Subgroups — C₂×C₃×#5188 #11866772

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#946	C₂	1	2	yes	maximal
3	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#835	C₂	1	2	yes	maximal, complemented
5	C₃×#5188	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#467	—	3	1	no	maximal
8	C₂×#5188	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
10	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃²×Q₁₆	—	2	4	no	—
12	C₂×C₃²×Q₁₆	C₂²	1	4	yes	complemented
13	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
14	C₃×#946	—	2	4	no	—
15	C₃×#946	C₂²	1	8	yes	—
16	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
17	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂×C₃×Dic₃⋊C₄	—	2	2	no	—
19	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₃×C₈	—	2	4	no	—
21	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
22	C₃×#835	C₂²	1	8	yes	complemented
23	C₃×#818	C₂²	1	4	yes	complemented
24	C₂²×C₃×Q₁₆	—	2	1	no	—
25	C₂²×C₃×Q₁₆	D₃	1	1	yes	characteristic, complemented
26	C₂²×C₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂³×C₃×C₈	—	3	1	no	—
28	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
29	C₂×#946	C₂×C₃	1	2	yes	—
30	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic
31	C₃×#467	—	3	8	no	—
32	C₂×C₃×#107	—	3	1	no	—
33	C₂×C₃×#103	—	3	2	no	—
34	C₂×#835	C₂×C₃	1	2	yes	complemented
35	#5188	C₂×C₃	1	8	yes	direct product factor
36	C₂×#818	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
38	C₂×C₃²×Q₈	—	2	2	no	—
39	C₂×C₃²×Q₈	—	2	4	no	—
40	C₂×C₃²×Q₈	—	2	4	no	—
41	C₂×C₃²×Q₈	C₂³	1	4	yes	—
42	C₂²×C₃²×C₄	—	2	2	no	—
43	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₃	—	2	2	no	—
45	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₃	—	2	2	no	—
47	C₂×C₃×C₄×D₃	—	2	2	no	—
48	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
49	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
50	C₃²×Q₁₆	—	2	8	no	—
51	C₂×C₃²×C₈	D₄	1	4	yes	—
52	C₂×C₃²×C₈	C₂³	1	2	yes	—
53	C₃×(C₂×D₃)⋊C₄	—	2	8	no	—
54	C₃×C₄⋊Dic₃	—	2	2	no	—
55	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
56	C₃×Dic₃⋊C₄	—	2	8	no	—
57	C₂×C₃×C₃⋊C₈	—	2	2	no	—
58	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
59	C₃×D₃×C₈	—	2	8	no	—
60	C₂×#467	—	3	1	no	Sylow
61	C₂²×C₃×Q₈	—	2	2	no	—
62	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	—
63	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
64	C₂³×C₃×C₄	—	3	1	no	—
65	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₃×Q₁₆	—	2	8	no	—
67	C₂×C₃×Q₁₆	—	2	4	no	—
68	C₂×C₃×Q₁₆	—	2	4	no	—
69	C₂×C₃×Q₁₆	—	2	4	no	—
70	C₂×C₃×Q₁₆	C₂×D₃	1	4	yes	complemented
71	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	complemented
72	C₂²×C₃×C₈	—	2	1	no	—
73	C₂²×C₃×C₈	—	3	1	no	—
74	C₂²×C₃×C₈	—	3	4	no	—
75	C₂²×C₃×C₈	—	6	4	no	—
76	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
78	C₃×C₂²⋊Q₈	—	3	8	no	—
79	C₃×C₂²⋊Q₈	—	6	4	no	—
80	C₂×C₃×C₄⋊C₄	—	3	2	no	—
81	C₂×C₃×C₄⋊C₄	—	6	2	no	—
82	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
83	#946	—	2	4	no	—
84	#946	C₂²×C₃	1	8	yes	—
85	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
86	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
87	C₂×Dic₃⋊C₄	—	2	2	no	—
88	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
89	C₂×D₃×C₈	—	2	4	no	—
90	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
91	C₃×#107	—	3	4	no	—
92	C₃×#103	—	3	8	no	—
93	#835	C₂²×C₃	1	8	yes	complemented
94	#818	C₂²×C₃	1	4	yes	complemented
95	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₃×D₃	—	2	2	no	—
97	C₂²×C₃×D₃	—	2	2	no	—
98	C₂²×C₃×D₃	Q₁₆	1	4	yes	complemented
99	C₂²×C₃×D₃	C₂×D₄	1	2	yes	—
100	C₃²×Q₈	—	2	4	no	—
101	C₃²×Q₈	—	2	4	no	—
102	C₃²×Q₈	—	4	4	no	—
103	C₂×C₃²×C₄	—	2	4	no	—
104	C₂×C₃²×C₄	—	4	4	no	—
105	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
107	C₂×C₃²×C₄	#41	1	2	yes	—
108	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
109	C₂×C₃×Dic₃	—	2	2	no	—
110	C₂×C₃×Dic₃	—	2	4	no	—
111	C₂×C₃×Dic₃	—	4	4	no	—
112	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
113	C₃×C₄×D₃	—	2	4	no	—
114	C₃×C₄×D₃	—	2	2	no	—
115	C₃×C₄×D₃	—	2	2	no	—
116	C₃²×C₈	C₂×D₄	1	4	yes	—
117	C₃×C₃⋊C₈	—	2	2	no	—
118	C₂²×Q₁₆	C₃×D₃	1	1	yes	characteristic, complemented
119	C₂³×C₈	—	3	1	no	—
120	C₂×C₂²⋊Q₈	—	3	2	no	—
121	#467	—	3	8	no	—
122	C₂×#107	—	3	1	no	—
123	C₂×#103	—	3	2	no	—
124	C₂⁴×C₃	—	3	1	no	—
125	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
126	C₂×C₃×Q₈	—	2	2	no	—
127	C₂×C₃×Q₈	—	2	2	no	—
128	C₂×C₃×Q₈	—	2	8	no	—
129	C₂×C₃×Q₈	—	2	4	no	—
130	C₂×C₃×Q₈	—	2	4	no	—
131	C₂×C₃×Q₈	—	2	4	no	—
132	C₂×C₃×Q₈	—	2	4	no	—
133	C₂×C₃×Q₈	—	2	4	no	—
134	C₂×C₃×Q₈	—	4	2	no	—
135	C₂×C₃×Q₈	—	4	4	no	—
136	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
137	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
138	C₂²×C₃×C₄	—	2	2	no	—
139	C₂²×C₃×C₄	—	2	2	no	—
140	C₂²×C₃×C₄	—	2	1	no	—
141	C₂²×C₃×C₄	—	3	1	no	—
142	C₂²×C₃×C₄	—	3	2	no	—
143	C₂²×C₃×C₄	—	3	2	no	—
144	C₂²×C₃×C₄	—	4	2	no	—
145	C₂²×C₃×C₄	—	6	2	no	—
146	C₂²×C₃×C₄	—	6	2	no	—
147	C₂²×C₃×C₄	—	6	2	no	—
148	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
149	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
150	C₂²×Dic₃	—	2	2	no	—
151	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
152	C₂×C₄×D₃	—	2	2	no	—
153	C₂×C₄×D₃	—	2	2	no	—
154	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
155	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
156	C₃×Q₁₆	—	2	16	no	—
157	C₃×Q₁₆	—	2	8	no	—
158	C₃×Q₁₆	—	2	8	no	—
159	C₂×C₃×C₈	—	2	4	no	—
160	C₂×C₃×C₈	—	2	2	no	—
161	C₂×C₃×C₈	—	3	2	no	—
162	C₂×C₃×C₈	—	6	2	no	—
163	C₂×C₃×C₈	—	6	8	no	—
164	C₂×C₃×C₈	#67	1	4	yes	—
165	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
166	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
167	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
168	C₃×C₄⋊C₄	—	3	4	no	—
169	C₃×C₄⋊C₄	—	6	8	no	—
170	C₃×C₄⋊C₄	—	6	2	no	—
171	C₃×C₂²⋊C₄	—	6	8	no	—
172	(C₂×D₃)⋊C₄	—	2	8	no	—
173	C₄⋊Dic₃	—	2	2	no	—
174	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
175	Dic₃⋊C₄	—	2	8	no	—
176	C₂×C₃⋊C₈	—	2	2	no	—
177	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
178	D₃×C₈	—	2	8	no	—
179	C₂²×C₃²	#121	1	2	yes	—
180	C₂²×C₃²	C₂×Q₁₆	1	2	yes	—
181	C₂²×C₃²	#135	1	2	yes	—
182	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₃×D₃	—	2	2	no	—
184	C₂×C₃×D₃	—	2	2	no	—
185	C₂×C₃×D₃	—	2	8	no	—
186	C₂×C₃×D₃	C₂×Q₁₆	1	4	yes	complemented
187	C₃²×C₄	—	4	4	no	—
188	C₃²×C₄	#121	1	2	yes	—
189	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
190	C₃²×C₄	C₂×#41	1	1	yes	characteristic
191	C₃×Dic₃	—	2	2	no	—
192	C₃×Dic₃	—	4	4	no	—
193	C₂²×Q₈	C₂×C₃×D₃	1	2	yes	—
194	C₂³×C₄	—	3	1	no	—
195	C₂×Q₁₆	—	2	4	no	—
196	C₂×Q₁₆	C₂×C₃×D₃	1	4	yes	complemented
197	C₂²×C₈	—	3	1	no	—
198	C₂²×C₈	—	3	4	no	—
199	C₂²×C₈	—	6	4	no	—
200	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
201	C₂²⋊Q₈	—	3	8	no	—
202	C₂²⋊Q₈	—	6	4	no	—
203	C₂×C₄⋊C₄	—	3	2	no	—
204	C₂×C₄⋊C₄	—	6	2	no	—
205	C₂×C₂²⋊C₄	—	6	2	no	—
206	#107	—	3	4	no	—
207	#103	—	3	8	no	—
208	C₂³×C₃	—	2	1	no	—
209	C₂³×C₃	—	3	4	no	—
210	C₂³×C₃	—	3	2	no	—
211	C₂³×C₃	—	6	2	no	—
212	C₂³×C₃	—	6	2	no	—
213	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
214	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
215	C₂²×D₃	—	2	2	no	—
216	C₂²×D₃	—	2	2	no	—
217	C₂²×D₃	C₃×Q₁₆	1	4	yes	complemented
218	C₂²×D₃	C₂×C₃×D₄	1	2	yes	—
219	C₃×Q₈	—	2	8	no	—
220	C₃×Q₈	—	2	4	no	—
221	C₃×Q₈	—	2	4	no	—
222	C₃×Q₈	—	2	4	no	—
223	C₃×Q₈	—	2	4	no	—
224	C₃×Q₈	—	4	4	no	—
225	C₃×Q₈	—	4	8	no	—
226	C₃×Q₈	—	4	4	no	—
227	C₃×Q₈	—	4	4	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	3	2	no	—
235	C₂×C₃×C₄	—	4	4	no	—
236	C₂×C₃×C₄	—	4	8	no	—
237	C₂×C₃×C₄	—	4	4	no	—
238	C₂×C₃×C₄	—	4	4	no	—
239	C₂×C₃×C₄	—	6	2	no	—
240	C₂×C₃×C₄	—	6	4	no	—
241	C₂×C₃×C₄	—	6	2	no	—
242	C₂×C₃×C₄	—	6	2	no	—
243	C₂×C₃×C₄	—	6	4	no	—
244	C₂×C₃×C₄	—	12	4	no	—
245	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
246	C₂×C₃×C₄	#237	1	2	yes	—
247	C₂×C₃×C₄	C₂×#67	1	2	yes	—
248	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
250	C₂×C₃×C₄	C₃×#41	1	2	yes	—
251	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
253	C₂×Dic₃	—	2	2	no	—
254	C₂×Dic₃	—	2	4	no	—
255	C₂×Dic₃	—	4	4	no	—
256	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
257	C₄×D₃	—	2	4	no	—
258	C₄×D₃	—	2	2	no	—
259	C₄×D₃	—	2	2	no	—
260	C₃×C₈	—	2	4	no	—
261	C₃×C₈	—	6	2	no	—
262	C₃×C₈	C₂×#67	1	4	yes	—
263	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
264	C₃⋊C₈	—	2	2	no	—
265	C₂×C₃²	#467	1	4	yes	complemented
266	C₂×C₃²	C₂×#121	1	1	yes	characteristic
267	C₂×C₃²	C₂²×Q₁₆	1	1	yes	characteristic
268	C₂×C₃²	C₂×#135	1	1	yes	characteristic
269	C₃×D₃	—	2	4	no	—
270	C₂⁴	—	3	1	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	3	1	no	—
277	C₂²×C₄	—	3	2	no	—
278	C₂²×C₄	—	3	2	no	—
279	C₂²×C₄	—	6	2	no	—
280	C₂²×C₄	—	6	2	no	—
281	C₂²×C₄	—	6	2	no	—
282	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
283	Q₁₆	—	2	8	no	—
284	C₂×C₈	—	3	2	no	—
285	C₂×C₈	—	6	2	no	—
286	C₂×C₈	—	6	8	no	—
287	C₂×C₈	C₃×#67	1	4	yes	—
288	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
289	C₄⋊C₄	—	3	4	no	—
290	C₄⋊C₄	—	6	8	no	—
291	C₄⋊C₄	—	6	2	no	—
292	C₂²⋊C₄	—	6	8	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	3	4	no	—
298	C₂²×C₃	—	6	8	no	—
299	C₂²×C₃	—	6	2	no	—
300	C₂²×C₃	—	6	2	no	—
301	C₂²×C₃	D₃×Q₁₆	1	2	yes	—
302	C₂²×C₃	#919	1	2	yes	—
303	C₂²×C₃	#938	1	2	yes	—
304	C₂²×C₃	C₃×#121	1	2	yes	—
305	C₂²×C₃	C₂×C₃×Q₁₆	1	2	yes	—
306	C₂²×C₃	C₃×#135	1	2	yes	—
307	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
308	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
309	C₂×D₃	—	2	2	no	—
310	C₂×D₃	—	2	2	no	—
311	C₂×D₃	—	2	8	no	—
312	C₂×D₃	C₂×C₃×Q₁₆	1	4	yes	complemented
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	4	8	no	—
317	C₃×C₄	—	4	4	no	—
318	C₃×C₄	—	4	4	no	—
319	C₃×C₄	—	6	2	no	—
320	C₃×C₄	—	12	4	no	—
321	C₃×C₄	#938	1	2	yes	—
322	C₃×C₄	C₃×#121	1	2	yes	—
323	C₃×C₄	C₂×#237	1	1	yes	characteristic
324	C₃×C₄	C₂²×#67	1	1	yes	characteristic
325	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
326	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
327	Dic₃	—	2	2	no	—
328	Dic₃	—	4	4	no	—
329	C₃²	C₂×#467	1	1	yes	characteristic, complemented, Sylow
330	C₂³	—	3	4	no	—
331	C₂³	—	3	2	no	—
332	C₂³	—	6	2	no	—
333	C₂³	—	6	2	no	—
334	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
335	Q₈	—	2	4	no	—
336	Q₈	—	2	4	no	—
337	Q₈	—	4	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	3	2	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	6	2	no	—
342	C₂×C₄	—	6	4	no	—
343	C₂×C₄	—	6	2	no	—
344	C₂×C₄	—	6	2	no	—
345	C₂×C₄	—	6	4	no	—
346	C₂×C₄	—	12	4	no	—
347	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
348	C₂×C₄	C₃×#237	1	2	yes	—
349	C₂×C₄	C₂×C₃×#67	1	2	yes	—
350	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
351	C₈	—	6	2	no	—
352	C₈	C₂×C₃×#67	1	4	yes	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	—	2	4	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	6	4	no	—
358	C₂×C₃	#5188	1	4	yes	direct product factor
359	C₂×C₃	C₃×#467	1	4	yes	complemented
360	C₂×C₃	C₂×D₃×Q₁₆	1	1	yes	characteristic
361	C₂×C₃	C₂×#919	1	1	yes	characteristic
362	C₂×C₃	C₂×#938	1	1	yes	characteristic
363	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
364	C₂×C₃	C₂²×C₃×Q₁₆	1	1	yes	characteristic
365	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
366	D₃	—	2	4	no	—
367	C₂²	—	3	4	no	—
368	C₂²	—	6	2	no	—
369	C₂²	—	6	8	no	—
370	C₂²	—	6	2	no	—
371	C₂²	C₃×D₃×Q₁₆	1	2	yes	—
372	C₂²	C₃×#919	1	2	yes	—
373	C₂²	C₃×#938	1	2	yes	—
374	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
375	C₄	—	4	4	no	—
376	C₄	—	6	2	no	—
377	C₄	—	12	4	no	—
378	C₄	C₃×#938	1	2	yes	—
379	C₄	C₂×C₃×#237	1	1	yes	characteristic
380	C₄	C₂²×C₃×#67	1	1	yes	characteristic
381	C₃	—	2	1	no	—
382	C₃	C₂×#5188	1	1	yes	characteristic, direct product factor
383	C₃	C₂×C₃×#467	1	1	yes	characteristic, complemented
384	C₂	—	6	4	no	—
385	C₂	C₃×#5188	1	4	yes	direct product factor
386	C₂	C₂×C₃×D₃×Q₁₆	1	1	yes	characteristic
387	C₂	C₂×C₃×#919	1	1	yes	characteristic
388	C₂	C₂×C₃×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂²×C₃²×Q₁₆	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂³×C₃×D₃	D₄
hypercenter	C₂²×C₃×Q₁₆	D₃
hypocenter	C₃	C₂×C₃×#467
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×Q₁₆	C₂	semidirect
4. C₂×C₃×#835	C₂	semidirect
5. C₃×#5188	C₂	direct (N × H)
6. C₂×C₃×#818	C₂	semidirect
8. C₂×#5188	C₃	direct (N × H)
12. C₂×C₃²×Q₁₆	C₂²	semidirect
22. C₃×#835	C₂²	semidirect
23. C₃×#818	C₂²	semidirect
25. C₂²×C₃×Q₁₆	D₃	semidirect
26. C₂²×C₃×Q₁₆	C₂×C₃	semidirect
34. C₂×#835	C₂×C₃	semidirect
35. #5188	C₂×C₃	direct (N × H)
36. C₂×#818	C₂×C₃	semidirect
70. C₂×C₃×Q₁₆	C₂×D₃	semidirect
71. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
93. #835	C₂²×C₃	semidirect
94. #818	C₂²×C₃	semidirect
98. C₂²×C₃×D₃	Q₁₆	semidirect
118. C₂²×Q₁₆	C₃×D₃	semidirect
186. C₂×C₃×D₃	C₂×Q₁₆	semidirect
196. C₂×Q₁₆	C₂×C₃×D₃	semidirect
217. C₂²×D₃	C₃×Q₁₆	semidirect
265. C₂×C₃²	#467	semidirect
312. C₂×D₃	C₂×C₃×Q₁₆	semidirect
329. C₃²	C₂×#467	semidirect
358. C₂×C₃	#5188	direct (N × H)
359. C₂×C₃	C₃×#467	semidirect
382. C₃	C₂×#5188	direct (N × H)
383. C₃	C₂×C₃×#467	semidirect
385. C₂	C₃×#5188	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×Q₁₆	2
C₂×C₃×#946	2
C₂²×C₃×D₃×C₈	2
C₂×C₃×#835	2
C₃×#5188	2
C₂×C₃×#818	2
C₂×C₃×#467	3
C₂×#5188	3

Subgroups — C2×C3×#5188 #11866772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5188 #11866772