Subgroups — C₃×#60619 #10679226

Order 768.

2206 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#535	C₂	1	1	yes	maximal, characteristic
3	C₃×#3140	C₂	1	4	yes	maximal, complemented
4	C₃×#3138	C₂	1	4	yes	maximal, complemented
5	C₃×#3136	C₂	1	16	yes	maximal, complemented
6	C₃×#2896	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#418	C₂	1	2	yes	maximal, complemented
8	C₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
9	#60619	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
11	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
13	C₃×#544	—	2	2	no	—
14	C₃×#544	C₂²	1	8	yes	complemented
15	C₃×#543	—	2	2	no	—
16	C₃×#535	—	2	4	no	—
17	C₃×#535	C₂²	1	8	yes	—
18	C₃×#533	—	2	4	no	—
19	C₃×#533	C₂²	1	4	yes	complemented
20	C₂×C₃×#127	C₂²	1	2	yes	—
21	C₂×C₃×#124	C₂²	1	2	yes	—
22	C₂×C₃×#121	—	2	2	no	—
23	C₂×C₃×#120	—	2	2	no	—
24	C₂×C₃×#117	C₂²	1	2	yes	—
25	C₂×C₃×#117	C₂²	1	1	yes	characteristic
26	C₃×#490	C₂²	1	16	yes	complemented
27	C₃×#489	C₂²	1	16	yes	complemented
28	C₃×#488	C₂²	1	16	yes	complemented
29	C₃×#486	C₂²	1	16	yes	complemented
30	C₃×#419	C₂²	1	4	yes	complemented
31	C₃×#418	C₂²	1	8	yes	—
32	C₃×#418	C₂²	1	8	yes	complemented
33	C₃×#418	C₂²	1	4	yes	complemented
34	C₃×#417	C₂²	1	8	yes	complemented
35	C₃×#416	C₂²	1	8	yes	complemented
36	C₂×C₃×#102	C₂²	1	8	yes	complemented
37	C₃×#405	C₂²	1	8	yes	complemented
38	C₃×C₄×M₁₆	C₂²	1	4	yes	complemented
39	#3458	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×#535	C₂×C₃	1	1	yes	characteristic
41	#3140	C₂×C₃	1	4	yes	complemented
42	#3138	C₂×C₃	1	4	yes	complemented
43	#3136	C₂×C₃	1	16	yes	complemented
44	#2896	C₂×C₃	1	2	yes	complemented
45	C₂×#418	C₂×C₃	1	2	yes	complemented
46	#2873	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂⁵×C₃	—	2	1	no	—
48	C₂×C₃×#41	—	2	2	no	—
49	C₂×C₃×#41	—	2	8	no	—
50	C₂×C₃×#41	C₂³	1	4	yes	—
51	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
52	C₂²×C₃×D₄	—	2	1	no	—
53	C₂²×C₃×D₄	—	2	1	no	—
54	C₂²×C₃×D₄	—	2	2	no	—
55	C₂²×C₃×D₄	—	2	4	no	—
56	C₂²×C₃×D₄	—	2	8	no	—
57	C₂²×C₃×D₄	C₂³	1	4	yes	—
58	C₂²×C₃×D₄	C₂³	1	2	yes	—
59	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
60	C₂³×C₃×C₄	—	2	1	no	—
61	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
62	C₂×C₃×M₁₆	—	2	8	no	—
63	C₂×C₃×M₁₆	C₂³	1	4	yes	—
64	C₂×C₃×M₁₆	C₂³	1	4	yes	—
65	C₂²×C₃×C₈	C₂³	1	4	yes	—
66	C₃×C₄⋊Q₈	—	2	8	no	—
67	C₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
68	C₃×#127	—	2	4	no	—
69	C₃×#127	C₂³	1	8	yes	—
70	C₃×#125	—	2	8	no	—
71	C₃×#125	C₂³	1	8	yes	complemented
72	C₃×#124	—	2	4	no	—
73	C₃×#124	C₂³	1	8	yes	—
74	C₃×C₂²⋊Q₈	—	2	8	no	—
75	C₃×C₂²⋊Q₈	—	2	16	no	—
76	C₃×#121	—	2	16	no	—
77	C₃×#120	—	2	16	no	—
78	C₃×C₄×Q₈	—	2	8	no	—
79	C₃×#117	—	2	2	no	—
80	C₃×#117	—	2	2	no	—
81	C₃×#117	D₄	1	4	yes	—
82	C₃×#117	C₂³	1	4	yes	—
83	C₃×#117	C₂³	1	4	yes	—
84	C₃×#117	C₂³	1	4	yes	—
85	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
86	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
89	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
90	C₂×C₃×C₄²	—	2	2	no	—
91	C₂×C₃×C₄²	C₂³	1	2	yes	—
92	C₃×#103	C₂³	1	16	yes	complemented
93	C₃×#102	C₂³	1	32	yes	—
94	C₃×#102	C₂³	1	16	yes	complemented
95	C₃×#97	C₂³	1	8	yes	complemented
96	C₃×C₄×C₈	C₂³	1	8	yes	complemented
97	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
98	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
99	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
100	#544	—	2	2	no	—
101	#544	C₂²×C₃	1	8	yes	complemented
102	#543	—	2	2	no	—
103	#535	—	2	4	no	—
104	#535	C₂²×C₃	1	8	yes	—
105	#533	—	2	4	no	—
106	#533	C₂²×C₃	1	4	yes	complemented
107	C₂×#127	C₂²×C₃	1	2	yes	—
108	C₂×#124	C₂²×C₃	1	2	yes	—
109	C₂×#121	—	2	2	no	—
110	C₂×#120	—	2	2	no	—
111	C₂×#117	C₂²×C₃	1	2	yes	—
112	C₂×#117	C₂²×C₃	1	1	yes	characteristic
113	#490	C₂²×C₃	1	16	yes	complemented
114	#489	C₂²×C₃	1	16	yes	complemented
115	#488	C₂²×C₃	1	16	yes	complemented
116	#486	C₂²×C₃	1	16	yes	complemented
117	#419	C₂²×C₃	1	4	yes	complemented
118	#418	C₂²×C₃	1	8	yes	—
119	#418	C₂²×C₃	1	8	yes	complemented
120	#418	C₂²×C₃	1	4	yes	complemented
121	#417	C₂²×C₃	1	8	yes	complemented
122	#416	C₂²×C₃	1	8	yes	complemented
123	C₂×#102	C₂²×C₃	1	8	yes	complemented
124	#405	C₂²×C₃	1	8	yes	complemented
125	C₄×M₁₆	C₂²×C₃	1	4	yes	complemented
126	C₂⁴×C₃	—	2	2	no	—
127	C₂⁴×C₃	—	2	1	no	—
128	C₂⁴×C₃	—	2	4	no	—
129	C₂⁴×C₃	—	4	4	no	—
130	C₂⁴×C₃	—	8	4	no	—
131	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
132	C₃×#41	—	2	8	no	—
133	C₃×#41	—	2	8	no	—
134	C₃×#41	—	4	8	no	—
135	C₂×C₃×Q₈	—	2	1	no	—
136	C₂×C₃×Q₈	—	2	8	no	—
137	C₂×C₃×Q₈	—	2	4	no	—
138	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
139	C₂×C₃×D₄	—	2	4	no	—
140	C₂×C₃×D₄	—	2	4	no	—
141	C₂×C₃×D₄	—	2	2	no	—
142	C₂×C₃×D₄	—	2	1	no	—
143	C₂×C₃×D₄	—	2	16	no	—
144	C₂×C₃×D₄	—	2	8	no	—
145	C₂×C₃×D₄	—	2	8	no	—
146	C₂×C₃×D₄	—	2	8	no	—
147	C₂×C₃×D₄	—	2	4	no	—
148	C₂×C₃×D₄	—	4	4	no	—
149	C₂×C₃×D₄	—	4	4	no	—
150	C₂×C₃×D₄	—	4	8	no	—
151	C₂×C₃×D₄	—	8	8	no	—
152	C₂×C₃×D₄	C₂⁴	1	4	yes	—
153	C₂×C₃×D₄	C₂⁴	1	2	yes	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₂²×C₃×C₄	—	2	4	no	—
156	C₂²×C₃×C₄	—	2	4	no	—
157	C₂²×C₃×C₄	—	4	4	no	—
158	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
159	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
160	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₃×C₄	#41	1	8	yes	—
162	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
164	C₃×M₁₆	—	2	8	no	—
165	C₃×M₁₆	—	2	8	no	—
166	C₂×C₃×C₈	—	2	8	no	—
167	C₂×C₃×C₈	C₂⁴	1	8	yes	—
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	8	no	—
170	C₃×C₄⋊C₄	—	2	16	no	—
171	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
172	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
173	C₃×C₂²⋊C₄	—	2	4	no	—
174	C₃×C₂²⋊C₄	—	2	4	no	—
175	C₃×C₂²⋊C₄	—	2	16	no	—
176	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
177	C₃×C₄²	—	2	4	no	—
178	C₃×C₄²	—	2	4	no	—
179	C₃×C₄²	C₂×D₄	1	4	yes	—
180	C₃×C₄²	C₂⁴	1	4	yes	—
181	C₂⁵	—	2	1	no	—
182	C₂×#41	—	2	2	no	—
183	C₂×#41	—	2	8	no	—
184	C₂×#41	C₂³×C₃	1	4	yes	—
185	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
186	C₂²×D₄	—	2	1	no	—
187	C₂²×D₄	—	2	1	no	—
188	C₂²×D₄	—	2	2	no	—
189	C₂²×D₄	—	2	4	no	—
190	C₂²×D₄	—	2	8	no	—
191	C₂²×D₄	C₂³×C₃	1	2	yes	—
192	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
193	C₂²×D₄	C₂³×C₃	1	4	yes	—
194	C₂³×C₄	—	2	1	no	—
195	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
196	C₂×M₁₆	—	2	8	no	—
197	C₂×M₁₆	C₂³×C₃	1	4	yes	—
198	C₂×M₁₆	C₂³×C₃	1	4	yes	—
199	C₂²×C₈	C₂³×C₃	1	4	yes	—
200	C₄⋊Q₈	—	2	8	no	—
201	C₄⋊Q₈	C₂³×C₃	1	8	yes	complemented
202	#127	—	2	4	no	—
203	#127	C₂³×C₃	1	8	yes	—
204	#125	—	2	8	no	—
205	#125	C₂³×C₃	1	8	yes	complemented
206	#124	—	2	4	no	—
207	#124	C₂³×C₃	1	8	yes	—
208	C₂²⋊Q₈	—	2	8	no	—
209	C₂²⋊Q₈	—	2	16	no	—
210	#121	—	2	16	no	—
211	#120	—	2	16	no	—
212	C₄×Q₈	—	2	8	no	—
213	#117	—	2	2	no	—
214	#117	—	2	2	no	—
215	#117	C₃×D₄	1	4	yes	—
216	#117	C₂³×C₃	1	4	yes	—
217	#117	C₂³×C₃	1	4	yes	—
218	#117	C₂³×C₃	1	4	yes	—
219	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
220	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
221	C₂×C₂²⋊C₄	—	2	2	no	—
222	C₂×C₂²⋊C₄	—	2	4	no	—
223	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
224	C₂×C₄²	—	2	2	no	—
225	C₂×C₄²	C₂³×C₃	1	2	yes	—
226	#103	C₂³×C₃	1	16	yes	complemented
227	#102	C₂³×C₃	1	32	yes	—
228	#102	C₂³×C₃	1	16	yes	complemented
229	#97	C₂³×C₃	1	8	yes	complemented
230	C₄×C₈	C₂³×C₃	1	8	yes	complemented
231	C₂³×C₃	—	2	4	no	—
232	C₂³×C₃	—	2	2	no	—
233	C₂³×C₃	—	4	2	no	—
234	C₂³×C₃	—	4	4	no	—
235	C₂³×C₃	—	4	8	no	—
236	C₂³×C₃	—	4	2	no	—
237	C₂³×C₃	—	4	4	no	—
238	C₂³×C₃	—	4	8	no	—
239	C₂³×C₃	—	8	8	no	—
240	C₂³×C₃	—	8	16	no	—
241	C₂³×C₃	#124	1	4	yes	—
242	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
243	C₂³×C₃	C₂²×D₄	1	2	yes	—
244	C₃×Q₈	—	2	4	no	—
245	C₃×Q₈	—	4	2	no	—
246	C₃×Q₈	—	8	8	no	—
247	C₃×D₄	—	2	8	no	—
248	C₃×D₄	—	2	4	no	—
249	C₃×D₄	—	4	8	no	—
250	C₃×D₄	—	4	8	no	—
251	C₃×D₄	—	4	4	no	—
252	C₃×D₄	—	4	2	no	—
253	C₃×D₄	—	8	16	no	—
254	C₂×C₃×C₄	—	2	8	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	4	4	no	—
257	C₂×C₃×C₄	—	4	2	no	—
258	C₂×C₃×C₄	—	4	8	no	—
259	C₂×C₃×C₄	—	8	4	no	—
260	C₂×C₃×C₄	#124	1	4	yes	—
261	C₂×C₃×C₄	#124	1	8	yes	—
262	C₂×C₃×C₄	C₂²×D₄	1	8	yes	—
263	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
265	C₂×C₃×C₄	C₂×#41	1	4	yes	—
266	C₂×C₃×C₄	C₂×#41	1	4	yes	—
267	C₂×C₃×C₄	C₂×#41	1	4	yes	—
268	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
269	C₃×C₈	—	2	8	no	—
270	C₂⁴	—	2	2	no	—
271	C₂⁴	—	2	1	no	—
272	C₂⁴	—	2	4	no	—
273	C₂⁴	—	4	4	no	—
274	C₂⁴	—	8	4	no	—
275	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
276	#41	—	2	8	no	—
277	#41	—	2	8	no	—
278	#41	—	4	8	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×Q₈	—	2	8	no	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	16	no	—
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	2	8	no	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	4	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	8	no	—
295	C₂×D₄	—	8	8	no	—
296	C₂×D₄	C₂⁴×C₃	1	4	yes	—
297	C₂×D₄	C₂⁴×C₃	1	2	yes	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
303	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
304	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
305	C₂²×C₄	C₃×#41	1	8	yes	—
306	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
308	M₁₆	—	2	8	no	—
309	M₁₆	—	2	8	no	—
310	C₂×C₈	—	2	8	no	—
311	C₂×C₈	C₂⁴×C₃	1	8	yes	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	16	no	—
315	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
316	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	—	2	16	no	—
320	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	4	no	—
323	C₄²	C₂×C₃×D₄	1	4	yes	—
324	C₄²	C₂⁴×C₃	1	4	yes	—
325	C₂²×C₃	—	2	2	no	—
326	C₂²×C₃	—	2	4	no	—
327	C₂²×C₃	—	4	4	no	—
328	C₂²×C₃	—	4	4	no	—
329	C₂²×C₃	—	4	8	no	—
330	C₂²×C₃	—	4	2	no	—
331	C₂²×C₃	—	4	4	no	—
332	C₂²×C₃	—	8	4	no	—
333	C₂²×C₃	—	8	8	no	—
334	C₂²×C₃	—	8	16	no	—
335	C₂²×C₃	C₂×#124	1	2	yes	—
336	C₂²×C₃	C₂×#124	1	4	yes	—
337	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
338	C₃×C₄	—	2	8	no	—
339	C₃×C₄	—	4	8	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	C₂×#124	1	4	yes	—
342	C₃×C₄	C₂×#124	1	2	yes	—
343	C₃×C₄	C₂²×#41	1	2	yes	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	8	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	4	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	8	8	no	—
353	C₂³	—	8	16	no	—
354	C₂³	C₃×#124	1	4	yes	—
355	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
356	C₂³	C₂²×C₃×D₄	1	2	yes	—
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	8	8	no	—
360	D₄	—	2	8	no	—
361	D₄	—	2	4	no	—
362	D₄	—	4	8	no	—
363	D₄	—	4	8	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	2	no	—
366	D₄	—	8	16	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	—	8	4	no	—
373	C₂×C₄	C₃×#124	1	4	yes	—
374	C₂×C₄	C₃×#124	1	8	yes	—
375	C₂×C₄	C₂²×C₃×D₄	1	8	yes	—
376	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
378	C₂×C₄	C₂×C₃×#41	1	4	yes	—
379	C₂×C₄	C₂×C₃×#41	1	4	yes	—
380	C₂×C₄	C₂×C₃×#41	1	4	yes	—
381	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
382	C₈	—	2	8	no	—
383	C₂×C₃	—	2	2	no	—
384	C₂×C₃	—	2	4	no	—
385	C₂×C₃	—	8	2	no	—
386	C₂×C₃	—	8	4	no	—
387	C₂×C₃	C₂²×#124	1	1	yes	characteristic
388	C₂×C₃	#3585	1	2	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	8	no	—
396	C₂²	—	8	8	no	—
397	C₂²	—	8	4	no	—
398	C₂²	—	8	16	no	—
399	C₂²	C₂×C₃×#124	1	2	yes	—
400	C₂²	C₂×C₃×#124	1	4	yes	—
401	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
402	C₄	—	2	8	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	8	no	—
405	C₄	C₂×C₃×#124	1	4	yes	—
406	C₄	C₂×C₃×#124	1	2	yes	—
407	C₄	C₂²×C₃×#41	1	2	yes	—
408	C₃	#60619	1	1	yes	characteristic, direct product factor, Sylow
409	C₂	—	2	2	no	—
410	C₂	—	2	4	no	—
411	C₂	—	8	4	no	—
412	C₂	—	8	2	no	—
413	C₂	C₂²×C₃×#124	1	1	yes	characteristic
414	C₂	C₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂×C₃×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3458	C₂	semidirect
3. C₃×#3140	C₂	semidirect
4. C₃×#3138	C₂	semidirect
5. C₃×#3136	C₂	semidirect
6. C₃×#2896	C₂	semidirect
7. C₂×C₃×#418	C₂	semidirect
8. C₃×#2873	C₂	semidirect
9. #60619	C₃	direct (N × H)
14. C₃×#544	C₂²	semidirect
19. C₃×#533	C₂²	semidirect
26. C₃×#490	C₂²	semidirect
27. C₃×#489	C₂²	semidirect
28. C₃×#488	C₂²	semidirect
29. C₃×#486	C₂²	semidirect
30. C₃×#419	C₂²	semidirect
32. C₃×#418	C₂²	semidirect
33. C₃×#418	C₂²	semidirect
34. C₃×#417	C₂²	semidirect
35. C₃×#416	C₂²	semidirect
36. C₂×C₃×#102	C₂²	semidirect
37. C₃×#405	C₂²	semidirect
38. C₃×C₄×M₁₆	C₂²	semidirect
39. #3458	C₂×C₃	semidirect
41. #3140	C₂×C₃	semidirect
42. #3138	C₂×C₃	semidirect
43. #3136	C₂×C₃	semidirect
44. #2896	C₂×C₃	semidirect
45. C₂×#418	C₂×C₃	semidirect
46. #2873	C₂×C₃	semidirect
67. C₃×C₄⋊Q₈	C₂³	semidirect
71. C₃×#125	C₂³	semidirect
92. C₃×#103	C₂³	semidirect
94. C₃×#102	C₂³	semidirect
95. C₃×#97	C₂³	semidirect
96. C₃×C₄×C₈	C₂³	semidirect
101. #544	C₂²×C₃	semidirect
106. #533	C₂²×C₃	semidirect
113. #490	C₂²×C₃	semidirect
114. #489	C₂²×C₃	semidirect
115. #488	C₂²×C₃	semidirect
116. #486	C₂²×C₃	semidirect
117. #419	C₂²×C₃	semidirect
119. #418	C₂²×C₃	semidirect
120. #418	C₂²×C₃	semidirect
121. #417	C₂²×C₃	semidirect
122. #416	C₂²×C₃	semidirect
123. C₂×#102	C₂²×C₃	semidirect
124. #405	C₂²×C₃	semidirect
125. C₄×M₁₆	C₂²×C₃	semidirect
201. C₄⋊Q₈	C₂³×C₃	semidirect
205. #125	C₂³×C₃	semidirect
226. #103	C₂³×C₃	semidirect
228. #102	C₂³×C₃	semidirect
229. #97	C₂³×C₃	semidirect
230. C₄×C₈	C₂³×C₃	semidirect
408. C₃	#60619	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×#3458	2
C₂×C₃×#535	2
C₃×#3140	2
C₃×#3138	2
C₃×#3136	2
C₃×#2896	2
C₂×C₃×#418	2
C₃×#2873	2
#60619	3

Subgroups — C3×#60619 #10679226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60619 #10679226