Subgroups — C₃²×#3081 #11770130

Order 1152.

1194 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	C₃²×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#518	C₂	1	1	yes	maximal, characteristic
3	C₃²×#478	C₂	1	2	yes	maximal, complemented
4	C₃²×#478	C₂	1	2	yes	maximal, complemented
5	C₃²×#476	C₂	1	2	yes	maximal, complemented
6	C₃²×#474	C₂	1	2	yes	maximal, complemented
7	C₃²×#428	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#427	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#418	C₂	1	1	yes	maximal, characteristic
11	C₂×C₃²×#102	C₂	1	1	yes	maximal, characteristic
12	C₃×#3081	C₃	1	4	yes	maximal, direct product factor
13	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
16	C₃²×C₄⋊Q₈	—	2	1	no	—
17	C₃²×C₄⋊Q₈	C₂²	1	2	yes	complemented
18	C₃²×#125	—	2	1	no	—
19	C₃²×#125	C₂²	1	2	yes	complemented
20	C₃²×C₂²⋊Q₈	—	2	2	no	—
21	C₃²×C₄×D₄	—	2	1	no	—
22	C₃²×C₄×D₄	—	2	1	no	—
23	C₃²×C₄×D₄	C₂²	1	2	yes	—
24	C₃²×C₄×D₄	C₂²	1	2	yes	—
25	C₃²×#117	C₂²	1	1	yes	characteristic
26	C₃²×#117	C₂²	1	1	yes	characteristic
27	C₃²×#117	C₂²	1	1	yes	characteristic
28	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃²×C₂²⋊C₄	—	2	2	no	—
30	C₃²×#107	C₂²	1	1	yes	characteristic, complemented
31	C₃²×#107	C₂²	1	2	yes	complemented
32	C₃²×#107	C₂²	1	1	yes	characteristic, complemented
33	C₃²×#106	C₂²	1	1	yes	characteristic, complemented
34	C₃²×#106	C₂²	1	2	yes	complemented
35	C₃²×#106	C₂²	1	1	yes	characteristic, complemented
36	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
37	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
38	C₃²×#102	C₂²	1	2	yes	—
39	C₃²×#102	C₂²	1	2	yes	—
40	C₃²×#102	C₂²	1	2	yes	—
41	C₃²×#102	C₂²	1	2	yes	—
42	C₃×#544	C₂×C₃	1	4	yes	complemented
43	C₃×#518	C₂×C₃	1	4	yes	—
44	C₃×#478	C₂×C₃	1	8	yes	complemented
45	C₃×#478	C₂×C₃	1	8	yes	complemented
46	C₃×#476	C₂×C₃	1	8	yes	complemented
47	C₃×#474	C₂×C₃	1	8	yes	complemented
48	C₃×#428	C₂×C₃	1	4	yes	complemented
49	C₃×#427	C₂×C₃	1	4	yes	complemented
50	C₃×#424	C₂×C₃	1	4	yes	complemented
51	C₃×#418	C₂×C₃	1	4	yes	—
52	C₂×C₃×#102	C₂×C₃	1	4	yes	—
53	C₂⁴×C₃²	—	2	1	no	—
54	C₂×C₃²×Q₈	—	2	2	no	—
55	C₂×C₃²×D₄	—	2	1	no	—
56	C₂×C₃²×D₄	—	2	2	no	—
57	C₂×C₃²×D₄	Q₈	1	4	yes	complemented
58	C₂×C₃²×D₄	C₂³	1	2	yes	—
59	C₂²×C₃²×C₄	—	2	1	no	—
60	C₂²×C₃²×C₄	—	2	2	no	—
61	C₂²×C₃²×C₄	—	2	2	no	—
62	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
63	C₃²×M₁₆	—	2	2	no	—
64	C₂×C₃²×C₈	—	2	2	no	—
65	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₃²×C₈	C₂³	1	2	yes	—
68	C₃²×C₄⋊C₄	—	2	1	no	—
69	C₃²×C₄⋊C₄	—	2	2	no	—
70	C₃²×C₄⋊C₄	—	2	2	no	—
71	C₃²×C₄⋊C₄	—	2	2	no	—
72	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
75	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₃²×C₂²⋊C₄	—	2	1	no	—
80	C₃²×C₂²⋊C₄	—	2	1	no	—
81	C₃²×C₂²⋊C₄	—	2	2	no	—
82	C₃²×C₂²⋊C₄	—	2	2	no	—
83	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
84	C₃²×C₄²	—	2	1	no	—
85	C₃²×C₄²	—	2	1	no	—
86	C₃²×C₄²	C₂³	1	2	yes	—
87	#3081	C₃²	1	1	yes	characteristic, direct product factor, Sylow
88	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
89	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
90	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
91	C₃×C₄⋊Q₈	—	2	4	no	—
92	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
93	C₃×#125	—	2	4	no	—
94	C₃×#125	C₂²×C₃	1	8	yes	complemented
95	C₃×C₂²⋊Q₈	—	2	8	no	—
96	C₃×C₄×D₄	—	2	4	no	—
97	C₃×C₄×D₄	—	2	4	no	—
98	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
99	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
100	C₃×#117	C₂²×C₃	1	4	yes	—
101	C₃×#117	C₂²×C₃	1	4	yes	—
102	C₃×#117	C₂²×C₃	1	4	yes	—
103	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
104	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
105	C₃×#107	C₂²×C₃	1	4	yes	complemented
106	C₃×#107	C₂²×C₃	1	4	yes	complemented
107	C₃×#107	C₂²×C₃	1	8	yes	complemented
108	C₃×#106	C₂²×C₃	1	4	yes	complemented
109	C₃×#106	C₂²×C₃	1	4	yes	complemented
110	C₃×#106	C₂²×C₃	1	8	yes	complemented
111	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	complemented
112	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	complemented
113	C₃×#102	C₂²×C₃	1	8	yes	—
114	C₃×#102	C₂²×C₃	1	8	yes	—
115	C₃×#102	C₂²×C₃	1	8	yes	—
116	C₃×#102	C₂²×C₃	1	8	yes	—
117	C₂³×C₃²	—	2	2	no	—
118	C₂³×C₃²	—	2	4	no	—
119	C₂³×C₃²	—	8	1	no	—
120	C₂³×C₃²	—	8	1	no	—
121	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
122	C₃²×Q₈	—	8	2	no	—
123	C₃²×D₄	—	2	4	no	—
124	C₃²×D₄	—	2	2	no	—
125	C₃²×D₄	C₂×Q₈	1	4	yes	—
126	C₂×C₃²×C₄	—	2	1	no	—
127	C₂×C₃²×C₄	—	2	1	no	—
128	C₂×C₃²×C₄	—	2	1	no	—
129	C₂×C₃²×C₄	—	2	1	no	—
130	C₂×C₃²×C₄	—	2	2	no	—
131	C₂×C₃²×C₄	—	8	2	no	—
132	C₂×C₃²×C₄	—	8	2	no	—
133	C₂×C₃²×C₄	—	8	1	no	—
134	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
135	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
136	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
138	C₂×C₃²×C₄	#41	1	2	yes	—
139	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
140	C₃²×C₈	—	2	1	no	—
141	C₃²×C₈	—	2	1	no	—
142	C₃²×C₈	—	2	2	no	—
143	#544	C₂×C₃²	1	1	yes	characteristic, complemented
144	#518	C₂×C₃²	1	1	yes	characteristic
145	#478	C₂×C₃²	1	2	yes	complemented
146	#478	C₂×C₃²	1	2	yes	complemented
147	#476	C₂×C₃²	1	2	yes	complemented
148	#474	C₂×C₃²	1	2	yes	complemented
149	#428	C₂×C₃²	1	1	yes	characteristic, complemented
150	#427	C₂×C₃²	1	1	yes	characteristic, complemented
151	#424	C₂×C₃²	1	1	yes	characteristic, complemented
152	#418	C₂×C₃²	1	1	yes	characteristic
153	C₂×#102	C₂×C₃²	1	1	yes	characteristic
154	C₂⁴×C₃	—	2	4	no	—
155	C₂×C₃×Q₈	—	2	8	no	—
156	C₂×C₃×D₄	—	2	4	no	—
157	C₂×C₃×D₄	—	2	8	no	—
158	C₂×C₃×D₄	C₃×Q₈	1	16	yes	complemented
159	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	—	2	8	no	—
162	C₂²×C₃×C₄	—	2	8	no	—
163	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
164	C₃×M₁₆	—	2	8	no	—
165	C₂×C₃×C₈	—	2	8	no	—
166	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
167	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
168	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
169	C₃×C₄⋊C₄	—	2	4	no	—
170	C₃×C₄⋊C₄	—	2	8	no	—
171	C₃×C₄⋊C₄	—	2	8	no	—
172	C₃×C₄⋊C₄	—	2	8	no	—
173	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
174	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
175	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
176	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
177	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
178	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
179	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
180	C₃×C₂²⋊C₄	—	2	4	no	—
181	C₃×C₂²⋊C₄	—	2	4	no	—
182	C₃×C₂²⋊C₄	—	2	8	no	—
183	C₃×C₂²⋊C₄	—	2	8	no	—
184	C₃×C₂²⋊C₄	C₃×D₄	1	8	yes	—
185	C₃×C₄²	—	2	4	no	—
186	C₃×C₄²	—	2	4	no	—
187	C₃×C₄²	C₂³×C₃	1	8	yes	—
188	C₂²×C₃²	—	2	1	no	—
189	C₂²×C₃²	—	2	1	no	—
190	C₂²×C₃²	—	2	4	no	—
191	C₂²×C₃²	—	4	2	no	—
192	C₂²×C₃²	—	4	2	no	—
193	C₂²×C₃²	—	8	4	no	—
194	C₂²×C₃²	C₂²⋊Q₈	1	2	yes	—
195	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
196	C₃²×C₄	—	2	2	no	—
197	C₃²×C₄	—	2	2	no	—
198	C₃²×C₄	—	4	1	no	—
199	C₃²×C₄	—	4	2	no	—
200	C₃²×C₄	—	4	1	no	—
201	C₃²×C₄	—	4	1	no	—
202	C₃²×C₄	—	4	1	no	—
203	C₃²×C₄	C₂²⋊Q₈	1	2	yes	—
204	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
205	C₃²×C₄	C₂×#41	1	1	yes	characteristic
206	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
207	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
208	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
209	C₄⋊Q₈	—	2	1	no	—
210	C₄⋊Q₈	C₂²×C₃²	1	2	yes	complemented
211	#125	—	2	1	no	—
212	#125	C₂²×C₃²	1	2	yes	complemented
213	C₂²⋊Q₈	—	2	2	no	—
214	C₄×D₄	—	2	1	no	—
215	C₄×D₄	—	2	1	no	—
216	C₄×D₄	C₂²×C₃²	1	2	yes	—
217	C₄×D₄	C₂²×C₃²	1	2	yes	—
218	#117	C₂²×C₃²	1	1	yes	characteristic
219	#117	C₂²×C₃²	1	1	yes	characteristic
220	#117	C₂²×C₃²	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	—	2	2	no	—
223	#107	C₂²×C₃²	1	1	yes	characteristic, complemented
224	#107	C₂²×C₃²	1	1	yes	characteristic, complemented
225	#107	C₂²×C₃²	1	2	yes	complemented
226	#106	C₂²×C₃²	1	1	yes	characteristic, complemented
227	#106	C₂²×C₃²	1	1	yes	characteristic, complemented
228	#106	C₂²×C₃²	1	2	yes	complemented
229	C₄⋊C₈	C₂²×C₃²	1	2	yes	complemented
230	C₄⋊C₈	C₂²×C₃²	1	2	yes	complemented
231	#102	C₂²×C₃²	1	2	yes	—
232	#102	C₂²×C₃²	1	2	yes	—
233	#102	C₂²×C₃²	1	2	yes	—
234	#102	C₂²×C₃²	1	2	yes	—
235	C₂³×C₃	—	2	8	no	—
236	C₂³×C₃	—	2	16	no	—
237	C₂³×C₃	—	8	4	no	—
238	C₂³×C₃	—	8	4	no	—
239	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
240	C₃×Q₈	—	8	8	no	—
241	C₃×D₄	—	2	16	no	—
242	C₃×D₄	—	2	8	no	—
243	C₃×D₄	C₂×C₃×Q₈	1	16	yes	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	8	no	—
249	C₂×C₃×C₄	—	8	8	no	—
250	C₂×C₃×C₄	—	8	8	no	—
251	C₂×C₃×C₄	—	8	4	no	—
252	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
253	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
254	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
255	C₂×C₃×C₄	C₂×C₃×Q₈	1	8	yes	—
256	C₂×C₃×C₄	C₃×#41	1	8	yes	—
257	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
258	C₃×C₈	—	2	4	no	—
259	C₃×C₈	—	2	4	no	—
260	C₃×C₈	—	2	8	no	—
261	C₂×C₃²	—	2	2	no	—
262	C₂×C₃²	—	4	4	no	—
263	C₂×C₃²	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₃²	#576	1	1	yes	characteristic
265	C₂×C₃²	#577	1	1	yes	characteristic
266	C₂⁴	—	2	1	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	C₃²×Q₈	1	4	yes	complemented
271	C₂×D₄	C₂³×C₃²	1	2	yes	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
276	M₁₆	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
279	C₂×C₈	C₂³×C₃²	1	2	yes	—
280	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
286	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
287	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
288	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
289	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
290	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
291	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	C₃²×D₄	1	2	yes	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	C₂³×C₃²	1	2	yes	—
300	C₂²×C₃	—	2	4	no	—
301	C₂²×C₃	—	2	4	no	—
302	C₂²×C₃	—	2	16	no	—
303	C₂²×C₃	—	4	8	no	—
304	C₂²×C₃	—	4	8	no	—
305	C₂²×C₃	—	8	16	no	—
306	C₂²×C₃	C₃×C₂²⋊Q₈	1	8	yes	—
307	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
308	C₃×C₄	—	2	8	no	—
309	C₃×C₄	—	2	8	no	—
310	C₃×C₄	—	4	4	no	—
311	C₃×C₄	—	4	8	no	—
312	C₃×C₄	—	4	4	no	—
313	C₃×C₄	—	4	4	no	—
314	C₃×C₄	—	4	4	no	—
315	C₃×C₄	C₃×C₂²⋊Q₈	1	8	yes	—
316	C₃×C₄	C₂²×C₃×Q₈	1	4	yes	—
317	C₃×C₄	C₂×C₃×#41	1	4	yes	—
318	C₃²	#3081	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	2	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	8	1	no	—
322	C₂³	—	8	1	no	—
323	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
324	Q₈	—	8	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	4	no	—
327	D₄	C₂×C₃²×Q₈	1	4	yes	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
337	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
338	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
339	C₂×C₄	C₂×C₃²×Q₈	1	2	yes	—
340	C₂×C₄	C₃²×#41	1	2	yes	—
341	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	2	2	no	—
345	C₂×C₃	—	2	8	no	—
346	C₂×C₃	—	4	16	no	—
347	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	4	yes	—
348	C₂×C₃	C₃×#576	1	4	yes	—
349	C₂×C₃	C₃×#577	1	4	yes	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	8	4	no	—
356	C₂²	C₃²×C₂²⋊Q₈	1	2	yes	—
357	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	C₃²×C₂²⋊Q₈	1	2	yes	—
366	C₄	C₂²×C₃²×Q₈	1	1	yes	characteristic
367	C₄	C₂×C₃²×#41	1	1	yes	characteristic
368	C₃	C₃×#3081	1	4	yes	direct product factor
369	C₂	—	2	2	no	—
370	C₂	—	4	4	no	—
371	C₂	C₂×C₃²×C₂²⋊Q₈	1	1	yes	characteristic
372	C₂	C₃²×#576	1	1	yes	characteristic
373	C₂	C₃²×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
prime radical	C₂²×C₃²×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×#544	C₂	semidirect
3. C₃²×#478	C₂	semidirect
4. C₃²×#478	C₂	semidirect
5. C₃²×#476	C₂	semidirect
6. C₃²×#474	C₂	semidirect
7. C₃²×#428	C₂	semidirect
8. C₃²×#427	C₂	semidirect
9. C₃²×#424	C₂	semidirect
12. C₃×#3081	C₃	direct (N × H)
17. C₃²×C₄⋊Q₈	C₂²	semidirect
19. C₃²×#125	C₂²	semidirect
30. C₃²×#107	C₂²	semidirect
31. C₃²×#107	C₂²	semidirect
32. C₃²×#107	C₂²	semidirect
33. C₃²×#106	C₂²	semidirect
34. C₃²×#106	C₂²	semidirect
35. C₃²×#106	C₂²	semidirect
36. C₃²×C₄⋊C₈	C₂²	semidirect
37. C₃²×C₄⋊C₈	C₂²	semidirect
42. C₃×#544	C₂×C₃	semidirect
44. C₃×#478	C₂×C₃	semidirect
45. C₃×#478	C₂×C₃	semidirect
46. C₃×#476	C₂×C₃	semidirect
47. C₃×#474	C₂×C₃	semidirect
48. C₃×#428	C₂×C₃	semidirect
49. C₃×#427	C₂×C₃	semidirect
50. C₃×#424	C₂×C₃	semidirect
57. C₂×C₃²×D₄	Q₈	semidirect
87. #3081	C₃²	direct (N × H)
92. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
94. C₃×#125	C₂²×C₃	semidirect
105. C₃×#107	C₂²×C₃	semidirect
106. C₃×#107	C₂²×C₃	semidirect
107. C₃×#107	C₂²×C₃	semidirect
108. C₃×#106	C₂²×C₃	semidirect
109. C₃×#106	C₂²×C₃	semidirect
110. C₃×#106	C₂²×C₃	semidirect
111. C₃×C₄⋊C₈	C₂²×C₃	semidirect
112. C₃×C₄⋊C₈	C₂²×C₃	semidirect
143. #544	C₂×C₃²	semidirect
145. #478	C₂×C₃²	semidirect
146. #478	C₂×C₃²	semidirect
147. #476	C₂×C₃²	semidirect
148. #474	C₂×C₃²	semidirect
149. #428	C₂×C₃²	semidirect
150. #427	C₂×C₃²	semidirect
151. #424	C₂×C₃²	semidirect
158. C₂×C₃×D₄	C₃×Q₈	semidirect
210. C₄⋊Q₈	C₂²×C₃²	semidirect
212. #125	C₂²×C₃²	semidirect
223. #107	C₂²×C₃²	semidirect
224. #107	C₂²×C₃²	semidirect
225. #107	C₂²×C₃²	semidirect
226. #106	C₂²×C₃²	semidirect
227. #106	C₂²×C₃²	semidirect
228. #106	C₂²×C₃²	semidirect
229. C₄⋊C₈	C₂²×C₃²	semidirect
230. C₄⋊C₈	C₂²×C₃²	semidirect
270. C₂×D₄	C₃²×Q₈	semidirect
318. C₃²	#3081	direct (N × H)
368. C₃	C₃×#3081	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×#544	2
C₃²×#518	2
C₃²×#478	2
C₃²×#476	2
C₃²×#474	2
C₃²×#428	2
C₃²×#427	2
C₃²×#424	2
C₃²×#418	2
C₂×C₃²×#102	2
C₃×#3081	3

Subgroups — C32×#3081 #11770130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3081 #11770130