Subgroups — C₂×#10590228 #11899400

Order 1152.

781 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×#63803	C₂	1	1	yes	maximal, characteristic
2	C₂×#63625	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#798	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#63543	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#63542	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	#10590228	C₂	1	8	yes	maximal, direct product factor
9	C₂×#4907	—	3	1	no	maximal
10	C₂×#4901	—	3	1	no	maximal
11	C₂×#3798	C₄	1	1	yes	characteristic
12	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
15	C₂×#3712	C₄	1	1	yes	characteristic
16	C₂×#3711	C₄	1	1	yes	characteristic
17	C₂×#3711	C₄	1	1	yes	characteristic
18	#63803	C₄	1	4	yes	—
19	#63803	C₂²	1	4	yes	—
20	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
22	#63625	C₂²	1	4	yes	complemented
23	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₃×#798	C₂²	1	4	yes	complemented
26	C₃×D₃×C₁₆	C₂²	1	4	yes	complemented
27	#63543	C₂²	1	4	yes	complemented
28	#63542	C₂²	1	4	yes	complemented
29	D₃×C₃⋊C₁₆	C₂²	1	4	yes	complemented
30	C₂×#901	—	3	1	no	—
31	C₂×#901	—	3	1	no	—
32	C₂×C₃×M₃₂	—	3	1	no	—
33	C₂²×C₃×C₁₆	—	3	1	no	—
34	C₂×#812	—	3	1	no	—
35	C₂²×C₃⋊C₁₆	—	3	1	no	—
36	#4907	—	3	8	no	—
37	#4901	—	3	8	no	—
38	C₂×#798	—	3	1	no	—
39	C₂×#798	—	3	1	no	—
40	C₂×#798	—	3	1	no	—
41	C₂×#798	—	6	1	no	—
42	C₂×#798	D₃	1	1	yes	characteristic, complemented
43	C₂×D₃×C₁₆	—	3	1	no	—
44	C₂×D₃×C₁₆	—	3	1	no	—
45	C₂×D₃×C₁₆	—	3	1	no	—
46	C₂×D₃×C₁₆	D₃	1	1	yes	characteristic, complemented
47	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
50	C₂×#627	C₈	1	1	yes	characteristic
51	C₂×#626	C₈	1	1	yes	characteristic
52	C₂×#626	C₈	1	1	yes	characteristic
53	C₂×#625	C₈	1	1	yes	characteristic
54	#3798	C₈	1	4	yes	—
55	#3798	C₂×C₄	1	4	yes	—
56	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
57	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
58	C₈×C₃⋊D₃	C₂×C₄	1	2	yes	—
59	C₈×C₃⋊D₃	C₂³	1	2	yes	—
60	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
62	C₃×D₃×C₈	C₂×C₄	1	2	yes	—
63	C₃×D₃×C₈	C₂×C₄	1	2	yes	—
64	C₃×D₃×C₈	C₂³	1	2	yes	—
65	C₃×D₃×C₈	C₂³	1	2	yes	—
66	#3712	C₂×C₄	1	4	yes	—
67	#3711	C₂×C₄	1	4	yes	—
68	#3711	C₂×C₄	1	4	yes	—
69	C₃²×C₁₆	C₂³	1	2	yes	—
70	C₃⋊(C₃⋊C₁₆)	C₂³	1	2	yes	—
71	C₃×C₃⋊C₁₆	C₂³	1	2	yes	—
72	C₃×C₃⋊C₁₆	C₂³	1	2	yes	—
73	C₂×#504	—	9	1	no	Sylow
74	C₂×#235	—	3	1	no	—
75	C₂×#235	—	3	1	no	—
76	C₂²×C₃×C₈	—	3	1	no	—
77	C₂²×C₃×C₈	—	3	1	no	—
78	C₂×#208	—	3	1	no	—
79	C₂×#208	—	3	1	no	—
80	#901	—	3	4	no	—
81	#901	—	3	4	no	—
82	#901	—	3	4	no	—
83	#901	—	3	4	no	—
84	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
85	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
86	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
87	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
88	C₂×D₃×C₈	—	3	1	no	—
89	C₂×D₃×C₈	—	3	1	no	—
90	C₂×D₃×C₈	—	6	1	no	—
91	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
92	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
93	C₃×M₃₂	—	3	4	no	—
94	C₂×C₃×C₁₆	—	2	1	no	—
95	C₂×C₃×C₁₆	—	3	1	no	—
96	C₂×C₃×C₁₆	—	3	1	no	—
97	C₂×C₃×C₁₆	—	3	4	no	—
98	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic
99	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic
100	#812	—	3	4	no	—
101	C₂×C₃⋊C₁₆	—	3	1	no	—
102	C₂×C₃⋊C₁₆	—	3	1	no	—
103	C₂×C₃⋊C₁₆	—	3	4	no	—
104	C₂×C₃⋊C₁₆	—	6	1	no	—
105	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic
106	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic
107	#798	—	3	4	no	—
108	#798	—	3	4	no	—
109	#798	—	3	4	no	—
110	#798	—	6	4	no	—
111	#798	C₂×D₃	1	4	yes	complemented
112	D₃×C₁₆	—	3	4	no	—
113	D₃×C₁₆	—	3	4	no	—
114	D₃×C₁₆	—	3	4	no	—
115	D₃×C₁₆	C₂×D₃	1	4	yes	complemented
116	C₂²×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
117	C₂²×C₃×D₃	C₂×C₈	1	1	yes	characteristic
118	C₂²×C₃×D₃	C₂×C₈	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃⋊Dic₃	C₂×C₈	1	1	yes	characteristic
121	C₄×C₃⋊D₃	C₂×C₈	1	2	yes	—
122	C₄×C₃⋊D₃	C₂²×C₄	1	2	yes	—
123	C₂×C₃×Dic₃	C₂×C₈	1	1	yes	characteristic
124	C₂×C₃×Dic₃	C₂×C₈	1	1	yes	characteristic
125	C₃×C₄×D₃	C₂×C₈	1	2	yes	—
126	C₃×C₄×D₃	C₂×C₈	1	2	yes	—
127	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
128	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
129	#627	C₂×C₈	1	4	yes	—
130	#626	C₂×C₈	1	4	yes	—
131	#626	C₂×C₈	1	4	yes	—
132	#625	C₂×C₈	1	4	yes	—
133	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
134	C₃²×C₈	C₂⁴	1	1	yes	characteristic
135	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	2	yes	—
136	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
137	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
138	C₂×#131	—	9	1	no	—
139	#504	—	9	8	no	—
140	C₂×M₃₂	—	3	1	no	—
141	C₂×M₃₂	—	9	1	no	—
142	C₂×M₃₂	—	9	1	no	—
143	C₂²×C₁₆	—	3	1	no	—
144	C₂²×C₁₆	—	9	1	no	—
145	C₂²×C₁₆	—	9	1	no	—
146	C₂²×C₃×C₄	—	3	1	no	—
147	C₂²×C₃×C₄	—	3	1	no	—
148	C₂×#67	—	3	1	no	—
149	C₂×#67	—	3	1	no	—
150	C₂×#67	—	3	1	no	—
151	C₂×#67	—	3	1	no	—
152	#235	—	3	4	no	—
153	#235	—	3	4	no	—
154	#235	—	3	4	no	—
155	#235	—	3	4	no	—
156	C₂×D₁₂	—	3	1	no	—
157	C₂×D₁₂	—	3	1	no	—
158	C₂×C₄×D₃	—	3	1	no	—
159	C₂×C₄×D₃	—	3	1	no	—
160	C₂×C₄×D₃	—	6	1	no	—
161	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
162	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
163	C₂×Dic₆	—	3	1	no	—
164	C₂×Dic₆	—	3	1	no	—
165	C₂×C₃×C₈	—	2	1	no	—
166	C₂×C₃×C₈	—	3	1	no	—
167	C₂×C₃×C₈	—	3	1	no	—
168	C₂×C₃×C₈	—	3	2	no	—
169	C₂×C₃×C₈	—	3	2	no	—
170	C₂×C₃×C₈	—	3	2	no	—
171	C₂×C₃×C₈	—	3	2	no	—
172	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
173	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
174	#208	—	3	4	no	—
175	#208	—	3	4	no	—
176	C₂×C₃⋊C₈	—	3	1	no	—
177	C₂×C₃⋊C₈	—	3	1	no	—
178	C₂×C₃⋊C₈	—	6	1	no	—
179	C₂×C₃⋊C₈	C₄×D₃	1	1	yes	characteristic
180	C₂×C₃⋊C₈	C₄×D₃	1	1	yes	characteristic
181	ΓL(1,𝔽₂₅)	—	3	4	no	—
182	ΓL(1,𝔽₂₅)	—	3	4	no	—
183	ΓL(1,𝔽₂₅)	—	3	4	no	—
184	ΓL(1,𝔽₂₅)	—	3	4	no	—
185	D₃×C₈	—	3	2	no	—
186	D₃×C₈	—	3	2	no	—
187	D₃×C₈	—	3	2	no	—
188	D₃×C₈	—	3	2	no	—
189	D₃×C₈	—	6	2	no	—
190	D₃×C₈	—	6	2	no	—
191	D₃×C₈	C₄×D₃	1	2	yes	—
192	D₃×C₈	C₄×D₃	1	2	yes	—
193	D₃×C₈	C₂²×D₃	1	2	yes	—
194	D₃×C₈	C₂²×D₃	1	2	yes	—
195	C₃×C₁₆	—	2	2	no	—
196	C₃×C₁₆	—	3	2	no	—
197	C₃×C₁₆	—	3	2	no	—
198	C₃×C₁₆	C₂²×D₃	1	2	yes	—
199	C₃×C₁₆	C₂²×D₃	1	2	yes	—
200	C₃⋊C₁₆	—	3	2	no	—
201	C₃⋊C₁₆	—	3	2	no	—
202	C₃⋊C₁₆	—	6	2	no	—
203	C₃⋊C₁₆	C₂²×D₃	1	2	yes	—
204	C₃⋊C₁₆	C₂²×D₃	1	2	yes	—
205	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
206	C₂×C₃⋊D₃	—	2	2	no	—
207	C₂×C₃⋊D₃	C₂²×C₈	1	2	yes	—
208	C₂×C₃×D₃	—	2	2	no	—
209	C₂×C₃×D₃	—	2	2	no	—
210	C₂×C₃×D₃	C₂²×C₈	1	2	yes	—
211	C₂×C₃×D₃	C₂²×C₈	1	2	yes	—
212	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
213	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
214	C₃⋊Dic₃	C₂²×C₈	1	2	yes	—
215	C₃×Dic₃	C₂²×C₈	1	2	yes	—
216	C₃×Dic₃	C₂²×C₈	1	2	yes	—
217	C₂×#41	—	9	1	no	—
218	#131	—	9	4	no	—
219	#131	—	9	4	no	—
220	C₂×M₁₆	—	9	1	no	—
221	C₂×M₁₆	—	9	1	no	—
222	C₂×M₁₆	—	9	1	no	—
223	C₂²×C₈	—	3	1	no	—
224	C₂²×C₈	—	3	1	no	—
225	C₂²×C₈	—	9	1	no	—
226	M₃₂	—	3	4	no	—
227	M₃₂	—	9	4	no	—
228	M₃₂	—	9	4	no	—
229	C₂×C₁₆	—	3	1	no	—
230	C₂×C₁₆	—	3	1	no	—
231	C₂×C₁₆	—	3	4	no	—
232	C₂×C₁₆	—	9	4	no	—
233	C₂×C₁₆	—	9	4	no	—
234	C₂×C₁₆	—	9	1	no	—
235	C₂×C₁₆	D₃²	1	1	yes	characteristic
236	C₂³×C₃	—	3	1	no	—
237	C₂³×C₃	—	3	1	no	—
238	C₂²×D₃	—	3	1	no	—
239	C₂²×D₃	—	3	1	no	—
240	C₂²×D₃	—	6	1	no	—
241	C₂²×D₃	D₃×C₈	1	1	yes	characteristic
242	C₂²×D₃	D₃×C₈	1	1	yes	characteristic
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	3	1	no	—
245	C₂×C₃×C₄	—	3	1	no	—
246	C₂×C₃×C₄	—	3	2	no	—
247	C₂×C₃×C₄	—	3	2	no	—
248	C₂×C₃×C₄	—	3	2	no	—
249	C₂×C₃×C₄	—	3	2	no	—
250	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
252	#67	—	3	4	no	—
253	#67	—	3	4	no	—
254	#67	—	3	4	no	—
255	#67	—	3	4	no	—
256	C₂×Dic₃	—	3	1	no	—
257	C₂×Dic₃	—	3	1	no	—
258	C₂×Dic₃	—	6	1	no	—
259	C₂×Dic₃	D₃×C₈	1	1	yes	characteristic
260	C₂×Dic₃	D₃×C₈	1	1	yes	characteristic
261	D₁₂	—	3	4	no	—
262	D₁₂	—	3	4	no	—
263	C₄×D₃	—	3	2	no	—
264	C₄×D₃	—	3	2	no	—
265	C₄×D₃	—	3	2	no	—
266	C₄×D₃	—	3	2	no	—
267	C₄×D₃	—	6	2	no	—
268	C₄×D₃	—	6	2	no	—
269	C₄×D₃	D₃×C₈	1	2	yes	—
270	C₄×D₃	D₃×C₈	1	2	yes	—
271	C₄×D₃	C₂×C₄×D₃	1	2	yes	—
272	C₄×D₃	C₂×C₄×D₃	1	2	yes	—
273	Dic₆	—	3	4	no	—
274	Dic₆	—	3	4	no	—
275	C₃×C₈	—	2	1	no	—
276	C₃×C₈	—	2	1	no	—
277	C₃×C₈	—	3	2	no	—
278	C₃×C₈	—	3	2	no	—
279	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
280	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
281	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
282	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
283	C₃⋊C₈	—	3	2	no	—
284	C₃⋊C₈	—	3	2	no	—
285	C₃⋊C₈	—	6	2	no	—
286	C₃⋊C₈	C₂×C₄×D₃	1	2	yes	—
287	C₃⋊C₈	C₂×C₄×D₃	1	2	yes	—
288	C₂×C₃²	#504	1	2	yes	complemented
289	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
290	C₃⋊D₃	—	2	2	no	—
291	C₃×D₃	—	2	2	no	—
292	C₃×D₃	—	2	2	no	—
293	#41	—	9	4	no	—
294	#41	—	9	4	no	—
295	C₂×Q₈	—	9	1	no	—
296	C₂×D₄	—	9	1	no	—
297	C₂×D₄	—	9	1	no	—
298	C₂×D₄	—	9	1	no	—
299	C₂²×C₄	—	3	1	no	—
300	C₂²×C₄	—	3	1	no	—
301	C₂²×C₄	—	9	1	no	—
302	M₁₆	—	9	4	no	—
303	M₁₆	—	9	4	no	—
304	M₁₆	—	9	4	no	—
305	C₂×C₈	—	3	1	no	—
306	C₂×C₈	—	3	1	no	—
307	C₂×C₈	—	3	2	no	—
308	C₂×C₈	—	3	2	no	—
309	C₂×C₈	—	3	2	no	—
310	C₂×C₈	—	3	2	no	—
311	C₂×C₈	—	9	1	no	—
312	C₂×C₈	—	9	2	no	—
313	C₂×C₈	—	9	2	no	—
314	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
315	C₁₆	—	3	2	no	—
316	C₁₆	—	3	2	no	—
317	C₁₆	—	9	2	no	—
318	C₁₆	C₂×D₃²	1	2	yes	—
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	3	2	no	—
321	C₂²×C₃	—	3	2	no	—
322	C₂²×C₃	—	6	2	no	—
323	C₂²×C₃	—	6	2	no	—
324	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
325	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
326	C₂×D₃	—	2	2	no	—
327	C₂×D₃	—	2	2	no	—
328	C₂×D₃	—	3	2	no	—
329	C₂×D₃	—	3	2	no	—
330	C₂×D₃	—	6	2	no	—
331	C₂×D₃	—	6	2	no	—
332	C₂×D₃	—	6	2	no	—
333	C₂×D₃	—	12	2	no	—
334	C₂×D₃	C₂×D₃×C₈	1	2	yes	—
335	C₂×D₃	C₂×D₃×C₈	1	2	yes	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	3	2	no	—
339	C₃×C₄	—	3	2	no	—
340	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
341	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
342	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
343	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
344	Dic₃	—	3	2	no	—
345	Dic₃	—	3	2	no	—
346	Dic₃	—	6	2	no	—
347	Dic₃	C₂×D₃×C₈	1	2	yes	—
348	Dic₃	C₂×D₃×C₈	1	2	yes	—
349	C₃²	C₂×#504	1	1	yes	characteristic, complemented, Sylow
350	C₂³	—	3	1	no	—
351	C₂³	—	3	1	no	—
352	C₂³	—	9	1	no	—
353	Q₈	—	9	4	no	—
354	D₄	—	9	4	no	—
355	D₄	—	9	4	no	—
356	D₄	—	9	4	no	—
357	C₂×C₄	—	3	1	no	—
358	C₂×C₄	—	3	1	no	—
359	C₂×C₄	—	3	2	no	—
360	C₂×C₄	—	3	2	no	—
361	C₂×C₄	—	3	2	no	—
362	C₂×C₄	—	3	2	no	—
363	C₂×C₄	—	9	1	no	—
364	C₂×C₄	—	9	2	no	—
365	C₂×C₄	—	9	2	no	—
366	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
367	C₈	—	3	2	no	—
368	C₈	—	3	2	no	—
369	C₈	—	9	2	no	—
370	C₈	C₄×D₃²	1	1	yes	characteristic
371	C₈	C₂²×D₃²	1	1	yes	characteristic
372	C₂×C₃	—	2	2	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	6	2	no	—
375	C₂×C₃	—	6	2	no	—
376	C₂×C₃	#4901	1	2	yes	complemented
377	C₂×C₃	#4907	1	2	yes	complemented
378	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
379	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
380	D₃	—	2	2	no	—
381	D₃	—	2	2	no	—
382	D₃	—	6	2	no	—
383	D₃	—	6	2	no	—
384	D₃	—	12	2	no	—
385	C₂²	—	3	2	no	—
386	C₂²	—	3	2	no	—
387	C₂²	—	6	2	no	—
388	C₂²	—	6	2	no	—
389	C₂²	—	9	2	no	—
390	C₂²	—	18	2	no	—
391	C₂²	D₃²×C₈	1	1	yes	characteristic
392	C₄	—	3	2	no	—
393	C₄	—	3	2	no	—
394	C₄	—	9	2	no	—
395	C₄	D₃²×C₈	1	1	yes	characteristic
396	C₄	C₂×C₄×D₃²	1	1	yes	characteristic
397	C₃	—	2	1	no	—
398	C₃	C₂×#4901	1	1	yes	characteristic, complemented
399	C₃	C₂×#4907	1	1	yes	characteristic, complemented
400	C₂	—	6	2	no	—
401	C₂	—	6	2	no	—
402	C₂	—	18	2	no	—
403	C₂	#10590228	1	2	yes	direct product factor
404	C₂	C₂×D₃²×C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃²
commutator	C₂×C₃²	C₂³×C₈
Frattini	C₈	C₂²×D₃²
Fitting	C₂×C₃²×C₁₆	C₂²
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂×#3798	C₄
cosocle	C₃²×C₈	C₂⁴
hypercenter	C₂×C₁₆	D₃²
hypocenter	C₃²	C₂×#504
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#63625	C₂	semidirect
3. C₂×C₃×#798	C₂	semidirect
4. C₂×C₃×D₃×C₁₆	C₂	semidirect
5. C₂×#63543	C₂	semidirect
6. C₂×#63542	C₂	semidirect
7. C₂×D₃×C₃⋊C₁₆	C₂	semidirect
8. #10590228	C₂	direct (N × H)
22. #63625	C₂²	semidirect
25. C₃×#798	C₂²	semidirect
26. C₃×D₃×C₁₆	C₂²	semidirect
27. #63543	C₂²	semidirect
28. #63542	C₂²	semidirect
29. D₃×C₃⋊C₁₆	C₂²	semidirect
42. C₂×#798	D₃	semidirect
46. C₂×D₃×C₁₆	D₃	semidirect
111. #798	C₂×D₃	semidirect
115. D₃×C₁₆	C₂×D₃	semidirect
288. C₂×C₃²	#504	semidirect
349. C₃²	C₂×#504	semidirect
376. C₂×C₃	#4901	semidirect
377. C₂×C₃	#4907	semidirect
398. C₃	C₂×#4901	semidirect
399. C₃	C₂×#4907	semidirect
403. C₂	#10590228	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×#63803	2
C₂×#63625	2
C₂×C₃×#798	2
C₂×C₃×D₃×C₁₆	2
C₂×#63543	2
C₂×#63542	2
C₂×D₃×C₃⋊C₁₆	2
#10590228	2
C₂×#4907	3
C₂×#4901	3

Subgroups — C2×#10590228 #11899400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10590228 #11899400