Subgroups — C₂×#11746998 #14414643

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×D₃×#168	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×(C₂×D₃)⋊#168	C₂	1	2	yes	maximal, complemented
6	#11746998	C₂	1	8	yes	maximal, direct product factor
7	C₂×D₄×#168	—	3	1	no	maximal, Hall
8	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
9	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
13	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
14	C₂×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
15	C₄×C₅×D₁₂	C₄	1	4	yes	—
16	C₄×C₅×D₁₂	C₂²	1	4	yes	—
17	C₂²×C₃×#168	C₂²	1	2	yes	—
18	C₂×D₃×#168	—	2	8	no	—
19	C₂×D₃×#168	C₂²	1	8	yes	complemented
20	C₄×C₃⋊#168	C₂²	1	4	yes	complemented
21	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
22	(C₂×D₃)⋊#168	C₂²	1	8	yes	complemented
23	C₂×#4834	—	5	1	no	maximal, Hall
24	C₂×C₄×C₅×D₄	—	3	1	no	—
25	C₂³×#168	—	3	2	no	—
26	C₂×C₂²⋊#168	—	3	2	no	—
27	D₄×#168	—	3	8	no	—
28	C₂×C₄⋊#168	D₃	1	1	yes	characteristic, complemented
29	C₂×C₄×#168	—	3	1	no	—
30	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
35	C₂×C₅×D₁₂	C₈	1	8	yes	complemented
36	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
37	C₂×C₄×C₅×D₃	—	2	4	no	—
38	C₂×C₄×C₅×D₃	—	2	4	no	—
39	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
40	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
41	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
42	C₃×C₄²×C₅	C₂³	1	2	yes	—
43	C₂×C₃⋊#168	—	2	2	no	—
44	C₂×C₃⋊#168	D₄	1	4	yes	complemented
45	C₂×C₃⋊#168	C₂³	1	2	yes	—
46	C₂×C₃⋊#168	C₂³	1	2	yes	—
47	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
48	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
49	C₂×C₃×#168	—	2	4	no	—
50	C₂×C₃×#168	C₂³	1	4	yes	—
51	D₃×#168	—	2	16	no	—
52	C₂²×D₃×C₈	—	5	2	no	—
53	C₂×C₄×D₁₂	D₅	1	1	yes	characteristic
54	C₂×C₃×C₄⋊C₈	—	5	1	no	—
55	C₂×(C₂×D₃)⋊C₈	—	5	2	no	—
56	C₂×C₄×C₃⋊C₈	—	5	1	no	—
57	#4834	—	5	8	no	—
58	C₂²×C₅×D₄	—	3	1	no	—
59	C₂³×C₄×C₅	—	3	2	no	—
60	C₄×C₅×D₄	—	3	4	no	—
61	C₄×C₅×D₄	—	3	4	no	—
62	C₂×C₅×C₄⋊C₄	—	3	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
64	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
65	C₂²×#168	—	3	1	no	—
66	C₂²×#168	—	3	1	no	—
67	C₂²×#168	—	3	8	no	—
68	C₂²×#168	—	6	8	no	—
69	C₂²×#168	C₂×D₃	1	2	yes	—
70	C₂²⋊#168	—	3	8	no	—
71	C₄⋊#168	C₂×D₃	1	4	yes	complemented
72	C₄×#168	—	3	4	no	—
73	C₂×C₈×D₄	—	15	1	no	Sylow
74	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₅×D₃	—	2	4	no	—
76	C₂²×C₅×D₃	—	2	4	no	—
77	C₂²×C₅×D₃	C₂×C₈	1	8	yes	complemented
78	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
81	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
82	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	#41	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
87	C₂×C₅×Dic₃	—	2	4	no	—
88	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
89	C₅×D₁₂	C₂×C₈	1	16	yes	complemented
90	C₄×C₅×D₃	—	2	8	no	—
91	C₄×C₅×D₃	—	2	4	no	—
92	C₄×C₅×D₃	—	2	4	no	—
93	C₃⋊#168	—	2	2	no	—
94	C₃⋊#168	C₂×D₄	1	4	yes	complemented
95	C₃×#168	—	2	4	no	—
96	C₂²×D₁₂	Dic₅	1	1	yes	characteristic
97	C₂²×C₄×D₃	C₂×D₅	1	2	yes	—
98	C₂²×C₃×C₈	—	5	2	no	—
99	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
100	C₂×(C₂×D₃)⋊C₄	Dic₅	1	2	yes	—
101	C₂×C₄⋊Dic₃	Dic₅	1	1	yes	characteristic
102	C₂²×C₃⋊C₈	—	5	1	no	—
103	C₂²×C₃⋊C₈	—	5	1	no	—
104	C₂×D₃×C₈	—	5	8	no	—
105	C₂×D₃×C₈	—	10	8	no	—
106	C₄×D₁₂	Dic₅	1	4	yes	—
107	C₄×D₁₂	C₂×D₅	1	4	yes	—
108	C₃×C₄⋊C₈	—	5	4	no	—
109	(C₂×D₃)⋊C₈	—	5	8	no	—
110	C₄×C₃⋊C₈	—	5	4	no	—
111	C₂⁴×C₅	—	3	2	no	—
112	C₂×C₅×D₄	—	3	8	no	—
113	C₂×C₅×D₄	—	3	4	no	—
114	C₂²×C₄×C₅	—	3	2	no	—
115	C₂²×C₄×C₅	—	3	4	no	—
116	C₂²×C₄×C₅	—	3	4	no	—
117	C₂²×C₄×C₅	—	6	4	no	—
118	C₂²×C₄×C₅	—	6	4	no	—
119	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
122	C₅×C₄⋊C₄	—	3	4	no	—
123	C₅×C₂²⋊C₄	—	3	8	no	—
124	C₄²×C₅	C₄×D₃	1	2	yes	—
125	C₄²×C₅	C₂²×D₃	1	2	yes	—
126	C₂×#168	—	2	4	no	—
127	C₂×#168	—	3	4	no	—
128	C₂×#168	—	3	2	no	—
129	C₂×#168	—	3	2	no	—
130	C₂×#168	—	6	16	no	—
131	C₂×#168	—	6	2	no	—
132	C₂×#168	C₂²×D₃	1	4	yes	—
133	C₂³×C₈	—	15	2	no	—
134	C₂×C₄×D₄	—	3	1	no	—
135	C₈×D₄	—	15	8	no	—
136	C₂×C₄⋊C₈	—	5	1	no	—
137	C₂×C₂²⋊C₈	—	15	2	no	—
138	C₂×C₄×C₈	—	15	1	no	—
139	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
140	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
141	C₂²×C₃×C₅	#131	1	2	yes	—
142	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₅×D₃	—	2	4	no	—
144	C₂×C₅×D₃	—	2	4	no	—
145	C₂×C₅×D₃	—	2	16	no	—
146	C₂×C₅×D₃	C₂²×C₈	1	8	yes	complemented
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
149	C₃×C₄×C₅	C₂²×C₈	1	4	yes	complemented
150	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
152	C₅×Dic₃	—	2	4	no	—
153	C₂³×D₃	C₂×Dic₅	1	2	yes	—
154	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
157	C₂²×Dic₃	C₂×Dic₅	1	2	yes	—
158	C₂×D₁₂	#168	1	8	yes	complemented
159	C₂×D₁₂	C₂×Dic₅	1	4	yes	—
160	C₂×C₄×D₃	—	2	4	no	—
161	C₂×C₄×D₃	—	2	4	no	—
162	C₂×C₄×D₃	C₂×Dic₅	1	4	yes	—
163	C₂×C₄×D₃	C₂²×D₅	1	4	yes	—
164	C₂×C₃×C₈	—	5	4	no	—
165	C₂×C₃×C₈	—	10	4	no	—
166	C₃×C₄²	C₂×Dic₅	1	2	yes	—
167	C₃×C₄²	C₂²×D₅	1	2	yes	—
168	(C₂×D₃)⋊C₄	C₂×Dic₅	1	8	yes	—
169	C₄⋊Dic₃	C₂×Dic₅	1	4	yes	—
170	C₂×C₃⋊C₈	—	5	4	no	—
171	C₂×C₃⋊C₈	—	5	2	no	—
172	C₂×C₃⋊C₈	—	5	2	no	—
173	C₂×C₃⋊C₈	—	10	2	no	—
174	D₃×C₈	—	10	16	no	—
175	C₂³×C₅	—	3	8	no	—
176	C₂³×C₅	—	3	4	no	—
177	C₂³×C₅	—	6	4	no	—
178	C₂³×C₅	—	6	4	no	—
179	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
180	C₅×D₄	—	3	16	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	3	4	no	—
183	C₂×C₄×C₅	—	6	4	no	—
184	C₂×C₄×C₅	—	6	8	no	—
185	C₂×C₄×C₅	—	6	4	no	—
186	C₂×C₄×C₅	—	6	4	no	—
187	C₂×C₄×C₅	D₃×C₈	1	4	yes	complemented
188	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
189	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
191	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
192	C₂×C₄×C₅	#239	1	2	yes	—
193	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
194	#168	—	2	4	no	—
195	#168	—	3	4	no	—
196	#168	—	6	2	no	—
197	C₂²×D₄	—	3	1	no	—
198	C₂³×C₄	—	3	2	no	—
199	C₂²×C₈	—	5	2	no	—
200	C₂²×C₈	—	15	8	no	—
201	C₂²×C₈	—	15	1	no	—
202	C₂²×C₈	—	15	1	no	—
203	C₂²×C₈	—	30	8	no	—
204	C₄×D₄	—	3	4	no	—
205	C₄×D₄	—	3	4	no	—
206	C₂×C₄⋊C₄	—	3	1	no	—
207	C₂×C₂²⋊C₄	—	3	2	no	—
208	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
209	C₄⋊C₈	—	5	4	no	—
210	C₂²⋊C₈	—	15	8	no	—
211	C₄×C₈	—	15	4	no	—
212	C₂×C₃×C₅	C₈×D₄	1	4	yes	complemented
213	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
215	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
216	C₅×D₃	—	2	8	no	—
217	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
218	C₂²×D₃	—	2	4	no	—
219	C₂²×D₃	—	2	4	no	—
220	C₂²×D₃	C₂×#168	1	8	yes	complemented
221	C₂²×D₃	C₂²×Dic₅	1	4	yes	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	C₂×#168	1	4	yes	complemented
224	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
225	C₂×C₃×C₄	#711	1	2	yes	—
226	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
227	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
228	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
230	C₂×Dic₃	—	2	4	no	—
231	C₂×Dic₃	C₂²×Dic₅	1	4	yes	—
232	D₁₂	C₂×#168	1	16	yes	complemented
233	C₄×D₃	—	2	4	no	—
234	C₄×D₃	—	2	4	no	—
235	C₄×D₃	—	2	8	no	—
236	C₃×C₈	—	10	4	no	—
237	C₃⋊C₈	—	5	4	no	—
238	C₃⋊C₈	—	10	2	no	—
239	C₂²×C₅	—	3	8	no	—
240	C₂²×C₅	—	6	4	no	—
241	C₂²×C₅	—	6	4	no	—
242	C₂²×C₅	—	6	16	no	—
243	C₂²×C₅	#893	1	2	yes	—
244	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
245	C₂²×C₅	#907	1	2	yes	—
246	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
247	C₄×C₅	—	2	2	no	—
248	C₄×C₅	—	6	4	no	—
249	C₄×C₅	#893	1	2	yes	—
250	C₄×C₅	C₂×D₃×C₈	1	4	yes	complemented
251	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
252	C₄×C₅	C₂×#239	1	1	yes	characteristic
253	C₂⁴	—	3	2	no	—
254	C₂×D₄	—	3	4	no	—
255	C₂×D₄	—	3	8	no	—
256	C₂²×C₄	—	3	2	no	—
257	C₂²×C₄	—	3	4	no	—
258	C₂²×C₄	—	3	4	no	—
259	C₂²×C₄	—	6	4	no	—
260	C₂²×C₄	—	6	4	no	—
261	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
262	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
264	C₂×C₈	—	5	4	no	—
265	C₂×C₈	—	10	4	no	—
266	C₂×C₈	—	15	4	no	—
267	C₂×C₈	—	15	2	no	—
268	C₂×C₈	—	15	2	no	—
269	C₂×C₈	—	30	16	no	—
270	C₂×C₈	—	30	2	no	—
271	C₄⋊C₄	—	3	4	no	—
272	C₂²⋊C₄	—	3	8	no	—
273	C₄²	D₃×Dic₅	1	2	yes	—
274	C₄²	C₂×D₃×D₅	1	2	yes	—
275	C₃×C₅	C₂×C₈×D₄	1	1	yes	characteristic, complemented, Hall
276	C₂²×C₃	C₂²×#168	1	2	yes	—
277	C₂²×C₃	D₄×Dic₅	1	2	yes	—
278	C₂²×C₃	#4094	1	2	yes	—
279	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
280	C₂×D₃	—	2	16	no	—
281	C₂×D₃	—	2	4	no	—
282	C₂×D₃	—	2	4	no	—
283	C₂×D₃	C₂²×#168	1	8	yes	complemented
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	C₂²×#168	1	4	yes	complemented
286	C₃×C₄	D₄×Dic₅	1	2	yes	—
287	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
288	C₃×C₄	C₂×#711	1	1	yes	characteristic
289	Dic₃	—	2	4	no	—
290	C₂×C₅	—	6	8	no	—
291	C₂×C₅	#4834	1	4	yes	complemented
292	C₂×C₅	C₂×#893	1	1	yes	characteristic
293	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
294	C₂×C₅	C₂×#907	1	1	yes	characteristic
295	C₂³	—	3	4	no	—
296	C₂³	—	3	8	no	—
297	C₂³	—	6	4	no	—
298	C₂³	—	6	4	no	—
299	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
300	D₄	—	3	16	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	3	4	no	—
303	C₂×C₄	—	6	4	no	—
304	C₂×C₄	—	6	8	no	—
305	C₂×C₄	—	6	4	no	—
306	C₂×C₄	—	6	4	no	—
307	C₂×C₄	D₃×#168	1	4	yes	complemented
308	C₂×C₄	#6768	1	2	yes	—
309	C₂×C₄	#6777	1	2	yes	—
310	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
311	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
312	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
313	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
314	C₈	—	10	4	no	—
315	C₈	—	15	4	no	—
316	C₈	—	30	2	no	—
317	C₂×C₃	D₄×#168	1	4	yes	complemented
318	C₂×C₃	C₂³×#168	1	1	yes	characteristic
319	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
320	C₂×C₃	C₂×#4094	1	1	yes	characteristic
321	D₃	—	2	8	no	—
322	C₅	C₂×#4834	1	1	yes	characteristic, complemented, Sylow
323	C₂²	—	3	8	no	—
324	C₂²	—	6	4	no	—
325	C₂²	—	6	4	no	—
326	C₂²	—	6	16	no	—
327	C₂²	C₂×D₃×#168	1	2	yes	—
328	C₂²	#91288	1	2	yes	—
329	C₂²	#91435	1	2	yes	—
330	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
331	C₄	—	2	2	no	—
332	C₄	—	6	4	no	—
333	C₄	C₂×D₃×#168	1	4	yes	complemented
334	C₄	#91435	1	2	yes	—
335	C₄	C₂×#6768	1	1	yes	characteristic
336	C₄	C₂×#6777	1	1	yes	characteristic
337	C₃	C₂×D₄×#168	1	1	yes	characteristic, complemented, Sylow
338	C₂	—	6	8	no	—
339	C₂	#11746998	1	4	yes	direct product factor
340	C₂	C₂²×D₃×#168	1	1	yes	characteristic
341	C₂	C₂×#91288	1	1	yes	characteristic
342	C₂	C₂×#91435	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₈
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₅×D₁₂	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₂×C₈×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂²×D₃×#168	C₂	semidirect
3. C₂×C₄×C₃⋊#168	C₂	semidirect
4. C₂×C₃×C₄⋊#168	C₂	semidirect
5. C₂×(C₂×D₃)⋊#168	C₂	semidirect
6. #11746998	C₂	direct (N × H)
19. C₂×D₃×#168	C₂²	semidirect
20. C₄×C₃⋊#168	C₂²	semidirect
21. C₃×C₄⋊#168	C₂²	semidirect
22. (C₂×D₃)⋊#168	C₂²	semidirect
28. C₂×C₄⋊#168	D₃	semidirect
35. C₂×C₅×D₁₂	C₈	semidirect
44. C₂×C₃⋊#168	D₄	semidirect
71. C₄⋊#168	C₂×D₃	semidirect
77. C₂²×C₅×D₃	C₂×C₈	semidirect
80. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
89. C₅×D₁₂	C₂×C₈	semidirect
94. C₃⋊#168	C₂×D₄	semidirect
146. C₂×C₅×D₃	C₂²×C₈	semidirect
149. C₃×C₄×C₅	C₂²×C₈	semidirect
158. C₂×D₁₂	#168	semidirect
187. C₂×C₄×C₅	D₃×C₈	semidirect
212. C₂×C₃×C₅	C₈×D₄	semidirect
220. C₂²×D₃	C₂×#168	semidirect
223. C₂×C₃×C₄	C₂×#168	semidirect
232. D₁₂	C₂×#168	semidirect
250. C₄×C₅	C₂×D₃×C₈	semidirect
275. C₃×C₅	C₂×C₈×D₄	semidirect
283. C₂×D₃	C₂²×#168	semidirect
285. C₃×C₄	C₂²×#168	semidirect
291. C₂×C₅	#4834	semidirect
307. C₂×C₄	D₃×#168	semidirect
317. C₂×C₃	D₄×#168	semidirect
322. C₅	C₂×#4834	semidirect
333. C₄	C₂×D₃×#168	semidirect
337. C₃	C₂×D₄×#168	semidirect
339. C₂	#11746998	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×C₄×C₅×D₁₂	2
C₂²×D₃×#168	2
C₂×C₄×C₃⋊#168	2
C₂×C₃×C₄⋊#168	2
C₂×(C₂×D₃)⋊#168	2
#11746998	2
C₂×D₄×#168	3
C₂×#4834	5

Subgroups — C2×#11746998 #14414643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11746998 #14414643