Subgroups — C₃²×#3273 #11770322

Order 1152.

1560 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₃²×#546	C₂	1	2	yes	maximal, complemented
3	C₃²×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#468	C₂	1	2	yes	maximal, complemented
5	C₃²×#463	C₂	1	2	yes	maximal, complemented
6	C₃²×#452	C₂	1	2	yes	maximal, complemented
7	C₃²×#447	C₂	1	2	yes	maximal, complemented
8	C₃²×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#436	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3273	C₃	1	4	yes	maximal, direct product factor
11	C₂×C₃²×#41	C₂²	1	2	yes	—
12	C₂²×C₃²×D₄	C₂²	1	2	yes	complemented
13	C₃²×AGL(1,ℤ/8)	—	2	8	no	—
14	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
16	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
17	C₂×C₃²×D₈	C₂²	1	2	yes	—
18	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
19	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₃²×M₁₆	C₂²	1	2	yes	complemented
21	C₃²×#124	C₂²	1	2	yes	complemented
22	C₃²×#123	—	2	2	no	—
23	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
24	C₃²×#121	—	2	2	no	—
25	C₃²×#121	C₂²	1	2	yes	—
26	C₃²×#120	—	2	2	no	—
27	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
28	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
29	C₂×C₃²×C₂²⋊C₄	—	2	2	no	—
30	C₃²×#107	C₂²	1	1	yes	characteristic, complemented
31	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#103	C₂²	1	2	yes	complemented
33	C₃²×#102	C₂²	1	2	yes	complemented
34	C₃²×#102	C₂²	1	2	yes	complemented
35	C₃²×C₂²⋊C₈	C₂²	1	2	yes	complemented
36	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	8	yes	complemented
38	C₃×#546	C₂×C₃	1	8	yes	complemented
39	C₃×#495	C₂×C₃	1	4	yes	complemented
40	C₃×#468	C₂×C₃	1	8	yes	complemented
41	C₃×#463	C₂×C₃	1	8	yes	complemented
42	C₃×#452	C₂×C₃	1	8	yes	complemented
43	C₃×#447	C₂×C₃	1	8	yes	complemented
44	C₃×C₄×D₈	C₂×C₃	1	4	yes	complemented
45	C₃×#436	C₂×C₃	1	4	yes	complemented
46	C₂⁴×C₃²	—	2	2	no	—
47	C₃²×#41	—	2	4	no	—
48	C₃²×#41	—	4	2	no	—
49	C₂×C₃²×Q₈	C₂³	1	2	yes	—
50	C₂×C₃²×D₄	—	2	4	no	—
51	C₂×C₃²×D₄	—	2	2	no	—
52	C₂×C₃²×D₄	—	2	2	no	—
53	C₂×C₃²×D₄	—	2	2	no	—
54	C₂×C₃²×D₄	—	4	2	no	—
55	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
56	C₂×C₃²×D₄	C₂³	1	2	yes	—
57	C₂×C₃²×D₄	C₂³	1	2	yes	—
58	C₂²×C₃²×C₄	—	2	2	no	—
59	C₂²×C₃²×C₄	—	2	2	no	—
60	C₂²×C₃²×C₄	C₂³	1	2	yes	—
61	C₃²×Q₁₆	—	4	1	no	—
62	C₃²×SD₁₆	—	2	4	no	—
63	C₃²×SD₁₆	—	2	4	no	—
64	C₃²×D₈	—	2	4	no	—
65	C₃²×D₈	—	4	1	no	—
66	C₃²×D₈	D₄	1	4	yes	complemented
67	C₃²×M₁₆	—	2	4	no	—
68	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃²×C₈	C₂³	1	2	yes	—
70	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
71	C₃²×C₄⋊C₄	—	2	2	no	—
72	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
74	C₃²×C₂²⋊C₄	—	2	2	no	—
75	C₃²×C₂²⋊C₄	—	2	2	no	—
76	C₃²×C₂²⋊C₄	—	2	2	no	—
77	C₃²×C₂²⋊C₄	—	2	2	no	—
78	C₃²×C₂²⋊C₄	—	2	2	no	—
79	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
80	C₃²×C₄²	C₂³	1	1	yes	characteristic
81	#3273	C₃²	1	1	yes	characteristic, direct product factor, Sylow
82	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
83	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	complemented
84	C₃×AGL(1,ℤ/8)	—	2	32	no	—
85	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	complemented
86	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
87	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
88	C₂×C₃×D₈	C₂²×C₃	1	8	yes	—
89	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
90	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
91	C₂×C₃×M₁₆	C₂²×C₃	1	8	yes	complemented
92	C₃×#124	C₂²×C₃	1	8	yes	complemented
93	C₃×#123	—	2	8	no	—
94	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
95	C₃×#121	—	2	8	no	—
96	C₃×#121	C₂²×C₃	1	8	yes	—
97	C₃×#120	—	2	8	no	—
98	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
99	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
100	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
101	C₃×#107	C₂²×C₃	1	4	yes	complemented
102	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
103	C₃×#103	C₂²×C₃	1	8	yes	complemented
104	C₃×#102	C₂²×C₃	1	8	yes	complemented
105	C₃×#102	C₂²×C₃	1	8	yes	complemented
106	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	complemented
107	C₃×C₄×C₈	C₂²×C₃	1	4	yes	complemented
108	C₂³×C₃²	—	2	2	no	—
109	C₂³×C₃²	—	2	2	no	—
110	C₂³×C₃²	—	4	4	no	—
111	C₂³×C₃²	—	4	4	no	—
112	C₂³×C₃²	—	8	2	no	—
113	C₂³×C₃²	C₂×D₄	1	2	yes	—
114	C₃²×Q₈	—	2	2	no	—
115	C₃²×Q₈	—	2	2	no	—
116	C₃²×D₄	—	2	2	no	—
117	C₃²×D₄	—	2	2	no	—
118	C₃²×D₄	—	2	2	no	—
119	C₃²×D₄	—	4	1	no	—
120	C₃²×D₄	—	4	4	no	—
121	C₃²×D₄	—	4	4	no	—
122	C₃²×D₄	—	8	2	no	—
123	C₃²×D₄	C₂×D₄	1	4	yes	—
124	C₂×C₃²×C₄	—	2	2	no	—
125	C₂×C₃²×C₄	—	2	2	no	—
126	C₂×C₃²×C₄	—	2	2	no	—
127	C₂×C₃²×C₄	—	2	2	no	—
128	C₂×C₃²×C₄	—	4	4	no	—
129	C₂×C₃²×C₄	—	8	2	no	—
130	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
133	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
134	C₃²×C₈	—	2	2	no	—
135	C₃²×C₈	—	2	1	no	—
136	C₃²×C₈	C₂×D₄	1	2	yes	—
137	C₂×AGL(1,ℤ/8)	C₂×C₃²	1	2	yes	complemented
138	#546	C₂×C₃²	1	2	yes	complemented
139	#495	C₂×C₃²	1	1	yes	characteristic, complemented
140	#468	C₂×C₃²	1	2	yes	complemented
141	#463	C₂×C₃²	1	2	yes	complemented
142	#452	C₂×C₃²	1	2	yes	complemented
143	#447	C₂×C₃²	1	2	yes	complemented
144	C₄×D₈	C₂×C₃²	1	1	yes	characteristic, complemented
145	#436	C₂×C₃²	1	1	yes	characteristic, complemented
146	C₂⁴×C₃	—	2	8	no	—
147	C₃×#41	—	2	16	no	—
148	C₃×#41	—	4	8	no	—
149	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
150	C₂×C₃×D₄	—	2	16	no	—
151	C₂×C₃×D₄	—	2	8	no	—
152	C₂×C₃×D₄	—	2	8	no	—
153	C₂×C₃×D₄	—	2	8	no	—
154	C₂×C₃×D₄	—	4	8	no	—
155	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
156	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
157	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
158	C₂²×C₃×C₄	—	2	8	no	—
159	C₂²×C₃×C₄	—	2	8	no	—
160	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
161	C₃×Q₁₆	—	4	4	no	—
162	C₃×SD₁₆	—	2	16	no	—
163	C₃×SD₁₆	—	2	16	no	—
164	C₃×D₈	—	2	16	no	—
165	C₃×D₈	—	4	4	no	—
166	C₃×D₈	C₃×D₄	1	16	yes	complemented
167	C₃×M₁₆	—	2	16	no	—
168	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
169	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
170	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
171	C₃×C₄⋊C₄	—	2	8	no	—
172	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
173	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
174	C₃×C₂²⋊C₄	—	2	8	no	—
175	C₃×C₂²⋊C₄	—	2	8	no	—
176	C₃×C₂²⋊C₄	—	2	8	no	—
177	C₃×C₂²⋊C₄	—	2	8	no	—
178	C₃×C₂²⋊C₄	—	2	8	no	—
179	C₃×C₂²⋊C₄	C₃×D₄	1	8	yes	—
180	C₃×C₄²	C₂³×C₃	1	4	yes	—
181	C₂²×C₃²	—	2	2	no	—
182	C₂²×C₃²	—	2	4	no	—
183	C₂²×C₃²	—	2	2	no	—
184	C₂²×C₃²	—	2	2	no	—
185	C₂²×C₃²	—	4	2	no	—
186	C₂²×C₃²	—	4	2	no	—
187	C₂²×C₃²	—	4	2	no	—
188	C₂²×C₃²	—	4	2	no	—
189	C₂²×C₃²	—	4	2	no	—
190	C₂²×C₃²	—	8	8	no	—
191	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
192	C₃²×C₄	—	2	2	no	—
193	C₃²×C₄	—	2	1	no	—
194	C₃²×C₄	—	2	1	no	—
195	C₃²×C₄	—	4	2	no	—
196	C₃²×C₄	—	4	2	no	—
197	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
198	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×#41	C₂²×C₃²	1	2	yes	—
200	C₂²×D₄	C₂²×C₃²	1	2	yes	complemented
201	AGL(1,ℤ/8)	—	2	8	no	—
202	C₂×Q₁₆	C₂²×C₃²	1	1	yes	characteristic, complemented
203	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
204	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
205	C₂×D₈	C₂²×C₃²	1	2	yes	—
206	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic
207	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic
208	C₂×M₁₆	C₂²×C₃²	1	2	yes	complemented
209	#124	C₂²×C₃²	1	2	yes	complemented
210	#123	—	2	2	no	—
211	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
212	#121	—	2	2	no	—
213	#121	C₂²×C₃²	1	2	yes	—
214	#120	—	2	2	no	—
215	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
216	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
217	C₂×C₂²⋊C₄	—	2	2	no	—
218	#107	C₂²×C₃²	1	1	yes	characteristic, complemented
219	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
220	#103	C₂²×C₃²	1	2	yes	complemented
221	#102	C₂²×C₃²	1	2	yes	complemented
222	#102	C₂²×C₃²	1	2	yes	complemented
223	C₂²⋊C₈	C₂²×C₃²	1	2	yes	complemented
224	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
225	C₂³×C₃	—	2	8	no	—
226	C₂³×C₃	—	2	8	no	—
227	C₂³×C₃	—	4	16	no	—
228	C₂³×C₃	—	4	16	no	—
229	C₂³×C₃	—	8	8	no	—
230	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
231	C₃×Q₈	—	2	8	no	—
232	C₃×Q₈	—	2	8	no	—
233	C₃×D₄	—	2	8	no	—
234	C₃×D₄	—	2	8	no	—
235	C₃×D₄	—	2	8	no	—
236	C₃×D₄	—	4	4	no	—
237	C₃×D₄	—	4	16	no	—
238	C₃×D₄	—	4	16	no	—
239	C₃×D₄	—	8	8	no	—
240	C₃×D₄	C₂×C₃×D₄	1	16	yes	—
241	C₂×C₃×C₄	—	2	8	no	—
242	C₂×C₃×C₄	—	2	8	no	—
243	C₂×C₃×C₄	—	2	8	no	—
244	C₂×C₃×C₄	—	2	8	no	—
245	C₂×C₃×C₄	—	4	16	no	—
246	C₂×C₃×C₄	—	8	8	no	—
247	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
248	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
249	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
250	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
251	C₃×C₈	—	2	8	no	—
252	C₃×C₈	—	2	4	no	—
253	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
254	C₂×C₃²	—	4	2	no	—
255	C₂×C₃²	—	4	4	no	—
256	C₂×C₃²	—	8	2	no	—
257	C₂×C₃²	D₄²	1	1	yes	characteristic
258	C₂×C₃²	#575	1	1	yes	characteristic
259	C₂×C₃²	#576	1	1	yes	characteristic
260	C₂⁴	—	2	2	no	—
261	#41	—	2	4	no	—
262	#41	—	4	2	no	—
263	C₂×Q₈	C₂³×C₃²	1	2	yes	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
270	C₂×D₄	C₂³×C₃²	1	2	yes	—
271	C₂×D₄	C₂³×C₃²	1	2	yes	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	C₂³×C₃²	1	2	yes	—
275	Q₁₆	—	4	1	no	—
276	SD₁₆	—	2	4	no	—
277	SD₁₆	—	2	4	no	—
278	D₈	—	2	4	no	—
279	D₈	—	4	1	no	—
280	D₈	C₃²×D₄	1	4	yes	complemented
281	M₁₆	—	2	4	no	—
282	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
283	C₂×C₈	C₂³×C₃²	1	2	yes	—
284	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
287	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₂²⋊C₄	—	2	2	no	—
290	C₂²⋊C₄	—	2	2	no	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	C₃²×D₄	1	2	yes	—
294	C₄²	C₂³×C₃²	1	1	yes	characteristic
295	C₂²×C₃	—	2	8	no	—
296	C₂²×C₃	—	2	8	no	—
297	C₂²×C₃	—	2	8	no	—
298	C₂²×C₃	—	2	16	no	—
299	C₂²×C₃	—	4	8	no	—
300	C₂²×C₃	—	4	8	no	—
301	C₂²×C₃	—	4	8	no	—
302	C₂²×C₃	—	4	8	no	—
303	C₂²×C₃	—	4	8	no	—
304	C₂²×C₃	—	8	32	no	—
305	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
306	C₃×C₄	—	2	4	no	—
307	C₃×C₄	—	2	4	no	—
308	C₃×C₄	—	2	8	no	—
309	C₃×C₄	—	4	8	no	—
310	C₃×C₄	—	4	8	no	—
311	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
312	C₃×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
313	C₃²	#3273	1	1	yes	characteristic, direct product factor, Sylow
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	8	2	no	—
319	C₂³	C₂×C₃²×D₄	1	2	yes	—
320	Q₈	—	2	2	no	—
321	Q₈	—	2	2	no	—
322	D₄	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	1	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	4	no	—
328	D₄	—	8	2	no	—
329	D₄	C₂×C₃²×D₄	1	4	yes	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
337	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
338	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
339	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
340	C₈	—	2	2	no	—
341	C₈	—	2	1	no	—
342	C₈	C₂×C₃²×D₄	1	2	yes	—
343	C₂×C₃	—	4	8	no	—
344	C₂×C₃	—	4	16	no	—
345	C₂×C₃	—	8	8	no	—
346	C₂×C₃	C₃×D₄²	1	4	yes	—
347	C₂×C₃	C₃×#575	1	4	yes	—
348	C₂×C₃	C₃×#576	1	4	yes	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	8	no	—
359	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	2	no	—
365	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
366	C₄	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
367	C₃	C₃×#3273	1	4	yes	direct product factor
368	C₂	—	4	2	no	—
369	C₂	—	4	4	no	—
370	C₂	—	8	2	no	—
371	C₂	C₃²×D₄²	1	1	yes	characteristic
372	C₂	C₃²×#575	1	1	yes	characteristic
373	C₂	C₃²×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×AGL(1,ℤ/8)	C₂	semidirect
2. C₃²×#546	C₂	semidirect
3. C₃²×#495	C₂	semidirect
4. C₃²×#468	C₂	semidirect
5. C₃²×#463	C₂	semidirect
6. C₃²×#452	C₂	semidirect
7. C₃²×#447	C₂	semidirect
8. C₃²×C₄×D₈	C₂	semidirect
9. C₃²×#436	C₂	semidirect
10. C₃×#3273	C₃	direct (N × H)
12. C₂²×C₃²×D₄	C₂²	semidirect
14. C₂×C₃²×Q₁₆	C₂²	semidirect
15. C₂×C₃²×SD₁₆	C₂²	semidirect
16. C₂×C₃²×SD₁₆	C₂²	semidirect
20. C₂×C₃²×M₁₆	C₂²	semidirect
21. C₃²×#124	C₂²	semidirect
23. C₃²×C₂²⋊Q₈	C₂²	semidirect
28. C₃²×C₄×D₄	C₂²	semidirect
30. C₃²×#107	C₂²	semidirect
31. C₃²×C₄⋊C₈	C₂²	semidirect
32. C₃²×#103	C₂²	semidirect
33. C₃²×#102	C₂²	semidirect
34. C₃²×#102	C₂²	semidirect
35. C₃²×C₂²⋊C₈	C₂²	semidirect
36. C₃²×C₄×C₈	C₂²	semidirect
37. C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	semidirect
38. C₃×#546	C₂×C₃	semidirect
39. C₃×#495	C₂×C₃	semidirect
40. C₃×#468	C₂×C₃	semidirect
41. C₃×#463	C₂×C₃	semidirect
42. C₃×#452	C₂×C₃	semidirect
43. C₃×#447	C₂×C₃	semidirect
44. C₃×C₄×D₈	C₂×C₃	semidirect
45. C₃×#436	C₂×C₃	semidirect
66. C₃²×D₈	D₄	semidirect
81. #3273	C₃²	direct (N × H)
83. C₂²×C₃×D₄	C₂²×C₃	semidirect
85. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
86. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
87. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
91. C₂×C₃×M₁₆	C₂²×C₃	semidirect
92. C₃×#124	C₂²×C₃	semidirect
94. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
99. C₃×C₄×D₄	C₂²×C₃	semidirect
101. C₃×#107	C₂²×C₃	semidirect
102. C₃×C₄⋊C₈	C₂²×C₃	semidirect
103. C₃×#103	C₂²×C₃	semidirect
104. C₃×#102	C₂²×C₃	semidirect
105. C₃×#102	C₂²×C₃	semidirect
106. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
107. C₃×C₄×C₈	C₂²×C₃	semidirect
137. C₂×AGL(1,ℤ/8)	C₂×C₃²	semidirect
138. #546	C₂×C₃²	semidirect
139. #495	C₂×C₃²	semidirect
140. #468	C₂×C₃²	semidirect
141. #463	C₂×C₃²	semidirect
142. #452	C₂×C₃²	semidirect
143. #447	C₂×C₃²	semidirect
144. C₄×D₈	C₂×C₃²	semidirect
145. #436	C₂×C₃²	semidirect
166. C₃×D₈	C₃×D₄	semidirect
200. C₂²×D₄	C₂²×C₃²	semidirect
202. C₂×Q₁₆	C₂²×C₃²	semidirect
203. C₂×SD₁₆	C₂²×C₃²	semidirect
204. C₂×SD₁₆	C₂²×C₃²	semidirect
208. C₂×M₁₆	C₂²×C₃²	semidirect
209. #124	C₂²×C₃²	semidirect
211. C₂²⋊Q₈	C₂²×C₃²	semidirect
216. C₄×D₄	C₂²×C₃²	semidirect
218. #107	C₂²×C₃²	semidirect
219. C₄⋊C₈	C₂²×C₃²	semidirect
220. #103	C₂²×C₃²	semidirect
221. #102	C₂²×C₃²	semidirect
222. #102	C₂²×C₃²	semidirect
223. C₂²⋊C₈	C₂²×C₃²	semidirect
224. C₄×C₈	C₂²×C₃²	semidirect
280. D₈	C₃²×D₄	semidirect
313. C₃²	#3273	direct (N × H)
367. C₃	C₃×#3273	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×C₃²×AGL(1,ℤ/8)	2
C₃²×#546	2
C₃²×#495	2
C₃²×#468	2
C₃²×#463	2
C₃²×#452	2
C₃²×#447	2
C₃²×C₄×D₈	2
C₃²×#436	2
C₃×#3273	3

Subgroups — C32×#3273 #11770322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3273 #11770322