Subgroups — C₂²×C₃×D₃×D₈ #11918530

Order 1152.

4121 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃²×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#213	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×D₃×D₈	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×C₃×D₈	—	3	1	no	maximal
8	C₂²×D₃×D₈	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁴×C₃×D₃	—	2	2	no	—
10	C₂²×C₃²×D₄	C₂²	1	2	yes	complemented
11	C₂²×C₃×#67	—	2	2	no	—
12	C₂×C₃×D₃×D₄	—	2	12	no	—
13	C₂×C₃×D₃×D₄	C₂²	1	24	yes	complemented
14	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
15	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
16	C₂×C₃²×D₈	C₂²	1	12	yes	complemented
17	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×#213	C₂²	1	24	yes	complemented
19	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×D₃×D₈	C₂²	1	64	yes	direct product factor
21	C₂×C₃×D₂₄	C₂²	1	12	yes	complemented
22	C₂×C₃×D₃×C₈	C₂²	1	12	yes	complemented
23	C₂³×C₃×D₄	—	3	2	no	—
24	C₂²×D₃×D₄	C₂×C₃	1	2	yes	complemented
25	C₂²×C₃×D₈	—	2	1	no	—
26	C₂²×C₃×D₈	—	3	2	no	—
27	C₂²×C₃×D₈	—	3	24	no	—
28	C₂²×C₃×D₈	—	3	1	no	—
29	C₂²×C₃×D₈	D₃	1	1	yes	characteristic, direct product factor
30	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂³×C₃×C₈	—	3	1	no	—
32	C₂²×#213	C₂×C₃	1	2	yes	complemented
33	C₂×D₃×D₈	C₂×C₃	1	24	yes	direct product factor
34	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂⁴×C₃²	—	2	2	no	—
37	C₂³×C₃×D₃	—	2	2	no	—
38	C₂³×C₃×D₃	—	2	24	no	—
39	C₂³×C₃×D₃	—	4	16	no	—
40	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
41	C₂×C₃²×D₄	—	2	6	no	—
42	C₂×C₃²×D₄	C₂³	1	12	yes	complemented
43	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
44	C₂×C₃×#67	—	2	24	no	—
45	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
46	C₃×D₃×D₄	—	2	48	no	—
47	C₃×D₃×D₄	C₂³	1	32	yes	complemented
48	C₂×C₃×D₁₂	—	2	6	no	—
49	C₂×C₃×D₁₂	C₂³	1	12	yes	complemented
50	C₂×C₃×C₄×D₃	D₄	1	6	yes	—
51	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
52	C₃²×D₈	C₂³	1	16	yes	complemented
53	C₂×C₃²×C₈	C₂³	1	6	yes	complemented
54	C₃×#213	C₂³	1	32	yes	complemented
55	C₂×C₃×C₃⋊C₈	C₂³	1	6	yes	complemented
56	C₃×D₂₄	C₂³	1	16	yes	complemented
57	C₃×D₃×C₈	C₂³	1	16	yes	complemented
58	C₂³×D₈	—	3	1	no	Sylow
59	C₂⁵×C₃	—	6	2	no	—
60	C₂⁴×D₃	—	2	2	no	—
61	C₂²×C₃×D₄	—	2	2	no	—
62	C₂²×C₃×D₄	—	3	24	no	—
63	C₂²×C₃×D₄	—	3	2	no	—
64	C₂²×C₃×D₄	—	6	12	no	—
65	C₂²×C₃×D₄	—	6	2	no	—
66	C₂²×C₃×D₄	C₂×D₃	1	2	yes	complemented
67	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	complemented
68	C₂³×C₃×C₄	—	3	1	no	—
69	C₂²×#67	—	2	2	no	—
70	C₂×D₃×D₄	—	2	12	no	—
71	C₂×D₃×D₄	C₂²×C₃	1	24	yes	complemented
72	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
73	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×D₈	—	2	12	no	—
75	C₂×C₃×D₈	—	3	24	no	—
76	C₂×C₃×D₈	—	3	64	no	—
77	C₂×C₃×D₈	—	3	12	no	—
78	C₂×C₃×D₈	C₂×D₃	1	12	yes	direct product factor
79	C₂×C₃×D₈	C₂²×C₃	1	12	yes	complemented
80	C₂²×C₃×C₈	—	2	1	no	—
81	C₂²×C₃×C₈	—	3	1	no	—
82	C₂²×C₃×C₈	—	3	12	no	—
83	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic, complemented
84	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
85	C₂×#213	C₂²×C₃	1	24	yes	complemented
86	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
87	D₃×D₈	C₂²×C₃	1	64	yes	direct product factor
88	C₂×D₂₄	C₂²×C₃	1	12	yes	complemented
89	C₂×D₃×C₈	C₂²×C₃	1	12	yes	complemented
90	C₂³×C₃²	—	2	12	no	—
91	C₂³×C₃²	—	4	8	no	—
92	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₃×D₃	—	2	12	no	—
94	C₂²×C₃×D₃	—	2	32	no	—
95	C₂²×C₃×D₃	—	4	8	no	—
96	C₂²×C₃×D₃	—	4	96	no	—
97	C₂²×C₃×D₃	D₈	1	8	yes	direct product factor
98	C₂²×C₃×D₃	C₂×D₄	1	6	yes	—
99	C₃²×D₄	—	2	12	no	—
100	C₃²×D₄	C₂⁴	1	8	yes	complemented
101	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
102	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
103	C₃×#67	—	2	32	no	—
104	C₂×C₃×Dic₃	C₂×D₄	1	6	yes	—
105	C₃×D₁₂	—	2	12	no	—
106	C₃×D₁₂	C₂⁴	1	8	yes	complemented
107	C₃×C₄×D₃	C₂×D₄	1	12	yes	—
108	C₃×C₄×D₃	C₂⁴	1	4	yes	—
109	C₃²×C₈	C₂⁴	1	4	yes	complemented
110	C₃×C₃⋊C₈	C₂⁴	1	4	yes	complemented
111	C₂³×D₄	—	3	2	no	—
112	C₂²×D₈	—	3	2	no	—
113	C₂²×D₈	—	3	24	no	—
114	C₂²×D₈	—	3	1	no	—
115	C₂²×D₈	C₃×D₃	1	1	yes	characteristic, direct product factor
116	C₂³×C₈	—	3	1	no	—
117	C₂⁴×C₃	—	2	2	no	—
118	C₂⁴×C₃	—	2	2	no	—
119	C₂⁴×C₃	—	3	1	no	—
120	C₂⁴×C₃	—	4	2	no	—
121	C₂⁴×C₃	—	6	24	no	—
122	C₂⁴×C₃	—	6	2	no	—
123	C₂⁴×C₃	—	12	16	no	—
124	C₂³×D₃	—	2	2	no	—
125	C₂³×D₃	—	2	24	no	—
126	C₂³×D₃	—	4	16	no	—
127	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
128	C₂×C₃×D₄	—	2	6	no	—
129	C₂×C₃×D₄	—	2	6	no	—
130	C₂×C₃×D₄	—	2	12	no	—
131	C₂×C₃×D₄	—	3	32	no	—
132	C₂×C₃×D₄	—	3	12	no	—
133	C₂×C₃×D₄	—	4	6	no	—
134	C₂×C₃×D₄	—	6	48	no	—
135	C₂×C₃×D₄	—	6	24	no	—
136	C₂×C₃×D₄	—	6	6	no	—
137	C₂×C₃×D₄	C₂²×D₃	1	12	yes	complemented
138	C₂×C₃×D₄	C₂³×C₃	1	12	yes	complemented
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	—	3	1	no	—
141	C₂²×C₃×C₄	—	3	6	no	—
142	C₂²×C₃×C₄	—	3	6	no	—
143	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
145	C₂×#67	—	2	24	no	—
146	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
147	D₃×D₄	—	2	48	no	—
148	D₃×D₄	C₂³×C₃	1	32	yes	complemented
149	C₂×D₁₂	—	2	6	no	—
150	C₂×D₁₂	C₂³×C₃	1	12	yes	complemented
151	C₂×C₄×D₃	C₃×D₄	1	6	yes	—
152	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
153	C₃×D₈	—	2	16	no	—
154	C₃×D₈	—	3	32	no	—
155	C₃×D₈	—	3	16	no	—
156	C₃×D₈	C₂²×D₃	1	16	yes	direct product factor
157	C₃×D₈	C₂³×C₃	1	16	yes	complemented
158	C₂×C₃×C₈	—	2	6	no	—
159	C₂×C₃×C₈	—	3	6	no	—
160	C₂×C₃×C₈	—	3	16	no	—
161	C₂×C₃×C₈	C₂²×D₃	1	6	yes	complemented
162	C₂×C₃×C₈	C₂³×C₃	1	6	yes	complemented
163	#213	C₂³×C₃	1	32	yes	complemented
164	C₂×C₃⋊C₈	C₂³×C₃	1	6	yes	complemented
165	D₂₄	C₂³×C₃	1	16	yes	complemented
166	D₃×C₈	C₂³×C₃	1	16	yes	complemented
167	C₂²×C₃²	—	2	8	no	—
168	C₂²×C₃²	—	4	24	no	—
169	C₂²×C₃²	C₂×D₈	1	4	yes	complemented
170	C₂²×C₃²	C₂²×D₄	1	3	yes	—
171	C₂×C₃×D₃	—	2	8	no	—
172	C₂×C₃×D₃	—	4	24	no	—
173	C₂×C₃×D₃	—	4	64	no	—
174	C₂×C₃×D₃	C₂×D₈	1	24	yes	direct product factor
175	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
176	C₃²×C₄	C₂²×D₄	1	3	yes	—
177	C₃²×C₄	C₂⁵	1	1	yes	characteristic
178	C₃×Dic₃	C₂²×D₄	1	4	yes	—
179	C₂⁵	—	6	2	no	—
180	C₂²×D₄	—	3	24	no	—
181	C₂²×D₄	—	3	2	no	—
182	C₂²×D₄	—	6	12	no	—
183	C₂²×D₄	—	6	2	no	—
184	C₂²×D₄	C₂×C₃×D₃	1	2	yes	complemented
185	C₂³×C₄	—	3	1	no	—
186	C₂×D₈	—	3	24	no	—
187	C₂×D₈	—	3	64	no	—
188	C₂×D₈	—	3	12	no	—
189	C₂×D₈	C₂×C₃×D₃	1	12	yes	direct product factor
190	C₂²×C₈	—	3	1	no	—
191	C₂²×C₈	—	3	12	no	—
192	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
193	C₂³×C₃	—	2	12	no	—
194	C₂³×C₃	—	2	12	no	—
195	C₂³×C₃	—	2	1	no	—
196	C₂³×C₃	—	3	8	no	—
197	C₂³×C₃	—	3	6	no	—
198	C₂³×C₃	—	4	12	no	—
199	C₂³×C₃	—	4	8	no	—
200	C₂³×C₃	—	4	8	no	—
201	C₂³×C₃	—	6	32	no	—
202	C₂³×C₃	—	6	12	no	—
203	C₂³×C₃	—	8	8	no	—
204	C₂³×C₃	—	12	96	no	—
205	C₂³×C₃	—	12	8	no	—
206	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
207	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂²×D₃	—	2	12	no	—
209	C₂²×D₃	—	2	32	no	—
210	C₂²×D₃	—	4	8	no	—
211	C₂²×D₃	—	4	96	no	—
212	C₂²×D₃	C₃×D₈	1	8	yes	direct product factor
213	C₂²×D₃	C₂×C₃×D₄	1	6	yes	—
214	C₃×D₄	—	2	12	no	—
215	C₃×D₄	—	2	12	no	—
216	C₃×D₄	—	2	8	no	—
217	C₃×D₄	—	3	8	no	—
218	C₃×D₄	—	4	12	no	—
219	C₃×D₄	—	6	32	no	—
220	C₃×D₄	—	6	12	no	—
221	C₃×D₄	C₂³×D₃	1	8	yes	complemented
222	C₃×D₄	C₂⁴×C₃	1	8	yes	complemented
223	C₂×C₃×C₄	—	2	3	no	—
224	C₂×C₃×C₄	—	2	3	no	—
225	C₂×C₃×C₄	—	3	6	no	—
226	C₂×C₃×C₄	—	3	12	no	—
227	C₂×C₃×C₄	—	3	4	no	—
228	C₂×C₃×C₄	D₃×D₄	1	3	yes	—
229	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
230	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
231	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
232	#67	—	2	32	no	—
233	C₂×Dic₃	C₂×C₃×D₄	1	6	yes	—
234	D₁₂	—	2	12	no	—
235	D₁₂	C₂⁴×C₃	1	8	yes	complemented
236	C₄×D₃	C₂×C₃×D₄	1	12	yes	—
237	C₄×D₃	C₂⁴×C₃	1	4	yes	—
238	C₃×C₈	—	2	4	no	—
239	C₃×C₈	—	3	4	no	—
240	C₃×C₈	C₂³×D₃	1	4	yes	complemented
241	C₃×C₈	C₂⁴×C₃	1	4	yes	complemented
242	C₃⋊C₈	C₂⁴×C₃	1	4	yes	complemented
243	C₂×C₃²	—	4	8	no	—
244	C₂×C₃²	C₂²×D₈	1	6	yes	complemented
245	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
246	C₃×D₃	—	4	8	no	—
247	C₃×D₃	C₂²×D₈	1	8	yes	direct product factor
248	C₂⁴	—	2	2	no	—
249	C₂⁴	—	3	1	no	—
250	C₂⁴	—	6	24	no	—
251	C₂⁴	—	6	2	no	—
252	C₂⁴	—	12	16	no	—
253	C₂×D₄	—	2	6	no	—
254	C₂×D₄	—	3	32	no	—
255	C₂×D₄	—	3	12	no	—
256	C₂×D₄	—	6	48	no	—
257	C₂×D₄	—	6	24	no	—
258	C₂×D₄	—	6	6	no	—
259	C₂×D₄	C₂²×C₃×D₃	1	12	yes	complemented
260	C₂²×C₄	—	3	1	no	—
261	C₂²×C₄	—	3	6	no	—
262	C₂²×C₄	—	3	6	no	—
263	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
264	D₈	—	3	32	no	—
265	D₈	—	3	16	no	—
266	D₈	C₂²×C₃×D₃	1	16	yes	direct product factor
267	C₂×C₈	—	3	6	no	—
268	C₂×C₈	—	3	16	no	—
269	C₂×C₈	C₂²×C₃×D₃	1	6	yes	complemented
270	C₂²×C₃	—	2	8	no	—
271	C₂²×C₃	—	2	8	no	—
272	C₂²×C₃	—	2	4	no	—
273	C₂²×C₃	—	2	3	no	—
274	C₂²×C₃	—	3	4	no	—
275	C₂²×C₃	—	3	24	no	—
276	C₂²×C₃	—	4	8	no	—
277	C₂²×C₃	—	4	24	no	—
278	C₂²×C₃	—	4	24	no	—
279	C₂²×C₃	—	6	8	no	—
280	C₂²×C₃	—	8	24	no	—
281	C₂²×C₃	—	12	64	no	—
282	C₂²×C₃	—	12	24	no	—
283	C₂²×C₃	D₃×D₈	1	4	yes	direct product factor
284	C₂²×C₃	C₂×C₃×D₈	1	4	yes	complemented
285	C₂²×C₃	C₂×D₃×D₄	1	3	yes	—
286	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
287	C₂×D₃	—	2	8	no	—
288	C₂×D₃	—	4	24	no	—
289	C₂×D₃	—	4	64	no	—
290	C₂×D₃	C₂×C₃×D₈	1	24	yes	direct product factor
291	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
292	C₃×C₄	—	2	3	no	—
293	C₃×C₄	—	2	1	no	—
294	C₃×C₄	—	3	4	no	—
295	C₃×C₄	C₂×D₃×D₄	1	3	yes	—
296	C₃×C₄	C₂²×C₃×D₄	1	3	yes	—
297	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
298	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
299	Dic₃	C₂²×C₃×D₄	1	4	yes	—
300	C₃²	C₂³×D₈	1	1	yes	characteristic, complemented, Sylow
301	C₂³	—	2	12	no	—
302	C₂³	—	3	8	no	—
303	C₂³	—	3	6	no	—
304	C₂³	—	4	8	no	—
305	C₂³	—	6	32	no	—
306	C₂³	—	6	12	no	—
307	C₂³	—	12	96	no	—
308	C₂³	—	12	8	no	—
309	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
310	D₄	—	2	12	no	—
311	D₄	—	3	8	no	—
312	D₄	—	6	32	no	—
313	D₄	—	6	12	no	—
314	D₄	C₂³×C₃×D₃	1	8	yes	complemented
315	C₂×C₄	—	3	6	no	—
316	C₂×C₄	—	3	12	no	—
317	C₂×C₄	—	3	4	no	—
318	C₂×C₄	C₃×D₃×D₄	1	3	yes	—
319	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
320	C₈	—	3	4	no	—
321	C₈	C₂³×C₃×D₃	1	4	yes	complemented
322	C₂×C₃	—	2	6	no	—
323	C₂×C₃	—	2	1	no	—
324	C₂×C₃	—	3	8	no	—
325	C₂×C₃	—	4	8	no	—
326	C₂×C₃	—	4	8	no	—
327	C₂×C₃	—	8	8	no	—
328	C₂×C₃	—	12	8	no	—
329	C₂×C₃	C₂×D₃×D₈	1	6	yes	direct product factor
330	C₂×C₃	C₂²×C₃×D₈	1	6	yes	complemented
331	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
332	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
333	D₃	—	4	8	no	—
334	D₃	C₂²×C₃×D₈	1	8	yes	direct product factor
335	C₂²	—	2	8	no	—
336	C₂²	—	3	24	no	—
337	C₂²	—	3	4	no	—
338	C₂²	—	4	24	no	—
339	C₂²	—	6	8	no	—
340	C₂²	—	12	64	no	—
341	C₂²	—	12	24	no	—
342	C₂²	C₃×D₃×D₈	1	4	yes	direct product factor
343	C₂²	C₂×C₃×D₃×D₄	1	3	yes	—
344	C₄	—	3	4	no	—
345	C₄	C₂×C₃×D₃×D₄	1	3	yes	—
346	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
347	C₃	—	2	1	no	—
348	C₃	C₂²×D₃×D₈	1	1	yes	characteristic, direct product factor
349	C₃	C₂³×C₃×D₈	1	1	yes	characteristic, complemented
350	C₂	—	3	8	no	—
351	C₂	—	4	8	no	—
352	C₂	—	12	8	no	—
353	C₂	C₂×C₃×D₃×D₈	1	6	yes	direct product factor
354	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×D₈	C₂
socle	C₂³×C₃²	C₂×D₄
hypercenter	C₂²×C₃×D₈	D₃
hypocenter	C₃	C₂³×C₃×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
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×D₃×D₄	C₂	semidirect
2. C₂²×C₃²×D₈	C₂	semidirect
3. C₂²×C₃×#213	C₂	semidirect
4. C₂×C₃×D₃×D₈	C₂	direct (N × H)
5. C₂²×C₃×D₂₄	C₂	semidirect
6. C₂²×C₃×D₃×C₈	C₂	semidirect
8. C₂²×D₃×D₈	C₃	direct (N × H)
10. C₂²×C₃²×D₄	C₂²	semidirect
13. C₂×C₃×D₃×D₄	C₂²	semidirect
14. C₂²×C₃×D₁₂	C₂²	semidirect
16. C₂×C₃²×D₈	C₂²	semidirect
17. C₂²×C₃²×C₈	C₂²	semidirect
18. C₂×C₃×#213	C₂²	semidirect
19. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
20. C₃×D₃×D₈	C₂²	direct (N × H)
21. C₂×C₃×D₂₄	C₂²	semidirect
22. C₂×C₃×D₃×C₈	C₂²	semidirect
24. C₂²×D₃×D₄	C₂×C₃	semidirect
29. C₂²×C₃×D₈	D₃	direct (N × H)
30. C₂²×C₃×D₈	C₂×C₃	semidirect
32. C₂²×#213	C₂×C₃	semidirect
33. C₂×D₃×D₈	C₂×C₃	direct (N × H)
34. C₂²×D₂₄	C₂×C₃	semidirect
35. C₂²×D₃×C₈	C₂×C₃	semidirect
42. C₂×C₃²×D₄	C₂³	semidirect
47. C₃×D₃×D₄	C₂³	semidirect
49. C₂×C₃×D₁₂	C₂³	semidirect
52. C₃²×D₈	C₂³	semidirect
53. C₂×C₃²×C₈	C₂³	semidirect
54. C₃×#213	C₂³	semidirect
55. C₂×C₃×C₃⋊C₈	C₂³	semidirect
56. C₃×D₂₄	C₂³	semidirect
57. C₃×D₃×C₈	C₂³	semidirect
66. C₂²×C₃×D₄	C₂×D₃	semidirect
67. C₂²×C₃×D₄	C₂²×C₃	semidirect
71. C₂×D₃×D₄	C₂²×C₃	semidirect
72. C₂²×D₁₂	C₂²×C₃	semidirect
78. C₂×C₃×D₈	C₂×D₃	direct (N × H)
79. C₂×C₃×D₈	C₂²×C₃	semidirect
83. C₂²×C₃×C₈	C₂×D₃	semidirect
84. C₂²×C₃×C₈	C₂²×C₃	semidirect
85. C₂×#213	C₂²×C₃	semidirect
86. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
87. D₃×D₈	C₂²×C₃	direct (N × H)
88. C₂×D₂₄	C₂²×C₃	semidirect
89. C₂×D₃×C₈	C₂²×C₃	semidirect
97. C₂²×C₃×D₃	D₈	direct (N × H)
100. C₃²×D₄	C₂⁴	semidirect
106. C₃×D₁₂	C₂⁴	semidirect
109. C₃²×C₈	C₂⁴	semidirect
110. C₃×C₃⋊C₈	C₂⁴	semidirect
115. C₂²×D₈	C₃×D₃	direct (N × H)
137. C₂×C₃×D₄	C₂²×D₃	semidirect
138. C₂×C₃×D₄	C₂³×C₃	semidirect
148. D₃×D₄	C₂³×C₃	semidirect
150. C₂×D₁₂	C₂³×C₃	semidirect
156. C₃×D₈	C₂²×D₃	direct (N × H)
157. C₃×D₈	C₂³×C₃	semidirect
161. C₂×C₃×C₈	C₂²×D₃	semidirect
162. C₂×C₃×C₈	C₂³×C₃	semidirect
163. #213	C₂³×C₃	semidirect
164. C₂×C₃⋊C₈	C₂³×C₃	semidirect
165. D₂₄	C₂³×C₃	semidirect
166. D₃×C₈	C₂³×C₃	semidirect
169. C₂²×C₃²	C₂×D₈	semidirect
174. C₂×C₃×D₃	C₂×D₈	direct (N × H)
184. C₂²×D₄	C₂×C₃×D₃	semidirect
189. C₂×D₈	C₂×C₃×D₃	direct (N × H)
192. C₂²×C₈	C₂×C₃×D₃	semidirect
212. C₂²×D₃	C₃×D₈	direct (N × H)
221. C₃×D₄	C₂³×D₃	semidirect
222. C₃×D₄	C₂⁴×C₃	semidirect
235. D₁₂	C₂⁴×C₃	semidirect
240. C₃×C₈	C₂³×D₃	semidirect
241. C₃×C₈	C₂⁴×C₃	semidirect
242. C₃⋊C₈	C₂⁴×C₃	semidirect
244. C₂×C₃²	C₂²×D₈	semidirect
247. C₃×D₃	C₂²×D₈	direct (N × H)
259. C₂×D₄	C₂²×C₃×D₃	semidirect
266. D₈	C₂²×C₃×D₃	direct (N × H)
269. C₂×C₈	C₂²×C₃×D₃	semidirect
283. C₂²×C₃	D₃×D₈	direct (N × H)
284. C₂²×C₃	C₂×C₃×D₈	semidirect
290. C₂×D₃	C₂×C₃×D₈	direct (N × H)
300. C₃²	C₂³×D₈	semidirect
314. D₄	C₂³×C₃×D₃	semidirect
321. C₈	C₂³×C₃×D₃	semidirect
329. C₂×C₃	C₂×D₃×D₈	direct (N × H)
330. C₂×C₃	C₂²×C₃×D₈	semidirect
334. D₃	C₂²×C₃×D₈	direct (N × H)
342. C₂²	C₃×D₃×D₈	direct (N × H)
348. C₃	C₂²×D₃×D₈	direct (N × H)
349. C₃	C₂³×C₃×D₈	semidirect
353. C₂	C₂×C₃×D₃×D₈	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×D₃×D₄	2
C₂²×C₃²×D₈	2
C₂²×C₃×#213	2
C₂×C₃×D₃×D₈	2
C₂²×C₃×D₂₄	2
C₂²×C₃×D₃×C₈	2
C₂³×C₃×D₈	3
C₂²×D₃×D₈	3

Subgroups — C22×C3×D3×D8 #11918530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×D₃×D₈ #11918530