Subgroups — C₃²×#3057 #11770106

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#535	C₂	1	1	yes	maximal, characteristic
5	C₃²×#468	C₂	1	4	yes	maximal, complemented
6	C₃²×#465	C₂	1	4	yes	maximal, complemented
7	C₃²×#427	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#419	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3057	C₃	1	4	yes	maximal, direct product factor
11	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₃²×SD₁₆	—	2	4	no	—
15	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
17	C₃²×#131	—	2	4	no	—
18	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃²×M₁₆	C₂²	1	2	yes	complemented
20	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
21	C₂²×C₃²×C₈	C₂²	1	2	yes	complemented
22	C₃²×C₄⋊Q₈	—	2	1	no	—
23	C₃²×#127	—	2	1	no	—
24	C₃²×#124	—	2	1	no	—
25	C₃²×#124	—	2	1	no	—
26	C₃²×#123	—	2	2	no	—
27	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₃²×#121	C₂²	1	4	yes	—
29	C₃²×#120	—	2	2	no	—
30	C₃²×#117	C₂²	1	1	yes	characteristic
31	C₃²×#117	C₂²	1	1	yes	characteristic
32	C₃²×#107	C₂²	1	2	yes	complemented
33	C₃²×#106	C₂²	1	2	yes	complemented
34	C₃²×#103	C₂²	1	4	yes	complemented
35	C₃²×#102	C₂²	1	4	yes	—
36	C₂²×C₃×SD₁₆	C₂×C₃	1	4	yes	complemented
37	C₂×C₃×#131	C₂×C₃	1	4	yes	complemented
38	C₃×#536	C₂×C₃	1	4	yes	complemented
39	C₃×#535	C₂×C₃	1	4	yes	—
40	C₃×#468	C₂×C₃	1	16	yes	complemented
41	C₃×#465	C₂×C₃	1	16	yes	complemented
42	C₃×#427	C₂×C₃	1	4	yes	complemented
43	C₃×#419	C₂×C₃	1	4	yes	complemented
44	C₃×#418	C₂×C₃	1	4	yes	complemented
45	C₂⁴×C₃²	—	2	1	no	—
46	C₃²×#41	—	2	2	no	—
47	C₃²×#41	—	2	2	no	—
48	C₂×C₃²×Q₈	—	2	1	no	—
49	C₂×C₃²×Q₈	—	2	2	no	—
50	C₂×C₃²×Q₈	—	2	2	no	—
51	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
52	C₂×C₃²×Q₈	C₂³	1	2	yes	—
53	C₂×C₃²×D₄	—	2	4	no	—
54	C₂×C₃²×D₄	—	2	2	no	—
55	C₂×C₃²×D₄	—	2	1	no	—
56	C₂×C₃²×D₄	—	2	2	no	—
57	C₂×C₃²×D₄	D₄	1	2	yes	—
58	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
59	C₂×C₃²×D₄	C₂³	1	2	yes	—
60	C₂²×C₃²×C₄	—	2	1	no	—
61	C₂²×C₃²×C₄	C₂³	1	2	yes	—
62	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
63	C₃²×SD₁₆	—	2	4	no	—
64	C₃²×SD₁₆	—	2	4	no	—
65	C₃²×M₁₆	—	2	2	no	—
66	C₃²×M₁₆	—	2	4	no	—
67	C₂×C₃²×C₈	—	2	4	no	—
68	C₂×C₃²×C₈	D₄	1	4	yes	complemented
69	C₂×C₃²×C₈	C₂³	1	2	yes	—
70	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
72	C₃²×C₄⋊C₄	—	2	4	no	—
73	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
74	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
75	C₃²×C₂²⋊C₄	—	2	1	no	—
76	C₃²×C₂²⋊C₄	—	2	1	no	—
77	C₃²×C₂²⋊C₄	—	2	4	no	—
78	C₃²×C₂²⋊C₄	—	2	4	no	—
79	C₃²×C₄²	—	2	1	no	—
80	C₃²×C₄²	—	2	1	no	—
81	#3057	C₃²	1	1	yes	characteristic, direct product factor, Sylow
82	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
83	C₂²×C₃×Q₈	C₂²×C₃	1	4	yes	—
84	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
85	C₂×C₃×SD₁₆	—	2	16	no	—
86	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
87	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
88	C₃×#131	—	2	16	no	—
89	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
90	C₂×C₃×M₁₆	C₂²×C₃	1	8	yes	complemented
91	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
92	C₂²×C₃×C₈	C₂²×C₃	1	8	yes	complemented
93	C₃×C₄⋊Q₈	—	2	4	no	—
94	C₃×#127	—	2	4	no	—
95	C₃×#124	—	2	4	no	—
96	C₃×#124	—	2	4	no	—
97	C₃×#123	—	2	8	no	—
98	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	complemented
99	C₃×#121	C₂²×C₃	1	16	yes	—
100	C₃×#120	—	2	8	no	—
101	C₃×#117	C₂²×C₃	1	4	yes	—
102	C₃×#117	C₂²×C₃	1	4	yes	—
103	C₃×#107	C₂²×C₃	1	8	yes	complemented
104	C₃×#106	C₂²×C₃	1	8	yes	complemented
105	C₃×#103	C₂²×C₃	1	16	yes	complemented
106	C₃×#102	C₂²×C₃	1	16	yes	—
107	C₂³×C₃²	—	2	2	no	—
108	C₂³×C₃²	—	4	2	no	—
109	C₂³×C₃²	—	8	2	no	—
110	C₂³×C₃²	C₂×D₄	1	2	yes	—
111	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
112	C₃²×Q₈	—	2	2	no	—
113	C₃²×Q₈	—	2	2	no	—
114	C₃²×Q₈	—	2	2	no	—
115	C₃²×Q₈	—	4	2	no	—
116	C₃²×D₄	—	2	4	no	—
117	C₃²×D₄	—	2	2	no	—
118	C₃²×D₄	—	2	2	no	—
119	C₃²×D₄	—	2	2	no	—
120	C₃²×D₄	—	4	2	no	—
121	C₃²×D₄	—	8	4	no	—
122	C₂×C₃²×C₄	—	2	2	no	—
123	C₂×C₃²×C₄	—	2	2	no	—
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	—	4	2	no	—
128	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
129	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
131	C₂×C₃²×C₄	#41	1	2	yes	—
132	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
133	C₃²×C₈	—	2	2	no	—
134	C₃²×C₈	C₂×D₄	1	2	yes	—
135	C₃²×C₈	C₂×D₄	1	2	yes	—
136	C₂²×SD₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
137	C₂×#131	C₂×C₃²	1	1	yes	characteristic, complemented
138	#536	C₂×C₃²	1	1	yes	characteristic, complemented
139	#535	C₂×C₃²	1	1	yes	characteristic
140	#468	C₂×C₃²	1	4	yes	complemented
141	#465	C₂×C₃²	1	4	yes	complemented
142	#427	C₂×C₃²	1	1	yes	characteristic, complemented
143	#419	C₂×C₃²	1	1	yes	characteristic, complemented
144	#418	C₂×C₃²	1	1	yes	characteristic, complemented
145	C₂⁴×C₃	—	2	4	no	—
146	C₃×#41	—	2	8	no	—
147	C₃×#41	—	2	8	no	—
148	C₂×C₃×Q₈	—	2	4	no	—
149	C₂×C₃×Q₈	—	2	8	no	—
150	C₂×C₃×Q₈	—	2	8	no	—
151	C₂×C₃×Q₈	C₃×D₄	1	4	yes	—
152	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
153	C₂×C₃×D₄	—	2	16	no	—
154	C₂×C₃×D₄	—	2	8	no	—
155	C₂×C₃×D₄	—	2	4	no	—
156	C₂×C₃×D₄	—	2	8	no	—
157	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
158	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
159	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
162	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
163	C₃×SD₁₆	—	2	16	no	—
164	C₃×SD₁₆	—	2	16	no	—
165	C₃×M₁₆	—	2	8	no	—
166	C₃×M₁₆	—	2	16	no	—
167	C₂×C₃×C₈	—	2	16	no	—
168	C₂×C₃×C₈	C₃×D₄	1	16	yes	complemented
169	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
170	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
171	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
172	C₃×C₄⋊C₄	—	2	16	no	—
173	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
174	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
175	C₃×C₂²⋊C₄	—	2	4	no	—
176	C₃×C₂²⋊C₄	—	2	4	no	—
177	C₃×C₂²⋊C₄	—	2	16	no	—
178	C₃×C₂²⋊C₄	—	2	16	no	—
179	C₃×C₄²	—	2	4	no	—
180	C₃×C₄²	—	2	4	no	—
181	C₂²×C₃²	—	2	2	no	—
182	C₂²×C₃²	—	2	2	no	—
183	C₂²×C₃²	—	2	4	no	—
184	C₂²×C₃²	—	4	2	no	—
185	C₂²×C₃²	—	4	4	no	—
186	C₂²×C₃²	—	8	4	no	—
187	C₂²×C₃²	#121	1	2	yes	—
188	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
189	C₃²×C₄	—	2	2	no	—
190	C₃²×C₄	—	4	2	no	—
191	C₃²×C₄	—	4	2	no	—
192	C₃²×C₄	—	4	2	no	—
193	C₃²×C₄	#121	1	2	yes	—
194	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
195	C₃²×C₄	C₂×#41	1	1	yes	characteristic
196	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
197	C₂²×Q₈	C₂²×C₃²	1	1	yes	characteristic
198	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
199	C₂×SD₁₆	—	2	4	no	—
200	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
201	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
202	#131	—	2	4	no	—
203	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
204	C₂×M₁₆	C₂²×C₃²	1	2	yes	complemented
205	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
206	C₂²×C₈	C₂²×C₃²	1	2	yes	complemented
207	C₄⋊Q₈	—	2	1	no	—
208	#127	—	2	1	no	—
209	#124	—	2	1	no	—
210	#124	—	2	1	no	—
211	#123	—	2	2	no	—
212	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	complemented
213	#121	C₂²×C₃²	1	4	yes	—
214	#120	—	2	2	no	—
215	#117	C₂²×C₃²	1	1	yes	characteristic
216	#117	C₂²×C₃²	1	1	yes	characteristic
217	#107	C₂²×C₃²	1	2	yes	complemented
218	#106	C₂²×C₃²	1	2	yes	complemented
219	#103	C₂²×C₃²	1	4	yes	complemented
220	#102	C₂²×C₃²	1	4	yes	—
221	C₂³×C₃	—	2	8	no	—
222	C₂³×C₃	—	4	8	no	—
223	C₂³×C₃	—	8	8	no	—
224	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
225	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
226	C₃×Q₈	—	2	8	no	—
227	C₃×Q₈	—	2	8	no	—
228	C₃×Q₈	—	2	8	no	—
229	C₃×Q₈	—	4	8	no	—
230	C₃×D₄	—	2	16	no	—
231	C₃×D₄	—	2	8	no	—
232	C₃×D₄	—	2	8	no	—
233	C₃×D₄	—	2	8	no	—
234	C₃×D₄	—	4	8	no	—
235	C₃×D₄	—	8	16	no	—
236	C₂×C₃×C₄	—	2	8	no	—
237	C₂×C₃×C₄	—	2	8	no	—
238	C₂×C₃×C₄	—	2	8	no	—
239	C₂×C₃×C₄	—	2	8	no	—
240	C₂×C₃×C₄	—	2	8	no	—
241	C₂×C₃×C₄	—	4	8	no	—
242	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
243	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
244	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
245	C₂×C₃×C₄	C₃×#41	1	8	yes	—
246	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
247	C₃×C₈	—	2	8	no	—
248	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
249	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
250	C₂×C₃²	—	2	2	no	—
251	C₂×C₃²	—	4	2	no	—
252	C₂×C₃²	—	8	2	no	—
253	C₂×C₃²	C₂×#121	1	1	yes	characteristic
254	C₂×C₃²	#577	1	2	yes	—
255	C₂⁴	—	2	1	no	—
256	#41	—	2	2	no	—
257	#41	—	2	2	no	—
258	C₂×Q₈	—	2	1	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	C₃²×D₄	1	1	yes	characteristic
262	C₂×Q₈	C₂³×C₃²	1	2	yes	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	C₃²×D₄	1	2	yes	—
268	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
269	C₂×D₄	C₂³×C₃²	1	2	yes	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	C₂³×C₃²	1	2	yes	—
272	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
273	SD₁₆	—	2	4	no	—
274	SD₁₆	—	2	4	no	—
275	M₁₆	—	2	2	no	—
276	M₁₆	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	C₃²×D₄	1	4	yes	complemented
279	C₂×C₈	C₂³×C₃²	1	2	yes	—
280	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
281	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
284	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
285	C₂²⋊C₄	—	2	1	no	—
286	C₂²⋊C₄	—	2	1	no	—
287	C₂²⋊C₄	—	2	4	no	—
288	C₂²⋊C₄	—	2	4	no	—
289	C₄²	—	2	1	no	—
290	C₄²	—	2	1	no	—
291	C₂²×C₃	—	2	8	no	—
292	C₂²×C₃	—	2	16	no	—
293	C₂²×C₃	—	2	8	no	—
294	C₂²×C₃	—	4	16	no	—
295	C₂²×C₃	—	4	8	no	—
296	C₂²×C₃	—	8	16	no	—
297	C₂²×C₃	C₃×#121	1	8	yes	—
298	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
299	C₃×C₄	—	2	8	no	—
300	C₃×C₄	—	4	8	no	—
301	C₃×C₄	—	4	8	no	—
302	C₃×C₄	—	4	8	no	—
303	C₃×C₄	C₃×#121	1	8	yes	—
304	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
305	C₃×C₄	C₂×C₃×#41	1	4	yes	—
306	C₃²	#3057	1	1	yes	characteristic, direct product factor, Sylow
307	C₂³	—	2	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	8	2	no	—
310	C₂³	C₂×C₃²×D₄	1	2	yes	—
311	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
312	Q₈	—	2	2	no	—
313	Q₈	—	2	2	no	—
314	Q₈	—	2	2	no	—
315	Q₈	—	4	2	no	—
316	D₄	—	2	4	no	—
317	D₄	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	4	2	no	—
321	D₄	—	8	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
329	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
330	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
331	C₂×C₄	C₃²×#41	1	2	yes	—
332	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
333	C₈	—	2	2	no	—
334	C₈	C₂×C₃²×D₄	1	2	yes	—
335	C₈	C₂×C₃²×D₄	1	2	yes	—
336	C₂×C₃	—	2	8	no	—
337	C₂×C₃	—	4	8	no	—
338	C₂×C₃	—	8	8	no	—
339	C₂×C₃	C₂×C₃×#121	1	4	yes	—
340	C₂×C₃	C₃×#577	1	8	yes	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	8	4	no	—
347	C₂²	C₃²×#121	1	2	yes	—
348	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	2	no	—
353	C₄	C₃²×#121	1	2	yes	—
354	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
355	C₄	C₂×C₃²×#41	1	1	yes	characteristic
356	C₃	C₃×#3057	1	4	yes	direct product factor
357	C₂	—	2	2	no	—
358	C₂	—	4	2	no	—
359	C₂	—	8	2	no	—
360	C₂	C₂×C₃²×#121	1	1	yes	characteristic
361	C₂	C₃²×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
prime radical	C₃²×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×SD₁₆	C₂	semidirect
2. C₂×C₃²×#131	C₂	semidirect
3. C₃²×#536	C₂	semidirect
5. C₃²×#468	C₂	semidirect
6. C₃²×#465	C₂	semidirect
7. C₃²×#427	C₂	semidirect
8. C₃²×#419	C₂	semidirect
9. C₃²×#418	C₂	semidirect
10. C₃×#3057	C₃	direct (N × H)
19. C₂×C₃²×M₁₆	C₂²	semidirect
21. C₂²×C₃²×C₈	C₂²	semidirect
27. C₃²×C₂²⋊Q₈	C₂²	semidirect
32. C₃²×#107	C₂²	semidirect
33. C₃²×#106	C₂²	semidirect
34. C₃²×#103	C₂²	semidirect
36. C₂²×C₃×SD₁₆	C₂×C₃	semidirect
37. C₂×C₃×#131	C₂×C₃	semidirect
38. C₃×#536	C₂×C₃	semidirect
40. C₃×#468	C₂×C₃	semidirect
41. C₃×#465	C₂×C₃	semidirect
42. C₃×#427	C₂×C₃	semidirect
43. C₃×#419	C₂×C₃	semidirect
44. C₃×#418	C₂×C₃	semidirect
68. C₂×C₃²×C₈	D₄	semidirect
81. #3057	C₃²	direct (N × H)
90. C₂×C₃×M₁₆	C₂²×C₃	semidirect
92. C₂²×C₃×C₈	C₂²×C₃	semidirect
98. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
103. C₃×#107	C₂²×C₃	semidirect
104. C₃×#106	C₂²×C₃	semidirect
105. C₃×#103	C₂²×C₃	semidirect
136. C₂²×SD₁₆	C₂×C₃²	semidirect
137. C₂×#131	C₂×C₃²	semidirect
138. #536	C₂×C₃²	semidirect
140. #468	C₂×C₃²	semidirect
141. #465	C₂×C₃²	semidirect
142. #427	C₂×C₃²	semidirect
143. #419	C₂×C₃²	semidirect
144. #418	C₂×C₃²	semidirect
168. C₂×C₃×C₈	C₃×D₄	semidirect
204. C₂×M₁₆	C₂²×C₃²	semidirect
206. C₂²×C₈	C₂²×C₃²	semidirect
212. C₂²⋊Q₈	C₂²×C₃²	semidirect
217. #107	C₂²×C₃²	semidirect
218. #106	C₂²×C₃²	semidirect
219. #103	C₂²×C₃²	semidirect
278. C₂×C₈	C₃²×D₄	semidirect
306. C₃²	#3057	direct (N × H)
356. C₃	C₃×#3057	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×C₃²×SD₁₆	2
C₂×C₃²×#131	2
C₃²×#536	2
C₃²×#535	2
C₃²×#468	2
C₃²×#465	2
C₃²×#427	2
C₃²×#419	2
C₃²×#418	2
C₃×#3057	3

Subgroups — C32×#3057 #11770106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3057 #11770106