Subgroups — C₂×C₃×#5089 #11873533

Order 1152.

1017 conjugacy classes of subgroups.

The subgroup lattice has 395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#875	C₂	1	1	yes	maximal, characteristic
3	C₃×#5089	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#810	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#809	C₂	1	2	yes	maximal
6	C₂×C₃×#803	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#489	—	3	1	no	maximal
8	C₂×#5089	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃²×Q₈	—	2	1	no	—
10	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
12	C₃²×C₄⋊Q₈	—	2	2	no	—
13	C₃²×C₄⋊Q₈	C₂²	1	4	yes	complemented
14	C₂×C₃²×C₄⋊C₄	—	2	1	no	—
15	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
17	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
18	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
20	C₃×#875	—	2	2	no	—
21	C₃×#875	C₂²	1	4	yes	—
22	C₃×#810	C₂²	1	8	yes	complemented
23	C₃×#809	C₂²	1	8	yes	—
24	C₃×#803	C₂²	1	4	yes	complemented
25	C₂×C₃×C₄⋊Q₈	—	2	1	no	—
26	C₂×C₃×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
27	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₃×#124	—	3	1	no	—
29	C₂×#875	C₂×C₃	1	1	yes	characteristic
30	C₃×#489	—	3	8	no	—
31	C₂×C₃×#103	—	3	2	no	—
32	C₂×C₃×#102	—	3	2	no	—
33	C₂×C₃×#97	—	3	1	no	—
34	#5089	C₂×C₃	1	8	yes	direct product factor
35	C₂×#810	C₂×C₃	1	2	yes	complemented
36	C₂×#809	C₂×C₃	1	2	yes	—
37	C₂×#803	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×C₃×D₃	—	2	1	no	—
39	C₂×C₃²×Q₈	—	2	4	no	—
40	C₂×C₃²×Q₈	—	4	4	no	—
41	C₂²×C₃²×C₄	—	2	2	no	—
42	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
43	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
44	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₃	—	2	1	no	—
46	C₂×C₃×D₁₂	—	2	4	no	—
47	C₂×C₃×D₁₂	—	2	1	no	—
48	C₂×C₃×D₁₂	C₂³	1	2	yes	—
49	C₂×C₃×Dic₆	—	2	4	no	—
50	C₂×C₃×Dic₆	—	2	1	no	—
51	C₂×C₃×Dic₆	C₂³	1	2	yes	—
52	C₃²×C₄⋊C₄	—	2	4	no	—
53	C₃²×C₄⋊C₄	—	2	2	no	—
54	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
55	C₃²×C₄²	D₄	1	2	yes	—
56	C₃²×C₄²	C₂³	1	2	yes	—
57	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
58	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
59	C₂×C₃×C₃⋊C₈	—	2	4	no	—
60	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
61	C₂×#489	—	3	1	no	Sylow
62	C₂²×C₃×Q₈	—	2	2	no	—
63	C₂²×C₃×Q₈	—	2	1	no	—
64	C₂²×C₃×Q₈	—	2	1	no	—
65	C₂²×C₃×Q₈	—	3	1	no	—
66	C₂²×C₃×D₄	—	3	1	no	—
67	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
68	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₃×C₈	—	3	2	no	—
70	C₃×C₄⋊Q₈	—	2	4	no	—
71	C₃×C₄⋊Q₈	—	2	2	no	—
72	C₃×C₄⋊Q₈	—	2	2	no	—
73	C₃×C₄⋊Q₈	—	2	4	no	—
74	C₃×C₄⋊Q₈	C₂×D₃	1	4	yes	complemented
75	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
76	C₃×#124	—	3	4	no	—
77	C₃×#124	—	6	2	no	—
78	C₂×C₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₃×C₄⋊C₄	—	2	2	no	—
82	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
83	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
85	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
86	C₂×C₃×C₄²	—	2	1	no	—
87	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
88	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
89	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
90	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
91	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
92	#875	—	2	2	no	—
93	#875	C₂²×C₃	1	4	yes	—
94	C₃×#103	—	3	8	no	—
95	C₃×#102	—	3	8	no	—
96	C₃×#97	—	3	4	no	—
97	#810	C₂²×C₃	1	8	yes	complemented
98	#809	C₂²×C₃	1	8	yes	—
99	#803	C₂²×C₃	1	4	yes	complemented
100	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₃×D₃	—	2	2	no	—
102	C₂²×C₃×D₃	—	4	2	no	—
103	C₂²×C₃×D₃	—	4	2	no	—
104	C₂²×C₃×D₃	—	4	2	no	—
105	C₃²×Q₈	—	4	8	no	—
106	C₂×C₃²×C₄	—	2	2	no	—
107	C₂×C₃²×C₄	—	2	2	no	—
108	C₂×C₃²×C₄	—	2	4	no	—
109	C₂×C₃²×C₄	—	4	4	no	—
110	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
111	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
112	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	#41	1	4	yes	—
114	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
115	C₂×C₃×Dic₃	—	2	2	no	—
116	C₂×C₃×Dic₃	—	4	2	no	—
117	C₃×D₁₂	—	2	4	no	—
118	C₃×D₁₂	—	4	2	no	—
119	C₃×Dic₆	—	2	4	no	—
120	C₃×Dic₆	—	4	2	no	—
121	C₃×C₃⋊C₈	—	2	4	no	—
122	C₂×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic, complemented
123	C₂×#124	—	3	1	no	—
124	#489	—	3	8	no	—
125	C₂×#103	—	3	2	no	—
126	C₂×#102	—	3	2	no	—
127	C₂×#97	—	3	1	no	—
128	C₂⁴×C₃	—	6	1	no	—
129	C₂³×D₃	—	2	1	no	—
130	C₂×C₃×Q₈	—	2	8	no	—
131	C₂×C₃×Q₈	—	2	4	no	—
132	C₂×C₃×Q₈	—	2	4	no	—
133	C₂×C₃×Q₈	—	3	2	no	—
134	C₂×C₃×Q₈	—	4	8	no	—
135	C₂×C₃×Q₈	—	4	4	no	—
136	C₂×C₃×Q₈	—	4	4	no	—
137	C₂×C₃×Q₈	—	6	1	no	—
138	C₂×C₃×Q₈	—	6	4	no	—
139	C₂×C₃×D₄	—	3	2	no	—
140	C₂×C₃×D₄	—	6	4	no	—
141	C₂×C₃×D₄	—	6	1	no	—
142	C₂²×C₃×C₄	—	2	4	no	—
143	C₂²×C₃×C₄	—	2	2	no	—
144	C₂²×C₃×C₄	—	2	2	no	—
145	C₂²×C₃×C₄	—	2	1	no	—
146	C₂²×C₃×C₄	—	2	1	no	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	—	6	1	no	—
149	C₂²×C₃×C₄	#67	1	1	yes	characteristic
150	C₂²×C₃×C₄	#67	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
155	C₂²×Dic₃	—	2	1	no	—
156	C₂×D₁₂	—	2	4	no	—
157	C₂×D₁₂	—	2	1	no	—
158	C₂×D₁₂	C₂³×C₃	1	2	yes	—
159	C₂×Dic₆	—	2	4	no	—
160	C₂×Dic₆	—	2	1	no	—
161	C₂×Dic₆	C₂³×C₃	1	2	yes	—
162	C₂×C₃×C₈	—	3	4	no	—
163	C₂×C₃×C₈	—	6	4	no	—
164	C₃×C₄⋊C₄	—	2	8	no	—
165	C₃×C₄⋊C₄	—	2	4	no	—
166	C₃×C₄⋊C₄	—	2	4	no	—
167	C₃×C₄⋊C₄	—	2	2	no	—
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	4	no	—
171	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
172	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
173	C₃×C₂²⋊C₄	—	6	4	no	—
174	C₃×C₂²⋊C₄	—	6	4	no	—
175	C₃×C₄²	—	2	2	no	—
176	C₃×C₄²	—	2	2	no	—
177	C₃×C₄²	#67	1	2	yes	—
178	C₃×C₄²	C₃×D₄	1	2	yes	—
179	C₃×C₄²	C₂²×D₃	1	2	yes	—
180	C₃×C₄²	C₂³×C₃	1	2	yes	—
181	(C₂×D₃)⋊C₄	—	2	4	no	—
182	(C₂×D₃)⋊C₄	—	2	4	no	—
183	C₂×C₃⋊C₈	—	2	4	no	—
184	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
185	C₂²×C₃²	#124	1	2	yes	—
186	C₂²×C₃²	AGL(1,ℤ/8)	1	2	yes	—
187	C₂²×C₃²	#137	1	2	yes	—
188	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₃×D₃	—	4	2	no	—
190	C₂×C₃×D₃	—	4	2	no	—
191	C₂×C₃×D₃	—	4	2	no	—
192	C₂×C₃×D₃	—	8	4	no	—
193	C₃²×C₄	—	2	2	no	—
194	C₃²×C₄	—	2	2	no	—
195	C₃²×C₄	—	4	4	no	—
196	C₃²×C₄	#124	1	2	yes	—
197	C₃²×C₄	C₂×#41	1	2	yes	—
198	C₃×Dic₃	—	4	2	no	—
199	C₂²×Q₈	—	2	1	no	—
200	C₂²×Q₈	—	3	1	no	—
201	C₂²×D₄	—	3	1	no	—
202	C₂²×C₈	—	3	2	no	—
203	C₄⋊Q₈	—	2	2	no	—
204	C₄⋊Q₈	C₂×C₃×D₃	1	4	yes	complemented
205	#124	—	3	4	no	—
206	#124	—	6	2	no	—
207	C₂×C₄⋊C₄	—	2	1	no	—
208	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
209	C₂×C₂²⋊C₄	—	6	1	no	—
210	C₂×C₂²⋊C₄	—	6	1	no	—
211	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
212	#103	—	3	8	no	—
213	#102	—	3	8	no	—
214	#97	—	3	4	no	—
215	C₂³×C₃	—	2	1	no	—
216	C₂³×C₃	—	6	2	no	—
217	C₂³×C₃	—	12	2	no	—
218	C₂³×C₃	—	12	2	no	—
219	C₂³×C₃	—	12	2	no	—
220	C₂³×C₃	C₂×#67	1	1	yes	characteristic
221	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
222	C₂²×D₃	—	2	2	no	—
223	C₂²×D₃	—	4	2	no	—
224	C₂²×D₃	—	4	2	no	—
225	C₂²×D₃	—	4	2	no	—
226	C₃×Q₈	—	4	16	no	—
227	C₃×Q₈	—	4	8	no	—
228	C₃×Q₈	—	4	8	no	—
229	C₃×Q₈	—	6	4	no	—
230	C₃×Q₈	—	12	2	no	—
231	C₃×D₄	—	6	4	no	—
232	C₃×D₄	—	12	2	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	8	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	4	8	no	—
248	C₂×C₃×C₄	—	4	4	no	—
249	C₂×C₃×C₄	—	4	4	no	—
250	C₂×C₃×C₄	—	6	2	no	—
251	C₂×C₃×C₄	—	12	2	no	—
252	C₂×C₃×C₄	#239	1	4	yes	—
253	C₂×C₃×C₄	C₂×#67	1	2	yes	—
254	C₂×C₃×C₄	C₂×#67	1	2	yes	—
255	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₃×#41	1	4	yes	—
260	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
262	C₂×Dic₃	—	2	2	no	—
263	C₂×Dic₃	—	4	2	no	—
264	D₁₂	—	2	4	no	—
265	D₁₂	—	4	2	no	—
266	Dic₆	—	2	4	no	—
267	Dic₆	—	4	2	no	—
268	C₃×C₈	—	6	4	no	—
269	C₃⋊C₈	—	2	4	no	—
270	C₂×C₃²	#489	1	4	yes	complemented
271	C₂×C₃²	C₂×#124	1	1	yes	characteristic
272	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₂×C₃²	C₂×#137	1	1	yes	characteristic
274	C₃×D₃	—	8	2	no	—
275	C₂⁴	—	6	1	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	3	2	no	—
278	C₂×Q₈	—	4	4	no	—
279	C₂×Q₈	—	6	1	no	—
280	C₂×Q₈	—	6	4	no	—
281	C₂×D₄	—	3	2	no	—
282	C₂×D₄	—	6	4	no	—
283	C₂×D₄	—	6	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	6	1	no	—
286	C₂²×C₄	C₃×#67	1	1	yes	characteristic
287	C₂²×C₄	C₃×#67	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
289	C₂×C₈	—	3	4	no	—
290	C₂×C₈	—	6	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
294	C₂²⋊C₄	—	6	4	no	—
295	C₂²⋊C₄	—	6	4	no	—
296	C₄²	C₃×#67	1	2	yes	—
297	C₄²	C₂²×C₃×D₃	1	2	yes	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	12	2	no	—
303	C₂²×C₃	—	12	2	no	—
304	C₂²×C₃	—	12	2	no	—
305	C₂²×C₃	—	24	4	no	—
306	C₂²×C₃	#932	1	2	yes	—
307	C₂²×C₃	#942	1	2	yes	—
308	C₂²×C₃	#947	1	2	yes	—
309	C₂²×C₃	C₃×#124	1	2	yes	—
310	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
311	C₂²×C₃	C₃×#137	1	2	yes	—
312	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
313	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
314	C₂×D₃	—	4	2	no	—
315	C₂×D₃	—	4	2	no	—
316	C₂×D₃	—	4	2	no	—
317	C₂×D₃	—	8	4	no	—
318	C₃×C₄	—	2	4	no	—
319	C₃×C₄	—	2	4	no	—
320	C₃×C₄	—	2	2	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	2	2	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	—	4	8	no	—
327	C₃×C₄	—	4	4	no	—
328	C₃×C₄	—	4	4	no	—
329	C₃×C₄	—	12	2	no	—
330	C₃×C₄	#947	1	2	yes	—
331	C₃×C₄	C₃×#124	1	2	yes	—
332	C₃×C₄	C₂×#239	1	2	yes	—
333	C₃×C₄	C₂×C₃×#41	1	2	yes	—
334	Dic₃	—	4	2	no	—
335	C₃²	C₂×#489	1	1	yes	characteristic, complemented, Sylow
336	C₂³	—	6	2	no	—
337	C₂³	—	12	2	no	—
338	C₂³	—	12	2	no	—
339	C₂³	—	12	2	no	—
340	C₂³	C₂×C₃×#67	1	1	yes	characteristic
341	Q₈	—	4	8	no	—
342	Q₈	—	6	4	no	—
343	Q₈	—	12	2	no	—
344	D₄	—	6	4	no	—
345	D₄	—	12	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	6	2	no	—
351	C₂×C₄	—	12	2	no	—
352	C₂×C₄	C₃×#239	1	4	yes	—
353	C₂×C₄	C₂×C₃×#67	1	2	yes	—
354	C₂×C₄	C₂×C₃×#67	1	2	yes	—
355	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
356	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
357	C₈	—	6	4	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	2	1	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	2	4	no	—
362	C₂×C₃	—	24	2	no	—
363	C₂×C₃	#5089	1	4	yes	direct product factor
364	C₂×C₃	C₃×#489	1	4	yes	complemented
365	C₂×C₃	C₂×#932	1	1	yes	characteristic
366	C₂×C₃	C₂×#942	1	1	yes	characteristic
367	C₂×C₃	C₂×#947	1	1	yes	characteristic
368	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
369	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
371	D₃	—	8	2	no	—
372	C₂²	—	12	2	no	—
373	C₂²	—	12	2	no	—
374	C₂²	—	12	2	no	—
375	C₂²	—	24	4	no	—
376	C₂²	C₃×#932	1	2	yes	—
377	C₂²	C₃×#942	1	2	yes	—
378	C₂²	C₃×#947	1	2	yes	—
379	C₂²	C₂²×C₃×#67	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	4	no	—
383	C₄	—	12	2	no	—
384	C₄	C₃×#947	1	2	yes	—
385	C₄	C₂×C₃×#239	1	2	yes	—
386	C₃	—	2	1	no	—
387	C₃	C₂×#5089	1	1	yes	characteristic, direct product factor
388	C₃	C₂×C₃×#489	1	1	yes	characteristic, complemented
389	C₂	—	24	2	no	—
390	C₂	C₃×#5089	1	4	yes	direct product factor
391	C₂	C₂×C₃×#932	1	1	yes	characteristic
392	C₂	C₂×C₃×#942	1	1	yes	characteristic
393	C₂	C₂×C₃×#947	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄⋊Q₈	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₁₂	C₂²
hypercenter	C₂×C₃×C₄⋊Q₈	D₃
hypocenter	C₃	C₂×C₃×#489
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₄⋊Q₈	C₂	semidirect
3. C₃×#5089	C₂	direct (N × H)
4. C₂×C₃×#810	C₂	semidirect
6. C₂×C₃×#803	C₂	semidirect
8. C₂×#5089	C₃	direct (N × H)
13. C₃²×C₄⋊Q₈	C₂²	semidirect
22. C₃×#810	C₂²	semidirect
24. C₃×#803	C₂²	semidirect
26. C₂×C₃×C₄⋊Q₈	D₃	semidirect
27. C₂×C₃×C₄⋊Q₈	C₂×C₃	semidirect
34. #5089	C₂×C₃	direct (N × H)
35. C₂×#810	C₂×C₃	semidirect
37. C₂×#803	C₂×C₃	semidirect
74. C₃×C₄⋊Q₈	C₂×D₃	semidirect
75. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
97. #810	C₂²×C₃	semidirect
99. #803	C₂²×C₃	semidirect
122. C₂×C₄⋊Q₈	C₃×D₃	semidirect
204. C₄⋊Q₈	C₂×C₃×D₃	semidirect
270. C₂×C₃²	#489	semidirect
335. C₃²	C₂×#489	semidirect
363. C₂×C₃	#5089	direct (N × H)
364. C₂×C₃	C₃×#489	semidirect
387. C₃	C₂×#5089	direct (N × H)
388. C₃	C₂×C₃×#489	semidirect
390. C₂	C₃×#5089	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×C₃²×C₄⋊Q₈	2
C₂×C₃×#875	2
C₃×#5089	2
C₂×C₃×#810	2
C₂×C₃×#809	2
C₂×C₃×#803	2
C₂×C₃×#489	3
C₂×#5089	3

Subgroups — C2×C3×#5089 #11873533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5089 #11873533