Subgroups — C₃×#35318 #10653925

Order 768.

2106 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#542	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2861	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2850	C₂	1	1	yes	maximal, characteristic
7	C₃×#2660	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2658	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2620	C₂	1	1	yes	maximal, characteristic
11	C₃×#2556	C₂	1	4	yes	maximal, complemented
12	C₃×#2553	C₂	1	4	yes	maximal, complemented
13	C₃×#2521	C₂	1	4	yes	maximal, complemented
14	C₃×#2519	C₂	1	4	yes	maximal, complemented
15	C₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₄×#124	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic, complemented
20	#35318	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#542	—	2	8	no	—
22	C₃×#541	—	2	8	no	—
23	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×#126	C₂²	1	2	yes	—
28	C₂×C₃×#126	C₂²	1	2	yes	—
29	C₂×C₃×#126	C₂²	1	2	yes	—
30	C₂×C₃×#125	C₂²	1	1	yes	characteristic
31	C₂×C₃×#125	C₂²	1	2	yes	—
32	C₂×C₃×#125	C₂²	1	2	yes	—
33	C₂×C₃×#124	C₂²	1	1	yes	characteristic
34	C₂×C₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₃×#124	C₂²	1	1	yes	characteristic
36	C₂×C₃×#124	C₂²	1	2	yes	—
37	C₂×C₃×#123	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
42	C₂×C₃×#121	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₃×#117	C₂²	1	1	yes	characteristic
48	C₂×C₃×#117	C₂²	1	1	yes	characteristic
49	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
50	C₃×#399	C₂²	1	4	yes	—
51	C₃×#399	C₂²	1	4	yes	—
52	C₃×#398	C₂²	1	4	yes	—
53	C₃×#398	C₂²	1	4	yes	—
54	C₃×#397	C₂²	1	4	yes	—
55	C₃×#396	C₂²	1	4	yes	—
56	C₃×#395	C₂²	1	4	yes	—
57	C₃×#394	C₂²	1	4	yes	—
58	C₃×#391	C₂²	1	1	yes	characteristic
59	C₃×#391	C₂²	1	1	yes	characteristic
60	C₃×#391	C₂²	1	1	yes	characteristic
61	C₃×#391	C₂²	1	4	yes	—
62	C₃×#391	C₂²	1	1	yes	characteristic
63	C₃×#391	C₂²	1	1	yes	characteristic
64	C₃×#391	C₂²	1	1	yes	characteristic
65	C₃×#390	C₂²	1	1	yes	characteristic
66	C₃×#390	C₂²	1	1	yes	characteristic
67	C₃×#389	C₂²	1	4	yes	—
68	C₃×#389	C₂²	1	4	yes	—
69	C₃×#388	C₂²	1	4	yes	—
70	C₃×#388	C₂²	1	4	yes	—
71	C₃×#388	C₂²	1	4	yes	—
72	C₃×#388	C₂²	1	4	yes	—
73	C₃×#388	C₂²	1	4	yes	—
74	C₃×#387	C₂²	1	4	yes	—
75	C₃×#387	C₂²	1	4	yes	—
76	C₃×#386	C₂²	1	4	yes	—
77	C₃×#385	C₂²	1	4	yes	—
78	C₃×#384	C₂²	1	1	yes	characteristic
79	C₃×#384	C₂²	1	1	yes	characteristic
80	C₃×#382	C₂²	1	1	yes	characteristic
81	C₃×#382	C₂²	1	1	yes	characteristic
82	C₃×#382	C₂²	1	4	yes	—
83	C₃×#380	C₂²	1	4	yes	—
84	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
85	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
86	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
87	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
88	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
89	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
90	C₃×#376	C₂²	1	1	yes	characteristic
91	C₃×#376	C₂²	1	1	yes	characteristic
92	C₃×C₄³	C₂²	1	1	yes	characteristic
93	C₃×C₄³	C₂²	1	1	yes	characteristic
94	C₂×#542	C₂×C₃	1	1	yes	characteristic
95	C₂×#541	C₂×C₃	1	1	yes	characteristic, complemented
96	#2862	C₂×C₃	1	1	yes	characteristic, complemented
97	#2861	C₂×C₃	1	1	yes	characteristic, complemented
98	#2857	C₂×C₃	1	1	yes	characteristic, complemented
99	#2850	C₂×C₃	1	1	yes	characteristic
100	#2660	C₂×C₃	1	1	yes	characteristic, complemented
101	#2658	C₂×C₃	1	1	yes	characteristic, complemented
102	#2621	C₂×C₃	1	1	yes	characteristic, complemented
103	#2620	C₂×C₃	1	1	yes	characteristic
104	#2556	C₂×C₃	1	4	yes	complemented
105	#2553	C₂×C₃	1	4	yes	complemented
106	#2521	C₂×C₃	1	4	yes	complemented
107	#2519	C₂×C₃	1	4	yes	complemented
108	#2327	C₂×C₃	1	1	yes	characteristic, complemented
109	#2326	C₂×C₃	1	1	yes	characteristic, complemented
110	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
111	C₄×#124	C₂×C₃	1	1	yes	characteristic, complemented
112	C₄×#117	C₂×C₃	1	1	yes	characteristic, complemented
113	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
114	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
115	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
116	C₂²×C₃×Q₈	C₂³	1	2	yes	—
117	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
118	C₂²×C₃×D₄	C₂³	1	2	yes	—
119	C₂³×C₃×C₄	C₂³	1	2	yes	—
120	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
121	C₂³×C₃×C₄	C₂³	1	2	yes	—
122	C₃×C₄⋊Q₈	—	2	4	no	—
123	C₃×C₄⋊Q₈	—	2	4	no	—
124	C₃×C₄⋊Q₈	—	2	4	no	—
125	C₃×C₄⋊Q₈	—	2	4	no	—
126	C₃×#126	—	2	8	no	—
127	C₃×#126	—	2	8	no	—
128	C₃×#126	—	2	8	no	—
129	C₃×#125	—	2	8	no	—
130	C₃×#125	—	2	8	no	—
131	C₃×#125	—	2	4	no	—
132	C₃×#124	—	2	8	no	—
133	C₃×#124	—	2	4	no	—
134	C₃×#124	—	2	4	no	—
135	C₃×#124	—	2	4	no	—
136	C₃×#123	—	2	8	no	—
137	C₃×C₂²⋊Q₈	—	2	4	no	—
138	C₃×C₂²⋊Q₈	—	2	4	no	—
139	C₃×C₂²⋊Q₈	—	2	4	no	—
140	C₃×C₂²⋊Q₈	—	2	8	no	—
141	C₃×#121	—	2	4	no	—
142	C₃×C₄×Q₈	—	2	4	no	—
143	C₃×C₄×Q₈	—	2	4	no	—
144	C₃×C₄×Q₈	—	2	4	no	—
145	C₃×C₄×D₄	—	2	4	no	—
146	C₃×#117	—	2	4	no	—
147	C₃×#117	D₄	1	8	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	4	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	2	yes	—
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	4	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	4	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₄²	—	2	4	no	—
185	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
187	C₂×C₃×C₄²	C₂³	1	2	yes	—
188	C₂×C₃×C₄²	C₂³	1	2	yes	—
189	C₂×C₃×C₄²	C₂³	1	2	yes	—
190	C₂×C₃×C₄²	C₂³	1	2	yes	—
191	C₂×C₃×C₄²	C₂³	1	2	yes	—
192	C₂×C₃×C₄²	C₂³	1	2	yes	—
193	C₂×C₃×C₄²	C₂³	1	2	yes	—
194	C₂×C₃×C₄²	C₂³	1	2	yes	—
195	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	4	yes	—
204	C₃×#95	C₂³	1	4	yes	—
205	C₃×#95	C₂³	1	4	yes	—
206	C₃×#95	C₂³	1	4	yes	—
207	C₃×#95	C₂³	1	4	yes	—
208	C₃×#95	C₂³	1	4	yes	—
209	C₃×#95	C₂³	1	4	yes	—
210	C₃×#95	C₂³	1	4	yes	—
211	#542	—	2	8	no	—
212	#541	—	2	8	no	—
213	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
214	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
217	C₂×#126	C₂²×C₃	1	2	yes	—
218	C₂×#126	C₂²×C₃	1	2	yes	—
219	C₂×#126	C₂²×C₃	1	2	yes	—
220	C₂×#125	C₂²×C₃	1	1	yes	characteristic
221	C₂×#125	C₂²×C₃	1	2	yes	—
222	C₂×#125	C₂²×C₃	1	2	yes	—
223	C₂×#124	C₂²×C₃	1	1	yes	characteristic
224	C₂×#124	C₂²×C₃	1	1	yes	characteristic
225	C₂×#124	C₂²×C₃	1	1	yes	characteristic
226	C₂×#124	C₂²×C₃	1	2	yes	—
227	C₂×#123	C₂²×C₃	1	2	yes	—
228	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
229	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
231	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
232	C₂×#121	C₂²×C₃	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
237	C₂×#117	C₂²×C₃	1	1	yes	characteristic
238	C₂×#117	C₂²×C₃	1	1	yes	characteristic
239	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
240	#399	C₂²×C₃	1	4	yes	—
241	#399	C₂²×C₃	1	4	yes	—
242	#398	C₂²×C₃	1	4	yes	—
243	#398	C₂²×C₃	1	4	yes	—
244	#397	C₂²×C₃	1	4	yes	—
245	#396	C₂²×C₃	1	4	yes	—
246	#395	C₂²×C₃	1	4	yes	—
247	#394	C₂²×C₃	1	4	yes	—
248	#391	C₂²×C₃	1	1	yes	characteristic
249	#391	C₂²×C₃	1	1	yes	characteristic
250	#391	C₂²×C₃	1	1	yes	characteristic
251	#391	C₂²×C₃	1	1	yes	characteristic
252	#391	C₂²×C₃	1	1	yes	characteristic
253	#391	C₂²×C₃	1	1	yes	characteristic
254	#391	C₂²×C₃	1	4	yes	—
255	#390	C₂²×C₃	1	1	yes	characteristic
256	#390	C₂²×C₃	1	1	yes	characteristic
257	#389	C₂²×C₃	1	4	yes	—
258	#389	C₂²×C₃	1	4	yes	—
259	#388	C₂²×C₃	1	4	yes	—
260	#388	C₂²×C₃	1	4	yes	—
261	#388	C₂²×C₃	1	4	yes	—
262	#388	C₂²×C₃	1	4	yes	—
263	#388	C₂²×C₃	1	4	yes	—
264	#387	C₂²×C₃	1	4	yes	—
265	#387	C₂²×C₃	1	4	yes	—
266	#386	C₂²×C₃	1	4	yes	—
267	#385	C₂²×C₃	1	4	yes	—
268	#384	C₂²×C₃	1	1	yes	characteristic
269	#384	C₂²×C₃	1	1	yes	characteristic
270	#382	C₂²×C₃	1	1	yes	characteristic
271	#382	C₂²×C₃	1	4	yes	—
272	#382	C₂²×C₃	1	1	yes	characteristic
273	#380	C₂²×C₃	1	4	yes	—
274	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
275	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
276	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
277	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
278	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
279	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
280	#376	C₂²×C₃	1	1	yes	characteristic
281	#376	C₂²×C₃	1	1	yes	characteristic
282	C₄³	C₂²×C₃	1	1	yes	characteristic
283	C₄³	C₂²×C₃	1	1	yes	characteristic
284	C₂⁴×C₃	C₂⁴	1	2	yes	—
285	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
286	C₂×C₃×Q₈	—	2	2	no	—
287	C₂×C₃×Q₈	—	2	2	no	—
288	C₂×C₃×Q₈	—	2	2	no	—
289	C₂×C₃×Q₈	—	2	4	no	—
290	C₂×C₃×Q₈	—	2	2	no	—
291	C₂×C₃×Q₈	—	2	2	no	—
292	C₂×C₃×Q₈	—	2	2	no	—
293	C₂×C₃×Q₈	—	2	2	no	—
294	C₂×C₃×Q₈	—	2	2	no	—
295	C₂×C₃×Q₈	—	2	2	no	—
296	C₂×C₃×Q₈	—	4	4	no	—
297	C₂×C₃×D₄	—	2	4	no	—
298	C₂×C₃×D₄	—	2	2	no	—
299	C₂×C₃×D₄	—	2	2	no	—
300	C₂×C₃×D₄	—	2	2	no	—
301	C₂×C₃×D₄	—	4	4	no	—
302	C₂²×C₃×C₄	—	2	2	no	—
303	C₂²×C₃×C₄	—	2	2	no	—
304	C₂²×C₃×C₄	—	2	4	no	—
305	C₂²×C₃×C₄	—	2	4	no	—
306	C₂²×C₃×C₄	—	2	4	no	—
307	C₂²×C₃×C₄	—	4	2	no	—
308	C₂²×C₃×C₄	—	4	4	no	—
309	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
310	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
311	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
312	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
313	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
314	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
315	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
316	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
317	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
318	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
321	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
323	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
324	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
325	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
326	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
327	C₃×C₄⋊C₄	—	2	2	no	—
328	C₃×C₄⋊C₄	—	2	2	no	—
329	C₃×C₄⋊C₄	—	2	4	no	—
330	C₃×C₄⋊C₄	—	2	2	no	—
331	C₃×C₄⋊C₄	—	2	2	no	—
332	C₃×C₄⋊C₄	—	2	4	no	—
333	C₃×C₄⋊C₄	—	2	4	no	—
334	C₃×C₄⋊C₄	—	2	4	no	—
335	C₃×C₄⋊C₄	—	2	4	no	—
336	C₃×C₄⋊C₄	—	2	4	no	—
337	C₃×C₄⋊C₄	—	2	4	no	—
338	C₃×C₄⋊C₄	—	2	4	no	—
339	C₃×C₄⋊C₄	—	2	4	no	—
340	C₃×C₄⋊C₄	—	2	4	no	—
341	C₃×C₄⋊C₄	—	2	4	no	—
342	C₃×C₄⋊C₄	—	2	4	no	—
343	C₃×C₄⋊C₄	—	2	8	no	—
344	C₃×C₄⋊C₄	—	2	8	no	—
345	C₃×C₄⋊C₄	—	4	4	no	—
346	C₃×C₄⋊C₄	—	4	4	no	—
347	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
348	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
349	C₃×C₂²⋊C₄	—	2	4	no	—
350	C₃×C₂²⋊C₄	—	2	4	no	—
351	C₃×C₂²⋊C₄	—	2	4	no	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	2	4	no	—
354	C₃×C₂²⋊C₄	—	2	4	no	—
355	C₃×C₂²⋊C₄	—	2	4	no	—
356	C₃×C₂²⋊C₄	—	2	4	no	—
357	C₃×C₂²⋊C₄	—	2	8	no	—
358	C₃×C₂²⋊C₄	—	2	8	no	—
359	C₃×C₂²⋊C₄	—	2	8	no	—
360	C₃×C₂²⋊C₄	—	4	4	no	—
361	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
362	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
363	C₃×C₄²	—	2	4	no	—
364	C₃×C₄²	—	2	4	no	—
365	C₃×C₄²	—	2	4	no	—
366	C₃×C₄²	—	2	4	no	—
367	C₃×C₄²	—	2	2	no	—
368	C₃×C₄²	—	2	2	no	—
369	C₃×C₄²	—	2	4	no	—
370	C₃×C₄²	—	2	4	no	—
371	C₃×C₄²	—	4	2	no	—
372	C₃×C₄²	—	4	2	no	—
373	C₃×C₄²	C₂×D₄	1	4	yes	—
374	C₃×C₄²	C₂×D₄	1	4	yes	—
375	C₃×C₄²	#41	1	4	yes	—
376	C₃×C₄²	#41	1	4	yes	—
377	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
378	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
379	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
380	C₂²×Q₈	C₂³×C₃	1	2	yes	—
381	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
382	C₂²×D₄	C₂³×C₃	1	2	yes	—
383	C₂³×C₄	C₂³×C₃	1	2	yes	—
384	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₃	1	2	yes	—
386	C₄⋊Q₈	—	2	4	no	—
387	C₄⋊Q₈	—	2	4	no	—
388	C₄⋊Q₈	—	2	4	no	—
389	C₄⋊Q₈	—	2	4	no	—
390	#126	—	2	8	no	—
391	#126	—	2	8	no	—
392	#126	—	2	8	no	—
393	#125	—	2	8	no	—
394	#125	—	2	8	no	—
395	#125	—	2	4	no	—
396	#124	—	2	8	no	—
397	#124	—	2	4	no	—
398	#124	—	2	4	no	—
399	#124	—	2	4	no	—
400	#123	—	2	8	no	—
401	C₂²⋊Q₈	—	2	4	no	—
402	C₂²⋊Q₈	—	2	4	no	—
403	C₂²⋊Q₈	—	2	4	no	—
404	C₂²⋊Q₈	—	2	8	no	—
405	#121	—	2	4	no	—
406	C₄×Q₈	—	2	4	no	—
407	C₄×Q₈	—	2	4	no	—
408	C₄×Q₈	—	2	4	no	—
409	C₄×D₄	—	2	4	no	—
410	#117	—	2	4	no	—
411	#117	C₃×D₄	1	8	yes	—
412	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	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×C₄⋊C₄	C₂³×C₃	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
431	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
432	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
448	C₂×C₄²	—	2	4	no	—
449	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₃	1	2	yes	—
451	C₂×C₄²	C₂³×C₃	1	2	yes	—
452	C₂×C₄²	C₂³×C₃	1	2	yes	—
453	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₃	1	2	yes	—
455	C₂×C₄²	C₂³×C₃	1	2	yes	—
456	C₂×C₄²	C₂³×C₃	1	2	yes	—
457	C₂×C₄²	C₂³×C₃	1	2	yes	—
458	C₂×C₄²	C₂³×C₃	1	2	yes	—
459	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
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	4	yes	—
468	#95	C₂³×C₃	1	4	yes	—
469	#95	C₂³×C₃	1	4	yes	—
470	#95	C₂³×C₃	1	4	yes	—
471	#95	C₂³×C₃	1	4	yes	—
472	#95	C₂³×C₃	1	4	yes	—
473	#95	C₂³×C₃	1	4	yes	—
474	#95	C₂³×C₃	1	4	yes	—
475	C₂³×C₃	—	2	1	no	—
476	C₂³×C₃	—	2	1	no	—
477	C₂³×C₃	—	2	2	no	—
478	C₂³×C₃	—	2	2	no	—
479	C₂³×C₃	—	2	2	no	—
480	C₂³×C₃	—	2	2	no	—
481	C₂³×C₃	—	2	2	no	—
482	C₂³×C₃	—	2	4	no	—
483	C₂³×C₃	—	2	4	no	—
484	C₂³×C₃	C₂²×D₄	1	2	yes	—
485	C₂³×C₃	C₂⁵	1	1	yes	characteristic
486	C₃×Q₈	—	4	4	no	—
487	C₃×Q₈	—	4	4	no	—
488	C₃×Q₈	—	4	4	no	—
489	C₃×Q₈	—	8	4	no	—
490	C₃×D₄	—	4	4	no	—
491	C₃×D₄	—	8	4	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	2	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	2	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	8	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	4	no	—
521	C₂×C₃×C₄	—	2	2	no	—
522	C₂×C₃×C₄	—	2	4	no	—
523	C₂×C₃×C₄	—	2	4	no	—
524	C₂×C₃×C₄	—	2	4	no	—
525	C₂×C₃×C₄	—	4	8	no	—
526	C₂×C₃×C₄	—	8	4	no	—
527	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
528	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
529	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
530	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
531	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
532	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
533	C₂×C₃×C₄	C₂×#41	1	4	yes	—
534	C₂×C₃×C₄	C₂×#41	1	4	yes	—
535	C₂×C₃×C₄	C₂×#41	1	2	yes	—
536	C₂×C₃×C₄	C₂×#41	1	2	yes	—
537	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
538	C₂⁴	C₂⁴×C₃	1	2	yes	—
539	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	2	4	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	4	4	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	4	no	—
563	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
564	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
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	1	yes	characteristic
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	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	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	2	8	no	—
599	C₄⋊C₄	—	4	4	no	—
600	C₄⋊C₄	—	4	4	no	—
601	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
602	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
616	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
617	C₄²	—	2	4	no	—
618	C₄²	—	2	4	no	—
619	C₄²	—	2	4	no	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	2	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	4	2	no	—
626	C₄²	—	4	2	no	—
627	C₄²	C₂×C₃×D₄	1	4	yes	—
628	C₄²	C₂×C₃×D₄	1	4	yes	—
629	C₄²	C₃×#41	1	4	yes	—
630	C₄²	C₃×#41	1	4	yes	—
631	C₂²×C₃	—	2	2	no	—
632	C₂²×C₃	—	2	2	no	—
633	C₂²×C₃	—	2	2	no	—
634	C₂²×C₃	—	4	2	no	—
635	C₂²×C₃	—	4	2	no	—
636	C₂²×C₃	—	4	2	no	—
637	C₂²×C₃	—	4	4	no	—
638	C₂²×C₃	—	4	4	no	—
639	C₂²×C₃	—	4	2	no	—
640	C₂²×C₃	—	4	2	no	—
641	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
642	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
643	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
644	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
645	C₂²×C₃	#585	1	2	yes	—
646	C₃×C₄	—	2	2	no	—
647	C₃×C₄	—	2	4	no	—
648	C₃×C₄	—	2	4	no	—
649	C₃×C₄	—	2	4	no	—
650	C₃×C₄	—	2	2	no	—
651	C₃×C₄	—	2	2	no	—
652	C₃×C₄	—	2	2	no	—
653	C₃×C₄	—	2	2	no	—
654	C₃×C₄	—	4	2	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	2	no	—
662	C₃×C₄	#532	1	4	yes	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	4	no	—
672	C₂³	C₂²×C₃×D₄	1	2	yes	—
673	C₂³	C₂⁵×C₃	1	1	yes	characteristic
674	Q₈	—	4	4	no	—
675	Q₈	—	4	4	no	—
676	Q₈	—	4	4	no	—
677	Q₈	—	8	4	no	—
678	D₄	—	4	4	no	—
679	D₄	—	8	4	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	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	8	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	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
716	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
717	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
718	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
719	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
720	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
721	C₂×C₄	C₂×C₃×#41	1	4	yes	—
722	C₂×C₄	C₂×C₃×#41	1	4	yes	—
723	C₂×C₄	C₂×C₃×#41	1	2	yes	—
724	C₂×C₄	C₂×C₃×#41	1	2	yes	—
725	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
726	C₂×C₃	—	4	2	no	—
727	C₂×C₃	—	8	2	no	—
728	C₂×C₃	C₂×#532	1	1	yes	characteristic
729	C₂×C₃	#3461	1	2	yes	—
730	C₂×C₃	#3495	1	2	yes	—
731	C₂×C₃	#3499	1	1	yes	characteristic
732	C₂×C₃	#3500	1	1	yes	characteristic
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
744	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
745	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
746	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
747	C₂²	C₃×#585	1	2	yes	—
748	C₄	—	2	2	no	—
749	C₄	—	2	4	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₃×#532	1	4	yes	—
765	C₃	#35318	1	1	yes	characteristic, direct product factor, Sylow
766	C₂	—	4	2	no	—
767	C₂	—	8	2	no	—
768	C₂	C₂×C₃×#532	1	1	yes	characteristic
769	C₂	C₃×#3461	1	2	yes	—
770	C₂	C₃×#3495	1	2	yes	—
771	C₂	C₃×#3499	1	1	yes	characteristic
772	C₂	C₃×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#121	C₂²
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
2. C₂×C₃×#541	C₂	semidirect
3. C₃×#2862	C₂	semidirect
4. C₃×#2861	C₂	semidirect
5. C₃×#2857	C₂	semidirect
7. C₃×#2660	C₂	semidirect
8. C₃×#2658	C₂	semidirect
9. C₃×#2621	C₂	semidirect
11. C₃×#2556	C₂	semidirect
12. C₃×#2553	C₂	semidirect
13. C₃×#2521	C₂	semidirect
14. C₃×#2519	C₂	semidirect
15. C₃×#2327	C₂	semidirect
16. C₃×#2326	C₂	semidirect
17. C₃×C₄×C₄⋊Q₈	C₂	semidirect
18. C₃×C₄×#124	C₂	semidirect
19. C₃×C₄×#117	C₂	semidirect
20. #35318	C₃	direct (N × H)
95. C₂×#541	C₂×C₃	semidirect
96. #2862	C₂×C₃	semidirect
97. #2861	C₂×C₃	semidirect
98. #2857	C₂×C₃	semidirect
100. #2660	C₂×C₃	semidirect
101. #2658	C₂×C₃	semidirect
102. #2621	C₂×C₃	semidirect
104. #2556	C₂×C₃	semidirect
105. #2553	C₂×C₃	semidirect
106. #2521	C₂×C₃	semidirect
107. #2519	C₂×C₃	semidirect
108. #2327	C₂×C₃	semidirect
109. #2326	C₂×C₃	semidirect
110. C₄×C₄⋊Q₈	C₂×C₃	semidirect
111. C₄×#124	C₂×C₃	semidirect
112. C₄×#117	C₂×C₃	semidirect
765. C₃	#35318	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×#542	2
C₂×C₃×#541	2
C₃×#2862	2
C₃×#2861	2
C₃×#2857	2
C₃×#2850	2
C₃×#2660	2
C₃×#2658	2
C₃×#2621	2
C₃×#2620	2
C₃×#2556	2
C₃×#2553	2
C₃×#2521	2
C₃×#2519	2
C₃×#2327	2
C₃×#2326	2
C₃×C₄×C₄⋊Q₈	2
C₃×C₄×#124	2
C₃×C₄×#117	2
#35318	3

Subgroups — C3×#35318 #10653925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35318 #10653925