Subgroups — C₃×Q₈×#638 #13179566

Order 1728.

2304 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×Q₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64155	C₂	1	3	yes	maximal, complemented
4	C₃×Q₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64153	C₂	1	3	yes	maximal, complemented
6	C₃×C₄×#638	C₂	1	3	yes	maximal
7	C₃×#64133	C₂	1	3	yes	maximal, complemented
8	Q₈×#638	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃×Q₈×#67	—	3	4	no	maximal
10	C₂×C₃³×Q₈	—	2	4	no	—
11	C₂×C₃³×Q₈	C₂²	1	3	yes	—
12	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃³×C₄	C₂²	1	3	yes	—
14	C₂×C₃×#638	C₂²	1	1	yes	characteristic
15	C₃×Q₈×C₃⋊D₃	—	2	4	no	—
16	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	3	yes	—
17	C₂×C₃×#634	C₂²	1	3	yes	—
18	C₃×#3757	C₂²	1	3	yes	—
19	C₃×#3752	C₂²	1	3	yes	—
20	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	3	yes	—
21	C₃×#3750	C₂²	1	6	yes	—
22	C₃×#3750	C₂²	1	3	yes	—
23	C₃×C₄×C₃⋊Dic₃	C₂²	1	3	yes	—
24	C₂²×C₃²×Q₈	—	2	4	no	—
25	C₂²×C₃²×Q₈	D₃	1	4	yes	complemented
26	C₂²×C₃²×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×Q₈×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₃×D₃×Q₈	—	3	4	no	—
29	#64155	C₂×C₃	1	3	yes	complemented
30	Q₈×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
31	#64153	C₂×C₃	1	3	yes	complemented
32	C₄×#638	C₂×C₃	1	3	yes	—
33	#64133	C₂×C₃	1	3	yes	complemented
34	C₃×#946	—	3	12	no	—
35	C₃×Q₈×Dic₃	—	3	4	no	—
36	C₃×#944	—	3	12	no	—
37	C₃×C₄×#67	—	3	12	no	—
38	C₃×#924	—	3	12	no	—
39	C₂³×C₃³	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
41	C₃³×Q₈	—	2	6	no	—
42	C₃³×Q₈	D₄	1	4	yes	complemented
43	C₂×C₃³×C₄	—	2	6	no	—
44	C₂×C₃³×C₄	C₂³	1	3	yes	—
45	C₂×C₃³×C₄	C₂³	1	3	yes	—
46	C₃×#638	Q₈	1	4	yes	direct product factor
47	C₂×C₃×C₃⋊Dic₃	C₂³	1	3	yes	—
48	C₂×C₃×C₃⋊Dic₃	C₂³	1	3	yes	—
49	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
50	C₃×C₄×C₃⋊D₃	—	2	6	no	—
51	C₃×#634	—	2	6	no	—
52	C₃×D₄×Q₈	—	9	1	no	—
53	Q₈×#67	—	3	4	no	—
54	C₂×C₃²×Q₈	—	2	32	no	—
55	C₂×C₃²×Q₈	—	2	12	no	—
56	C₂×C₃²×Q₈	—	2	4	no	—
57	C₂×C₃²×Q₈	—	2	16	no	—
58	C₂×C₃²×Q₈	—	2	4	no	—
59	C₂×C₃²×Q₈	C₂×D₃	1	12	yes	—
60	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
61	C₂×C₃²×Q₈	C₂²×C₃	1	3	yes	—
62	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₃²×C₄	—	2	12	no	—
64	C₂²×C₃²×C₄	C₂×D₃	1	12	yes	—
65	C₂²×C₃²×C₄	C₂²×C₃	1	3	yes	—
66	C₂×#638	C₂²×C₃	1	1	yes	characteristic
67	Q₈×C₃⋊D₃	—	2	4	no	—
68	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	3	yes	—
69	C₂×#634	C₂²×C₃	1	3	yes	—
70	C₂×C₃×#67	—	3	4	no	—
71	C₃×D₃×Q₈	—	6	16	no	—
72	C₂×C₃×C₄×D₃	—	3	12	no	—
73	C₂×C₃×Dic₆	—	3	12	no	—
74	#3757	C₂²×C₃	1	3	yes	—
75	#3752	C₂²×C₃	1	3	yes	—
76	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	3	yes	—
77	#3750	C₂²×C₃	1	6	yes	—
78	#3750	C₂²×C₃	1	3	yes	—
79	C₄×C₃⋊Dic₃	C₂²×C₃	1	3	yes	—
80	C₃×#217	—	3	12	no	—
81	C₃×(C₂×D₃)⋊C₄	—	3	12	no	—
82	C₃×C₄⋊Dic₃	—	3	12	no	—
83	C₃×Dic₃⋊C₄	—	3	24	no	—
84	C₃×Dic₃⋊C₄	—	3	12	no	—
85	C₃×C₄×Dic₃	—	3	12	no	—
86	C₂²×C₃³	—	2	1	no	—
87	C₂²×C₃³	—	2	1	no	—
88	C₂²×C₃³	C₂×Q₈	1	2	yes	complemented
89	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
90	C₂×C₃×C₃⋊D₃	—	2	1	no	—
91	C₂×C₃×C₃⋊D₃	—	2	1	no	—
92	C₂×C₃×C₃⋊D₃	C₂×Q₈	1	2	yes	complemented
93	C₃³×C₄	—	2	3	no	—
94	C₃³×C₄	C₂×D₄	1	6	yes	—
95	C₃×C₃⋊Dic₃	—	2	3	no	—
96	C₃×C₃⋊Dic₃	—	2	3	no	—
97	C₃×C₃⋊Dic₃	C₂×Q₈	1	2	yes	complemented
98	C₂²×C₃×Q₈	—	2	4	no	—
99	C₂²×C₃×Q₈	—	9	1	no	—
100	C₂²×C₃×Q₈	C₃×D₃	1	4	yes	complemented
101	C₂²×C₃×Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
102	C₂×D₃×Q₈	—	3	4	no	—
103	C₃×C₄⋊Q₈	—	9	3	no	—
104	C₃×C₂²⋊Q₈	—	9	3	no	—
105	C₃×C₂²⋊Q₈	—	9	3	no	—
106	C₃×C₄×Q₈	—	9	1	no	—
107	C₃×C₄×D₄	—	9	3	no	—
108	#946	—	3	12	no	—
109	Q₈×Dic₃	—	3	4	no	—
110	#944	—	3	12	no	—
111	C₄×#67	—	3	12	no	—
112	#924	—	3	12	no	—
113	C₂³×C₃²	—	2	4	no	—
114	C₂³×C₃²	C₂²×D₃	1	4	yes	—
115	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
116	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
117	C₂²×C₃×D₃	—	3	4	no	—
118	C₃²×Q₈	—	2	48	no	—
119	C₃²×Q₈	—	2	24	no	—
120	C₃²×Q₈	—	2	6	no	—
121	C₃²×Q₈	—	2	16	no	—
122	C₃²×Q₈	#67	1	16	yes	complemented
123	C₃²×Q₈	C₃×D₄	1	4	yes	complemented
124	C₂×C₃²×C₄	—	2	48	no	—
125	C₂×C₃²×C₄	—	2	24	no	—
126	C₂×C₃²×C₄	—	2	6	no	—
127	C₂×C₃²×C₄	—	2	12	no	—
128	C₂×C₃²×C₄	—	2	12	no	—
129	C₂×C₃²×C₄	C₂²×D₃	1	12	yes	—
130	C₂×C₃²×C₄	C₂²×D₃	1	12	yes	—
131	C₂×C₃²×C₄	C₂³×C₃	1	3	yes	—
132	C₂×C₃²×C₄	C₂³×C₃	1	3	yes	—
133	#638	C₃×Q₈	1	4	yes	direct product factor
134	C₂×C₃⋊Dic₃	C₂³×C₃	1	3	yes	—
135	C₂×C₃⋊Dic₃	C₂³×C₃	1	3	yes	—
136	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
137	C₄×C₃⋊D₃	—	2	6	no	—
138	#634	—	2	6	no	—
139	C₃×#67	—	3	16	no	—
140	C₂×C₃×Dic₃	—	3	4	no	—
141	C₂×C₃×Dic₃	—	3	12	no	—
142	C₂×C₃×Dic₃	—	3	12	no	—
143	C₃×C₄×D₃	—	6	24	no	—
144	C₃×Dic₆	—	6	24	no	—
145	D₄×Q₈	—	9	1	no	Sylow
146	C₂×C₃³	—	2	2	no	—
147	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₃³	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
150	C₃×C₃⋊D₃	—	2	2	no	—
151	C₂×C₃×Q₈	—	2	32	no	—
152	C₂×C₃×Q₈	—	2	16	no	—
153	C₂×C₃×Q₈	—	2	4	no	—
154	C₂×C₃×Q₈	—	2	12	no	—
155	C₂×C₃×Q₈	—	2	4	no	—
156	C₂×C₃×Q₈	—	9	3	no	—
157	C₂×C₃×Q₈	—	18	4	no	—
158	C₂×C₃×Q₈	C₂×C₃×D₃	1	12	yes	—
159	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
160	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	3	yes	—
161	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
162	C₂×C₃×D₄	—	9	1	no	—
163	C₂²×C₃×C₄	—	2	12	no	—
164	C₂²×C₃×C₄	—	9	3	no	—
165	C₂²×C₃×C₄	C₂×C₃×D₃	1	12	yes	—
166	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	3	yes	—
167	C₂×#67	—	3	4	no	—
168	D₃×Q₈	—	6	16	no	—
169	C₂×C₄×D₃	—	3	12	no	—
170	C₂×Dic₆	—	3	12	no	—
171	C₃×C₄⋊C₄	—	9	3	no	—
172	C₃×C₄⋊C₄	—	9	6	no	—
173	C₃×C₄⋊C₄	—	9	3	no	—
174	C₃×C₂²⋊C₄	—	9	3	no	—
175	C₃×C₂²⋊C₄	—	9	3	no	—
176	C₃×C₄²	—	9	3	no	—
177	#217	—	3	12	no	—
178	(C₂×D₃)⋊C₄	—	3	12	no	—
179	C₄⋊Dic₃	—	3	12	no	—
180	Dic₃⋊C₄	—	3	24	no	—
181	Dic₃⋊C₄	—	3	12	no	—
182	C₄×Dic₃	—	3	12	no	—
183	C₂²×C₃²	—	2	8	no	—
184	C₂²×C₃²	—	2	8	no	—
185	C₂²×C₃²	—	2	4	no	—
186	C₂²×C₃²	—	2	4	no	—
187	C₂²×C₃²	—	2	1	no	—
188	C₂²×C₃²	—	2	1	no	—
189	C₂²×C₃²	—	2	4	no	—
190	C₂²×C₃²	—	2	8	no	—
191	C₂²×C₃²	D₃×Q₈	1	8	yes	complemented
192	C₂²×C₃²	C₂×C₃×Q₈	1	2	yes	complemented
193	C₂²×C₃²	C₂³×D₃	1	4	yes	—
194	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
195	C₂×C₃⋊D₃	—	2	1	no	—
196	C₂×C₃⋊D₃	—	2	1	no	—
197	C₂×C₃⋊D₃	C₂×C₃×Q₈	1	2	yes	complemented
198	C₂×C₃×D₃	—	3	8	no	—
199	C₂×C₃×D₃	—	6	4	no	—
200	C₂×C₃×D₃	—	6	4	no	—
201	C₃²×C₄	—	2	24	no	—
202	C₃²×C₄	—	2	12	no	—
203	C₃²×C₄	—	2	3	no	—
204	C₃²×C₄	—	2	24	no	—
205	C₃²×C₄	C₂×#67	1	24	yes	—
206	C₃²×C₄	C₂×C₃×D₄	1	6	yes	—
207	C₃⋊Dic₃	—	2	3	no	—
208	C₃⋊Dic₃	—	2	3	no	—
209	C₃⋊Dic₃	C₂×C₃×Q₈	1	2	yes	complemented
210	C₃×Dic₃	—	3	8	no	—
211	C₃×Dic₃	—	6	12	no	—
212	C₃×Dic₃	—	6	12	no	—
213	C₂²×Q₈	—	9	1	no	—
214	C₂²×Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
215	C₄⋊Q₈	—	9	3	no	—
216	C₂²⋊Q₈	—	9	3	no	—
217	C₂²⋊Q₈	—	9	3	no	—
218	C₄×Q₈	—	9	1	no	—
219	C₄×D₄	—	9	3	no	—
220	C₃³	D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
221	C₂³×C₃	—	2	4	no	—
222	C₂³×C₃	—	9	1	no	—
223	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
224	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
225	C₂²×D₃	—	3	4	no	—
226	C₃×Q₈	—	2	48	no	—
227	C₃×Q₈	—	2	24	no	—
228	C₃×Q₈	—	2	6	no	—
229	C₃×Q₈	—	2	16	no	—
230	C₃×Q₈	—	18	6	no	—
231	C₃×Q₈	C₃×#67	1	16	yes	complemented
232	C₃×Q₈	#638	1	4	yes	direct product factor
233	C₃×D₄	—	9	4	no	—
234	C₂×C₃×C₄	—	2	48	no	—
235	C₂×C₃×C₄	—	2	24	no	—
236	C₂×C₃×C₄	—	2	6	no	—
237	C₂×C₃×C₄	—	2	12	no	—
238	C₂×C₃×C₄	—	2	12	no	—
239	C₂×C₃×C₄	—	9	1	no	—
240	C₂×C₃×C₄	—	9	3	no	—
241	C₂×C₃×C₄	—	9	3	no	—
242	C₂×C₃×C₄	—	18	6	no	—
243	C₂×C₃×C₄	C₂²×C₃×D₃	1	12	yes	—
244	C₂×C₃×C₄	C₂²×C₃×D₃	1	12	yes	—
245	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	3	yes	—
246	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	3	yes	—
247	#67	—	3	16	no	—
248	C₂×Dic₃	—	3	4	no	—
249	C₂×Dic₃	—	3	12	no	—
250	C₂×Dic₃	—	3	12	no	—
251	C₄×D₃	—	6	24	no	—
252	Dic₆	—	6	24	no	—
253	C₂×C₃²	—	2	16	no	—
254	C₂×C₃²	—	2	8	no	—
255	C₂×C₃²	—	2	2	no	—
256	C₂×C₃²	—	2	4	no	—
257	C₂×C₃²	—	2	4	no	—
258	C₂×C₃²	—	2	4	no	—
259	C₂×C₃²	C₂×D₃×Q₈	1	4	yes	—
260	C₂×C₃²	#1007	1	4	yes	—
261	C₂×C₃²	C₂²×#67	1	4	yes	—
262	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
263	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
264	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
265	C₃⋊D₃	—	2	2	no	—
266	C₃×D₃	—	6	8	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	9	3	no	—
269	C₂×Q₈	—	18	4	no	—
270	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	3	yes	—
271	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
272	C₂×D₄	—	9	1	no	—
273	C₂²×C₄	—	9	3	no	—
274	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	3	yes	—
275	C₄⋊C₄	—	9	3	no	—
276	C₄⋊C₄	—	9	3	no	—
277	C₄⋊C₄	—	9	6	no	—
278	C₂²⋊C₄	—	9	3	no	—
279	C₂²⋊C₄	—	9	3	no	—
280	C₄²	—	9	3	no	—
281	C₂²×C₃	—	2	8	no	—
282	C₂²×C₃	—	2	8	no	—
283	C₂²×C₃	—	2	4	no	—
284	C₂²×C₃	—	2	4	no	—
285	C₂²×C₃	—	2	1	no	—
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	2	8	no	—
289	C₂²×C₃	—	9	2	no	—
290	C₂²×C₃	—	18	1	no	—
291	C₂²×C₃	—	18	1	no	—
292	C₂²×C₃	C₃×D₃×Q₈	1	8	yes	complemented
293	C₂²×C₃	Q₈×C₃⋊D₃	1	2	yes	complemented
294	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
295	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
296	C₂×D₃	—	3	8	no	—
297	C₂×D₃	—	6	4	no	—
298	C₂×D₃	—	6	4	no	—
299	C₃×C₄	—	2	24	no	—
300	C₃×C₄	—	2	12	no	—
301	C₃×C₄	—	2	3	no	—
302	C₃×C₄	—	2	24	no	—
303	C₃×C₄	—	9	2	no	—
304	C₃×C₄	—	18	3	no	—
305	C₃×C₄	—	18	3	no	—
306	C₃×C₄	C₂×C₃×#67	1	24	yes	—
307	C₃×C₄	C₂×#638	1	6	yes	—
308	Dic₃	—	3	8	no	—
309	Dic₃	—	6	12	no	—
310	Dic₃	—	6	12	no	—
311	C₃²	—	2	4	no	—
312	C₃²	Q₈×#67	1	4	yes	complemented
313	C₃²	C₃×D₄×Q₈	1	1	yes	characteristic, complemented
314	C₂³	—	9	1	no	—
315	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
316	Q₈	—	2	6	no	—
317	Q₈	—	18	6	no	—
318	Q₈	C₃×#638	1	4	yes	direct product factor
319	D₄	—	9	4	no	—
320	C₂×C₄	—	2	6	no	—
321	C₂×C₄	—	9	1	no	—
322	C₂×C₄	—	9	3	no	—
323	C₂×C₄	—	9	3	no	—
324	C₂×C₄	—	18	6	no	—
325	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	3	yes	—
326	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	3	yes	—
327	C₂×C₃	—	2	16	no	—
328	C₂×C₃	—	2	8	no	—
329	C₂×C₃	—	2	2	no	—
330	C₂×C₃	—	2	4	no	—
331	C₂×C₃	—	2	4	no	—
332	C₂×C₃	—	2	4	no	—
333	C₂×C₃	—	18	2	no	—
334	C₂×C₃	C₂×C₃×D₃×Q₈	1	4	yes	—
335	C₂×C₃	C₃×#1007	1	4	yes	—
336	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
337	C₂×C₃	C₂×Q₈×C₃⋊D₃	1	1	yes	characteristic
338	C₂×C₃	#64364	1	1	yes	characteristic
339	C₂×C₃	C₂²×#638	1	1	yes	characteristic
340	D₃	—	6	8	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	9	2	no	—
344	C₂²	—	18	1	no	—
345	C₂²	—	18	1	no	—
346	C₂²	C₃×Q₈×C₃⋊D₃	1	2	yes	complemented
347	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
348	C₄	—	2	3	no	—
349	C₄	—	9	2	no	—
350	C₄	—	18	3	no	—
351	C₄	—	18	3	no	—
352	C₄	C₂×C₃×#638	1	6	yes	—
353	C₃	—	2	4	no	—
354	C₃	C₃×Q₈×#67	1	4	yes	complemented
355	C₃	Q₈×#638	1	1	yes	characteristic, direct product factor
356	C₂	—	2	2	no	—
357	C₂	—	18	2	no	—
358	C₂	C₂×C₃×Q₈×C₃⋊D₃	1	1	yes	characteristic
359	C₂	C₃×#64364	1	1	yes	characteristic
360	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃×#638	C₂²
hypercenter	C₂²×C₃×Q₈	C₃⋊D₃
hypocenter	C₃²	C₃×D₄×Q₈
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×Q₈	C₂	semidirect
2. C₂×C₃×Q₈×C₃⋊D₃	C₂	semidirect
3. C₃×#64155	C₂	semidirect
4. C₃×Q₈×C₃⋊Dic₃	C₂	semidirect
5. C₃×#64153	C₂	semidirect
7. C₃×#64133	C₂	semidirect
8. Q₈×#638	C₃	direct (N × H)
25. C₂²×C₃²×Q₈	D₃	semidirect
26. C₂²×C₃²×Q₈	C₂×C₃	semidirect
27. C₂×Q₈×C₃⋊D₃	C₂×C₃	semidirect
29. #64155	C₂×C₃	semidirect
30. Q₈×C₃⋊Dic₃	C₂×C₃	semidirect
31. #64153	C₂×C₃	semidirect
33. #64133	C₂×C₃	semidirect
42. C₃³×Q₈	D₄	semidirect
46. C₃×#638	Q₈	direct (N × H)
88. C₂²×C₃³	C₂×Q₈	semidirect
92. C₂×C₃×C₃⋊D₃	C₂×Q₈	semidirect
97. C₃×C₃⋊Dic₃	C₂×Q₈	semidirect
100. C₂²×C₃×Q₈	C₃×D₃	semidirect
101. C₂²×C₃×Q₈	C₃⋊D₃	semidirect
122. C₃²×Q₈	#67	semidirect
123. C₃²×Q₈	C₃×D₄	semidirect
133. #638	C₃×Q₈	direct (N × H)
191. C₂²×C₃²	D₃×Q₈	semidirect
192. C₂²×C₃²	C₂×C₃×Q₈	semidirect
197. C₂×C₃⋊D₃	C₂×C₃×Q₈	semidirect
209. C₃⋊Dic₃	C₂×C₃×Q₈	semidirect
214. C₂²×Q₈	C₃×C₃⋊D₃	semidirect
220. C₃³	D₄×Q₈	semidirect
231. C₃×Q₈	C₃×#67	semidirect
232. C₃×Q₈	#638	direct (N × H)
292. C₂²×C₃	C₃×D₃×Q₈	semidirect
293. C₂²×C₃	Q₈×C₃⋊D₃	semidirect
312. C₃²	Q₈×#67	semidirect
313. C₃²	C₃×D₄×Q₈	semidirect
318. Q₈	C₃×#638	direct (N × H)
346. C₂²	C₃×Q₈×C₃⋊D₃	semidirect
354. C₃	C₃×Q₈×#67	semidirect
355. C₃	Q₈×#638	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×C₃³×Q₈	2
C₂×C₃×Q₈×C₃⋊D₃	2
C₃×#64155	2
C₃×Q₈×C₃⋊Dic₃	2
C₃×#64153	2
C₃×C₄×#638	2
C₃×#64133	2
Q₈×#638	3
C₃×Q₈×#67	3

Subgroups — C3×Q8×#638 #13179566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₈×#638 #13179566