Subgroups — C₃²×#3101 #11770150

Order 1152.

1344 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×C₄×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃²×#483	C₂	1	2	yes	maximal, complemented
4	C₃²×#476	C₂	1	2	yes	maximal, complemented
5	C₃²×#461	C₂	1	2	yes	maximal, complemented
6	C₃²×#450	C₂	1	2	yes	maximal
7	C₃²×C₄×SD₁₆	C₂	1	4	yes	maximal, complemented
8	C₃²×#431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3101	C₃	1	4	yes	maximal, direct product factor
10	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃²×C₄	—	2	1	no	—
12	C₂×C₃²×SD₁₆	C₂²	1	4	yes	—
13	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₃²×#125	—	2	1	no	—
16	C₃²×C₂²⋊Q₈	—	2	1	no	—
17	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₃²×C₄×Q₈	—	2	1	no	—
19	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
20	C₃²×C₄×D₄	—	2	1	no	—
21	C₃²×C₄×D₄	—	2	1	no	—
22	C₃²×C₄×D₄	C₂²	1	2	yes	—
23	C₃²×C₄×D₄	C₂²	1	2	yes	—
24	C₃²×#117	—	2	1	no	—
25	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃²×C₂²⋊C₄	—	2	1	no	—
27	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
28	C₃²×#106	C₂²	1	4	yes	complemented
29	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
30	C₃²×#103	C₂²	1	4	yes	complemented
31	C₃²×#102	C₂²	1	4	yes	—
32	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
34	C₃×#533	C₂×C₃	1	4	yes	complemented
35	C₂×C₃×C₄×D₄	C₂×C₃	1	4	yes	—
36	C₃×#483	C₂×C₃	1	8	yes	complemented
37	C₃×#476	C₂×C₃	1	8	yes	complemented
38	C₃×#461	C₂×C₃	1	8	yes	complemented
39	C₃×#450	C₂×C₃	1	8	yes	—
40	C₃×C₄×SD₁₆	C₂×C₃	1	16	yes	complemented
41	C₃×#431	C₂×C₃	1	4	yes	complemented
42	C₂⁴×C₃²	—	2	1	no	—
43	C₂×C₃²×Q₈	—	2	1	no	—
44	C₂×C₃²×Q₈	C₂³	1	2	yes	—
45	C₂×C₃²×D₄	—	2	4	no	—
46	C₂×C₃²×D₄	—	2	1	no	—
47	C₂×C₃²×D₄	C₂³	1	2	yes	—
48	C₂²×C₃²×C₄	—	2	1	no	—
49	C₂²×C₃²×C₄	—	2	2	no	—
50	C₂²×C₃²×C₄	—	2	2	no	—
51	C₂²×C₃²×C₄	—	4	4	no	—
52	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
53	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
54	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
55	C₃²×SD₁₆	—	2	8	no	—
56	C₂×C₃²×C₈	C₂³	1	4	yes	—
57	C₃²×C₄⋊C₄	—	2	1	no	—
58	C₃²×C₄⋊C₄	—	2	1	no	—
59	C₃²×C₄⋊C₄	—	2	1	no	—
60	C₃²×C₄⋊C₄	—	2	1	no	—
61	C₃²×C₄⋊C₄	—	2	2	no	—
62	C₃²×C₄⋊C₄	—	2	2	no	—
63	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
64	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃²×C₂²⋊C₄	—	2	2	no	—
66	C₃²×C₂²⋊C₄	—	2	2	no	—
67	C₃²×C₂²⋊C₄	—	2	2	no	—
68	C₃²×C₄²	—	2	2	no	—
69	C₃²×C₄²	D₄	1	1	yes	characteristic
70	C₃²×C₄²	D₄	1	1	yes	characteristic
71	C₃²×C₄²	C₂³	1	1	yes	characteristic
72	C₃²×C₄²	C₂³	1	1	yes	characteristic
73	#3101	C₃²	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
75	C₂³×C₃×C₄	—	2	4	no	—
76	C₂×C₃×SD₁₆	C₂²×C₃	1	16	yes	—
77	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
78	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
79	C₃×#125	—	2	4	no	—
80	C₃×C₂²⋊Q₈	—	2	4	no	—
81	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
82	C₃×C₄×Q₈	—	2	4	no	—
83	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	complemented
84	C₃×C₄×D₄	—	2	4	no	—
85	C₃×C₄×D₄	—	2	4	no	—
86	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
87	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
88	C₃×#117	—	2	4	no	—
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
90	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
91	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
92	C₃×#106	C₂²×C₃	1	16	yes	complemented
93	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	complemented
94	C₃×#103	C₂²×C₃	1	16	yes	complemented
95	C₃×#102	C₂²×C₃	1	16	yes	—
96	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	—
97	C₃×C₄×C₈	C₂²×C₃	1	8	yes	complemented
98	C₂³×C₃²	—	2	4	no	—
99	C₂³×C₃²	—	2	2	no	—
100	C₂³×C₃²	—	4	2	no	—
101	C₂³×C₃²	—	4	2	no	—
102	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
103	C₃²×Q₈	—	2	4	no	—
104	C₃²×Q₈	—	4	2	no	—
105	C₃²×D₄	—	2	4	no	—
106	C₃²×D₄	—	2	2	no	—
107	C₃²×D₄	#41	1	4	yes	—
108	C₂×C₃²×C₄	—	2	2	no	—
109	C₂×C₃²×C₄	—	2	2	no	—
110	C₂×C₃²×C₄	—	2	2	no	—
111	C₂×C₃²×C₄	—	2	2	no	—
112	C₂×C₃²×C₄	—	4	1	no	—
113	C₂×C₃²×C₄	—	4	2	no	—
114	C₂×C₃²×C₄	—	4	4	no	—
115	C₂×C₃²×C₄	—	4	4	no	—
116	C₂×C₃²×C₄	SD₁₆	1	4	yes	complemented
117	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
123	C₃²×C₈	—	2	4	no	—
124	#533	C₂×C₃²	1	1	yes	characteristic, complemented
125	C₂×C₄×D₄	C₂×C₃²	1	1	yes	characteristic
126	#483	C₂×C₃²	1	2	yes	complemented
127	#476	C₂×C₃²	1	2	yes	complemented
128	#461	C₂×C₃²	1	2	yes	complemented
129	#450	C₂×C₃²	1	2	yes	—
130	C₄×SD₁₆	C₂×C₃²	1	4	yes	complemented
131	#431	C₂×C₃²	1	1	yes	characteristic, complemented
132	C₂⁴×C₃	—	2	4	no	—
133	C₂×C₃×Q₈	—	2	4	no	—
134	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
135	C₂×C₃×D₄	—	2	16	no	—
136	C₂×C₃×D₄	—	2	4	no	—
137	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
138	C₂²×C₃×C₄	—	2	4	no	—
139	C₂²×C₃×C₄	—	2	8	no	—
140	C₂²×C₃×C₄	—	2	8	no	—
141	C₂²×C₃×C₄	—	4	16	no	—
142	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
143	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
144	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
145	C₃×SD₁₆	—	2	32	no	—
146	C₂×C₃×C₈	C₂³×C₃	1	16	yes	—
147	C₃×C₄⋊C₄	—	2	4	no	—
148	C₃×C₄⋊C₄	—	2	4	no	—
149	C₃×C₄⋊C₄	—	2	4	no	—
150	C₃×C₄⋊C₄	—	2	4	no	—
151	C₃×C₄⋊C₄	—	2	8	no	—
152	C₃×C₄⋊C₄	—	2	8	no	—
153	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
154	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
155	C₃×C₂²⋊C₄	—	2	8	no	—
156	C₃×C₂²⋊C₄	—	2	8	no	—
157	C₃×C₂²⋊C₄	—	2	8	no	—
158	C₃×C₄²	—	2	8	no	—
159	C₃×C₄²	C₃×D₄	1	4	yes	—
160	C₃×C₄²	C₃×D₄	1	4	yes	—
161	C₃×C₄²	C₂³×C₃	1	4	yes	—
162	C₃×C₄²	C₂³×C₃	1	4	yes	—
163	C₂²×C₃²	—	2	1	no	—
164	C₂²×C₃²	—	2	1	no	—
165	C₂²×C₃²	—	2	4	no	—
166	C₂²×C₃²	—	4	8	no	—
167	C₂²×C₃²	—	4	2	no	—
168	C₂²×C₃²	—	4	2	no	—
169	C₂²×C₃²	C₂×SD₁₆	1	2	yes	—
170	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
171	C₃²×C₄	—	2	1	no	—
172	C₃²×C₄	—	2	1	no	—
173	C₃²×C₄	—	2	1	no	—
174	C₃²×C₄	—	4	2	no	—
175	C₃²×C₄	—	4	2	no	—
176	C₃²×C₄	—	4	2	no	—
177	C₃²×C₄	C₂×SD₁₆	1	2	yes	—
178	C₃²×C₄	C₂×SD₁₆	1	2	yes	—
179	C₃²×C₄	C₂×#41	1	2	yes	—
180	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
181	C₂³×C₄	—	2	1	no	—
182	C₂×SD₁₆	C₂²×C₃²	1	4	yes	—
183	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
184	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
185	#125	—	2	1	no	—
186	C₂²⋊Q₈	—	2	1	no	—
187	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
188	C₄×Q₈	—	2	1	no	—
189	C₄×Q₈	C₂²×C₃²	1	2	yes	complemented
190	C₄×D₄	—	2	1	no	—
191	C₄×D₄	—	2	1	no	—
192	C₄×D₄	C₂²×C₃²	1	2	yes	—
193	C₄×D₄	C₂²×C₃²	1	2	yes	—
194	#117	—	2	1	no	—
195	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
196	C₂×C₂²⋊C₄	—	2	1	no	—
197	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
198	#106	C₂²×C₃²	1	4	yes	complemented
199	C₄⋊C₈	C₂²×C₃²	1	2	yes	complemented
200	#103	C₂²×C₃²	1	4	yes	complemented
201	#102	C₂²×C₃²	1	4	yes	—
202	C₂²⋊C₈	C₂²×C₃²	1	2	yes	—
203	C₄×C₈	C₂²×C₃²	1	2	yes	complemented
204	C₂³×C₃	—	2	16	no	—
205	C₂³×C₃	—	2	8	no	—
206	C₂³×C₃	—	4	8	no	—
207	C₂³×C₃	—	4	8	no	—
208	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
209	C₃×Q₈	—	2	16	no	—
210	C₃×Q₈	—	4	8	no	—
211	C₃×D₄	—	2	16	no	—
212	C₃×D₄	—	2	8	no	—
213	C₃×D₄	C₃×#41	1	16	yes	—
214	C₂×C₃×C₄	—	2	8	no	—
215	C₂×C₃×C₄	—	2	8	no	—
216	C₂×C₃×C₄	—	2	8	no	—
217	C₂×C₃×C₄	—	2	8	no	—
218	C₂×C₃×C₄	—	4	4	no	—
219	C₂×C₃×C₄	—	4	8	no	—
220	C₂×C₃×C₄	—	4	16	no	—
221	C₂×C₃×C₄	—	4	16	no	—
222	C₂×C₃×C₄	C₃×SD₁₆	1	16	yes	complemented
223	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
224	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
225	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
226	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
227	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
228	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
229	C₃×C₈	—	2	16	no	—
230	C₂×C₃²	—	2	2	no	—
231	C₂×C₃²	—	4	4	no	—
232	C₂×C₃²	#525	1	1	yes	characteristic
233	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
234	C₂×C₃²	#575	1	1	yes	characteristic
235	C₂⁴	—	2	1	no	—
236	C₂×Q₈	—	2	1	no	—
237	C₂×Q₈	C₂³×C₃²	1	2	yes	—
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	—	2	1	no	—
240	C₂×D₄	C₂³×C₃²	1	2	yes	—
241	C₂²×C₄	—	2	1	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	4	4	no	—
245	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
246	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
247	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
248	SD₁₆	—	2	8	no	—
249	C₂×C₈	C₂³×C₃²	1	4	yes	—
250	C₄⋊C₄	—	2	1	no	—
251	C₄⋊C₄	—	2	1	no	—
252	C₄⋊C₄	—	2	1	no	—
253	C₄⋊C₄	—	2	1	no	—
254	C₄⋊C₄	—	2	2	no	—
255	C₄⋊C₄	—	2	2	no	—
256	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
257	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
258	C₂²⋊C₄	—	2	2	no	—
259	C₂²⋊C₄	—	2	2	no	—
260	C₂²⋊C₄	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	C₃²×D₄	1	1	yes	characteristic
263	C₄²	C₃²×D₄	1	1	yes	characteristic
264	C₄²	C₂³×C₃²	1	1	yes	characteristic
265	C₄²	C₂³×C₃²	1	1	yes	characteristic
266	C₂²×C₃	—	2	4	no	—
267	C₂²×C₃	—	2	4	no	—
268	C₂²×C₃	—	2	16	no	—
269	C₂²×C₃	—	4	32	no	—
270	C₂²×C₃	—	4	8	no	—
271	C₂²×C₃	—	4	8	no	—
272	C₂²×C₃	C₂×C₃×SD₁₆	1	8	yes	—
273	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
274	C₃×C₄	—	2	4	no	—
275	C₃×C₄	—	2	4	no	—
276	C₃×C₄	—	2	4	no	—
277	C₃×C₄	—	4	8	no	—
278	C₃×C₄	—	4	8	no	—
279	C₃×C₄	—	4	8	no	—
280	C₃×C₄	C₂×C₃×SD₁₆	1	8	yes	—
281	C₃×C₄	C₂×C₃×SD₁₆	1	8	yes	—
282	C₃×C₄	C₂×C₃×#41	1	8	yes	—
283	C₃²	#3101	1	1	yes	characteristic, direct product factor, Sylow
284	C₂³	—	2	4	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	4	2	no	—
287	C₂³	—	4	2	no	—
288	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
289	Q₈	—	2	4	no	—
290	Q₈	—	4	2	no	—
291	D₄	—	2	4	no	—
292	D₄	—	2	2	no	—
293	D₄	C₃²×#41	1	4	yes	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	C₃²×SD₁₆	1	4	yes	complemented
303	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
304	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
305	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
306	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
307	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
308	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
309	C₈	—	2	4	no	—
310	C₂×C₃	—	2	8	no	—
311	C₂×C₃	—	4	16	no	—
312	C₂×C₃	C₃×#525	1	4	yes	—
313	C₂×C₃	C₂²×C₃×SD₁₆	1	4	yes	—
314	C₂×C₃	C₃×#575	1	4	yes	—
315	C₂²	—	2	1	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	4	no	—
318	C₂²	—	4	8	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	C₂×C₃²×SD₁₆	1	2	yes	—
322	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
323	C₄	—	2	1	no	—
324	C₄	—	2	1	no	—
325	C₄	—	2	1	no	—
326	C₄	—	4	2	no	—
327	C₄	—	4	2	no	—
328	C₄	—	4	2	no	—
329	C₄	C₂×C₃²×SD₁₆	1	2	yes	—
330	C₄	C₂×C₃²×SD₁₆	1	2	yes	—
331	C₄	C₂×C₃²×#41	1	2	yes	—
332	C₃	C₃×#3101	1	4	yes	direct product factor
333	C₂	—	2	2	no	—
334	C₂	—	4	4	no	—
335	C₂	C₃²×#525	1	1	yes	characteristic
336	C₂	C₂²×C₃²×SD₁₆	1	1	yes	characteristic
337	C₂	C₃²×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂²×C₃²×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×#533	C₂	semidirect
3. C₃²×#483	C₂	semidirect
4. C₃²×#476	C₂	semidirect
5. C₃²×#461	C₂	semidirect
7. C₃²×C₄×SD₁₆	C₂	semidirect
8. C₃²×#431	C₂	semidirect
9. C₃×#3101	C₃	direct (N × H)
13. C₃²×C₄⋊Q₈	C₂²	semidirect
14. C₃²×C₄⋊Q₈	C₂²	semidirect
19. C₃²×C₄×Q₈	C₂²	semidirect
28. C₃²×#106	C₂²	semidirect
29. C₃²×C₄⋊C₈	C₂²	semidirect
30. C₃²×#103	C₂²	semidirect
33. C₃²×C₄×C₈	C₂²	semidirect
34. C₃×#533	C₂×C₃	semidirect
36. C₃×#483	C₂×C₃	semidirect
37. C₃×#476	C₂×C₃	semidirect
38. C₃×#461	C₂×C₃	semidirect
40. C₃×C₄×SD₁₆	C₂×C₃	semidirect
41. C₃×#431	C₂×C₃	semidirect
73. #3101	C₃²	direct (N × H)
77. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
78. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
83. C₃×C₄×Q₈	C₂²×C₃	semidirect
92. C₃×#106	C₂²×C₃	semidirect
93. C₃×C₄⋊C₈	C₂²×C₃	semidirect
94. C₃×#103	C₂²×C₃	semidirect
97. C₃×C₄×C₈	C₂²×C₃	semidirect
116. C₂×C₃²×C₄	SD₁₆	semidirect
124. #533	C₂×C₃²	semidirect
126. #483	C₂×C₃²	semidirect
127. #476	C₂×C₃²	semidirect
128. #461	C₂×C₃²	semidirect
130. C₄×SD₁₆	C₂×C₃²	semidirect
131. #431	C₂×C₃²	semidirect
183. C₄⋊Q₈	C₂²×C₃²	semidirect
184. C₄⋊Q₈	C₂²×C₃²	semidirect
189. C₄×Q₈	C₂²×C₃²	semidirect
198. #106	C₂²×C₃²	semidirect
199. C₄⋊C₈	C₂²×C₃²	semidirect
200. #103	C₂²×C₃²	semidirect
203. C₄×C₈	C₂²×C₃²	semidirect
222. C₂×C₃×C₄	C₃×SD₁₆	semidirect
283. C₃²	#3101	direct (N × H)
302. C₂×C₄	C₃²×SD₁₆	semidirect
332. C₃	C₃×#3101	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#533	2
C₂×C₃²×C₄×D₄	2
C₃²×#483	2
C₃²×#476	2
C₃²×#461	2
C₃²×#450	2
C₃²×C₄×SD₁₆	2
C₃²×#431	2
C₃×#3101	3

Subgroups — C32×#3101 #11770150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3101 #11770150