Subgroups — C₂²×C₃×#464 #10679015

Order 768.

2918 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#124	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₃×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#464	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₃×#102	C₂	1	1	yes	maximal, characteristic
9	C₂²×#464	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
11	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
12	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃×Q₁₆	—	2	8	no	—
14	C₂²×C₃×Q₁₆	C₂²	1	12	yes	complemented
15	C₂²×C₃×SD₁₆	—	2	8	no	—
16	C₂²×C₃×SD₁₆	C₂²	1	12	yes	—
17	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×#124	—	2	6	no	—
20	C₂×C₃×#124	C₂²	1	12	yes	—
21	C₂×C₃×C₄×Q₈	—	2	6	no	—
22	C₂×C₃×C₄×Q₈	C₂²	1	12	yes	complemented
23	C₂²×C₃×C₄⋊C₄	—	2	1	no	—
24	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
26	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
27	C₂²×C₃×C₄²	—	2	1	no	—
28	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
29	C₃×#464	C₂²	1	64	yes	direct product factor
30	C₂×C₃×C₄⋊C₈	C₂²	1	12	yes	complemented
31	C₂×C₃×#103	C₂²	1	12	yes	complemented
32	C₂×C₃×#102	C₂²	1	12	yes	—
33	C₂³×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂³×SD₁₆	C₂×C₃	1	1	yes	characteristic
35	C₂²×#124	C₂×C₃	1	1	yes	characteristic
36	C₂²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#464	C₂×C₃	1	24	yes	direct product factor
38	C₂²×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×#103	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂²×#102	C₂×C₃	1	1	yes	characteristic
41	C₂⁵×C₃	—	2	1	no	—
42	C₂²×C₃×Q₈	—	2	3	no	—
43	C₂²×C₃×Q₈	—	2	3	no	—
44	C₂²×C₃×Q₈	—	2	4	no	—
45	C₂²×C₃×Q₈	—	2	4	no	—
46	C₂²×C₃×Q₈	—	2	4	no	—
47	C₂²×C₃×Q₈	D₄	1	8	yes	—
48	C₂²×C₃×Q₈	C₂³	1	6	yes	—
49	C₂²×C₃×Q₈	C₂³	1	6	yes	—
50	C₂²×C₃×D₄	—	2	4	no	—
51	C₂²×C₃×D₄	—	2	3	no	—
52	C₂²×C₃×D₄	—	2	4	no	—
53	C₂²×C₃×D₄	C₂³	1	6	yes	—
54	C₂³×C₃×C₄	—	2	1	no	—
55	C₂³×C₃×C₄	—	2	1	no	—
56	C₂³×C₃×C₄	—	2	1	no	—
57	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
58	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
59	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
60	C₂×C₃×Q₁₆	—	2	48	no	—
61	C₂×C₃×Q₁₆	C₂³	1	16	yes	complemented
62	C₂×C₃×SD₁₆	—	2	48	no	—
63	C₂×C₃×SD₁₆	C₂³	1	16	yes	—
64	C₂²×C₃×C₈	—	2	4	no	—
65	C₂²×C₃×C₈	—	2	4	no	—
66	C₂²×C₃×C₈	C₂³	1	6	yes	—
67	C₂²×C₃×C₈	C₂³	1	6	yes	—
68	C₃×#124	—	2	24	no	—
69	C₃×#124	C₂³	1	16	yes	—
70	C₃×C₄×Q₈	—	2	24	no	—
71	C₃×C₄×Q₈	C₂³	1	16	yes	complemented
72	C₂×C₃×C₄⋊C₄	—	2	12	no	—
73	C₂×C₃×C₄⋊C₄	—	2	3	no	—
74	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
75	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
76	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
77	C₂×C₃×C₄²	—	2	12	no	—
78	C₂×C₃×C₄²	D₄	1	6	yes	—
79	C₂×C₃×C₄²	C₂³	1	6	yes	—
80	C₃×C₄⋊C₈	C₂³	1	16	yes	complemented
81	C₃×#103	C₂³	1	16	yes	complemented
82	C₃×#102	C₂³	1	16	yes	—
83	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
85	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
86	C₂²×Q₁₆	—	2	8	no	—
87	C₂²×Q₁₆	C₂²×C₃	1	12	yes	complemented
88	C₂²×SD₁₆	—	2	8	no	—
89	C₂²×SD₁₆	C₂²×C₃	1	12	yes	—
90	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
91	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
92	C₂×#124	—	2	6	no	—
93	C₂×#124	C₂²×C₃	1	12	yes	—
94	C₂×C₄×Q₈	—	2	6	no	—
95	C₂×C₄×Q₈	C₂²×C₃	1	12	yes	complemented
96	C₂²×C₄⋊C₄	—	2	1	no	—
97	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂²×C₂²⋊C₄	—	2	1	no	—
99	C₂²×C₂²⋊C₄	—	2	1	no	—
100	C₂²×C₄²	—	2	1	no	—
101	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
102	#464	C₂²×C₃	1	64	yes	direct product factor
103	C₂×C₄⋊C₈	C₂²×C₃	1	12	yes	complemented
104	C₂×#103	C₂²×C₃	1	12	yes	complemented
105	C₂×#102	C₂²×C₃	1	12	yes	—
106	C₂⁴×C₃	—	2	6	no	—
107	C₂⁴×C₃	—	4	4	no	—
108	C₂⁴×C₃	—	4	4	no	—
109	C₂⁴×C₃	—	4	4	no	—
110	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×Q₈	—	2	24	no	—
112	C₂×C₃×Q₈	—	2	6	no	—
113	C₂×C₃×Q₈	—	2	6	no	—
114	C₂×C₃×Q₈	—	2	12	no	—
115	C₂×C₃×Q₈	—	2	12	no	—
116	C₂×C₃×Q₈	—	2	12	no	—
117	C₂×C₃×Q₈	—	4	12	no	—
118	C₂×C₃×Q₈	C₂×D₄	1	24	yes	—
119	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
120	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
121	C₂×C₃×D₄	—	2	12	no	—
122	C₂×C₃×D₄	—	2	6	no	—
123	C₂×C₃×D₄	—	2	12	no	—
124	C₂×C₃×D₄	—	4	12	no	—
125	C₂×C₃×D₄	C₂⁴	1	4	yes	—
126	C₂²×C₃×C₄	—	2	8	no	—
127	C₂²×C₃×C₄	—	2	4	no	—
128	C₂²×C₃×C₄	—	2	4	no	—
129	C₂²×C₃×C₄	—	2	6	no	—
130	C₂²×C₃×C₄	—	2	6	no	—
131	C₂²×C₃×C₄	—	2	6	no	—
132	C₂²×C₃×C₄	—	4	4	no	—
133	C₂²×C₃×C₄	—	4	4	no	—
134	C₂²×C₃×C₄	C₂×D₄	1	6	yes	—
135	C₂²×C₃×C₄	C₂×D₄	1	6	yes	—
136	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
137	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
138	C₂²×C₃×C₄	#41	1	4	yes	—
139	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
140	C₃×Q₁₆	—	2	32	no	—
141	C₃×SD₁₆	—	2	32	no	—
142	C₂×C₃×C₈	—	2	12	no	—
143	C₂×C₃×C₈	—	2	12	no	—
144	C₂×C₃×C₈	C₂⁴	1	4	yes	—
145	C₂×C₃×C₈	C₂⁴	1	4	yes	—
146	C₃×C₄⋊C₄	—	2	16	no	—
147	C₃×C₄⋊C₄	—	2	6	no	—
148	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
149	C₃×C₂²⋊C₄	—	2	16	no	—
150	C₃×C₂²⋊C₄	—	2	16	no	—
151	C₃×C₄²	—	2	16	no	—
152	C₃×C₄²	C₂×D₄	1	12	yes	—
153	C₃×C₄²	C₂⁴	1	4	yes	—
154	C₂⁵	—	2	1	no	—
155	C₂²×Q₈	—	2	3	no	—
156	C₂²×Q₈	—	2	3	no	—
157	C₂²×Q₈	—	2	4	no	—
158	C₂²×Q₈	—	2	4	no	—
159	C₂²×Q₈	—	2	4	no	—
160	C₂²×Q₈	C₃×D₄	1	8	yes	—
161	C₂²×Q₈	C₂³×C₃	1	6	yes	—
162	C₂²×Q₈	C₂³×C₃	1	6	yes	—
163	C₂²×D₄	—	2	4	no	—
164	C₂²×D₄	—	2	3	no	—
165	C₂²×D₄	—	2	4	no	—
166	C₂²×D₄	C₂³×C₃	1	6	yes	—
167	C₂³×C₄	—	2	1	no	—
168	C₂³×C₄	—	2	1	no	—
169	C₂³×C₄	—	2	1	no	—
170	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
171	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
172	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
173	C₂×Q₁₆	—	2	48	no	—
174	C₂×Q₁₆	C₂³×C₃	1	16	yes	complemented
175	C₂×SD₁₆	—	2	48	no	—
176	C₂×SD₁₆	C₂³×C₃	1	16	yes	—
177	C₂²×C₈	—	2	4	no	—
178	C₂²×C₈	—	2	4	no	—
179	C₂²×C₈	C₂³×C₃	1	6	yes	—
180	C₂²×C₈	C₂³×C₃	1	6	yes	—
181	#124	—	2	24	no	—
182	#124	C₂³×C₃	1	16	yes	—
183	C₄×Q₈	—	2	24	no	—
184	C₄×Q₈	C₂³×C₃	1	16	yes	complemented
185	C₂×C₄⋊C₄	—	2	12	no	—
186	C₂×C₄⋊C₄	—	2	3	no	—
187	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
188	C₂×C₂²⋊C₄	—	2	12	no	—
189	C₂×C₂²⋊C₄	—	2	12	no	—
190	C₂×C₄²	—	2	12	no	—
191	C₂×C₄²	C₃×D₄	1	6	yes	—
192	C₂×C₄²	C₂³×C₃	1	6	yes	—
193	C₄⋊C₈	C₂³×C₃	1	16	yes	complemented
194	#103	C₂³×C₃	1	16	yes	complemented
195	#102	C₂³×C₃	1	16	yes	—
196	C₂³×C₃	—	2	4	no	—
197	C₂³×C₃	—	4	12	no	—
198	C₂³×C₃	—	4	12	no	—
199	C₂³×C₃	—	4	12	no	—
200	C₂³×C₃	—	8	16	no	—
201	C₂³×C₃	#121	1	4	yes	—
202	C₂³×C₃	#135	1	4	yes	—
203	C₂³×C₃	#137	1	4	yes	—
204	C₂³×C₃	C₂²×D₄	1	3	yes	—
205	C₃×Q₈	—	2	24	no	—
206	C₃×Q₈	—	2	4	no	—
207	C₃×Q₈	—	2	4	no	—
208	C₃×Q₈	—	2	4	no	—
209	C₃×Q₈	—	4	12	no	—
210	C₃×Q₈	C₂²×D₄	1	8	yes	—
211	C₃×D₄	—	2	4	no	—
212	C₃×D₄	—	2	4	no	—
213	C₃×D₄	—	4	12	no	—
214	C₂×C₃×C₄	—	2	24	no	—
215	C₂×C₃×C₄	—	2	12	no	—
216	C₂×C₃×C₄	—	2	12	no	—
217	C₂×C₃×C₄	—	2	4	no	—
218	C₂×C₃×C₄	—	2	4	no	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	4	12	no	—
221	C₂×C₃×C₄	—	4	12	no	—
222	C₂×C₃×C₄	#121	1	12	yes	—
223	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
224	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
225	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
226	C₂×C₃×C₄	C₂²×D₄	1	6	yes	—
227	C₂×C₃×C₄	C₂×#41	1	6	yes	—
228	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
229	C₃×C₈	—	2	4	no	—
230	C₃×C₈	—	2	4	no	—
231	C₂⁴	—	2	6	no	—
232	C₂⁴	—	4	4	no	—
233	C₂⁴	—	4	4	no	—
234	C₂⁴	—	4	4	no	—
235	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×Q₈	—	2	24	no	—
237	C₂×Q₈	—	2	6	no	—
238	C₂×Q₈	—	2	6	no	—
239	C₂×Q₈	—	2	12	no	—
240	C₂×Q₈	—	2	12	no	—
241	C₂×Q₈	—	2	12	no	—
242	C₂×Q₈	—	4	12	no	—
243	C₂×Q₈	C₂×C₃×D₄	1	24	yes	—
244	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
245	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
246	C₂×D₄	—	2	12	no	—
247	C₂×D₄	—	2	6	no	—
248	C₂×D₄	—	2	12	no	—
249	C₂×D₄	—	4	12	no	—
250	C₂×D₄	C₂⁴×C₃	1	4	yes	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	6	no	—
255	C₂²×C₄	—	2	6	no	—
256	C₂²×C₄	—	2	6	no	—
257	C₂²×C₄	—	4	4	no	—
258	C₂²×C₄	—	4	4	no	—
259	C₂²×C₄	C₂×C₃×D₄	1	6	yes	—
260	C₂²×C₄	C₂×C₃×D₄	1	6	yes	—
261	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
262	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
263	C₂²×C₄	C₃×#41	1	4	yes	—
264	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
265	Q₁₆	—	2	32	no	—
266	SD₁₆	—	2	32	no	—
267	C₂×C₈	—	2	12	no	—
268	C₂×C₈	—	2	12	no	—
269	C₂×C₈	C₂⁴×C₃	1	4	yes	—
270	C₂×C₈	C₂⁴×C₃	1	4	yes	—
271	C₄⋊C₄	—	2	16	no	—
272	C₄⋊C₄	—	2	6	no	—
273	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
274	C₂²⋊C₄	—	2	16	no	—
275	C₂²⋊C₄	—	2	16	no	—
276	C₄²	—	2	16	no	—
277	C₄²	C₂×C₃×D₄	1	12	yes	—
278	C₄²	C₂⁴×C₃	1	4	yes	—
279	C₂²×C₃	—	4	4	no	—
280	C₂²×C₃	—	4	4	no	—
281	C₂²×C₃	—	4	4	no	—
282	C₂²×C₃	—	8	24	no	—
283	C₂²×C₃	#464	1	16	yes	direct product factor
284	C₂²×C₃	C₂×#121	1	6	yes	—
285	C₂²×C₃	C₂×#135	1	6	yes	—
286	C₂²×C₃	C₂×#137	1	6	yes	—
287	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
288	C₃×C₄	—	2	8	no	—
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	2	4	no	—
291	C₃×C₄	—	4	4	no	—
292	C₃×C₄	—	4	4	no	—
293	C₃×C₄	C₂×#121	1	6	yes	—
294	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
295	C₃×C₄	C₂²×#41	1	1	yes	characteristic
296	C₂³	—	2	4	no	—
297	C₂³	—	4	12	no	—
298	C₂³	—	4	12	no	—
299	C₂³	—	4	12	no	—
300	C₂³	—	8	16	no	—
301	C₂³	C₃×#121	1	4	yes	—
302	C₂³	C₃×#135	1	4	yes	—
303	C₂³	C₃×#137	1	4	yes	—
304	C₂³	C₂²×C₃×D₄	1	3	yes	—
305	Q₈	—	2	4	no	—
306	Q₈	—	2	24	no	—
307	Q₈	—	2	4	no	—
308	Q₈	—	2	4	no	—
309	Q₈	—	4	12	no	—
310	Q₈	C₂²×C₃×D₄	1	8	yes	—
311	D₄	—	2	4	no	—
312	D₄	—	2	4	no	—
313	D₄	—	4	12	no	—
314	C₂×C₄	—	2	12	no	—
315	C₂×C₄	—	2	12	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	24	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	4	12	no	—
321	C₂×C₄	—	4	12	no	—
322	C₂×C₄	C₃×#121	1	12	yes	—
323	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
324	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
325	C₂×C₄	C₂²×C₃×D₄	1	6	yes	—
326	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
327	C₂×C₄	C₂×C₃×#41	1	6	yes	—
328	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
329	C₈	—	2	4	no	—
330	C₈	—	2	4	no	—
331	C₂×C₃	—	8	4	no	—
332	C₂×C₃	C₂×#464	1	12	yes	direct product factor
333	C₂×C₃	C₂²×#121	1	1	yes	characteristic
334	C₂×C₃	C₂²×#135	1	1	yes	characteristic
335	C₂×C₃	C₂²×#137	1	1	yes	characteristic
336	C₂²	—	4	4	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	8	24	no	—
340	C₂²	C₃×#464	1	16	yes	direct product factor
341	C₂²	C₂×C₃×#121	1	6	yes	—
342	C₂²	C₂×C₃×#135	1	6	yes	—
343	C₂²	C₂×C₃×#137	1	6	yes	—
344	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
345	C₄	—	2	8	no	—
346	C₄	—	2	4	no	—
347	C₄	—	2	4	no	—
348	C₄	—	4	4	no	—
349	C₄	—	4	4	no	—
350	C₄	C₂×C₃×#121	1	6	yes	—
351	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
352	C₄	C₂²×C₃×#41	1	1	yes	characteristic
353	C₃	C₂²×#464	1	1	yes	characteristic, direct product factor, Sylow
354	C₂	—	8	4	no	—
355	C₂	C₂×C₃×#464	1	12	yes	direct product factor
356	C₂	C₂²×C₃×#121	1	1	yes	characteristic
357	C₂	C₂²×C₃×#135	1	1	yes	characteristic
358	C₂	C₂²×C₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×Q₁₆	C₂	semidirect
4. C₂²×C₃×C₄×Q₈	C₂	semidirect
5. C₂×C₃×#464	C₂	direct (N × H)
6. C₂²×C₃×C₄⋊C₈	C₂	semidirect
7. C₂²×C₃×#103	C₂	semidirect
9. C₂²×#464	C₃	direct (N × H)
14. C₂²×C₃×Q₁₆	C₂²	semidirect
22. C₂×C₃×C₄×Q₈	C₂²	semidirect
29. C₃×#464	C₂²	direct (N × H)
30. C₂×C₃×C₄⋊C₈	C₂²	semidirect
31. C₂×C₃×#103	C₂²	semidirect
33. C₂³×Q₁₆	C₂×C₃	semidirect
36. C₂²×C₄×Q₈	C₂×C₃	semidirect
37. C₂×#464	C₂×C₃	direct (N × H)
38. C₂²×C₄⋊C₈	C₂×C₃	semidirect
39. C₂²×#103	C₂×C₃	semidirect
61. C₂×C₃×Q₁₆	C₂³	semidirect
71. C₃×C₄×Q₈	C₂³	semidirect
80. C₃×C₄⋊C₈	C₂³	semidirect
81. C₃×#103	C₂³	semidirect
87. C₂²×Q₁₆	C₂²×C₃	semidirect
95. C₂×C₄×Q₈	C₂²×C₃	semidirect
102. #464	C₂²×C₃	direct (N × H)
103. C₂×C₄⋊C₈	C₂²×C₃	semidirect
104. C₂×#103	C₂²×C₃	semidirect
174. C₂×Q₁₆	C₂³×C₃	semidirect
184. C₄×Q₈	C₂³×C₃	semidirect
193. C₄⋊C₈	C₂³×C₃	semidirect
194. #103	C₂³×C₃	semidirect
283. C₂²×C₃	#464	direct (N × H)
332. C₂×C₃	C₂×#464	direct (N × H)
340. C₂²	C₃×#464	direct (N × H)
353. C₃	C₂²×#464	direct (N × H)
355. C₂	C₂×C₃×#464	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃×Q₁₆	2
C₂³×C₃×SD₁₆	2
C₂²×C₃×#124	2
C₂²×C₃×C₄×Q₈	2
C₂×C₃×#464	2
C₂²×C₃×C₄⋊C₈	2
C₂²×C₃×#103	2
C₂²×C₃×#102	2
C₂²×#464	3

Subgroups — C22×C3×#464 #10679015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#464 #10679015