Subgroups — C₂×C₃×#65448 #14427976

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4084	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3964	C₂	1	2	yes	maximal, complemented
5	C₃×#65448	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#3949	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65448	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
9	C₂²×C₃×C₂²⋊D₅	—	2	2	no	—
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×D₈	—	2	4	no	—
12	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₂²⋊Dic₅	—	2	2	no	—
15	C₃×#4084	—	2	4	no	—
16	C₃×#4084	C₂²	1	8	yes	complemented
17	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
18	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
19	C₂×C₃×#676	—	2	4	no	—
20	C₂×C₃×#676	C₂²	1	4	yes	complemented
21	C₃×#3964	C₂²	1	8	yes	complemented
22	C₃×#3949	C₂²	1	4	yes	complemented
23	C₂×C₃×#469	—	5	1	no	maximal, Hall
24	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×#4084	C₂×C₃	1	2	yes	complemented
26	C₂²×#676	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#3964	C₂×C₃	1	2	yes	complemented
28	#65448	C₂×C₃	1	8	yes	direct product factor
29	C₂×#3949	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂⁴×C₃×C₅	—	2	2	no	—
31	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
32	C₂×C₃×C₅×D₄	—	2	4	no	—
33	C₂×C₃×C₅×D₄	—	2	2	no	—
34	C₂×C₃×C₅×D₄	—	2	4	no	—
35	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
38	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
39	C₂²×C₃×Dic₅	—	2	2	no	—
40	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	—	2	2	no	—
42	C₂×C₃×C₄×D₅	—	2	2	no	—
43	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
45	C₃×C₅×D₈	—	2	8	no	—
46	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
47	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
48	C₃×C₂²⋊Dic₅	—	2	8	no	—
49	C₃×C₄⋊Dic₅	—	2	2	no	—
50	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
51	C₂×C₃×#168	—	2	2	no	—
52	C₂×C₃×#168	C₂³	1	2	yes	—
53	C₃×#676	—	2	8	no	—
54	C₂²×C₃×D₈	D₅	1	1	yes	characteristic, complemented
55	C₂²×C₃×M₁₆	—	5	1	no	—
56	C₂×C₃×#121	—	5	2	no	—
57	C₃×#469	—	5	8	no	—
58	C₂×C₃×#106	—	5	1	no	—
59	C₂×C₃×#102	—	5	2	no	—
60	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
61	C₂²×C₂²⋊D₅	—	2	2	no	—
62	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₅×D₈	—	2	4	no	—
64	C₂×C₅×D₈	C₂²×C₃	1	4	yes	complemented
65	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₂²⋊Dic₅	—	2	2	no	—
67	#4084	—	2	4	no	—
68	#4084	C₂²×C₃	1	8	yes	complemented
69	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
70	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
71	C₂×#676	—	2	4	no	—
72	C₂×#676	C₂²×C₃	1	4	yes	complemented
73	#3964	C₂²×C₃	1	8	yes	complemented
74	#3949	C₂²×C₃	1	4	yes	complemented
75	C₂×#469	—	5	1	no	Sylow
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	—	4	4	no	—
78	C₂³×C₃×C₅	—	4	4	no	—
79	C₂³×C₃×C₅	—	4	4	no	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₃×D₅	—	2	2	no	—
82	C₂²×C₃×D₅	—	2	4	no	—
83	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
84	C₃×C₅×D₄	—	2	4	no	—
85	C₃×C₅×D₄	—	2	4	no	—
86	C₃×C₅×D₄	—	4	4	no	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	#41	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
91	C₃×C₂²⋊D₅	—	4	16	no	—
92	C₂×C₃×Dic₅	—	2	2	no	—
93	C₂×C₃×Dic₅	—	2	4	no	—
94	C₂×C₃×Dic₅	—	4	4	no	—
95	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
96	C₃×C₄×D₅	—	2	4	no	—
97	C₃×C₄×D₅	—	2	2	no	—
98	C₃×C₄×D₅	—	2	2	no	—
99	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
100	C₃×#168	—	2	2	no	—
101	C₂²×C₃×D₄	—	10	2	no	—
102	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
103	C₂³×C₃×C₄	—	5	1	no	—
104	C₂×C₃×D₈	—	2	4	no	—
105	C₂×C₃×D₈	C₂×D₅	1	4	yes	complemented
106	C₂×C₃×M₁₆	—	5	4	no	—
107	C₂×C₃×M₁₆	—	10	4	no	—
108	C₂²×C₃×C₈	—	5	1	no	—
109	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
110	C₃×#121	—	5	8	no	—
111	C₃×#121	—	10	4	no	—
112	C₂×C₃×C₄⋊C₄	—	5	2	no	—
113	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
114	C₃×#106	—	5	4	no	—
115	C₃×#102	—	5	8	no	—
116	C₂⁴×C₅	—	2	2	no	—
117	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	4	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	2	4	no	—
121	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
122	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
123	C₂×C₂²⋊D₅	—	2	8	no	—
124	C₂×C₂²⋊D₅	—	4	8	no	—
125	C₂²×Dic₅	—	2	2	no	—
126	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
127	C₂×C₄×D₅	—	2	2	no	—
128	C₂×C₄×D₅	—	2	2	no	—
129	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
130	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
131	C₅×D₈	—	2	8	no	—
132	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
133	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
134	C₂²⋊Dic₅	—	2	8	no	—
135	C₄⋊Dic₅	—	2	2	no	—
136	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
137	C₂×#168	—	2	2	no	—
138	C₂×#168	C₂³×C₃	1	2	yes	—
139	#676	—	2	8	no	—
140	C₂²×D₈	C₃×D₅	1	1	yes	characteristic, complemented
141	C₂²×M₁₆	—	5	1	no	—
142	C₂×#121	—	5	2	no	—
143	#469	—	5	8	no	—
144	C₂×#106	—	5	1	no	—
145	C₂×#102	—	5	2	no	—
146	C₂²×C₃×C₅	—	4	4	no	—
147	C₂²×C₃×C₅	—	4	4	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	—	8	8	no	—
150	C₂²×C₃×C₅	#121	1	2	yes	—
151	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
152	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₃×D₅	—	2	2	no	—
154	C₂×C₃×D₅	—	2	4	no	—
155	C₂×C₃×D₅	—	4	4	no	—
156	C₃×C₄×C₅	#121	1	2	yes	—
157	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
158	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
159	C₃×Dic₅	—	2	2	no	—
160	C₃×Dic₅	—	4	4	no	—
161	C₂⁴×C₃	—	2	2	no	—
162	C₂⁴×C₃	—	5	1	no	—
163	C₂×C₃×D₄	—	2	2	no	—
164	C₂×C₃×D₄	—	2	4	no	—
165	C₂×C₃×D₄	—	2	4	no	—
166	C₂×C₃×D₄	—	10	8	no	—
167	C₂×C₃×D₄	—	20	8	no	—
168	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
169	C₂²×C₃×C₄	—	5	1	no	—
170	C₂²×C₃×C₄	—	5	2	no	—
171	C₂²×C₃×C₄	—	5	2	no	—
172	C₂²×C₃×C₄	—	10	2	no	—
173	C₂²×C₃×C₄	—	10	2	no	—
174	C₂²×C₃×C₄	—	10	2	no	—
175	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
176	C₃×D₈	—	2	8	no	—
177	C₃×M₁₆	—	10	8	no	—
178	C₂×C₃×C₈	—	5	2	no	—
179	C₂×C₃×C₈	—	10	2	no	—
180	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
181	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
182	C₃×C₄⋊C₄	—	5	4	no	—
183	C₃×C₄⋊C₄	—	10	2	no	—
184	C₃×C₂²⋊C₄	—	10	8	no	—
185	C₂³×C₅	—	2	4	no	—
186	C₂³×C₅	—	4	4	no	—
187	C₂³×C₅	—	4	4	no	—
188	C₂³×C₅	—	4	4	no	—
189	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
190	C₂²×D₅	—	2	2	no	—
191	C₂²×D₅	—	2	4	no	—
192	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	2	4	no	—
195	C₅×D₄	—	4	4	no	—
196	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
198	C₂×C₄×C₅	C₃×#41	1	2	yes	—
199	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
200	C₂²⋊D₅	—	4	16	no	—
201	C₂×Dic₅	—	2	2	no	—
202	C₂×Dic₅	—	2	4	no	—
203	C₂×Dic₅	—	4	4	no	—
204	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
205	C₄×D₅	—	2	4	no	—
206	C₄×D₅	—	2	2	no	—
207	C₄×D₅	—	2	2	no	—
208	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
209	#168	—	2	2	no	—
210	C₂²×D₄	—	10	2	no	—
211	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
212	C₂³×C₄	—	5	1	no	—
213	C₂×D₈	—	2	4	no	—
214	C₂×D₈	C₂×C₃×D₅	1	4	yes	complemented
215	C₂×M₁₆	—	5	4	no	—
216	C₂×M₁₆	—	10	4	no	—
217	C₂²×C₈	—	5	1	no	—
218	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
219	#121	—	5	8	no	—
220	#121	—	10	4	no	—
221	C₂×C₄⋊C₄	—	5	2	no	—
222	C₂×C₂²⋊C₄	—	10	2	no	—
223	#106	—	5	4	no	—
224	#102	—	5	8	no	—
225	C₂×C₃×C₅	—	8	4	no	—
226	C₂×C₃×C₅	#469	1	4	yes	complemented
227	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
228	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
229	C₃×D₅	—	4	2	no	—
230	C₂³×C₃	—	2	4	no	—
231	C₂³×C₃	—	4	4	no	—
232	C₂³×C₃	—	4	4	no	—
233	C₂³×C₃	—	4	4	no	—
234	C₂³×C₃	—	5	2	no	—
235	C₂³×C₃	—	10	4	no	—
236	C₂³×C₃	—	10	2	no	—
237	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
238	C₃×D₄	—	2	4	no	—
239	C₃×D₄	—	2	4	no	—
240	C₃×D₄	—	4	4	no	—
241	C₃×D₄	—	20	16	no	—
242	C₂×C₃×C₄	—	5	2	no	—
243	C₂×C₃×C₄	—	10	2	no	—
244	C₂×C₃×C₄	—	10	2	no	—
245	C₂×C₃×C₄	—	10	2	no	—
246	C₂×C₃×C₄	—	10	4	no	—
247	C₂×C₃×C₄	—	10	4	no	—
248	C₂×C₃×C₄	—	20	4	no	—
249	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
250	C₂×C₃×C₄	#711	1	2	yes	—
251	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
252	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
253	C₃×C₈	—	10	2	no	—
254	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	complemented
255	C₂²×C₅	—	4	4	no	—
256	C₂²×C₅	—	4	4	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	—	8	8	no	—
259	C₂²×C₅	C₃×#121	1	2	yes	—
260	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
261	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
262	C₂×D₅	—	2	4	no	—
263	C₂×D₅	—	2	2	no	—
264	C₂×D₅	—	4	4	no	—
265	C₄×C₅	C₃×#121	1	2	yes	—
266	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
267	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
268	Dic₅	—	2	2	no	—
269	Dic₅	—	4	4	no	—
270	C₂⁴	—	2	2	no	—
271	C₂⁴	—	5	1	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	10	8	no	—
276	C₂×D₄	—	20	8	no	—
277	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
278	C₂²×C₄	—	5	1	no	—
279	C₂²×C₄	—	5	2	no	—
280	C₂²×C₄	—	5	2	no	—
281	C₂²×C₄	—	10	2	no	—
282	C₂²×C₄	—	10	2	no	—
283	C₂²×C₄	—	10	2	no	—
284	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
285	D₈	—	2	8	no	—
286	M₁₆	—	10	8	no	—
287	C₂×C₈	—	5	2	no	—
288	C₂×C₈	—	10	2	no	—
289	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	complemented
290	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
291	C₄⋊C₄	—	5	4	no	—
292	C₄⋊C₄	—	10	2	no	—
293	C₂²⋊C₄	—	10	8	no	—
294	C₃×C₅	C₂×#469	1	1	yes	characteristic, complemented, Hall
295	C₂²×C₃	—	4	4	no	—
296	C₂²×C₃	—	4	4	no	—
297	C₂²×C₃	—	4	4	no	—
298	C₂²×C₃	—	8	8	no	—
299	C₂²×C₃	—	10	4	no	—
300	C₂²×C₃	—	10	2	no	—
301	C₂²×C₃	—	20	4	no	—
302	C₂²×C₃	#4057	1	4	yes	—
303	C₂²×C₃	#4084	1	2	yes	—
304	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
305	C₃×C₄	—	10	2	no	—
306	C₃×C₄	—	20	4	no	—
307	C₃×C₄	#4084	1	2	yes	—
308	C₃×C₄	C₂×#711	1	1	yes	characteristic
309	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
310	C₂×C₅	—	8	4	no	—
311	C₂×C₅	C₃×#469	1	4	yes	complemented
312	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
313	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
314	D₅	—	4	2	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	5	2	no	—
320	C₂³	—	10	2	no	—
321	C₂³	—	10	4	no	—
322	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
323	D₄	—	2	4	no	—
324	D₄	—	2	4	no	—
325	D₄	—	4	4	no	—
326	D₄	—	20	16	no	—
327	C₂×C₄	—	5	2	no	—
328	C₂×C₄	—	10	2	no	—
329	C₂×C₄	—	10	4	no	—
330	C₂×C₄	—	10	2	no	—
331	C₂×C₄	—	10	2	no	—
332	C₂×C₄	—	10	4	no	—
333	C₂×C₄	—	20	4	no	—
334	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
335	C₂×C₄	C₃×#711	1	2	yes	—
336	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
337	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
338	C₈	—	10	2	no	—
339	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	complemented
340	C₂×C₃	—	8	4	no	—
341	C₂×C₃	—	20	2	no	—
342	C₂×C₃	#65448	1	4	yes	direct product factor
343	C₂×C₃	C₂×#4057	1	2	yes	—
344	C₂×C₃	C₂×#4084	1	1	yes	characteristic
345	C₅	C₂×C₃×#469	1	1	yes	characteristic, complemented, Sylow
346	C₂²	—	4	4	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	8	8	no	—
350	C₂²	—	10	2	no	—
351	C₂²	—	10	4	no	—
352	C₂²	—	20	4	no	—
353	C₂²	C₃×#4057	1	4	yes	—
354	C₂²	C₃×#4084	1	2	yes	—
355	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
356	C₄	—	10	2	no	—
357	C₄	—	20	4	no	—
358	C₄	C₃×#4084	1	2	yes	—
359	C₄	C₂×C₃×#711	1	1	yes	characteristic
360	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
361	C₃	C₂×#65448	1	1	yes	characteristic, direct product factor, Sylow
362	C₂	—	8	4	no	—
363	C₂	—	20	2	no	—
364	C₂	C₃×#65448	1	4	yes	direct product factor
365	C₂	C₂×C₃×#4057	1	2	yes	—
366	C₂	C₂×C₃×#4084	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×D₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂²×C₃×D₈	D₅
hypocenter	C₅	C₂×C₃×#469
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂×C₃×#4084	C₂	semidirect
3. C₂²×C₃×#676	C₂	semidirect
4. C₂×C₃×#3964	C₂	semidirect
5. C₃×#65448	C₂	direct (N × H)
6. C₂×C₃×#3949	C₂	semidirect
7. C₂×#65448	C₃	direct (N × H)
12. C₂×C₃×C₅×D₈	C₂²	semidirect
16. C₃×#4084	C₂²	semidirect
20. C₂×C₃×#676	C₂²	semidirect
21. C₃×#3964	C₂²	semidirect
22. C₃×#3949	C₂²	semidirect
24. C₂²×C₅×D₈	C₂×C₃	semidirect
25. C₂×#4084	C₂×C₃	semidirect
26. C₂²×#676	C₂×C₃	semidirect
27. C₂×#3964	C₂×C₃	semidirect
28. #65448	C₂×C₃	direct (N × H)
29. C₂×#3949	C₂×C₃	semidirect
46. C₂×C₃×C₅×C₈	D₄	semidirect
54. C₂²×C₃×D₈	D₅	semidirect
64. C₂×C₅×D₈	C₂²×C₃	semidirect
68. #4084	C₂²×C₃	semidirect
72. C₂×#676	C₂²×C₃	semidirect
73. #3964	C₂²×C₃	semidirect
74. #3949	C₂²×C₃	semidirect
99. C₃×C₅×C₈	C₂×D₄	semidirect
105. C₂×C₃×D₈	C₂×D₅	semidirect
132. C₂×C₅×C₈	C₃×D₄	semidirect
140. C₂²×D₈	C₃×D₅	semidirect
180. C₂×C₃×C₈	C₂²⋊D₅	semidirect
208. C₅×C₈	C₂×C₃×D₄	semidirect
214. C₂×D₈	C₂×C₃×D₅	semidirect
226. C₂×C₃×C₅	#469	semidirect
254. C₃×C₈	C₂×C₂²⋊D₅	semidirect
289. C₂×C₈	C₃×C₂²⋊D₅	semidirect
294. C₃×C₅	C₂×#469	semidirect
311. C₂×C₅	C₃×#469	semidirect
339. C₈	C₂×C₃×C₂²⋊D₅	semidirect
342. C₂×C₃	#65448	direct (N × H)
345. C₅	C₂×C₃×#469	semidirect
361. C₃	C₂×#65448	direct (N × H)
364. C₂	C₃×#65448	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×C₃×C₅×D₈	2
C₂×C₃×#4084	2
C₂²×C₃×#676	2
C₂×C₃×#3964	2
C₃×#65448	2
C₂×C₃×#3949	2
C₂×#65448	3
C₂×C₃×#469	5

Subgroups — C2×C3×#65448 #14427976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65448 #14427976