Subgroups — C₂×#10590912 #11858650

Order 1152.

973 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	C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×#208	C₂	1	2	yes	maximal
3	C₂×#63646	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#63577	C₂	1	2	yes	maximal, complemented
6	#10590912	C₂	1	8	yes	maximal, direct product factor
7	C₂×#5125	—	3	1	no	maximal
8	C₂×#4893	—	3	1	no	maximal
9	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂×#3748	C₂²	1	2	yes	—
12	C₂×C₃×#208	C₂²	1	2	yes	—
13	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×ΓL(1,𝔽₂₅)	C₄	1	4	yes	—
15	C₂×C₃×ΓL(1,𝔽₂₅)	C₄	1	4	yes	—
16	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
17	C₂×#3711	—	2	2	no	—
18	D₃×#208	—	2	4	no	—
19	D₃×#208	C₂²	1	8	yes	—
20	C₂×D₃×C₃⋊C₈	—	2	2	no	—
21	#63646	C₂²	1	4	yes	complemented
22	C₃×#819	C₂²	1	4	yes	complemented
23	#63577	C₂²	1	8	yes	complemented
24	C₂²×C₃×M₁₆	—	3	1	no	—
25	C₂²×#208	—	3	2	no	—
26	C₂×D₃×M₁₆	—	3	2	no	—
27	C₂²×ΓL(1,𝔽₂₅)	D₃	1	1	yes	characteristic
28	C₂×C₃×#108	—	3	1	no	—
29	#5125	—	3	8	no	—
30	C₂×#822	—	3	2	no	—
31	C₂×#819	—	3	1	no	—
32	C₂×#819	—	3	1	no	—
33	C₂×#819	—	3	2	no	—
34	C₂×#819	—	6	1	no	—
35	C₂×#819	D₃	1	1	yes	characteristic, complemented
36	#4893	—	3	8	no	—
37	C₂³×C₃×D₃	Q₈	1	1	yes	characteristic
38	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₃	Q₈	1	1	yes	characteristic
40	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
43	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
44	C₂×C₃×C₄×D₃	Q₈	1	2	yes	—
45	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
46	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
47	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
48	C₂×C₃²×C₈	C₂³	1	2	yes	—
49	#3748	—	2	2	no	—
50	#3748	C₂³	1	4	yes	—
51	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
52	C₃×#208	—	2	2	no	—
53	C₃×#208	C₂³	1	4	yes	—
54	C₂×C₃×C₃⋊C₈	—	2	2	no	—
55	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
57	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
58	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	16	yes	—
59	#3711	—	2	8	no	—
60	D₃×C₃⋊C₈	—	2	8	no	—
61	C₂×#430	—	9	1	no	Sylow
62	C₂³×C₃×C₄	—	3	1	no	—
63	C₂²×C₄×D₃	C₂×D₃	1	1	yes	characteristic
64	C₂×C₃×M₁₆	—	3	4	no	—
65	C₂×C₃×M₁₆	—	3	4	no	—
66	C₂×C₃×M₁₆	—	3	4	no	—
67	C₂×C₃×M₁₆	—	3	2	no	—
68	C₂²×C₃×C₈	—	2	1	no	—
69	C₂²×C₃×C₈	—	3	1	no	—
70	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
71	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
72	C₂×#208	—	3	2	no	—
73	C₂×#208	—	3	2	no	—
74	C₂×#208	—	3	8	no	—
75	C₂×#208	—	6	2	no	—
76	C₂×#208	—	6	2	no	—
77	C₂×#208	—	6	4	no	—
78	C₂×#208	C₂×D₃	1	2	yes	—
79	C₂²×C₃⋊C₈	—	6	2	no	—
80	C₂²×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
81	D₃×M₁₆	—	3	8	no	—
82	D₃×M₁₆	—	6	4	no	—
83	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
84	C₂×ΓL(1,𝔽₂₅)	Dic₃	1	4	yes	—
85	C₂×ΓL(1,𝔽₂₅)	Dic₃	1	4	yes	—
86	C₂×ΓL(1,𝔽₂₅)	C₂×D₃	1	4	yes	—
87	C₂×D₃×C₈	—	6	2	no	—
88	C₃×#108	—	3	4	no	—
89	#822	—	3	8	no	—
90	#819	—	3	4	no	—
91	#819	—	3	4	no	—
92	#819	—	3	8	no	—
93	#819	—	6	4	no	—
94	#819	C₂×D₃	1	4	yes	complemented
95	C₂³×C₃²	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₃×D₃	—	4	2	no	—
97	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
98	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
99	C₂²×C₃×D₃	C₂×Q₈	1	2	yes	—
100	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
106	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
107	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
108	C₂×C₃×Dic₃	C₂×Q₈	1	2	yes	—
109	C₃×C₄×D₃	C₄⋊C₄	1	4	yes	—
110	C₃×C₄×D₃	C₄⋊C₄	1	4	yes	—
111	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
112	C₃×C₄×D₃	C₂×D₄	1	4	yes	—
113	C₃²×C₈	C₂²×C₄	1	4	yes	—
114	C₃⋊(C₃⋊C₈)	—	2	4	no	—
115	C₃×C₃⋊C₈	—	2	4	no	—
116	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
117	C₂²×M₁₆	—	3	1	no	—
118	C₂²×M₁₆	—	9	2	no	—
119	#430	—	9	8	no	—
120	C₂×#108	—	3	1	no	—
121	C₂×#108	—	9	2	no	—
122	C₂×#108	—	9	1	no	—
123	C₂⁴×C₃	—	3	1	no	—
124	C₂³×D₃	Dic₆	1	1	yes	characteristic
125	C₂²×C₃×C₄	—	2	1	no	—
126	C₂²×C₃×C₄	—	3	1	no	—
127	C₂²×C₃×C₄	—	3	2	no	—
128	C₂²×C₃×C₄	—	3	2	no	—
129	C₂²×C₃×C₄	—	3	2	no	—
130	C₂²×C₃×C₄	—	3	2	no	—
131	C₂²×C₃×C₄	—	3	2	no	—
132	C₂²×C₃×C₄	—	3	2	no	—
133	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
135	C₂²×Dic₃	Dic₆	1	1	yes	characteristic
136	C₂×C₄×D₃	Dic₆	1	2	yes	—
137	C₂×C₄×D₃	D₁₂	1	2	yes	—
138	C₂×C₄×D₃	D₁₂	1	2	yes	—
139	C₂×C₄×D₃	C₂×Dic₃	1	2	yes	—
140	C₂×C₄×D₃	C₂×Dic₃	1	2	yes	—
141	C₂×C₄×D₃	C₂²×D₃	1	2	yes	—
142	C₃×M₁₆	—	3	16	no	—
143	C₃×M₁₆	—	3	4	no	—
144	C₃×M₁₆	—	6	2	no	—
145	C₂×C₃×C₈	—	2	2	no	—
146	C₂×C₃×C₈	—	2	2	no	—
147	C₂×C₃×C₈	—	2	2	no	—
148	C₂×C₃×C₈	—	3	2	no	—
149	C₂×C₃×C₈	—	3	2	no	—
150	C₂×C₃×C₈	—	3	2	no	—
151	C₂×C₃×C₈	—	6	2	no	—
152	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
153	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
154	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
155	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
156	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
157	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
158	#208	—	2	2	no	—
159	#208	—	3	4	no	—
160	#208	—	3	4	no	—
161	#208	—	6	4	no	—
162	#208	—	6	8	no	—
163	#208	—	6	2	no	—
164	#208	—	6	2	no	—
165	#208	—	12	2	no	—
166	#208	C₂²×D₃	1	4	yes	—
167	C₂×C₃⋊C₈	—	2	2	no	—
168	C₂×C₃⋊C₈	—	6	8	no	—
169	C₂×C₃⋊C₈	—	6	2	no	—
170	C₂×C₃⋊C₈	—	6	2	no	—
171	C₂×C₃⋊C₈	—	12	2	no	—
172	C₂×C₃⋊C₈	C₂×Dic₃	1	2	yes	—
173	C₂×C₃⋊C₈	C₂×Dic₃	1	2	yes	—
174	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
175	ΓL(1,𝔽₂₅)	—	6	8	no	—
176	ΓL(1,𝔽₂₅)	C₂×Dic₃	1	16	yes	—
177	D₃×C₈	—	6	8	no	—
178	C₂²×C₃²	—	2	2	no	—
179	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₃×D₃	—	2	4	no	—
183	C₂×C₃×D₃	—	4	2	no	—
184	C₂×C₃×D₃	—	4	2	no	—
185	C₂×C₃×D₃	C₂×C₄⋊C₄	1	4	yes	—
186	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
189	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
190	C₃×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
191	C₂³×C₄	—	3	1	no	—
192	C₂×M₁₆	—	3	4	no	—
193	C₂×M₁₆	—	3	4	no	—
194	C₂×M₁₆	—	3	4	no	—
195	C₂×M₁₆	—	3	2	no	—
196	C₂×M₁₆	—	9	8	no	—
197	C₂×M₁₆	—	9	2	no	—
198	C₂×M₁₆	—	18	2	no	—
199	C₂×M₁₆	—	18	4	no	—
200	C₂²×C₈	—	3	1	no	—
201	C₂²×C₈	—	18	2	no	—
202	C₂²×C₈	D₃²	1	1	yes	characteristic
203	#108	—	3	4	no	—
204	#108	—	9	8	no	—
205	#108	—	9	4	no	—
206	C₂³×C₃	—	2	1	no	—
207	C₂³×C₃	—	3	2	no	—
208	C₂³×C₃	—	3	2	no	—
209	C₂³×C₃	—	3	2	no	—
210	C₂³×C₃	—	12	2	no	—
211	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
212	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
213	C₂²×D₃	—	4	2	no	—
214	C₂²×D₃	C₄⋊Dic₃	1	2	yes	—
215	C₂²×D₃	C₄⋊Dic₃	1	2	yes	—
216	C₂²×D₃	C₂×Dic₆	1	2	yes	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	3	2	no	—
224	C₂×C₃×C₄	—	3	2	no	—
225	C₂×C₃×C₄	—	3	2	no	—
226	C₂×C₃×C₄	—	3	4	no	—
227	C₂×C₃×C₄	—	3	4	no	—
228	C₂×C₃×C₄	—	3	4	no	—
229	C₂×C₃×C₄	—	3	4	no	—
230	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
231	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
235	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
236	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
237	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
242	C₂×Dic₃	C₄⋊Dic₃	1	2	yes	—
243	C₂×Dic₃	C₄⋊Dic₃	1	2	yes	—
244	C₂×Dic₃	C₂×Dic₆	1	2	yes	—
245	C₄×D₃	C₄⋊Dic₃	1	4	yes	—
246	C₄×D₃	C₄⋊Dic₃	1	4	yes	—
247	C₄×D₃	C₂×D₁₂	1	4	yes	—
248	C₄×D₃	C₂²×Dic₃	1	4	yes	—
249	C₃×C₈	—	2	4	no	—
250	C₃×C₈	—	3	4	no	—
251	C₃×C₈	—	6	4	no	—
252	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
253	C₃×C₈	C₂²×Dic₃	1	4	yes	—
254	C₃⋊C₈	—	2	4	no	—
255	C₃⋊C₈	—	6	4	no	—
256	C₃⋊C₈	—	6	4	no	—
257	C₃⋊C₈	—	12	4	no	—
258	C₃⋊C₈	C₂²×Dic₃	1	4	yes	—
259	C₂×C₃²	—	2	1	no	—
260	C₂×C₃²	—	2	1	no	—
261	C₂×C₃²	#430	1	2	yes	complemented
262	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
263	C₃×D₃	—	2	4	no	—
264	C₂⁴	—	3	1	no	—
265	C₂²×C₄	—	3	1	no	—
266	C₂²×C₄	—	3	2	no	—
267	C₂²×C₄	—	3	2	no	—
268	C₂²×C₄	—	3	2	no	—
269	C₂²×C₄	—	3	2	no	—
270	C₂²×C₄	—	3	2	no	—
271	C₂²×C₄	—	3	2	no	—
272	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
273	M₁₆	—	3	16	no	—
274	M₁₆	—	3	4	no	—
275	M₁₆	—	6	2	no	—
276	M₁₆	—	9	4	no	—
277	M₁₆	—	18	8	no	—
278	M₁₆	—	18	2	no	—
279	C₂×C₈	—	3	2	no	—
280	C₂×C₈	—	3	2	no	—
281	C₂×C₈	—	3	2	no	—
282	C₂×C₈	—	6	2	no	—
283	C₂×C₈	—	18	8	no	—
284	C₂×C₈	—	18	2	no	—
285	C₂×C₈	D₃×Dic₃	1	2	yes	—
286	C₂×C₈	D₃×Dic₃	1	2	yes	—
287	C₂×C₈	C₂×D₃²	1	2	yes	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	3	4	no	—
294	C₂²×C₃	—	4	2	no	—
295	C₂²×C₃	—	6	4	no	—
296	C₂²×C₃	—	12	2	no	—
297	C₂²×C₃	—	12	2	no	—
298	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
299	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
300	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
301	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
302	C₂²×C₃	C₂²×Dic₆	1	1	yes	characteristic
303	C₂²×C₃	C₂×D₃×Q₈	1	1	yes	characteristic
304	C₂×D₃	—	2	4	no	—
305	C₂×D₃	—	4	2	no	—
306	C₂×D₃	—	4	2	no	—
307	C₂×D₃	C₂×C₄⋊Dic₃	1	4	yes	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	3	4	no	—
313	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
314	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
315	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
316	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
317	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
318	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
319	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
320	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
321	Dic₃	C₂×C₄⋊Dic₃	1	4	yes	—
322	C₃²	C₂×#430	1	1	yes	characteristic, complemented, Sylow
323	C₂³	—	3	2	no	—
324	C₂³	—	3	2	no	—
325	C₂³	—	3	2	no	—
326	C₂³	—	12	2	no	—
327	C₂³	D₃×Dic₆	1	1	yes	characteristic
328	C₂×C₄	—	3	2	no	—
329	C₂×C₄	—	3	2	no	—
330	C₂×C₄	—	3	2	no	—
331	C₂×C₄	—	3	4	no	—
332	C₂×C₄	—	3	4	no	—
333	C₂×C₄	—	3	4	no	—
334	C₂×C₄	—	3	4	no	—
335	C₂×C₄	D₃×Dic₆	1	1	yes	characteristic
336	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
337	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
338	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
339	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
341	C₈	—	3	4	no	—
342	C₈	—	6	4	no	—
343	C₈	—	18	4	no	—
344	C₈	C₂×D₃×Dic₃	1	4	yes	—
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	—	2	2	no	—
351	C₂×C₃	—	4	1	no	—
352	C₂×C₃	—	4	1	no	—
353	C₂×C₃	—	6	4	no	—
354	C₂×C₃	#4893	1	2	yes	complemented
355	C₂×C₃	#5125	1	2	yes	complemented
356	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
357	C₂×C₃	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
358	D₃	—	2	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	3	4	no	—
361	C₂²	—	6	4	no	—
362	C₂²	—	12	2	no	—
363	C₂²	—	12	2	no	—
364	C₂²	D₃×C₄⋊Dic₃	1	1	yes	characteristic
365	C₂²	D₃×C₄⋊Dic₃	1	1	yes	characteristic
366	C₂²	C₂×D₃×Dic₆	1	1	yes	characteristic
367	C₄	—	3	4	no	—
368	C₄	D₃×C₄⋊Dic₃	1	1	yes	characteristic
369	C₄	D₃×C₄⋊Dic₃	1	1	yes	characteristic
370	C₄	C₂×D₃×D₁₂	1	1	yes	characteristic
371	C₄	C₂²×D₃×Dic₃	1	1	yes	characteristic
372	C₃	—	2	1	no	—
373	C₃	C₂×#4893	1	1	yes	characteristic, complemented
374	C₃	C₂×#5125	1	1	yes	characteristic, complemented
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	6	4	no	—
378	C₂	#10590912	1	2	yes	direct product factor
379	C₂	C₂×D₃×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×D₁₂
commutator	C₃²×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂²×C₃²	C₂×C₄⋊C₄
prime radical	C₂³×C₃×D₃	Q₈
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₂×#430
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#63646	C₂	semidirect
4. C₂×C₃×#819	C₂	semidirect
5. C₂×#63577	C₂	semidirect
6. #10590912	C₂	direct (N × H)
21. #63646	C₂²	semidirect
22. C₃×#819	C₂²	semidirect
23. #63577	C₂²	semidirect
35. C₂×#819	D₃	semidirect
94. #819	C₂×D₃	semidirect
261. C₂×C₃²	#430	semidirect
322. C₃²	C₂×#430	semidirect
354. C₂×C₃	#4893	semidirect
355. C₂×C₃	#5125	semidirect
373. C₃	C₂×#4893	semidirect
374. C₃	C₂×#5125	semidirect
378. C₂	#10590912	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×C₃×ΓL(1,𝔽₂₅)	2
C₂×D₃×#208	2
C₂×#63646	2
C₂×C₃×#819	2
C₂×#63577	2
#10590912	2
C₂×#5125	3
C₂×#4893	3

Subgroups — C2×#10590912 #11858650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10590912 #11858650