Subgroups — C₂²×C₃×#450 #10678955

Order 768.

7126 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#450	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃×#102	C₂	1	2	yes	maximal, complemented
6	C₂²×C₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#450	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂⁶×C₃	—	2	1	no	—
9	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
10	C₂³×C₃×D₄	—	2	16	no	—
11	C₂³×C₃×D₄	—	2	6	no	—
12	C₂³×C₃×D₄	—	2	1	no	—
13	C₂³×C₃×D₄	C₂²	1	12	yes	—
14	C₂³×C₃×D₄	C₂²	1	2	yes	—
15	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃×SD₁₆	—	2	16	no	—
17	C₂²×C₃×SD₁₆	C₂²	1	24	yes	complemented
18	C₂³×C₃×C₈	C₂²	1	2	yes	complemented
19	C₂×C₃×C₂²⋊Q₈	—	2	6	no	—
20	C₂×C₃×C₂²⋊Q₈	C₂²	1	12	yes	complemented
21	C₂²×C₃×C₄⋊C₄	—	2	1	no	—
22	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
24	C₃×#450	C₂²	1	64	yes	direct product factor
25	C₂×C₃×#102	C₂²	1	24	yes	complemented
26	C₂×C₃×C₂²⋊C₈	C₂²	1	12	yes	complemented
27	C₂⁴×D₄	C₂×C₃	1	1	yes	characteristic
28	C₂³×SD₁₆	C₂×C₃	1	2	yes	complemented
29	C₂²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×#450	C₂×C₃	1	24	yes	direct product factor
31	C₂²×#102	C₂×C₃	1	2	yes	complemented
32	C₂²×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂⁵×C₃	—	2	16	no	—
34	C₂⁵×C₃	—	2	12	no	—
35	C₂⁵×C₃	—	2	2	no	—
36	C₂⁵×C₃	—	4	8	no	—
37	C₂⁵×C₃	—	4	8	no	—
38	C₂⁵×C₃	D₄	1	1	yes	characteristic
39	C₂²×C₃×Q₈	—	2	3	no	—
40	C₂²×C₃×Q₈	—	2	8	no	—
41	C₂²×C₃×Q₈	C₂³	1	6	yes	complemented
42	C₂²×C₃×D₄	—	2	16	no	—
43	C₂²×C₃×D₄	—	2	96	no	—
44	C₂²×C₃×D₄	—	2	96	no	—
45	C₂²×C₃×D₄	—	2	12	no	—
46	C₂²×C₃×D₄	—	2	24	no	—
47	C₂²×C₃×D₄	—	2	6	no	—
48	C₂²×C₃×D₄	—	2	8	no	—
49	C₂²×C₃×D₄	D₄	1	16	yes	—
50	C₂²×C₃×D₄	C₂³	1	16	yes	—
51	C₂²×C₃×D₄	C₂³	1	12	yes	—
52	C₂³×C₃×C₄	—	2	8	no	—
53	C₂³×C₃×C₄	—	2	1	no	—
54	C₂³×C₃×C₄	—	2	1	no	—
55	C₂³×C₃×C₄	D₄	1	6	yes	—
56	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
57	C₂³×C₃×C₄	C₂³	1	6	yes	—
58	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
59	C₂×C₃×SD₁₆	—	2	96	no	—
60	C₂×C₃×SD₁₆	C₂³	1	32	yes	complemented
61	C₂²×C₃×C₈	—	2	8	no	—
62	C₂²×C₃×C₈	C₂³	1	12	yes	complemented
63	C₃×C₂²⋊Q₈	—	2	24	no	—
64	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
65	C₂×C₃×C₄⋊C₄	—	2	12	no	—
66	C₂×C₃×C₄⋊C₄	—	2	3	no	—
67	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	complemented
68	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
69	C₃×#102	C₂³	1	32	yes	complemented
70	C₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
71	C₂⁶	—	2	1	no	—
72	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
73	C₂³×D₄	—	2	16	no	—
74	C₂³×D₄	—	2	1	no	—
75	C₂³×D₄	—	2	6	no	—
76	C₂³×D₄	C₂²×C₃	1	12	yes	—
77	C₂³×D₄	C₂²×C₃	1	2	yes	—
78	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂²×SD₁₆	—	2	16	no	—
80	C₂²×SD₁₆	C₂²×C₃	1	24	yes	complemented
81	C₂³×C₈	C₂²×C₃	1	2	yes	complemented
82	C₂×C₂²⋊Q₈	—	2	6	no	—
83	C₂×C₂²⋊Q₈	C₂²×C₃	1	12	yes	complemented
84	C₂²×C₄⋊C₄	—	2	1	no	—
85	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₂²×C₂²⋊C₄	—	2	1	no	—
87	#450	C₂²×C₃	1	64	yes	direct product factor
88	C₂×#102	C₂²×C₃	1	24	yes	complemented
89	C₂×C₂²⋊C₈	C₂²×C₃	1	12	yes	complemented
90	C₂⁴×C₃	—	2	4	no	—
91	C₂⁴×C₃	—	2	4	no	—
92	C₂⁴×C₃	—	2	96	no	—
93	C₂⁴×C₃	—	2	16	no	—
94	C₂⁴×C₃	—	2	16	no	—
95	C₂⁴×C₃	—	2	12	no	—
96	C₂⁴×C₃	—	4	48	no	—
97	C₂⁴×C₃	—	4	128	no	—
98	C₂⁴×C₃	—	4	8	no	—
99	C₂⁴×C₃	—	4	48	no	—
100	C₂⁴×C₃	—	4	8	no	—
101	C₂⁴×C₃	SD₁₆	1	8	yes	complemented
102	C₂⁴×C₃	C₂×D₄	1	6	yes	—
103	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×Q₈	—	2	6	no	—
105	C₂×C₃×Q₈	—	2	24	no	—
106	C₂×C₃×Q₈	—	4	12	no	—
107	C₂×C₃×Q₈	C₂⁴	1	4	yes	complemented
108	C₂×C₃×D₄	—	2	96	no	—
109	C₂×C₃×D₄	—	2	192	no	—
110	C₂×C₃×D₄	—	2	64	no	—
111	C₂×C₃×D₄	—	2	48	no	—
112	C₂×C₃×D₄	—	2	16	no	—
113	C₂×C₃×D₄	—	2	12	no	—
114	C₂×C₃×D₄	—	2	24	no	—
115	C₂×C₃×D₄	C₂×D₄	1	48	yes	—
116	C₂×C₃×D₄	C₂⁴	1	8	yes	—
117	C₂²×C₃×C₄	—	2	4	no	—
118	C₂²×C₃×C₄	—	2	24	no	—
119	C₂²×C₃×C₄	—	2	24	no	—
120	C₂²×C₃×C₄	—	2	6	no	—
121	C₂²×C₃×C₄	—	2	6	no	—
122	C₂²×C₃×C₄	—	4	4	no	—
123	C₂²×C₃×C₄	—	4	4	no	—
124	C₂²×C₃×C₄	C₂×D₄	1	6	yes	—
125	C₂²×C₃×C₄	C₂×D₄	1	12	yes	—
126	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
127	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
128	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
129	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
130	C₃×SD₁₆	—	2	64	no	—
131	C₂×C₃×C₈	—	2	24	no	—
132	C₂×C₃×C₈	C₂⁴	1	8	yes	complemented
133	C₃×C₄⋊C₄	—	2	16	no	—
134	C₃×C₄⋊C₄	—	2	6	no	—
135	C₃×C₄⋊C₄	C₂⁴	1	4	yes	complemented
136	C₃×C₂²⋊C₄	—	2	16	no	—
137	C₂⁵	—	2	16	no	—
138	C₂⁵	—	2	12	no	—
139	C₂⁵	—	2	2	no	—
140	C₂⁵	—	4	8	no	—
141	C₂⁵	—	4	8	no	—
142	C₂⁵	C₃×D₄	1	1	yes	characteristic
143	C₂²×Q₈	—	2	3	no	—
144	C₂²×Q₈	—	2	8	no	—
145	C₂²×Q₈	C₂³×C₃	1	6	yes	complemented
146	C₂²×D₄	—	2	16	no	—
147	C₂²×D₄	—	2	96	no	—
148	C₂²×D₄	—	2	96	no	—
149	C₂²×D₄	—	2	12	no	—
150	C₂²×D₄	—	2	24	no	—
151	C₂²×D₄	—	2	6	no	—
152	C₂²×D₄	—	2	8	no	—
153	C₂²×D₄	C₃×D₄	1	16	yes	—
154	C₂²×D₄	C₂³×C₃	1	16	yes	—
155	C₂²×D₄	C₂³×C₃	1	12	yes	—
156	C₂³×C₄	—	2	8	no	—
157	C₂³×C₄	—	2	1	no	—
158	C₂³×C₄	—	2	1	no	—
159	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
160	C₂³×C₄	C₃×D₄	1	6	yes	—
161	C₂³×C₄	C₂³×C₃	1	6	yes	—
162	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
163	C₂×SD₁₆	—	2	96	no	—
164	C₂×SD₁₆	C₂³×C₃	1	32	yes	complemented
165	C₂²×C₈	—	2	8	no	—
166	C₂²×C₈	C₂³×C₃	1	12	yes	complemented
167	C₂²⋊Q₈	—	2	24	no	—
168	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
169	C₂×C₄⋊C₄	—	2	12	no	—
170	C₂×C₄⋊C₄	—	2	3	no	—
171	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	complemented
172	C₂×C₂²⋊C₄	—	2	12	no	—
173	#102	C₂³×C₃	1	32	yes	complemented
174	C₂²⋊C₈	C₂³×C₃	1	16	yes	complemented
175	C₂³×C₃	—	2	12	no	—
176	C₂³×C₃	—	2	12	no	—
177	C₂³×C₃	—	2	32	no	—
178	C₂³×C₃	—	2	64	no	—
179	C₂³×C₃	—	2	48	no	—
180	C₂³×C₃	—	2	8	no	—
181	C₂³×C₃	—	4	384	no	—
182	C₂³×C₃	—	4	32	no	—
183	C₂³×C₃	—	4	24	no	—
184	C₂³×C₃	—	4	32	no	—
185	C₂³×C₃	—	4	24	no	—
186	C₂³×C₃	—	4	64	no	—
187	C₂³×C₃	#120	1	4	yes	—
188	C₂³×C₃	C₂×SD₁₆	1	4	yes	—
189	C₂³×C₃	C₂×SD₁₆	1	24	yes	complemented
190	C₂³×C₃	AGL(1,ℤ/8)	1	4	yes	—
191	C₂³×C₃	C₂²×D₄	1	4	yes	—
192	C₂³×C₃	C₂²×D₄	1	3	yes	—
193	C₃×Q₈	—	2	8	no	—
194	C₃×Q₈	—	4	12	no	—
195	C₃×D₄	—	2	64	no	—
196	C₃×D₄	—	2	48	no	—
197	C₃×D₄	—	2	8	no	—
198	C₃×D₄	C₂²×D₄	1	16	yes	—
199	C₂×C₃×C₄	—	2	12	no	—
200	C₂×C₃×C₄	—	2	24	no	—
201	C₂×C₃×C₄	—	2	8	no	—
202	C₂×C₃×C₄	—	2	4	no	—
203	C₂×C₃×C₄	—	2	4	no	—
204	C₂×C₃×C₄	—	4	12	no	—
205	C₂×C₃×C₄	—	4	12	no	—
206	C₂×C₃×C₄	#120	1	12	yes	—
207	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
208	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
209	C₂×C₃×C₄	C₂²×D₄	1	12	yes	—
210	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
211	C₃×C₈	—	2	8	no	—
212	C₂⁴	—	2	4	no	—
213	C₂⁴	—	2	4	no	—
214	C₂⁴	—	2	96	no	—
215	C₂⁴	—	2	16	no	—
216	C₂⁴	—	2	16	no	—
217	C₂⁴	—	2	12	no	—
218	C₂⁴	—	4	48	no	—
219	C₂⁴	—	4	128	no	—
220	C₂⁴	—	4	8	no	—
221	C₂⁴	—	4	48	no	—
222	C₂⁴	—	4	8	no	—
223	C₂⁴	C₃×SD₁₆	1	8	yes	complemented
224	C₂⁴	C₂×C₃×D₄	1	6	yes	—
225	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
226	C₂×Q₈	—	2	6	no	—
227	C₂×Q₈	—	2	24	no	—
228	C₂×Q₈	—	4	12	no	—
229	C₂×Q₈	C₂⁴×C₃	1	4	yes	complemented
230	C₂×D₄	—	2	96	no	—
231	C₂×D₄	—	2	192	no	—
232	C₂×D₄	—	2	64	no	—
233	C₂×D₄	—	2	48	no	—
234	C₂×D₄	—	2	16	no	—
235	C₂×D₄	—	2	24	no	—
236	C₂×D₄	—	2	12	no	—
237	C₂×D₄	C₂×C₃×D₄	1	48	yes	—
238	C₂×D₄	C₂⁴×C₃	1	8	yes	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	24	no	—
241	C₂²×C₄	—	2	24	no	—
242	C₂²×C₄	—	2	6	no	—
243	C₂²×C₄	—	2	6	no	—
244	C₂²×C₄	—	4	4	no	—
245	C₂²×C₄	—	4	4	no	—
246	C₂²×C₄	C₂×C₃×D₄	1	6	yes	—
247	C₂²×C₄	C₂×C₃×D₄	1	12	yes	—
248	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
249	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
250	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
251	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
252	SD₁₆	—	2	64	no	—
253	C₂×C₈	—	2	24	no	—
254	C₂×C₈	C₂⁴×C₃	1	8	yes	complemented
255	C₄⋊C₄	—	2	16	no	—
256	C₄⋊C₄	—	2	6	no	—
257	C₄⋊C₄	C₂⁴×C₃	1	4	yes	complemented
258	C₂²⋊C₄	—	2	16	no	—
259	C₂²×C₃	—	2	4	no	—
260	C₂²×C₃	—	2	48	no	—
261	C₂²×C₃	—	2	4	no	—
262	C₂²×C₃	—	2	16	no	—
263	C₂²×C₃	—	4	128	no	—
264	C₂²×C₃	—	4	96	no	—
265	C₂²×C₃	—	4	8	no	—
266	C₂²×C₃	—	4	8	no	—
267	C₂²×C₃	#450	1	16	yes	direct product factor
268	C₂²×C₃	C₂×#120	1	6	yes	—
269	C₂²×C₃	C₂²×SD₁₆	1	6	yes	—
270	C₂²×C₃	C₂²×SD₁₆	1	8	yes	complemented
271	C₂²×C₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
272	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
273	C₃×C₄	—	2	4	no	—
274	C₃×C₄	—	4	4	no	—
275	C₃×C₄	—	4	4	no	—
276	C₃×C₄	C₂×#120	1	6	yes	—
277	C₃×C₄	C₂³×D₄	1	2	yes	—
278	C₂³	—	2	12	no	—
279	C₂³	—	2	32	no	—
280	C₂³	—	2	12	no	—
281	C₂³	—	2	64	no	—
282	C₂³	—	2	8	no	—
283	C₂³	—	2	48	no	—
284	C₂³	—	4	384	no	—
285	C₂³	—	4	32	no	—
286	C₂³	—	4	24	no	—
287	C₂³	—	4	32	no	—
288	C₂³	—	4	24	no	—
289	C₂³	—	4	64	no	—
290	C₂³	C₃×#120	1	4	yes	—
291	C₂³	C₂×C₃×SD₁₆	1	4	yes	—
292	C₂³	C₂×C₃×SD₁₆	1	24	yes	complemented
293	C₂³	C₃×AGL(1,ℤ/8)	1	4	yes	—
294	C₂³	C₂²×C₃×D₄	1	4	yes	—
295	C₂³	C₂²×C₃×D₄	1	3	yes	—
296	Q₈	—	2	8	no	—
297	Q₈	—	4	12	no	—
298	D₄	—	2	64	no	—
299	D₄	—	2	8	no	—
300	D₄	—	2	48	no	—
301	D₄	C₂²×C₃×D₄	1	16	yes	—
302	C₂×C₄	—	2	12	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	24	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	4	12	no	—
308	C₂×C₄	—	4	12	no	—
309	C₂×C₄	C₃×#120	1	12	yes	—
310	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
311	C₂×C₄	C₂²×C₃×D₄	1	12	yes	—
312	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
313	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
314	C₈	—	2	8	no	—
315	C₂×C₃	—	2	8	no	—
316	C₂×C₃	—	4	16	no	—
317	C₂×C₃	C₂×#450	1	12	yes	direct product factor
318	C₂×C₃	C₂²×#120	1	1	yes	characteristic
319	C₂×C₃	C₂³×SD₁₆	1	1	yes	characteristic
320	C₂×C₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
321	C₂²	—	2	4	no	—
322	C₂²	—	2	48	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	2	16	no	—
325	C₂²	—	4	128	no	—
326	C₂²	—	4	96	no	—
327	C₂²	—	4	8	no	—
328	C₂²	—	4	8	no	—
329	C₂²	C₃×#450	1	16	yes	direct product factor
330	C₂²	C₂×C₃×#120	1	6	yes	—
331	C₂²	C₂²×C₃×SD₁₆	1	6	yes	—
332	C₂²	C₂²×C₃×SD₁₆	1	8	yes	complemented
333	C₂²	C₂×C₃×AGL(1,ℤ/8)	1	6	yes	—
334	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
335	C₄	—	2	4	no	—
336	C₄	—	4	4	no	—
337	C₄	—	4	4	no	—
338	C₄	C₂×C₃×#120	1	6	yes	—
339	C₄	C₂³×C₃×D₄	1	2	yes	—
340	C₃	C₂²×#450	1	1	yes	characteristic, direct product factor, Sylow
341	C₂	—	2	8	no	—
342	C₂	—	4	16	no	—
343	C₂	C₂×C₃×#450	1	12	yes	direct product factor
344	C₂	C₂²×C₃×#120	1	1	yes	characteristic
345	C₂	C₂³×C₃×SD₁₆	1	1	yes	characteristic
346	C₂	C₂²×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×SD₁₆	C₂	semidirect
3. C₂²×C₃×C₂²⋊Q₈	C₂	semidirect
4. C₂×C₃×#450	C₂	direct (N × H)
5. C₂²×C₃×#102	C₂	semidirect
6. C₂²×C₃×C₂²⋊C₈	C₂	semidirect
7. C₂²×#450	C₃	direct (N × H)
9. C₂³×C₃×Q₈	C₂²	semidirect
17. C₂²×C₃×SD₁₆	C₂²	semidirect
18. C₂³×C₃×C₈	C₂²	semidirect
20. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
22. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
24. C₃×#450	C₂²	direct (N × H)
25. C₂×C₃×#102	C₂²	semidirect
26. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
28. C₂³×SD₁₆	C₂×C₃	semidirect
29. C₂²×C₂²⋊Q₈	C₂×C₃	semidirect
30. C₂×#450	C₂×C₃	direct (N × H)
31. C₂²×#102	C₂×C₃	semidirect
32. C₂²×C₂²⋊C₈	C₂×C₃	semidirect
41. C₂²×C₃×Q₈	C₂³	semidirect
60. C₂×C₃×SD₁₆	C₂³	semidirect
62. C₂²×C₃×C₈	C₂³	semidirect
64. C₃×C₂²⋊Q₈	C₂³	semidirect
67. C₂×C₃×C₄⋊C₄	C₂³	semidirect
69. C₃×#102	C₂³	semidirect
70. C₃×C₂²⋊C₈	C₂³	semidirect
72. C₂³×Q₈	C₂²×C₃	semidirect
80. C₂²×SD₁₆	C₂²×C₃	semidirect
81. C₂³×C₈	C₂²×C₃	semidirect
83. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
85. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
87. #450	C₂²×C₃	direct (N × H)
88. C₂×#102	C₂²×C₃	semidirect
89. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
101. C₂⁴×C₃	SD₁₆	semidirect
107. C₂×C₃×Q₈	C₂⁴	semidirect
132. C₂×C₃×C₈	C₂⁴	semidirect
135. C₃×C₄⋊C₄	C₂⁴	semidirect
145. C₂²×Q₈	C₂³×C₃	semidirect
164. C₂×SD₁₆	C₂³×C₃	semidirect
166. C₂²×C₈	C₂³×C₃	semidirect
168. C₂²⋊Q₈	C₂³×C₃	semidirect
171. C₂×C₄⋊C₄	C₂³×C₃	semidirect
173. #102	C₂³×C₃	semidirect
174. C₂²⋊C₈	C₂³×C₃	semidirect
189. C₂³×C₃	C₂×SD₁₆	semidirect
223. C₂⁴	C₃×SD₁₆	semidirect
229. C₂×Q₈	C₂⁴×C₃	semidirect
254. C₂×C₈	C₂⁴×C₃	semidirect
257. C₄⋊C₄	C₂⁴×C₃	semidirect
267. C₂²×C₃	#450	direct (N × H)
270. C₂²×C₃	C₂²×SD₁₆	semidirect
292. C₂³	C₂×C₃×SD₁₆	semidirect
317. C₂×C₃	C₂×#450	direct (N × H)
329. C₂²	C₃×#450	direct (N × H)
332. C₂²	C₂²×C₃×SD₁₆	semidirect
340. C₃	C₂²×#450	direct (N × H)
343. C₂	C₂×C₃×#450	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×D₄	2
C₂³×C₃×SD₁₆	2
C₂²×C₃×C₂²⋊Q₈	2
C₂×C₃×#450	2
C₂²×C₃×#102	2
C₂²×C₃×C₂²⋊C₈	2
C₂²×#450	3

Subgroups — C22×C3×#450 #10678955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#450 #10678955