Subgroups — C₃×#36834 #10655441

Order 768.

1454 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2851	C₂	1	2	yes	maximal
2	C₃×#2788	C₂	1	2	yes	maximal
3	C₃×#2787	C₂	1	2	yes	maximal
4	C₃×#2774	C₂	1	2	yes	maximal, complemented
5	C₃×#2770	C₂	1	2	yes	maximal
6	C₃×#2768	C₂	1	2	yes	maximal
7	C₃×#2766	C₂	1	2	yes	maximal, complemented
8	C₃×#2726	C₂	1	2	yes	maximal, complemented
9	C₃×#2719	C₂	1	2	yes	maximal, complemented
10	C₃×#2655	C₂	1	2	yes	maximal, complemented
11	C₃×#2611	C₂	1	1	yes	maximal, characteristic
12	C₃×#2606	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2599	C₂	1	1	yes	maximal, characteristic
14	C₃×#2590	C₂	1	2	yes	maximal, complemented
15	C₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2475	C₂	1	2	yes	maximal
17	C₃×#2336	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2296	C₂	1	1	yes	maximal, characteristic
20	#36834	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₃×#125	C₂²	1	2	yes	—
23	C₂×C₃×#125	C₂²	1	2	yes	—
24	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×#117	C₂²	1	1	yes	characteristic
26	C₂×C₃×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
28	C₃×#401	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	1	yes	characteristic
35	C₃×#400	C₂²	1	2	yes	—
36	C₃×#399	C₂²	1	1	yes	characteristic
37	C₃×#398	C₂²	1	2	yes	—
38	C₃×#398	C₂²	1	2	yes	—
39	C₃×#398	C₂²	1	2	yes	—
40	C₃×#398	C₂²	1	1	yes	characteristic
41	C₃×#398	C₂²	1	2	yes	—
42	C₃×#398	C₂²	1	2	yes	—
43	C₃×#398	C₂²	1	1	yes	characteristic
44	C₃×#398	C₂²	1	2	yes	—
45	C₃×#398	C₂²	1	2	yes	—
46	C₃×#398	C₂²	1	2	yes	—
47	C₃×#398	C₂²	1	2	yes	—
48	C₃×#398	C₂²	1	2	yes	—
49	C₃×#397	C₂²	1	2	yes	—
50	C₃×#397	C₂²	1	1	yes	characteristic
51	C₃×#397	C₂²	1	1	yes	characteristic
52	C₃×#396	C₂²	1	2	yes	—
53	C₃×#395	C₂²	1	1	yes	characteristic
54	C₃×#395	C₂²	1	2	yes	—
55	C₃×#393	C₂²	1	1	yes	characteristic
56	C₃×#391	C₂²	1	2	yes	—
57	C₃×#389	C₂²	1	2	yes	—
58	C₃×#389	C₂²	1	2	yes	—
59	C₃×#389	C₂²	1	2	yes	—
60	C₃×#389	C₂²	1	2	yes	—
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	2	yes	—
65	C₃×#389	C₂²	1	2	yes	—
66	C₃×#389	C₂²	1	2	yes	—
67	C₃×#389	C₂²	1	2	yes	—
68	C₃×#389	C₂²	1	2	yes	—
69	C₃×#388	C₂²	1	2	yes	—
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#388	C₂²	1	2	yes	—
72	C₃×#388	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×#387	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×#385	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	2	yes	—
95	C₃×#385	C₂²	1	2	yes	—
96	C₃×#383	C₂²	1	2	yes	—
97	C₃×#383	C₂²	1	1	yes	characteristic
98	C₃×#382	C₂²	1	2	yes	—
99	C₃×#382	C₂²	1	2	yes	—
100	C₃×#380	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	2	yes	—
102	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
104	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₃×#376	C₂²	1	1	yes	characteristic
108	#2851	C₂×C₃	1	2	yes	—
109	#2788	C₂×C₃	1	2	yes	—
110	#2787	C₂×C₃	1	2	yes	—
111	#2774	C₂×C₃	1	2	yes	complemented
112	#2770	C₂×C₃	1	2	yes	—
113	#2768	C₂×C₃	1	2	yes	—
114	#2766	C₂×C₃	1	2	yes	complemented
115	#2726	C₂×C₃	1	2	yes	complemented
116	#2719	C₂×C₃	1	2	yes	complemented
117	#2655	C₂×C₃	1	2	yes	complemented
118	#2611	C₂×C₃	1	1	yes	characteristic
119	#2606	C₂×C₃	1	1	yes	characteristic, complemented
120	#2599	C₂×C₃	1	1	yes	characteristic
121	#2590	C₂×C₃	1	2	yes	complemented
122	#2584	C₂×C₃	1	1	yes	characteristic, complemented
123	#2475	C₂×C₃	1	2	yes	—
124	#2336	C₂×C₃	1	1	yes	characteristic, complemented
125	#2320	C₂×C₃	1	1	yes	characteristic, complemented
126	#2296	C₂×C₃	1	1	yes	characteristic
127	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
128	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
129	C₂³×C₃×C₄	C₂³	1	2	yes	—
130	C₃×#125	—	2	4	no	—
131	C₃×#125	—	4	4	no	—
132	C₃×#125	—	4	4	no	—
133	C₃×C₄×Q₈	—	2	4	no	—
134	C₃×#117	—	2	4	no	—
135	C₃×#117	—	4	2	no	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	—	4	2	no	—
175	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄²	C₂³	1	2	yes	—
177	C₂×C₃×C₄²	C₂³	1	2	yes	—
178	C₂×C₃×C₄²	C₂³	1	2	yes	—
179	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	C₃×#95	C₂³	1	1	yes	characteristic
187	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
222	C₂×#125	C₂²×C₃	1	2	yes	—
223	C₂×#125	C₂²×C₃	1	2	yes	—
224	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
225	C₂×#117	C₂²×C₃	1	1	yes	characteristic
226	C₂×#117	C₂²×C₃	1	1	yes	characteristic
227	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
228	#401	C₂²×C₃	1	2	yes	—
229	#400	C₂²×C₃	1	2	yes	—
230	#400	C₂²×C₃	1	1	yes	characteristic
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	#399	C₂²×C₃	1	1	yes	characteristic
237	#398	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	1	yes	characteristic
242	#398	C₂²×C₃	1	2	yes	—
243	#398	C₂²×C₃	1	2	yes	—
244	#398	C₂²×C₃	1	1	yes	characteristic
245	#398	C₂²×C₃	1	2	yes	—
246	#398	C₂²×C₃	1	2	yes	—
247	#398	C₂²×C₃	1	2	yes	—
248	#398	C₂²×C₃	1	2	yes	—
249	#397	C₂²×C₃	1	1	yes	characteristic
250	#397	C₂²×C₃	1	1	yes	characteristic
251	#397	C₂²×C₃	1	2	yes	—
252	#396	C₂²×C₃	1	2	yes	—
253	#395	C₂²×C₃	1	2	yes	—
254	#395	C₂²×C₃	1	1	yes	characteristic
255	#393	C₂²×C₃	1	1	yes	characteristic
256	#391	C₂²×C₃	1	2	yes	—
257	#389	C₂²×C₃	1	2	yes	—
258	#389	C₂²×C₃	1	2	yes	—
259	#389	C₂²×C₃	1	2	yes	—
260	#389	C₂²×C₃	1	2	yes	—
261	#389	C₂²×C₃	1	2	yes	—
262	#389	C₂²×C₃	1	2	yes	—
263	#389	C₂²×C₃	1	2	yes	—
264	#389	C₂²×C₃	1	2	yes	—
265	#389	C₂²×C₃	1	2	yes	—
266	#389	C₂²×C₃	1	2	yes	—
267	#389	C₂²×C₃	1	2	yes	—
268	#389	C₂²×C₃	1	2	yes	—
269	#388	C₂²×C₃	1	2	yes	—
270	#388	C₂²×C₃	1	2	yes	—
271	#388	C₂²×C₃	1	2	yes	—
272	#388	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	#387	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	#385	C₂²×C₃	1	2	yes	—
294	#385	C₂²×C₃	1	2	yes	—
295	#385	C₂²×C₃	1	2	yes	—
296	#383	C₂²×C₃	1	2	yes	—
297	#383	C₂²×C₃	1	1	yes	characteristic
298	#382	C₂²×C₃	1	2	yes	—
299	#382	C₂²×C₃	1	2	yes	—
300	#380	C₂²×C₃	1	2	yes	—
301	#380	C₂²×C₃	1	2	yes	—
302	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
303	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
307	#376	C₂²×C₃	1	1	yes	characteristic
308	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
309	C₂×C₃×Q₈	—	2	2	no	—
310	C₂×C₃×Q₈	—	4	2	no	—
311	C₂²×C₃×C₄	—	2	2	no	—
312	C₂²×C₃×C₄	—	2	2	no	—
313	C₂²×C₃×C₄	—	2	2	no	—
314	C₂²×C₃×C₄	—	2	4	no	—
315	C₂²×C₃×C₄	—	4	2	no	—
316	C₂²×C₃×C₄	—	4	2	no	—
317	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
319	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
320	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
321	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
322	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
323	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
324	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	1	yes	characteristic
331	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
332	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
335	C₃×C₄⋊C₄	—	2	2	no	—
336	C₃×C₄⋊C₄	—	2	2	no	—
337	C₃×C₄⋊C₄	—	2	2	no	—
338	C₃×C₄⋊C₄	—	2	4	no	—
339	C₃×C₄⋊C₄	—	2	2	no	—
340	C₃×C₄⋊C₄	—	2	2	no	—
341	C₃×C₄⋊C₄	—	2	4	no	—
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	—	4	2	no	—
351	C₃×C₄⋊C₄	—	4	2	no	—
352	C₃×C₄⋊C₄	—	4	2	no	—
353	C₃×C₄⋊C₄	—	4	2	no	—
354	C₃×C₄⋊C₄	—	4	2	no	—
355	C₃×C₄⋊C₄	—	4	2	no	—
356	C₃×C₄⋊C₄	—	4	2	no	—
357	C₃×C₄⋊C₄	—	4	2	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	2	no	—
364	C₃×C₄⋊C₄	—	4	2	no	—
365	C₃×C₄⋊C₄	—	4	2	no	—
366	C₃×C₂²⋊C₄	—	2	4	no	—
367	C₃×C₂²⋊C₄	—	2	4	no	—
368	C₃×C₂²⋊C₄	—	2	2	no	—
369	C₃×C₂²⋊C₄	—	2	2	no	—
370	C₃×C₂²⋊C₄	—	4	2	no	—
371	C₃×C₂²⋊C₄	—	4	2	no	—
372	C₃×C₂²⋊C₄	—	4	2	no	—
373	C₃×C₄²	—	2	2	no	—
374	C₃×C₄²	—	2	4	no	—
375	C₃×C₄²	—	2	4	no	—
376	C₃×C₄²	—	4	1	no	—
377	C₃×C₄²	—	4	1	no	—
378	C₃×C₄²	—	4	2	no	—
379	C₃×C₄²	—	4	2	no	—
380	C₃×C₄²	—	4	1	no	—
381	C₃×C₄²	—	4	1	no	—
382	C₃×C₄²	—	4	2	no	—
383	C₃×C₄²	#41	1	4	yes	—
384	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₃	1	2	yes	—
387	#125	—	2	4	no	—
388	#125	—	4	4	no	—
389	#125	—	4	4	no	—
390	C₄×Q₈	—	2	4	no	—
391	#117	—	2	4	no	—
392	#117	—	4	2	no	—
393	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₄²	—	4	2	no	—
432	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₃	1	2	yes	—
434	C₂×C₄²	C₂³×C₃	1	2	yes	—
435	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₃	1	2	yes	—
438	C₂×C₄²	C₂³×C₃	1	2	yes	—
439	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₃	1	2	yes	—
442	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
443	#95	C₂³×C₃	1	1	yes	characteristic
444	#95	C₂³×C₃	1	1	yes	characteristic
445	#95	C₂³×C₃	1	2	yes	—
446	#95	C₂³×C₃	1	2	yes	—
447	#95	C₂³×C₃	1	2	yes	—
448	#95	C₂³×C₃	1	2	yes	—
449	#95	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	C₂³×C₃	—	2	1	no	—
479	C₂³×C₃	—	2	1	no	—
480	C₂³×C₃	—	2	2	no	—
481	C₂³×C₃	—	2	2	no	—
482	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
483	C₂³×C₃	C₂⁵	1	1	yes	characteristic
484	C₃×Q₈	—	4	4	no	—
485	C₂×C₃×C₄	—	2	8	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	2	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	2	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	2	no	—
493	C₂×C₃×C₄	—	2	2	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	2	no	—
497	C₂×C₃×C₄	—	2	2	no	—
498	C₂×C₃×C₄	—	2	2	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	2	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	2	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	2	no	—
510	C₂×C₃×C₄	—	2	2	no	—
511	C₂×C₃×C₄	—	2	2	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	2	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	4	8	no	—
532	C₂×C₃×C₄	C₂×#41	1	2	yes	—
533	C₂×C₃×C₄	C₂×#41	1	2	yes	—
534	C₂×C₃×C₄	C₂×#41	1	2	yes	—
535	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
536	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
537	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	4	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₄⋊C₄	—	4	2	no	—
582	C₄⋊C₄	—	4	2	no	—
583	C₄⋊C₄	—	4	2	no	—
584	C₄⋊C₄	—	4	2	no	—
585	C₄⋊C₄	—	4	2	no	—
586	C₄⋊C₄	—	4	2	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	4	2	no	—
589	C₄⋊C₄	—	4	2	no	—
590	C₄⋊C₄	—	4	2	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	4	2	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	4	no	—
604	C₄²	—	2	4	no	—
605	C₄²	—	4	1	no	—
606	C₄²	—	4	1	no	—
607	C₄²	—	4	1	no	—
608	C₄²	—	4	1	no	—
609	C₄²	—	4	2	no	—
610	C₄²	—	4	2	no	—
611	C₄²	—	4	2	no	—
612	C₄²	C₃×#41	1	4	yes	—
613	C₂²×C₃	—	2	2	no	—
614	C₂²×C₃	—	2	4	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	—	4	2	no	—
618	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
619	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
620	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
621	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
622	C₂²×C₃	#585	1	2	yes	—
623	C₃×C₄	—	2	2	no	—
624	C₃×C₄	—	2	2	no	—
625	C₃×C₄	—	2	2	no	—
626	C₃×C₄	—	2	2	no	—
627	C₃×C₄	—	2	4	no	—
628	C₃×C₄	—	4	1	no	—
629	C₃×C₄	—	4	2	no	—
630	C₃×C₄	—	4	2	no	—
631	C₃×C₄	—	4	2	no	—
632	C₃×C₄	—	4	2	no	—
633	C₃×C₄	—	4	1	no	—
634	C₃×C₄	—	4	2	no	—
635	C₃×C₄	—	4	2	no	—
636	C₃×C₄	—	4	2	no	—
637	C₃×C₄	—	4	2	no	—
638	C₃×C₄	—	4	2	no	—
639	C₃×C₄	—	4	2	no	—
640	C₃×C₄	—	4	2	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
646	C₂³	C₂⁵×C₃	1	1	yes	characteristic
647	Q₈	—	4	4	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	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	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	4	8	no	—
695	C₂×C₄	C₂×C₃×#41	1	2	yes	—
696	C₂×C₄	C₂×C₃×#41	1	2	yes	—
697	C₂×C₄	C₂×C₃×#41	1	2	yes	—
698	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
699	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
700	C₂×C₃	—	4	2	no	—
701	C₂×C₃	#3455	1	1	yes	characteristic
702	C₂×C₃	#3492	1	1	yes	characteristic
703	C₂×C₃	#3509	1	1	yes	characteristic
704	C₂×C₃	#3541	1	2	yes	—
705	C₂×C₃	#3563	1	2	yes	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	2	no	—
711	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
712	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
713	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
714	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
715	C₂²	C₃×#585	1	2	yes	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	4	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₃	#36834	1	1	yes	characteristic, direct product factor, Sylow
735	C₂	—	4	2	no	—
736	C₂	C₃×#3455	1	1	yes	characteristic
737	C₂	C₃×#3492	1	1	yes	characteristic
738	C₂	C₃×#3509	1	1	yes	characteristic
739	C₂	C₃×#3541	1	2	yes	—
740	C₂	C₃×#3563	1	2	yes	—

	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
4. C₃×#2774	C₂	semidirect
7. C₃×#2766	C₂	semidirect
8. C₃×#2726	C₂	semidirect
9. C₃×#2719	C₂	semidirect
10. C₃×#2655	C₂	semidirect
12. C₃×#2606	C₂	semidirect
14. C₃×#2590	C₂	semidirect
15. C₃×#2584	C₂	semidirect
17. C₃×#2336	C₂	semidirect
18. C₃×#2320	C₂	semidirect
20. #36834	C₃	direct (N × H)
111. #2774	C₂×C₃	semidirect
114. #2766	C₂×C₃	semidirect
115. #2726	C₂×C₃	semidirect
116. #2719	C₂×C₃	semidirect
117. #2655	C₂×C₃	semidirect
119. #2606	C₂×C₃	semidirect
121. #2590	C₂×C₃	semidirect
122. #2584	C₂×C₃	semidirect
124. #2336	C₂×C₃	semidirect
125. #2320	C₂×C₃	semidirect
734. C₃	#36834	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×#2851	2
C₃×#2788	2
C₃×#2787	2
C₃×#2774	2
C₃×#2770	2
C₃×#2768	2
C₃×#2766	2
C₃×#2726	2
C₃×#2719	2
C₃×#2655	2
C₃×#2611	2
C₃×#2606	2
C₃×#2599	2
C₃×#2590	2
C₃×#2584	2
C₃×#2475	2
C₃×#2336	2
C₃×#2320	2
C₃×#2296	2
#36834	3

Subgroups — C3×#36834 #10655441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36834 #10655441