²	C₂³×C₃	1	2	yes	—
441	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₃	1	2	yes	—
444	C₂×C₄²	C₂³×C₃	1	2	yes	—
445	C₂×C₄²	C₂³×C₃	1	2	yes	—
446	C₂×C₄²	C₂³×C₃	1	2	yes	—
447	C₂×C₄²	C₂³×C₃	1	2	yes	—
448	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
450	#95	C₂³×C₃	1	2	yes	—
451	#95	C₂³×C₃	1	2	yes	—
452	#95	C₂³×C₃	1	2	yes	—
453	#95	C₂³×C₃	1	2	yes	—
454	#95	C₂³×C₃	1	2	yes	—
455	#95	C₂³×C₃	1	2	yes	—
456	#95	C₂³×C₃	1	2	yes	—
457	#95	C₂³×C₃	1	2	yes	—
458	#95	C₂³×C₃	1	2	yes	—
459	#95	C₂³×C₃	1	2	yes	—
460	#95	C₂³×C₃	1	2	yes	—
461	#95	C₂³×C₃	1	2	yes	—
462	#95	C₂³×C₃	1	2	yes	—
463	#95	C₂³×C₃	1	2	yes	—
464	#95	C₂³×C₃	1	2	yes	—
465	#95	C₂³×C₃	1	2	yes	—
466	#95	C₂³×C₃	1	2	yes	—
467	#95	C₂³×C₃	1	2	yes	—
468	#95	C₂³×C₃	1	2	yes	—
469	#95	C₂³×C₃	1	2	yes	—
470	#95	C₂³×C₃	1	2	yes	—
471	#95	C₂³×C₃	1	2	yes	—
472	#95	C₂³×C₃	1	2	yes	—
473	#95	C₂³×C₃	1	2	yes	—
474	#95	C₂³×C₃	1	2	yes	—
475	#95	C₂³×C₃	1	2	yes	—
476	#95	C₂³×C₃	1	2	yes	—
477	#95	C₂³×C₃	1	2	yes	—
478	#95	C₂³×C₃	1	2	yes	—
479	#95	C₂³×C₃	1	2	yes	—
480	#95	C₂³×C₃	1	2	yes	—
481	#95	C₂³×C₃	1	2	yes	—
482	#95	C₂³×C₃	1	2	yes	—
483	#95	C₂³×C₃	1	2	yes	—
484	C₂³×C₃	—	2	1	no	—
485	C₂³×C₃	—	2	1	no	—
486	C₂³×C₃	—	2	1	no	—
487	C₂³×C₃	—	2	1	no	—
488	C₂³×C₃	—	2	1	no	—
489	C₂³×C₃	—	2	1	no	—
490	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
491	C₂³×C₃	C₂⁵	1	1	yes	characteristic
492	C₃×Q₈	—	4	4	no	—
493	C₃×Q₈	—	8	2	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	2	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	2	no	—
505	C₂×C₃×C₄	—	2	2	no	—
506	C₂×C₃×C₄	—	2	2	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	2	2	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	2	no	—
514	C₂×C₃×C₄	—	2	2	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	2	2	no	—
517	C₂×C₃×C₄	—	2	2	no	—
518	C₂×C₃×C₄	—	2	2	no	—
519	C₂×C₃×C₄	—	2	2	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	2	no	—
522	C₂×C₃×C₄	—	2	2	no	—
523	C₂×C₃×C₄	—	2	2	no	—
524	C₂×C₃×C₄	—	2	2	no	—
525	C₂×C₃×C₄	—	2	2	no	—
526	C₂×C₃×C₄	—	2	2	no	—
527	C₂×C₃×C₄	—	2	2	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	2	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	2	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	2	2	no	—
541	C₂×C₃×C₄	—	2	1	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	4	4	no	—
544	C₂×C₃×C₄	—	4	4	no	—
545	C₂×C₃×C₄	—	4	4	no	—
546	C₂×C₃×C₄	C₂×#41	1	4	yes	—
547	C₂×C₃×C₄	C₂×#41	1	2	yes	—
548	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
549	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
550	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
551	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	4	1	no	—
555	C₂×Q₈	—	4	1	no	—
556	C₂×Q₈	—	4	1	no	—
557	C₂×Q₈	—	4	1	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	—	4	1	no	—
566	C₂²×C₄	—	4	1	no	—
567	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	4	1	no	—
599	C₄⋊C₄	—	4	2	no	—
600	C₄⋊C₄	—	4	1	no	—
601	C₄⋊C₄	—	4	1	no	—
602	C₄⋊C₄	—	4	1	no	—
603	C₄⋊C₄	—	4	2	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	1	no	—
610	C₄⋊C₄	—	4	1	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	C₃×#41	1	4	yes	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	2	no	—
625	C₄²	—	2	2	no	—
626	C₄²	—	2	4	no	—
627	C₄²	—	4	1	no	—
628	C₄²	—	4	1	no	—
629	C₄²	—	4	2	no	—
630	C₄²	—	4	2	no	—
631	C₄²	—	4	2	no	—
632	C₄²	—	4	2	no	—
633	C₂²×C₃	—	2	2	no	—
634	C₂²×C₃	—	2	2	no	—
635	C₂²×C₃	—	2	2	no	—
636	C₂²×C₃	—	4	1	no	—
637	C₂²×C₃	—	4	1	no	—
638	C₂²×C₃	—	4	1	no	—
639	C₂²×C₃	—	4	1	no	—
640	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
641	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
642	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
643	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
644	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
645	C₂²×C₃	#585	1	1	yes	characteristic
646	C₂²×C₃	#585	1	1	yes	characteristic
647	C₃×C₄	—	2	2	no	—
648	C₃×C₄	—	2	4	no	—
649	C₃×C₄	—	2	2	no	—
650	C₃×C₄	—	2	2	no	—
651	C₃×C₄	—	2	2	no	—
652	C₃×C₄	—	4	2	no	—
653	C₃×C₄	—	4	2	no	—
654	C₃×C₄	—	4	1	no	—
655	C₃×C₄	—	4	2	no	—
656	C₃×C₄	—	4	2	no	—
657	C₃×C₄	—	4	2	no	—
658	C₃×C₄	—	4	2	no	—
659	C₃×C₄	—	4	2	no	—
660	C₃×C₄	—	4	2	no	—
661	C₃×C₄	—	4	1	no	—
662	C₃×C₄	—	4	2	no	—
663	C₃×C₄	—	4	2	no	—
664	C₃×C₄	—	4	2	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
672	C₂³	C₂⁵×C₃	1	1	yes	characteristic
673	Q₈	—	4	4	no	—
674	Q₈	—	8	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	C₂×C₃×#41	1	4	yes	—
728	C₂×C₄	C₂×C₃×#41	1	2	yes	—
729	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
730	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
731	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
732	C₂×C₃	—	4	2	no	—
733	C₂×C₃	#3460	1	1	yes	characteristic
734	C₂×C₃	#3515	1	1	yes	characteristic
735	C₂×C₃	#3523	1	1	yes	characteristic
736	C₂×C₃	#3535	1	1	yes	characteristic
737	C₂×C₃	#3538	1	1	yes	characteristic
738	C₂×C₃	#3553	1	1	yes	characteristic
739	C₂×C₃	#3555	1	1	yes	characteristic
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
748	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
749	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
750	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
751	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
752	C₂²	C₃×#585	1	1	yes	characteristic
753	C₂²	C₃×#585	1	1	yes	characteristic
754	C₄	—	2	2	no	—
755	C₄	—	2	4	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	1	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₃	#37168	1	1	yes	characteristic, direct product factor, Sylow
773	C₂	—	4	2	no	—
774	C₂	C₃×#3460	1	1	yes	characteristic
775	C₂	C₃×#3515	1	1	yes	characteristic
776	C₂	C₃×#3523	1	1	yes	characteristic
777	C₂	C₃×#3535	1	1	yes	characteristic
778	C₂	C₃×#3538	1	1	yes	characteristic
779	C₂	C₃×#3553	1	1	yes	characteristic
780	C₂	C₃×#3555	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₃×#2806	C₂	semidirect
4. C₃×#2805	C₂	semidirect
5. C₃×#2805	C₂	semidirect
6. C₃×#2791	C₂	semidirect
8. C₃×#2758	C₂	semidirect
11. C₃×#2726	C₂	semidirect
13. C₃×#2634	C₂	semidirect
16. C₃×#2524	C₂	semidirect
17. C₃×#2506	C₂	semidirect
18. C₃×#2336	C₂	semidirect
20. #37168	C₃	direct (N × H)
110. #2806	C₂×C₃	semidirect
111. #2805	C₂×C₃	semidirect
112. #2805	C₂×C₃	semidirect
113. #2791	C₂×C₃	semidirect
115. #2758	C₂×C₃	semidirect
118. #2726	C₂×C₃	semidirect
120. #2634	C₂×C₃	semidirect
123. #2524	C₂×C₃	semidirect
124. #2506	C₂×C₃	semidirect
125. #2336	C₂×C₃	semidirect
772. C₃	#37168	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×#2855	2
C₃×#2851	2
C₃×#2806	2
C₃×#2805	2
C₃×#2791	2
C₃×#2770	2
C₃×#2758	2
C₃×#2739	2
C₃×#2738	2
C₃×#2726	2
C₃×#2720	2
C₃×#2634	2
C₃×#2577	2
C₃×#2556	2
C₃×#2524	2
C₃×#2506	2
C₃×#2336	2
C₃×C₄×C₂²⋊Q₈	2
#37168	3

Subgroups — C3×#37168 #10655775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37168 #10655775