Subgroups — C₃×#71835 #11775079

Order 1152.

591 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#533	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₃×#4925	C₂	1	1	yes	maximal, characteristic
4	C₃×#4538	C₂	1	4	yes	maximal
5	C₃×#1503	—	3	1	no	maximal
6	#71835	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₃²×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
8	C₃²×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
9	C₃²×#125	—	2	1	no	—
10	C₃²×C₂²⋊Q₈	—	2	1	no	—
11	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
12	C₃²×C₄×Q₈	—	2	1	no	—
13	C₃²×C₄×Q₈	C₄	1	2	yes	complemented
14	C₃²×#117	—	2	1	no	—
15	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
17	C₂×C₃×C₄×Dic₃	—	2	1	no	—
18	C₃×C₃⋊#95	C₂²	1	2	yes	—
19	C₃×#830	C₂²	1	2	yes	—
20	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
21	C₃×C₄×C₃⋊C₈	—	2	1	no	—
22	C₃×#533	—	2	1	no	—
23	C₃×#533	D₃	1	1	yes	characteristic
24	C₃×#533	C₂×C₃	1	1	yes	characteristic
25	C₃×#431	—	3	1	no	—
26	C₃×C₄×C₄⋊C₄	—	3	1	no	—
27	C₄×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
28	#4925	C₂×C₃	1	1	yes	characteristic
29	C₃×#328	—	3	4	no	—
30	#4538	C₂×C₃	1	4	yes	—
31	C₂×C₃²×Q₈	—	2	1	no	—
32	C₂×C₃²×Q₈	C₂×C₄	1	2	yes	—
33	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
34	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
35	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
36	C₂²×C₃×Dic₃	—	2	2	no	—
37	C₃²×C₄⋊C₄	—	2	1	no	—
38	C₃²×C₄⋊C₄	—	2	1	no	—
39	C₃²×C₄⋊C₄	—	2	1	no	—
40	C₃²×C₄⋊C₄	—	2	2	no	—
41	C₃²×C₄⋊C₄	—	2	2	no	—
42	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₃²×C₂²⋊C₄	—	2	2	no	—
44	C₃²×C₄²	—	2	2	no	—
45	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
46	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
47	C₃²×C₄²	D₄	1	1	yes	characteristic
48	C₃²×C₄²	D₄	1	1	yes	characteristic
49	C₃×C₄⋊Dic₃	—	2	4	no	—
50	C₃×C₄×Dic₃	—	4	2	no	—
51	C₂×C₃×C₃⋊C₈	—	2	2	no	—
52	#1503	—	3	1	no	Sylow
53	C₃×C₄⋊Q₈	—	2	1	no	—
54	C₃×C₄⋊Q₈	—	2	1	no	—
55	C₃×C₄⋊Q₈	Dic₃	1	1	yes	characteristic, complemented
56	C₃×C₄⋊Q₈	Dic₃	1	1	yes	characteristic, complemented
57	C₃×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic, complemented
58	C₃×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic, complemented
59	C₃×#125	—	2	2	no	—
60	C₃×#125	—	2	1	no	—
61	C₃×#125	—	2	1	no	—
62	C₃×C₂²⋊Q₈	—	2	2	no	—
63	C₃×C₂²⋊Q₈	—	2	1	no	—
64	C₃×C₂²⋊Q₈	—	2	1	no	—
65	C₃×C₂²⋊Q₈	—	2	2	no	—
66	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
67	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
68	C₃×C₄×Q₈	—	2	2	no	—
69	C₃×C₄×Q₈	—	2	1	no	—
70	C₃×C₄×Q₈	—	2	1	no	—
71	C₃×C₄×Q₈	—	2	2	no	—
72	C₃×C₄×Q₈	Dic₃	1	2	yes	complemented
73	C₃×C₄×Q₈	C₃×C₄	1	2	yes	complemented
74	C₃×#117	—	2	2	no	—
75	C₃×#117	—	2	1	no	—
76	C₃×#117	—	2	1	no	—
77	C₂×C₃×C₄⋊C₄	—	6	1	no	—
78	C₂×C₃×C₄²	—	2	1	no	—
79	C₂×C₃×C₄²	—	6	1	no	—
80	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
81	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄⋊Dic₃	—	2	1	no	—
83	C₂×C₄×Dic₃	—	2	1	no	—
84	C₃×C₄⋊C₈	—	6	1	no	—
85	C₃×C₂²⋊C₈	—	3	2	no	—
86	C₃×C₄×C₈	—	6	1	no	—
87	C₃×#95	—	3	2	no	—
88	C₃⋊#95	C₂²×C₃	1	2	yes	—
89	#830	C₂²×C₃	1	2	yes	—
90	C₄⋊(C₃⋊C₈)	—	2	1	no	—
91	C₄×C₃⋊C₈	—	2	1	no	—
92	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
93	C₃²×Q₈	—	4	2	no	—
94	C₃²×Q₈	—	4	2	no	—
95	C₂×C₃²×C₄	—	2	2	no	—
96	C₂×C₃²×C₄	—	2	2	no	—
97	C₂×C₃²×C₄	—	2	2	no	—
98	C₂×C₃²×C₄	—	4	1	no	—
99	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
104	C₂×C₃²×C₄	Q₁₆	1	2	yes	—
105	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×Dic₃	—	2	4	no	—
108	C₂×C₃×Dic₃	—	4	2	no	—
109	C₂×C₃×Dic₃	—	4	2	no	—
110	C₃×C₃⋊C₈	—	4	2	no	—
111	#533	C₃×D₃	1	1	yes	characteristic
112	#431	—	3	1	no	—
113	C₄×C₄⋊C₄	—	3	1	no	—
114	#328	—	3	4	no	—
115	C₂×C₃×Q₈	—	2	2	no	—
116	C₂×C₃×Q₈	—	2	1	no	—
117	C₂×C₃×Q₈	—	2	1	no	—
118	C₂×C₃×Q₈	—	2	2	no	—
119	C₂×C₃×Q₈	C₂×Dic₃	1	2	yes	—
120	C₂×C₃×Q₈	C₂×C₃×C₄	1	2	yes	—
121	C₂²×C₃×C₄	—	2	1	no	—
122	C₂²×C₃×C₄	—	2	1	no	—
123	C₂²×C₃×C₄	—	2	1	no	—
124	C₂²×C₃×C₄	—	6	2	no	—
125	C₂²×C₃×C₄	#67	1	1	yes	characteristic
126	C₂²×C₃×C₄	#67	1	1	yes	characteristic
127	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
128	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
129	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
130	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
131	C₂²×Dic₃	—	2	2	no	—
132	C₂×C₃×C₈	—	6	2	no	—
133	C₃×C₄⋊C₄	—	2	2	no	—
134	C₃×C₄⋊C₄	—	2	2	no	—
135	C₃×C₄⋊C₄	—	2	4	no	—
136	C₃×C₄⋊C₄	—	2	4	no	—
137	C₃×C₄⋊C₄	—	2	2	no	—
138	C₃×C₄⋊C₄	—	2	1	no	—
139	C₃×C₄⋊C₄	—	2	1	no	—
140	C₃×C₄⋊C₄	—	2	1	no	—
141	C₃×C₄⋊C₄	—	2	2	no	—
142	C₃×C₄⋊C₄	—	2	1	no	—
143	C₃×C₄⋊C₄	—	2	1	no	—
144	C₃×C₄⋊C₄	—	2	1	no	—
145	C₃×C₄⋊C₄	—	2	2	no	—
146	C₃×C₄⋊C₄	—	2	2	no	—
147	C₃×C₄⋊C₄	—	2	2	no	—
148	C₃×C₄⋊C₄	—	2	2	no	—
149	C₃×C₄⋊C₄	—	6	4	no	—
150	C₃×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
151	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
152	C₃×C₂²⋊C₄	—	2	4	no	—
153	C₃×C₂²⋊C₄	—	2	2	no	—
154	C₃×C₂²⋊C₄	—	2	2	no	—
155	C₃×C₄²	—	2	4	no	—
156	C₃×C₄²	—	2	2	no	—
157	C₃×C₄²	—	2	2	no	—
158	C₃×C₄²	—	2	1	no	—
159	C₃×C₄²	—	2	1	no	—
160	C₃×C₄²	—	2	1	no	—
161	C₃×C₄²	—	2	1	no	—
162	C₃×C₄²	—	12	2	no	—
163	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
164	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
165	C₃×C₄²	#67	1	1	yes	characteristic
166	C₃×C₄²	#67	1	1	yes	characteristic
167	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
168	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
169	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
170	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
171	C₄⋊Dic₃	—	2	4	no	—
172	C₄×Dic₃	—	4	2	no	—
173	C₂×C₃⋊C₈	—	2	2	no	—
174	C₂²×C₃²	—	2	1	no	—
175	C₂²×C₃²	—	2	1	no	—
176	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
178	C₂²×C₃²	C₂×Q₁₆	1	1	yes	characteristic
179	C₃²×C₄	—	2	1	no	—
180	C₃²×C₄	—	2	1	no	—
181	C₃²×C₄	—	2	1	no	—
182	C₃²×C₄	—	4	2	no	—
183	C₃²×C₄	—	4	2	no	—
184	C₃²×C₄	#103	1	2	yes	—
185	C₃²×C₄	#103	1	2	yes	—
186	C₃²×C₄	#104	1	2	yes	—
187	C₃×Dic₃	—	4	4	no	—
188	C₄⋊Q₈	C₃×Dic₃	1	1	yes	characteristic, complemented
189	C₄⋊Q₈	C₃×Dic₃	1	1	yes	characteristic, complemented
190	#125	—	2	1	no	—
191	C₂²⋊Q₈	—	2	1	no	—
192	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
193	C₄×Q₈	—	2	1	no	—
194	C₄×Q₈	C₃×Dic₃	1	2	yes	complemented
195	#117	—	2	1	no	—
196	C₂×C₄⋊C₄	—	6	1	no	—
197	C₂×C₄²	—	6	1	no	—
198	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
199	C₄⋊C₈	—	6	1	no	—
200	C₂²⋊C₈	—	3	2	no	—
201	C₄×C₈	—	6	1	no	—
202	#95	—	3	2	no	—
203	C₂³×C₃	—	2	1	no	—
204	C₂³×C₃	C₂×#67	1	1	yes	characteristic
205	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
206	C₃×Q₈	—	4	2	no	—
207	C₃×Q₈	—	4	2	no	—
208	C₃×Q₈	—	4	4	no	—
209	C₃×Q₈	—	4	4	no	—
210	C₃×Q₈	—	4	2	no	—
211	C₃×Q₈	—	4	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	4	no	—
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	4	2	no	—
229	C₂×C₃×C₄	—	4	1	no	—
230	C₂×C₃×C₄	—	4	1	no	—
231	C₂×C₃×C₄	—	4	2	no	—
232	C₂×C₃×C₄	—	6	4	no	—
233	C₂×C₃×C₄	—	12	2	no	—
234	C₂×C₃×C₄	—	12	2	no	—
235	C₂×C₃×C₄	#215	1	2	yes	—
236	C₂×C₃×C₄	#216	1	2	yes	—
237	C₂×C₃×C₄	#217	1	1	yes	characteristic
238	C₂×C₃×C₄	#217	1	1	yes	characteristic
239	C₂×C₃×C₄	#217	1	1	yes	characteristic
240	C₂×C₃×C₄	#217	1	1	yes	characteristic
241	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
246	C₂×C₃×C₄	C₃×Q₁₆	1	2	yes	—
247	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×Dic₃	—	2	4	no	—
252	C₂×Dic₃	—	4	2	no	—
253	C₂×Dic₃	—	4	2	no	—
254	C₃×C₈	—	12	2	no	—
255	C₃⋊C₈	—	4	2	no	—
256	C₂×C₃²	—	2	1	no	—
257	C₂×C₃²	—	2	1	no	—
258	C₂×C₃²	#410	1	1	yes	characteristic
259	C₂×C₃²	C₂×#103	1	1	yes	characteristic
260	C₂×C₃²	C₂×#104	1	1	yes	characteristic
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	C₂×C₃×Dic₃	1	2	yes	—
263	C₂²×C₄	—	6	2	no	—
264	C₂²×C₄	C₃×#67	1	1	yes	characteristic
265	C₂²×C₄	C₃×#67	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
267	C₂×C₈	—	6	2	no	—
268	C₄⋊C₄	—	2	1	no	—
269	C₄⋊C₄	—	2	1	no	—
270	C₄⋊C₄	—	2	1	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	6	4	no	—
274	C₄⋊C₄	C₂×C₃×Dic₃	1	2	yes	—
275	C₂²⋊C₄	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	12	2	no	—
278	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
279	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
280	C₄²	C₃×#67	1	1	yes	characteristic
281	C₄²	C₃×#67	1	1	yes	characteristic
282	C₂²×C₃	—	2	1	no	—
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	2	1	no	—
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	4	1	no	—
290	C₂²×C₃	—	4	1	no	—
291	C₂²×C₃	C₂×#215	1	1	yes	characteristic
292	C₂²×C₃	C₂×#216	1	1	yes	characteristic
293	C₂²×C₃	C₂×#217	1	1	yes	characteristic
294	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
295	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
296	C₂²×C₃	C₂×C₃×Q₁₆	1	1	yes	characteristic
297	C₃×C₄	—	2	2	no	—
298	C₃×C₄	—	2	1	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	4	1	no	—
308	C₃×C₄	—	4	1	no	—
309	C₃×C₄	—	4	4	no	—
310	C₃×C₄	—	4	4	no	—
311	C₃×C₄	—	4	2	no	—
312	C₃×C₄	—	4	2	no	—
313	C₃×C₄	—	4	2	no	—
314	C₃×C₄	—	4	2	no	—
315	C₃×C₄	—	12	4	no	—
316	C₃×C₄	#835	1	2	yes	—
317	C₃×C₄	#835	1	2	yes	—
318	C₃×C₄	#837	1	2	yes	—
319	C₃×C₄	C₃×#103	1	2	yes	—
320	C₃×C₄	C₃×#103	1	2	yes	—
321	C₃×C₄	C₃×#104	1	2	yes	—
322	Dic₃	—	4	4	no	—
323	C₃²	#1503	1	1	yes	characteristic, complemented, Sylow
324	C₂³	C₂×C₃×#67	1	1	yes	characteristic
325	Q₈	—	4	2	no	—
326	Q₈	—	4	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	6	4	no	—
332	C₂×C₄	—	12	2	no	—
333	C₂×C₄	—	12	2	no	—
334	C₂×C₄	C₃×#215	1	2	yes	—
335	C₂×C₄	C₃×#216	1	2	yes	—
336	C₂×C₄	C₃×#217	1	1	yes	characteristic
337	C₂×C₄	C₃×#217	1	1	yes	characteristic
338	C₂×C₄	C₃×#217	1	1	yes	characteristic
339	C₂×C₄	C₃×#217	1	1	yes	characteristic
340	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
341	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
342	C₈	—	12	2	no	—
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	4	1	no	—
351	C₂×C₃	—	4	1	no	—
352	C₂×C₃	C₂×#835	1	1	yes	characteristic
353	C₂×C₃	C₂×#837	1	1	yes	characteristic
354	C₂×C₃	#5240	1	1	yes	characteristic
355	C₂×C₃	C₃×#410	1	1	yes	characteristic
356	C₂×C₃	C₂×C₃×#103	1	1	yes	characteristic
357	C₂×C₃	C₂×C₃×#104	1	1	yes	characteristic
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	C₂×C₃×#215	1	1	yes	characteristic
361	C₂²	C₂×C₃×#216	1	1	yes	characteristic
362	C₂²	C₂×C₃×#217	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	12	4	no	—
369	C₄	C₃×#835	1	2	yes	—
370	C₄	C₃×#835	1	2	yes	—
371	C₄	C₃×#837	1	2	yes	—
372	C₃	—	2	1	no	—
373	C₃	#71835	1	1	yes	characteristic, direct product factor
374	C₃	C₃×#1503	1	1	yes	characteristic, complemented
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	C₂×C₃×#835	1	1	yes	characteristic
378	C₂	C₂×C₃×#837	1	1	yes	characteristic
379	C₂	C₃×#5240	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	#217
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×#533	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₂³×C₃²	C₂×D₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×#533	D₃
hypocenter	C₃	C₃×#1503
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#533

Complements

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

N	H ≅ G/N	type
6. #71835	C₃	direct (N × H)
7. C₃²×C₄⋊Q₈	C₄	semidirect
8. C₃²×C₄⋊Q₈	C₄	semidirect
13. C₃²×C₄×Q₈	C₄	semidirect
55. C₃×C₄⋊Q₈	Dic₃	semidirect
56. C₃×C₄⋊Q₈	Dic₃	semidirect
57. C₃×C₄⋊Q₈	C₃×C₄	semidirect
58. C₃×C₄⋊Q₈	C₃×C₄	semidirect
72. C₃×C₄×Q₈	Dic₃	semidirect
73. C₃×C₄×Q₈	C₃×C₄	semidirect
188. C₄⋊Q₈	C₃×Dic₃	semidirect
189. C₄⋊Q₈	C₃×Dic₃	semidirect
194. C₄×Q₈	C₃×Dic₃	semidirect
323. C₃²	#1503	semidirect
373. C₃	#71835	direct (N × H)
374. C₃	C₃×#1503	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#533	2
C₃×C₄×C₄⋊Dic₃	2
C₃×#4925	2
C₃×#4538	2
C₃×#1503	3
#71835	3

Subgroups — C3×#71835 #11775079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#71835 #11775079