Subgroups — C₃²×#5048 #13162484

Order 1728.

1040 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×#215	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#930	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₃²×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#809	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#465	—	3	1	no	maximal
9	C₃×#5048	C₃	1	4	yes	maximal, direct product factor
10	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃²×#67	—	2	1	no	—
13	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
14	C₃³×C₄⋊C₄	—	2	1	no	—
15	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃³×C₂²⋊C₄	—	2	1	no	—
17	C₃²×#215	—	2	2	no	—
18	C₃²×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₃²×C₃⋊C₈	—	2	2	no	—
21	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₃²×SD₁₆	—	3	1	no	—
24	C₂²×C₃²×C₈	—	3	1	no	—
25	C₃²×C₂²⋊Q₈	—	2	4	no	—
26	C₃²×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
27	C₃²×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
28	C₃²×#121	—	3	1	no	—
29	C₂×C₃×#215	C₂×C₃	1	4	yes	complemented
30	C₃×#930	C₂×C₃	1	4	yes	—
31	C₂²×C₃×C₃⋊C₈	C₂×C₃	1	4	yes	complemented
32	C₃²×#106	—	3	1	no	—
33	C₃²×#103	—	3	1	no	—
34	C₃²×#102	—	3	1	no	—
35	C₃×#835	C₂×C₃	1	4	yes	complemented
36	C₃×#809	C₂×C₃	1	4	yes	complemented
37	C₃×#808	C₂×C₃	1	4	yes	complemented
38	C₂³×C₃³	D₄	1	1	yes	characteristic
39	C₂²×C₃²×D₃	—	2	1	no	—
40	C₃³×Q₈	—	2	1	no	—
41	C₃³×Q₈	—	2	1	no	—
42	C₂×C₃³×C₄	—	2	1	no	—
43	C₂×C₃³×C₄	—	2	1	no	—
44	C₂×C₃³×C₄	—	2	1	no	—
45	C₂×C₃³×C₄	—	2	1	no	—
46	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
47	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
48	C₃²×#67	—	4	2	no	—
49	C₂×C₃²×Dic₃	—	2	1	no	—
50	C₃²×D₁₂	—	2	1	no	—
51	C₃²×D₁₂	—	2	1	no	—
52	C₃²×C₃⋊C₈	—	2	1	no	—
53	C₃²×C₃⋊C₈	D₄	1	2	yes	complemented
54	C₃×#465	—	3	4	no	—
55	#5048	C₃²	1	1	yes	characteristic, direct product factor
56	C₂×C₃²×Q₈	—	2	4	no	—
57	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
58	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
59	C₂×C₃²×D₄	—	3	1	no	—
60	C₂×C₃²×D₄	—	6	1	no	—
61	C₂²×C₃²×C₄	—	2	4	no	—
62	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
63	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
64	C₂×C₃×#67	—	2	4	no	—
65	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
66	C₃²×SD₁₆	—	6	2	no	—
67	C₂×C₃²×C₈	—	3	1	no	—
68	C₂×C₃²×C₈	—	3	1	no	—
69	C₂×C₃²×C₈	—	6	2	no	—
70	C₃²×C₄⋊C₄	—	2	8	no	—
71	C₃²×C₄⋊C₄	—	2	4	no	—
72	C₃²×C₄⋊C₄	—	2	1	no	—
73	C₃²×C₄⋊C₄	—	2	4	no	—
74	C₃²×C₄⋊C₄	—	3	1	no	—
75	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
76	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
77	C₃²×C₂²⋊C₄	—	2	8	no	—
78	C₃²×C₂²⋊C₄	—	2	1	no	—
79	C₃²×C₂²⋊C₄	—	2	4	no	—
80	C₃²×C₂²⋊C₄	—	6	1	no	—
81	C₃×#215	—	2	8	no	—
82	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
83	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
84	C₂×C₃×C₃⋊C₈	—	2	8	no	—
85	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
86	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
87	C₂²×C₃³	—	2	1	no	—
88	C₂²×C₃³	—	2	1	no	—
89	C₂²×C₃³	SD₁₆	1	2	yes	complemented
90	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃²×D₃	—	4	1	no	—
92	C₂×C₃²×D₃	—	4	1	no	—
93	C₂×C₃²×D₃	—	4	1	no	—
94	C₃³×C₄	—	2	1	no	—
95	C₃³×C₄	—	4	1	no	—
96	C₃³×C₄	—	4	1	no	—
97	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
98	C₃³×C₄	#41	1	1	yes	characteristic
99	C₃²×Dic₃	—	4	1	no	—
100	C₂×C₃×SD₁₆	—	3	4	no	—
101	C₂²×C₃×C₈	—	3	4	no	—
102	C₃×C₂²⋊Q₈	—	2	4	no	—
103	C₃×C₂²⋊Q₈	C₃×D₃	1	4	yes	complemented
104	C₃×C₂²⋊Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
105	C₃×#121	—	3	4	no	—
106	C₂×#215	C₂×C₃²	1	1	yes	characteristic, complemented
107	#930	C₂×C₃²	1	1	yes	characteristic
108	C₂²×C₃⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
109	C₃×#106	—	3	4	no	—
110	C₃×#103	—	3	4	no	—
111	C₃×#102	—	3	4	no	—
112	#835	C₂×C₃²	1	1	yes	characteristic, complemented
113	#809	C₂×C₃²	1	1	yes	characteristic, complemented
114	#808	C₂×C₃²	1	1	yes	characteristic, complemented
115	C₂³×C₃²	—	2	4	no	—
116	C₂³×C₃²	—	6	1	no	—
117	C₂³×C₃²	#67	1	1	yes	characteristic
118	C₂³×C₃²	C₃×D₄	1	4	yes	—
119	C₂²×C₃×D₃	—	2	4	no	—
120	C₃²×Q₈	—	2	1	no	—
121	C₃²×Q₈	—	2	1	no	—
122	C₃²×Q₈	—	2	4	no	—
123	C₃²×Q₈	—	2	4	no	—
124	C₃²×Q₈	—	4	4	no	—
125	C₃²×Q₈	—	4	4	no	—
126	C₃²×D₄	—	6	1	no	—
127	C₃²×D₄	—	6	1	no	—
128	C₃²×D₄	—	12	2	no	—
129	C₂×C₃²×C₄	—	2	1	no	—
130	C₂×C₃²×C₄	—	2	1	no	—
131	C₂×C₃²×C₄	—	2	8	no	—
132	C₂×C₃²×C₄	—	2	8	no	—
133	C₂×C₃²×C₄	—	2	1	no	—
134	C₂×C₃²×C₄	—	2	1	no	—
135	C₂×C₃²×C₄	—	2	4	no	—
136	C₂×C₃²×C₄	—	2	4	no	—
137	C₂×C₃²×C₄	—	2	4	no	—
138	C₂×C₃²×C₄	—	2	4	no	—
139	C₂×C₃²×C₄	—	2	4	no	—
140	C₂×C₃²×C₄	—	2	4	no	—
141	C₂×C₃²×C₄	—	4	4	no	—
142	C₂×C₃²×C₄	—	4	4	no	—
143	C₂×C₃²×C₄	—	6	1	no	—
144	C₂×C₃²×C₄	#67	1	1	yes	characteristic
145	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
146	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
147	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
148	C₃×#67	—	4	8	no	—
149	C₂×C₃×Dic₃	—	2	4	no	—
150	C₃×D₁₂	—	2	4	no	—
151	C₃×D₁₂	—	2	4	no	—
152	C₃²×C₈	—	3	2	no	—
153	C₃²×C₈	—	6	1	no	—
154	C₃×C₃⋊C₈	—	2	4	no	—
155	C₃×C₃⋊C₈	C₃×D₄	1	8	yes	complemented
156	#465	—	3	1	no	Sylow
157	C₂×C₃³	—	2	2	no	—
158	C₂×C₃³	#121	1	1	yes	characteristic
159	C₂×C₃³	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×C₃³	#135	1	1	yes	characteristic
161	C₃²×D₃	—	8	1	no	—
162	C₂×C₃×Q₈	—	2	4	no	—
163	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
164	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
165	C₂×C₃×D₄	—	3	4	no	—
166	C₂×C₃×D₄	—	6	4	no	—
167	C₂²×C₃×C₄	—	2	4	no	—
168	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
169	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
170	C₂×#67	—	2	1	no	—
171	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
172	C₃×SD₁₆	—	6	8	no	—
173	C₂×C₃×C₈	—	3	4	no	—
174	C₂×C₃×C₈	—	3	4	no	—
175	C₂×C₃×C₈	—	6	8	no	—
176	C₃×C₄⋊C₄	—	2	8	no	—
177	C₃×C₄⋊C₄	—	2	4	no	—
178	C₃×C₄⋊C₄	—	2	1	no	—
179	C₃×C₄⋊C₄	—	2	4	no	—
180	C₃×C₄⋊C₄	—	3	4	no	—
181	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
182	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
183	C₃×C₂²⋊C₄	—	2	8	no	—
184	C₃×C₂²⋊C₄	—	2	4	no	—
185	C₃×C₂²⋊C₄	—	2	1	no	—
186	C₃×C₂²⋊C₄	—	6	4	no	—
187	#215	—	2	2	no	—
188	(C₂×D₃)⋊C₄	—	2	1	no	—
189	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
190	C₂×C₃⋊C₈	—	2	2	no	—
191	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
192	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
193	C₂²×C₃²	—	2	1	no	—
194	C₂²×C₃²	—	2	1	no	—
195	C₂²×C₃²	—	2	8	no	—
196	C₂²×C₃²	—	2	4	no	—
197	C₂²×C₃²	—	2	4	no	—
198	C₂²×C₃²	—	2	4	no	—
199	C₂²×C₃²	—	4	4	no	—
200	C₂²×C₃²	—	4	4	no	—
201	C₂²×C₃²	—	12	1	no	—
202	C₂²×C₃²	—	12	1	no	—
203	C₂²×C₃²	—	12	1	no	—
204	C₂²×C₃²	#215	1	2	yes	complemented
205	C₂²×C₃²	C₃×SD₁₆	1	8	yes	complemented
206	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
207	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
208	C₂×C₃×D₃	—	4	4	no	—
209	C₂×C₃×D₃	—	4	4	no	—
210	C₂×C₃×D₃	—	4	4	no	—
211	C₃²×C₄	—	2	1	no	—
212	C₃²×C₄	—	2	4	no	—
213	C₃²×C₄	—	2	4	no	—
214	C₃²×C₄	—	2	4	no	—
215	C₃²×C₄	—	4	4	no	—
216	C₃²×C₄	—	4	8	no	—
217	C₃²×C₄	—	4	8	no	—
218	C₃²×C₄	—	4	1	no	—
219	C₃²×C₄	—	4	1	no	—
220	C₃²×C₄	—	4	4	no	—
221	C₃²×C₄	—	4	4	no	—
222	C₃²×C₄	—	12	1	no	—
223	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
224	C₃²×C₄	#237	1	1	yes	characteristic
225	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
226	C₃²×C₄	C₃×#41	1	4	yes	—
227	C₃×Dic₃	—	4	4	no	—
228	C₂×SD₁₆	—	3	1	no	—
229	C₂²×C₈	—	3	1	no	—
230	C₂²⋊Q₈	C₃²×D₃	1	1	yes	characteristic, complemented
231	#121	—	3	1	no	—
232	#106	—	3	1	no	—
233	#103	—	3	1	no	—
234	#102	—	3	1	no	—
235	C₃³	#465	1	1	yes	characteristic, complemented, Sylow
236	C₂³×C₃	—	2	4	no	—
237	C₂³×C₃	—	6	4	no	—
238	C₂³×C₃	C₃×#67	1	4	yes	—
239	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
240	C₂²×D₃	—	2	1	no	—
241	C₃×Q₈	—	2	4	no	—
242	C₃×Q₈	—	2	4	no	—
243	C₃×Q₈	—	2	1	no	—
244	C₃×Q₈	—	2	1	no	—
245	C₃×Q₈	—	4	4	no	—
246	C₃×Q₈	—	4	4	no	—
247	C₃×D₄	—	6	4	no	—
248	C₃×D₄	—	6	4	no	—
249	C₃×D₄	—	12	8	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	8	no	—
255	C₂×C₃×C₄	—	2	8	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	4	4	no	—
263	C₂×C₃×C₄	—	4	4	no	—
264	C₂×C₃×C₄	—	6	4	no	—
265	C₂×C₃×C₄	C₃×#67	1	4	yes	—
266	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
268	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
269	#67	—	4	2	no	—
270	C₂×Dic₃	—	2	1	no	—
271	D₁₂	—	2	1	no	—
272	D₁₂	—	2	1	no	—
273	C₃×C₈	—	3	8	no	—
274	C₃×C₈	—	6	4	no	—
275	C₃⋊C₈	—	2	1	no	—
276	C₃⋊C₈	C₃²×D₄	1	2	yes	complemented
277	C₂×C₃²	—	2	2	no	—
278	C₂×C₃²	—	2	4	no	—
279	C₂×C₃²	—	2	4	no	—
280	C₂×C₃²	—	2	4	no	—
281	C₂×C₃²	—	2	8	no	—
282	C₂×C₃²	—	4	8	no	—
283	C₂×C₃²	—	24	1	no	—
284	C₂×C₃²	#939	1	1	yes	characteristic
285	C₂×C₃²	C₂×#215	1	1	yes	characteristic
286	C₂×C₃²	#950	1	1	yes	characteristic
287	C₂×C₃²	C₃×#121	1	4	yes	—
288	C₂×C₃²	C₂×C₃×SD₁₆	1	4	yes	—
289	C₂×C₃²	C₃×#135	1	4	yes	—
290	C₃×D₃	—	8	4	no	—
291	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
292	C₂×D₄	—	3	1	no	—
293	C₂×D₄	—	6	1	no	—
294	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
295	SD₁₆	—	6	2	no	—
296	C₂×C₈	—	3	1	no	—
297	C₂×C₈	—	3	1	no	—
298	C₂×C₈	—	6	2	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	3	1	no	—
301	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
302	C₂²⋊C₄	—	2	1	no	—
303	C₂²⋊C₄	—	6	1	no	—
304	C₂²×C₃	—	2	4	no	—
305	C₂²×C₃	—	2	4	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	2	1	no	—
308	C₂²×C₃	—	2	4	no	—
309	C₂²×C₃	—	2	8	no	—
310	C₂²×C₃	—	4	4	no	—
311	C₂²×C₃	—	4	4	no	—
312	C₂²×C₃	—	12	4	no	—
313	C₂²×C₃	—	12	4	no	—
314	C₂²×C₃	—	12	4	no	—
315	C₂²×C₃	C₃×#215	1	8	yes	complemented
316	C₂²×C₃	C₃²×SD₁₆	1	2	yes	complemented
317	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
318	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
319	C₂×D₃	—	4	1	no	—
320	C₂×D₃	—	4	1	no	—
321	C₂×D₃	—	4	1	no	—
322	C₃×C₄	—	2	4	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	4	no	—
325	C₃×C₄	—	2	4	no	—
326	C₃×C₄	—	4	4	no	—
327	C₃×C₄	—	4	8	no	—
328	C₃×C₄	—	4	8	no	—
329	C₃×C₄	—	4	4	no	—
330	C₃×C₄	—	4	4	no	—
331	C₃×C₄	—	4	1	no	—
332	C₃×C₄	—	4	1	no	—
333	C₃×C₄	—	12	4	no	—
334	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
335	C₃×C₄	C₃×#237	1	4	yes	—
336	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
337	C₃×C₄	C₃²×#41	1	1	yes	characteristic
338	Dic₃	—	4	1	no	—
339	C₃²	—	2	4	no	—
340	C₃²	#5048	1	1	yes	characteristic, direct product factor
341	C₃²	C₃×#465	1	4	yes	complemented
342	C₂³	—	6	1	no	—
343	C₂³	C₃²×#67	1	1	yes	characteristic
344	Q₈	—	2	1	no	—
345	Q₈	—	2	1	no	—
346	D₄	—	6	1	no	—
347	D₄	—	6	1	no	—
348	D₄	—	12	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	6	1	no	—
354	C₂×C₄	C₃²×#67	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
356	C₈	—	3	2	no	—
357	C₈	—	6	1	no	—
358	C₂×C₃	—	2	2	no	—
359	C₂×C₃	—	2	8	no	—
360	C₂×C₃	—	2	4	no	—
361	C₂×C₃	—	2	4	no	—
362	C₂×C₃	—	2	4	no	—
363	C₂×C₃	—	4	8	no	—
364	C₂×C₃	—	24	4	no	—
365	C₂×C₃	C₃×#939	1	4	yes	—
366	C₂×C₃	C₂×C₃×#215	1	4	yes	—
367	C₂×C₃	C₃×#950	1	4	yes	—
368	C₂×C₃	C₃²×#121	1	1	yes	characteristic
369	C₂×C₃	C₂×C₃²×SD₁₆	1	1	yes	characteristic
370	C₂×C₃	C₃²×#135	1	1	yes	characteristic
371	D₃	—	8	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	12	1	no	—
375	C₂²	—	12	1	no	—
376	C₂²	—	12	1	no	—
377	C₂²	C₃²×#215	1	2	yes	complemented
378	C₂²	C₂×C₃²×#67	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	12	1	no	—
383	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
384	C₄	C₃²×#237	1	1	yes	characteristic
385	C₃	—	2	4	no	—
386	C₃	C₃×#5048	1	4	yes	direct product factor
387	C₃	C₃²×#465	1	1	yes	characteristic, complemented
388	C₂	—	2	2	no	—
389	C₂	—	24	1	no	—
390	C₂	C₃²×#939	1	1	yes	characteristic
391	C₂	C₂×C₃²×#215	1	1	yes	characteristic
392	C₂	C₃²×#950	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂³×C₃²
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₃³×C₂²⋊Q₈	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₃²×#930	C₂
hypercenter	C₃²×C₂²⋊Q₈	D₃
hypocenter	C₃	C₃²×#465
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃²×C₄ ◁ C₃²×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₂²⋊Q₈	C₂	semidirect
2. C₂×C₃²×#215	C₂	semidirect
4. C₂²×C₃²×C₃⋊C₈	C₂	semidirect
5. C₃²×#835	C₂	semidirect
6. C₃²×#809	C₂	semidirect
7. C₃²×#808	C₂	semidirect
9. C₃×#5048	C₃	direct (N × H)
26. C₃²×C₂²⋊Q₈	D₃	semidirect
27. C₃²×C₂²⋊Q₈	C₂×C₃	semidirect
29. C₂×C₃×#215	C₂×C₃	semidirect
31. C₂²×C₃×C₃⋊C₈	C₂×C₃	semidirect
35. C₃×#835	C₂×C₃	semidirect
36. C₃×#809	C₂×C₃	semidirect
37. C₃×#808	C₂×C₃	semidirect
53. C₃²×C₃⋊C₈	D₄	semidirect
55. #5048	C₃²	direct (N × H)
89. C₂²×C₃³	SD₁₆	semidirect
103. C₃×C₂²⋊Q₈	C₃×D₃	semidirect
104. C₃×C₂²⋊Q₈	C₂×C₃²	semidirect
106. C₂×#215	C₂×C₃²	semidirect
108. C₂²×C₃⋊C₈	C₂×C₃²	semidirect
112. #835	C₂×C₃²	semidirect
113. #809	C₂×C₃²	semidirect
114. #808	C₂×C₃²	semidirect
155. C₃×C₃⋊C₈	C₃×D₄	semidirect
204. C₂²×C₃²	#215	semidirect
205. C₂²×C₃²	C₃×SD₁₆	semidirect
230. C₂²⋊Q₈	C₃²×D₃	semidirect
235. C₃³	#465	semidirect
276. C₃⋊C₈	C₃²×D₄	semidirect
315. C₂²×C₃	C₃×#215	semidirect
316. C₂²×C₃	C₃²×SD₁₆	semidirect
340. C₃²	#5048	direct (N × H)
341. C₃²	C₃×#465	semidirect
377. C₂²	C₃²×#215	semidirect
386. C₃	C₃×#5048	direct (N × H)
387. C₃	C₃²×#465	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃³×C₂²⋊Q₈	2
C₂×C₃²×#215	2
C₃²×#930	2
C₂²×C₃²×C₃⋊C₈	2
C₃²×#835	2
C₃²×#809	2
C₃²×#808	2
C₃²×#465	3
C₃×#5048	3

Subgroups — C32×#5048 #13162484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5048 #13162484