Subgroups — C₂×C₃×#5088 #11873361

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 363 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×#874	C₂	1	1	yes	maximal, characteristic
3	C₃×#5088	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#809	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#486	—	3	1	no	maximal
7	C₂×#5088	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃²×Q₈	—	2	1	no	—
9	C₂²×C₃×D₁₂	—	2	1	no	—
10	C₂²×C₃×D₁₂	—	2	1	no	—
11	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
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	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
18	C₃×#874	—	2	2	no	—
19	C₃×#874	C₂²	1	4	yes	—
20	C₃×#809	C₂²	1	16	yes	complemented
21	C₃×C₄×C₃⋊C₈	C₂²	1	4	yes	complemented
22	C₂×C₃×C₄⋊Q₈	—	2	1	no	—
23	C₂×C₃×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
24	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×C₃×#127	—	3	1	no	—
26	C₂×#874	C₂×C₃	1	1	yes	characteristic
27	C₃×#486	—	3	8	no	—
28	C₂×C₃×#102	—	3	4	no	—
29	C₂×C₃×C₄×C₈	—	3	1	no	—
30	#5088	C₂×C₃	1	8	yes	direct product factor
31	C₂×#809	C₂×C₃	1	4	yes	complemented
32	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂³×C₃×D₃	—	2	2	no	—
34	C₂×C₃²×Q₈	—	2	4	no	—
35	C₂×C₃²×Q₈	—	4	4	no	—
36	C₂²×C₃²×C₄	—	2	2	no	—
37	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
38	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂×C₃×D₁₂	—	2	8	no	—
41	C₂×C₃×D₁₂	—	2	4	no	—
42	C₂×C₃×D₁₂	—	2	4	no	—
43	C₂×C₃×D₁₂	—	2	2	no	—
44	C₂×C₃×D₁₂	—	4	4	no	—
45	C₂×C₃×D₁₂	—	4	4	no	—
46	C₂×C₃×D₁₂	C₂³	1	4	yes	—
47	C₃²×C₄⋊C₄	—	2	4	no	—
48	C₃²×C₄⋊C₄	—	2	2	no	—
49	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
50	C₃²×C₄²	D₄	1	2	yes	—
51	C₃²×C₄²	C₂³	1	2	yes	—
52	C₂×C₃×C₃⋊C₈	—	2	4	no	—
53	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
54	C₂×#486	—	3	1	no	Sylow
55	C₂²×C₃×Q₈	—	2	2	no	—
56	C₂²×C₃×Q₈	—	2	1	no	—
57	C₂²×C₃×Q₈	—	2	1	no	—
58	C₂²×C₃×D₄	—	3	2	no	—
59	C₂²×C₃×D₄	—	6	1	no	—
60	C₂²×C₃×D₄	—	6	1	no	—
61	C₂²×D₁₂	—	2	1	no	—
62	C₂²×D₁₂	—	2	1	no	—
63	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
64	C₂²×C₃×C₈	—	3	2	no	—
65	C₃×C₄⋊Q₈	—	2	4	no	—
66	C₃×C₄⋊Q₈	—	2	2	no	—
67	C₃×C₄⋊Q₈	—	2	2	no	—
68	C₃×C₄⋊Q₈	—	2	4	no	—
69	C₃×C₄⋊Q₈	C₂×D₃	1	4	yes	complemented
70	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
71	C₃×#127	—	3	4	no	—
72	C₃×#127	—	6	2	no	—
73	C₂×C₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
78	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₃×C₄²	—	2	1	no	—
80	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
81	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
83	#874	—	2	2	no	—
84	#874	C₂²×C₃	1	4	yes	—
85	C₃×#102	—	3	16	no	—
86	C₃×C₄×C₈	—	3	4	no	—
87	#809	C₂²×C₃	1	16	yes	complemented
88	C₄×C₃⋊C₈	C₂²×C₃	1	4	yes	complemented
89	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×D₃	—	2	4	no	—
91	C₂²×C₃×D₃	—	4	4	no	—
92	C₂²×C₃×D₃	—	4	4	no	—
93	C₂²×C₃×D₃	—	4	4	no	—
94	C₃²×Q₈	—	4	8	no	—
95	C₂×C₃²×C₄	—	2	4	no	—
96	C₂×C₃²×C₄	—	4	4	no	—
97	C₂×C₃²×C₄	D₈	1	4	yes	—
98	C₂×C₃²×C₄	SD₁₆	1	4	yes	—
99	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
101	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
102	C₂×C₃²×C₄	#41	1	4	yes	—
103	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
104	C₃×D₁₂	—	2	8	no	—
105	C₃×D₁₂	—	4	4	no	—
106	C₃×D₁₂	—	4	8	no	—
107	C₃×D₁₂	—	4	8	no	—
108	C₃×C₃⋊C₈	—	2	4	no	—
109	C₂×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic, complemented
110	C₂×#127	—	3	1	no	—
111	#486	—	3	8	no	—
112	C₂×#102	—	3	4	no	—
113	C₂×C₄×C₈	—	3	1	no	—
114	C₂⁴×C₃	—	6	2	no	—
115	C₂³×D₃	—	2	2	no	—
116	C₂×C₃×Q₈	—	2	8	no	—
117	C₂×C₃×Q₈	—	2	4	no	—
118	C₂×C₃×Q₈	—	2	4	no	—
119	C₂×C₃×Q₈	—	4	8	no	—
120	C₂×C₃×Q₈	—	4	4	no	—
121	C₂×C₃×Q₈	—	4	4	no	—
122	C₂×C₃×D₄	—	3	4	no	—
123	C₂×C₃×D₄	—	6	8	no	—
124	C₂×C₃×D₄	—	6	4	no	—
125	C₂×C₃×D₄	—	6	4	no	—
126	C₂×C₃×D₄	—	6	2	no	—
127	C₂×C₃×D₄	—	12	4	no	—
128	C₂×C₃×D₄	—	12	4	no	—
129	C₂²×C₃×C₄	—	2	4	no	—
130	C₂²×C₃×C₄	—	2	2	no	—
131	C₂²×C₃×C₄	—	2	2	no	—
132	C₂²×C₃×C₄	—	2	1	no	—
133	C₂²×C₃×C₄	—	2	1	no	—
134	C₂²×C₃×C₄	—	2	1	no	—
135	C₂²×C₃×C₄	#67	1	1	yes	characteristic
136	C₂²×C₃×C₄	#67	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
141	C₂×D₁₂	—	2	8	no	—
142	C₂×D₁₂	—	2	2	no	—
143	C₂×D₁₂	—	2	4	no	—
144	C₂×D₁₂	—	2	4	no	—
145	C₂×D₁₂	—	4	4	no	—
146	C₂×D₁₂	—	4	4	no	—
147	C₂×D₁₂	C₂³×C₃	1	4	yes	—
148	C₂×C₃×C₈	—	3	4	no	—
149	C₂×C₃×C₈	—	6	4	no	—
150	C₃×C₄⋊C₄	—	2	8	no	—
151	C₃×C₄⋊C₄	—	2	4	no	—
152	C₃×C₄⋊C₄	—	2	4	no	—
153	C₃×C₄⋊C₄	—	2	2	no	—
154	C₃×C₄⋊C₄	—	2	4	no	—
155	C₃×C₄⋊C₄	—	2	2	no	—
156	C₃×C₄⋊C₄	—	2	4	no	—
157	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
158	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
159	C₃×C₄²	—	2	2	no	—
160	C₃×C₄²	—	2	2	no	—
161	C₃×C₄²	#67	1	2	yes	—
162	C₃×C₄²	C₃×D₄	1	2	yes	—
163	C₃×C₄²	C₂²×D₃	1	2	yes	—
164	C₃×C₄²	C₂³×C₃	1	2	yes	—
165	C₂×C₃⋊C₈	—	2	4	no	—
166	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
167	C₂²×C₃²	#124	1	2	yes	—
168	C₂²×C₃²	C₂×D₈	1	2	yes	—
169	C₂²×C₃²	C₂×SD₁₆	1	2	yes	—
170	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₃×D₃	—	4	4	no	—
172	C₂×C₃×D₃	—	4	4	no	—
173	C₂×C₃×D₃	—	4	4	no	—
174	C₂×C₃×D₃	—	8	8	no	—
175	C₃²×C₄	—	4	4	no	—
176	C₃²×C₄	#124	1	2	yes	—
177	C₃²×C₄	C₂×D₈	1	4	yes	—
178	C₃²×C₄	C₂×SD₁₆	1	4	yes	—
179	C₃²×C₄	C₂×#41	1	2	yes	—
180	C₂²×Q₈	—	2	1	no	—
181	C₂²×D₄	—	3	2	no	—
182	C₂²×D₄	—	6	1	no	—
183	C₂²×D₄	—	6	1	no	—
184	C₂²×C₈	—	3	2	no	—
185	C₄⋊Q₈	—	2	2	no	—
186	C₄⋊Q₈	C₂×C₃×D₃	1	4	yes	complemented
187	#127	—	3	4	no	—
188	#127	—	6	2	no	—
189	C₂×C₄⋊C₄	—	2	1	no	—
190	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
191	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
192	#102	—	3	16	no	—
193	C₄×C₈	—	3	4	no	—
194	C₂³×C₃	—	2	1	no	—
195	C₂³×C₃	—	6	4	no	—
196	C₂³×C₃	—	12	4	no	—
197	C₂³×C₃	—	12	4	no	—
198	C₂³×C₃	—	12	4	no	—
199	C₂³×C₃	C₂×#67	1	1	yes	characteristic
200	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
201	C₂²×D₃	—	2	4	no	—
202	C₂²×D₃	—	4	4	no	—
203	C₂²×D₃	—	4	4	no	—
204	C₂²×D₃	—	4	4	no	—
205	C₃×Q₈	—	4	16	no	—
206	C₃×Q₈	—	4	8	no	—
207	C₃×Q₈	—	4	8	no	—
208	C₃×D₄	—	6	8	no	—
209	C₃×D₄	—	12	8	no	—
210	C₃×D₄	—	12	8	no	—
211	C₃×D₄	—	12	4	no	—
212	C₂×C₃×C₄	—	2	8	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	2	4	no	—
215	C₂×C₃×C₄	—	2	1	no	—
216	C₂×C₃×C₄	—	2	4	no	—
217	C₂×C₃×C₄	—	2	4	no	—
218	C₂×C₃×C₄	—	2	4	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	4	8	no	—
223	C₂×C₃×C₄	—	4	4	no	—
224	C₂×C₃×C₄	—	4	4	no	—
225	C₂×C₃×C₄	#213	1	4	yes	—
226	C₂×C₃×C₄	#215	1	4	yes	—
227	C₂×C₃×C₄	C₃×D₈	1	4	yes	—
228	C₂×C₃×C₄	C₃×SD₁₆	1	4	yes	—
229	C₂×C₃×C₄	#239	1	4	yes	—
230	C₂×C₃×C₄	C₂×#67	1	2	yes	—
231	C₂×C₃×C₄	C₂×#67	1	2	yes	—
232	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
235	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
236	C₂×C₃×C₄	C₃×#41	1	4	yes	—
237	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
239	D₁₂	—	2	8	no	—
240	D₁₂	—	4	4	no	—
241	D₁₂	—	4	8	no	—
242	D₁₂	—	4	8	no	—
243	C₃×C₈	—	6	4	no	—
244	C₃⋊C₈	—	2	4	no	—
245	C₂×C₃²	#486	1	4	yes	complemented
246	C₂×C₃²	C₂×#124	1	1	yes	characteristic
247	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
248	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
249	C₃×D₃	—	8	4	no	—
250	C₂⁴	—	6	2	no	—
251	C₂×Q₈	—	2	4	no	—
252	C₂×Q₈	—	4	4	no	—
253	C₂×D₄	—	3	4	no	—
254	C₂×D₄	—	6	8	no	—
255	C₂×D₄	—	6	4	no	—
256	C₂×D₄	—	6	4	no	—
257	C₂×D₄	—	6	2	no	—
258	C₂×D₄	—	12	4	no	—
259	C₂×D₄	—	12	4	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	C₃×#67	1	1	yes	characteristic
262	C₂²×C₄	C₃×#67	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
264	C₂×C₈	—	3	4	no	—
265	C₂×C₈	—	6	4	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
269	C₄²	C₃×#67	1	2	yes	—
270	C₄²	C₂²×C₃×D₃	1	2	yes	—
271	C₂²×C₃	—	2	2	no	—
272	C₂²×C₃	—	2	2	no	—
273	C₂²×C₃	—	2	2	no	—
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	12	4	no	—
276	C₂²×C₃	—	12	4	no	—
277	C₂²×C₃	—	12	4	no	—
278	C₂²×C₃	—	24	8	no	—
279	C₂²×C₃	C₂×#213	1	2	yes	—
280	C₂²×C₃	C₂×#215	1	2	yes	—
281	C₂²×C₃	#947	1	2	yes	—
282	C₂²×C₃	C₃×#124	1	2	yes	—
283	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
284	C₂²×C₃	C₂×C₃×SD₁₆	1	2	yes	—
285	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
286	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
287	C₂×D₃	—	4	4	no	—
288	C₂×D₃	—	4	4	no	—
289	C₂×D₃	—	4	4	no	—
290	C₂×D₃	—	8	8	no	—
291	C₃×C₄	—	2	4	no	—
292	C₃×C₄	—	2	4	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	2	no	—
295	C₃×C₄	—	4	8	no	—
296	C₃×C₄	—	4	4	no	—
297	C₃×C₄	—	4	4	no	—
298	C₃×C₄	C₂×#213	1	4	yes	—
299	C₃×C₄	C₂×#215	1	4	yes	—
300	C₃×C₄	#947	1	2	yes	—
301	C₃×C₄	C₃×#124	1	2	yes	—
302	C₃×C₄	C₂×C₃×D₈	1	4	yes	—
303	C₃×C₄	C₂×C₃×SD₁₆	1	4	yes	—
304	C₃×C₄	C₂×#239	1	2	yes	—
305	C₃×C₄	C₂×C₃×#41	1	2	yes	—
306	C₃²	C₂×#486	1	1	yes	characteristic, complemented, Sylow
307	C₂³	—	6	4	no	—
308	C₂³	—	12	4	no	—
309	C₂³	—	12	4	no	—
310	C₂³	—	12	4	no	—
311	C₂³	C₂×C₃×#67	1	1	yes	characteristic
312	Q₈	—	4	8	no	—
313	D₄	—	6	8	no	—
314	D₄	—	12	8	no	—
315	D₄	—	12	8	no	—
316	D₄	—	12	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	C₃×#213	1	4	yes	—
320	C₂×C₄	C₃×#215	1	4	yes	—
321	C₂×C₄	C₃×#239	1	4	yes	—
322	C₂×C₄	C₂×C₃×#67	1	2	yes	—
323	C₂×C₄	C₂×C₃×#67	1	2	yes	—
324	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
325	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
326	C₈	—	6	4	no	—
327	C₂×C₃	—	2	1	no	—
328	C₂×C₃	—	2	1	no	—
329	C₂×C₃	—	2	1	no	—
330	C₂×C₃	—	2	4	no	—
331	C₂×C₃	—	24	4	no	—
332	C₂×C₃	#5088	1	4	yes	direct product factor
333	C₂×C₃	C₃×#486	1	4	yes	complemented
334	C₂×C₃	C₂²×#213	1	1	yes	characteristic
335	C₂×C₃	C₂²×#215	1	1	yes	characteristic
336	C₂×C₃	C₂×#947	1	1	yes	characteristic
337	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
338	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
339	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
340	D₃	—	8	4	no	—
341	C₂²	—	12	4	no	—
342	C₂²	—	12	4	no	—
343	C₂²	—	12	4	no	—
344	C₂²	—	24	8	no	—
345	C₂²	C₂×C₃×#213	1	2	yes	—
346	C₂²	C₂×C₃×#215	1	2	yes	—
347	C₂²	C₃×#947	1	2	yes	—
348	C₂²	C₂²×C₃×#67	1	1	yes	characteristic
349	C₄	—	4	4	no	—
350	C₄	C₂×C₃×#213	1	4	yes	—
351	C₄	C₂×C₃×#215	1	4	yes	—
352	C₄	C₃×#947	1	2	yes	—
353	C₄	C₂×C₃×#239	1	2	yes	—
354	C₃	—	2	1	no	—
355	C₃	C₂×#5088	1	1	yes	characteristic, direct product factor
356	C₃	C₂×C₃×#486	1	1	yes	characteristic, complemented
357	C₂	—	24	4	no	—
358	C₂	C₃×#5088	1	4	yes	direct product factor
359	C₂	C₂²×C₃×#213	1	1	yes	characteristic
360	C₂	C₂²×C₃×#215	1	1	yes	characteristic
361	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	C₂×C₃×#874	C₂
hypercenter	C₂×C₃×C₄⋊Q₈	D₃
hypocenter	C₃	C₂×C₃×#486
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×#5088	C₂	direct (N × H)
4. C₂×C₃×#809	C₂	semidirect
5. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
7. C₂×#5088	C₃	direct (N × H)
13. C₃²×C₄⋊Q₈	C₂²	semidirect
20. C₃×#809	C₂²	semidirect
21. C₃×C₄×C₃⋊C₈	C₂²	semidirect
23. C₂×C₃×C₄⋊Q₈	D₃	semidirect
24. C₂×C₃×C₄⋊Q₈	C₂×C₃	semidirect
30. #5088	C₂×C₃	direct (N × H)
31. C₂×#809	C₂×C₃	semidirect
32. C₂×C₄×C₃⋊C₈	C₂×C₃	semidirect
69. C₃×C₄⋊Q₈	C₂×D₃	semidirect
70. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
87. #809	C₂²×C₃	semidirect
88. C₄×C₃⋊C₈	C₂²×C₃	semidirect
109. C₂×C₄⋊Q₈	C₃×D₃	semidirect
186. C₄⋊Q₈	C₂×C₃×D₃	semidirect
245. C₂×C₃²	#486	semidirect
306. C₃²	C₂×#486	semidirect
332. C₂×C₃	#5088	direct (N × H)
333. C₂×C₃	C₃×#486	semidirect
355. C₃	C₂×#5088	direct (N × H)
356. C₃	C₂×C₃×#486	semidirect
358. C₂	C₃×#5088	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×#874	2
C₃×#5088	2
C₂×C₃×#809	2
C₂×C₃×C₄×C₃⋊C₈	2
C₂×C₃×#486	3
C₂×#5088	3

Subgroups — C2×C3×#5088 #11873361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5088 #11873361