Subgroups — C₂×C₃×#5193 #11899540

Order 1152.

933 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5193	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#828	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#826	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#812	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#509	—	3	1	no	maximal
8	C₂×#5193	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃²×#41	—	2	1	no	—
10	C₂²×C₃×D₁₂	—	2	1	no	—
11	C₃²×#135	—	2	2	no	—
12	C₃²×#135	C₂²	1	4	yes	complemented
13	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃²×SD₁₆	—	2	1	no	—
15	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×D₂₄	—	2	2	no	—
18	C₂×C₃×D₂₄	—	2	1	no	—
19	C₂×C₃×D₂₄	C₂²	1	2	yes	—
20	C₂×C₃×D₂₄	C₂²	1	4	yes	complemented
21	C₃×#828	C₂²	1	8	yes	complemented
22	C₃×#826	C₂²	1	8	yes	complemented
23	C₃×#812	C₂²	1	4	yes	complemented
24	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	complemented
25	C₂×C₃×#135	—	2	1	no	—
26	C₂×C₃×#135	D₃	1	1	yes	characteristic, complemented
27	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×C₃×D₈	—	3	1	no	—
29	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
30	C₃×#509	—	3	8	no	—
31	C₂×C₃×SD₃₂	—	3	2	no	—
32	C₂×C₃×D₁₆	—	3	2	no	—
33	C₂×C₃×M₃₂	—	3	1	no	—
34	#5193	C₂×C₃	1	8	yes	direct product factor
35	C₂×#828	C₂×C₃	1	2	yes	complemented
36	C₂×#826	C₂×C₃	1	2	yes	complemented
37	C₂×#812	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×C₃×D₃	—	4	1	no	—
39	C₃²×#41	—	2	4	no	—
40	C₃²×#41	—	4	2	no	—
41	C₂×C₃²×Q₈	—	2	1	no	—
42	C₂×C₃²×D₄	—	2	1	no	—
43	C₂×C₃²×D₄	—	4	1	no	—
44	C₂²×C₃²×C₄	—	4	1	no	—
45	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
46	C₂×C₃×D₁₂	—	2	2	no	—
47	C₂×C₃×D₁₂	—	2	4	no	—
48	C₂×C₃×D₁₂	—	4	1	no	—
49	C₂×C₃×D₁₂	—	4	2	no	—
50	C₃²×Q₁₆	—	2	1	no	—
51	C₃²×Q₁₆	C₂³	1	2	yes	complemented
52	C₃²×SD₁₆	—	2	4	no	—
53	C₃²×D₈	—	2	1	no	—
54	C₃²×D₈	C₂³	1	2	yes	complemented
55	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
56	C₂×C₃²×C₈	D₄	1	2	yes	—
57	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
58	C₂×C₃²×C₈	C₂³	1	2	yes	—
59	C₃×D₂₄	—	2	2	no	—
60	C₃×D₂₄	—	2	4	no	—
61	C₃×D₂₄	C₂³	1	4	yes	—
62	C₃×C₃⋊C₁₆	C₂³	1	4	yes	complemented
63	C₂×#509	—	3	1	no	Sylow
64	C₂×C₃×#41	—	2	2	no	—
65	C₂×C₃×#41	—	2	1	no	—
66	C₂×C₃×#41	—	2	1	no	—
67	C₂²×C₃×D₄	—	6	1	no	—
68	C₂²×D₁₂	—	2	1	no	—
69	C₃×#135	—	2	4	no	—
70	C₃×#135	—	2	2	no	—
71	C₃×#135	—	2	2	no	—
72	C₃×#135	—	2	4	no	—
73	C₃×#135	C₂×D₃	1	4	yes	complemented
74	C₃×#135	C₂²×C₃	1	4	yes	complemented
75	C₂×C₃×Q₁₆	—	2	1	no	—
76	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
77	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
78	C₂×C₃×SD₁₆	—	2	2	no	—
79	C₂×C₃×SD₁₆	—	2	1	no	—
80	C₂×C₃×SD₁₆	—	2	1	no	—
81	C₂×C₃×D₈	—	2	1	no	—
82	C₂×C₃×D₈	—	3	2	no	—
83	C₂×C₃×D₈	—	3	4	no	—
84	C₂×C₃×D₈	—	6	1	no	—
85	C₂×C₃×D₈	—	6	2	no	—
86	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic, complemented
87	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₂²×C₃×C₈	—	2	1	no	—
89	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
90	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
91	C₂×D₂₄	—	2	2	no	—
92	C₂×D₂₄	—	2	1	no	—
93	C₂×D₂₄	C₂²×C₃	1	2	yes	—
94	C₂×D₂₄	C₂²×C₃	1	4	yes	complemented
95	C₃×SD₃₂	—	3	8	no	—
96	C₃×D₁₆	—	3	8	no	—
97	C₃×M₃₂	—	3	4	no	—
98	C₂×C₃×C₁₆	—	3	2	no	—
99	#828	C₂²×C₃	1	8	yes	complemented
100	#826	C₂²×C₃	1	8	yes	complemented
101	#812	C₂²×C₃	1	4	yes	complemented
102	C₂×C₃⋊C₁₆	C₂²×C₃	1	2	yes	complemented
103	C₂³×C₃²	—	4	1	no	—
104	C₂³×C₃²	D₈	1	1	yes	characteristic
105	C₂²×C₃×D₃	—	4	4	no	—
106	C₂²×C₃×D₃	—	4	2	no	—
107	C₂²×C₃×D₃	—	8	4	no	—
108	C₃²×Q₈	—	2	2	no	—
109	C₃²×Q₈	—	4	1	no	—
110	C₃²×D₄	—	2	2	no	—
111	C₃²×D₄	—	4	4	no	—
112	C₃²×D₄	—	4	1	no	—
113	C₂×C₃²×C₄	—	4	1	no	—
114	C₂×C₃²×C₄	—	4	4	no	—
115	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
116	C₂×C₃²×C₄	D₈	1	2	yes	—
117	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
119	C₃×D₁₂	—	2	4	no	—
120	C₃×D₁₂	—	4	4	no	—
121	C₃×D₁₂	—	4	2	no	—
122	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
123	C₃²×C₈	C₂×D₄	1	2	yes	—
124	C₃²×C₈	C₂⁴	1	1	yes	characteristic
125	C₂×#135	C₃×D₃	1	1	yes	characteristic, complemented
126	C₂²×D₈	—	3	1	no	—
127	#509	—	3	8	no	—
128	C₂×SD₃₂	—	3	2	no	—
129	C₂×D₁₆	—	3	2	no	—
130	C₂×M₃₂	—	3	1	no	—
131	C₂⁴×C₃	—	12	1	no	—
132	C₂³×D₃	—	4	1	no	—
133	C₃×#41	—	2	8	no	—
134	C₃×#41	—	2	4	no	—
135	C₃×#41	—	2	4	no	—
136	C₃×#41	—	4	4	no	—
137	C₃×#41	—	4	2	no	—
138	C₃×#41	—	4	2	no	—
139	C₂×C₃×Q₈	—	2	2	no	—
140	C₂×C₃×Q₈	—	2	1	no	—
141	C₂×C₃×Q₈	—	2	1	no	—
142	C₂×C₃×D₄	—	2	2	no	—
143	C₂×C₃×D₄	—	2	1	no	—
144	C₂×C₃×D₄	—	2	1	no	—
145	C₂×C₃×D₄	—	4	2	no	—
146	C₂×C₃×D₄	—	4	1	no	—
147	C₂×C₃×D₄	—	4	1	no	—
148	C₂×C₃×D₄	—	6	4	no	—
149	C₂×C₃×D₄	—	6	2	no	—
150	C₂×C₃×D₄	—	12	2	no	—
151	C₂×C₃×D₄	—	12	1	no	—
152	C₂²×C₃×C₄	—	2	1	no	—
153	C₂²×C₃×C₄	—	4	2	no	—
154	C₂²×C₃×C₄	—	4	1	no	—
155	C₂²×C₃×C₄	—	4	1	no	—
156	C₂²×C₃×C₄	#67	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
158	C₂×D₁₂	—	2	2	no	—
159	C₂×D₁₂	—	2	4	no	—
160	C₂×D₁₂	—	4	1	no	—
161	C₂×D₁₂	—	4	2	no	—
162	C₃×Q₁₆	—	2	2	no	—
163	C₃×Q₁₆	—	2	1	no	—
164	C₃×Q₁₆	—	2	1	no	—
165	C₃×Q₁₆	—	2	2	no	—
166	C₃×Q₁₆	C₂²×D₃	1	2	yes	complemented
167	C₃×Q₁₆	C₂³×C₃	1	2	yes	complemented
168	C₃×SD₁₆	—	2	8	no	—
169	C₃×SD₁₆	—	2	4	no	—
170	C₃×SD₁₆	—	2	4	no	—
171	C₃×D₈	—	2	2	no	—
172	C₃×D₈	—	2	1	no	—
173	C₃×D₈	—	2	1	no	—
174	C₃×D₈	—	2	2	no	—
175	C₃×D₈	—	3	4	no	—
176	C₃×D₈	—	6	2	no	—
177	C₃×D₈	—	6	4	no	—
178	C₃×D₈	C₂²×D₃	1	2	yes	complemented
179	C₃×D₈	C₂³×C₃	1	2	yes	complemented
180	C₂×C₃×C₈	—	2	1	no	—
181	C₂×C₃×C₈	—	2	2	no	—
182	C₂×C₃×C₈	—	2	1	no	—
183	C₂×C₃×C₈	—	2	2	no	—
184	C₂×C₃×C₈	#67	1	1	yes	characteristic
185	C₂×C₃×C₈	#67	1	2	yes	—
186	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
187	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
188	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
189	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
190	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
192	D₂₄	—	2	2	no	—
193	D₂₄	—	2	4	no	—
194	D₂₄	C₂³×C₃	1	4	yes	—
195	C₃×C₁₆	—	3	4	no	—
196	C₃⋊C₁₆	C₂³×C₃	1	4	yes	complemented
197	C₂²×C₃²	—	2	2	no	—
198	C₂²×C₃²	—	4	2	no	—
199	C₂²×C₃²	—	8	2	no	—
200	C₂²×C₃²	C₂×D₈	1	2	yes	—
201	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
202	C₂×C₃×D₃	—	4	4	no	—
203	C₂×C₃×D₃	—	8	8	no	—
204	C₂×C₃×D₃	—	8	4	no	—
205	C₃²×C₄	—	4	2	no	—
206	C₃²×C₄	C₂×D₈	1	2	yes	—
207	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
208	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
209	C₂×#41	—	2	1	no	—
210	C₂²×D₄	—	6	1	no	—
211	#135	—	2	2	no	—
212	#135	C₂×C₃×D₃	1	4	yes	complemented
213	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
214	C₂×SD₁₆	—	2	1	no	—
215	C₂×D₈	—	3	2	no	—
216	C₂×D₈	—	3	4	no	—
217	C₂×D₈	—	6	1	no	—
218	C₂×D₈	—	6	2	no	—
219	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
220	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
221	SD₃₂	—	3	8	no	—
222	D₁₆	—	3	8	no	—
223	M₃₂	—	3	4	no	—
224	C₂×C₁₆	—	3	2	no	—
225	C₂³×C₃	—	2	1	no	—
226	C₂³×C₃	—	4	2	no	—
227	C₂³×C₃	—	4	1	no	—
228	C₂³×C₃	—	4	1	no	—
229	C₂³×C₃	—	12	4	no	—
230	C₂³×C₃	—	12	2	no	—
231	C₂³×C₃	—	24	4	no	—
232	C₂³×C₃	#213	1	1	yes	characteristic
233	C₂³×C₃	C₃×D₈	1	1	yes	characteristic
234	C₂²×D₃	—	4	4	no	—
235	C₂²×D₃	—	4	2	no	—
236	C₂²×D₃	—	8	4	no	—
237	C₃×Q₈	—	2	4	no	—
238	C₃×Q₈	—	2	2	no	—
239	C₃×Q₈	—	2	2	no	—
240	C₃×Q₈	—	4	2	no	—
241	C₃×Q₈	—	4	1	no	—
242	C₃×Q₈	—	4	1	no	—
243	C₃×D₄	—	2	4	no	—
244	C₃×D₄	—	2	2	no	—
245	C₃×D₄	—	2	2	no	—
246	C₃×D₄	—	4	2	no	—
247	C₃×D₄	—	4	8	no	—
248	C₃×D₄	—	4	4	no	—
249	C₃×D₄	—	4	4	no	—
250	C₃×D₄	—	4	1	no	—
251	C₃×D₄	—	4	1	no	—
252	C₃×D₄	—	6	4	no	—
253	C₃×D₄	—	12	4	no	—
254	C₃×D₄	—	12	2	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	4	8	no	—
260	C₂×C₃×C₄	—	4	2	no	—
261	C₂×C₃×C₄	—	4	1	no	—
262	C₂×C₃×C₄	—	4	1	no	—
263	C₂×C₃×C₄	—	4	4	no	—
264	C₂×C₃×C₄	—	4	4	no	—
265	C₂×C₃×C₄	#213	1	2	yes	—
266	C₂×C₃×C₄	#213	1	1	yes	characteristic
267	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
268	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
269	C₂×C₃×C₄	C₂×#67	1	2	yes	—
270	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
273	D₁₂	—	2	4	no	—
274	D₁₂	—	4	4	no	—
275	D₁₂	—	4	2	no	—
276	C₃×C₈	—	2	1	no	—
277	C₃×C₈	—	2	1	no	—
278	C₃×C₈	—	2	2	no	—
279	C₃×C₈	C₂×#67	1	1	yes	characteristic
280	C₃×C₈	C₂×#67	1	2	yes	—
281	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
282	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
283	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
284	C₃×C₈	C₂⁴×C₃	1	1	yes	characteristic
285	C₂×C₃²	—	2	2	no	—
286	C₂×C₃²	—	8	2	no	—
287	C₂×C₃²	#509	1	2	yes	complemented
288	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
289	C₃×D₃	—	8	4	no	—
290	C₂⁴	—	12	1	no	—
291	#41	—	2	4	no	—
292	#41	—	4	2	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	6	2	no	—
297	C₂×D₄	—	6	4	no	—
298	C₂×D₄	—	12	1	no	—
299	C₂×D₄	—	12	2	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	C₃×#67	1	1	yes	characteristic
302	Q₁₆	—	2	1	no	—
303	Q₁₆	C₂²×C₃×D₃	1	2	yes	complemented
304	SD₁₆	—	2	4	no	—
305	D₈	—	2	1	no	—
306	D₈	—	3	4	no	—
307	D₈	—	6	2	no	—
308	D₈	—	6	4	no	—
309	D₈	C₂²×C₃×D₃	1	2	yes	complemented
310	C₂×C₈	C₃×#67	1	1	yes	characteristic
311	C₂×C₈	C₃×#67	1	2	yes	—
312	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
313	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
314	C₁₆	—	3	4	no	—
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	—	2	2	no	—
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	4	2	no	—
320	C₂²×C₃	—	4	4	no	—
321	C₂²×C₃	—	4	2	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	8	4	no	—
324	C₂²×C₃	—	8	2	no	—
325	C₂²×C₃	—	8	2	no	—
326	C₂²×C₃	—	12	4	no	—
327	C₂²×C₃	—	24	8	no	—
328	C₂²×C₃	—	24	4	no	—
329	C₂²×C₃	C₂×#213	1	2	yes	—
330	C₂²×C₃	C₂×#213	1	1	yes	characteristic
331	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
332	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
333	C₂×D₃	—	4	4	no	—
334	C₂×D₃	—	8	8	no	—
335	C₂×D₃	—	8	4	no	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	4	4	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	4	2	no	—
342	C₃×C₄	C₂×#213	1	2	yes	—
343	C₃×C₄	C₂×#213	1	1	yes	characteristic
344	C₃×C₄	C₂×C₃×D₈	1	2	yes	—
345	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
346	C₃×C₄	C₂²×#67	1	1	yes	characteristic
347	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
348	C₃²	C₂×#509	1	1	yes	characteristic, complemented, Sylow
349	C₂³	—	4	1	no	—
350	C₂³	—	12	4	no	—
351	C₂³	—	12	2	no	—
352	C₂³	—	24	4	no	—
353	C₂³	C₃×#213	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	D₄	—	2	2	no	—
357	D₄	—	4	4	no	—
358	D₄	—	4	1	no	—
359	D₄	—	6	4	no	—
360	D₄	—	12	4	no	—
361	D₄	—	12	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	C₃×#213	1	1	yes	characteristic
365	C₂×C₄	C₃×#213	1	2	yes	—
366	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
367	C₂×C₄	C₂×C₃×#67	1	2	yes	—
368	C₈	C₂×C₃×#67	1	1	yes	characteristic
369	C₈	C₂×C₃×#67	1	2	yes	—
370	C₈	C₂³×C₃×D₃	1	1	yes	characteristic
371	C₂×C₃	—	2	2	no	—
372	C₂×C₃	—	2	2	no	—
373	C₂×C₃	—	2	2	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	4	2	no	—
376	C₂×C₃	—	8	4	no	—
377	C₂×C₃	—	8	2	no	—
378	C₂×C₃	—	8	2	no	—
379	C₂×C₃	—	24	4	no	—
380	C₂×C₃	#5193	1	2	yes	direct product factor
381	C₂×C₃	C₃×#509	1	2	yes	complemented
382	C₂×C₃	C₂²×#213	1	1	yes	characteristic
383	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
384	D₃	—	8	4	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	12	4	no	—
389	C₂²	—	24	8	no	—
390	C₂²	—	24	4	no	—
391	C₂²	C₂×C₃×#213	1	2	yes	—
392	C₂²	C₂×C₃×#213	1	1	yes	characteristic
393	C₄	—	4	2	no	—
394	C₄	C₂×C₃×#213	1	2	yes	—
395	C₄	C₂×C₃×#213	1	1	yes	characteristic
396	C₄	C₂²×C₃×#67	1	1	yes	characteristic
397	C₃	—	2	1	no	—
398	C₃	C₂×#5193	1	1	yes	characteristic, direct product factor
399	C₃	C₂×C₃×#509	1	1	yes	characteristic, complemented
400	C₂	—	2	2	no	—
401	C₂	—	8	2	no	—
402	C₂	—	24	4	no	—
403	C₂	C₃×#5193	1	2	yes	direct product factor
404	C₂	C₂²×C₃×#213	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×#213
commutator, cosocle	C₃×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₃
Fitting	C₂×C₃²×#135	C₂
socle	C₂²×C₃²	C₂×D₈
hypercenter	C₂×C₃×#135	D₃
hypocenter	C₃	C₂×C₃×#509
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#135	C₂	semidirect
2. C₂²×C₃×D₂₄	C₂	semidirect
3. C₃×#5193	C₂	direct (N × H)
4. C₂×C₃×#828	C₂	semidirect
5. C₂×C₃×#826	C₂	semidirect
6. C₂×C₃×#812	C₂	semidirect
8. C₂×#5193	C₃	direct (N × H)
12. C₃²×#135	C₂²	semidirect
13. C₂×C₃²×Q₁₆	C₂²	semidirect
15. C₂×C₃²×D₈	C₂²	semidirect
20. C₂×C₃×D₂₄	C₂²	semidirect
21. C₃×#828	C₂²	semidirect
22. C₃×#826	C₂²	semidirect
23. C₃×#812	C₂²	semidirect
24. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
26. C₂×C₃×#135	D₃	semidirect
27. C₂×C₃×#135	C₂×C₃	semidirect
29. C₂²×D₂₄	C₂×C₃	semidirect
34. #5193	C₂×C₃	direct (N × H)
35. C₂×#828	C₂×C₃	semidirect
36. C₂×#826	C₂×C₃	semidirect
37. C₂×#812	C₂×C₃	semidirect
51. C₃²×Q₁₆	C₂³	semidirect
54. C₃²×D₈	C₂³	semidirect
62. C₃×C₃⋊C₁₆	C₂³	semidirect
73. C₃×#135	C₂×D₃	semidirect
74. C₃×#135	C₂²×C₃	semidirect
76. C₂×C₃×Q₁₆	C₂×D₃	semidirect
77. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
86. C₂×C₃×D₈	C₂×D₃	semidirect
87. C₂×C₃×D₈	C₂²×C₃	semidirect
94. C₂×D₂₄	C₂²×C₃	semidirect
99. #828	C₂²×C₃	semidirect
100. #826	C₂²×C₃	semidirect
101. #812	C₂²×C₃	semidirect
102. C₂×C₃⋊C₁₆	C₂²×C₃	semidirect
125. C₂×#135	C₃×D₃	semidirect
166. C₃×Q₁₆	C₂²×D₃	semidirect
167. C₃×Q₁₆	C₂³×C₃	semidirect
178. C₃×D₈	C₂²×D₃	semidirect
179. C₃×D₈	C₂³×C₃	semidirect
196. C₃⋊C₁₆	C₂³×C₃	semidirect
212. #135	C₂×C₃×D₃	semidirect
213. C₂×Q₁₆	C₂×C₃×D₃	semidirect
219. C₂×D₈	C₂×C₃×D₃	semidirect
287. C₂×C₃²	#509	semidirect
303. Q₁₆	C₂²×C₃×D₃	semidirect
309. D₈	C₂²×C₃×D₃	semidirect
348. C₃²	C₂×#509	semidirect
380. C₂×C₃	#5193	direct (N × H)
381. C₂×C₃	C₃×#509	semidirect
398. C₃	C₂×#5193	direct (N × H)
399. C₃	C₂×C₃×#509	semidirect
403. C₂	C₃×#5193	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×C₃²×#135	2
C₂²×C₃×D₂₄	2
C₃×#5193	2
C₂×C₃×#828	2
C₂×C₃×#826	2
C₂×C₃×#812	2
C₂×C₃×#509	3
C₂×#5193	3

Subgroups — C2×C3×#5193 #11899540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5193 #11899540